%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG063+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Sun Sep 27 06:49:22 AM UTC 2026
% Result : Theorem 4.24s 9.65s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 19
% Syntax : Number of formulae : 185 ( 57 unt; 14 def)
% Number of atoms : 1204 ( 924 equ)
% Maximal formula atoms : 250 ( 6 avg)
% Number of connectives : 1283 ( 264 ~; 707 |; 298 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 101 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax3,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('theBenchmark.p',ax3) ).
fof(ax4,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('theBenchmark.p',ax4) ).
fof(ax5,axiom,
( e3 != e4
& e2 != e4
& e2 != e3
& e1 != e4
& e1 != e3
& e1 != e2
& e0 != e4
& e0 != e3
& e0 != e2
& e0 != e1 ),
file('theBenchmark.p',ax5) ).
fof(ax6,axiom,
( e4 = op(e1,e1)
& e3 = op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1)))
& e2 = op(op(e1,e1),op(e1,e1))
& e0 = op(e1,op(op(e1,e1),op(e1,e1))) ),
file('theBenchmark.p',ax6) ).
fof(co1,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,e4) = e4
| op(e3,e3) = e4
| op(e2,e2) = e4
| op(e1,e1) = e4
| op(e0,e0) = e4 )
& ( op(e4,e4) = e3
| op(e3,e3) = e3
| op(e2,e2) = e3
| op(e1,e1) = e3
| op(e0,e0) = e3 )
& ( op(e4,e4) = e2
| op(e3,e3) = e2
| op(e2,e2) = e2
| op(e1,e1) = e2
| op(e0,e0) = e2 )
& ( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e2,e2) = e1
| op(e1,e1) = e1
| op(e0,e0) = e1 )
& ( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e2,e2) = e0
| op(e1,e1) = e0
| op(e0,e0) = e0 ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,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,e4) = e4
| op(e3,e3) = e4
| op(e2,e2) = e4
| op(e1,e1) = e4
| op(e0,e0) = e4 )
& ( op(e4,e4) = e3
| op(e3,e3) = e3
| op(e2,e2) = e3
| op(e1,e1) = e3
| op(e0,e0) = e3 )
& ( op(e4,e4) = e2
| op(e3,e3) = e2
| op(e2,e2) = e2
| op(e1,e1) = e2
| op(e0,e0) = e2 )
& ( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e2,e2) = e1
| op(e1,e1) = e1
| op(e0,e0) = e1 )
& ( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e2,e2) = e0
| op(e1,e1) = e0
| op(e0,e0) = e0 ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_75,plain,
( op(e4,e3) = e0
| op(e3,e3) = e0
| op(e2,e3) = e0
| op(e1,e3) = e0
| op(e0,e3) = e0 ),
inference(clausify,[status(thm)],[ax3]) ).
cnf(c_168,plain,
op(e3,e3) != op(e2,e3),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_169,plain,
op(e2,e3) != op(e3,e3),
inference(copy,[status(thm)],[c_168]) ).
cnf(c_172,plain,
op(e4,e3) != op(e3,e3),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_173,plain,
op(e3,e3) != op(e4,e3),
inference(copy,[status(thm)],[c_172]) ).
cnf(c_198,plain,
op(e0,e3) != op(e0,e0),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_199,plain,
op(e0,e0) != op(e0,e3),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_228,plain,
op(e1,e3) != op(e1,e2),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_229,plain,
op(e1,e2) != op(e1,e3),
inference(copy,[status(thm)],[c_228]) ).
cnf(c_294,plain,
e1 != e0,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_295,plain,
e0 != e1,
inference(copy,[status(thm)],[c_294]) ).
cnf(c_296,plain,
e2 != e0,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_297,plain,
e0 != e2,
inference(copy,[status(thm)],[c_296]) ).
cnf(c_298,plain,
e3 != e0,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_299,plain,
e0 != e3,
inference(copy,[status(thm)],[c_298]) ).
cnf(c_300,plain,
e4 != e0,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_301,plain,
e0 != e4,
inference(copy,[status(thm)],[c_300]) ).
cnf(c_302,plain,
e2 != e1,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_303,plain,
e1 != e2,
inference(copy,[status(thm)],[c_302]) ).
cnf(c_304,plain,
e3 != e1,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_305,plain,
e1 != e3,
inference(copy,[status(thm)],[c_304]) ).
cnf(c_306,plain,
e4 != e1,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_307,plain,
e1 != e4,
inference(copy,[status(thm)],[c_306]) ).
cnf(c_308,plain,
e3 != e2,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_309,plain,
e2 != e3,
inference(copy,[status(thm)],[c_308]) ).
cnf(c_310,plain,
e4 != e2,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_311,plain,
e2 != e4,
inference(copy,[status(thm)],[c_310]) ).
cnf(c_312,plain,
e4 != e3,
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_313,plain,
e3 != e4,
inference(copy,[status(thm)],[c_312]) ).
cnf(c_314,plain,
op(e1,op(op(e1,e1),op(e1,e1))) = e0,
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_315,plain,
op(op(e1,e1),op(e1,e1)) = e2,
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_316,plain,
op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1))) = e3,
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_1283,plain,
op(e2,op(op(e1,e1),op(e1,e1))) = e3,
inference(paramod,[status(thm)],[c_315,c_316]) ).
cnf(c_317,plain,
op(e2,e2) = e3,
inference(paramod,[status(thm)],[c_315,c_1283]) ).
cnf(c_318,plain,
op(e1,e1) = e4,
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_319,negated_conjecture,
( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e2,e2) = e0
| op(e1,e1) = e0
| op(e0,e0) = e0 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1284,negated_conjecture,
( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e2,e2) = e0
| e4 = e0
| op(e0,e0) = e0 ),
inference(paramod,[status(thm)],[c_318,c_319]) ).
cnf(c_1285,negated_conjecture,
( op(e4,e4) = e0
| op(e3,e3) = e0
| e3 = e0
| e4 = e0
| op(e0,e0) = e0 ),
inference(paramod,[status(thm)],[c_317,c_1284]) ).
cnf(c_1286,negated_conjecture,
( op(e4,e4) = e0
| op(e3,e3) = e0
| e3 = e0
| e0 = e4
| op(e0,e0) = e0 ),
inference(copy,[status(thm)],[c_1285]) ).
cnf(c_1287,negated_conjecture,
( op(e4,e4) = e0
| op(e3,e3) = e0
| e0 = e3
| e0 = e4
| op(e0,e0) = e0 ),
inference(copy,[status(thm)],[c_1286]) ).
cnf(c_1288,negated_conjecture,
( op(e4,e4) = e0
| op(e3,e3) = e0
| e0 = e3
| op(e0,e0) = e0 ),
inference(resolve,[status(thm)],[c_301,c_1287]) ).
cnf(c_320,negated_conjecture,
( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e0,e0) = e0 ),
inference(resolve,[status(thm)],[c_299,c_1288]) ).
cnf(c_321,negated_conjecture,
( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e2,e2) = e1
| op(e1,e1) = e1
| op(e0,e0) = e1 ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_1289,negated_conjecture,
( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e2,e2) = e1
| e4 = e1
| op(e0,e0) = e1 ),
inference(paramod,[status(thm)],[c_318,c_321]) ).
cnf(c_1290,negated_conjecture,
( op(e4,e4) = e1
| op(e3,e3) = e1
| e3 = e1
| e4 = e1
| op(e0,e0) = e1 ),
inference(paramod,[status(thm)],[c_317,c_1289]) ).
cnf(c_1291,negated_conjecture,
( op(e4,e4) = e1
| op(e3,e3) = e1
| e3 = e1
| e1 = e4
| op(e0,e0) = e1 ),
inference(copy,[status(thm)],[c_1290]) ).
cnf(c_1292,negated_conjecture,
( op(e4,e4) = e1
| op(e3,e3) = e1
| e1 = e3
| e1 = e4
| op(e0,e0) = e1 ),
inference(copy,[status(thm)],[c_1291]) ).
cnf(c_1293,negated_conjecture,
( op(e4,e4) = e1
| op(e3,e3) = e1
| e1 = e3
| op(e0,e0) = e1 ),
inference(resolve,[status(thm)],[c_307,c_1292]) ).
cnf(c_322,negated_conjecture,
( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e0,e0) = e1 ),
inference(resolve,[status(thm)],[c_305,c_1293]) ).
fof(def_defn_00,definition,
( defn_00
<=> ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 ) ),
introduced(definition,[new_symbols(definition,[defn_00])],[]) ).
fof(def_defn_10,definition,
( defn_10
<=> ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 ) ),
introduced(definition,[new_symbols(definition,[defn_10])],[]) ).
fof(def_defn_20,definition,
( defn_20
<=> ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 ) ),
introduced(definition,[new_symbols(definition,[defn_20])],[]) ).
fof(def_defn_30,definition,
( defn_30
<=> ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 ) ),
introduced(definition,[new_symbols(definition,[defn_30])],[]) ).
fof(def_defn_40,definition,
( defn_40
<=> ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 ) ),
introduced(definition,[new_symbols(definition,[defn_40])],[]) ).
fof(def_defn_50,definition,
( defn_50
<=> ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 ) ),
introduced(definition,[new_symbols(definition,[defn_50])],[]) ).
fof(def_defn_60,definition,
( defn_60
<=> ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 ) ),
introduced(definition,[new_symbols(definition,[defn_60])],[]) ).
fof(def_defn_70,definition,
( defn_70
<=> ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 ) ),
introduced(definition,[new_symbols(definition,[defn_70])],[]) ).
fof(def_defn_80,definition,
( defn_80
<=> ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 ) ),
introduced(definition,[new_symbols(definition,[defn_80])],[]) ).
fof(def_defn_90,definition,
( defn_90
<=> ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 ) ),
introduced(definition,[new_symbols(definition,[defn_90])],[]) ).
fof(def_defn_100,definition,
( defn_100
<=> ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 ) ),
introduced(definition,[new_symbols(definition,[defn_100])],[]) ).
fof(def_defn_110,definition,
( defn_110
<=> ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 ) ),
introduced(definition,[new_symbols(definition,[defn_110])],[]) ).
fof(def_defn_120,definition,
( defn_120
<=> ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 ) ),
introduced(definition,[new_symbols(definition,[defn_120])],[]) ).
fof(def_defn_130,definition,
( defn_130
<=> ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 ) ),
introduced(definition,[new_symbols(definition,[defn_130])],[]) ).
cnf(c_355,negated_conjecture,
( op(e2,e2) = e4
| op(e4,e4) = e1
| op(e4,e4) = e0
| op(e4,e4) = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_50
| defn_40
| defn_30
| defn_20
| defn_10
| defn_00 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_00,def_defn_10,def_defn_20,def_defn_30,def_defn_40,def_defn_50,def_defn_60,def_defn_70,def_defn_80,def_defn_90,def_defn_100,def_defn_110,def_defn_120,def_defn_130]) ).
cnf(c_1294,negated_conjecture,
( e3 = e4
| op(e4,e4) = e1
| op(e4,e4) = e0
| op(e4,e4) = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_50
| defn_40
| defn_30
| defn_20
| defn_10
| defn_00 ),
inference(paramod,[status(thm)],[c_317,c_355]) ).
cnf(c_356,negated_conjecture,
( op(e4,e4) = e1
| op(e4,e4) = e0
| op(e4,e4) = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_50
| defn_40
| defn_30
| defn_20
| defn_10
| defn_00 ),
inference(resolve,[status(thm)],[c_313,c_1294]) ).
cnf(c_571,negated_conjecture,
( op(e1,e1) = e3
| ~ defn_130 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_130]) ).
cnf(c_1295,negated_conjecture,
( e4 = e3
| ~ defn_130 ),
inference(paramod,[status(thm)],[c_318,c_571]) ).
cnf(c_1296,negated_conjecture,
( e3 = e4
| ~ defn_130 ),
inference(copy,[status(thm)],[c_1295]) ).
cnf(c_572,negated_conjecture,
~ defn_130,
inference(resolve,[status(thm)],[c_313,c_1296]) ).
cnf(c_574,negated_conjecture,
( op(e0,e0) = e3
| ~ defn_120 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_120]) ).
cnf(c_578,negated_conjecture,
( op(e2,e2) = e4
| ~ defn_110 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_110]) ).
cnf(c_1297,negated_conjecture,
( e3 = e4
| ~ defn_110 ),
inference(paramod,[status(thm)],[c_317,c_578]) ).
cnf(c_579,negated_conjecture,
~ defn_110,
inference(resolve,[status(thm)],[c_313,c_1297]) ).
cnf(c_581,negated_conjecture,
( op(e3,e3) = e2
| ~ defn_100 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_100]) ).
cnf(c_584,negated_conjecture,
( op(e1,e1) = e2
| ~ defn_90 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_90]) ).
cnf(c_1298,negated_conjecture,
( e4 = e2
| ~ defn_90 ),
inference(paramod,[status(thm)],[c_318,c_584]) ).
cnf(c_1299,negated_conjecture,
( e2 = e4
| ~ defn_90 ),
inference(copy,[status(thm)],[c_1298]) ).
cnf(c_585,negated_conjecture,
~ defn_90,
inference(resolve,[status(thm)],[c_311,c_1299]) ).
cnf(c_589,negated_conjecture,
( op(e2,e2) = e0
| ~ defn_80 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_80]) ).
cnf(c_1300,negated_conjecture,
( e3 = e0
| ~ defn_80 ),
inference(paramod,[status(thm)],[c_317,c_589]) ).
cnf(c_1301,negated_conjecture,
( e0 = e3
| ~ defn_80 ),
inference(copy,[status(thm)],[c_1300]) ).
cnf(c_590,negated_conjecture,
~ defn_80,
inference(resolve,[status(thm)],[c_299,c_1301]) ).
cnf(c_592,negated_conjecture,
( op(e4,e4) = e1
| ~ defn_70 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_70]) ).
cnf(c_596,negated_conjecture,
( op(e1,e1) = e3
| ~ defn_60 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_60]) ).
cnf(c_1302,negated_conjecture,
( e4 = e3
| ~ defn_60 ),
inference(paramod,[status(thm)],[c_318,c_596]) ).
cnf(c_1303,negated_conjecture,
( e3 = e4
| ~ defn_60 ),
inference(copy,[status(thm)],[c_1302]) ).
cnf(c_597,negated_conjecture,
~ defn_60,
inference(resolve,[status(thm)],[c_313,c_1303]) ).
cnf(c_599,negated_conjecture,
( op(e2,e2) = e1
| ~ defn_50 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_50]) ).
cnf(c_1304,negated_conjecture,
( e3 = e1
| ~ defn_50 ),
inference(paramod,[status(thm)],[c_317,c_599]) ).
cnf(c_1305,negated_conjecture,
( e1 = e3
| ~ defn_50 ),
inference(copy,[status(thm)],[c_1304]) ).
cnf(c_600,negated_conjecture,
~ defn_50,
inference(resolve,[status(thm)],[c_305,c_1305]) ).
cnf(c_604,negated_conjecture,
( op(e1,e1) = e0
| ~ defn_40 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_40]) ).
cnf(c_1306,negated_conjecture,
( e4 = e0
| ~ defn_40 ),
inference(paramod,[status(thm)],[c_318,c_604]) ).
cnf(c_1307,negated_conjecture,
( e0 = e4
| ~ defn_40 ),
inference(copy,[status(thm)],[c_1306]) ).
cnf(c_605,negated_conjecture,
~ defn_40,
inference(resolve,[status(thm)],[c_301,c_1307]) ).
cnf(c_607,negated_conjecture,
( op(e4,e4) = e0
| ~ defn_30 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_30]) ).
cnf(c_611,negated_conjecture,
( op(e0,e0) = e3
| ~ defn_20 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_20]) ).
cnf(c_613,negated_conjecture,
( op(e2,e2) = e0
| ~ defn_10 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_10]) ).
cnf(c_1308,negated_conjecture,
( e3 = e0
| ~ defn_10 ),
inference(paramod,[status(thm)],[c_317,c_613]) ).
cnf(c_1309,negated_conjecture,
( e0 = e3
| ~ defn_10 ),
inference(copy,[status(thm)],[c_1308]) ).
cnf(c_614,negated_conjecture,
~ defn_10,
inference(resolve,[status(thm)],[c_299,c_1309]) ).
cnf(c_616,negated_conjecture,
( op(e1,e1) = e0
| ~ defn_00 ),
inference(clausify,[status(thm)],[co1_neg,def_defn_00]) ).
cnf(c_1310,negated_conjecture,
( e4 = e0
| ~ defn_00 ),
inference(paramod,[status(thm)],[c_318,c_616]) ).
cnf(c_1311,negated_conjecture,
( e0 = e4
| ~ defn_00 ),
inference(copy,[status(thm)],[c_1310]) ).
cnf(c_617,negated_conjecture,
~ defn_00,
inference(resolve,[status(thm)],[c_301,c_1311]) ).
cnf(c_1312,plain,
op(e1,op(e4,op(e1,e1))) = e0,
inference(paramod,[status(thm)],[c_318,c_314]) ).
cnf(c_618,plain,
op(e1,op(e4,e4)) = e0,
inference(paramod,[status(thm)],[c_318,c_1312]) ).
cnf(c_1313,plain,
op(e4,op(e1,e1)) = e2,
inference(paramod,[status(thm)],[c_318,c_315]) ).
cnf(c_635,plain,
op(e4,e4) = e2,
inference(paramod,[status(thm)],[c_318,c_1313]) ).
cnf(c_1314,negated_conjecture,
( op(e4,e4) = e1
| op(e4,e4) = e0
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_50
| defn_40
| defn_30
| defn_20
| defn_10
| defn_00 ),
inference(paramod,[status(thm)],[c_635,c_356]) ).
cnf(c_1315,negated_conjecture,
( op(e4,e4) = e1
| e2 = e0
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_50
| defn_40
| defn_30
| defn_20
| defn_10
| defn_00 ),
inference(paramod,[status(thm)],[c_635,c_1314]) ).
cnf(c_1316,negated_conjecture,
( e2 = e1
| e2 = e0
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_50
| defn_40
| defn_30
| defn_20
| defn_10
| defn_00 ),
inference(paramod,[status(thm)],[c_635,c_1315]) ).
cnf(c_1317,negated_conjecture,
( e2 = e1
| e0 = e2
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_50
| defn_40
| defn_30
| defn_20
| defn_10
| defn_00 ),
inference(copy,[status(thm)],[c_1316]) ).
cnf(c_1318,negated_conjecture,
( e1 = e2
| e0 = e2
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_50
| defn_40
| defn_30
| defn_20
| defn_10
| defn_00 ),
inference(copy,[status(thm)],[c_1317]) ).
cnf(c_1319,negated_conjecture,
( e1 = e2
| e0 = e2
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_50
| defn_40
| defn_30
| defn_20
| defn_10 ),
inference(resolve,[status(thm)],[c_617,c_1318]) ).
cnf(c_1320,negated_conjecture,
( e1 = e2
| e0 = e2
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_50
| defn_40
| defn_30
| defn_20 ),
inference(resolve,[status(thm)],[c_614,c_1319]) ).
cnf(c_1321,negated_conjecture,
( e1 = e2
| e0 = e2
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_50
| defn_30
| defn_20 ),
inference(resolve,[status(thm)],[c_605,c_1320]) ).
cnf(c_1322,negated_conjecture,
( e1 = e2
| e0 = e2
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_60
| defn_30
| defn_20 ),
inference(resolve,[status(thm)],[c_600,c_1321]) ).
cnf(c_1323,negated_conjecture,
( e1 = e2
| e0 = e2
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_80
| defn_70
| defn_30
| defn_20 ),
inference(resolve,[status(thm)],[c_597,c_1322]) ).
cnf(c_1324,negated_conjecture,
( e1 = e2
| e0 = e2
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_90
| defn_70
| defn_30
| defn_20 ),
inference(resolve,[status(thm)],[c_590,c_1323]) ).
cnf(c_1325,negated_conjecture,
( e1 = e2
| e0 = e2
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_110
| defn_100
| defn_70
| defn_30
| defn_20 ),
inference(resolve,[status(thm)],[c_585,c_1324]) ).
cnf(c_1326,negated_conjecture,
( e1 = e2
| e0 = e2
| e2 = e3
| op(e3,e3) = e2
| defn_130
| defn_120
| defn_100
| defn_70
| defn_30
| defn_20 ),
inference(resolve,[status(thm)],[c_579,c_1325]) ).
cnf(c_1327,negated_conjecture,
( e1 = e2
| e0 = e2
| e2 = e3
| op(e3,e3) = e2
| defn_120
| defn_100
| defn_70
| defn_30
| defn_20 ),
inference(resolve,[status(thm)],[c_572,c_1326]) ).
cnf(c_1328,negated_conjecture,
( e1 = e2
| e0 = e2
| op(e3,e3) = e2
| defn_120
| defn_100
| defn_70
| defn_30
| defn_20 ),
inference(resolve,[status(thm)],[c_309,c_1327]) ).
cnf(c_1329,negated_conjecture,
( e1 = e2
| op(e3,e3) = e2
| defn_120
| defn_100
| defn_70
| defn_30
| defn_20 ),
inference(resolve,[status(thm)],[c_297,c_1328]) ).
cnf(c_657,negated_conjecture,
( op(e3,e3) = e2
| defn_120
| defn_100
| defn_70
| defn_30
| defn_20 ),
inference(resolve,[status(thm)],[c_303,c_1329]) ).
cnf(c_672,plain,
op(e1,e2) = e0,
inference(paramod,[status(thm)],[c_635,c_618]) ).
cnf(c_1330,negated_conjecture,
( e2 = e0
| ~ defn_30 ),
inference(paramod,[status(thm)],[c_635,c_607]) ).
cnf(c_1331,negated_conjecture,
( e0 = e2
| ~ defn_30 ),
inference(copy,[status(thm)],[c_1330]) ).
cnf(c_673,negated_conjecture,
~ defn_30,
inference(resolve,[status(thm)],[c_297,c_1331]) ).
cnf(c_1332,negated_conjecture,
( e2 = e1
| ~ defn_70 ),
inference(paramod,[status(thm)],[c_635,c_592]) ).
cnf(c_1333,negated_conjecture,
( e1 = e2
| ~ defn_70 ),
inference(copy,[status(thm)],[c_1332]) ).
cnf(c_674,negated_conjecture,
~ defn_70,
inference(resolve,[status(thm)],[c_303,c_1333]) ).
cnf(c_1334,negated_conjecture,
( e2 = e1
| op(e3,e3) = e1
| op(e0,e0) = e1 ),
inference(paramod,[status(thm)],[c_635,c_322]) ).
cnf(c_1335,negated_conjecture,
( e1 = e2
| op(e3,e3) = e1
| op(e0,e0) = e1 ),
inference(copy,[status(thm)],[c_1334]) ).
cnf(c_675,negated_conjecture,
( op(e3,e3) = e1
| op(e0,e0) = e1 ),
inference(resolve,[status(thm)],[c_303,c_1335]) ).
cnf(c_1336,negated_conjecture,
( e2 = e0
| op(e3,e3) = e0
| op(e0,e0) = e0 ),
inference(paramod,[status(thm)],[c_635,c_320]) ).
cnf(c_1337,negated_conjecture,
( e0 = e2
| op(e3,e3) = e0
| op(e0,e0) = e0 ),
inference(copy,[status(thm)],[c_1336]) ).
cnf(c_676,negated_conjecture,
( op(e3,e3) = e0
| op(e0,e0) = e0 ),
inference(resolve,[status(thm)],[c_297,c_1337]) ).
cnf(c_1338,plain,
e0 != op(e1,e3),
inference(paramod,[status(thm)],[c_672,c_229]) ).
cnf(c_708,plain,
op(e1,e3) != e0,
inference(copy,[status(thm)],[c_1338]) ).
cnf(c_1339,negated_conjecture,
( op(e3,e3) = e2
| defn_120
| defn_100
| defn_70
| defn_20 ),
inference(resolve,[status(thm)],[c_673,c_657]) ).
cnf(c_713,negated_conjecture,
( op(e3,e3) = e2
| defn_120
| defn_100
| defn_20 ),
inference(resolve,[status(thm)],[c_674,c_1339]) ).
cnf(c_729,plain,
( op(e4,e3) = e0
| op(e3,e3) = e0
| op(e2,e3) = e0
| op(e0,e3) = e0 ),
inference(resolve,[status(thm)],[c_708,c_75]) ).
cnf(c_1340,plain,
( e0 != op(e0,e3)
| op(e3,e3) = e0 ),
inference(paramod,[status(thm)],[c_676,c_199]) ).
cnf(c_868,plain,
( op(e0,e3) != e0
| op(e3,e3) = e0 ),
inference(copy,[status(thm)],[c_1340]) ).
cnf(c_1341,plain,
( op(e3,e3) = e1
| e0 = e1
| op(e3,e3) = e0 ),
inference(paramod,[status(thm)],[c_676,c_675]) ).
cnf(c_872,plain,
( op(e3,e3) = e1
| op(e3,e3) = e0 ),
inference(resolve,[status(thm)],[c_295,c_1341]) ).
cnf(c_962,plain,
( op(e0,e0) = e3
| op(e3,e3) = e2
| defn_120
| defn_100 ),
inference(resolve,[status(thm)],[c_713,c_611]) ).
cnf(c_1342,plain,
( op(e4,e3) = e0
| op(e3,e3) = e0
| op(e2,e3) = e0
| op(e3,e3) = e0 ),
inference(resolve,[status(thm)],[c_868,c_729]) ).
cnf(c_1160,plain,
( op(e4,e3) = e0
| op(e2,e3) = e0
| op(e3,e3) = e0 ),
inference(copy,[status(thm)],[c_1342]) ).
cnf(c_1165,plain,
( op(e2,e3) != e0
| op(e3,e3) = e1 ),
inference(paramod,[status(thm)],[c_872,c_169]) ).
cnf(c_1343,plain,
( e0 != op(e4,e3)
| op(e3,e3) = e1 ),
inference(paramod,[status(thm)],[c_872,c_173]) ).
cnf(c_1166,plain,
( op(e4,e3) != e0
| op(e3,e3) = e1 ),
inference(copy,[status(thm)],[c_1343]) ).
cnf(c_1344,negated_conjecture,
( op(e0,e0) = e3
| op(e0,e0) = e3
| op(e3,e3) = e2
| defn_100 ),
inference(resolve,[status(thm)],[c_962,c_574]) ).
cnf(c_1223,negated_conjecture,
( op(e0,e0) = e3
| op(e3,e3) = e2
| defn_100 ),
inference(copy,[status(thm)],[c_1344]) ).
cnf(c_1345,negated_conjecture,
( op(e3,e3) = e2
| op(e0,e0) = e3
| op(e3,e3) = e2 ),
inference(resolve,[status(thm)],[c_1223,c_581]) ).
cnf(c_1224,negated_conjecture,
( op(e0,e0) = e3
| op(e3,e3) = e2 ),
inference(copy,[status(thm)],[c_1345]) ).
cnf(c_1346,plain,
( op(e3,e3) = e1
| e3 = e1
| op(e3,e3) = e2 ),
inference(paramod,[status(thm)],[c_1224,c_675]) ).
cnf(c_1347,plain,
( op(e3,e3) = e1
| e1 = e3
| op(e3,e3) = e2 ),
inference(copy,[status(thm)],[c_1346]) ).
cnf(c_1233,plain,
( op(e3,e3) = e1
| op(e3,e3) = e2 ),
inference(resolve,[status(thm)],[c_305,c_1347]) ).
cnf(c_1348,plain,
( op(e3,e3) = e0
| e3 = e0
| op(e3,e3) = e2 ),
inference(paramod,[status(thm)],[c_1224,c_676]) ).
cnf(c_1349,plain,
( op(e3,e3) = e0
| e0 = e3
| op(e3,e3) = e2 ),
inference(copy,[status(thm)],[c_1348]) ).
cnf(c_1234,plain,
( op(e3,e3) = e0
| op(e3,e3) = e2 ),
inference(resolve,[status(thm)],[c_299,c_1349]) ).
cnf(c_1350,plain,
( e0 = e1
| op(e3,e3) = e2
| op(e3,e3) = e2 ),
inference(paramod,[status(thm)],[c_1234,c_1233]) ).
cnf(c_1351,plain,
( e0 = e1
| op(e3,e3) = e2 ),
inference(copy,[status(thm)],[c_1350]) ).
cnf(c_1265,plain,
op(e3,e3) = e2,
inference(resolve,[status(thm)],[c_295,c_1351]) ).
cnf(c_1352,plain,
( op(e4,e3) != e0
| e2 = e1 ),
inference(paramod,[status(thm)],[c_1265,c_1166]) ).
cnf(c_1353,plain,
( op(e4,e3) != e0
| e1 = e2 ),
inference(copy,[status(thm)],[c_1352]) ).
cnf(c_1277,plain,
op(e4,e3) != e0,
inference(resolve,[status(thm)],[c_303,c_1353]) ).
cnf(c_1354,plain,
( op(e2,e3) != e0
| e2 = e1 ),
inference(paramod,[status(thm)],[c_1265,c_1165]) ).
cnf(c_1355,plain,
( op(e2,e3) != e0
| e1 = e2 ),
inference(copy,[status(thm)],[c_1354]) ).
cnf(c_1278,plain,
op(e2,e3) != e0,
inference(resolve,[status(thm)],[c_303,c_1355]) ).
cnf(c_1356,plain,
( op(e4,e3) = e0
| op(e2,e3) = e0
| e2 = e0 ),
inference(paramod,[status(thm)],[c_1265,c_1160]) ).
cnf(c_1357,plain,
( op(e4,e3) = e0
| op(e2,e3) = e0
| e0 = e2 ),
inference(copy,[status(thm)],[c_1356]) ).
cnf(c_1358,plain,
( op(e4,e3) = e0
| op(e2,e3) = e0 ),
inference(resolve,[status(thm)],[c_297,c_1357]) ).
cnf(c_1359,plain,
op(e4,e3) = e0,
inference(resolve,[status(thm)],[c_1278,c_1358]) ).
cnf(c_1282,plain,
$false,
inference(resolve,[status(thm)],[c_1277,c_1359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG063+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.42 % Computer : n026.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Sat Sep 26 21:07:46 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.43 % Process 1950129 was started by sandbox2 on n026,
% 0.16/5.43 % Sat Sep 26 21:07:46 2026
% 0.16/5.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 4.14/9.48
% 4.14/9.48 % From the command line: assign(max_seconds, 300).
% 4.24/9.65
% 4.24/9.65 % SZS status Theorem for theBenchmark
% 4.24/9.65
% 4.24/9.65 % Proof 1 at 0.12 (+ 0.03) seconds.
% 4.24/9.65 % Length of proof is 93.
% 4.24/9.65 % Level of proof is 12.
% 4.24/9.65 % Maximum clause weight is 34.000.
% 4.24/9.65 % Given clauses 268.
% 4.24/9.65
% 4.24/9.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------