%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG063+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 : Fri Sep 25 12:53:19 PM UTC 2026
% Result : Theorem 1.14s 1.06s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 30
% Syntax : Number of formulae : 231 ( 62 unt; 25 def)
% Number of atoms : 1290 ( 911 equ)
% Maximal formula atoms : 125 ( 5 avg)
% Number of connectives : 1455 ( 418 ~; 634 |; 403 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 101 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 28 ( 26 usr; 27 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 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',ax1) ).
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',ax4) ).
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',ax5) ).
fof(f6,axiom,
( e4 = op(e1,e1)
& e3 = op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1)))
& e2 = op(op(e1,e1),op(e1,e1))
& e0 = op(e1,op(op(e1,e1),op(e1,e1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
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,e4) = e4
| op(e3,e3) = e4
| op(e2,e2) = e4
| op(e1,e1) = e4
| op(e0,e0) = e4 )
& ( op(e4,e4) = e3
| op(e3,e3) = e3
| op(e2,e2) = e3
| op(e1,e1) = e3
| op(e0,e0) = e3 )
& ( op(e4,e4) = e2
| op(e3,e3) = e2
| op(e2,e2) = e2
| op(e1,e1) = e2
| op(e0,e0) = e2 )
& ( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e2,e2) = e1
| op(e1,e1) = e1
| op(e0,e0) = e1 )
& ( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e2,e2) = e0
| op(e1,e1) = e0
| op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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,e4) = e4
| op(e3,e3) = e4
| op(e2,e2) = e4
| op(e1,e1) = e4
| op(e0,e0) = e4 )
& ( op(e4,e4) = e3
| op(e3,e3) = e3
| op(e2,e2) = e3
| op(e1,e1) = e3
| op(e0,e0) = e3 )
& ( op(e4,e4) = e2
| op(e3,e3) = e2
| op(e2,e2) = e2
| op(e1,e1) = e2
| op(e0,e0) = e2 )
& ( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e2,e2) = e1
| op(e1,e1) = e1
| op(e0,e0) = e1 )
& ( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e2,e2) = e0
| op(e1,e1) = e0
| op(e0,e0) = e0 ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
( ( ( 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(flattening,[],[f8]) ).
fof(f35,plain,
( ~ sP23
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f36,plain,
( ~ sP22
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f37,plain,
( ~ sP21
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f38,plain,
( ~ sP20
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f39,plain,
( ~ sP19
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f40,plain,
( ~ sP18
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f41,plain,
( ~ sP17
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f42,plain,
( ~ sP16
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f43,plain,
( ~ sP15
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f44,plain,
( ~ sP14
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f45,plain,
( ~ sP13
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f46,plain,
( ~ sP12
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f47,plain,
( ~ sP11
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f48,plain,
( ~ sP10
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f49,plain,
( ~ sP9
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f50,plain,
( ~ sP8
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f51,plain,
( ~ sP7
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f52,plain,
( ~ sP6
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f53,plain,
( ~ sP5
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f54,plain,
( ~ sP4
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f55,plain,
( ~ sP3
| ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f56,plain,
( ~ sP2
| ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f57,plain,
( ~ sP1
| ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f77,plain,
( e4 = op(e1,e1)
| e3 = op(e1,e1)
| e2 = op(e1,e1)
| e1 = op(e1,e1)
| e0 = op(e1,e1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f220,plain,
op(e1,e2) != op(e2,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f245,plain,
e3 != e4,
inference(cnf_transformation,[],[f5]) ).
fof(f246,plain,
e2 != e4,
inference(cnf_transformation,[],[f5]) ).
fof(f247,plain,
e2 != e3,
inference(cnf_transformation,[],[f5]) ).
fof(f248,plain,
e1 != e4,
inference(cnf_transformation,[],[f5]) ).
fof(f249,plain,
e1 != e3,
inference(cnf_transformation,[],[f5]) ).
fof(f250,plain,
e1 != e2,
inference(cnf_transformation,[],[f5]) ).
fof(f251,plain,
e0 != e4,
inference(cnf_transformation,[],[f5]) ).
fof(f252,plain,
e0 != e3,
inference(cnf_transformation,[],[f5]) ).
fof(f253,plain,
e0 != e2,
inference(cnf_transformation,[],[f5]) ).
fof(f254,plain,
e0 != e1,
inference(cnf_transformation,[],[f5]) ).
fof(f255,plain,
e4 = op(e1,e1),
inference(cnf_transformation,[],[f6]) ).
fof(f256,plain,
e3 = op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1))),
inference(cnf_transformation,[],[f6]) ).
fof(f257,plain,
e2 = op(op(e1,e1),op(e1,e1)),
inference(cnf_transformation,[],[f6]) ).
fof(f258,plain,
e0 = op(e1,op(op(e1,e1),op(e1,e1))),
inference(cnf_transformation,[],[f6]) ).
fof(f260,plain,
( ~ sP23
| e0 = op(e1,e1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f263,plain,
( ~ sP22
| e0 = op(e2,e2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f266,plain,
( ~ sP21
| e0 = op(e3,e3) ),
inference(cnf_transformation,[],[f37]) ).
fof(f267,plain,
( ~ sP21
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f37]) ).
fof(f269,plain,
( ~ sP20
| e0 = op(e4,e4) ),
inference(cnf_transformation,[],[f38]) ).
fof(f273,plain,
( ~ sP19
| e0 = op(e1,e1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f274,plain,
( ~ sP18
| e1 != op(e1,e1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f275,plain,
( ~ sP18
| e1 = op(e1,e1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f279,plain,
( ~ sP17
| e2 = op(e1,e1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f282,plain,
( ~ sP16
| e3 = op(e1,e1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f284,plain,
( ~ sP15
| e1 = op(e4,e4) ),
inference(cnf_transformation,[],[f43]) ).
fof(f288,plain,
( ~ sP14
| e0 = op(e2,e2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f290,plain,
( ~ sP13
| e2 = op(e1,e1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f292,plain,
( ~ sP12
| e2 != op(e2,e2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f293,plain,
( ~ sP12
| e2 = op(e2,e2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f296,plain,
( ~ sP11
| e2 = op(e3,e3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f300,plain,
( ~ sP10
| e4 = op(e2,e2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f302,plain,
( ~ sP9
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f49]) ).
fof(f303,plain,
( ~ sP9
| e0 = op(e3,e3) ),
inference(cnf_transformation,[],[f49]) ).
fof(f305,plain,
( ~ sP8
| e3 = op(e1,e1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f309,plain,
( ~ sP7
| e2 = op(e3,e3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f310,plain,
( ~ sP6
| e3 != op(e3,e3) ),
inference(cnf_transformation,[],[f52]) ).
fof(f311,plain,
( ~ sP6
| e3 = op(e3,e3) ),
inference(cnf_transformation,[],[f52]) ).
fof(f314,plain,
( ~ sP5
| e3 = op(e4,e4) ),
inference(cnf_transformation,[],[f53]) ).
fof(f318,plain,
( ~ sP4
| e0 = op(e4,e4) ),
inference(cnf_transformation,[],[f54]) ).
fof(f321,plain,
( ~ sP3
| e1 = op(e4,e4) ),
inference(cnf_transformation,[],[f55]) ).
fof(f323,plain,
( ~ sP2
| e4 = op(e2,e2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f327,plain,
( ~ sP1
| e3 = op(e4,e4) ),
inference(cnf_transformation,[],[f57]) ).
fof(f331,plain,
( sP0
| sP1
| sP2
| sP3
| sP4
| sP5
| sP6
| sP7
| sP8
| sP9
| sP10
| sP11
| sP12
| sP13
| sP14
| sP15
| sP16
| sP17
| sP18
| sP19
| sP20
| sP21
| sP22
| sP23
| e0 != op(e0,e0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f332,plain,
( sP0
| sP1
| sP2
| sP3
| sP4
| sP5
| sP6
| sP7
| sP8
| sP9
| sP10
| sP11
| sP12
| sP13
| sP14
| sP15
| sP16
| sP17
| sP18
| sP19
| sP20
| sP21
| sP22
| sP23
| e0 = op(e0,e0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f337,plain,
( e1 = op(e4,e4)
| e1 = op(e3,e3)
| e1 = op(e2,e2)
| e1 = op(e1,e1)
| op(e0,e0) = e1 ),
inference(cnf_transformation,[],[f34]) ).
fof(f338,plain,
( e0 = op(e4,e4)
| e0 = op(e3,e3)
| e0 = op(e2,e2)
| e0 = op(e1,e1)
| e0 = op(e0,e0) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_55,plain,
( ( op(e1,e1) = e4 )
| ( op(e1,e1) = e3 )
| ( op(e1,e1) = e2 )
| ( op(e1,e1) = e1 )
| ( op(e1,e1) = e0 ) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_159,plain,
op(e1,e2) != op(e2,e2),
inference(cnf_transformation,[],[f220]) ).
tcf(c_235,plain,
e0 != e1,
inference(cnf_transformation,[],[f254]) ).
tcf(c_236,plain,
e0 != e2,
inference(cnf_transformation,[],[f253]) ).
tcf(c_237,plain,
e0 != e3,
inference(cnf_transformation,[],[f252]) ).
tcf(c_238,plain,
e0 != e4,
inference(cnf_transformation,[],[f251]) ).
tcf(c_239,plain,
e1 != e2,
inference(cnf_transformation,[],[f250]) ).
tcf(c_240,plain,
e1 != e3,
inference(cnf_transformation,[],[f249]) ).
tcf(c_241,plain,
e1 != e4,
inference(cnf_transformation,[],[f248]) ).
tcf(c_242,plain,
e2 != e3,
inference(cnf_transformation,[],[f247]) ).
tcf(c_243,plain,
e2 != e4,
inference(cnf_transformation,[],[f246]) ).
tcf(c_244,plain,
e3 != e4,
inference(cnf_transformation,[],[f245]) ).
tcf(c_245,plain,
op(e1,op(op(e1,e1),op(e1,e1))) = e0,
inference(cnf_transformation,[],[f258]) ).
tcf(c_246,plain,
op(op(e1,e1),op(e1,e1)) = e2,
inference(cnf_transformation,[],[f257]) ).
tcf(c_247,plain,
op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1))) = e3,
inference(cnf_transformation,[],[f256]) ).
tcf(c_248,plain,
op(e1,e1) = e4,
inference(cnf_transformation,[],[f255]) ).
tcf(c_250,plain,
( ( op(e1,e1) = e0 )
| ~ sP23 ),
inference(cnf_transformation,[],[f260]) ).
tcf(c_253,plain,
( ( op(e2,e2) = e0 )
| ~ sP22 ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_255,plain,
( ( op(e0,e0) = e3 )
| ~ sP21 ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_256,plain,
( ( op(e3,e3) = e0 )
| ~ sP21 ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_259,plain,
( ( op(e4,e4) = e0 )
| ~ sP20 ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_261,plain,
( ( op(e1,e1) = e0 )
| ~ sP19 ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_265,plain,
( ( op(e1,e1) = e1 )
| ~ sP18 ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_266,plain,
( ~ sP18
| ( op(e1,e1) != e1 ) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_267,plain,
( ( op(e1,e1) = e2 )
| ~ sP17 ),
inference(cnf_transformation,[],[f279]) ).
tcf(c_270,plain,
( ( op(e1,e1) = e3 )
| ~ sP16 ),
inference(cnf_transformation,[],[f282]) ).
tcf(c_274,plain,
( ( op(e4,e4) = e1 )
| ~ sP15 ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_276,plain,
( ( op(e2,e2) = e0 )
| ~ sP14 ),
inference(cnf_transformation,[],[f288]) ).
tcf(c_280,plain,
( ( op(e1,e1) = e2 )
| ~ sP13 ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_283,plain,
( ( op(e2,e2) = e2 )
| ~ sP12 ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_284,plain,
( ~ sP12
| ( op(e2,e2) != e2 ) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_286,plain,
( ( op(e3,e3) = e2 )
| ~ sP11 ),
inference(cnf_transformation,[],[f296]) ).
tcf(c_288,plain,
( ( op(e2,e2) = e4 )
| ~ sP10 ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_291,plain,
( ( op(e3,e3) = e0 )
| ~ sP9 ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_292,plain,
( ( op(e0,e0) = e3 )
| ~ sP9 ),
inference(cnf_transformation,[],[f302]) ).
tcf(c_295,plain,
( ( op(e1,e1) = e3 )
| ~ sP8 ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_297,plain,
( ( op(e3,e3) = e2 )
| ~ sP7 ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_301,plain,
( ( op(e3,e3) = e3 )
| ~ sP6 ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_302,plain,
( ~ sP6
| ( op(e3,e3) != e3 ) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_304,plain,
( ( op(e4,e4) = e3 )
| ~ sP5 ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_306,plain,
( ( op(e4,e4) = e0 )
| ~ sP4 ),
inference(cnf_transformation,[],[f318]) ).
tcf(c_309,plain,
( ( op(e4,e4) = e1 )
| ~ sP3 ),
inference(cnf_transformation,[],[f321]) ).
tcf(c_313,plain,
( ( op(e2,e2) = e4 )
| ~ sP2 ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_315,plain,
( ( op(e4,e4) = e3 )
| ~ sP1 ),
inference(cnf_transformation,[],[f327]) ).
tcf(c_321,negated_conjecture,
( ( op(e4,e4) = e0 )
| ( op(e3,e3) = e0 )
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e0 ) ),
inference(cnf_transformation,[],[f338]) ).
tcf(c_322,negated_conjecture,
( ( op(e4,e4) = e1 )
| ( op(e3,e3) = e1 )
| ( op(e2,e2) = e1 )
| ( op(e1,e1) = e1 )
| ( op(e0,e0) = e1 ) ),
inference(cnf_transformation,[],[f337]) ).
tcf(c_327,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| sP4
| sP5
| sP6
| sP7
| sP8
| sP9
| sP10
| sP11
| sP12
| sP13
| sP14
| sP15
| sP16
| sP17
| sP18
| sP19
| sP20
| sP21
| sP22
| sP23
| ( op(e0,e0) = e0 ) ),
inference(cnf_transformation,[],[f332]) ).
tcf(c_328,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| sP4
| sP5
| sP6
| sP7
| sP8
| sP9
| sP10
| sP11
| sP12
| sP13
| sP14
| sP15
| sP16
| sP17
| sP18
| sP19
| sP20
| sP21
| sP22
| sP23
| ( op(e0,e0) != e0 ) ),
inference(cnf_transformation,[],[f331]) ).
tcf(c_335,plain,
~ sP6,
inference(global_subsumption_just,[status(thm)],[c_301,c_301,c_302]) ).
tcf(c_339,plain,
~ sP12,
inference(global_subsumption_just,[status(thm)],[c_283,c_283,c_284]) ).
tcf(c_345,plain,
~ sP18,
inference(global_subsumption_just,[status(thm)],[c_265,c_265,c_266]) ).
tcf(c_367,plain,
op(e1,e1) = e4,
inference(global_subsumption_just,[status(thm)],[c_55,c_248]) ).
tcf(c_1711,plain,
( ( e3 = e4 )
| ~ sP8 ),
inference(light_normalisation,[status(thm)],[c_295,c_367]) ).
tcf(c_1712,plain,
~ sP8,
inference(forward_subsumption_resolution,[status(thm)],[c_1711,c_244]) ).
tcf(c_1737,plain,
( ( e2 = e4 )
| ~ sP13 ),
inference(light_normalisation,[status(thm)],[c_280,c_367]) ).
tcf(c_1738,plain,
~ sP13,
inference(forward_subsumption_resolution,[status(thm)],[c_1737,c_243]) ).
tcf(c_1755,plain,
( ( e3 = e4 )
| ~ sP16 ),
inference(light_normalisation,[status(thm)],[c_270,c_367]) ).
tcf(c_1756,plain,
~ sP16,
inference(forward_subsumption_resolution,[status(thm)],[c_1755,c_244]) ).
tcf(c_1761,plain,
( ( e2 = e4 )
| ~ sP17 ),
inference(light_normalisation,[status(thm)],[c_267,c_367]) ).
tcf(c_1762,plain,
~ sP17,
inference(forward_subsumption_resolution,[status(thm)],[c_1761,c_243]) ).
tcf(c_1767,plain,
( ( e0 = e4 )
| ~ sP19 ),
inference(light_normalisation,[status(thm)],[c_261,c_367]) ).
tcf(c_1768,plain,
~ sP19,
inference(forward_subsumption_resolution,[status(thm)],[c_1767,c_238]) ).
tcf(c_1793,plain,
( ( e0 = e4 )
| ~ sP23 ),
inference(light_normalisation,[status(thm)],[c_250,c_367]) ).
tcf(c_1794,plain,
~ sP23,
inference(forward_subsumption_resolution,[status(thm)],[c_1793,c_238]) ).
tcf(c_1859,plain,
op(e4,e4) = e2,
inference(light_normalisation,[status(thm)],[c_246,c_367]) ).
tcf(c_1868,plain,
( ( e0 = e2 )
| ~ sP20 ),
inference(demodulation,[status(thm)],[c_259,c_1859]) ).
tcf(c_1869,plain,
( ( e1 = e2 )
| ~ sP15 ),
inference(demodulation,[status(thm)],[c_274,c_1859]) ).
tcf(c_1871,plain,
( ( e2 = e3 )
| ~ sP5 ),
inference(demodulation,[status(thm)],[c_304,c_1859]) ).
tcf(c_1872,plain,
( ( e0 = e2 )
| ~ sP4 ),
inference(demodulation,[status(thm)],[c_306,c_1859]) ).
tcf(c_1873,plain,
( ( e1 = e2 )
| ~ sP3 ),
inference(demodulation,[status(thm)],[c_309,c_1859]) ).
tcf(c_1875,plain,
( ( e2 = e3 )
| ~ sP1 ),
inference(demodulation,[status(thm)],[c_315,c_1859]) ).
tcf(c_1876,plain,
~ sP1,
inference(forward_subsumption_resolution,[status(thm)],[c_1875,c_242]) ).
tcf(c_1877,plain,
~ sP3,
inference(forward_subsumption_resolution,[status(thm)],[c_1873,c_239]) ).
tcf(c_1878,plain,
~ sP4,
inference(forward_subsumption_resolution,[status(thm)],[c_1872,c_236]) ).
tcf(c_1879,plain,
~ sP5,
inference(forward_subsumption_resolution,[status(thm)],[c_1871,c_242]) ).
tcf(c_1880,plain,
~ sP15,
inference(forward_subsumption_resolution,[status(thm)],[c_1869,c_239]) ).
tcf(c_1881,plain,
~ sP20,
inference(forward_subsumption_resolution,[status(thm)],[c_1868,c_236]) ).
tcf(c_1882,plain,
op(e1,e2) = e0,
inference(light_normalisation,[status(thm)],[c_245,c_367,c_1859]) ).
tcf(c_1884,plain,
op(e2,e2) != e0,
inference(demodulation,[status(thm)],[c_159,c_1882]) ).
tcf(c_1891,plain,
~ sP14,
inference(backward_subsumption_resolution,[status(thm)],[c_276,c_1884]) ).
tcf(c_1892,plain,
~ sP22,
inference(backward_subsumption_resolution,[status(thm)],[c_253,c_1884]) ).
tcf(c_1893,plain,
op(e2,e2) = e3,
inference(light_normalisation,[status(thm)],[c_247,c_367,c_1859]) ).
tcf(c_1903,plain,
( ( e3 = e4 )
| ~ sP10 ),
inference(demodulation,[status(thm)],[c_288,c_1893]) ).
tcf(c_1905,plain,
( ( e3 = e4 )
| ~ sP2 ),
inference(demodulation,[status(thm)],[c_313,c_1893]) ).
tcf(c_1906,plain,
~ sP2,
inference(forward_subsumption_resolution,[status(thm)],[c_1905,c_244]) ).
tcf(c_1907,plain,
~ sP10,
inference(forward_subsumption_resolution,[status(thm)],[c_1903,c_244]) ).
tcf(c_1931,plain,
( ( e1 = e4 )
| ( e1 = e3 )
| ( e1 = e2 )
| ( op(e3,e3) = e1 )
| ( op(e0,e0) = e1 ) ),
inference(light_normalisation,[status(thm)],[c_322,c_367,c_1859,c_1893]) ).
tcf(c_1932,plain,
( ( op(e3,e3) = e1 )
| ( op(e0,e0) = e1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1931,c_241,c_240,c_239]) ).
tcf(c_1939,plain,
( ( e0 = e4 )
| ( e0 = e3 )
| ( e0 = e2 )
| ( op(e3,e3) = e0 )
| ( op(e0,e0) = e0 ) ),
inference(light_normalisation,[status(thm)],[c_321,c_367,c_1859,c_1893]) ).
tcf(c_1940,plain,
( ( op(e3,e3) = e0 )
| ( op(e0,e0) = e0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1939,c_238,c_237,c_236]) ).
tcf(c_3986,definition,
iPr_def_13 = op(e0,e0),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_3990,plain,
( ( iPr_def_13 = e0 )
| ( iPr_def_12 = e0 ) ),
inference(demodulation,[status(thm)],[c_1940]) ).
tcf(c_3991,plain,
( ( iPr_def_13 = e1 )
| ( iPr_def_12 = e1 ) ),
inference(demodulation,[status(thm)],[c_1932]) ).
tcf(c_4780,plain,
( ( e0 = iPr_def_12 )
| ( e1 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_3990,c_235]) ).
tcf(c_4787,plain,
( ( e1 = iPr_def_12 )
| ( e0 = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_3991,c_4780]) ).
fof(f10,definition,
( ~ sP0
| ( op(e4,e4) != e4
& op(e4,e4) = e4
& op(e4,e4) = e4 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f11,definition,
( ~ sP1
| ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f12,definition,
( ~ sP2
| ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f13,definition,
( ~ sP3
| ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f14,definition,
( ~ sP4
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f15,definition,
( ~ sP5
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 ) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f16,definition,
( ~ sP6
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f17,definition,
( ~ sP7
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f18,definition,
( ~ sP8
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f19,definition,
( ~ sP9
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f20,definition,
( ~ sP10
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 ) ),
introduced(definition,[new_symbols(definition,[sP10])],[predicate_definition_introduction]) ).
fof(f21,definition,
( ~ sP11
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP11])],[predicate_definition_introduction]) ).
fof(f22,definition,
( ~ sP12
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f23,definition,
( ~ sP13
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP13])],[predicate_definition_introduction]) ).
fof(f24,definition,
( ~ sP14
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP14])],[predicate_definition_introduction]) ).
fof(f25,definition,
( ~ sP15
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 ) ),
introduced(definition,[new_symbols(definition,[sP15])],[predicate_definition_introduction]) ).
fof(f26,definition,
( ~ sP16
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP16])],[predicate_definition_introduction]) ).
fof(f27,definition,
( ~ sP17
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP17])],[predicate_definition_introduction]) ).
fof(f28,definition,
( ~ sP18
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP18])],[predicate_definition_introduction]) ).
fof(f29,definition,
( ~ sP19
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP19])],[predicate_definition_introduction]) ).
fof(f30,definition,
( ~ sP20
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 ) ),
introduced(definition,[new_symbols(definition,[sP20])],[predicate_definition_introduction]) ).
fof(f31,definition,
( ~ sP21
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP21])],[predicate_definition_introduction]) ).
fof(f32,definition,
( ~ sP22
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP22])],[predicate_definition_introduction]) ).
fof(f33,definition,
( ~ sP23
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP23])],[predicate_definition_introduction]) ).
fof(f34,plain,
( ( sP0
| sP1
| sP2
| sP3
| sP4
| sP5
| sP6
| sP7
| sP8
| sP9
| sP10
| sP11
| sP12
| sP13
| sP14
| sP15
| sP16
| sP17
| sP18
| sP19
| sP20
| sP21
| sP22
| sP23
| ( 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(definition_folding,[],[f9,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11,f10]) ).
fof(f58,plain,
( ~ sP0
| ( op(e4,e4) != e4
& op(e4,e4) = e4
& op(e4,e4) = e4 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f328,plain,
( ~ sP0
| e4 != op(e4,e4) ),
inference(cnf_transformation,[],[f58]) ).
fof(f329,plain,
( ~ sP0
| e4 = op(e4,e4) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_319,plain,
( ( op(e4,e4) = e4 )
| ~ sP0 ),
inference(cnf_transformation,[],[f329]) ).
tcf(c_320,plain,
( ~ sP0
| ( op(e4,e4) != e4 ) ),
inference(cnf_transformation,[],[f328]) ).
tcf(c_329,plain,
~ sP0,
inference(global_subsumption_just,[status(thm)],[c_319,c_319,c_320]) ).
tcf(c_357,plain,
( sP7
| sP8
| sP9
| sP10
| sP11
| sP19
| sP20
| sP21
| sP22
| sP23
| sP17
| sP16
| sP15
| sP14
| sP13
| sP5
| sP4
| sP3
| sP2
| sP1 ),
inference(global_subsumption_just,[status(thm)],[c_327,c_327,c_328,c_329,c_335,c_339,c_345]) ).
tcf(c_358,negated_conjecture,
( sP1
| sP2
| sP3
| sP4
| sP5
| sP7
| sP8
| sP9
| sP10
| sP11
| sP13
| sP14
| sP15
| sP16
| sP17
| sP19
| sP20
| sP21
| sP22
| sP23 ),
inference(renaming,[status(thm)],[c_357]) ).
tcf(c_369,plain,
( sP7
| sP8
| sP9
| sP10
| sP11
| sP19
| sP20
| sP21
| sP22
| sP23
| sP17
| sP16
| sP15
| sP14
| sP13
| sP5
| sP4
| sP3
| sP2
| sP1 ),
inference(global_subsumption_just,[status(thm)],[c_328,c_358]) ).
tcf(c_370,negated_conjecture,
( sP1
| sP2
| sP3
| sP4
| sP5
| sP7
| sP8
| sP9
| sP10
| sP11
| sP13
| sP14
| sP15
| sP16
| sP17
| sP19
| sP20
| sP21
| sP22
| sP23 ),
inference(renaming,[status(thm)],[c_369]) ).
tcf(c_1908,plain,
( sP7
| sP9
| sP11
| sP21 ),
inference(forward_subsumption_resolution,[status(thm)],[c_370,c_1876,c_1906,c_1877,c_1878,c_1879,c_1712,c_1907,c_1738,c_1891,c_1880,c_1756,c_1762,c_1768,c_1881,c_1892,c_1794]) ).
tcf(c_2680,plain,
( sP9
| sP11
| sP21
| ( op(e3,e3) = e2 ) ),
inference(resolution,[status(thm)],[c_1908,c_297]) ).
tcf(c_2681,plain,
( sP9
| ( op(e3,e3) = e2 )
| sP21 ),
inference(global_subsumption_just,[status(thm)],[c_2680,c_286,c_2680]) ).
tcf(c_2682,plain,
( sP9
| sP21
| ( op(e3,e3) = e2 ) ),
inference(renaming,[status(thm)],[c_2681]) ).
tcf(c_2705,plain,
( sP9
| ( op(e3,e3) = e2 )
| ( op(e3,e3) = e0 ) ),
inference(resolution,[status(thm)],[c_2682,c_256]) ).
tcf(c_2706,plain,
( ( op(e3,e3) = e0 )
| ( op(e3,e3) = e2 ) ),
inference(global_subsumption_just,[status(thm)],[c_2705,c_291,c_2705]) ).
tcf(c_2707,plain,
( ( op(e3,e3) = e2 )
| ( op(e3,e3) = e0 ) ),
inference(renaming,[status(thm)],[c_2706]) ).
tcf(c_2714,plain,
( sP9
| ( op(e3,e3) = e2 )
| ( op(e0,e0) = e3 ) ),
inference(resolution,[status(thm)],[c_2682,c_255]) ).
tcf(c_2715,plain,
( ( op(e0,e0) = e3 )
| ( op(e3,e3) = e2 ) ),
inference(global_subsumption_just,[status(thm)],[c_2714,c_292,c_2714]) ).
tcf(c_2716,plain,
( ( op(e3,e3) = e2 )
| ( op(e0,e0) = e3 ) ),
inference(renaming,[status(thm)],[c_2715]) ).
tcf(c_2740,plain,
( sP21
| ( op(e3,e3) = e2 )
| ( op(e0,e0) = e3 ) ),
inference(resolution,[status(thm)],[c_2682,c_292]) ).
tcf(c_2741,plain,
( ( op(e0,e0) = e3 )
| ( op(e3,e3) = e2 ) ),
inference(global_subsumption_just,[status(thm)],[c_2740,c_2716]) ).
tcf(c_2742,plain,
( ( op(e3,e3) = e2 )
| ( op(e0,e0) = e3 ) ),
inference(renaming,[status(thm)],[c_2741]) ).
tcf(c_3988,plain,
( ( iPr_def_13 = e3 )
| ( iPr_def_12 = e2 ) ),
inference(demodulation,[status(thm)],[c_2742,c_3986]) ).
tcf(c_3989,plain,
( ( iPr_def_12 = e2 )
| ( iPr_def_12 = e0 ) ),
inference(demodulation,[status(thm)],[c_2707]) ).
tcf(c_4797,plain,
( ( e0 = iPr_def_12 )
| ( e1 != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_3989,c_239]) ).
tcf(c_4800,plain,
( ( e2 = iPr_def_12 )
| ( e1 != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_3988,c_240]) ).
tcf(c_4806,plain,
e0 = iPr_def_12,
inference(global_subsumption_just,[status(thm)],[c_4787,c_4787,c_4797]) ).
tcf(c_4810,plain,
e2 != iPr_def_12,
inference(demodulation,[status(thm)],[c_236,c_4806]) ).
tcf(c_4812,plain,
e1 != iPr_def_12,
inference(demodulation,[status(thm)],[c_235,c_4806]) ).
tcf(c_4843,plain,
e1 != iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_4800,c_4800,c_4810]) ).
tcf(c_4845,plain,
e1 = iPr_def_12,
inference(superposition,[status(thm)],[c_3991,c_4843]) ).
tcf(c_4846,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4845,c_4812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG063+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 04:40:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 1.14/1.06 % SZS status Started for theBenchmark.p
% 1.14/1.06 % SZS status Theorem for theBenchmark.p
% 1.14/1.06
% 1.14/1.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.14/1.06
% 1.14/1.06 % ------ iProver source info
% 1.14/1.06
% 1.14/1.06 % git: date: 2026-07-19 20:42:38 +0200
% 1.14/1.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.14/1.06 % git: non_committed_changes: false
% 1.14/1.06
% 1.14/1.06 % ------ Parsing...
% 1.14/1.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.14/1.06
% 1.14/1.06 % ------ Preprocessing... sup_sim: 155 sf_s rm: 20 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.14/1.06
% 1.14/1.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.14/1.06
% 1.14/1.06 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.14/1.06 % ------ Proving...
% 1.14/1.06 % ------ Problem Properties
% 1.14/1.06
% 1.14/1.06 %
% 1.14/1.06 % clauses 194
% 1.14/1.06 % conjectures 0
% 1.14/1.06 % EPR 16
% 1.14/1.06 % Horn 127
% 1.14/1.06 % unary 126
% 1.14/1.06 % binary 8
% 1.14/1.06 % lits 368
% 1.14/1.06 % lits eq 368
% 1.14/1.06 % fd_pure 0
% 1.14/1.06 % fd_pseudo 0
% 1.14/1.06 % fd_cond 0
% 1.14/1.06 % fd_pseudo_cond 0
% 1.14/1.06 % AC symbols 0
% 1.14/1.06
% 1.14/1.06 % ------ Schedule dynamic 5 is on
% 1.14/1.06
% 1.14/1.06 % ------ no conjectures: strip conj schedule
% 1.14/1.06
% 1.14/1.06 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.14/1.06
% 1.14/1.06
% 1.14/1.06 % ------
% 1.14/1.06 % Current options:
% 1.14/1.06 % ------
% 1.14/1.06
% 1.14/1.06
% 1.14/1.06 %
% 1.14/1.06
% 1.14/1.06 % ------ Proving...
% 1.14/1.06 %
% 1.14/1.06
% 1.14/1.06 % SZS status Theorem for theBenchmark.p
% 1.14/1.06
% 1.14/1.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.14/1.07
% 1.14/1.07
%------------------------------------------------------------------------------