%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG054+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.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 12:53:18 PM UTC 2026
% Result : Theorem 3.08s 1.28s
% Output : CNFRefutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 22
% Syntax : Number of formulae : 202 ( 124 unt; 15 def)
% Number of atoms : 1174 (1096 equ)
% Maximal formula atoms : 250 ( 5 avg)
% Number of connectives : 1174 ( 279 ~; 614 |; 281 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 101 ( 4 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 : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 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/sandbox/benchmark/theBenchmark.p',ax1) ).
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',ax2) ).
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',ax3) ).
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',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/sandbox/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/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f7,conjecture,
~ ( ( 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 )
& ( op(e4,e4) = e4
| op(e3,e3) = e4
| op(e2,e2) = e4
| op(e1,e1) = e4
| op(e0,e0) = e4 )
& ( op(e4,e4) = e3
| op(e3,e3) = e3
| op(e2,e2) = e3
| op(e1,e1) = e3
| op(e0,e0) = e3 )
& ( op(e4,e4) = e2
| op(e3,e3) = e2
| op(e2,e2) = e2
| op(e1,e1) = e2
| op(e0,e0) = e2 )
& ( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e2,e2) = e1
| op(e1,e1) = e1
| op(e0,e0) = e1 )
& ( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e2,e2) = e0
| op(e1,e1) = e0
| op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f8,negated_conjecture,
~ ~ ( ( 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 )
& ( 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,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 )
& ( 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(f11,plain,
( e4 = op(e4,e3)
| e3 = op(e4,e3)
| e2 = op(e4,e3)
| e1 = op(e4,e3)
| e0 = op(e4,e3) ),
inference(cnf_transformation,[],[f1]) ).
fof(f13,plain,
( e4 = op(e4,e1)
| e3 = op(e4,e1)
| e2 = op(e4,e1)
| e1 = op(e4,e1)
| e0 = op(e4,e1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f17,plain,
( e4 = op(e3,e2)
| e3 = op(e3,e2)
| e2 = op(e3,e2)
| e1 = op(e3,e2)
| e0 = op(e3,e2) ),
inference(cnf_transformation,[],[f1]) ).
fof(f25,plain,
( e4 = op(e1,e4)
| e3 = op(e1,e4)
| e2 = op(e1,e4)
| e1 = op(e1,e4)
| e0 = op(e1,e4) ),
inference(cnf_transformation,[],[f1]) ).
fof(f28,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(f35,plain,
( e4 = unit
| e3 = unit
| e2 = unit
| e1 = unit
| e0 = unit ),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
e4 = op(e4,unit),
inference(cnf_transformation,[],[f2]) ).
fof(f37,plain,
e4 = op(unit,e4),
inference(cnf_transformation,[],[f2]) ).
fof(f38,plain,
e3 = op(e3,unit),
inference(cnf_transformation,[],[f2]) ).
fof(f54,plain,
( e0 = op(e4,e4)
| e0 = op(e3,e4)
| e0 = op(e2,e4)
| e0 = op(e1,e4)
| e0 = op(e0,e4) ),
inference(cnf_transformation,[],[f3]) ).
fof(f55,plain,
( e0 = op(e4,e4)
| e0 = op(e4,e3)
| e0 = op(e4,e2)
| e0 = op(e4,e1)
| e0 = op(e4,e0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f79,plain,
( e3 = op(e1,e4)
| e3 = op(e1,e3)
| e3 = op(e1,e2)
| e3 = op(e1,e1)
| e3 = op(e1,e0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f81,plain,
( e2 = op(e1,e4)
| e2 = op(e1,e3)
| e2 = op(e1,e2)
| e2 = op(e1,e1)
| e2 = op(e1,e0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f88,plain,
( e3 = op(e4,e0)
| e3 = op(e3,e0)
| e3 = op(e2,e0)
| e3 = op(e1,e0)
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f3]) ).
fof(f96,plain,
op(e4,e3) != op(e4,e4),
inference(cnf_transformation,[],[f4]) ).
fof(f98,plain,
op(e4,e2) != op(e4,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f99,plain,
op(e4,e1) != op(e4,e4),
inference(cnf_transformation,[],[f4]) ).
fof(f100,plain,
op(e4,e1) != op(e4,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f106,plain,
op(e3,e3) != op(e3,e4),
inference(cnf_transformation,[],[f4]) ).
fof(f108,plain,
op(e3,e2) != op(e3,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f115,plain,
op(e3,e0) != op(e3,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f124,plain,
op(e2,e0) != op(e2,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f139,plain,
op(e0,e1) != op(e0,e4),
inference(cnf_transformation,[],[f4]) ).
fof(f156,plain,
op(e3,e3) != op(e4,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f159,plain,
op(e1,e3) != op(e4,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f161,plain,
op(e1,e3) != op(e2,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f162,plain,
op(e0,e3) != op(e4,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f166,plain,
op(e3,e2) != op(e4,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f168,plain,
op(e2,e2) != op(e3,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f170,plain,
op(e1,e2) != op(e3,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f176,plain,
op(e3,e1) != op(e4,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f179,plain,
op(e1,e1) != op(e4,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f182,plain,
op(e0,e1) != op(e4,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f196,plain,
e3 != e4,
inference(cnf_transformation,[],[f5]) ).
fof(f197,plain,
e2 != e4,
inference(cnf_transformation,[],[f5]) ).
fof(f198,plain,
e2 != e3,
inference(cnf_transformation,[],[f5]) ).
fof(f199,plain,
e1 != e4,
inference(cnf_transformation,[],[f5]) ).
fof(f200,plain,
e1 != e3,
inference(cnf_transformation,[],[f5]) ).
fof(f201,plain,
e1 != e2,
inference(cnf_transformation,[],[f5]) ).
fof(f202,plain,
e0 != e4,
inference(cnf_transformation,[],[f5]) ).
fof(f203,plain,
e0 != e3,
inference(cnf_transformation,[],[f5]) ).
fof(f204,plain,
e0 != e2,
inference(cnf_transformation,[],[f5]) ).
fof(f205,plain,
e0 != e1,
inference(cnf_transformation,[],[f5]) ).
fof(f206,plain,
e4 = op(e1,e1),
inference(cnf_transformation,[],[f6]) ).
fof(f207,plain,
e3 = op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1))),
inference(cnf_transformation,[],[f6]) ).
fof(f208,plain,
e2 = op(op(e1,e1),op(e1,e1)),
inference(cnf_transformation,[],[f6]) ).
fof(f209,plain,
e0 = op(e1,op(op(e1,e1),op(e1,e1))),
inference(cnf_transformation,[],[f6]) ).
fof(f212,plain,
( e4 = op(e4,e2)
| e2 != op(e4,e4) ),
inference(cnf_transformation,[],[f9]) ).
fof(f218,plain,
( e3 = op(e3,e1)
| e1 != op(e3,e3) ),
inference(cnf_transformation,[],[f9]) ).
fof(f221,plain,
( e2 = op(e2,e3)
| e3 != op(e2,e2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f225,plain,
( e1 = op(e1,e4)
| e4 != op(e1,e1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f231,plain,
( e0 = op(e0,e3)
| op(e0,e0) != e3 ),
inference(cnf_transformation,[],[f9]) ).
fof(f233,plain,
( e0 = op(e0,e1)
| op(e0,e0) != e1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f238,plain,
( e1 = op(e4,e4)
| e1 = op(e3,e3)
| e1 = op(e2,e2)
| e1 = op(e1,e1)
| op(e0,e0) = e1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f239,plain,
( e0 = op(e4,e4)
| e0 = op(e3,e3)
| e0 = op(e2,e2)
| e0 = op(e1,e1)
| e0 = op(e0,e0) ),
inference(cnf_transformation,[],[f9]) ).
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,[],[f28]) ).
tcf(c_58,plain,
( ( op(e1,e4) = e4 )
| ( op(e1,e4) = e3 )
| ( op(e1,e4) = e2 )
| ( op(e1,e4) = e1 )
| ( op(e1,e4) = e0 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_66,plain,
( ( op(e3,e2) = e4 )
| ( op(e3,e2) = e3 )
| ( op(e3,e2) = e2 )
| ( op(e3,e2) = e1 )
| ( op(e3,e2) = e0 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_70,plain,
( ( op(e4,e1) = e4 )
| ( op(e4,e1) = e3 )
| ( op(e4,e1) = e2 )
| ( op(e4,e1) = e1 )
| ( op(e4,e1) = e0 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_72,plain,
( ( op(e4,e3) = e4 )
| ( op(e4,e3) = e3 )
| ( op(e4,e3) = e2 )
| ( op(e4,e3) = e1 )
| ( op(e4,e3) = e0 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_81,plain,
op(e3,unit) = e3,
inference(cnf_transformation,[],[f38]) ).
tcf(c_82,plain,
op(unit,e4) = e4,
inference(cnf_transformation,[],[f37]) ).
tcf(c_83,plain,
op(e4,unit) = e4,
inference(cnf_transformation,[],[f36]) ).
tcf(c_84,plain,
( ( e4 = unit )
| ( e3 = unit )
| ( e2 = unit )
| ( e1 = unit )
| ( e0 = unit ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_92,plain,
( ( op(e4,e0) = e3 )
| ( op(e3,e0) = e3 )
| ( op(e2,e0) = e3 )
| ( op(e1,e0) = e3 )
| ( op(e0,e0) = e3 ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_99,plain,
( ( op(e1,e4) = e2 )
| ( op(e1,e3) = e2 )
| ( op(e1,e2) = e2 )
| ( op(e1,e1) = e2 )
| ( op(e1,e0) = e2 ) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_101,plain,
( ( op(e1,e4) = e3 )
| ( op(e1,e3) = e3 )
| ( op(e1,e2) = e3 )
| ( op(e1,e1) = e3 )
| ( op(e1,e0) = e3 ) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_125,plain,
( ( op(e4,e4) = e0 )
| ( op(e4,e3) = e0 )
| ( op(e4,e2) = e0 )
| ( op(e4,e1) = e0 )
| ( op(e4,e0) = e0 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_126,plain,
( ( op(e4,e4) = e0 )
| ( op(e3,e4) = e0 )
| ( op(e2,e4) = e0 )
| ( op(e1,e4) = e0 )
| ( op(e0,e4) = e0 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_148,plain,
op(e0,e1) != op(e4,e1),
inference(cnf_transformation,[],[f182]) ).
tcf(c_151,plain,
op(e1,e1) != op(e4,e1),
inference(cnf_transformation,[],[f179]) ).
tcf(c_154,plain,
op(e3,e1) != op(e4,e1),
inference(cnf_transformation,[],[f176]) ).
tcf(c_160,plain,
op(e1,e2) != op(e3,e2),
inference(cnf_transformation,[],[f170]) ).
tcf(c_162,plain,
op(e2,e2) != op(e3,e2),
inference(cnf_transformation,[],[f168]) ).
tcf(c_164,plain,
op(e3,e2) != op(e4,e2),
inference(cnf_transformation,[],[f166]) ).
tcf(c_168,plain,
op(e0,e3) != op(e4,e3),
inference(cnf_transformation,[],[f162]) ).
tcf(c_169,plain,
op(e1,e3) != op(e2,e3),
inference(cnf_transformation,[],[f161]) ).
tcf(c_171,plain,
op(e1,e3) != op(e4,e3),
inference(cnf_transformation,[],[f159]) ).
tcf(c_174,plain,
op(e3,e3) != op(e4,e3),
inference(cnf_transformation,[],[f156]) ).
tcf(c_191,plain,
op(e0,e1) != op(e0,e4),
inference(cnf_transformation,[],[f139]) ).
tcf(c_206,plain,
op(e2,e0) != op(e2,e2),
inference(cnf_transformation,[],[f124]) ).
tcf(c_215,plain,
op(e3,e0) != op(e3,e1),
inference(cnf_transformation,[],[f115]) ).
tcf(c_222,plain,
op(e3,e2) != op(e3,e3),
inference(cnf_transformation,[],[f108]) ).
tcf(c_224,plain,
op(e3,e3) != op(e3,e4),
inference(cnf_transformation,[],[f106]) ).
tcf(c_230,plain,
op(e4,e1) != op(e4,e3),
inference(cnf_transformation,[],[f100]) ).
tcf(c_231,plain,
op(e4,e1) != op(e4,e4),
inference(cnf_transformation,[],[f99]) ).
tcf(c_232,plain,
op(e4,e2) != op(e4,e3),
inference(cnf_transformation,[],[f98]) ).
tcf(c_234,plain,
op(e4,e3) != op(e4,e4),
inference(cnf_transformation,[],[f96]) ).
tcf(c_235,plain,
e0 != e1,
inference(cnf_transformation,[],[f205]) ).
tcf(c_236,plain,
e0 != e2,
inference(cnf_transformation,[],[f204]) ).
tcf(c_237,plain,
e0 != e3,
inference(cnf_transformation,[],[f203]) ).
tcf(c_238,plain,
e0 != e4,
inference(cnf_transformation,[],[f202]) ).
tcf(c_239,plain,
e1 != e2,
inference(cnf_transformation,[],[f201]) ).
tcf(c_240,plain,
e1 != e3,
inference(cnf_transformation,[],[f200]) ).
tcf(c_241,plain,
e1 != e4,
inference(cnf_transformation,[],[f199]) ).
tcf(c_242,plain,
e2 != e3,
inference(cnf_transformation,[],[f198]) ).
tcf(c_243,plain,
e2 != e4,
inference(cnf_transformation,[],[f197]) ).
tcf(c_244,plain,
e3 != e4,
inference(cnf_transformation,[],[f196]) ).
tcf(c_245,plain,
op(e1,op(op(e1,e1),op(e1,e1))) = e0,
inference(cnf_transformation,[],[f209]) ).
tcf(c_246,plain,
op(op(e1,e1),op(e1,e1)) = e2,
inference(cnf_transformation,[],[f208]) ).
tcf(c_247,plain,
op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1))) = e3,
inference(cnf_transformation,[],[f207]) ).
tcf(c_248,plain,
op(e1,e1) = e4,
inference(cnf_transformation,[],[f206]) ).
tcf(c_249,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,[],[f239]) ).
tcf(c_250,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,[],[f238]) ).
tcf(c_254,negated_conjecture,
( ( op(e0,e1) = e0 )
| ( op(e0,e0) != e1 ) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_256,negated_conjecture,
( ( op(e0,e3) = e0 )
| ( op(e0,e0) != e3 ) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_261,negated_conjecture,
( ( op(e1,e4) = e1 )
| ( op(e1,e1) != e4 ) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_264,negated_conjecture,
( ( op(e2,e3) = e2 )
| ( op(e2,e2) != e3 ) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_267,negated_conjecture,
( ( op(e3,e1) = e3 )
| ( op(e3,e3) != e1 ) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_272,negated_conjecture,
( ( op(e4,e2) = e4 )
| ( op(e4,e4) != e2 ) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_286,plain,
op(e1,e4) = e1,
inference(global_subsumption_just,[status(thm)],[c_58,c_248,c_261]) ).
tcf(c_288,plain,
op(e1,e1) = e4,
inference(global_subsumption_just,[status(thm)],[c_55,c_248]) ).
tcf(c_1367,plain,
op(e4,e1) != e4,
inference(light_normalisation,[status(thm)],[c_151,c_288]) ).
tcf(c_1371,plain,
op(e4,e4) = e2,
inference(light_normalisation,[status(thm)],[c_246,c_288]) ).
tcf(c_1377,plain,
op(e4,e1) != e2,
inference(demodulation,[status(thm)],[c_231,c_1371]) ).
tcf(c_1379,plain,
op(e4,e3) != e2,
inference(demodulation,[status(thm)],[c_234,c_1371]) ).
tcf(c_1380,plain,
op(e1,e2) = e0,
inference(light_normalisation,[status(thm)],[c_245,c_288,c_1371]) ).
tcf(c_1383,plain,
op(e3,e2) != e0,
inference(demodulation,[status(thm)],[c_160,c_1380]) ).
tcf(c_1390,plain,
( ( op(e4,e2) = e4 )
| ( e2 != e2 ) ),
inference(demodulation,[status(thm)],[c_272,c_1371]) ).
tcf(c_1391,plain,
op(e4,e2) = e4,
inference(equality_resolution_simp,[status(thm)],[c_1390]) ).
tcf(c_1396,plain,
op(e3,e2) != e4,
inference(demodulation,[status(thm)],[c_164,c_1391]) ).
tcf(c_1399,plain,
op(e4,e3) != e4,
inference(demodulation,[status(thm)],[c_232,c_1391]) ).
tcf(c_1440,plain,
op(e2,e2) = e3,
inference(light_normalisation,[status(thm)],[c_247,c_288,c_1371]) ).
tcf(c_1442,plain,
( ( op(e2,e3) = e2 )
| ( e3 != e3 ) ),
inference(demodulation,[status(thm)],[c_264,c_1440]) ).
tcf(c_1446,plain,
op(e3,e2) != e3,
inference(demodulation,[status(thm)],[c_162,c_1440]) ).
tcf(c_1447,plain,
op(e2,e0) != e3,
inference(demodulation,[status(thm)],[c_206,c_1440]) ).
tcf(c_1452,plain,
op(e2,e3) = e2,
inference(equality_resolution_simp,[status(thm)],[c_1442]) ).
tcf(c_1455,plain,
op(e1,e3) != e2,
inference(demodulation,[status(thm)],[c_169,c_1452]) ).
tcf(c_1471,plain,
( ( e1 = e4 )
| ( e1 = e3 )
| ( e1 = e2 )
| ( op(e3,e3) = e1 )
| ( op(e0,e0) = e1 ) ),
inference(light_normalisation,[status(thm)],[c_250,c_288,c_1371,c_1440]) ).
tcf(c_1472,plain,
( ( op(e3,e3) = e1 )
| ( op(e0,e0) = e1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1471,c_241,c_240,c_239]) ).
tcf(c_1479,plain,
( ( e0 = e4 )
| ( e0 = e3 )
| ( e0 = e2 )
| ( op(e3,e3) = e0 )
| ( op(e0,e0) = e0 ) ),
inference(light_normalisation,[status(thm)],[c_249,c_288,c_1371,c_1440]) ).
tcf(c_1480,plain,
( ( op(e3,e3) = e0 )
| ( op(e0,e0) = e0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1479,c_238,c_237,c_236]) ).
tcf(c_1528,plain,
( ( e0 = e2 )
| ( e0 = e1 )
| ( op(e3,e4) = e0 )
| ( op(e2,e4) = e0 )
| ( op(e0,e4) = e0 ) ),
inference(light_normalisation,[status(thm)],[c_126,c_286,c_1371]) ).
tcf(c_1529,plain,
( ( op(e3,e4) = e0 )
| ( op(e2,e4) = e0 )
| ( op(e0,e4) = e0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1528,c_236,c_235]) ).
tcf(c_1539,plain,
( ( e0 = e4 )
| ( e0 = e2 )
| ( op(e4,e3) = e0 )
| ( op(e4,e1) = e0 )
| ( op(e4,e0) = e0 ) ),
inference(light_normalisation,[status(thm)],[c_125,c_1371,c_1391]) ).
tcf(c_1540,plain,
( ( op(e4,e3) = e0 )
| ( op(e4,e1) = e0 )
| ( op(e4,e0) = e0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1539,c_238,c_236]) ).
tcf(c_1707,plain,
( ( e3 = e4 )
| ( e1 = e3 )
| ( e0 = e3 )
| ( op(e1,e3) = e3 )
| ( op(e1,e0) = e3 ) ),
inference(light_normalisation,[status(thm)],[c_101,c_288,c_286,c_1380]) ).
tcf(c_1708,plain,
( ( op(e1,e3) = e3 )
| ( op(e1,e0) = e3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1707,c_244,c_240,c_237]) ).
tcf(c_1723,plain,
( ( e2 = e4 )
| ( e1 = e2 )
| ( e0 = e2 )
| ( op(e1,e3) = e2 )
| ( op(e1,e0) = e2 ) ),
inference(light_normalisation,[status(thm)],[c_99,c_288,c_286,c_1380]) ).
tcf(c_1724,plain,
op(e1,e0) = e2,
inference(forward_subsumption_resolution,[status(thm)],[c_1723,c_243,c_239,c_236,c_1455]) ).
tcf(c_1725,plain,
( ( e2 = e3 )
| ( op(e1,e3) = e3 ) ),
inference(demodulation,[status(thm)],[c_1708,c_1724]) ).
tcf(c_1739,plain,
op(e1,e3) = e3,
inference(forward_subsumption_resolution,[status(thm)],[c_1725,c_242]) ).
tcf(c_1745,plain,
op(e4,e3) != e3,
inference(demodulation,[status(thm)],[c_171,c_1739]) ).
tcf(c_1809,plain,
( ( e2 = e3 )
| ( op(e4,e0) = e3 )
| ( op(e3,e0) = e3 )
| ( op(e2,e0) = e3 )
| ( op(e0,e0) = e3 ) ),
inference(light_normalisation,[status(thm)],[c_92,c_1724]) ).
tcf(c_1810,plain,
( ( op(e4,e0) = e3 )
| ( op(e3,e0) = e3 )
| ( op(e0,e0) = e3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1809,c_242,c_1447]) ).
tcf(c_1891,plain,
( ( op(e4,e3) = e1 )
| ( op(e4,e3) = e0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_72,c_1399,c_1745,c_1379]) ).
tcf(c_1898,plain,
( ( op(e4,e1) = e3 )
| ( op(e4,e1) = e1 )
| ( op(e4,e1) = e0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_70,c_1367,c_1377]) ).
tcf(c_1938,plain,
( ( op(e3,e2) = e2 )
| ( op(e3,e2) = e1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_66,c_1396,c_1446,c_1383]) ).
tcf(c_2914,definition,
iPr_def_10 = op(e0,e0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2916,definition,
iPr_def_12 = op(e0,e3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2919,definition,
iPr_def_15 = op(e3,e0),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_2920,definition,
iPr_def_16 = op(e3,e2),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_2921,definition,
iPr_def_17 = op(e3,e3),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_2922,definition,
iPr_def_18 = op(e4,e0),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_2923,definition,
iPr_def_19 = op(e4,e3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_2924,definition,
iPr_def_20 = op(e0,e1),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_2926,definition,
iPr_def_22 = op(e3,e1),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_2927,definition,
iPr_def_23 = op(e3,e4),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_2928,definition,
iPr_def_24 = op(e4,e1),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_2929,definition,
iPr_def_25 = op(e1,e3),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_2930,definition,
iPr_def_26 = op(e1,e0),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_2932,definition,
iPr_def_28 = op(e2,e3),
introduced(definition,[new_symbols(definition,[iPr_def_28])],[]) ).
tcf(c_2933,definition,
iPr_def_29 = op(e4,e2),
introduced(definition,[new_symbols(definition,[iPr_def_29])],[]) ).
tcf(c_2940,plain,
( ( iPr_def_16 = e2 )
| ( iPr_def_16 = e1 ) ),
inference(demodulation,[status(thm)],[c_1938,c_2920]) ).
tcf(c_2943,plain,
( ( iPr_def_19 = e1 )
| ( iPr_def_19 = e0 ) ),
inference(demodulation,[status(thm)],[c_1891,c_2923]) ).
tcf(c_2948,plain,
( ( iPr_def_18 = e3 )
| ( iPr_def_15 = e3 )
| ( iPr_def_10 = e3 ) ),
inference(demodulation,[status(thm)],[c_1810]) ).
tcf(c_2956,plain,
iPr_def_25 = e3,
inference(demodulation,[status(thm)],[c_1739,c_2929]) ).
tcf(c_2959,plain,
iPr_def_26 = e2,
inference(demodulation,[status(thm)],[c_1724,c_2930]) ).
tcf(c_2970,plain,
( ( iPr_def_24 = e0 )
| ( iPr_def_19 = e0 )
| ( iPr_def_18 = e0 ) ),
inference(demodulation,[status(thm)],[c_1540]) ).
tcf(c_2972,plain,
( ( iPr_def_17 = e0 )
| ( iPr_def_10 = e0 ) ),
inference(demodulation,[status(thm)],[c_1480]) ).
tcf(c_2973,plain,
( ( iPr_def_17 = e1 )
| ( iPr_def_10 = e1 ) ),
inference(demodulation,[status(thm)],[c_1472]) ).
tcf(c_2977,plain,
iPr_def_28 = e2,
inference(demodulation,[status(thm)],[c_1452,c_2932]) ).
tcf(c_2984,plain,
iPr_def_29 = e4,
inference(demodulation,[status(thm)],[c_1391,c_2933]) ).
tcf(c_2986,negated_conjecture,
( ( iPr_def_22 = e3 )
| ( iPr_def_17 != e1 ) ),
inference(demodulation,[status(thm)],[c_267]) ).
tcf(c_2989,negated_conjecture,
( ( iPr_def_12 = e0 )
| ( iPr_def_10 != e3 ) ),
inference(demodulation,[status(thm)],[c_256]) ).
tcf(c_2990,negated_conjecture,
( ( iPr_def_20 = e0 )
| ( iPr_def_10 != e1 ) ),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_3591,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( e1 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2986,c_2956]) ).
tcf(c_3628,plain,
e0 != iPr_def_29,
inference(light_normalisation,[status(thm)],[c_238,c_2984]) ).
tcf(c_3629,plain,
iPr_def_26 = iPr_def_28,
inference(light_normalisation,[status(thm)],[c_2977,c_2959]) ).
tcf(c_3692,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( e1 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2973,c_3591]) ).
tcf(c_3710,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_10 = iPr_def_17 )
| ( e1 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2973,c_3692]) ).
tcf(c_3771,plain,
e1 != iPr_def_29,
inference(light_normalisation,[status(thm)],[c_241,c_2984]) ).
tcf(c_3778,plain,
iPr_def_25 != iPr_def_26,
inference(light_normalisation,[status(thm)],[c_242,c_2956,c_2959]) ).
tcf(c_3782,plain,
iPr_def_26 != iPr_def_29,
inference(light_normalisation,[status(thm)],[c_243,c_2959,c_2984]) ).
tcf(c_3783,plain,
iPr_def_25 != iPr_def_29,
inference(light_normalisation,[status(thm)],[c_244,c_2956,c_2984]) ).
tcf(c_4023,plain,
op(iPr_def_25,unit) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_81,c_2956]) ).
tcf(c_4080,plain,
op(unit,iPr_def_29) = iPr_def_29,
inference(light_normalisation,[status(thm)],[c_82,c_2984]) ).
tcf(c_4081,plain,
op(iPr_def_29,unit) = iPr_def_29,
inference(light_normalisation,[status(thm)],[c_83,c_2984]) ).
tcf(c_4091,plain,
op(iPr_def_29,iPr_def_29) = iPr_def_26,
inference(light_normalisation,[status(thm)],[c_1371,c_2959,c_2984]) ).
tcf(c_4237,plain,
op(iPr_def_25,iPr_def_26) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_2920,c_2956,c_2959]) ).
tcf(c_4259,plain,
op(iPr_def_29,e0) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_2922,c_2984]) ).
tcf(c_4314,plain,
op(iPr_def_29,iPr_def_25) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_2923,c_2956,c_2984]) ).
tcf(c_4337,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_4314,c_4259,c_4237,c_4091,c_4081,c_4080,c_4023,c_3783,c_3782,c_3778,c_3771,c_3710,c_3629,c_3628,c_2990,c_2989,c_2984,c_2977,c_2973,c_2972,c_2970,c_2956,c_2948,c_2943,c_2940,c_2928,c_2927,c_2926,c_2924,c_2923,c_2921,c_2920,c_2919,c_2916,c_2914,c_1898,c_1529,c_235,c_230,c_224,c_222,c_215,c_191,c_174,c_168,c_154,c_148,c_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG054+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 04:36:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.08/1.28 % SZS status Started for theBenchmark.p
% 3.08/1.28 % SZS status Theorem for theBenchmark.p
% 3.08/1.28
% 3.08/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.08/1.28
% 3.08/1.28 % ------ iProver source info
% 3.08/1.28
% 3.08/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.08/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.08/1.28 % git: non_committed_changes: false
% 3.08/1.28
% 3.08/1.28 % ------ Parsing...
% 3.08/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.08/1.28
% 3.08/1.28 % ------ Preprocessing... sup_sim: 191 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.08/1.28
% 3.08/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.08/1.28
% 3.08/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.08/1.28 % ------ Proving...
% 3.08/1.28 % ------ Problem Properties
% 3.08/1.28
% 3.08/1.28 %
% 3.08/1.28 % clauses 184
% 3.08/1.28 % conjectures 6
% 3.08/1.28 % EPR 68
% 3.08/1.28 % Horn 133
% 3.08/1.28 % unary 127
% 3.08/1.28 % binary 23
% 3.08/1.28 % lits 289
% 3.08/1.28 % lits eq 289
% 3.08/1.28 % fd_pure 0
% 3.08/1.28 % fd_pseudo 0
% 3.08/1.28 % fd_cond 0
% 3.08/1.28 % fd_pseudo_cond 0
% 3.08/1.28 % AC symbols 0
% 3.08/1.28
% 3.08/1.28 % ------ Schedule dynamic 5 is on
% 3.08/1.28
% 3.08/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.08/1.28
% 3.08/1.28
% 3.08/1.28 % ------
% 3.08/1.28 % Current options:
% 3.08/1.28 % ------
% 3.08/1.28
% 3.08/1.28
% 3.08/1.28 %
% 3.08/1.28
% 3.08/1.28 % ------ Proving...
% 3.08/1.28 %
% 3.08/1.28
% 3.08/1.28 % SZS status Theorem for theBenchmark.p
% 3.08/1.28
% 3.08/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.08/1.28
% 3.08/1.28
%------------------------------------------------------------------------------