TSTP Solution File: ALG115+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG115+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 16:08:10 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Proof 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 559
% Syntax : Number of formulae : 1761 ( 350 unt; 14 typ; 0 def)
% Number of atoms : 15365 (15287 equ)
% Maximal formula atoms : 288 ( 8 avg)
% Number of connectives : 16804 (3186 ~;7662 |;5105 &)
% ( 851 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 72 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 6 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(op2_type,type,
op2: ( $i * $i ) > $i ).
tff(h2_type,type,
h2: $i > $i ).
tff(e13_type,type,
e13: $i ).
tff(op1_type,type,
op1: ( $i * $i ) > $i ).
tff(h4_type,type,
h4: $i > $i ).
tff(h3_type,type,
h3: $i > $i ).
tff(h1_type,type,
h1: $i > $i ).
tff(e21_type,type,
e21: $i ).
tff(e20_type,type,
e20: $i ).
tff(e22_type,type,
e22: $i ).
tff(e23_type,type,
e23: $i ).
tff(e11_type,type,
e11: $i ).
tff(e10_type,type,
e10: $i ).
tff(e12_type,type,
e12: $i ).
tff(1,plain,
( ( h1(e13) = h2(e13) )
<=> ( h2(e13) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( h1(e13) != h2(e13) )
<=> ( h2(e13) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[1]) ).
tff(3,plain,
( ( op2(h2(e13),h3(e13)) != h2(e13) )
<=> ( h1(e13) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) )
<=> ( op2(h2(e13),h3(e13)) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( e20 != e21 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ( e20 != e21 )
<=> ( e20 != e21 ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 )
& ( e21 != e23 )
& ( e22 != e23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
tff(8,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 )
& ( e21 != e23 ) ),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 ) ),
inference(and_elim,[status(thm)],[8]) ).
tff(10,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 ) ),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
( ( e20 != e21 )
& ( e20 != e22 ) ),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
e20 != e21,
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
e20 != e21,
inference(modus_ponens,[status(thm)],[12,6]) ).
tff(14,plain,
op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[13,5]) ).
tff(15,plain,
op2(h2(e13),h3(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[14,4]) ).
tff(16,plain,
h1(e13) != h2(e13),
inference(modus_ponens,[status(thm)],[15,3]) ).
tff(17,plain,
h2(e13) != h1(e13),
inference(modus_ponens,[status(thm)],[16,2]) ).
tff(18,plain,
( ( op2(h3(e13),h3(e13)) = h1(e13) )
<=> ( h1(e13) = op2(h3(e13),h3(e13)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(19,plain,
( ( h3(op1(e13,e13)) = op2(op2(h2(e13),h4(e13)),op2(h2(e13),h4(e13))) )
<=> ( h3(op1(e13,e13)) = op2(h3(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ( h3(op1(e13,e13)) = op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( h3(op1(e13,e13)) = op2(op2(h2(e13),h4(e13)),op2(h2(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( h3(e11) = op2(e22,e22) )
<=> ( h3(op1(e13,e13)) = op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( h3(e11) = op2(e22,e22) )
<=> ( h3(e11) = op2(e22,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
( ( h3(e13) = e22 )
& ( h3(e10) = op2(op2(e22,e22),op2(op2(e22,e22),e22)) )
& ( h3(e11) = op2(e22,e22) )
& ( h3(e12) = op2(op2(e22,e22),e22) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
tff(24,plain,
( ( h3(e13) = e22 )
& ( h3(e10) = op2(op2(e22,e22),op2(op2(e22,e22),e22)) )
& ( h3(e11) = op2(e22,e22) ) ),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
h3(e11) = op2(e22,e22),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
h3(e11) = op2(e22,e22),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
h3(op1(e13,e13)) = op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[26,21]) ).
tff(28,plain,
h3(op1(e13,e13)) = op2(op2(h2(e13),h4(e13)),op2(h2(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
h3(op1(e13,e13)) = op2(h3(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[28,19]) ).
tff(30,plain,
( ( h3(op1(e13,e13)) = h1(e13) )
<=> ( op2(h3(e13),h3(e13)) = h1(e13) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( h3(op1(e13,e13)) = h1(e13) )
<=> ( h1(e13) = op2(h3(e13),h3(e13)) ) ),
inference(transitivity,[status(thm)],[30,18]) ).
tff(32,plain,
( ( h1(e13) = op2(h3(e13),h3(e13)) )
<=> ( h3(op1(e13,e13)) = h1(e13) ) ),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ( h1(e13) != op2(h3(e13),h3(e13)) )
<=> ( h3(op1(e13,e13)) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( h1(e13) != h3(op1(e13,e13)) )
<=> ( h1(e13) != op2(h3(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( op2(h2(e13),h3(e13)) != h3(op1(e13,e13)) )
<=> ( h1(e13) != h3(op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(h2(e13),h3(e13)) != h3(op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( op2(e21,e22) != op2(e22,e22) )
<=> ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( op2(e21,e22) != op2(e22,e22) )
<=> ( op2(e21,e22) != op2(e22,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) )
& ( op2(e22,e22) != op2(e22,e23) )
& ( op2(e23,e20) != op2(e23,e21) )
& ( op2(e23,e20) != op2(e23,e22) )
& ( op2(e23,e20) != op2(e23,e23) )
& ( op2(e23,e21) != op2(e23,e22) )
& ( op2(e23,e21) != op2(e23,e23) )
& ( op2(e23,e22) != op2(e23,e23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
tff(40,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) )
& ( op2(e22,e22) != op2(e22,e23) )
& ( op2(e23,e20) != op2(e23,e21) )
& ( op2(e23,e20) != op2(e23,e22) )
& ( op2(e23,e20) != op2(e23,e23) )
& ( op2(e23,e21) != op2(e23,e22) )
& ( op2(e23,e21) != op2(e23,e23) ) ),
inference(and_elim,[status(thm)],[39]) ).
tff(41,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) )
& ( op2(e22,e22) != op2(e22,e23) )
& ( op2(e23,e20) != op2(e23,e21) )
& ( op2(e23,e20) != op2(e23,e22) )
& ( op2(e23,e20) != op2(e23,e23) )
& ( op2(e23,e21) != op2(e23,e22) ) ),
inference(and_elim,[status(thm)],[40]) ).
tff(42,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) )
& ( op2(e22,e22) != op2(e22,e23) )
& ( op2(e23,e20) != op2(e23,e21) )
& ( op2(e23,e20) != op2(e23,e22) )
& ( op2(e23,e20) != op2(e23,e23) ) ),
inference(and_elim,[status(thm)],[41]) ).
tff(43,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) )
& ( op2(e22,e22) != op2(e22,e23) )
& ( op2(e23,e20) != op2(e23,e21) )
& ( op2(e23,e20) != op2(e23,e22) ) ),
inference(and_elim,[status(thm)],[42]) ).
tff(44,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) )
& ( op2(e22,e22) != op2(e22,e23) )
& ( op2(e23,e20) != op2(e23,e21) ) ),
inference(and_elim,[status(thm)],[43]) ).
tff(45,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) )
& ( op2(e22,e22) != op2(e22,e23) ) ),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) ) ),
inference(and_elim,[status(thm)],[45]) ).
tff(47,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) ) ),
inference(and_elim,[status(thm)],[46]) ).
tff(48,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) ) ),
inference(and_elim,[status(thm)],[47]) ).
tff(49,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) ) ),
inference(and_elim,[status(thm)],[48]) ).
tff(50,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) ) ),
inference(and_elim,[status(thm)],[49]) ).
tff(51,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) ) ),
inference(and_elim,[status(thm)],[50]) ).
tff(52,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) ) ),
inference(and_elim,[status(thm)],[51]) ).
tff(53,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) ) ),
inference(and_elim,[status(thm)],[52]) ).
tff(54,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) ) ),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) ) ),
inference(and_elim,[status(thm)],[54]) ).
tff(56,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) ) ),
inference(and_elim,[status(thm)],[55]) ).
tff(57,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) ) ),
inference(and_elim,[status(thm)],[56]) ).
tff(58,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) ) ),
inference(and_elim,[status(thm)],[57]) ).
tff(59,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) ) ),
inference(and_elim,[status(thm)],[58]) ).
tff(60,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) ) ),
inference(and_elim,[status(thm)],[59]) ).
tff(61,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) ) ),
inference(and_elim,[status(thm)],[60]) ).
tff(62,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) ) ),
inference(and_elim,[status(thm)],[61]) ).
tff(63,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) ) ),
inference(and_elim,[status(thm)],[62]) ).
tff(64,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) ) ),
inference(and_elim,[status(thm)],[63]) ).
tff(65,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) ) ),
inference(and_elim,[status(thm)],[64]) ).
tff(66,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) ) ),
inference(and_elim,[status(thm)],[65]) ).
tff(67,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) ) ),
inference(and_elim,[status(thm)],[66]) ).
tff(68,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) ) ),
inference(and_elim,[status(thm)],[67]) ).
tff(69,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) ) ),
inference(and_elim,[status(thm)],[68]) ).
tff(70,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) ) ),
inference(and_elim,[status(thm)],[69]) ).
tff(71,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) ) ),
inference(and_elim,[status(thm)],[70]) ).
tff(72,plain,
op2(e21,e22) != op2(e22,e22),
inference(and_elim,[status(thm)],[71]) ).
tff(73,plain,
op2(e21,e22) != op2(e22,e22),
inference(modus_ponens,[status(thm)],[72,38]) ).
tff(74,plain,
op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[73,37]) ).
tff(75,plain,
op2(h2(e13),h3(e13)) != h3(op1(e13,e13)),
inference(modus_ponens,[status(thm)],[74,36]) ).
tff(76,plain,
h1(e13) != h3(op1(e13,e13)),
inference(modus_ponens,[status(thm)],[75,35]) ).
tff(77,plain,
h1(e13) != op2(h3(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[76,34]) ).
tff(78,plain,
h3(op1(e13,e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[77,33]) ).
tff(79,plain,
( ( ( h2(e13) = h1(e13) )
| ( h3(op1(e13,e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h3(op1(e13,e13)) = h1(e13) )
| ( op2(h1(e13),h1(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( ( h2(e13) = h1(e13) )
| ( h3(op1(e13,e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h3(op1(e13,e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ( ( h1(op1(e13,e13)) = h1(e13) )
| ( h2(e13) = h1(e13) )
| ( h3(op1(e13,e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h3(op1(e13,e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) )
<=> ( h3(op1(e13,e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( h2(e13) = op2(h2(e13),h3(e13)) )
<=> ( h2(e13) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
<=> ( h1(op1(e13,e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( h1(op1(e13,e13)) = h1(e13) )
| ( h2(e13) = h1(e13) )
| ( h3(op1(e13,e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[84,83,82]) ).
tff(86,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h3(op1(e13,e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[85,81]) ).
tff(87,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( h2(e13) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) ) ) ),
inference(monotonicity,[status(thm)],[91,90,89]) ).
tff(93,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[92,88]) ).
tff(94,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| $false
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( op2(e21,e21) != op2(e21,e22) )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ( op2(e21,e21) != op2(e21,e22) )
<=> ( op2(e21,e21) != op2(e21,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
op2(e21,e21) != op2(e21,e22),
inference(and_elim,[status(thm)],[53]) ).
tff(98,plain,
op2(e21,e21) != op2(e21,e22),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[98,95]) ).
tff(100,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> $false ),
inference(iff_false,[status(thm)],[99]) ).
tff(101,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| $false
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(transitivity,[status(thm)],[101,94]) ).
tff(103,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( op2(e23,e23) = e20 )
<=> ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( op2(e22,e22) = e20 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( op2(e21,e21) = e20 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ( op2(e20,e20) = e20 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(monotonicity,[status(thm)],[107,106,105,104]) ).
tff(109,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(transitivity,[status(thm)],[108,103]) ).
tff(110,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 ) )
<=> ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,axiom,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) )
& ( ( ( op2(e20,op2(e20,e20)) != e20 )
& ( op2(e20,op2(e20,e21)) != e21 )
& ( op2(e20,op2(e20,e22)) != e22 )
& ( op2(e20,op2(e20,e23)) != e23 ) )
| ( ( op2(e21,op2(e21,e20)) != e20 )
& ( op2(e21,op2(e21,e21)) != e21 )
& ( op2(e21,op2(e21,e22)) != e22 )
& ( op2(e21,op2(e21,e23)) != e23 ) )
| ( ( op2(e22,op2(e22,e20)) != e20 )
& ( op2(e22,op2(e22,e21)) != e21 )
& ( op2(e22,op2(e22,e22)) != e22 )
& ( op2(e22,op2(e22,e23)) != e23 ) )
| ( ( op2(e23,op2(e23,e20)) != e20 )
& ( op2(e23,op2(e23,e21)) != e21 )
& ( op2(e23,op2(e23,e22)) != e22 )
& ( op2(e23,op2(e23,e23)) != e23 ) ) )
& ( ( ( op2(e20,e20) = e20 )
& ( op2(e20,e20) = e20 )
& ( op2(e20,e20) = e20 )
& ( op2(e20,e20) = e20 ) )
| ( ( op2(e20,e20) = e20 )
& ( op2(e20,e20) = e20 )
& ( op2(e21,e20) = e20 )
& ( op2(e20,e21) = e20 ) )
| ( ( op2(e20,e20) = e20 )
& ( op2(e20,e20) = e20 )
& ( op2(e22,e20) = e20 )
& ( op2(e20,e22) = e20 ) )
| ( ( op2(e20,e20) = e20 )
& ( op2(e20,e20) = e20 )
& ( op2(e23,e20) = e20 )
& ( op2(e20,e23) = e20 ) )
| ( ( op2(e20,e21) = e20 )
& ( op2(e21,e20) = e20 )
& ( op2(e20,e21) = e21 )
& ( op2(e21,e20) = e21 ) )
| ( ( op2(e20,e21) = e20 )
& ( op2(e21,e20) = e20 )
& ( op2(e21,e21) = e21 )
& ( op2(e21,e21) = e21 ) )
| ( ( op2(e20,e21) = e20 )
& ( op2(e21,e20) = e20 )
& ( op2(e22,e21) = e21 )
& ( op2(e21,e22) = e21 ) )
| ( ( op2(e20,e21) = e20 )
& ( op2(e21,e20) = e20 )
& ( op2(e23,e21) = e21 )
& ( op2(e21,e23) = e21 ) )
| ( ( op2(e20,e22) = e20 )
& ( op2(e22,e20) = e20 )
& ( op2(e20,e22) = e22 )
& ( op2(e22,e20) = e22 ) )
| ( ( op2(e20,e22) = e20 )
& ( op2(e22,e20) = e20 )
& ( op2(e21,e22) = e22 )
& ( op2(e22,e21) = e22 ) )
| ( ( op2(e20,e22) = e20 )
& ( op2(e22,e20) = e20 )
& ( op2(e22,e22) = e22 )
& ( op2(e22,e22) = e22 ) )
| ( ( op2(e20,e22) = e20 )
& ( op2(e22,e20) = e20 )
& ( op2(e23,e22) = e22 )
& ( op2(e22,e23) = e22 ) )
| ( ( op2(e20,e23) = e20 )
& ( op2(e23,e20) = e20 )
& ( op2(e20,e23) = e23 )
& ( op2(e23,e20) = e23 ) )
| ( ( op2(e20,e23) = e20 )
& ( op2(e23,e20) = e20 )
& ( op2(e21,e23) = e23 )
& ( op2(e23,e21) = e23 ) )
| ( ( op2(e20,e23) = e20 )
& ( op2(e23,e20) = e20 )
& ( op2(e22,e23) = e23 )
& ( op2(e23,e22) = e23 ) )
| ( ( op2(e20,e23) = e20 )
& ( op2(e23,e20) = e20 )
& ( op2(e23,e23) = e23 )
& ( op2(e23,e23) = e23 ) )
| ( ( op2(e21,e20) = e21 )
& ( op2(e20,e21) = e21 )
& ( op2(e20,e20) = e20 )
& ( op2(e20,e20) = e20 ) )
| ( ( op2(e21,e20) = e21 )
& ( op2(e20,e21) = e21 )
& ( op2(e21,e20) = e20 )
& ( op2(e20,e21) = e20 ) )
| ( ( op2(e21,e20) = e21 )
& ( op2(e20,e21) = e21 )
& ( op2(e22,e20) = e20 )
& ( op2(e20,e22) = e20 ) )
| ( ( op2(e21,e20) = e21 )
& ( op2(e20,e21) = e21 )
& ( op2(e23,e20) = e20 )
& ( op2(e20,e23) = e20 ) )
| ( ( op2(e21,e21) = e21 )
& ( op2(e21,e21) = e21 )
& ( op2(e20,e21) = e21 )
& ( op2(e21,e20) = e21 ) )
| ( ( op2(e21,e21) = e21 )
& ( op2(e21,e21) = e21 )
& ( op2(e21,e21) = e21 )
& ( op2(e21,e21) = e21 ) )
| ( ( op2(e21,e21) = e21 )
& ( op2(e21,e21) = e21 )
& ( op2(e22,e21) = e21 )
& ( op2(e21,e22) = e21 ) )
| ( ( op2(e21,e21) = e21 )
& ( op2(e21,e21) = e21 )
& ( op2(e23,e21) = e21 )
& ( op2(e21,e23) = e21 ) )
| ( ( op2(e21,e22) = e21 )
& ( op2(e22,e21) = e21 )
& ( op2(e20,e22) = e22 )
& ( op2(e22,e20) = e22 ) )
| ( ( op2(e21,e22) = e21 )
& ( op2(e22,e21) = e21 )
& ( op2(e21,e22) = e22 )
& ( op2(e22,e21) = e22 ) )
| ( ( op2(e21,e22) = e21 )
& ( op2(e22,e21) = e21 )
& ( op2(e22,e22) = e22 )
& ( op2(e22,e22) = e22 ) )
| ( ( op2(e21,e22) = e21 )
& ( op2(e22,e21) = e21 )
& ( op2(e23,e22) = e22 )
& ( op2(e22,e23) = e22 ) )
| ( ( op2(e21,e23) = e21 )
& ( op2(e23,e21) = e21 )
& ( op2(e20,e23) = e23 )
& ( op2(e23,e20) = e23 ) )
| ( ( op2(e21,e23) = e21 )
& ( op2(e23,e21) = e21 )
& ( op2(e21,e23) = e23 )
& ( op2(e23,e21) = e23 ) )
| ( ( op2(e21,e23) = e21 )
& ( op2(e23,e21) = e21 )
& ( op2(e22,e23) = e23 )
& ( op2(e23,e22) = e23 ) )
| ( ( op2(e21,e23) = e21 )
& ( op2(e23,e21) = e21 )
& ( op2(e23,e23) = e23 )
& ( op2(e23,e23) = e23 ) )
| ( ( op2(e22,e20) = e22 )
& ( op2(e20,e22) = e22 )
& ( op2(e20,e20) = e20 )
& ( op2(e20,e20) = e20 ) )
| ( ( op2(e22,e20) = e22 )
& ( op2(e20,e22) = e22 )
& ( op2(e21,e20) = e20 )
& ( op2(e20,e21) = e20 ) )
| ( ( op2(e22,e20) = e22 )
& ( op2(e20,e22) = e22 )
& ( op2(e22,e20) = e20 )
& ( op2(e20,e22) = e20 ) )
| ( ( op2(e22,e20) = e22 )
& ( op2(e20,e22) = e22 )
& ( op2(e23,e20) = e20 )
& ( op2(e20,e23) = e20 ) )
| ( ( op2(e22,e21) = e22 )
& ( op2(e21,e22) = e22 )
& ( op2(e20,e21) = e21 )
& ( op2(e21,e20) = e21 ) )
| ( ( op2(e22,e21) = e22 )
& ( op2(e21,e22) = e22 )
& ( op2(e21,e21) = e21 )
& ( op2(e21,e21) = e21 ) )
| ( ( op2(e22,e21) = e22 )
& ( op2(e21,e22) = e22 )
& ( op2(e22,e21) = e21 )
& ( op2(e21,e22) = e21 ) )
| ( ( op2(e22,e21) = e22 )
& ( op2(e21,e22) = e22 )
& ( op2(e23,e21) = e21 )
& ( op2(e21,e23) = e21 ) )
| ( ( op2(e22,e22) = e22 )
& ( op2(e22,e22) = e22 )
& ( op2(e20,e22) = e22 )
& ( op2(e22,e20) = e22 ) )
| ( ( op2(e22,e22) = e22 )
& ( op2(e22,e22) = e22 )
& ( op2(e21,e22) = e22 )
& ( op2(e22,e21) = e22 ) )
| ( ( op2(e22,e22) = e22 )
& ( op2(e22,e22) = e22 )
& ( op2(e22,e22) = e22 )
& ( op2(e22,e22) = e22 ) )
| ( ( op2(e22,e22) = e22 )
& ( op2(e22,e22) = e22 )
& ( op2(e23,e22) = e22 )
& ( op2(e22,e23) = e22 ) )
| ( ( op2(e22,e23) = e22 )
& ( op2(e23,e22) = e22 )
& ( op2(e20,e23) = e23 )
& ( op2(e23,e20) = e23 ) )
| ( ( op2(e22,e23) = e22 )
& ( op2(e23,e22) = e22 )
& ( op2(e21,e23) = e23 )
& ( op2(e23,e21) = e23 ) )
| ( ( op2(e22,e23) = e22 )
& ( op2(e23,e22) = e22 )
& ( op2(e22,e23) = e23 )
& ( op2(e23,e22) = e23 ) )
| ( ( op2(e22,e23) = e22 )
& ( op2(e23,e22) = e22 )
& ( op2(e23,e23) = e23 )
& ( op2(e23,e23) = e23 ) )
| ( ( op2(e23,e20) = e23 )
& ( op2(e20,e23) = e23 )
& ( op2(e20,e20) = e20 )
& ( op2(e20,e20) = e20 ) )
| ( ( op2(e23,e20) = e23 )
& ( op2(e20,e23) = e23 )
& ( op2(e21,e20) = e20 )
& ( op2(e20,e21) = e20 ) )
| ( ( op2(e23,e20) = e23 )
& ( op2(e20,e23) = e23 )
& ( op2(e22,e20) = e20 )
& ( op2(e20,e22) = e20 ) )
| ( ( op2(e23,e20) = e23 )
& ( op2(e20,e23) = e23 )
& ( op2(e23,e20) = e20 )
& ( op2(e20,e23) = e20 ) )
| ( ( op2(e23,e21) = e23 )
& ( op2(e21,e23) = e23 )
& ( op2(e20,e21) = e21 )
& ( op2(e21,e20) = e21 ) )
| ( ( op2(e23,e21) = e23 )
& ( op2(e21,e23) = e23 )
& ( op2(e21,e21) = e21 )
& ( op2(e21,e21) = e21 ) )
| ( ( op2(e23,e21) = e23 )
& ( op2(e21,e23) = e23 )
& ( op2(e22,e21) = e21 )
& ( op2(e21,e22) = e21 ) )
| ( ( op2(e23,e21) = e23 )
& ( op2(e21,e23) = e23 )
& ( op2(e23,e21) = e21 )
& ( op2(e21,e23) = e21 ) )
| ( ( op2(e23,e22) = e23 )
& ( op2(e22,e23) = e23 )
& ( op2(e20,e22) = e22 )
& ( op2(e22,e20) = e22 ) )
| ( ( op2(e23,e22) = e23 )
& ( op2(e22,e23) = e23 )
& ( op2(e21,e22) = e22 )
& ( op2(e22,e21) = e22 ) )
| ( ( op2(e23,e22) = e23 )
& ( op2(e22,e23) = e23 )
& ( op2(e22,e22) = e22 )
& ( op2(e22,e22) = e22 ) )
| ( ( op2(e23,e22) = e23 )
& ( op2(e22,e23) = e23 )
& ( op2(e23,e22) = e22 )
& ( op2(e22,e23) = e22 ) )
| ( ( op2(e23,e23) = e23 )
& ( op2(e23,e23) = e23 )
& ( op2(e20,e23) = e23 )
& ( op2(e23,e20) = e23 ) )
| ( ( op2(e23,e23) = e23 )
& ( op2(e23,e23) = e23 )
& ( op2(e21,e23) = e23 )
& ( op2(e23,e21) = e23 ) )
| ( ( op2(e23,e23) = e23 )
& ( op2(e23,e23) = e23 )
& ( op2(e22,e23) = e23 )
& ( op2(e23,e22) = e23 ) )
| ( ( op2(e23,e23) = e23 )
& ( op2(e23,e23) = e23 )
& ( op2(e23,e23) = e23 )
& ( op2(e23,e23) = e23 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
tff(116,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) )
& ( ( ( op2(e20,op2(e20,e20)) != e20 )
& ( op2(e20,op2(e20,e21)) != e21 )
& ( op2(e20,op2(e20,e22)) != e22 )
& ( op2(e20,op2(e20,e23)) != e23 ) )
| ( ( op2(e21,op2(e21,e20)) != e20 )
& ( op2(e21,op2(e21,e21)) != e21 )
& ( op2(e21,op2(e21,e22)) != e22 )
& ( op2(e21,op2(e21,e23)) != e23 ) )
| ( ( op2(e22,op2(e22,e20)) != e20 )
& ( op2(e22,op2(e22,e21)) != e21 )
& ( op2(e22,op2(e22,e22)) != e22 )
& ( op2(e22,op2(e22,e23)) != e23 ) )
| ( ( op2(e23,op2(e23,e20)) != e20 )
& ( op2(e23,op2(e23,e21)) != e21 )
& ( op2(e23,op2(e23,e22)) != e22 )
& ( op2(e23,op2(e23,e23)) != e23 ) ) ) ),
inference(and_elim,[status(thm)],[115]) ).
tff(117,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) ) ),
inference(and_elim,[status(thm)],[116]) ).
tff(118,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(and_elim,[status(thm)],[117]) ).
tff(119,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e23) = e21 ) ) ),
inference(and_elim,[status(thm)],[118]) ).
tff(120,plain,
( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) ),
inference(and_elim,[status(thm)],[119]) ).
tff(121,plain,
( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[120,114]) ).
tff(122,plain,
( ( op2(e20,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[121,110]) ).
tff(123,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[122,109]) ).
tff(124,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[123,103]) ).
tff(125,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[124,102]) ).
tff(126,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[125,93]) ).
tff(127,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[126,87]) ).
tff(128,plain,
( ( h2(e13) = h1(e13) )
| ( h3(op1(e13,e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[127,86]) ).
tff(129,plain,
( ( h2(e13) = h1(e13) )
| ( h3(op1(e13,e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[128,80]) ).
tff(130,plain,
( ( h2(e13) = h1(e13) )
| ( h3(op1(e13,e13)) = h1(e13) )
| ( op2(h1(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[129,79]) ).
tff(131,plain,
op2(h1(e13),h1(e13)) = h1(e13),
inference(unit_resolution,[status(thm)],[130,78,17]) ).
tff(132,plain,
( ( h1(op1(e13,e13)) = op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) )
<=> ( h1(op1(e13,e13)) = op2(h1(e13),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ( h1(op1(e13,e13)) = op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) )
<=> ( h1(op1(e13,e13)) = op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( h1(e11) = op2(e20,e20) )
<=> ( h1(op1(e13,e13)) = op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( h1(e11) = op2(e20,e20) )
<=> ( h1(e11) = op2(e20,e20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,axiom,
( ( h1(e13) = e20 )
& ( h1(e10) = op2(op2(e20,e20),op2(op2(e20,e20),e20)) )
& ( h1(e11) = op2(e20,e20) )
& ( h1(e12) = op2(op2(e20,e20),e20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
tff(137,plain,
( ( h1(e13) = e20 )
& ( h1(e10) = op2(op2(e20,e20),op2(op2(e20,e20),e20)) )
& ( h1(e11) = op2(e20,e20) ) ),
inference(and_elim,[status(thm)],[136]) ).
tff(138,plain,
h1(e11) = op2(e20,e20),
inference(and_elim,[status(thm)],[137]) ).
tff(139,plain,
h1(e11) = op2(e20,e20),
inference(modus_ponens,[status(thm)],[138,135]) ).
tff(140,plain,
h1(op1(e13,e13)) = op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))),
inference(modus_ponens,[status(thm)],[139,134]) ).
tff(141,plain,
h1(op1(e13,e13)) = op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))),
inference(modus_ponens,[status(thm)],[140,133]) ).
tff(142,plain,
h1(op1(e13,e13)) = op2(h1(e13),h1(e13)),
inference(modus_ponens,[status(thm)],[141,132]) ).
tff(143,plain,
h1(op1(e13,e13)) = h1(e13),
inference(transitivity,[status(thm)],[142,131]) ).
tff(144,plain,
( ( h1(op1(e13,e13)) = h4(e13) )
<=> ( h1(e13) = h4(e13) ) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
( ( h1(e13) = h4(e13) )
<=> ( h1(op1(e13,e13)) = h4(e13) ) ),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
( ( h1(e13) != h4(e13) )
<=> ( h1(op1(e13,e13)) != h4(e13) ) ),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
( ( op2(h2(e13),h3(e13)) != h4(e13) )
<=> ( h1(e13) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) )
<=> ( op2(h2(e13),h3(e13)) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
( ( e20 != e23 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(150,plain,
( ( e20 != e23 )
<=> ( e20 != e23 ) ),
inference(rewrite,[status(thm)],]) ).
tff(151,plain,
e20 != e23,
inference(and_elim,[status(thm)],[10]) ).
tff(152,plain,
e20 != e23,
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13),
inference(modus_ponens,[status(thm)],[152,149]) ).
tff(154,plain,
op2(h2(e13),h3(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[153,148]) ).
tff(155,plain,
h1(e13) != h4(e13),
inference(modus_ponens,[status(thm)],[154,147]) ).
tff(156,plain,
h1(op1(e13,e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[155,146]) ).
tff(157,plain,
( ( h1(e13) = h3(e13) )
<=> ( h3(e13) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(158,plain,
( ( h1(op1(e13,e13)) = h3(e13) )
<=> ( h1(e13) = h3(e13) ) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(159,plain,
( ( h1(op1(e13,e13)) = h3(e13) )
<=> ( h3(e13) = h1(e13) ) ),
inference(transitivity,[status(thm)],[158,157]) ).
tff(160,plain,
( ( h3(e13) = h1(e13) )
<=> ( h1(op1(e13,e13)) = h3(e13) ) ),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ( h3(e13) != h1(e13) )
<=> ( h1(op1(e13,e13)) != h3(e13) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( h1(e13) != h3(e13) )
<=> ( h3(e13) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[157]) ).
tff(163,plain,
( ( op2(h2(e13),h3(e13)) != h3(e13) )
<=> ( h1(e13) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(164,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(h2(e13),h3(e13)) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,plain,
( ( op2(e21,e22) != op2(e21,e23) )
<=> ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(166,plain,
( ( op2(e21,e22) != op2(e21,e23) )
<=> ( op2(e21,e22) != op2(e21,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(167,plain,
op2(e21,e22) != op2(e21,e23),
inference(and_elim,[status(thm)],[51]) ).
tff(168,plain,
op2(e21,e22) != op2(e21,e23),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(h4(e13),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[168,165]) ).
tff(170,plain,
op2(h2(e13),h3(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[169,164]) ).
tff(171,plain,
h1(e13) != h3(e13),
inference(modus_ponens,[status(thm)],[170,163]) ).
tff(172,plain,
h3(e13) != h1(e13),
inference(modus_ponens,[status(thm)],[171,162]) ).
tff(173,plain,
h1(op1(e13,e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[172,161]) ).
tff(174,plain,
( ( ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( h1(op1(e13,e13)) = h3(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(175,plain,
( ( h3(op1(e13,e13)) = h3(e13) )
<=> ( op2(h3(e13),h3(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(176,plain,
( ( ( h3(op1(e13,e13)) = h3(e13) )
| ( h1(op1(e13,e13)) = h3(e13) ) )
<=> ( ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( h1(op1(e13,e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
( ( ( h3(op1(e13,e13)) = h3(e13) )
| ( h1(op1(e13,e13)) = h3(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[176,174]) ).
tff(178,plain,
( ( ( h3(op1(e13,e13)) = h3(e13) )
| ( h1(op1(e13,e13)) = h3(e13) ) )
<=> ( ( h3(op1(e13,e13)) = h3(e13) )
| ( h1(op1(e13,e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
<=> ( h1(op1(e13,e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(180,plain,
( ( ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) ) )
<=> ( ( h3(op1(e13,e13)) = h3(e13) )
| ( h1(op1(e13,e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ( ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) ) )
<=> ( ( h3(op1(e13,e13)) = h3(e13) )
| ( h1(op1(e13,e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[180,178]) ).
tff(182,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) ) )
<=> ( ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(183,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( h3(op1(e13,e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(185,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[184,183]) ).
tff(186,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[185,182]) ).
tff(187,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| $false
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| $false )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(188,plain,
( ( e21 != e22 )
<=> ( op2(h4(e13),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(189,plain,
( ( e21 != e22 )
<=> ( e21 != e22 ) ),
inference(rewrite,[status(thm)],]) ).
tff(190,plain,
e21 != e22,
inference(and_elim,[status(thm)],[9]) ).
tff(191,plain,
e21 != e22,
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
op2(h4(e13),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[191,188]) ).
tff(193,plain,
( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> $false ),
inference(iff_false,[status(thm)],[192]) ).
tff(194,plain,
( ( op2(e21,e21) != op2(e21,e23) )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,plain,
( ( op2(e21,e21) != op2(e21,e23) )
<=> ( op2(e21,e21) != op2(e21,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(196,plain,
op2(e21,e21) != op2(e21,e23),
inference(and_elim,[status(thm)],[52]) ).
tff(197,plain,
op2(e21,e21) != op2(e21,e23),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[197,194]) ).
tff(199,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> $false ),
inference(iff_false,[status(thm)],[198]) ).
tff(200,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| $false
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| $false ) ),
inference(monotonicity,[status(thm)],[199,193]) ).
tff(201,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[200,187]) ).
tff(202,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(203,plain,
( ( op2(e23,e23) = e22 )
<=> ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(204,plain,
( ( op2(e22,e22) = e22 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(205,plain,
( ( op2(e21,e21) = e22 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(206,plain,
( ( op2(e20,e20) = e22 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(207,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[206,205,204,203]) ).
tff(208,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[207,202]) ).
tff(209,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(210,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(211,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(212,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(transitivity,[status(thm)],[212,210]) ).
tff(214,plain,
( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(and_elim,[status(thm)],[118]) ).
tff(215,plain,
( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[214,213]) ).
tff(216,plain,
( ( op2(e20,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[215,209]) ).
tff(217,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[216,208]) ).
tff(218,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[217,202]) ).
tff(219,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[218,201]) ).
tff(220,plain,
( ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[219,186]) ).
tff(221,plain,
( ( h3(op1(e13,e13)) = h3(e13) )
| ( h1(op1(e13,e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[220,181]) ).
tff(222,plain,
( ( h3(op1(e13,e13)) = h3(e13) )
| ( h1(op1(e13,e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[221,178]) ).
tff(223,plain,
( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[222,177]) ).
tff(224,plain,
op2(h3(e13),h3(e13)) = h3(e13),
inference(unit_resolution,[status(thm)],[223,173]) ).
tff(225,plain,
h3(op1(e13,e13)) = h3(e13),
inference(transitivity,[status(thm)],[29,224]) ).
tff(226,plain,
( ( h3(op1(e13,e13)) = h4(e13) )
<=> ( h3(e13) = h4(e13) ) ),
inference(monotonicity,[status(thm)],[225]) ).
tff(227,plain,
( ( h3(e13) = h4(e13) )
<=> ( h3(op1(e13,e13)) = h4(e13) ) ),
inference(symmetry,[status(thm)],[226]) ).
tff(228,plain,
( ( h3(e13) != h4(e13) )
<=> ( h3(op1(e13,e13)) != h4(e13) ) ),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
( ( op2(op2(h4(e13),h4(e13)),h4(e13)) != h4(e13) )
<=> ( h3(e13) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(230,plain,
( ( e22 != e23 )
<=> ( op2(op2(h4(e13),h4(e13)),h4(e13)) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(231,plain,
( ( e22 != e23 )
<=> ( e22 != e23 ) ),
inference(rewrite,[status(thm)],]) ).
tff(232,plain,
e22 != e23,
inference(and_elim,[status(thm)],[7]) ).
tff(233,plain,
e22 != e23,
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
op2(op2(h4(e13),h4(e13)),h4(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[233,230]) ).
tff(235,plain,
h3(e13) != h4(e13),
inference(modus_ponens,[status(thm)],[234,229]) ).
tff(236,plain,
h3(op1(e13,e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[235,228]) ).
tff(237,plain,
( ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( h1(op1(e13,e13)) = h4(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(238,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h4(e13) )
<=> ( h1(op1(e13,e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(239,plain,
( ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h4(e13) ) )
<=> ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( h1(op1(e13,e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
( ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h4(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[239,237]) ).
tff(241,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) )
<=> ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(242,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
<=> ( h3(op1(e13,e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(243,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
<=> ( h2(op1(e13,e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(244,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
<=> ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(245,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[244,243,242]) ).
tff(246,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) )
<=> ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[245,241]) ).
tff(247,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| $false )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(248,plain,
( ( e21 != e23 )
<=> ( op2(h4(e13),h4(e13)) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(249,plain,
( ( e21 != e23 )
<=> ( e21 != e23 ) ),
inference(rewrite,[status(thm)],]) ).
tff(250,plain,
e21 != e23,
inference(and_elim,[status(thm)],[8]) ).
tff(251,plain,
e21 != e23,
inference(modus_ponens,[status(thm)],[250,249]) ).
tff(252,plain,
op2(h4(e13),h4(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[251,248]) ).
tff(253,plain,
( ( op2(h4(e13),h4(e13)) = h4(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[252]) ).
tff(254,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(h4(e13),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| $false ) ),
inference(monotonicity,[status(thm)],[253]) ).
tff(255,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(h4(e13),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[254,247]) ).
tff(256,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(h4(e13),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(h4(e13),h4(e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(257,plain,
( ( op2(e23,e23) = e23 )
<=> ( op2(h4(e13),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(258,plain,
( ( op2(e22,e22) = e23 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(259,plain,
( ( op2(e21,e21) = e23 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(260,plain,
( ( op2(e20,e20) = e23 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(261,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(h4(e13),h4(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[260,259,258,257]) ).
tff(262,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(h4(e13),h4(e13)) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[261,256]) ).
tff(263,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) )
<=> ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(264,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) )
<=> ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(265,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 ) )
<=> ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(266,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) )
<=> ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) ) ),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) )
<=> ( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) ) ),
inference(transitivity,[status(thm)],[266,264]) ).
tff(268,plain,
( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) ),
inference(and_elim,[status(thm)],[117]) ).
tff(269,plain,
( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
( ( op2(e20,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[269,263]) ).
tff(271,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(h4(e13),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[270,262]) ).
tff(272,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(h4(e13),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[271,256]) ).
tff(273,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[272,255]) ).
tff(274,plain,
( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[273,246]) ).
tff(275,plain,
( ( h1(op1(e13,e13)) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[274,240]) ).
tff(276,plain,
h2(op1(e13,e13)) = h4(e13),
inference(unit_resolution,[status(thm)],[275,236,156]) ).
tff(277,plain,
( ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) )
<=> ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(278,plain,
( ( h2(e11) = op2(e21,e21) )
<=> ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(279,plain,
( ( h2(e11) = op2(e21,e21) )
<=> ( h2(e11) = op2(e21,e21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(280,axiom,
( ( h2(e13) = e21 )
& ( h2(e10) = op2(op2(e21,e21),op2(op2(e21,e21),e21)) )
& ( h2(e11) = op2(e21,e21) )
& ( h2(e12) = op2(op2(e21,e21),e21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
tff(281,plain,
( ( h2(e13) = e21 )
& ( h2(e10) = op2(op2(e21,e21),op2(op2(e21,e21),e21)) )
& ( h2(e11) = op2(e21,e21) ) ),
inference(and_elim,[status(thm)],[280]) ).
tff(282,plain,
h2(e11) = op2(e21,e21),
inference(and_elim,[status(thm)],[281]) ).
tff(283,plain,
h2(e11) = op2(e21,e21),
inference(modus_ponens,[status(thm)],[282,279]) ).
tff(284,plain,
h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[283,278]) ).
tff(285,plain,
h2(op1(e13,e13)) = op2(h2(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[284,277]) ).
tff(286,plain,
op2(h2(e13),h2(e13)) = h2(op1(e13,e13)),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
op2(h2(e13),h2(e13)) = h4(e13),
inference(transitivity,[status(thm)],[286,276]) ).
tff(288,plain,
( ( h3(e13) = op2(h4(e13),h3(e13)) )
<=> ( op2(h4(e13),h3(e13)) = h3(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(289,plain,
( ( op2(h3(e13),h3(e13)) = op2(h4(e13),h3(e13)) )
<=> ( h3(e13) = op2(h4(e13),h3(e13)) ) ),
inference(monotonicity,[status(thm)],[224]) ).
tff(290,plain,
( ( op2(h3(e13),h3(e13)) = op2(h4(e13),h3(e13)) )
<=> ( op2(h4(e13),h3(e13)) = h3(e13) ) ),
inference(transitivity,[status(thm)],[289,288]) ).
tff(291,plain,
( ( op2(h3(e13),h3(e13)) != op2(h4(e13),h3(e13)) )
<=> ( op2(h4(e13),h3(e13)) != h3(e13) ) ),
inference(monotonicity,[status(thm)],[290]) ).
tff(292,plain,
( ( h3(op1(e13,e13)) != op2(h4(e13),h3(e13)) )
<=> ( op2(h3(e13),h3(e13)) != op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(293,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( h3(op1(e13,e13)) != op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(294,plain,
( ( op2(e22,e22) != op2(e23,e22) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(295,plain,
( ( op2(e22,e22) != op2(e23,e22) )
<=> ( op2(e22,e22) != op2(e23,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(296,plain,
op2(e22,e22) != op2(e23,e22),
inference(and_elim,[status(thm)],[69]) ).
tff(297,plain,
op2(e22,e22) != op2(e23,e22),
inference(modus_ponens,[status(thm)],[296,295]) ).
tff(298,plain,
op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[297,294]) ).
tff(299,plain,
h3(op1(e13,e13)) != op2(h4(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[298,293]) ).
tff(300,plain,
op2(h3(e13),h3(e13)) != op2(h4(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[299,292]) ).
tff(301,plain,
op2(h4(e13),h3(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[300,291]) ).
tff(302,plain,
( ( h1(e13) = op2(h4(e13),h3(e13)) )
<=> ( op2(h4(e13),h3(e13)) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(303,plain,
( ( h1(e13) != op2(h4(e13),h3(e13)) )
<=> ( op2(h4(e13),h3(e13)) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[302]) ).
tff(304,plain,
( ( op2(h2(e13),h3(e13)) != op2(h4(e13),h3(e13)) )
<=> ( h1(e13) != op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(305,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(h2(e13),h3(e13)) != op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(306,plain,
( ( op2(e21,e22) != op2(e23,e22) )
<=> ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(307,plain,
( ( op2(e21,e22) != op2(e23,e22) )
<=> ( op2(e21,e22) != op2(e23,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(308,plain,
op2(e21,e22) != op2(e23,e22),
inference(and_elim,[status(thm)],[70]) ).
tff(309,plain,
op2(e21,e22) != op2(e23,e22),
inference(modus_ponens,[status(thm)],[308,307]) ).
tff(310,plain,
op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[309,306]) ).
tff(311,plain,
op2(h2(e13),h3(e13)) != op2(h4(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[310,305]) ).
tff(312,plain,
h1(e13) != op2(h4(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[311,304]) ).
tff(313,plain,
op2(h4(e13),h3(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[312,303]) ).
tff(314,plain,
( ( h1(e13) = op2(h4(e13),h1(e13)) )
<=> ( op2(h4(e13),h1(e13)) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(315,plain,
( ( op2(h1(e13),h1(e13)) = op2(h4(e13),h1(e13)) )
<=> ( h1(e13) = op2(h4(e13),h1(e13)) ) ),
inference(monotonicity,[status(thm)],[131]) ).
tff(316,plain,
( ( op2(h1(e13),h1(e13)) = op2(h4(e13),h1(e13)) )
<=> ( op2(h4(e13),h1(e13)) = h1(e13) ) ),
inference(transitivity,[status(thm)],[315,314]) ).
tff(317,plain,
( ( op2(h1(e13),h1(e13)) != op2(h4(e13),h1(e13)) )
<=> ( op2(h4(e13),h1(e13)) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[316]) ).
tff(318,plain,
( ( h1(op1(e13,e13)) != op2(h4(e13),h1(e13)) )
<=> ( op2(h1(e13),h1(e13)) != op2(h4(e13),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(319,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(h4(e13),op2(h2(e13),h3(e13))) )
<=> ( h1(op1(e13,e13)) != op2(h4(e13),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(320,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) != op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) )
<=> ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(h4(e13),op2(h2(e13),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(321,plain,
( ( op2(e20,e20) != op2(e23,e20) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) != op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(322,plain,
( ( op2(e20,e20) != op2(e23,e20) )
<=> ( op2(e20,e20) != op2(e23,e20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(323,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) ) ),
inference(and_elim,[status(thm)],[71]) ).
tff(324,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) ) ),
inference(and_elim,[status(thm)],[323]) ).
tff(325,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) ) ),
inference(and_elim,[status(thm)],[324]) ).
tff(326,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) ) ),
inference(and_elim,[status(thm)],[325]) ).
tff(327,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) ) ),
inference(and_elim,[status(thm)],[326]) ).
tff(328,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) ) ),
inference(and_elim,[status(thm)],[327]) ).
tff(329,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) ) ),
inference(and_elim,[status(thm)],[328]) ).
tff(330,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) ) ),
inference(and_elim,[status(thm)],[329]) ).
tff(331,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) ) ),
inference(and_elim,[status(thm)],[330]) ).
tff(332,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) ) ),
inference(and_elim,[status(thm)],[331]) ).
tff(333,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) ) ),
inference(and_elim,[status(thm)],[332]) ).
tff(334,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) ) ),
inference(and_elim,[status(thm)],[333]) ).
tff(335,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) ) ),
inference(and_elim,[status(thm)],[334]) ).
tff(336,plain,
op2(e20,e20) != op2(e23,e20),
inference(and_elim,[status(thm)],[335]) ).
tff(337,plain,
op2(e20,e20) != op2(e23,e20),
inference(modus_ponens,[status(thm)],[336,322]) ).
tff(338,plain,
op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) != op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))),
inference(modus_ponens,[status(thm)],[337,321]) ).
tff(339,plain,
op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(h4(e13),op2(h2(e13),h3(e13))),
inference(modus_ponens,[status(thm)],[338,320]) ).
tff(340,plain,
h1(op1(e13,e13)) != op2(h4(e13),h1(e13)),
inference(modus_ponens,[status(thm)],[339,319]) ).
tff(341,plain,
op2(h1(e13),h1(e13)) != op2(h4(e13),h1(e13)),
inference(modus_ponens,[status(thm)],[340,318]) ).
tff(342,plain,
op2(h4(e13),h1(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[341,317]) ).
tff(343,plain,
( ( ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h2(e13)) = h1(e13) )
| ( op2(h4(e13),h3(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(344,plain,
( ( ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(345,plain,
( ( ( op2(h4(e13),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) ) )
<=> ( ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(346,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(347,plain,
( ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(h4(e13),h2(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(348,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(h4(e13),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(349,plain,
( ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( op2(h4(e13),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) ) ) ),
inference(monotonicity,[status(thm)],[348,347,346,89]) ).
tff(350,plain,
( ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[349,345]) ).
tff(351,plain,
( ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(352,plain,
( ( op2(e23,e22) = e20 )
<=> ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(353,plain,
( ( op2(e23,e21) = e20 )
<=> ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(354,plain,
( ( op2(e23,e20) = e20 )
<=> ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(355,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(monotonicity,[status(thm)],[354,353,352,104]) ).
tff(356,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(transitivity,[status(thm)],[355,351]) ).
tff(357,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(358,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(359,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 ) )
<=> ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(360,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(monotonicity,[status(thm)],[359]) ).
tff(361,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(transitivity,[status(thm)],[360,358]) ).
tff(362,axiom,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
& ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
& ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e20,e22) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e22) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e20,e23) = e21 )
| ( op2(e21,e23) = e21 )
| ( op2(e22,e23) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
& ( ( op2(e20,e23) = e22 )
| ( op2(e21,e23) = e22 )
| ( op2(e22,e23) = e22 )
| ( op2(e23,e23) = e22 ) )
& ( ( op2(e23,e20) = e23 )
| ( op2(e23,e21) = e23 )
| ( op2(e23,e22) = e23 )
| ( op2(e23,e23) = e23 ) )
& ( ( op2(e20,e23) = e23 )
| ( op2(e21,e23) = e23 )
| ( op2(e22,e23) = e23 )
| ( op2(e23,e23) = e23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(363,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
& ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
& ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e20,e22) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e22) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e20,e23) = e21 )
| ( op2(e21,e23) = e21 )
| ( op2(e22,e23) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
& ( ( op2(e20,e23) = e22 )
| ( op2(e21,e23) = e22 )
| ( op2(e22,e23) = e22 )
| ( op2(e23,e23) = e22 ) )
& ( ( op2(e23,e20) = e23 )
| ( op2(e23,e21) = e23 )
| ( op2(e23,e22) = e23 )
| ( op2(e23,e23) = e23 ) ) ),
inference(and_elim,[status(thm)],[362]) ).
tff(364,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
& ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
& ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e20,e22) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e22) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e20,e23) = e21 )
| ( op2(e21,e23) = e21 )
| ( op2(e22,e23) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
& ( ( op2(e20,e23) = e22 )
| ( op2(e21,e23) = e22 )
| ( op2(e22,e23) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(and_elim,[status(thm)],[363]) ).
tff(365,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
& ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
& ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e20,e22) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e22) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e20,e23) = e21 )
| ( op2(e21,e23) = e21 )
| ( op2(e22,e23) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(and_elim,[status(thm)],[364]) ).
tff(366,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
& ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
& ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e20,e22) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e22) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
& ( ( op2(e20,e23) = e21 )
| ( op2(e21,e23) = e21 )
| ( op2(e22,e23) = e21 )
| ( op2(e23,e23) = e21 ) ) ),
inference(and_elim,[status(thm)],[365]) ).
tff(367,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
& ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
& ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e20,e22) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e22) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) ) ),
inference(and_elim,[status(thm)],[366]) ).
tff(368,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
& ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
& ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e20,e22) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e22) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(and_elim,[status(thm)],[367]) ).
tff(369,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
& ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
& ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e20,e22) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e22) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(and_elim,[status(thm)],[368]) ).
tff(370,plain,
( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) ),
inference(and_elim,[status(thm)],[369]) ).
tff(371,plain,
( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[370,361]) ).
tff(372,plain,
( ( op2(e23,e20) = e20 )
| ( op2(e23,e21) = e20 )
| ( op2(e23,e22) = e20 )
| ( op2(e23,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[371,357]) ).
tff(373,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[372,356]) ).
tff(374,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[373,351]) ).
tff(375,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[374,351]) ).
tff(376,plain,
( ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[375,350]) ).
tff(377,plain,
( ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[376,344]) ).
tff(378,plain,
( ( h2(e13) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h2(e13)) = h1(e13) )
| ( op2(h4(e13),h3(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[377,343]) ).
tff(379,plain,
op2(h4(e13),h2(e13)) = h1(e13),
inference(unit_resolution,[status(thm)],[378,342,313,17]) ).
tff(380,plain,
( ( op2(h4(e13),h2(e13)) = h3(e13) )
<=> ( h1(e13) = h3(e13) ) ),
inference(monotonicity,[status(thm)],[379]) ).
tff(381,plain,
( ( op2(h4(e13),h2(e13)) = h3(e13) )
<=> ( h3(e13) = h1(e13) ) ),
inference(transitivity,[status(thm)],[380,157]) ).
tff(382,plain,
( ( h3(e13) = h1(e13) )
<=> ( op2(h4(e13),h2(e13)) = h3(e13) ) ),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
( ( h3(e13) != h1(e13) )
<=> ( op2(h4(e13),h2(e13)) != h3(e13) ) ),
inference(monotonicity,[status(thm)],[382]) ).
tff(384,plain,
op2(h4(e13),h2(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[172,383]) ).
tff(385,plain,
( ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h3(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(386,plain,
( ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| $false
| ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(387,plain,
( ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) )
<=> ( op2(h4(e13),h1(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(388,plain,
( ( op2(h4(e13),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( h2(e13) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(389,plain,
h2(e13) != h3(e13),
inference(modus_ponens,[status(thm)],[192,388]) ).
tff(390,plain,
( ( h2(e13) = h3(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[389]) ).
tff(391,plain,
( ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( h2(e13) = h3(e13) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| $false
| ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[390,387]) ).
tff(392,plain,
( ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( h2(e13) = h3(e13) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[391,386]) ).
tff(393,plain,
( ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( h2(e13) = h3(e13) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( h2(e13) = h3(e13) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(394,plain,
( ( ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( h2(e13) = h3(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( h2(e13) = h3(e13) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(395,plain,
( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( h2(e13) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(396,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(h4(e13),h3(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(397,plain,
( ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(h4(e13),h2(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(398,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(399,plain,
( ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( h2(e13) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[398,397,396,395]) ).
tff(400,plain,
( ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( h2(e13) = h3(e13) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[399,394]) ).
tff(401,plain,
( ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(402,plain,
( ( op2(e23,e22) = e22 )
<=> ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(403,plain,
( ( op2(e23,e21) = e22 )
<=> ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(404,plain,
( ( op2(e23,e20) = e22 )
<=> ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(405,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[404,403,402,203]) ).
tff(406,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[405,401]) ).
tff(407,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(408,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(409,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 ) )
<=> ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(410,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(monotonicity,[status(thm)],[409]) ).
tff(411,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(transitivity,[status(thm)],[410,408]) ).
tff(412,plain,
( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(and_elim,[status(thm)],[365]) ).
tff(413,plain,
( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[412,411]) ).
tff(414,plain,
( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[413,407]) ).
tff(415,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[414,406]) ).
tff(416,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[415,401]) ).
tff(417,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[416,401]) ).
tff(418,plain,
( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( h2(e13) = h3(e13) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[417,400]) ).
tff(419,plain,
( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( h2(e13) = h3(e13) )
| ( op2(h4(e13),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[418,393]) ).
tff(420,plain,
( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[419,392]) ).
tff(421,plain,
( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[420,385]) ).
tff(422,plain,
( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[421,385]) ).
tff(423,plain,
( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[422,385]) ).
tff(424,plain,
( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h2(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[423,385]) ).
tff(425,plain,
op2(h4(e13),h1(e13)) = h3(e13),
inference(unit_resolution,[status(thm)],[424,384,301]) ).
tff(426,plain,
op2(op2(h2(e13),h2(e13)),h2(e13)) = op2(h4(e13),h2(e13)),
inference(monotonicity,[status(thm)],[287]) ).
tff(427,plain,
op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13),
inference(transitivity,[status(thm)],[426,379]) ).
tff(428,plain,
op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) = op2(h4(e13),h1(e13)),
inference(monotonicity,[status(thm)],[287,427]) ).
tff(429,plain,
( ( h2(op1(op1(e13,e13),e13)) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),h2(e13)) )
<=> ( h2(op1(op1(e13,e13),e13)) = op2(op2(h2(e13),h2(e13)),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(430,plain,
( ( h2(op1(op1(e13,e13),e13)) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) )
<=> ( h2(op1(op1(e13,e13),e13)) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(431,plain,
( ( h2(e12) = op2(op2(e21,e21),e21) )
<=> ( h2(op1(op1(e13,e13),e13)) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(432,plain,
( ( h2(e12) = op2(op2(e21,e21),e21) )
<=> ( h2(e12) = op2(op2(e21,e21),e21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(433,plain,
h2(e12) = op2(op2(e21,e21),e21),
inference(and_elim,[status(thm)],[280]) ).
tff(434,plain,
h2(e12) = op2(op2(e21,e21),e21),
inference(modus_ponens,[status(thm)],[433,432]) ).
tff(435,plain,
h2(op1(op1(e13,e13),e13)) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[434,431]) ).
tff(436,plain,
h2(op1(op1(e13,e13),e13)) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),h2(e13)),
inference(modus_ponens,[status(thm)],[435,430]) ).
tff(437,plain,
h2(op1(op1(e13,e13),e13)) = op2(op2(h2(e13),h2(e13)),h2(e13)),
inference(modus_ponens,[status(thm)],[436,429]) ).
tff(438,plain,
op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))),
inference(monotonicity,[status(thm)],[285,437]) ).
tff(439,plain,
op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13),
inference(transitivity,[status(thm)],[438,428,425]) ).
tff(440,plain,
op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) = op2(h3(e13),h4(e13)),
inference(monotonicity,[status(thm)],[439,287]) ).
tff(441,plain,
op2(h3(e13),h4(e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))),
inference(symmetry,[status(thm)],[440]) ).
tff(442,plain,
( ( h1(e13) = op2(h1(e13),h4(e13)) )
<=> ( op2(h1(e13),h4(e13)) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(443,plain,
( ( op2(h1(e13),h1(e13)) = op2(h1(e13),h4(e13)) )
<=> ( h1(e13) = op2(h1(e13),h4(e13)) ) ),
inference(monotonicity,[status(thm)],[131]) ).
tff(444,plain,
( ( op2(h1(e13),h1(e13)) = op2(h1(e13),h4(e13)) )
<=> ( op2(h1(e13),h4(e13)) = h1(e13) ) ),
inference(transitivity,[status(thm)],[443,442]) ).
tff(445,plain,
( ( op2(h1(e13),h1(e13)) != op2(h1(e13),h4(e13)) )
<=> ( op2(h1(e13),h4(e13)) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
( ( h1(op1(e13,e13)) != op2(h1(e13),h4(e13)) )
<=> ( op2(h1(e13),h1(e13)) != op2(h1(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(447,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(h2(e13),h3(e13)),h4(e13)) )
<=> ( h1(op1(e13,e13)) != op2(h1(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(448,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) != op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(h2(e13),h3(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(449,plain,
( ( op2(e20,e20) != op2(e20,e23) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) != op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(450,plain,
( ( op2(e20,e20) != op2(e20,e23) )
<=> ( op2(e20,e20) != op2(e20,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(451,plain,
op2(e20,e20) != op2(e20,e23),
inference(and_elim,[status(thm)],[60]) ).
tff(452,plain,
op2(e20,e20) != op2(e20,e23),
inference(modus_ponens,[status(thm)],[451,450]) ).
tff(453,plain,
op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) != op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)),
inference(modus_ponens,[status(thm)],[452,449]) ).
tff(454,plain,
op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(h2(e13),h3(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[453,448]) ).
tff(455,plain,
h1(op1(e13,e13)) != op2(h1(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[454,447]) ).
tff(456,plain,
op2(h1(e13),h1(e13)) != op2(h1(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[455,446]) ).
tff(457,plain,
op2(h1(e13),h4(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[456,445]) ).
tff(458,plain,
( ( ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( h2(e13) = h1(e13) )
| ( h3(e13) = h1(e13) )
| ( op2(h3(e13),h4(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h3(e13) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h3(e13),h4(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(459,plain,
( ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) )
<=> ( op2(h3(e13),h4(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(460,plain,
( ( h3(e13) = op2(h2(e13),h3(e13)) )
<=> ( h3(e13) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(461,plain,
( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
<=> ( op2(h1(e13),h4(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(462,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( h2(e13) = h1(e13) )
| ( h3(e13) = h1(e13) )
| ( op2(h3(e13),h4(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[461,83,460,459]) ).
tff(463,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h3(e13) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h3(e13),h4(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[462,458]) ).
tff(464,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(465,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h3(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(466,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(467,plain,
( ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( h3(e13) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(468,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(469,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h3(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) ) ) ),
inference(monotonicity,[status(thm)],[468,467,466,89]) ).
tff(470,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[469,465]) ).
tff(471,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(472,plain,
( ( op2(e22,e23) = e20 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(473,plain,
( ( op2(e21,e23) = e20 )
<=> ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(474,plain,
( ( op2(e20,e23) = e20 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(475,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(monotonicity,[status(thm)],[474,473,472,104]) ).
tff(476,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ) ),
inference(transitivity,[status(thm)],[475,471]) ).
tff(477,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(478,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(479,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 ) )
<=> ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(480,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(monotonicity,[status(thm)],[479]) ).
tff(481,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) )
<=> ( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) ) ),
inference(transitivity,[status(thm)],[480,478]) ).
tff(482,plain,
( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) ),
inference(and_elim,[status(thm)],[368]) ).
tff(483,plain,
( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[482,481]) ).
tff(484,plain,
( ( op2(e20,e23) = e20 )
| ( op2(e21,e23) = e20 )
| ( op2(e22,e23) = e20 )
| ( op2(e23,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[483,477]) ).
tff(485,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[484,476]) ).
tff(486,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[485,471]) ).
tff(487,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[486,471]) ).
tff(488,plain,
( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[487,470]) ).
tff(489,plain,
( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( h2(e13) = op2(h2(e13),h3(e13)) )
| ( h3(e13) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[488,464]) ).
tff(490,plain,
( ( h2(e13) = h1(e13) )
| ( h3(e13) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h3(e13),h4(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[489,463]) ).
tff(491,plain,
op2(h3(e13),h4(e13)) = h1(e13),
inference(unit_resolution,[status(thm)],[490,457,17,172]) ).
tff(492,plain,
h1(e13) = op2(h3(e13),h4(e13)),
inference(symmetry,[status(thm)],[491]) ).
tff(493,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
<=> ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(494,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
<=> ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(495,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) )
<=> ( op1(e13,e13) != op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(monotonicity,[status(thm)],[494]) ).
tff(496,plain,
( ( e10 != e11 )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(497,plain,
( ( e10 != e11 )
<=> ( e10 != e11 ) ),
inference(rewrite,[status(thm)],]) ).
tff(498,axiom,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 )
& ( e11 != e13 )
& ( e12 != e13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
tff(499,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 )
& ( e11 != e13 ) ),
inference(and_elim,[status(thm)],[498]) ).
tff(500,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 ) ),
inference(and_elim,[status(thm)],[499]) ).
tff(501,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 ) ),
inference(and_elim,[status(thm)],[500]) ).
tff(502,plain,
( ( e10 != e11 )
& ( e10 != e12 ) ),
inference(and_elim,[status(thm)],[501]) ).
tff(503,plain,
e10 != e11,
inference(and_elim,[status(thm)],[502]) ).
tff(504,plain,
e10 != e11,
inference(modus_ponens,[status(thm)],[503,497]) ).
tff(505,plain,
op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[504,496]) ).
tff(506,plain,
op1(e13,e13) != op1(op1(e13,e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[505,495]) ).
tff(507,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(508,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(monotonicity,[status(thm)],[507]) ).
tff(509,plain,
( ( op1(e11,e12) != op1(e12,e12) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(510,plain,
( ( op1(e11,e12) != op1(e12,e12) )
<=> ( op1(e11,e12) != op1(e12,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(511,axiom,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) )
& ( op1(e13,e10) != op1(e13,e11) )
& ( op1(e13,e10) != op1(e13,e12) )
& ( op1(e13,e10) != op1(e13,e13) )
& ( op1(e13,e11) != op1(e13,e12) )
& ( op1(e13,e11) != op1(e13,e13) )
& ( op1(e13,e12) != op1(e13,e13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(512,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) )
& ( op1(e13,e10) != op1(e13,e11) )
& ( op1(e13,e10) != op1(e13,e12) )
& ( op1(e13,e10) != op1(e13,e13) )
& ( op1(e13,e11) != op1(e13,e12) )
& ( op1(e13,e11) != op1(e13,e13) ) ),
inference(and_elim,[status(thm)],[511]) ).
tff(513,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) )
& ( op1(e13,e10) != op1(e13,e11) )
& ( op1(e13,e10) != op1(e13,e12) )
& ( op1(e13,e10) != op1(e13,e13) )
& ( op1(e13,e11) != op1(e13,e12) ) ),
inference(and_elim,[status(thm)],[512]) ).
tff(514,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) )
& ( op1(e13,e10) != op1(e13,e11) )
& ( op1(e13,e10) != op1(e13,e12) )
& ( op1(e13,e10) != op1(e13,e13) ) ),
inference(and_elim,[status(thm)],[513]) ).
tff(515,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) )
& ( op1(e13,e10) != op1(e13,e11) )
& ( op1(e13,e10) != op1(e13,e12) ) ),
inference(and_elim,[status(thm)],[514]) ).
tff(516,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) )
& ( op1(e13,e10) != op1(e13,e11) ) ),
inference(and_elim,[status(thm)],[515]) ).
tff(517,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) ) ),
inference(and_elim,[status(thm)],[516]) ).
tff(518,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) ) ),
inference(and_elim,[status(thm)],[517]) ).
tff(519,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) ) ),
inference(and_elim,[status(thm)],[518]) ).
tff(520,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) ) ),
inference(and_elim,[status(thm)],[519]) ).
tff(521,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) ) ),
inference(and_elim,[status(thm)],[520]) ).
tff(522,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) ) ),
inference(and_elim,[status(thm)],[521]) ).
tff(523,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) ) ),
inference(and_elim,[status(thm)],[522]) ).
tff(524,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) ) ),
inference(and_elim,[status(thm)],[523]) ).
tff(525,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) ) ),
inference(and_elim,[status(thm)],[524]) ).
tff(526,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) ) ),
inference(and_elim,[status(thm)],[525]) ).
tff(527,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) ) ),
inference(and_elim,[status(thm)],[526]) ).
tff(528,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) ) ),
inference(and_elim,[status(thm)],[527]) ).
tff(529,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) ) ),
inference(and_elim,[status(thm)],[528]) ).
tff(530,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) ) ),
inference(and_elim,[status(thm)],[529]) ).
tff(531,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) ) ),
inference(and_elim,[status(thm)],[530]) ).
tff(532,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) ) ),
inference(and_elim,[status(thm)],[531]) ).
tff(533,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) ) ),
inference(and_elim,[status(thm)],[532]) ).
tff(534,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) ) ),
inference(and_elim,[status(thm)],[533]) ).
tff(535,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) ) ),
inference(and_elim,[status(thm)],[534]) ).
tff(536,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) ) ),
inference(and_elim,[status(thm)],[535]) ).
tff(537,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) ) ),
inference(and_elim,[status(thm)],[536]) ).
tff(538,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) ) ),
inference(and_elim,[status(thm)],[537]) ).
tff(539,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) ) ),
inference(and_elim,[status(thm)],[538]) ).
tff(540,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) ) ),
inference(and_elim,[status(thm)],[539]) ).
tff(541,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) ) ),
inference(and_elim,[status(thm)],[540]) ).
tff(542,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) ) ),
inference(and_elim,[status(thm)],[541]) ).
tff(543,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) ) ),
inference(and_elim,[status(thm)],[542]) ).
tff(544,plain,
op1(e11,e12) != op1(e12,e12),
inference(and_elim,[status(thm)],[543]) ).
tff(545,plain,
op1(e11,e12) != op1(e12,e12),
inference(modus_ponens,[status(thm)],[544,510]) ).
tff(546,plain,
op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[545,509]) ).
tff(547,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[546,508]) ).
tff(548,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(549,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| $false
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(550,plain,
( ( op1(e11,e11) != op1(e11,e12) )
<=> ( op1(op1(e13,e13),op1(e13,e13)) != op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(551,plain,
( ( op1(e11,e11) != op1(e11,e12) )
<=> ( op1(e11,e11) != op1(e11,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(552,plain,
op1(e11,e11) != op1(e11,e12),
inference(and_elim,[status(thm)],[525]) ).
tff(553,plain,
op1(e11,e11) != op1(e11,e12),
inference(modus_ponens,[status(thm)],[552,551]) ).
tff(554,plain,
op1(op1(e13,e13),op1(e13,e13)) != op1(op1(e13,e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[553,550]) ).
tff(555,plain,
( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
<=> $false ),
inference(iff_false,[status(thm)],[554]) ).
tff(556,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| $false
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(monotonicity,[status(thm)],[555]) ).
tff(557,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(transitivity,[status(thm)],[556,549]) ).
tff(558,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(559,plain,
( ( op1(e13,e13) = e10 )
<=> ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(560,plain,
( ( op1(e12,e12) = e10 )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(561,plain,
( ( op1(e11,e11) = e10 )
<=> ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(562,plain,
( ( op1(e10,e10) = e10 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(563,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(monotonicity,[status(thm)],[562,561,560,559]) ).
tff(564,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(transitivity,[status(thm)],[563,558]) ).
tff(565,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(566,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(567,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 ) )
<=> ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(568,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(monotonicity,[status(thm)],[567]) ).
tff(569,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(transitivity,[status(thm)],[568,566]) ).
tff(570,axiom,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) )
& ( ( ( op1(e10,op1(e10,e10)) != e10 )
& ( op1(e10,op1(e10,e11)) != e11 )
& ( op1(e10,op1(e10,e12)) != e12 )
& ( op1(e10,op1(e10,e13)) != e13 ) )
| ( ( op1(e11,op1(e11,e10)) != e10 )
& ( op1(e11,op1(e11,e11)) != e11 )
& ( op1(e11,op1(e11,e12)) != e12 )
& ( op1(e11,op1(e11,e13)) != e13 ) )
| ( ( op1(e12,op1(e12,e10)) != e10 )
& ( op1(e12,op1(e12,e11)) != e11 )
& ( op1(e12,op1(e12,e12)) != e12 )
& ( op1(e12,op1(e12,e13)) != e13 ) )
| ( ( op1(e13,op1(e13,e10)) != e10 )
& ( op1(e13,op1(e13,e11)) != e11 )
& ( op1(e13,op1(e13,e12)) != e12 )
& ( op1(e13,op1(e13,e13)) != e13 ) ) )
& ( ( ( op1(e10,e10) = e10 )
& ( op1(e10,e10) = e10 )
& ( op1(e10,e10) = e10 )
& ( op1(e10,e10) = e10 ) )
| ( ( op1(e10,e10) = e10 )
& ( op1(e10,e10) = e10 )
& ( op1(e11,e10) = e10 )
& ( op1(e10,e11) = e10 ) )
| ( ( op1(e10,e10) = e10 )
& ( op1(e10,e10) = e10 )
& ( op1(e12,e10) = e10 )
& ( op1(e10,e12) = e10 ) )
| ( ( op1(e10,e10) = e10 )
& ( op1(e10,e10) = e10 )
& ( op1(e13,e10) = e10 )
& ( op1(e10,e13) = e10 ) )
| ( ( op1(e10,e11) = e10 )
& ( op1(e11,e10) = e10 )
& ( op1(e10,e11) = e11 )
& ( op1(e11,e10) = e11 ) )
| ( ( op1(e10,e11) = e10 )
& ( op1(e11,e10) = e10 )
& ( op1(e11,e11) = e11 )
& ( op1(e11,e11) = e11 ) )
| ( ( op1(e10,e11) = e10 )
& ( op1(e11,e10) = e10 )
& ( op1(e12,e11) = e11 )
& ( op1(e11,e12) = e11 ) )
| ( ( op1(e10,e11) = e10 )
& ( op1(e11,e10) = e10 )
& ( op1(e13,e11) = e11 )
& ( op1(e11,e13) = e11 ) )
| ( ( op1(e10,e12) = e10 )
& ( op1(e12,e10) = e10 )
& ( op1(e10,e12) = e12 )
& ( op1(e12,e10) = e12 ) )
| ( ( op1(e10,e12) = e10 )
& ( op1(e12,e10) = e10 )
& ( op1(e11,e12) = e12 )
& ( op1(e12,e11) = e12 ) )
| ( ( op1(e10,e12) = e10 )
& ( op1(e12,e10) = e10 )
& ( op1(e12,e12) = e12 )
& ( op1(e12,e12) = e12 ) )
| ( ( op1(e10,e12) = e10 )
& ( op1(e12,e10) = e10 )
& ( op1(e13,e12) = e12 )
& ( op1(e12,e13) = e12 ) )
| ( ( op1(e10,e13) = e10 )
& ( op1(e13,e10) = e10 )
& ( op1(e10,e13) = e13 )
& ( op1(e13,e10) = e13 ) )
| ( ( op1(e10,e13) = e10 )
& ( op1(e13,e10) = e10 )
& ( op1(e11,e13) = e13 )
& ( op1(e13,e11) = e13 ) )
| ( ( op1(e10,e13) = e10 )
& ( op1(e13,e10) = e10 )
& ( op1(e12,e13) = e13 )
& ( op1(e13,e12) = e13 ) )
| ( ( op1(e10,e13) = e10 )
& ( op1(e13,e10) = e10 )
& ( op1(e13,e13) = e13 )
& ( op1(e13,e13) = e13 ) )
| ( ( op1(e11,e10) = e11 )
& ( op1(e10,e11) = e11 )
& ( op1(e10,e10) = e10 )
& ( op1(e10,e10) = e10 ) )
| ( ( op1(e11,e10) = e11 )
& ( op1(e10,e11) = e11 )
& ( op1(e11,e10) = e10 )
& ( op1(e10,e11) = e10 ) )
| ( ( op1(e11,e10) = e11 )
& ( op1(e10,e11) = e11 )
& ( op1(e12,e10) = e10 )
& ( op1(e10,e12) = e10 ) )
| ( ( op1(e11,e10) = e11 )
& ( op1(e10,e11) = e11 )
& ( op1(e13,e10) = e10 )
& ( op1(e10,e13) = e10 ) )
| ( ( op1(e11,e11) = e11 )
& ( op1(e11,e11) = e11 )
& ( op1(e10,e11) = e11 )
& ( op1(e11,e10) = e11 ) )
| ( ( op1(e11,e11) = e11 )
& ( op1(e11,e11) = e11 )
& ( op1(e11,e11) = e11 )
& ( op1(e11,e11) = e11 ) )
| ( ( op1(e11,e11) = e11 )
& ( op1(e11,e11) = e11 )
& ( op1(e12,e11) = e11 )
& ( op1(e11,e12) = e11 ) )
| ( ( op1(e11,e11) = e11 )
& ( op1(e11,e11) = e11 )
& ( op1(e13,e11) = e11 )
& ( op1(e11,e13) = e11 ) )
| ( ( op1(e11,e12) = e11 )
& ( op1(e12,e11) = e11 )
& ( op1(e10,e12) = e12 )
& ( op1(e12,e10) = e12 ) )
| ( ( op1(e11,e12) = e11 )
& ( op1(e12,e11) = e11 )
& ( op1(e11,e12) = e12 )
& ( op1(e12,e11) = e12 ) )
| ( ( op1(e11,e12) = e11 )
& ( op1(e12,e11) = e11 )
& ( op1(e12,e12) = e12 )
& ( op1(e12,e12) = e12 ) )
| ( ( op1(e11,e12) = e11 )
& ( op1(e12,e11) = e11 )
& ( op1(e13,e12) = e12 )
& ( op1(e12,e13) = e12 ) )
| ( ( op1(e11,e13) = e11 )
& ( op1(e13,e11) = e11 )
& ( op1(e10,e13) = e13 )
& ( op1(e13,e10) = e13 ) )
| ( ( op1(e11,e13) = e11 )
& ( op1(e13,e11) = e11 )
& ( op1(e11,e13) = e13 )
& ( op1(e13,e11) = e13 ) )
| ( ( op1(e11,e13) = e11 )
& ( op1(e13,e11) = e11 )
& ( op1(e12,e13) = e13 )
& ( op1(e13,e12) = e13 ) )
| ( ( op1(e11,e13) = e11 )
& ( op1(e13,e11) = e11 )
& ( op1(e13,e13) = e13 )
& ( op1(e13,e13) = e13 ) )
| ( ( op1(e12,e10) = e12 )
& ( op1(e10,e12) = e12 )
& ( op1(e10,e10) = e10 )
& ( op1(e10,e10) = e10 ) )
| ( ( op1(e12,e10) = e12 )
& ( op1(e10,e12) = e12 )
& ( op1(e11,e10) = e10 )
& ( op1(e10,e11) = e10 ) )
| ( ( op1(e12,e10) = e12 )
& ( op1(e10,e12) = e12 )
& ( op1(e12,e10) = e10 )
& ( op1(e10,e12) = e10 ) )
| ( ( op1(e12,e10) = e12 )
& ( op1(e10,e12) = e12 )
& ( op1(e13,e10) = e10 )
& ( op1(e10,e13) = e10 ) )
| ( ( op1(e12,e11) = e12 )
& ( op1(e11,e12) = e12 )
& ( op1(e10,e11) = e11 )
& ( op1(e11,e10) = e11 ) )
| ( ( op1(e12,e11) = e12 )
& ( op1(e11,e12) = e12 )
& ( op1(e11,e11) = e11 )
& ( op1(e11,e11) = e11 ) )
| ( ( op1(e12,e11) = e12 )
& ( op1(e11,e12) = e12 )
& ( op1(e12,e11) = e11 )
& ( op1(e11,e12) = e11 ) )
| ( ( op1(e12,e11) = e12 )
& ( op1(e11,e12) = e12 )
& ( op1(e13,e11) = e11 )
& ( op1(e11,e13) = e11 ) )
| ( ( op1(e12,e12) = e12 )
& ( op1(e12,e12) = e12 )
& ( op1(e10,e12) = e12 )
& ( op1(e12,e10) = e12 ) )
| ( ( op1(e12,e12) = e12 )
& ( op1(e12,e12) = e12 )
& ( op1(e11,e12) = e12 )
& ( op1(e12,e11) = e12 ) )
| ( ( op1(e12,e12) = e12 )
& ( op1(e12,e12) = e12 )
& ( op1(e12,e12) = e12 )
& ( op1(e12,e12) = e12 ) )
| ( ( op1(e12,e12) = e12 )
& ( op1(e12,e12) = e12 )
& ( op1(e13,e12) = e12 )
& ( op1(e12,e13) = e12 ) )
| ( ( op1(e12,e13) = e12 )
& ( op1(e13,e12) = e12 )
& ( op1(e10,e13) = e13 )
& ( op1(e13,e10) = e13 ) )
| ( ( op1(e12,e13) = e12 )
& ( op1(e13,e12) = e12 )
& ( op1(e11,e13) = e13 )
& ( op1(e13,e11) = e13 ) )
| ( ( op1(e12,e13) = e12 )
& ( op1(e13,e12) = e12 )
& ( op1(e12,e13) = e13 )
& ( op1(e13,e12) = e13 ) )
| ( ( op1(e12,e13) = e12 )
& ( op1(e13,e12) = e12 )
& ( op1(e13,e13) = e13 )
& ( op1(e13,e13) = e13 ) )
| ( ( op1(e13,e10) = e13 )
& ( op1(e10,e13) = e13 )
& ( op1(e10,e10) = e10 )
& ( op1(e10,e10) = e10 ) )
| ( ( op1(e13,e10) = e13 )
& ( op1(e10,e13) = e13 )
& ( op1(e11,e10) = e10 )
& ( op1(e10,e11) = e10 ) )
| ( ( op1(e13,e10) = e13 )
& ( op1(e10,e13) = e13 )
& ( op1(e12,e10) = e10 )
& ( op1(e10,e12) = e10 ) )
| ( ( op1(e13,e10) = e13 )
& ( op1(e10,e13) = e13 )
& ( op1(e13,e10) = e10 )
& ( op1(e10,e13) = e10 ) )
| ( ( op1(e13,e11) = e13 )
& ( op1(e11,e13) = e13 )
& ( op1(e10,e11) = e11 )
& ( op1(e11,e10) = e11 ) )
| ( ( op1(e13,e11) = e13 )
& ( op1(e11,e13) = e13 )
& ( op1(e11,e11) = e11 )
& ( op1(e11,e11) = e11 ) )
| ( ( op1(e13,e11) = e13 )
& ( op1(e11,e13) = e13 )
& ( op1(e12,e11) = e11 )
& ( op1(e11,e12) = e11 ) )
| ( ( op1(e13,e11) = e13 )
& ( op1(e11,e13) = e13 )
& ( op1(e13,e11) = e11 )
& ( op1(e11,e13) = e11 ) )
| ( ( op1(e13,e12) = e13 )
& ( op1(e12,e13) = e13 )
& ( op1(e10,e12) = e12 )
& ( op1(e12,e10) = e12 ) )
| ( ( op1(e13,e12) = e13 )
& ( op1(e12,e13) = e13 )
& ( op1(e11,e12) = e12 )
& ( op1(e12,e11) = e12 ) )
| ( ( op1(e13,e12) = e13 )
& ( op1(e12,e13) = e13 )
& ( op1(e12,e12) = e12 )
& ( op1(e12,e12) = e12 ) )
| ( ( op1(e13,e12) = e13 )
& ( op1(e12,e13) = e13 )
& ( op1(e13,e12) = e12 )
& ( op1(e12,e13) = e12 ) )
| ( ( op1(e13,e13) = e13 )
& ( op1(e13,e13) = e13 )
& ( op1(e10,e13) = e13 )
& ( op1(e13,e10) = e13 ) )
| ( ( op1(e13,e13) = e13 )
& ( op1(e13,e13) = e13 )
& ( op1(e11,e13) = e13 )
& ( op1(e13,e11) = e13 ) )
| ( ( op1(e13,e13) = e13 )
& ( op1(e13,e13) = e13 )
& ( op1(e12,e13) = e13 )
& ( op1(e13,e12) = e13 ) )
| ( ( op1(e13,e13) = e13 )
& ( op1(e13,e13) = e13 )
& ( op1(e13,e13) = e13 )
& ( op1(e13,e13) = e13 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
tff(571,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) )
& ( ( ( op1(e10,op1(e10,e10)) != e10 )
& ( op1(e10,op1(e10,e11)) != e11 )
& ( op1(e10,op1(e10,e12)) != e12 )
& ( op1(e10,op1(e10,e13)) != e13 ) )
| ( ( op1(e11,op1(e11,e10)) != e10 )
& ( op1(e11,op1(e11,e11)) != e11 )
& ( op1(e11,op1(e11,e12)) != e12 )
& ( op1(e11,op1(e11,e13)) != e13 ) )
| ( ( op1(e12,op1(e12,e10)) != e10 )
& ( op1(e12,op1(e12,e11)) != e11 )
& ( op1(e12,op1(e12,e12)) != e12 )
& ( op1(e12,op1(e12,e13)) != e13 ) )
| ( ( op1(e13,op1(e13,e10)) != e10 )
& ( op1(e13,op1(e13,e11)) != e11 )
& ( op1(e13,op1(e13,e12)) != e12 )
& ( op1(e13,op1(e13,e13)) != e13 ) ) ) ),
inference(and_elim,[status(thm)],[570]) ).
tff(572,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) ) ),
inference(and_elim,[status(thm)],[571]) ).
tff(573,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(and_elim,[status(thm)],[572]) ).
tff(574,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e13) = e11 ) ) ),
inference(and_elim,[status(thm)],[573]) ).
tff(575,plain,
( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) ),
inference(and_elim,[status(thm)],[574]) ).
tff(576,plain,
( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[575,569]) ).
tff(577,plain,
( ( op1(e10,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[576,565]) ).
tff(578,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[577,564]) ).
tff(579,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[578,558]) ).
tff(580,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[579,557]) ).
tff(581,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[580,548]) ).
tff(582,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[581,548]) ).
tff(583,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[582,548]) ).
tff(584,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[583,548]) ).
tff(585,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[584,548]) ).
tff(586,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[585,548]) ).
tff(587,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[586,548]) ).
tff(588,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)),
inference(unit_resolution,[status(thm)],[587,547,506]) ).
tff(589,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(monotonicity,[status(thm)],[588]) ).
tff(590,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
<=> ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(transitivity,[status(thm)],[589,493]) ).
tff(591,plain,
( ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(symmetry,[status(thm)],[590]) ).
tff(592,plain,
( ( op1(op1(e13,e13),e13) != op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(e13,e13),e13) ) ),
inference(monotonicity,[status(thm)],[591]) ).
tff(593,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),e13) )
<=> ( op1(op1(e13,e13),e13) != op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(monotonicity,[status(thm)],[493]) ).
tff(594,plain,
( ( op1(e11,e12) != op1(e11,e13) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(595,plain,
( ( op1(e11,e12) != op1(e11,e13) )
<=> ( op1(e11,e12) != op1(e11,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(596,plain,
op1(e11,e12) != op1(e11,e13),
inference(and_elim,[status(thm)],[523]) ).
tff(597,plain,
op1(e11,e12) != op1(e11,e13),
inference(modus_ponens,[status(thm)],[596,595]) ).
tff(598,plain,
op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[597,594]) ).
tff(599,plain,
op1(op1(e13,e13),e13) != op1(op1(e13,e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[598,593]) ).
tff(600,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[599,592]) ).
tff(601,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(602,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| $false
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| $false )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(603,plain,
( ( e11 != e12 )
<=> ( op1(e13,e13) != op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(604,plain,
( ( e11 != e12 )
<=> ( e11 != e12 ) ),
inference(rewrite,[status(thm)],]) ).
tff(605,plain,
e11 != e12,
inference(and_elim,[status(thm)],[500]) ).
tff(606,plain,
e11 != e12,
inference(modus_ponens,[status(thm)],[605,604]) ).
tff(607,plain,
op1(e13,e13) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[606,603]) ).
tff(608,plain,
( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
<=> $false ),
inference(iff_false,[status(thm)],[607]) ).
tff(609,plain,
( ( op1(e11,e11) != op1(e11,e13) )
<=> ( op1(op1(e13,e13),op1(e13,e13)) != op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(610,plain,
( ( op1(e11,e11) != op1(e11,e13) )
<=> ( op1(e11,e11) != op1(e11,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(611,plain,
op1(e11,e11) != op1(e11,e13),
inference(and_elim,[status(thm)],[524]) ).
tff(612,plain,
op1(e11,e11) != op1(e11,e13),
inference(modus_ponens,[status(thm)],[611,610]) ).
tff(613,plain,
op1(op1(e13,e13),op1(e13,e13)) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[612,609]) ).
tff(614,plain,
( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
<=> $false ),
inference(iff_false,[status(thm)],[613]) ).
tff(615,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| $false
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| $false ) ),
inference(monotonicity,[status(thm)],[614,608]) ).
tff(616,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[615,602]) ).
tff(617,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(618,plain,
( ( op1(e13,e13) = e12 )
<=> ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(619,plain,
( ( op1(e12,e12) = e12 )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(620,plain,
( ( op1(e11,e11) = e12 )
<=> ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(621,plain,
( ( op1(e10,e10) = e12 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(622,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ) ),
inference(monotonicity,[status(thm)],[621,620,619,618]) ).
tff(623,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[622,617]) ).
tff(624,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(625,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(626,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(627,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(monotonicity,[status(thm)],[626]) ).
tff(628,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(transitivity,[status(thm)],[627,625]) ).
tff(629,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) ),
inference(and_elim,[status(thm)],[573]) ).
tff(630,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[629,628]) ).
tff(631,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[630,624]) ).
tff(632,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[631,623]) ).
tff(633,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[632,617]) ).
tff(634,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[633,616]) ).
tff(635,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[634,601]) ).
tff(636,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[635,601]) ).
tff(637,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[636,601]) ).
tff(638,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[637,601]) ).
tff(639,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[638,601]) ).
tff(640,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[639,601]) ).
tff(641,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[640,601]) ).
tff(642,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13),
inference(unit_resolution,[status(thm)],[641,600]) ).
tff(643,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(monotonicity,[status(thm)],[642]) ).
tff(644,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),e13) ) ),
inference(monotonicity,[status(thm)],[643]) ).
tff(645,plain,
( ( op1(e10,e12) != op1(e12,e12) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(646,plain,
( ( op1(e10,e12) != op1(e12,e12) )
<=> ( op1(e10,e12) != op1(e12,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(647,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) ) ),
inference(and_elim,[status(thm)],[543]) ).
tff(648,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) ) ),
inference(and_elim,[status(thm)],[647]) ).
tff(649,plain,
op1(e10,e12) != op1(e12,e12),
inference(and_elim,[status(thm)],[648]) ).
tff(650,plain,
op1(e10,e12) != op1(e12,e12),
inference(modus_ponens,[status(thm)],[649,646]) ).
tff(651,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[650,645]) ).
tff(652,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[651,644]) ).
tff(653,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(654,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| $false )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(655,plain,
( ( op1(e10,e13) != op1(e11,e13) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) != op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(656,plain,
( ( op1(e10,e13) != op1(e11,e13) )
<=> ( op1(e10,e13) != op1(e11,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(657,plain,
op1(e10,e13) != op1(e11,e13),
inference(and_elim,[status(thm)],[540]) ).
tff(658,plain,
op1(e10,e13) != op1(e11,e13),
inference(modus_ponens,[status(thm)],[657,656]) ).
tff(659,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[658,655]) ).
tff(660,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) )
<=> $false ),
inference(iff_false,[status(thm)],[659]) ).
tff(661,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| $false ) ),
inference(monotonicity,[status(thm)],[660]) ).
tff(662,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[661,654]) ).
tff(663,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(664,plain,
( ( op1(e10,e13) = e12 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(665,plain,
( ( op1(e10,e12) = e12 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(666,plain,
( ( op1(e10,e11) = e12 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(667,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) ) ) ),
inference(monotonicity,[status(thm)],[621,666,665,664]) ).
tff(668,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[667,663]) ).
tff(669,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(670,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(671,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(672,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ) ),
inference(monotonicity,[status(thm)],[671]) ).
tff(673,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ) ),
inference(transitivity,[status(thm)],[672,670]) ).
tff(674,axiom,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) )
& ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
& ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e10,e12) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e12) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e10,e13) = e11 )
| ( op1(e11,e13) = e11 )
| ( op1(e12,e13) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
& ( ( op1(e10,e13) = e12 )
| ( op1(e11,e13) = e12 )
| ( op1(e12,e13) = e12 )
| ( op1(e13,e13) = e12 ) )
& ( ( op1(e13,e10) = e13 )
| ( op1(e13,e11) = e13 )
| ( op1(e13,e12) = e13 )
| ( op1(e13,e13) = e13 ) )
& ( ( op1(e10,e13) = e13 )
| ( op1(e11,e13) = e13 )
| ( op1(e12,e13) = e13 )
| ( op1(e13,e13) = e13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(675,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) )
& ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
& ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e10,e12) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e12) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e10,e13) = e11 )
| ( op1(e11,e13) = e11 )
| ( op1(e12,e13) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
& ( ( op1(e10,e13) = e12 )
| ( op1(e11,e13) = e12 )
| ( op1(e12,e13) = e12 )
| ( op1(e13,e13) = e12 ) )
& ( ( op1(e13,e10) = e13 )
| ( op1(e13,e11) = e13 )
| ( op1(e13,e12) = e13 )
| ( op1(e13,e13) = e13 ) ) ),
inference(and_elim,[status(thm)],[674]) ).
tff(676,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) )
& ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
& ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e10,e12) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e12) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e10,e13) = e11 )
| ( op1(e11,e13) = e11 )
| ( op1(e12,e13) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
& ( ( op1(e10,e13) = e12 )
| ( op1(e11,e13) = e12 )
| ( op1(e12,e13) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(and_elim,[status(thm)],[675]) ).
tff(677,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) )
& ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
& ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e10,e12) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e12) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e10,e13) = e11 )
| ( op1(e11,e13) = e11 )
| ( op1(e12,e13) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(and_elim,[status(thm)],[676]) ).
tff(678,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) )
& ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
& ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e10,e12) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e12) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
& ( ( op1(e10,e13) = e11 )
| ( op1(e11,e13) = e11 )
| ( op1(e12,e13) = e11 )
| ( op1(e13,e13) = e11 ) ) ),
inference(and_elim,[status(thm)],[677]) ).
tff(679,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) )
& ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
& ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e10,e12) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e12) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) ) ),
inference(and_elim,[status(thm)],[678]) ).
tff(680,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) )
& ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
& ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e10,e12) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e12) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(and_elim,[status(thm)],[679]) ).
tff(681,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) )
& ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
& ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e10,e12) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e12) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(and_elim,[status(thm)],[680]) ).
tff(682,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) )
& ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
& ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e10,e12) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e12) = e13 ) ) ),
inference(and_elim,[status(thm)],[681]) ).
tff(683,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) )
& ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
& ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) ) ),
inference(and_elim,[status(thm)],[682]) ).
tff(684,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) )
& ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) ) ),
inference(and_elim,[status(thm)],[683]) ).
tff(685,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
& ( ( op1(e12,e10) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e13) = e12 ) ) ),
inference(and_elim,[status(thm)],[684]) ).
tff(686,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
& ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ) ),
inference(and_elim,[status(thm)],[685]) ).
tff(687,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) )
& ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ) ),
inference(and_elim,[status(thm)],[686]) ).
tff(688,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e13,e12) = e10 ) ) ),
inference(and_elim,[status(thm)],[687]) ).
tff(689,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) ) ),
inference(and_elim,[status(thm)],[688]) ).
tff(690,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e10,e11) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e13,e11) = e13 ) ) ),
inference(and_elim,[status(thm)],[689]) ).
tff(691,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) )
& ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ) ),
inference(and_elim,[status(thm)],[690]) ).
tff(692,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) )
& ( ( op1(e10,e11) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e12,e11) = e12 )
| ( op1(e13,e11) = e12 ) ) ),
inference(and_elim,[status(thm)],[691]) ).
tff(693,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
& ( ( op1(e11,e10) = e12 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e13) = e12 ) ) ),
inference(and_elim,[status(thm)],[692]) ).
tff(694,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
& ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) ) ),
inference(and_elim,[status(thm)],[693]) ).
tff(695,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
& ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) ) ),
inference(and_elim,[status(thm)],[694]) ).
tff(696,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) ) ),
inference(and_elim,[status(thm)],[695]) ).
tff(697,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ) ),
inference(and_elim,[status(thm)],[696]) ).
tff(698,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) ) ),
inference(and_elim,[status(thm)],[697]) ).
tff(699,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) ) ),
inference(and_elim,[status(thm)],[698]) ).
tff(700,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) ) ),
inference(and_elim,[status(thm)],[699]) ).
tff(701,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ) ),
inference(and_elim,[status(thm)],[700]) ).
tff(702,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ),
inference(and_elim,[status(thm)],[701]) ).
tff(703,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[702,673]) ).
tff(704,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[703,669]) ).
tff(705,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[704,668]) ).
tff(706,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[705,663]) ).
tff(707,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[706,663]) ).
tff(708,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[707,662]) ).
tff(709,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[708,653]) ).
tff(710,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[709,653]) ).
tff(711,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[710,653]) ).
tff(712,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[711,653]) ).
tff(713,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[712,653]) ).
tff(714,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[713,653]) ).
tff(715,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(e13,e13),e13),
inference(unit_resolution,[status(thm)],[714,652,600]) ).
tff(716,plain,
h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = h2(op1(op1(e13,e13),e13)),
inference(monotonicity,[status(thm)],[715]) ).
tff(717,plain,
h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))),
inference(transitivity,[status(thm)],[716,437,426,379,492,441]) ).
tff(718,plain,
op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) = op2(h3(e13),h3(e13)),
inference(monotonicity,[status(thm)],[439,439]) ).
tff(719,plain,
op2(h3(e13),h3(e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))),
inference(symmetry,[status(thm)],[718]) ).
tff(720,plain,
h3(e13) = op2(h3(e13),h3(e13)),
inference(symmetry,[status(thm)],[224]) ).
tff(721,plain,
( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),h2(e13))) )
<=> ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(722,plain,
( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13)))) )
<=> ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),h2(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(723,plain,
( ( h2(e10) = op2(op2(e21,e21),op2(op2(e21,e21),e21)) )
<=> ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(724,plain,
( ( h2(e10) = op2(op2(e21,e21),op2(op2(e21,e21),e21)) )
<=> ( h2(e10) = op2(op2(e21,e21),op2(op2(e21,e21),e21)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(725,plain,
( ( h2(e13) = e21 )
& ( h2(e10) = op2(op2(e21,e21),op2(op2(e21,e21),e21)) ) ),
inference(and_elim,[status(thm)],[281]) ).
tff(726,plain,
h2(e10) = op2(op2(e21,e21),op2(op2(e21,e21),e21)),
inference(and_elim,[status(thm)],[725]) ).
tff(727,plain,
h2(e10) = op2(op2(e21,e21),op2(op2(e21,e21),e21)),
inference(modus_ponens,[status(thm)],[726,724]) ).
tff(728,plain,
h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13)))),
inference(modus_ponens,[status(thm)],[727,723]) ).
tff(729,plain,
h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),op2(op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),h2(e13))),
inference(modus_ponens,[status(thm)],[728,722]) ).
tff(730,plain,
h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),
inference(modus_ponens,[status(thm)],[729,721]) ).
tff(731,plain,
h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),
inference(monotonicity,[status(thm)],[588]) ).
tff(732,plain,
h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))),
inference(transitivity,[status(thm)],[731,730,438,428,425,720,719]) ).
tff(733,plain,
( ( h2(e13) = op2(h3(e13),h2(e13)) )
<=> ( op2(h3(e13),h2(e13)) = h2(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(734,plain,
op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) = op2(h3(e13),h2(e13)),
inference(monotonicity,[status(thm)],[439]) ).
tff(735,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(736,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) ) ),
inference(monotonicity,[status(thm)],[588]) ).
tff(737,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(transitivity,[status(thm)],[736,735]) ).
tff(738,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) != op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(monotonicity,[status(thm)],[737]) ).
tff(739,plain,
( ( op1(e10,e10) != op1(e10,e13) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(740,plain,
( ( op1(e10,e10) != op1(e10,e13) )
<=> ( op1(e10,e10) != op1(e10,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(741,plain,
op1(e10,e10) != op1(e10,e13),
inference(and_elim,[status(thm)],[532]) ).
tff(742,plain,
op1(e10,e10) != op1(e10,e13),
inference(modus_ponens,[status(thm)],[741,740]) ).
tff(743,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13),
inference(modus_ponens,[status(thm)],[742,739]) ).
tff(744,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) != op1(op1(e13,e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[743,738]) ).
tff(745,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(746,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| $false
| $false
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(747,plain,
( ( op1(e10,e13) != op1(e13,e13) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(748,plain,
( ( op1(e10,e13) != op1(e13,e13) )
<=> ( op1(e10,e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(749,plain,
op1(e10,e13) != op1(e13,e13),
inference(and_elim,[status(thm)],[538]) ).
tff(750,plain,
op1(e10,e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[749,748]) ).
tff(751,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[750,747]) ).
tff(752,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(e13,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[751]) ).
tff(753,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| $false
| $false
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[752,660]) ).
tff(754,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[753,746]) ).
tff(755,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(756,plain,
( ( op1(e10,e13) = e13 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(757,plain,
( ( op1(e10,e13) = e11 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(758,plain,
( ( op1(e10,e13) = e10 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(759,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[758,757,664,756]) ).
tff(760,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[759,755]) ).
tff(761,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(762,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(763,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 ) )
<=> ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(764,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[763]) ).
tff(765,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[764,762]) ).
tff(766,axiom,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
& ( ( op1(e11,e11) = e10 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e11) = e13 ) )
& ( ( op1(e11,e12) = e10 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e12) = e13 ) )
& ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e10) = e11 )
| ( op1(e12,e10) = e12 )
| ( op1(e12,e10) = e13 ) )
& ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
& ( ( op1(e12,e12) = e10 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e12) = e13 ) )
& ( ( op1(e12,e13) = e10 )
| ( op1(e12,e13) = e11 )
| ( op1(e12,e13) = e12 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) )
& ( ( op1(e13,e13) = e10 )
| ( op1(e13,e13) = e11 )
| ( op1(e13,e13) = e12 )
| ( op1(e13,e13) = e13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(767,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
& ( ( op1(e11,e11) = e10 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e11) = e13 ) )
& ( ( op1(e11,e12) = e10 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e12) = e13 ) )
& ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e10) = e11 )
| ( op1(e12,e10) = e12 )
| ( op1(e12,e10) = e13 ) )
& ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
& ( ( op1(e12,e12) = e10 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e12) = e13 ) )
& ( ( op1(e12,e13) = e10 )
| ( op1(e12,e13) = e11 )
| ( op1(e12,e13) = e12 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) )
& ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) ) ),
inference(and_elim,[status(thm)],[766]) ).
tff(768,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
& ( ( op1(e11,e11) = e10 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e11) = e13 ) )
& ( ( op1(e11,e12) = e10 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e12) = e13 ) )
& ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e10) = e11 )
| ( op1(e12,e10) = e12 )
| ( op1(e12,e10) = e13 ) )
& ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
& ( ( op1(e12,e12) = e10 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e12) = e13 ) )
& ( ( op1(e12,e13) = e10 )
| ( op1(e12,e13) = e11 )
| ( op1(e12,e13) = e12 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) )
& ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) ) ),
inference(and_elim,[status(thm)],[767]) ).
tff(769,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
& ( ( op1(e11,e11) = e10 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e11) = e13 ) )
& ( ( op1(e11,e12) = e10 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e12) = e13 ) )
& ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e10) = e11 )
| ( op1(e12,e10) = e12 )
| ( op1(e12,e10) = e13 ) )
& ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
& ( ( op1(e12,e12) = e10 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e12) = e13 ) )
& ( ( op1(e12,e13) = e10 )
| ( op1(e12,e13) = e11 )
| ( op1(e12,e13) = e12 )
| ( op1(e12,e13) = e13 ) )
& ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) ) ),
inference(and_elim,[status(thm)],[768]) ).
tff(770,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
& ( ( op1(e11,e11) = e10 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e11) = e13 ) )
& ( ( op1(e11,e12) = e10 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e12) = e13 ) )
& ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e10) = e11 )
| ( op1(e12,e10) = e12 )
| ( op1(e12,e10) = e13 ) )
& ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
& ( ( op1(e12,e12) = e10 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e12) = e13 ) )
& ( ( op1(e12,e13) = e10 )
| ( op1(e12,e13) = e11 )
| ( op1(e12,e13) = e12 )
| ( op1(e12,e13) = e13 ) ) ),
inference(and_elim,[status(thm)],[769]) ).
tff(771,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
& ( ( op1(e11,e11) = e10 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e11) = e13 ) )
& ( ( op1(e11,e12) = e10 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e12) = e13 ) )
& ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e10) = e11 )
| ( op1(e12,e10) = e12 )
| ( op1(e12,e10) = e13 ) )
& ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
& ( ( op1(e12,e12) = e10 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e12) = e12 )
| ( op1(e12,e12) = e13 ) ) ),
inference(and_elim,[status(thm)],[770]) ).
tff(772,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
& ( ( op1(e11,e11) = e10 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e11) = e13 ) )
& ( ( op1(e11,e12) = e10 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e12) = e13 ) )
& ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e10) = e11 )
| ( op1(e12,e10) = e12 )
| ( op1(e12,e10) = e13 ) )
& ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ) ),
inference(and_elim,[status(thm)],[771]) ).
tff(773,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
& ( ( op1(e11,e11) = e10 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e11) = e13 ) )
& ( ( op1(e11,e12) = e10 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e12) = e13 ) )
& ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
& ( ( op1(e12,e10) = e10 )
| ( op1(e12,e10) = e11 )
| ( op1(e12,e10) = e12 )
| ( op1(e12,e10) = e13 ) ) ),
inference(and_elim,[status(thm)],[772]) ).
tff(774,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
& ( ( op1(e11,e11) = e10 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e11) = e13 ) )
& ( ( op1(e11,e12) = e10 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e12) = e13 ) )
& ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ) ),
inference(and_elim,[status(thm)],[773]) ).
tff(775,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
& ( ( op1(e11,e11) = e10 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e11) = e13 ) )
& ( ( op1(e11,e12) = e10 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e12) = e12 )
| ( op1(e11,e12) = e13 ) ) ),
inference(and_elim,[status(thm)],[774]) ).
tff(776,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
& ( ( op1(e11,e11) = e10 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e11) = e12 )
| ( op1(e11,e11) = e13 ) ) ),
inference(and_elim,[status(thm)],[775]) ).
tff(777,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) ) ),
inference(and_elim,[status(thm)],[776]) ).
tff(778,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) ) ),
inference(and_elim,[status(thm)],[777]) ).
tff(779,plain,
( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) ),
inference(and_elim,[status(thm)],[778]) ).
tff(780,plain,
( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[779,765]) ).
tff(781,plain,
( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[780,761]) ).
tff(782,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[781,760]) ).
tff(783,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[782,755]) ).
tff(784,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[783,755]) ).
tff(785,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[784,754]) ).
tff(786,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[785,745]) ).
tff(787,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[786,745]) ).
tff(788,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[787,745]) ).
tff(789,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[788,745]) ).
tff(790,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[789,745]) ).
tff(791,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[790,745]) ).
tff(792,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = e13,
inference(unit_resolution,[status(thm)],[791,744]) ).
tff(793,plain,
h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = h2(e13),
inference(monotonicity,[status(thm)],[792]) ).
tff(794,plain,
( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
<=> ( h2(e13) = op2(h3(e13),h2(e13)) ) ),
inference(monotonicity,[status(thm)],[793,734]) ).
tff(795,plain,
( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
<=> ( op2(h3(e13),h2(e13)) = h2(e13) ) ),
inference(transitivity,[status(thm)],[794,733]) ).
tff(796,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
<=> ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) ) ),
inference(symmetry,[status(thm)],[795]) ).
tff(797,plain,
( ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) )
<=> ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(798,plain,
( ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| $false
| $false )
<=> ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(799,plain,
( ( op2(op2(h2(e13),h3(e13)),h4(e13)) != h3(e13) )
<=> ( op2(h1(e13),h4(e13)) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(800,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),h4(e13)) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(801,plain,
( ( op2(e20,e23) != op2(e21,e23) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(802,plain,
( ( op2(e20,e23) != op2(e21,e23) )
<=> ( op2(e20,e23) != op2(e21,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(803,plain,
op2(e20,e23) != op2(e21,e23),
inference(and_elim,[status(thm)],[68]) ).
tff(804,plain,
op2(e20,e23) != op2(e21,e23),
inference(modus_ponens,[status(thm)],[803,802]) ).
tff(805,plain,
op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[804,801]) ).
tff(806,plain,
op2(op2(h2(e13),h3(e13)),h4(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[805,800]) ).
tff(807,plain,
op2(h1(e13),h4(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[806,799]) ).
tff(808,plain,
( ( op2(h1(e13),h4(e13)) = h3(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[807]) ).
tff(809,plain,
( ( op2(op2(h2(e13),h3(e13)),h4(e13)) != h2(e13) )
<=> ( op2(h1(e13),h4(e13)) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(810,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) != op2(h4(e13),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),h4(e13)) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(811,plain,
( ( op2(e20,e23) != op2(e23,e23) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) != op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(812,plain,
( ( op2(e20,e23) != op2(e23,e23) )
<=> ( op2(e20,e23) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(813,plain,
op2(e20,e23) != op2(e23,e23),
inference(and_elim,[status(thm)],[66]) ).
tff(814,plain,
op2(e20,e23) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[813,812]) ).
tff(815,plain,
op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) != op2(h4(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[814,811]) ).
tff(816,plain,
op2(op2(h2(e13),h3(e13)),h4(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[815,810]) ).
tff(817,plain,
op2(h1(e13),h4(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[816,809]) ).
tff(818,plain,
( ( op2(h1(e13),h4(e13)) = h2(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[817]) ).
tff(819,plain,
( ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h2(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) ) )
<=> ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[818,808]) ).
tff(820,plain,
( ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h2(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) ) )
<=> ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[819,798]) ).
tff(821,plain,
( ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h2(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) ) )
<=> ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h2(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(822,plain,
( ( ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h2(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) ) )
<=> ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h2(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(823,plain,
( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) )
<=> ( op2(h1(e13),h4(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(824,plain,
( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) )
<=> ( op2(h1(e13),h4(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(825,plain,
( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) )
<=> ( op2(h1(e13),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(826,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) ) )
<=> ( ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h2(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[461,825,824,823]) ).
tff(827,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) ) )
<=> ( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h2(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[826,822]) ).
tff(828,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(829,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(830,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = h4(e13) )
<=> ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(831,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(832,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(h4(e13),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(833,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[468,832,831,830]) ).
tff(834,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[833,829]) ).
tff(835,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(836,plain,
( ( op2(e20,e23) = e23 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(837,plain,
( ( op2(e20,e23) = e22 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(838,plain,
( ( op2(e20,e23) = e21 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(839,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[474,838,837,836]) ).
tff(840,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[839,835]) ).
tff(841,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(842,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(843,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 ) )
<=> ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(844,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) ) ),
inference(monotonicity,[status(thm)],[843]) ).
tff(845,plain,
( ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) ) ),
inference(transitivity,[status(thm)],[844,842]) ).
tff(846,axiom,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
& ( ( op2(e21,e21) = e20 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e21) = e23 ) )
& ( ( op2(e21,e22) = e20 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e22) = e23 ) )
& ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e20) = e21 )
| ( op2(e22,e20) = e22 )
| ( op2(e22,e20) = e23 ) )
& ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
& ( ( op2(e22,e22) = e20 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e22) = e23 ) )
& ( ( op2(e22,e23) = e20 )
| ( op2(e22,e23) = e21 )
| ( op2(e22,e23) = e22 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e23,e21) = e20 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) )
& ( ( op2(e23,e23) = e20 )
| ( op2(e23,e23) = e21 )
| ( op2(e23,e23) = e22 )
| ( op2(e23,e23) = e23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(847,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
& ( ( op2(e21,e21) = e20 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e21) = e23 ) )
& ( ( op2(e21,e22) = e20 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e22) = e23 ) )
& ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e20) = e21 )
| ( op2(e22,e20) = e22 )
| ( op2(e22,e20) = e23 ) )
& ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
& ( ( op2(e22,e22) = e20 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e22) = e23 ) )
& ( ( op2(e22,e23) = e20 )
| ( op2(e22,e23) = e21 )
| ( op2(e22,e23) = e22 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e23,e21) = e20 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) ) ),
inference(and_elim,[status(thm)],[846]) ).
tff(848,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
& ( ( op2(e21,e21) = e20 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e21) = e23 ) )
& ( ( op2(e21,e22) = e20 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e22) = e23 ) )
& ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e20) = e21 )
| ( op2(e22,e20) = e22 )
| ( op2(e22,e20) = e23 ) )
& ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
& ( ( op2(e22,e22) = e20 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e22) = e23 ) )
& ( ( op2(e22,e23) = e20 )
| ( op2(e22,e23) = e21 )
| ( op2(e22,e23) = e22 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e23,e21) = e20 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e21) = e23 ) ) ),
inference(and_elim,[status(thm)],[847]) ).
tff(849,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
& ( ( op2(e21,e21) = e20 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e21) = e23 ) )
& ( ( op2(e21,e22) = e20 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e22) = e23 ) )
& ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e20) = e21 )
| ( op2(e22,e20) = e22 )
| ( op2(e22,e20) = e23 ) )
& ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
& ( ( op2(e22,e22) = e20 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e22) = e23 ) )
& ( ( op2(e22,e23) = e20 )
| ( op2(e22,e23) = e21 )
| ( op2(e22,e23) = e22 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) ) ),
inference(and_elim,[status(thm)],[848]) ).
tff(850,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
& ( ( op2(e21,e21) = e20 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e21) = e23 ) )
& ( ( op2(e21,e22) = e20 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e22) = e23 ) )
& ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e20) = e21 )
| ( op2(e22,e20) = e22 )
| ( op2(e22,e20) = e23 ) )
& ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
& ( ( op2(e22,e22) = e20 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e22) = e23 ) )
& ( ( op2(e22,e23) = e20 )
| ( op2(e22,e23) = e21 )
| ( op2(e22,e23) = e22 )
| ( op2(e22,e23) = e23 ) ) ),
inference(and_elim,[status(thm)],[849]) ).
tff(851,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
& ( ( op2(e21,e21) = e20 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e21) = e23 ) )
& ( ( op2(e21,e22) = e20 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e22) = e23 ) )
& ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e20) = e21 )
| ( op2(e22,e20) = e22 )
| ( op2(e22,e20) = e23 ) )
& ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
& ( ( op2(e22,e22) = e20 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e22) = e23 ) ) ),
inference(and_elim,[status(thm)],[850]) ).
tff(852,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
& ( ( op2(e21,e21) = e20 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e21) = e23 ) )
& ( ( op2(e21,e22) = e20 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e22) = e23 ) )
& ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e20) = e21 )
| ( op2(e22,e20) = e22 )
| ( op2(e22,e20) = e23 ) )
& ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ) ),
inference(and_elim,[status(thm)],[851]) ).
tff(853,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
& ( ( op2(e21,e21) = e20 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e21) = e23 ) )
& ( ( op2(e21,e22) = e20 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e22) = e23 ) )
& ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e20) = e21 )
| ( op2(e22,e20) = e22 )
| ( op2(e22,e20) = e23 ) ) ),
inference(and_elim,[status(thm)],[852]) ).
tff(854,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
& ( ( op2(e21,e21) = e20 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e21) = e23 ) )
& ( ( op2(e21,e22) = e20 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e22) = e23 ) )
& ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ) ),
inference(and_elim,[status(thm)],[853]) ).
tff(855,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
& ( ( op2(e21,e21) = e20 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e21) = e23 ) )
& ( ( op2(e21,e22) = e20 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e22) = e23 ) ) ),
inference(and_elim,[status(thm)],[854]) ).
tff(856,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
& ( ( op2(e21,e21) = e20 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e21) = e23 ) ) ),
inference(and_elim,[status(thm)],[855]) ).
tff(857,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) ) ),
inference(and_elim,[status(thm)],[856]) ).
tff(858,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) ) ),
inference(and_elim,[status(thm)],[857]) ).
tff(859,plain,
( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) ),
inference(and_elim,[status(thm)],[858]) ).
tff(860,plain,
( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[859,845]) ).
tff(861,plain,
( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[860,841]) ).
tff(862,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[861,840]) ).
tff(863,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[862,835]) ).
tff(864,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[863,835]) ).
tff(865,plain,
( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[864,834]) ).
tff(866,plain,
( ( op2(op2(h2(e13),h3(e13)),h4(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[865,828]) ).
tff(867,plain,
( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h2(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[866,827]) ).
tff(868,plain,
( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h2(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[867,821]) ).
tff(869,plain,
( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[868,820]) ).
tff(870,plain,
( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[869,797]) ).
tff(871,plain,
( ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[870,797]) ).
tff(872,plain,
op2(h1(e13),h4(e13)) = h4(e13),
inference(unit_resolution,[status(thm)],[871,457]) ).
tff(873,plain,
( ( op2(h1(e13),h3(e13)) = op2(h1(e13),h4(e13)) )
<=> ( op2(h1(e13),h3(e13)) = h4(e13) ) ),
inference(monotonicity,[status(thm)],[872]) ).
tff(874,plain,
( ( op2(h1(e13),h3(e13)) != op2(h1(e13),h4(e13)) )
<=> ( op2(h1(e13),h3(e13)) != h4(e13) ) ),
inference(monotonicity,[status(thm)],[873]) ).
tff(875,plain,
( ( op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(op2(h2(e13),h3(e13)),h4(e13)) )
<=> ( op2(h1(e13),h3(e13)) != op2(h1(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(876,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(op2(h2(e13),h3(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(877,plain,
( ( op2(e20,e22) != op2(e20,e23) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(878,plain,
( ( op2(e20,e22) != op2(e20,e23) )
<=> ( op2(e20,e22) != op2(e20,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(879,plain,
op2(e20,e22) != op2(e20,e23),
inference(and_elim,[status(thm)],[57]) ).
tff(880,plain,
op2(e20,e22) != op2(e20,e23),
inference(modus_ponens,[status(thm)],[879,878]) ).
tff(881,plain,
op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)),
inference(modus_ponens,[status(thm)],[880,877]) ).
tff(882,plain,
op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(op2(h2(e13),h3(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[881,876]) ).
tff(883,plain,
op2(h1(e13),h3(e13)) != op2(h1(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[882,875]) ).
tff(884,plain,
op2(h1(e13),h3(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[883,874]) ).
tff(885,plain,
( ( op2(h1(e13),h3(e13)) = op2(h3(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) = h3(e13) ) ),
inference(monotonicity,[status(thm)],[224]) ).
tff(886,plain,
( ( op2(h1(e13),h3(e13)) != op2(h3(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) != h3(e13) ) ),
inference(monotonicity,[status(thm)],[885]) ).
tff(887,plain,
( ( op2(h1(e13),h3(e13)) != h3(op1(e13,e13)) )
<=> ( op2(h1(e13),h3(e13)) != op2(h3(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(888,plain,
( ( op2(op2(h2(e13),h3(e13)),h3(e13)) != h3(op1(e13,e13)) )
<=> ( op2(h1(e13),h3(e13)) != h3(op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(889,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(op2(h2(e13),h3(e13)),h3(e13)) != h3(op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(890,plain,
( ( op2(e20,e22) != op2(e22,e22) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(891,plain,
( ( op2(e20,e22) != op2(e22,e22) )
<=> ( op2(e20,e22) != op2(e22,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(892,plain,
op2(e20,e22) != op2(e22,e22),
inference(and_elim,[status(thm)],[324]) ).
tff(893,plain,
op2(e20,e22) != op2(e22,e22),
inference(modus_ponens,[status(thm)],[892,891]) ).
tff(894,plain,
op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[893,890]) ).
tff(895,plain,
op2(op2(h2(e13),h3(e13)),h3(e13)) != h3(op1(e13,e13)),
inference(modus_ponens,[status(thm)],[894,889]) ).
tff(896,plain,
op2(h1(e13),h3(e13)) != h3(op1(e13,e13)),
inference(modus_ponens,[status(thm)],[895,888]) ).
tff(897,plain,
op2(h1(e13),h3(e13)) != op2(h3(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[896,887]) ).
tff(898,plain,
op2(h1(e13),h3(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[897,886]) ).
tff(899,plain,
( ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(900,plain,
( ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| $false
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(901,plain,
( ( op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(h2(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) != h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(902,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(903,plain,
( ( op2(e20,e22) != op2(e21,e22) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(904,plain,
( ( op2(e20,e22) != op2(e21,e22) )
<=> ( op2(e20,e22) != op2(e21,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(905,plain,
op2(e20,e22) != op2(e21,e22),
inference(and_elim,[status(thm)],[325]) ).
tff(906,plain,
op2(e20,e22) != op2(e21,e22),
inference(modus_ponens,[status(thm)],[905,904]) ).
tff(907,plain,
op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[906,903]) ).
tff(908,plain,
op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(h2(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[907,902]) ).
tff(909,plain,
op2(h1(e13),h3(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[908,901]) ).
tff(910,plain,
( ( op2(h1(e13),h3(e13)) = h1(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[909]) ).
tff(911,plain,
( ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| $false
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[910]) ).
tff(912,plain,
( ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[911,900]) ).
tff(913,plain,
( ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(914,plain,
( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) )
<=> ( op2(h1(e13),h3(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(915,plain,
( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) )
<=> ( op2(h1(e13),h3(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(916,plain,
( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(917,plain,
( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
<=> ( op2(h1(e13),h3(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(918,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[917,916,915,914]) ).
tff(919,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[918,913]) ).
tff(920,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(921,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(922,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
<=> ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(923,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(924,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(925,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(926,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[925,924,923,922]) ).
tff(927,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[926,921]) ).
tff(928,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(929,plain,
( ( op2(e20,e22) = e23 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(930,plain,
( ( op2(e20,e22) = e22 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(931,plain,
( ( op2(e20,e22) = e21 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(932,plain,
( ( op2(e20,e22) = e20 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(933,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[932,931,930,929]) ).
tff(934,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[933,928]) ).
tff(935,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(936,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(937,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 ) )
<=> ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(938,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ) ),
inference(monotonicity,[status(thm)],[937]) ).
tff(939,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ) ),
inference(transitivity,[status(thm)],[938,936]) ).
tff(940,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ) ),
inference(and_elim,[status(thm)],[858]) ).
tff(941,plain,
( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ),
inference(and_elim,[status(thm)],[940]) ).
tff(942,plain,
( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ),
inference(modus_ponens,[status(thm)],[941,939]) ).
tff(943,plain,
( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ),
inference(modus_ponens,[status(thm)],[942,935]) ).
tff(944,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[943,934]) ).
tff(945,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[944,928]) ).
tff(946,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[945,928]) ).
tff(947,plain,
( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[946,927]) ).
tff(948,plain,
( ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[947,920]) ).
tff(949,plain,
( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[948,919]) ).
tff(950,plain,
( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[949,913]) ).
tff(951,plain,
( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[950,912]) ).
tff(952,plain,
( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[951,899]) ).
tff(953,plain,
( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[952,899]) ).
tff(954,plain,
op2(h1(e13),h3(e13)) = h2(e13),
inference(unit_resolution,[status(thm)],[953,898,884]) ).
tff(955,plain,
( ( op2(h1(e13),h2(e13)) = op2(h1(e13),h3(e13)) )
<=> ( op2(h1(e13),h2(e13)) = h2(e13) ) ),
inference(monotonicity,[status(thm)],[954]) ).
tff(956,plain,
( ( op2(h1(e13),h2(e13)) != op2(h1(e13),h3(e13)) )
<=> ( op2(h1(e13),h2(e13)) != h2(e13) ) ),
inference(monotonicity,[status(thm)],[955]) ).
tff(957,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) != op2(op2(h2(e13),h3(e13)),h3(e13)) )
<=> ( op2(h1(e13),h2(e13)) != op2(h1(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(958,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(op2(h2(e13),h3(e13)),h2(e13)) != op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(959,plain,
( ( op2(e20,e21) != op2(e20,e22) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(960,plain,
( ( op2(e20,e21) != op2(e20,e22) )
<=> ( op2(e20,e21) != op2(e20,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(961,plain,
op2(e20,e21) != op2(e20,e22),
inference(and_elim,[status(thm)],[59]) ).
tff(962,plain,
op2(e20,e21) != op2(e20,e22),
inference(modus_ponens,[status(thm)],[961,960]) ).
tff(963,plain,
op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[962,959]) ).
tff(964,plain,
op2(op2(h2(e13),h3(e13)),h2(e13)) != op2(op2(h2(e13),h3(e13)),h3(e13)),
inference(modus_ponens,[status(thm)],[963,958]) ).
tff(965,plain,
op2(h1(e13),h2(e13)) != op2(h1(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[964,957]) ).
tff(966,plain,
op2(h1(e13),h2(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[965,956]) ).
tff(967,plain,
( ( h4(e13) = h2(e13) )
<=> ( h2(e13) = h4(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(968,plain,
( ( op2(h2(e13),h2(e13)) = h2(e13) )
<=> ( h4(e13) = h2(e13) ) ),
inference(monotonicity,[status(thm)],[287]) ).
tff(969,plain,
( ( op2(h2(e13),h2(e13)) = h2(e13) )
<=> ( h2(e13) = h4(e13) ) ),
inference(transitivity,[status(thm)],[968,967]) ).
tff(970,plain,
( ( h2(e13) = h4(e13) )
<=> ( op2(h2(e13),h2(e13)) = h2(e13) ) ),
inference(symmetry,[status(thm)],[969]) ).
tff(971,plain,
( ( h2(e13) != h4(e13) )
<=> ( op2(h2(e13),h2(e13)) != h2(e13) ) ),
inference(monotonicity,[status(thm)],[970]) ).
tff(972,plain,
( ( op2(h4(e13),h4(e13)) != h4(e13) )
<=> ( h2(e13) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(973,plain,
h2(e13) != h4(e13),
inference(modus_ponens,[status(thm)],[252,972]) ).
tff(974,plain,
op2(h2(e13),h2(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[973,971]) ).
tff(975,plain,
( ( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h1(e13),h2(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) )
<=> ( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h1(e13),h2(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(976,plain,
( ( ( op2(h2(e13),h2(e13)) = h2(e13) )
| ( op2(h1(e13),h2(e13)) = h2(e13) )
| $false
| ( op2(h3(e13),h2(e13)) = h2(e13) ) )
<=> ( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h1(e13),h2(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(977,plain,
( ( op2(h4(e13),op2(h4(e13),h4(e13))) != op2(h4(e13),h4(e13)) )
<=> ( op2(h4(e13),h2(e13)) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(978,plain,
( ( op2(e23,e21) != op2(e23,e23) )
<=> ( op2(h4(e13),op2(h4(e13),h4(e13))) != op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(979,plain,
( ( op2(e23,e21) != op2(e23,e23) )
<=> ( op2(e23,e21) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(980,plain,
op2(e23,e21) != op2(e23,e23),
inference(and_elim,[status(thm)],[40]) ).
tff(981,plain,
op2(e23,e21) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[980,979]) ).
tff(982,plain,
op2(h4(e13),op2(h4(e13),h4(e13))) != op2(h4(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[981,978]) ).
tff(983,plain,
op2(h4(e13),h2(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[982,977]) ).
tff(984,plain,
( ( op2(h4(e13),h2(e13)) = h2(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[983]) ).
tff(985,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
<=> ( op2(h1(e13),h2(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(986,plain,
( ( h2(op1(e13,e13)) = h2(e13) )
<=> ( op2(h2(e13),h2(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(987,plain,
( ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) ) )
<=> ( ( op2(h2(e13),h2(e13)) = h2(e13) )
| ( op2(h1(e13),h2(e13)) = h2(e13) )
| $false
| ( op2(h3(e13),h2(e13)) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[986,985,984]) ).
tff(988,plain,
( ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) ) )
<=> ( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h1(e13),h2(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[987,976]) ).
tff(989,plain,
( ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) ) )
<=> ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(990,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) ) )
<=> ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(991,plain,
( ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( op2(h4(e13),h2(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(992,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( op2(h3(e13),h2(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(993,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( h2(op1(e13,e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(994,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(995,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[994,993,992,991]) ).
tff(996,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) )
<=> ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[995,990]) ).
tff(997,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(998,plain,
( ( op2(e23,e21) = e21 )
<=> ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(999,plain,
( ( op2(e22,e21) = e21 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1000,plain,
( ( op2(e21,e21) = e21 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1001,plain,
( ( op2(e20,e21) = e21 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1002,plain,
( ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[1001,1000,999,998]) ).
tff(1003,plain,
( ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[1002,997]) ).
tff(1004,plain,
( ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
<=> ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1005,plain,
( ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
<=> ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1006,plain,
( ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 ) )
<=> ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1007,plain,
( ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
<=> ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) ) ),
inference(monotonicity,[status(thm)],[1006]) ).
tff(1008,plain,
( ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
<=> ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) ) ),
inference(transitivity,[status(thm)],[1007,1005]) ).
tff(1009,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
& ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
& ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
& ( ( op2(e20,e22) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e23,e22) = e23 ) ) ),
inference(and_elim,[status(thm)],[369]) ).
tff(1010,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
& ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
& ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) ) ),
inference(and_elim,[status(thm)],[1009]) ).
tff(1011,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
& ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) ) ),
inference(and_elim,[status(thm)],[1010]) ).
tff(1012,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
& ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) ) ),
inference(and_elim,[status(thm)],[1011]) ).
tff(1013,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
& ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ) ),
inference(and_elim,[status(thm)],[1012]) ).
tff(1014,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) )
& ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ) ),
inference(and_elim,[status(thm)],[1013]) ).
tff(1015,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e23,e22) = e20 ) ) ),
inference(and_elim,[status(thm)],[1014]) ).
tff(1016,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) )
& ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) ) ),
inference(and_elim,[status(thm)],[1015]) ).
tff(1017,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
& ( ( op2(e20,e21) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e23,e21) = e23 ) ) ),
inference(and_elim,[status(thm)],[1016]) ).
tff(1018,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ) ),
inference(and_elim,[status(thm)],[1017]) ).
tff(1019,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) ) ),
inference(and_elim,[status(thm)],[1018]) ).
tff(1020,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) ) ),
inference(and_elim,[status(thm)],[1019]) ).
tff(1021,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) ) ),
inference(and_elim,[status(thm)],[1020]) ).
tff(1022,plain,
( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) ),
inference(and_elim,[status(thm)],[1021]) ).
tff(1023,plain,
( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) ),
inference(modus_ponens,[status(thm)],[1022,1008]) ).
tff(1024,plain,
( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) ),
inference(modus_ponens,[status(thm)],[1023,1004]) ).
tff(1025,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1024,1003]) ).
tff(1026,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1025,997]) ).
tff(1027,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1026,997]) ).
tff(1028,plain,
( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1027,996]) ).
tff(1029,plain,
( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1028,989]) ).
tff(1030,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h1(e13),h2(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1029,988]) ).
tff(1031,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h1(e13),h2(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1030,975]) ).
tff(1032,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h1(e13),h2(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1031,975]) ).
tff(1033,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h1(e13),h2(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1032,975]) ).
tff(1034,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h1(e13),h2(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1033,975]) ).
tff(1035,plain,
op2(h3(e13),h2(e13)) = h2(e13),
inference(unit_resolution,[status(thm)],[1034,974,966]) ).
tff(1036,plain,
h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)),
inference(modus_ponens,[status(thm)],[1035,796]) ).
tff(1037,plain,
( ( h4(e13) = op2(h3(e13),h1(e13)) )
<=> ( op2(h3(e13),h1(e13)) = h4(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1038,plain,
op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) = op2(h3(e13),h1(e13)),
inference(monotonicity,[status(thm)],[439,427]) ).
tff(1039,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
<=> ( op1(op1(e13,e13),e13) = op1(e13,e13) ) ),
inference(monotonicity,[status(thm)],[642]) ).
tff(1040,plain,
( ( op1(op1(e13,e13),e13) = op1(e13,e13) )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(symmetry,[status(thm)],[1039]) ).
tff(1041,plain,
( ( op1(op1(e13,e13),e13) != op1(e13,e13) )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) ),
inference(monotonicity,[status(thm)],[1040]) ).
tff(1042,plain,
( ( op1(e11,e13) != op1(e13,e13) )
<=> ( op1(op1(e13,e13),e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1043,plain,
( ( op1(e11,e13) != op1(e13,e13) )
<=> ( op1(e11,e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1044,plain,
op1(e11,e13) != op1(e13,e13),
inference(and_elim,[status(thm)],[536]) ).
tff(1045,plain,
op1(e11,e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1044,1043]) ).
tff(1046,plain,
op1(op1(e13,e13),e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1045,1042]) ).
tff(1047,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1046,1041]) ).
tff(1048,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1049,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| $false
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| $false )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1050,plain,
( ( op1(e13,e12) != op1(e13,e13) )
<=> ( op1(e13,op1(op1(e13,e13),e13)) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1051,plain,
( ( op1(e13,e12) != op1(e13,e13) )
<=> ( op1(e13,e12) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1052,plain,
op1(e13,e12) != op1(e13,e13),
inference(and_elim,[status(thm)],[511]) ).
tff(1053,plain,
op1(e13,e12) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1052,1051]) ).
tff(1054,plain,
op1(e13,op1(op1(e13,e13),e13)) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1053,1050]) ).
tff(1055,plain,
( ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1054]) ).
tff(1056,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[505]) ).
tff(1057,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| $false
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| $false ) ),
inference(monotonicity,[status(thm)],[1056,1055]) ).
tff(1058,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ) ),
inference(transitivity,[status(thm)],[1057,1049]) ).
tff(1059,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1060,plain,
( ( op1(e13,e12) = e11 )
<=> ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1061,plain,
( ( op1(e12,e12) = e11 )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1062,plain,
( ( op1(e11,e12) = e11 )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1063,plain,
( ( op1(e10,e12) = e11 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1064,plain,
( ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) ) ) ),
inference(monotonicity,[status(thm)],[1063,1062,1061,1060]) ).
tff(1065,plain,
( ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) ) ) ),
inference(transitivity,[status(thm)],[1064,1059]) ).
tff(1066,plain,
( ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
<=> ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1067,plain,
( ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
<=> ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1068,plain,
( ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 ) )
<=> ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1069,plain,
( ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
<=> ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ) ),
inference(monotonicity,[status(thm)],[1068]) ).
tff(1070,plain,
( ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
<=> ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ) ),
inference(transitivity,[status(thm)],[1069,1067]) ).
tff(1071,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(and_elim,[status(thm)],[686]) ).
tff(1072,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(modus_ponens,[status(thm)],[1071,1070]) ).
tff(1073,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(modus_ponens,[status(thm)],[1072,1066]) ).
tff(1074,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1073,1065]) ).
tff(1075,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1074,1059]) ).
tff(1076,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1075,1059]) ).
tff(1077,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1076,1058]) ).
tff(1078,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1077,1048]) ).
tff(1079,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1078,1048]) ).
tff(1080,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1079,1048]) ).
tff(1081,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1080,1048]) ).
tff(1082,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1081,1048]) ).
tff(1083,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1082,1048]) ).
tff(1084,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) = op1(e13,e13),
inference(unit_resolution,[status(thm)],[1083,1047]) ).
tff(1085,plain,
h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = h2(op1(e13,e13)),
inference(monotonicity,[status(thm)],[1084]) ).
tff(1086,plain,
h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = h4(e13),
inference(transitivity,[status(thm)],[1085,276]) ).
tff(1087,plain,
( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
<=> ( h4(e13) = op2(h3(e13),h1(e13)) ) ),
inference(monotonicity,[status(thm)],[1086,1038]) ).
tff(1088,plain,
( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
<=> ( op2(h3(e13),h1(e13)) = h4(e13) ) ),
inference(transitivity,[status(thm)],[1087,1037]) ).
tff(1089,plain,
( ( op2(h3(e13),h1(e13)) = h4(e13) )
<=> ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) ) ),
inference(symmetry,[status(thm)],[1088]) ).
tff(1090,plain,
( ( h4(e13) = op2(h3(e13),h4(e13)) )
<=> ( op2(h3(e13),h4(e13)) = h4(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1091,plain,
( ( op2(h1(e13),h4(e13)) = op2(h3(e13),h4(e13)) )
<=> ( h4(e13) = op2(h3(e13),h4(e13)) ) ),
inference(monotonicity,[status(thm)],[872]) ).
tff(1092,plain,
( ( op2(h1(e13),h4(e13)) = op2(h3(e13),h4(e13)) )
<=> ( op2(h3(e13),h4(e13)) = h4(e13) ) ),
inference(transitivity,[status(thm)],[1091,1090]) ).
tff(1093,plain,
( ( op2(h1(e13),h4(e13)) != op2(h3(e13),h4(e13)) )
<=> ( op2(h3(e13),h4(e13)) != h4(e13) ) ),
inference(monotonicity,[status(thm)],[1092]) ).
tff(1094,plain,
( ( op2(op2(h2(e13),h3(e13)),h4(e13)) != op2(h3(e13),h4(e13)) )
<=> ( op2(h1(e13),h4(e13)) != op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1095,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),h4(e13)) != op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1096,plain,
( ( op2(e20,e23) != op2(e22,e23) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1097,plain,
( ( op2(e20,e23) != op2(e22,e23) )
<=> ( op2(e20,e23) != op2(e22,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1098,plain,
op2(e20,e23) != op2(e22,e23),
inference(and_elim,[status(thm)],[67]) ).
tff(1099,plain,
op2(e20,e23) != op2(e22,e23),
inference(modus_ponens,[status(thm)],[1098,1097]) ).
tff(1100,plain,
op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[1099,1096]) ).
tff(1101,plain,
op2(op2(h2(e13),h3(e13)),h4(e13)) != op2(h3(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[1100,1095]) ).
tff(1102,plain,
op2(h1(e13),h4(e13)) != op2(h3(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[1101,1094]) ).
tff(1103,plain,
op2(h3(e13),h4(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[1102,1093]) ).
tff(1104,plain,
( ( h4(e13) = op2(h3(e13),h2(e13)) )
<=> ( op2(h3(e13),h2(e13)) = h4(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1105,plain,
( ( op2(h2(e13),h2(e13)) = op2(h3(e13),h2(e13)) )
<=> ( h4(e13) = op2(h3(e13),h2(e13)) ) ),
inference(monotonicity,[status(thm)],[287]) ).
tff(1106,plain,
( ( op2(h2(e13),h2(e13)) = op2(h3(e13),h2(e13)) )
<=> ( op2(h3(e13),h2(e13)) = h4(e13) ) ),
inference(transitivity,[status(thm)],[1105,1104]) ).
tff(1107,plain,
( ( op2(h2(e13),h2(e13)) != op2(h3(e13),h2(e13)) )
<=> ( op2(h3(e13),h2(e13)) != h4(e13) ) ),
inference(monotonicity,[status(thm)],[1106]) ).
tff(1108,plain,
( ( h2(op1(e13,e13)) != op2(h3(e13),h2(e13)) )
<=> ( op2(h2(e13),h2(e13)) != op2(h3(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1109,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) )
<=> ( h2(op1(e13,e13)) != op2(h3(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1110,plain,
( ( op2(e21,e21) != op2(e22,e21) )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1111,plain,
( ( op2(e21,e21) != op2(e22,e21) )
<=> ( op2(e21,e21) != op2(e22,e21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1112,plain,
op2(e21,e21) != op2(e22,e21),
inference(and_elim,[status(thm)],[328]) ).
tff(1113,plain,
op2(e21,e21) != op2(e22,e21),
inference(modus_ponens,[status(thm)],[1112,1111]) ).
tff(1114,plain,
op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[1113,1110]) ).
tff(1115,plain,
h2(op1(e13,e13)) != op2(h3(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[1114,1109]) ).
tff(1116,plain,
op2(h2(e13),h2(e13)) != op2(h3(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[1115,1108]) ).
tff(1117,plain,
op2(h3(e13),h2(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[1116,1107]) ).
tff(1118,plain,
( ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) )
| ( op2(h3(e13),h1(e13)) = h4(e13) ) )
<=> ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) )
| ( op2(h3(e13),h1(e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1119,plain,
( ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h1(e13)) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) ) )
<=> ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) )
| ( op2(h3(e13),h1(e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1120,plain,
( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) )
<=> ( op2(h3(e13),h1(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1121,plain,
( ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) ) )
<=> ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h1(e13)) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[1120]) ).
tff(1122,plain,
( ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) ) )
<=> ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) )
| ( op2(h3(e13),h1(e13)) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[1121,1119]) ).
tff(1123,plain,
( ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) ) )
<=> ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1124,plain,
( ( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h4(e13)) = h4(e13) ) )
<=> ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1125,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) )
<=> ( op2(h3(e13),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1126,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
<=> ( op2(h3(e13),h2(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1127,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
<=> ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1128,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) )
<=> ( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h4(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[1127,1126,242,1125]) ).
tff(1129,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) )
<=> ( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[1128,1124]) ).
tff(1130,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1131,plain,
( ( op2(e22,e23) = e23 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1132,plain,
( ( op2(e22,e21) = e23 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1133,plain,
( ( op2(e22,e20) = e23 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1134,plain,
( ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[1133,1132,258,1131]) ).
tff(1135,plain,
( ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[1134,1130]) ).
tff(1136,plain,
( ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
<=> ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1137,plain,
( ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
<=> ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1138,plain,
( ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 ) )
<=> ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1139,plain,
( ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
<=> ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) ) ),
inference(monotonicity,[status(thm)],[1138]) ).
tff(1140,plain,
( ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) )
<=> ( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) ) ),
inference(transitivity,[status(thm)],[1139,1137]) ).
tff(1141,plain,
( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) ),
inference(and_elim,[status(thm)],[1010]) ).
tff(1142,plain,
( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[1141,1140]) ).
tff(1143,plain,
( ( op2(e22,e20) = e23 )
| ( op2(e22,e21) = e23 )
| ( op2(e22,e22) = e23 )
| ( op2(e22,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[1142,1136]) ).
tff(1144,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1143,1135]) ).
tff(1145,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1144,1130]) ).
tff(1146,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1145,1130]) ).
tff(1147,plain,
( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1146,1129]) ).
tff(1148,plain,
( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),op2(h2(e13),h3(e13))) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1147,1123]) ).
tff(1149,plain,
( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) )
| ( op2(h3(e13),h1(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1148,1122]) ).
tff(1150,plain,
( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) )
| ( op2(h3(e13),h1(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1149,1118]) ).
tff(1151,plain,
( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) )
| ( op2(h3(e13),h1(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1150,1118]) ).
tff(1152,plain,
( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) )
| ( op2(h3(e13),h1(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1151,1118]) ).
tff(1153,plain,
( ( op2(h3(e13),h4(e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( op2(h3(e13),h2(e13)) = h4(e13) )
| ( op2(h3(e13),h1(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1152,1118]) ).
tff(1154,plain,
op2(h3(e13),h1(e13)) = h4(e13),
inference(unit_resolution,[status(thm)],[1153,1117,236,1103]) ).
tff(1155,plain,
h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))),
inference(modus_ponens,[status(thm)],[1154,1089]) ).
tff(1156,plain,
op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) = op2(h4(e13),h3(e13)),
inference(monotonicity,[status(thm)],[287,439]) ).
tff(1157,plain,
op2(h4(e13),h3(e13)) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))),
inference(symmetry,[status(thm)],[1156]) ).
tff(1158,plain,
( ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h1(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1159,plain,
( ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| $false
| ( op2(h4(e13),h3(e13)) = h1(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1160,plain,
( ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) )
<=> ( op2(h4(e13),h3(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1161,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) )
<=> ( op2(h4(e13),h3(e13)) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1162,plain,
( ( op2(e23,e22) != op2(e23,e23) )
<=> ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1163,plain,
( ( op2(e23,e22) != op2(e23,e23) )
<=> ( op2(e23,e22) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1164,plain,
op2(e23,e22) != op2(e23,e23),
inference(and_elim,[status(thm)],[39]) ).
tff(1165,plain,
op2(e23,e22) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[1164,1163]) ).
tff(1166,plain,
op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[1165,1162]) ).
tff(1167,plain,
op2(h4(e13),h3(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[1166,1161]) ).
tff(1168,plain,
( ( op2(h4(e13),h3(e13)) = h2(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1167]) ).
tff(1169,plain,
( ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h2(e13) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| $false
| ( op2(h4(e13),h3(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[1168,1160]) ).
tff(1170,plain,
( ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h2(e13) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[1169,1159]) ).
tff(1171,plain,
( ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h2(e13) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h2(e13) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1172,plain,
( ( ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h3(e13)) = h2(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h4(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h2(e13) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1173,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
<=> ( op2(h4(e13),h3(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1174,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( op2(h4(e13),h3(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1175,plain,
( ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(h4(e13),h3(e13)) = h2(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[346,1174,396,1173]) ).
tff(1176,plain,
( ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h2(e13) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[1175,1172]) ).
tff(1177,plain,
( ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) )
<=> ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1178,plain,
( ( op2(e23,e22) = e23 )
<=> ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1179,plain,
( ( op2(e23,e22) = e21 )
<=> ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1180,plain,
( ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) )
<=> ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[352,1179,402,1178]) ).
tff(1181,plain,
( ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) )
<=> ( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[1180,1177]) ).
tff(1182,plain,
( ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) )
<=> ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1183,plain,
( ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) )
<=> ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1184,plain,
( ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 ) )
<=> ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1185,plain,
( ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) )
<=> ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) ) ),
inference(monotonicity,[status(thm)],[1184]) ).
tff(1186,plain,
( ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) )
<=> ( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) ) ),
inference(transitivity,[status(thm)],[1185,1183]) ).
tff(1187,plain,
( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) ),
inference(and_elim,[status(thm)],[847]) ).
tff(1188,plain,
( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) ),
inference(modus_ponens,[status(thm)],[1187,1186]) ).
tff(1189,plain,
( ( op2(e23,e22) = e20 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e22) = e23 ) ),
inference(modus_ponens,[status(thm)],[1188,1182]) ).
tff(1190,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1189,1181]) ).
tff(1191,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1190,1177]) ).
tff(1192,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1191,1177]) ).
tff(1193,plain,
( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h2(e13) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1192,1176]) ).
tff(1194,plain,
( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h2(e13) )
| ( op2(h4(e13),h3(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1193,1171]) ).
tff(1195,plain,
( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1194,1170]) ).
tff(1196,plain,
( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1195,1158]) ).
tff(1197,plain,
( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1196,1158]) ).
tff(1198,plain,
( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1197,1158]) ).
tff(1199,plain,
( ( op2(h4(e13),h3(e13)) = h4(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1198,1158]) ).
tff(1200,plain,
op2(h4(e13),h3(e13)) = h4(e13),
inference(unit_resolution,[status(thm)],[1199,301,313]) ).
tff(1201,plain,
h4(e13) = op2(h4(e13),h3(e13)),
inference(symmetry,[status(thm)],[1200]) ).
tff(1202,plain,
( ( e13 = op1(e13,e13) )
<=> ( op1(e13,e13) = e13 ) ),
inference(commutativity,[status(thm)],]) ).
tff(1203,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(monotonicity,[status(thm)],[588]) ).
tff(1204,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 ) ),
inference(symmetry,[status(thm)],[1203]) ).
tff(1205,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != e13 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != e13 ) ),
inference(monotonicity,[status(thm)],[1204]) ).
tff(1206,plain,
( ( e10 != e13 )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1207,plain,
( ( e10 != e13 )
<=> ( e10 != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1208,plain,
e10 != e13,
inference(and_elim,[status(thm)],[501]) ).
tff(1209,plain,
e10 != e13,
inference(modus_ponens,[status(thm)],[1208,1207]) ).
tff(1210,plain,
op1(op1(e13,e13),op1(op1(e13,e13),e13)) != e13,
inference(modus_ponens,[status(thm)],[1209,1206]) ).
tff(1211,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != e13,
inference(modus_ponens,[status(thm)],[1210,1205]) ).
tff(1212,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
<=> ( op1(op1(e13,e13),e13) = e13 ) ),
inference(monotonicity,[status(thm)],[642]) ).
tff(1213,plain,
( ( op1(op1(e13,e13),e13) = e13 )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(symmetry,[status(thm)],[1212]) ).
tff(1214,plain,
( ( op1(op1(e13,e13),e13) != e13 )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != e13 ) ),
inference(monotonicity,[status(thm)],[1213]) ).
tff(1215,plain,
( ( e12 != e13 )
<=> ( op1(op1(e13,e13),e13) != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1216,plain,
( ( e12 != e13 )
<=> ( e12 != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1217,plain,
e12 != e13,
inference(and_elim,[status(thm)],[498]) ).
tff(1218,plain,
e12 != e13,
inference(modus_ponens,[status(thm)],[1217,1216]) ).
tff(1219,plain,
op1(op1(e13,e13),e13) != e13,
inference(modus_ponens,[status(thm)],[1218,1215]) ).
tff(1220,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != e13,
inference(modus_ponens,[status(thm)],[1219,1214]) ).
tff(1221,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1222,plain,
( ( $false
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1223,plain,
( ( e11 != e13 )
<=> ( op1(e13,e13) != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1224,plain,
( ( e11 != e13 )
<=> ( e11 != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1225,plain,
e11 != e13,
inference(and_elim,[status(thm)],[499]) ).
tff(1226,plain,
e11 != e13,
inference(modus_ponens,[status(thm)],[1225,1224]) ).
tff(1227,plain,
op1(e13,e13) != e13,
inference(modus_ponens,[status(thm)],[1226,1223]) ).
tff(1228,plain,
( ( op1(e13,e13) = e13 )
<=> $false ),
inference(iff_false,[status(thm)],[1227]) ).
tff(1229,plain,
( ( ( op1(e13,e13) = e13 )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) )
<=> ( $false
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1228]) ).
tff(1230,plain,
( ( ( op1(e13,e13) = e13 )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(transitivity,[status(thm)],[1229,1222]) ).
tff(1231,plain,
( ( ( op1(e13,e13) = e13 )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(e13,e13) = e13 )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1232,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(e13,e13) = e13 ) )
<=> ( ( op1(e13,e13) = e13 )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1233,plain,
( ( op1(e12,e12) = e13 )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1234,plain,
( ( op1(e11,e11) = e13 )
<=> ( op1(op1(e13,e13),op1(e13,e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1235,plain,
( ( op1(e10,e10) = e13 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1236,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(e13,e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1235,1234,1233]) ).
tff(1237,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) )
<=> ( ( op1(e13,e13) = e13 )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(transitivity,[status(thm)],[1236,1232]) ).
tff(1238,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) )
<=> ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1239,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) )
<=> ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1240,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 ) )
<=> ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1241,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) )
<=> ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1240]) ).
tff(1242,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) )
<=> ( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[1241,1239]) ).
tff(1243,plain,
( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) ),
inference(and_elim,[status(thm)],[572]) ).
tff(1244,plain,
( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1243,1242]) ).
tff(1245,plain,
( ( op1(e10,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e13,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1244,1238]) ).
tff(1246,plain,
( ( op1(e13,e13) = e13 )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1245,1237]) ).
tff(1247,plain,
( ( op1(e13,e13) = e13 )
| ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1246,1231]) ).
tff(1248,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1247,1230]) ).
tff(1249,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1248,1221]) ).
tff(1250,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1249,1221]) ).
tff(1251,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1250,1221]) ).
tff(1252,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1251,1221]) ).
tff(1253,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1252,1221]) ).
tff(1254,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1253,1221]) ).
tff(1255,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1254,1221]) ).
tff(1256,plain,
op1(op1(e13,e13),op1(e13,e13)) = e13,
inference(unit_resolution,[status(thm)],[1255,1220,1211]) ).
tff(1257,plain,
( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
<=> ( e13 = op1(e13,e13) ) ),
inference(monotonicity,[status(thm)],[1256]) ).
tff(1258,plain,
( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
<=> ( op1(e13,e13) = e13 ) ),
inference(transitivity,[status(thm)],[1257,1202]) ).
tff(1259,plain,
( ( op1(e13,e13) = e13 )
<=> ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(symmetry,[status(thm)],[1258]) ).
tff(1260,plain,
( ( op1(e13,e13) != e13 )
<=> ( op1(op1(e13,e13),op1(e13,e13)) != op1(e13,e13) ) ),
inference(monotonicity,[status(thm)],[1259]) ).
tff(1261,plain,
op1(op1(e13,e13),op1(e13,e13)) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1227,1260]) ).
tff(1262,plain,
( ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1263,plain,
( ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| $false
| $false )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1264,plain,
( ( op1(op1(e13,e13),e13) = op1(e13,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1046]) ).
tff(1265,plain,
( ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),e13) = op1(e13,e13) ) )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[1056,1264]) ).
tff(1266,plain,
( ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),e13) = op1(e13,e13) ) )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(transitivity,[status(thm)],[1265,1263]) ).
tff(1267,plain,
( ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),e13) = op1(e13,e13) ) )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),e13) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1268,plain,
( ( op1(e11,e13) = e11 )
<=> ( op1(op1(e13,e13),e13) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1269,plain,
( ( op1(e11,e11) = e11 )
<=> ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1270,plain,
( ( op1(e11,e10) = e11 )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1271,plain,
( ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),e13) = op1(e13,e13) ) ) ),
inference(monotonicity,[status(thm)],[1270,1269,1062,1268]) ).
tff(1272,plain,
( ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),e13) = op1(e13,e13) ) ) ),
inference(transitivity,[status(thm)],[1271,1267]) ).
tff(1273,plain,
( ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
<=> ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1274,plain,
( ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
<=> ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1275,plain,
( ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 ) )
<=> ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1276,plain,
( ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
<=> ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) ) ),
inference(monotonicity,[status(thm)],[1275]) ).
tff(1277,plain,
( ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) )
<=> ( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) ) ),
inference(transitivity,[status(thm)],[1276,1274]) ).
tff(1278,plain,
( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) ),
inference(and_elim,[status(thm)],[695]) ).
tff(1279,plain,
( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) ),
inference(modus_ponens,[status(thm)],[1278,1277]) ).
tff(1280,plain,
( ( op1(e11,e10) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e11,e13) = e11 ) ),
inference(modus_ponens,[status(thm)],[1279,1273]) ).
tff(1281,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),e13) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1280,1272]) ).
tff(1282,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),e13) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1281,1267]) ).
tff(1283,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),e13) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1282,1267]) ).
tff(1284,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1283,1266]) ).
tff(1285,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1284,1262]) ).
tff(1286,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1285,1262]) ).
tff(1287,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1286,1262]) ).
tff(1288,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1287,1262]) ).
tff(1289,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1288,1262]) ).
tff(1290,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1289,1262]) ).
tff(1291,plain,
op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,e13),
inference(unit_resolution,[status(thm)],[1290,1261]) ).
tff(1292,plain,
h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = h2(op1(e13,e13)),
inference(monotonicity,[status(thm)],[1291]) ).
tff(1293,plain,
h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))),
inference(transitivity,[status(thm)],[1292,276,1201,1157]) ).
tff(1294,plain,
op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) = op2(h1(e13),h3(e13)),
inference(monotonicity,[status(thm)],[427,439]) ).
tff(1295,plain,
op2(h1(e13),h3(e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))),
inference(symmetry,[status(thm)],[1294]) ).
tff(1296,plain,
h2(e13) = op2(h1(e13),h3(e13)),
inference(symmetry,[status(thm)],[954]) ).
tff(1297,plain,
( ( e13 = op1(op1(op1(e13,e13),e13),e13) )
<=> ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(commutativity,[status(thm)],]) ).
tff(1298,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(op1(e13,e13),e13),e13) )
<=> ( e13 = op1(op1(op1(e13,e13),e13),e13) ) ),
inference(monotonicity,[status(thm)],[792]) ).
tff(1299,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(op1(e13,e13),e13),e13) )
<=> ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(transitivity,[status(thm)],[1298,1297]) ).
tff(1300,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) != op1(op1(op1(e13,e13),e13),e13) )
<=> ( op1(op1(op1(e13,e13),e13),e13) != e13 ) ),
inference(monotonicity,[status(thm)],[1299]) ).
tff(1301,plain,
( ( op1(e10,e13) != op1(e12,e13) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) != op1(op1(op1(e13,e13),e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1302,plain,
( ( op1(e10,e13) != op1(e12,e13) )
<=> ( op1(e10,e13) != op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1303,plain,
op1(e10,e13) != op1(e12,e13),
inference(and_elim,[status(thm)],[539]) ).
tff(1304,plain,
op1(e10,e13) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[1303,1302]) ).
tff(1305,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) != op1(op1(op1(e13,e13),e13),e13),
inference(modus_ponens,[status(thm)],[1304,1301]) ).
tff(1306,plain,
op1(op1(op1(e13,e13),e13),e13) != e13,
inference(modus_ponens,[status(thm)],[1305,1300]) ).
tff(1307,plain,
( ( e13 = op1(op1(op1(e13,e13),e13),op1(e13,e13)) )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 ) ),
inference(commutativity,[status(thm)],]) ).
tff(1308,plain,
( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(op1(e13,e13),e13),op1(e13,e13)) )
<=> ( e13 = op1(op1(op1(e13,e13),e13),op1(e13,e13)) ) ),
inference(monotonicity,[status(thm)],[1256]) ).
tff(1309,plain,
( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(op1(e13,e13),e13),op1(e13,e13)) )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 ) ),
inference(transitivity,[status(thm)],[1308,1307]) ).
tff(1310,plain,
( ( op1(op1(e13,e13),op1(e13,e13)) != op1(op1(op1(e13,e13),e13),op1(e13,e13)) )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) != e13 ) ),
inference(monotonicity,[status(thm)],[1309]) ).
tff(1311,plain,
( ( op1(e11,e11) != op1(e12,e11) )
<=> ( op1(op1(e13,e13),op1(e13,e13)) != op1(op1(op1(e13,e13),e13),op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1312,plain,
( ( op1(e11,e11) != op1(e12,e11) )
<=> ( op1(e11,e11) != op1(e12,e11) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1313,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) ) ),
inference(and_elim,[status(thm)],[648]) ).
tff(1314,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) ) ),
inference(and_elim,[status(thm)],[1313]) ).
tff(1315,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) ) ),
inference(and_elim,[status(thm)],[1314]) ).
tff(1316,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) ) ),
inference(and_elim,[status(thm)],[1315]) ).
tff(1317,plain,
op1(e11,e11) != op1(e12,e11),
inference(and_elim,[status(thm)],[1316]) ).
tff(1318,plain,
op1(e11,e11) != op1(e12,e11),
inference(modus_ponens,[status(thm)],[1317,1312]) ).
tff(1319,plain,
op1(op1(e13,e13),op1(e13,e13)) != op1(op1(op1(e13,e13),e13),op1(e13,e13)),
inference(modus_ponens,[status(thm)],[1318,1311]) ).
tff(1320,plain,
op1(op1(op1(e13,e13),e13),op1(e13,e13)) != e13,
inference(modus_ponens,[status(thm)],[1319,1310]) ).
tff(1321,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1322,plain,
( ( op1(e12,e13) = e13 )
<=> ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1323,plain,
( ( op1(e12,e11) = e13 )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1324,plain,
( ( op1(e12,e10) = e13 )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1325,plain,
( ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1324,1323,1233,1322]) ).
tff(1326,plain,
( ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[1325,1321]) ).
tff(1327,plain,
( ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
<=> ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1328,plain,
( ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
<=> ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1329,plain,
( ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 ) )
<=> ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1330,plain,
( ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
<=> ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1329]) ).
tff(1331,plain,
( ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) )
<=> ( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[1330,1328]) ).
tff(1332,plain,
( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) ),
inference(and_elim,[status(thm)],[683]) ).
tff(1333,plain,
( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1332,1331]) ).
tff(1334,plain,
( ( op1(e12,e10) = e13 )
| ( op1(e12,e11) = e13 )
| ( op1(e12,e12) = e13 )
| ( op1(e12,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1333,1327]) ).
tff(1335,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1334,1326]) ).
tff(1336,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1335,1321]) ).
tff(1337,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1336,1321]) ).
tff(1338,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1337,1321]) ).
tff(1339,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1338,1321]) ).
tff(1340,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1339,1321]) ).
tff(1341,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1340,1321]) ).
tff(1342,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1341,1321]) ).
tff(1343,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1342,1321]) ).
tff(1344,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1343,1321]) ).
tff(1345,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = e13,
inference(unit_resolution,[status(thm)],[1344,1320,1220,1306]) ).
tff(1346,plain,
h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = h2(e13),
inference(monotonicity,[status(thm)],[1345]) ).
tff(1347,plain,
h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))),
inference(transitivity,[status(thm)],[1346,1296,1295]) ).
tff(1348,plain,
op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) = op2(h4(e13),h4(e13)),
inference(monotonicity,[status(thm)],[287,287]) ).
tff(1349,plain,
op2(h4(e13),h4(e13)) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))),
inference(symmetry,[status(thm)],[1348]) ).
tff(1350,plain,
( ( h2(e13) = e21 )
<=> ( h2(e13) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1351,plain,
( ( h2(e13) = e21 )
<=> ( h2(e13) = e21 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1352,plain,
h2(e13) = e21,
inference(and_elim,[status(thm)],[725]) ).
tff(1353,plain,
h2(e13) = e21,
inference(modus_ponens,[status(thm)],[1352,1351]) ).
tff(1354,plain,
h2(e13) = op2(h4(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[1353,1350]) ).
tff(1355,plain,
h2(op1(op1(e13,e13),op1(e13,e13))) = h2(e13),
inference(monotonicity,[status(thm)],[1256]) ).
tff(1356,plain,
h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))),
inference(transitivity,[status(thm)],[1355,1354,1349]) ).
tff(1357,plain,
( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) != h3(e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(1358,plain,
( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) ),
inference(unit_resolution,[status(thm)],[1357,439]) ).
tff(1359,plain,
( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) )
| ( h2(op1(e13,e13)) != h4(e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(1360,plain,
( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ),
inference(unit_resolution,[status(thm)],[1359,276]) ).
tff(1361,plain,
( ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1362,plain,
( ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| $false
| ( op2(h1(e13),h2(e13)) = h3(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1363,plain,
( ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| $false
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[808]) ).
tff(1364,plain,
( ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[1363,1362]) ).
tff(1365,plain,
( ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1366,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) )
<=> ( op2(h1(e13),h2(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1367,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[179,917,823,1366]) ).
tff(1368,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[1367,1365]) ).
tff(1369,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1370,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1371,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1372,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[184,1371,923,831]) ).
tff(1373,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[1372,1370]) ).
tff(1374,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1375,plain,
( ( op2(e20,e21) = e22 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1376,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[206,1375,930,837]) ).
tff(1377,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[1376,1374]) ).
tff(1378,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1379,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1380,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1381,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ) ),
inference(monotonicity,[status(thm)],[1380]) ).
tff(1382,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ) ),
inference(transitivity,[status(thm)],[1381,1379]) ).
tff(1383,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) ) ),
inference(and_elim,[status(thm)],[1021]) ).
tff(1384,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ) ),
inference(and_elim,[status(thm)],[1383]) ).
tff(1385,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ) ),
inference(and_elim,[status(thm)],[1384]) ).
tff(1386,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) ) ),
inference(and_elim,[status(thm)],[1385]) ).
tff(1387,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) ) ),
inference(and_elim,[status(thm)],[1386]) ).
tff(1388,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) ) ),
inference(and_elim,[status(thm)],[1387]) ).
tff(1389,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ) ),
inference(and_elim,[status(thm)],[1388]) ).
tff(1390,plain,
( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ),
inference(and_elim,[status(thm)],[1389]) ).
tff(1391,plain,
( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[1390,1382]) ).
tff(1392,plain,
( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[1391,1378]) ).
tff(1393,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1392,1377]) ).
tff(1394,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1393,1374]) ).
tff(1395,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1394,1374]) ).
tff(1396,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1395,1373]) ).
tff(1397,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1396,1369]) ).
tff(1398,plain,
( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1397,1368]) ).
tff(1399,plain,
( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h4(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1398,1365]) ).
tff(1400,plain,
( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1399,1364]) ).
tff(1401,plain,
( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1400,1361]) ).
tff(1402,plain,
( ( h1(op1(e13,e13)) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h1(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1401,1361]) ).
tff(1403,plain,
op2(h1(e13),h2(e13)) = h3(e13),
inference(unit_resolution,[status(thm)],[1402,898,173]) ).
tff(1404,plain,
op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) = op2(h1(e13),h2(e13)),
inference(monotonicity,[status(thm)],[427]) ).
tff(1405,plain,
op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) = h3(e13),
inference(transitivity,[status(thm)],[1404,1403]) ).
tff(1406,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1407,plain,
( ( op1(e12,e13) = e10 )
<=> ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1408,plain,
( ( op1(e11,e13) = e10 )
<=> ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1409,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(monotonicity,[status(thm)],[758,1408,1407,559]) ).
tff(1410,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(transitivity,[status(thm)],[1409,1406]) ).
tff(1411,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1412,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1413,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 ) )
<=> ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1414,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(monotonicity,[status(thm)],[1413]) ).
tff(1415,plain,
( ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(transitivity,[status(thm)],[1414,1412]) ).
tff(1416,plain,
( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) ),
inference(and_elim,[status(thm)],[680]) ).
tff(1417,plain,
( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[1416,1415]) ).
tff(1418,plain,
( ( op1(e10,e13) = e10 )
| ( op1(e11,e13) = e10 )
| ( op1(e12,e13) = e10 )
| ( op1(e13,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[1417,1411]) ).
tff(1419,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1418,1410]) ).
tff(1420,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1419,1406]) ).
tff(1421,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1420,1406]) ).
tff(1422,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1421,1406]) ).
tff(1423,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1422,1406]) ).
tff(1424,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1423,1406]) ).
tff(1425,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1424,1406]) ).
tff(1426,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1425,1406]) ).
tff(1427,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1426,1406]) ).
tff(1428,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(e13,e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1427,1406]) ).
tff(1429,plain,
op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)),
inference(unit_resolution,[status(thm)],[1428,744,506,599]) ).
tff(1430,plain,
h2(op1(op1(op1(e13,e13),e13),e13)) = h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),
inference(monotonicity,[status(thm)],[1429]) ).
tff(1431,plain,
h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),
inference(transitivity,[status(thm)],[1430,730]) ).
tff(1432,plain,
( ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
<=> ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) ) ),
inference(monotonicity,[status(thm)],[1431,1405]) ).
tff(1433,plain,
( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
<=> ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) ) ),
inference(symmetry,[status(thm)],[1432]) ).
tff(1434,plain,
h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)),
inference(modus_ponens,[status(thm)],[439,1433]) ).
tff(1435,plain,
( ( h3(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( h3(e13) = op2(h2(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1436,plain,
( ( h3(e13) = e22 )
<=> ( h3(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1437,plain,
( ( h3(e13) = e22 )
<=> ( h3(e13) = e22 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1438,plain,
( ( h3(e13) = e22 )
& ( h3(e10) = op2(op2(e22,e22),op2(op2(e22,e22),e22)) ) ),
inference(and_elim,[status(thm)],[24]) ).
tff(1439,plain,
h3(e13) = e22,
inference(and_elim,[status(thm)],[1438]) ).
tff(1440,plain,
h3(e13) = e22,
inference(modus_ponens,[status(thm)],[1439,1437]) ).
tff(1441,plain,
h3(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[1440,1436]) ).
tff(1442,plain,
h3(e13) = op2(h2(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[1441,1435]) ).
tff(1443,plain,
op2(h2(e13),h4(e13)) = h3(e13),
inference(symmetry,[status(thm)],[1442]) ).
tff(1444,plain,
op2(h2(e13),h2(op1(e13,e13))) = op2(h2(e13),h4(e13)),
inference(monotonicity,[status(thm)],[276]) ).
tff(1445,plain,
op2(h2(e13),h2(op1(e13,e13))) = h3(e13),
inference(transitivity,[status(thm)],[1444,1443]) ).
tff(1446,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(op1(e13,e13),e13)) )
<=> ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1447,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,op1(op1(e13,e13),e13)) )
<=> ( op1(e13,op1(op1(e13,e13),e13)) != op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(monotonicity,[status(thm)],[1446]) ).
tff(1448,plain,
( ( op1(e11,e12) != op1(e13,e12) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1449,plain,
( ( op1(e11,e12) != op1(e13,e12) )
<=> ( op1(e11,e12) != op1(e13,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1450,plain,
op1(e11,e12) != op1(e13,e12),
inference(and_elim,[status(thm)],[542]) ).
tff(1451,plain,
op1(e11,e12) != op1(e13,e12),
inference(modus_ponens,[status(thm)],[1450,1449]) ).
tff(1452,plain,
op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[1451,1448]) ).
tff(1453,plain,
op1(e13,op1(op1(e13,e13),e13)) != op1(op1(e13,e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[1452,1447]) ).
tff(1454,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) )
<=> ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1455,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) ) ),
inference(monotonicity,[status(thm)],[588]) ).
tff(1456,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) )
<=> ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(transitivity,[status(thm)],[1455,1454]) ).
tff(1457,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) )
<=> ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(monotonicity,[status(thm)],[1456]) ).
tff(1458,plain,
( ( op1(e10,e10) != op1(e13,e10) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1459,plain,
( ( op1(e10,e10) != op1(e13,e10) )
<=> ( op1(e10,e10) != op1(e13,e10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1460,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) ) ),
inference(and_elim,[status(thm)],[1316]) ).
tff(1461,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) ) ),
inference(and_elim,[status(thm)],[1460]) ).
tff(1462,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) ) ),
inference(and_elim,[status(thm)],[1461]) ).
tff(1463,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) ) ),
inference(and_elim,[status(thm)],[1462]) ).
tff(1464,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) ) ),
inference(and_elim,[status(thm)],[1463]) ).
tff(1465,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) ) ),
inference(and_elim,[status(thm)],[1464]) ).
tff(1466,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) ) ),
inference(and_elim,[status(thm)],[1465]) ).
tff(1467,plain,
op1(e10,e10) != op1(e13,e10),
inference(and_elim,[status(thm)],[1466]) ).
tff(1468,plain,
op1(e10,e10) != op1(e13,e10),
inference(modus_ponens,[status(thm)],[1467,1459]) ).
tff(1469,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))),
inference(modus_ponens,[status(thm)],[1468,1458]) ).
tff(1470,plain,
op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(e13,e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[1469,1457]) ).
tff(1471,plain,
( ( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) )
<=> ( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1472,plain,
( ( op1(e13,e12) = e10 )
<=> ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1473,plain,
( ( op1(e13,e11) = e10 )
<=> ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1474,plain,
( ( op1(e13,e10) = e10 )
<=> ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1475,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(monotonicity,[status(thm)],[1474,1473,1472,559]) ).
tff(1476,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ) ),
inference(transitivity,[status(thm)],[1475,1471]) ).
tff(1477,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1478,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1479,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 ) )
<=> ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1480,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(monotonicity,[status(thm)],[1479]) ).
tff(1481,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) )
<=> ( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) ) ),
inference(transitivity,[status(thm)],[1480,1478]) ).
tff(1482,plain,
( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) ),
inference(and_elim,[status(thm)],[681]) ).
tff(1483,plain,
( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[1482,1481]) ).
tff(1484,plain,
( ( op1(e13,e10) = e10 )
| ( op1(e13,e11) = e10 )
| ( op1(e13,e12) = e10 )
| ( op1(e13,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[1483,1477]) ).
tff(1485,plain,
( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1484,1476]) ).
tff(1486,plain,
( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1485,1471]) ).
tff(1487,plain,
( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1486,1471]) ).
tff(1488,plain,
( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1487,1471]) ).
tff(1489,plain,
( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1488,1471]) ).
tff(1490,plain,
( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1489,1471]) ).
tff(1491,plain,
( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1490,1471]) ).
tff(1492,plain,
( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1491,1471]) ).
tff(1493,plain,
( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1492,1471]) ).
tff(1494,plain,
( ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,e13) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(modus_ponens,[status(thm)],[1493,1471]) ).
tff(1495,plain,
op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)),
inference(unit_resolution,[status(thm)],[1494,1470,1453,506]) ).
tff(1496,plain,
h2(op1(e13,op1(e13,e13))) = h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),
inference(monotonicity,[status(thm)],[1495]) ).
tff(1497,plain,
h2(op1(e13,op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),
inference(transitivity,[status(thm)],[1496,730]) ).
tff(1498,plain,
( ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
<=> ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) ) ),
inference(monotonicity,[status(thm)],[1497,1445]) ).
tff(1499,plain,
( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
<=> ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) ) ),
inference(symmetry,[status(thm)],[1498]) ).
tff(1500,plain,
h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))),
inference(modus_ponens,[status(thm)],[439,1499]) ).
tff(1501,plain,
op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) = op2(h2(e13),h3(e13)),
inference(monotonicity,[status(thm)],[439]) ).
tff(1502,plain,
op2(h2(e13),h3(e13)) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))),
inference(symmetry,[status(thm)],[1501]) ).
tff(1503,plain,
( ( h1(e13) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( h1(e13) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1504,plain,
( ( h1(e13) = e20 )
<=> ( h1(e13) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1505,plain,
( ( h1(e13) = e20 )
<=> ( h1(e13) = e20 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1506,plain,
( ( h1(e13) = e20 )
& ( h1(e10) = op2(op2(e20,e20),op2(op2(e20,e20),e20)) ) ),
inference(and_elim,[status(thm)],[137]) ).
tff(1507,plain,
h1(e13) = e20,
inference(and_elim,[status(thm)],[1506]) ).
tff(1508,plain,
h1(e13) = e20,
inference(modus_ponens,[status(thm)],[1507,1505]) ).
tff(1509,plain,
h1(e13) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[1508,1504]) ).
tff(1510,plain,
h1(e13) = op2(h2(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[1509,1503]) ).
tff(1511,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(monotonicity,[status(thm)],[642]) ).
tff(1512,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(e13,e13),e13) ) ),
inference(monotonicity,[status(thm)],[1511]) ).
tff(1513,plain,
( ( op1(e12,e10) != op1(e12,e12) )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1514,plain,
( ( op1(e12,e10) != op1(e12,e12) )
<=> ( op1(e12,e10) != op1(e12,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1515,plain,
op1(e12,e10) != op1(e12,e12),
inference(and_elim,[status(thm)],[521]) ).
tff(1516,plain,
op1(e12,e10) != op1(e12,e12),
inference(modus_ponens,[status(thm)],[1515,1514]) ).
tff(1517,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[1516,1513]) ).
tff(1518,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[1517,1512]) ).
tff(1519,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1520,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| $false
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1521,plain,
( ( op1(e11,e10) != op1(e11,e13) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1522,plain,
( ( op1(e11,e10) != op1(e11,e13) )
<=> ( op1(e11,e10) != op1(e11,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1523,plain,
op1(e11,e10) != op1(e11,e13),
inference(and_elim,[status(thm)],[526]) ).
tff(1524,plain,
op1(e11,e10) != op1(e11,e13),
inference(modus_ponens,[status(thm)],[1523,1522]) ).
tff(1525,plain,
op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[1524,1521]) ).
tff(1526,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1525]) ).
tff(1527,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| $false
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ) ),
inference(monotonicity,[status(thm)],[1526]) ).
tff(1528,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[1527,1520]) ).
tff(1529,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1530,plain,
( ( op1(e13,e10) = e12 )
<=> ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1531,plain,
( ( op1(e12,e10) = e12 )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1532,plain,
( ( op1(e11,e10) = e12 )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1533,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ) ),
inference(monotonicity,[status(thm)],[621,1532,1531,1530]) ).
tff(1534,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[1533,1529]) ).
tff(1535,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1536,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1537,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1538,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) ) ),
inference(monotonicity,[status(thm)],[1537]) ).
tff(1539,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) ) ),
inference(transitivity,[status(thm)],[1538,1536]) ).
tff(1540,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) ),
inference(and_elim,[status(thm)],[700]) ).
tff(1541,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) ),
inference(modus_ponens,[status(thm)],[1540,1539]) ).
tff(1542,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) ),
inference(modus_ponens,[status(thm)],[1541,1535]) ).
tff(1543,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1542,1534]) ).
tff(1544,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1543,1529]) ).
tff(1545,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1544,1529]) ).
tff(1546,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1545,1528]) ).
tff(1547,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1546,1519]) ).
tff(1548,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1547,1519]) ).
tff(1549,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1548,1519]) ).
tff(1550,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1549,1519]) ).
tff(1551,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1550,1519]) ).
tff(1552,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1551,1519]) ).
tff(1553,plain,
op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op1(op1(e13,e13),e13),
inference(unit_resolution,[status(thm)],[1552,1518,600]) ).
tff(1554,plain,
h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = h2(op1(op1(e13,e13),e13)),
inference(monotonicity,[status(thm)],[1553]) ).
tff(1555,plain,
h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))),
inference(transitivity,[status(thm)],[1554,437,426,379,1510,1502]) ).
tff(1556,plain,
op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) = op2(h1(e13),h1(e13)),
inference(monotonicity,[status(thm)],[427,427]) ).
tff(1557,plain,
op2(h1(e13),h1(e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))),
inference(symmetry,[status(thm)],[1556]) ).
tff(1558,plain,
h1(e13) = op2(h1(e13),h1(e13)),
inference(symmetry,[status(thm)],[131]) ).
tff(1559,plain,
h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = h2(op1(op1(e13,e13),e13)),
inference(monotonicity,[status(thm)],[642]) ).
tff(1560,plain,
h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))),
inference(transitivity,[status(thm)],[1559,437,426,379,1558,1557]) ).
tff(1561,plain,
( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) != h1(e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(1562,plain,
( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) ),
inference(unit_resolution,[status(thm)],[1561,427]) ).
tff(1563,plain,
( ( h2(e13) = op2(h2(e13),h1(e13)) )
<=> ( op2(h2(e13),h1(e13)) = h2(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1564,plain,
op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) = op2(h2(e13),h1(e13)),
inference(monotonicity,[status(thm)],[427]) ).
tff(1565,plain,
( ( op1(op1(e13,e13),e13) = op1(e13,op1(op1(e13,e13),e13)) )
<=> ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1566,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(op1(e13,e13),e13)) )
<=> ( op1(op1(e13,e13),e13) = op1(e13,op1(op1(e13,e13),e13)) ) ),
inference(monotonicity,[status(thm)],[642]) ).
tff(1567,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(op1(e13,e13),e13)) )
<=> ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(transitivity,[status(thm)],[1566,1565]) ).
tff(1568,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(op1(e13,e13),e13)) )
<=> ( op1(e13,op1(op1(e13,e13),e13)) != op1(op1(e13,e13),e13) ) ),
inference(monotonicity,[status(thm)],[1567]) ).
tff(1569,plain,
( ( op1(e12,e12) != op1(e13,e12) )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1570,plain,
( ( op1(e12,e12) != op1(e13,e12) )
<=> ( op1(e12,e12) != op1(e13,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1571,plain,
op1(e12,e12) != op1(e13,e12),
inference(and_elim,[status(thm)],[541]) ).
tff(1572,plain,
op1(e12,e12) != op1(e13,e12),
inference(modus_ponens,[status(thm)],[1571,1570]) ).
tff(1573,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[1572,1569]) ).
tff(1574,plain,
op1(e13,op1(op1(e13,e13),e13)) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[1573,1568]) ).
tff(1575,plain,
( ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1576,plain,
( ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| $false
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1577,plain,
( ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| $false
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1055]) ).
tff(1578,plain,
( ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(transitivity,[status(thm)],[1577,1576]) ).
tff(1579,plain,
( ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1580,plain,
( ( op1(e13,e12) = e13 )
<=> ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1581,plain,
( ( op1(e13,e12) = e12 )
<=> ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1582,plain,
( ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) )
<=> ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1472,1060,1581,1580]) ).
tff(1583,plain,
( ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) )
<=> ( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(transitivity,[status(thm)],[1582,1579]) ).
tff(1584,plain,
( ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) )
<=> ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1585,plain,
( ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) )
<=> ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1586,plain,
( ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 ) )
<=> ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1587,plain,
( ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) )
<=> ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1586]) ).
tff(1588,plain,
( ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) )
<=> ( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) ) ),
inference(transitivity,[status(thm)],[1587,1585]) ).
tff(1589,plain,
( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) ),
inference(and_elim,[status(thm)],[767]) ).
tff(1590,plain,
( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1589,1588]) ).
tff(1591,plain,
( ( op1(e13,e12) = e10 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1590,1584]) ).
tff(1592,plain,
( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1591,1583]) ).
tff(1593,plain,
( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1592,1579]) ).
tff(1594,plain,
( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1593,1579]) ).
tff(1595,plain,
( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1594,1578]) ).
tff(1596,plain,
( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1595,1575]) ).
tff(1597,plain,
( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1596,1575]) ).
tff(1598,plain,
( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1597,1575]) ).
tff(1599,plain,
( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1598,1575]) ).
tff(1600,plain,
( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1599,1575]) ).
tff(1601,plain,
( ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[1600,1575]) ).
tff(1602,plain,
op1(e13,op1(op1(e13,e13),e13)) = e13,
inference(unit_resolution,[status(thm)],[1601,1574,1453]) ).
tff(1603,plain,
h2(op1(e13,op1(op1(e13,e13),e13))) = h2(e13),
inference(monotonicity,[status(thm)],[1602]) ).
tff(1604,plain,
( ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
<=> ( h2(e13) = op2(h2(e13),h1(e13)) ) ),
inference(monotonicity,[status(thm)],[1603,1564]) ).
tff(1605,plain,
( ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
<=> ( op2(h2(e13),h1(e13)) = h2(e13) ) ),
inference(transitivity,[status(thm)],[1604,1563]) ).
tff(1606,plain,
( ( op2(h2(e13),h1(e13)) = h2(e13) )
<=> ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) ) ),
inference(symmetry,[status(thm)],[1605]) ).
tff(1607,plain,
( ( $false
| ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) )
<=> ( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1608,plain,
( ( h1(e13) = h2(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[16]) ).
tff(1609,plain,
( ( ( h1(e13) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) )
<=> ( $false
| ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[1608]) ).
tff(1610,plain,
( ( ( h1(e13) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) )
<=> ( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[1609,1607]) ).
tff(1611,plain,
( ( ( op2(h2(e13),h2(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) )
| $false
| ( h1(e13) = h2(e13) ) )
<=> ( ( h1(e13) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1612,plain,
( ( op2(h2(e13),h3(e13)) = h2(e13) )
<=> ( h1(e13) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1613,plain,
( ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) )
<=> ( h3(e13) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1614,plain,
( ( op2(e21,e23) != op2(e23,e23) )
<=> ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1615,plain,
( ( op2(e21,e23) != op2(e23,e23) )
<=> ( op2(e21,e23) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1616,plain,
op2(e21,e23) != op2(e23,e23),
inference(and_elim,[status(thm)],[64]) ).
tff(1617,plain,
op2(e21,e23) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[1616,1615]) ).
tff(1618,plain,
op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[1617,1614]) ).
tff(1619,plain,
h3(e13) != h2(e13),
inference(modus_ponens,[status(thm)],[1618,1613]) ).
tff(1620,plain,
( ( h3(e13) = h2(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1619]) ).
tff(1621,plain,
( ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) )
<=> ( op2(h2(e13),h1(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1622,plain,
( ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h2(e13),h2(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) )
| $false
| ( h1(e13) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[986,1621,1620,1612]) ).
tff(1623,plain,
( ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) )
<=> ( ( h1(e13) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[1622,1611]) ).
tff(1624,plain,
( ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) )
<=> ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1625,plain,
( ( ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) ) )
<=> ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1626,plain,
( ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
<=> ( h3(e13) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1627,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( op2(h2(e13),h3(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1628,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(h4(e13),h4(e13)) )
<=> ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1629,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) )
<=> ( ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[1628,993,1627,1626]) ).
tff(1630,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) )
<=> ( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[1629,1625]) ).
tff(1631,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1632,plain,
( ( op2(e21,e23) = e21 )
<=> ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1633,plain,
( ( op2(e21,e22) = e21 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1634,plain,
( ( op2(e21,e20) = e21 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1635,plain,
( ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[1634,1000,1633,1632]) ).
tff(1636,plain,
( ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[1635,1631]) ).
tff(1637,plain,
( ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
<=> ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1638,plain,
( ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
<=> ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1639,plain,
( ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 ) )
<=> ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1640,plain,
( ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
<=> ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) ) ),
inference(monotonicity,[status(thm)],[1639]) ).
tff(1641,plain,
( ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
<=> ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) ) ),
inference(transitivity,[status(thm)],[1640,1638]) ).
tff(1642,plain,
( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) ),
inference(and_elim,[status(thm)],[1383]) ).
tff(1643,plain,
( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) ),
inference(modus_ponens,[status(thm)],[1642,1641]) ).
tff(1644,plain,
( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) ),
inference(modus_ponens,[status(thm)],[1643,1637]) ).
tff(1645,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1644,1636]) ).
tff(1646,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1645,1631]) ).
tff(1647,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1646,1631]) ).
tff(1648,plain,
( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1647,1630]) ).
tff(1649,plain,
( ( h2(op1(e13,e13)) = h2(e13) )
| ( op2(h2(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1648,1624]) ).
tff(1650,plain,
( ( h1(e13) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1649,1623]) ).
tff(1651,plain,
( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h2(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1650,1610]) ).
tff(1652,plain,
op2(h2(e13),h1(e13)) = h2(e13),
inference(unit_resolution,[status(thm)],[1651,974]) ).
tff(1653,plain,
h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))),
inference(modus_ponens,[status(thm)],[1652,1606]) ).
tff(1654,plain,
op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) = op2(h1(e13),h4(e13)),
inference(monotonicity,[status(thm)],[427,287]) ).
tff(1655,plain,
op2(h1(e13),h4(e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))),
inference(symmetry,[status(thm)],[1654]) ).
tff(1656,plain,
h4(e13) = op2(h1(e13),h4(e13)),
inference(symmetry,[status(thm)],[872]) ).
tff(1657,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) ) ),
inference(monotonicity,[status(thm)],[1084]) ).
tff(1658,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) != op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) != op1(e13,e13) ) ),
inference(monotonicity,[status(thm)],[1657]) ).
tff(1659,plain,
( ( op1(e10,e11) != op1(e10,e12) )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) != op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1660,plain,
( ( op1(e10,e11) != op1(e10,e12) )
<=> ( op1(e10,e11) != op1(e10,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1661,plain,
op1(e10,e11) != op1(e10,e12),
inference(and_elim,[status(thm)],[531]) ).
tff(1662,plain,
op1(e10,e11) != op1(e10,e12),
inference(modus_ponens,[status(thm)],[1661,1660]) ).
tff(1663,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) != op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[1662,1659]) ).
tff(1664,plain,
op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1663,1658]) ).
tff(1665,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1666,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| $false )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1667,plain,
( ( op1(e13,e11) != op1(e13,e13) )
<=> ( op1(e13,op1(e13,e13)) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1668,plain,
( ( op1(e13,e11) != op1(e13,e13) )
<=> ( op1(e13,e11) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1669,plain,
op1(e13,e11) != op1(e13,e13),
inference(and_elim,[status(thm)],[512]) ).
tff(1670,plain,
op1(e13,e11) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1669,1668]) ).
tff(1671,plain,
op1(e13,op1(e13,e13)) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1670,1667]) ).
tff(1672,plain,
( ( op1(e13,op1(e13,e13)) = op1(e13,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1671]) ).
tff(1673,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| $false ) ),
inference(monotonicity,[status(thm)],[1672]) ).
tff(1674,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(transitivity,[status(thm)],[1673,1666]) ).
tff(1675,plain,
( ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1676,plain,
( ( op1(e13,e11) = e11 )
<=> ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1677,plain,
( ( op1(e12,e11) = e11 )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1678,plain,
( ( op1(e10,e11) = e11 )
<=> ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1679,plain,
( ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(monotonicity,[status(thm)],[1678,1269,1677,1676]) ).
tff(1680,plain,
( ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
<=> ( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(transitivity,[status(thm)],[1679,1675]) ).
tff(1681,plain,
( ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
<=> ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1682,plain,
( ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
<=> ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1683,plain,
( ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 ) )
<=> ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1684,plain,
( ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
<=> ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) ) ),
inference(monotonicity,[status(thm)],[1683]) ).
tff(1685,plain,
( ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) )
<=> ( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) ) ),
inference(transitivity,[status(thm)],[1684,1682]) ).
tff(1686,plain,
( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) ),
inference(and_elim,[status(thm)],[694]) ).
tff(1687,plain,
( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) ),
inference(modus_ponens,[status(thm)],[1686,1685]) ).
tff(1688,plain,
( ( op1(e10,e11) = e11 )
| ( op1(e11,e11) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e13,e11) = e11 ) ),
inference(modus_ponens,[status(thm)],[1687,1681]) ).
tff(1689,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1688,1680]) ).
tff(1690,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1689,1675]) ).
tff(1691,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1690,1675]) ).
tff(1692,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1691,1674]) ).
tff(1693,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1692,1665]) ).
tff(1694,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1693,1665]) ).
tff(1695,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1694,1665]) ).
tff(1696,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1695,1665]) ).
tff(1697,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1696,1665]) ).
tff(1698,plain,
( ( op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1697,1665]) ).
tff(1699,plain,
op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13),
inference(unit_resolution,[status(thm)],[1698,1261,1664]) ).
tff(1700,plain,
h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = h2(op1(e13,e13)),
inference(monotonicity,[status(thm)],[1699]) ).
tff(1701,plain,
h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))),
inference(transitivity,[status(thm)],[1700,276,1656,1655]) ).
tff(1702,plain,
( ~ ~ ( ~ ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
| ~ ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(e13,op1(e13,e13))) != op2(h2(e13),h2(op1(e13,e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),e13)) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
| ~ ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) )
| ( h2(op1(e13,op1(op1(e13,e13),e13))) != op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(e13,e13),op1(e13,e13))) != op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) != op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) ) )
<=> ( ~ ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
| ~ ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(e13,op1(e13,e13))) != op2(h2(e13),h2(op1(e13,e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),e13)) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
| ~ ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) )
| ( h2(op1(e13,op1(op1(e13,e13),e13))) != op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(e13,e13),op1(e13,e13))) != op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) != op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1703,plain,
( ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) )
<=> ~ ( ~ ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
| ~ ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(e13,op1(e13,e13))) != op2(h2(e13),h2(op1(e13,e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),e13)) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
| ~ ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) )
| ( h2(op1(e13,op1(op1(e13,e13),e13))) != op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(e13,e13),op1(e13,e13))) != op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) != op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1704,plain,
( ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) )
<=> ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1705,plain,
( ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
<=> ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1706,plain,
( ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1707,plain,
( ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) )
<=> ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[1706,1705,1704]) ).
tff(1708,plain,
( ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) )
<=> ~ ( ~ ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
| ~ ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(e13,op1(e13,e13))) != op2(h2(e13),h2(op1(e13,e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),e13)) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
| ~ ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) )
| ( h2(op1(e13,op1(op1(e13,e13),e13))) != op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(e13,e13),op1(e13,e13))) != op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) != op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) ) ) ),
inference(transitivity,[status(thm)],[1707,1703]) ).
tff(1709,plain,
( ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) )
<=> ~ ~ ( ~ ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
| ~ ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(e13,op1(e13,e13))) != op2(h2(e13),h2(op1(e13,e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),e13)) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
| ~ ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) )
| ( h2(op1(e13,op1(op1(e13,e13),e13))) != op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(e13,e13),op1(e13,e13))) != op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) != op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) ) ) ),
inference(monotonicity,[status(thm)],[1708]) ).
tff(1710,plain,
( ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) )
<=> ( ~ ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
| ~ ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(e13,op1(e13,e13))) != op2(h2(e13),h2(op1(e13,e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),e13)) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
| ~ ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) )
| ( h2(op1(e13,op1(op1(e13,e13),e13))) != op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(e13,e13),op1(e13,e13))) != op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) != op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) ) ) ),
inference(transitivity,[status(thm)],[1709,1702]) ).
tff(1711,plain,
( ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) )
<=> ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1712,plain,
( ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) )
<=> ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[1711]) ).
tff(1713,plain,
( ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(e13),h2(e13)) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) )
<=> ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1714,plain,
( ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(e13),h2(e13)) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) )
<=> ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(e13),h2(e13)) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1715,plain,
( ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(e13),h2(e13)) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) )
<=> ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(e13),h2(e13)) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[1714]) ).
tff(1716,plain,
( ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = h1(e13) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h1(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h1(e13) )
| ( h2(e13) = h1(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h3(e13) )
| ( h2(op1(e13,e13)) = h3(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h3(e13) )
| ( h2(e13) = h3(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) )
<=> ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(e13),h2(e13)) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1717,plain,
( ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = h1(e13) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h1(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h1(e13) )
| ( h2(e13) = h1(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h3(e13) )
| ( h2(op1(e13,e13)) = h3(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h3(e13) )
| ( h2(e13) = h3(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) )
<=> ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = h1(e13) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h1(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h1(e13) )
| ( h2(e13) = h1(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h3(e13) )
| ( h2(op1(e13,e13)) = h3(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h3(e13) )
| ( h2(e13) = h3(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1718,plain,
( ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = h1(e13) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h1(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h1(e13) )
| ( h2(e13) = h1(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h3(e13) )
| ( h2(op1(e13,e13)) = h3(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h3(e13) )
| ( h2(e13) = h3(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) )
<=> ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = h1(e13) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h1(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h1(e13) )
| ( h2(e13) = h1(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h3(e13) )
| ( h2(op1(e13,e13)) = h3(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h3(e13) )
| ( h2(e13) = h3(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[1717]) ).
tff(1719,plain,
( ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) )
<=> ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = h1(e13) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h1(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h1(e13) )
| ( h2(e13) = h1(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h3(e13) )
| ( h2(op1(e13,e13)) = h3(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h3(e13) )
| ( h2(e13) = h3(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1720,plain,
( ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) )
<=> ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1721,plain,
( ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) )
<=> ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[1720]) ).
tff(1722,plain,
( ~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
<=> ~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1723,plain,
( ~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
<=> ~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1724,plain,
( ~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e13) = e21 )
| ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
<=> ~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1725,plain,
( ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e13) = e21 )
| ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
<=> ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e13) = e21 )
| ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1726,plain,
( ~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e13) = e21 )
| ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
<=> ~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e13) = e21 )
| ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) ) ),
inference(monotonicity,[status(thm)],[1725]) ).
tff(1727,plain,
( ~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 )
| ( h2(e13) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
<=> ~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e13) = e21 )
| ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1728,axiom,
~ ( ( ( h1(op1(e10,e10)) = op2(h1(e10),h1(e10)) )
& ( h1(op1(e10,e11)) = op2(h1(e10),h1(e11)) )
& ( h1(op1(e10,e12)) = op2(h1(e10),h1(e12)) )
& ( h1(op1(e10,e13)) = op2(h1(e10),h1(e13)) )
& ( h1(op1(e11,e10)) = op2(h1(e11),h1(e10)) )
& ( h1(op1(e11,e11)) = op2(h1(e11),h1(e11)) )
& ( h1(op1(e11,e12)) = op2(h1(e11),h1(e12)) )
& ( h1(op1(e11,e13)) = op2(h1(e11),h1(e13)) )
& ( h1(op1(e12,e10)) = op2(h1(e12),h1(e10)) )
& ( h1(op1(e12,e11)) = op2(h1(e12),h1(e11)) )
& ( h1(op1(e12,e12)) = op2(h1(e12),h1(e12)) )
& ( h1(op1(e12,e13)) = op2(h1(e12),h1(e13)) )
& ( h1(op1(e13,e10)) = op2(h1(e13),h1(e10)) )
& ( h1(op1(e13,e11)) = op2(h1(e13),h1(e11)) )
& ( h1(op1(e13,e12)) = op2(h1(e13),h1(e12)) )
& ( h1(op1(e13,e13)) = op2(h1(e13),h1(e13)) )
& ( ( h1(e10) = e20 )
| ( h1(e11) = e20 )
| ( h1(e12) = e20 )
| ( h1(e13) = e20 ) )
& ( ( h1(e10) = e21 )
| ( h1(e11) = e21 )
| ( h1(e12) = e21 )
| ( h1(e13) = e21 ) )
& ( ( h1(e10) = e22 )
| ( h1(e11) = e22 )
| ( h1(e12) = e22 )
| ( h1(e13) = e22 ) )
& ( ( h1(e10) = e23 )
| ( h1(e11) = e23 )
| ( h1(e12) = e23 )
| ( h1(e13) = e23 ) ) )
| ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 )
| ( h2(e13) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
| ( ( h3(op1(e10,e10)) = op2(h3(e10),h3(e10)) )
& ( h3(op1(e10,e11)) = op2(h3(e10),h3(e11)) )
& ( h3(op1(e10,e12)) = op2(h3(e10),h3(e12)) )
& ( h3(op1(e10,e13)) = op2(h3(e10),h3(e13)) )
& ( h3(op1(e11,e10)) = op2(h3(e11),h3(e10)) )
& ( h3(op1(e11,e11)) = op2(h3(e11),h3(e11)) )
& ( h3(op1(e11,e12)) = op2(h3(e11),h3(e12)) )
& ( h3(op1(e11,e13)) = op2(h3(e11),h3(e13)) )
& ( h3(op1(e12,e10)) = op2(h3(e12),h3(e10)) )
& ( h3(op1(e12,e11)) = op2(h3(e12),h3(e11)) )
& ( h3(op1(e12,e12)) = op2(h3(e12),h3(e12)) )
& ( h3(op1(e12,e13)) = op2(h3(e12),h3(e13)) )
& ( h3(op1(e13,e10)) = op2(h3(e13),h3(e10)) )
& ( h3(op1(e13,e11)) = op2(h3(e13),h3(e11)) )
& ( h3(op1(e13,e12)) = op2(h3(e13),h3(e12)) )
& ( h3(op1(e13,e13)) = op2(h3(e13),h3(e13)) )
& ( ( h3(e10) = e20 )
| ( h3(e11) = e20 )
| ( h3(e12) = e20 )
| ( h3(e13) = e20 ) )
& ( ( h3(e10) = e21 )
| ( h3(e11) = e21 )
| ( h3(e12) = e21 )
| ( h3(e13) = e21 ) )
& ( ( h3(e10) = e22 )
| ( h3(e11) = e22 )
| ( h3(e12) = e22 )
| ( h3(e13) = e22 ) )
& ( ( h3(e10) = e23 )
| ( h3(e11) = e23 )
| ( h3(e12) = e23 )
| ( h3(e13) = e23 ) ) )
| ( ( h4(op1(e10,e10)) = op2(h4(e10),h4(e10)) )
& ( h4(op1(e10,e11)) = op2(h4(e10),h4(e11)) )
& ( h4(op1(e10,e12)) = op2(h4(e10),h4(e12)) )
& ( h4(op1(e10,e13)) = op2(h4(e10),h4(e13)) )
& ( h4(op1(e11,e10)) = op2(h4(e11),h4(e10)) )
& ( h4(op1(e11,e11)) = op2(h4(e11),h4(e11)) )
& ( h4(op1(e11,e12)) = op2(h4(e11),h4(e12)) )
& ( h4(op1(e11,e13)) = op2(h4(e11),h4(e13)) )
& ( h4(op1(e12,e10)) = op2(h4(e12),h4(e10)) )
& ( h4(op1(e12,e11)) = op2(h4(e12),h4(e11)) )
& ( h4(op1(e12,e12)) = op2(h4(e12),h4(e12)) )
& ( h4(op1(e12,e13)) = op2(h4(e12),h4(e13)) )
& ( h4(op1(e13,e10)) = op2(h4(e13),h4(e10)) )
& ( h4(op1(e13,e11)) = op2(h4(e13),h4(e11)) )
& ( h4(op1(e13,e12)) = op2(h4(e13),h4(e12)) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(e10) = e20 )
| ( h4(e11) = e20 )
| ( h4(e12) = e20 )
| ( h4(e13) = e20 ) )
& ( ( h4(e10) = e21 )
| ( h4(e11) = e21 )
| ( h4(e12) = e21 )
| ( h4(e13) = e21 ) )
& ( ( h4(e10) = e22 )
| ( h4(e11) = e22 )
| ( h4(e12) = e22 )
| ( h4(e13) = e22 ) )
& ( ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 )
| ( h4(e13) = e23 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(1729,plain,
~ ( ( ( h1(op1(e10,e10)) = op2(h1(e10),h1(e10)) )
& ( h1(op1(e10,e11)) = op2(h1(e10),h1(e11)) )
& ( h1(op1(e10,e12)) = op2(h1(e10),h1(e12)) )
& ( h1(op1(e10,e13)) = op2(h1(e10),h1(e13)) )
& ( h1(op1(e11,e10)) = op2(h1(e11),h1(e10)) )
& ( h1(op1(e11,e11)) = op2(h1(e11),h1(e11)) )
& ( h1(op1(e11,e12)) = op2(h1(e11),h1(e12)) )
& ( h1(op1(e11,e13)) = op2(h1(e11),h1(e13)) )
& ( h1(op1(e12,e10)) = op2(h1(e12),h1(e10)) )
& ( h1(op1(e12,e11)) = op2(h1(e12),h1(e11)) )
& ( h1(op1(e12,e12)) = op2(h1(e12),h1(e12)) )
& ( h1(op1(e12,e13)) = op2(h1(e12),h1(e13)) )
& ( h1(op1(e13,e10)) = op2(h1(e13),h1(e10)) )
& ( h1(op1(e13,e11)) = op2(h1(e13),h1(e11)) )
& ( h1(op1(e13,e12)) = op2(h1(e13),h1(e12)) )
& ( h1(op1(e13,e13)) = op2(h1(e13),h1(e13)) )
& ( ( h1(e10) = e20 )
| ( h1(e11) = e20 )
| ( h1(e12) = e20 )
| ( h1(e13) = e20 ) )
& ( ( h1(e10) = e21 )
| ( h1(e11) = e21 )
| ( h1(e12) = e21 )
| ( h1(e13) = e21 ) )
& ( ( h1(e10) = e22 )
| ( h1(e11) = e22 )
| ( h1(e12) = e22 )
| ( h1(e13) = e22 ) )
& ( ( h1(e10) = e23 )
| ( h1(e11) = e23 )
| ( h1(e12) = e23 )
| ( h1(e13) = e23 ) ) )
| ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 )
| ( h2(e13) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
| ( ( h3(op1(e10,e10)) = op2(h3(e10),h3(e10)) )
& ( h3(op1(e10,e11)) = op2(h3(e10),h3(e11)) )
& ( h3(op1(e10,e12)) = op2(h3(e10),h3(e12)) )
& ( h3(op1(e10,e13)) = op2(h3(e10),h3(e13)) )
& ( h3(op1(e11,e10)) = op2(h3(e11),h3(e10)) )
& ( h3(op1(e11,e11)) = op2(h3(e11),h3(e11)) )
& ( h3(op1(e11,e12)) = op2(h3(e11),h3(e12)) )
& ( h3(op1(e11,e13)) = op2(h3(e11),h3(e13)) )
& ( h3(op1(e12,e10)) = op2(h3(e12),h3(e10)) )
& ( h3(op1(e12,e11)) = op2(h3(e12),h3(e11)) )
& ( h3(op1(e12,e12)) = op2(h3(e12),h3(e12)) )
& ( h3(op1(e12,e13)) = op2(h3(e12),h3(e13)) )
& ( h3(op1(e13,e10)) = op2(h3(e13),h3(e10)) )
& ( h3(op1(e13,e11)) = op2(h3(e13),h3(e11)) )
& ( h3(op1(e13,e12)) = op2(h3(e13),h3(e12)) )
& ( h3(op1(e13,e13)) = op2(h3(e13),h3(e13)) )
& ( ( h3(e10) = e20 )
| ( h3(e11) = e20 )
| ( h3(e12) = e20 )
| ( h3(e13) = e20 ) )
& ( ( h3(e10) = e21 )
| ( h3(e11) = e21 )
| ( h3(e12) = e21 )
| ( h3(e13) = e21 ) )
& ( ( h3(e10) = e22 )
| ( h3(e11) = e22 )
| ( h3(e12) = e22 )
| ( h3(e13) = e22 ) )
& ( ( h3(e10) = e23 )
| ( h3(e11) = e23 )
| ( h3(e12) = e23 )
| ( h3(e13) = e23 ) ) ) ),
inference(or_elim,[status(thm)],[1728]) ).
tff(1730,plain,
~ ( ( ( h1(op1(e10,e10)) = op2(h1(e10),h1(e10)) )
& ( h1(op1(e10,e11)) = op2(h1(e10),h1(e11)) )
& ( h1(op1(e10,e12)) = op2(h1(e10),h1(e12)) )
& ( h1(op1(e10,e13)) = op2(h1(e10),h1(e13)) )
& ( h1(op1(e11,e10)) = op2(h1(e11),h1(e10)) )
& ( h1(op1(e11,e11)) = op2(h1(e11),h1(e11)) )
& ( h1(op1(e11,e12)) = op2(h1(e11),h1(e12)) )
& ( h1(op1(e11,e13)) = op2(h1(e11),h1(e13)) )
& ( h1(op1(e12,e10)) = op2(h1(e12),h1(e10)) )
& ( h1(op1(e12,e11)) = op2(h1(e12),h1(e11)) )
& ( h1(op1(e12,e12)) = op2(h1(e12),h1(e12)) )
& ( h1(op1(e12,e13)) = op2(h1(e12),h1(e13)) )
& ( h1(op1(e13,e10)) = op2(h1(e13),h1(e10)) )
& ( h1(op1(e13,e11)) = op2(h1(e13),h1(e11)) )
& ( h1(op1(e13,e12)) = op2(h1(e13),h1(e12)) )
& ( h1(op1(e13,e13)) = op2(h1(e13),h1(e13)) )
& ( ( h1(e10) = e20 )
| ( h1(e11) = e20 )
| ( h1(e12) = e20 )
| ( h1(e13) = e20 ) )
& ( ( h1(e10) = e21 )
| ( h1(e11) = e21 )
| ( h1(e12) = e21 )
| ( h1(e13) = e21 ) )
& ( ( h1(e10) = e22 )
| ( h1(e11) = e22 )
| ( h1(e12) = e22 )
| ( h1(e13) = e22 ) )
& ( ( h1(e10) = e23 )
| ( h1(e11) = e23 )
| ( h1(e12) = e23 )
| ( h1(e13) = e23 ) ) )
| ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 )
| ( h2(e13) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) ) ),
inference(or_elim,[status(thm)],[1729]) ).
tff(1731,plain,
~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 )
| ( h2(e13) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) ),
inference(or_elim,[status(thm)],[1730]) ).
tff(1732,plain,
~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e13) = e21 )
| ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[1731,1727]) ).
tff(1733,plain,
~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e13) = e21 )
| ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[1732,1726]) ).
tff(1734,plain,
~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[1733,1724]) ).
tff(1735,plain,
~ ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[1734,1723]) ).
tff(1736,plain,
~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[1735,1722]) ).
tff(1737,plain,
~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h2(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[1736,1721]) ).
tff(1738,plain,
~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = h1(e13) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h1(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h1(e13) )
| ( h2(e13) = h1(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h3(e13) )
| ( h2(op1(e13,e13)) = h3(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h3(e13) )
| ( h2(e13) = h3(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[1737,1719]) ).
tff(1739,plain,
~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(h2(op1(e13,e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(e13,e13),e13)) = op2(h2(op1(e13,e13)),h2(e13)) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(e13,e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(op1(op1(e13,e13),e13)),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(op1(op1(e13,e13),e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),h2(op1(op1(e13,e13),op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),h2(op1(op1(e13,e13),e13))) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(op1(e13,e13)) = h1(e13) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h1(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h1(e13) )
| ( h2(e13) = h1(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h3(e13) )
| ( h2(op1(e13,e13)) = h3(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h3(e13) )
| ( h2(e13) = h3(e13) ) )
& ( ( h2(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(e13) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h2(op1(op1(e13,e13),e13)) = h4(e13) )
| ( h2(e13) = h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[1738,1718]) ).
tff(1740,plain,
~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(e13),h2(e13)) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[1739,1716]) ).
tff(1741,plain,
~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(e13),h2(e13)) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[1740,1715]) ).
tff(1742,plain,
~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[1741,1713]) ).
tff(1743,plain,
~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[1742,1712]) ).
tff(1744,plain,
~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[1743,1712]) ).
tff(1745,plain,
~ ( ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) = op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
& ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(e13,e13),op1(e13,e13))) = op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
& ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( h2(op1(op1(op1(e13,e13),e13),e13)) = op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
& ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) = op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
& ( h2(op1(e13,op1(e13,e13))) = op2(h2(e13),h2(op1(e13,e13))) )
& ( h2(op1(e13,op1(op1(e13,e13),e13))) = op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
& ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
& ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
& ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[1744,1712]) ).
tff(1746,plain,
( ~ ( ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h3(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h3(e13) ) )
| ~ ( ( h2(e13) = h1(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h1(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h1(e13) ) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(e13),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(e13,op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(h2(e13),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(e13,op1(e13,e13))) != op2(h2(e13),h2(op1(e13,e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),e13)) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),h2(e13)) )
| ~ ( ( h2(op1(e13,e13)) = h4(e13) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) = h4(e13) )
| ( op2(op2(h2(e13),h2(e13)),h2(e13)) = h4(e13) ) )
| ( h2(op1(e13,op1(op1(e13,e13),e13))) != op2(h2(e13),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(e13,e13),op1(e13,e13))) != op2(op2(h2(e13),h2(e13)),op2(h2(e13),h2(e13))) )
| ( op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))) != op2(op2(h2(e13),h2(e13)),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(op2(h2(e13),h2(e13)),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(e13,e13),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(e13),h2(e13)),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(op2(h2(e13),h2(e13)),h2(e13))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),e13)) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),h2(e13)) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(op1(e13,e13),op1(op1(e13,e13),e13)))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13)))) )
| ( h2(op1(op1(op1(e13,e13),op1(op1(e13,e13),e13)),op1(e13,e13))) != op2(op2(h2(op1(e13,e13)),h2(op1(op1(e13,e13),e13))),op2(h2(e13),h2(e13))) ) ),
inference(modus_ponens,[status(thm)],[1745,1710]) ).
tff(1747,plain,
$false,
inference(unit_resolution,[status(thm)],[1746,1701,1653,1562,1560,1555,1500,1434,1360,1358,1356,438,1347,1293,1155,1036,732,717]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG115+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 13:52:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------