TSTP Solution File: ALG113+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG113+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 16:08:07 EDT 2022
% Result : Theorem 0.12s 0.48s
% Output : Proof 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 470
% Syntax : Number of formulae : 1383 ( 292 unt; 22 typ; 0 def)
% Number of atoms : 13405 (13318 equ)
% Maximal formula atoms : 384 ( 9 avg)
% Number of connectives : 15028 (2984 ~;6550 |;4869 &)
% ( 625 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 16 ( 14 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(op2_type,type,
op2: ( $i * $i ) > $i ).
tff(h1_type,type,
h1: $i > $i ).
tff(e12_type,type,
e12: $i ).
tff(e13_type,type,
e13: $i ).
tff(h9_type,type,
h9: $i > $i ).
tff(op1_type,type,
op1: ( $i * $i ) > $i ).
tff(h4_type,type,
h4: $i > $i ).
tff(h3_type,type,
h3: $i > $i ).
tff(h2_type,type,
h2: $i > $i ).
tff(e20_type,type,
e20: $i ).
tff(e21_type,type,
e21: $i ).
tff(e10_type,type,
e10: $i ).
tff(e11_type,type,
e11: $i ).
tff(h5_type,type,
h5: $i > $i ).
tff(e22_type,type,
e22: $i ).
tff(e23_type,type,
e23: $i ).
tff(h6_type,type,
h6: $i > $i ).
tff(h11_type,type,
h11: $i > $i ).
tff(h8_type,type,
h8: $i > $i ).
tff(h10_type,type,
h10: $i > $i ).
tff(h7_type,type,
h7: $i > $i ).
tff(h12_type,type,
h12: $i > $i ).
tff(1,plain,
( ( h4(op1(e12,e13)) = op2(op2(h1(e12),h3(e13)),h1(e12)) )
<=> ( h4(op1(e12,e13)) = op2(h1(e13),h1(e12)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( h4(op1(e12,e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) )
<=> ( h4(op1(e12,e13)) = op2(op2(h1(e12),h3(e13)),h1(e12)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( h4(e10) = op2(e21,e20) )
<=> ( h4(op1(e12,e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( h4(e10) = op2(e21,e20) )
<=> ( h4(e10) = op2(e21,e20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
( ( h4(e12) = e21 )
& ( h4(e13) = e20 )
& ( h4(e10) = op2(e21,e20) )
& ( h4(e11) = op2(op2(e21,e20),e20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
tff(6,plain,
( ( h4(e12) = e21 )
& ( h4(e13) = e20 )
& ( h4(e10) = op2(e21,e20) ) ),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
h4(e10) = op2(e21,e20),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
h4(e10) = op2(e21,e20),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
h4(op1(e12,e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))),
inference(modus_ponens,[status(thm)],[8,3]) ).
tff(10,plain,
h4(op1(e12,e13)) = op2(op2(h1(e12),h3(e13)),h1(e12)),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
h4(op1(e12,e13)) = op2(h1(e13),h1(e12)),
inference(modus_ponens,[status(thm)],[10,1]) ).
tff(12,plain,
( ( h1(e12) = h3(e13) )
<=> ( h3(e13) = h1(e12) ) ),
inference(commutativity,[status(thm)],]) ).
tff(13,plain,
( ( h1(e12) = op2(h1(e13),h1(e12)) )
<=> ( op2(h1(e13),h1(e12)) = h1(e12) ) ),
inference(commutativity,[status(thm)],]) ).
tff(14,plain,
( ( h1(e12) != op2(h1(e13),h1(e12)) )
<=> ( op2(h1(e13),h1(e12)) != h1(e12) ) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ( h1(e12) != h4(op1(e12,e13)) )
<=> ( h1(e12) != op2(h1(e13),h1(e12)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( op2(h1(e12),h1(e12)) != h4(op1(e12,e13)) )
<=> ( h1(e12) != h4(op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) )
<=> ( op2(h1(e12),h1(e12)) != h4(op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( op2(e20,e20) != op2(e21,e20) )
<=> ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( op2(e20,e20) != op2(e21,e20) )
<=> ( op2(e20,e20) != op2(e21,e20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,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/sandbox/benchmark/theBenchmark.p',ax6) ).
tff(21,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)],[20]) ).
tff(22,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)],[21]) ).
tff(23,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)],[22]) ).
tff(24,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)],[23]) ).
tff(25,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)],[24]) ).
tff(26,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)],[25]) ).
tff(27,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)],[26]) ).
tff(28,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)],[27]) ).
tff(29,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)],[28]) ).
tff(30,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)],[29]) ).
tff(31,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)],[30]) ).
tff(32,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)],[31]) ).
tff(33,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)],[32]) ).
tff(34,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)],[33]) ).
tff(35,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)],[34]) ).
tff(36,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)],[35]) ).
tff(37,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)],[36]) ).
tff(38,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)],[37]) ).
tff(39,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)],[38]) ).
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
inference(and_elim,[status(thm)],[64]) ).
tff(66,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) ) ),
inference(and_elim,[status(thm)],[65]) ).
tff(67,plain,
op2(e20,e20) != op2(e21,e20),
inference(and_elim,[status(thm)],[66]) ).
tff(68,plain,
op2(e20,e20) != op2(e21,e20),
inference(modus_ponens,[status(thm)],[67,19]) ).
tff(69,plain,
op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))),
inference(modus_ponens,[status(thm)],[68,18]) ).
tff(70,plain,
op2(h1(e12),h1(e12)) != h4(op1(e12,e13)),
inference(modus_ponens,[status(thm)],[69,17]) ).
tff(71,plain,
h1(e12) != h4(op1(e12,e13)),
inference(modus_ponens,[status(thm)],[70,16]) ).
tff(72,plain,
h1(e12) != op2(h1(e13),h1(e12)),
inference(modus_ponens,[status(thm)],[71,15]) ).
tff(73,plain,
op2(h1(e13),h1(e12)) != h1(e12),
inference(modus_ponens,[status(thm)],[72,14]) ).
tff(74,plain,
( ( ( op2(h1(e13),h1(e12)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| $false )
<=> ( ( h5(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e12)) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(h2(e13),h3(e13)) )
<=> ( h1(e13) != h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ( op2(e20,e23) != op2(e22,e23) )
<=> ( op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ( op2(e20,e23) != op2(e22,e23) )
<=> ( op2(e20,e23) != op2(e22,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
op2(e20,e23) != op2(e22,e23),
inference(and_elim,[status(thm)],[48]) ).
tff(79,plain,
op2(e20,e23) != op2(e22,e23),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(h2(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[79,76]) ).
tff(81,plain,
h1(e13) != h1(e12),
inference(modus_ponens,[status(thm)],[80,75]) ).
tff(82,plain,
( ( h1(e13) = h1(e12) )
<=> $false ),
inference(iff_false,[status(thm)],[81]) ).
tff(83,plain,
( ( h4(op1(e12,e13)) = h1(e12) )
<=> ( op2(h1(e13),h1(e12)) = h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) ) )
<=> ( ( op2(h1(e13),h1(e12)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| $false ) ),
inference(monotonicity,[status(thm)],[83,82]) ).
tff(85,plain,
( ( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) ) )
<=> ( ( h5(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e12)) = h1(e12) ) ) ),
inference(transitivity,[status(thm)],[84,74]) ).
tff(86,plain,
( ( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) ) )
<=> ( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| $false
| ( h1(e13) = h1(e12) ) )
<=> ( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( op2(h1(e13),h1(e13)) = h1(e12) )
<=> ( h1(e13) = h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) != op2(h2(e13),h3(e13)) )
<=> ( h6(op1(e12,e13)) != h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( op2(e21,e23) != op2(e22,e23) )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) != op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ( op2(e21,e23) != op2(e22,e23) )
<=> ( op2(e21,e23) != op2(e22,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
op2(e21,e23) != op2(e22,e23),
inference(and_elim,[status(thm)],[46]) ).
tff(93,plain,
op2(e21,e23) != op2(e22,e23),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) != op2(h2(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[93,90]) ).
tff(95,plain,
h6(op1(e12,e13)) != h1(e12),
inference(modus_ponens,[status(thm)],[94,89]) ).
tff(96,plain,
( ( h6(op1(e12,e13)) = h1(e12) )
<=> $false ),
inference(iff_false,[status(thm)],[95]) ).
tff(97,plain,
( ( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h6(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) ) )
<=> ( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| $false
| ( h1(e13) = h1(e12) ) ) ),
inference(monotonicity,[status(thm)],[96,88]) ).
tff(98,plain,
( ( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h6(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) ) )
<=> ( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) ) ) ),
inference(transitivity,[status(thm)],[97,87]) ).
tff(99,plain,
( ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) )
<=> ( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h6(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( op2(e21,e23) = e20 )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( op2(e21,e22) = e20 )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( op2(e21,e21) = e20 )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( op2(e21,e20) = e20 )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
<=> ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) ) ) ),
inference(monotonicity,[status(thm)],[105,104,103,102]) ).
tff(107,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
<=> ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[106,101]) ).
tff(108,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,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/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(114,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)],[113]) ).
tff(115,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)],[114]) ).
tff(116,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)],[115]) ).
tff(117,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)],[116]) ).
tff(118,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)],[117]) ).
tff(119,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)],[118]) ).
tff(120,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)],[119]) ).
tff(121,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)],[120]) ).
tff(122,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)],[121]) ).
tff(123,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)],[122]) ).
tff(124,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)],[123]) ).
tff(125,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)],[124]) ).
tff(126,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)],[125]) ).
tff(127,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)],[126]) ).
tff(128,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)],[127]) ).
tff(129,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)],[128]) ).
tff(130,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)],[129]) ).
tff(131,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)],[130]) ).
tff(132,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)],[131]) ).
tff(133,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)],[132]) ).
tff(134,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)],[133]) ).
tff(135,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)],[134]) ).
tff(136,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)],[135]) ).
tff(137,plain,
( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ),
inference(and_elim,[status(thm)],[136]) ).
tff(138,plain,
( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[137,112]) ).
tff(139,plain,
( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[138,108]) ).
tff(140,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[139,107]) ).
tff(141,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[140,100]) ).
tff(142,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[141,100]) ).
tff(143,plain,
( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h6(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[142,99]) ).
tff(144,plain,
( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[143,98]) ).
tff(145,plain,
( ( h4(op1(e12,e13)) = h1(e12) )
| ( h5(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[144,86]) ).
tff(146,plain,
( ( h5(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e12)) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[145,85]) ).
tff(147,plain,
h5(op1(e12,e13)) = h1(e12),
inference(unit_resolution,[status(thm)],[146,73]) ).
tff(148,plain,
( ( h5(op1(e12,e13)) = h3(e13) )
<=> ( h1(e12) = h3(e13) ) ),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ( h5(op1(e12,e13)) = h3(e13) )
<=> ( h3(e13) = h1(e12) ) ),
inference(transitivity,[status(thm)],[148,12]) ).
tff(150,plain,
( ( h3(e13) = h1(e12) )
<=> ( h5(op1(e12,e13)) = h3(e13) ) ),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
( ( h3(e13) != h1(e12) )
<=> ( h5(op1(e12,e13)) != h3(e13) ) ),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ( h1(e12) != h3(e13) )
<=> ( h3(e13) != h1(e12) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(153,plain,
( ( op2(h2(e13),h3(e13)) != op2(h3(e13),h3(e13)) )
<=> ( h1(e12) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(154,plain,
( ( op2(e22,e23) != op2(e23,e23) )
<=> ( op2(h2(e13),h3(e13)) != op2(h3(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(155,plain,
( ( op2(e22,e23) != op2(e23,e23) )
<=> ( op2(e22,e23) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
op2(e22,e23) != op2(e23,e23),
inference(and_elim,[status(thm)],[44]) ).
tff(157,plain,
op2(e22,e23) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
op2(h2(e13),h3(e13)) != op2(h3(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[157,154]) ).
tff(159,plain,
h1(e12) != h3(e13),
inference(modus_ponens,[status(thm)],[158,153]) ).
tff(160,plain,
h3(e13) != h1(e12),
inference(modus_ponens,[status(thm)],[159,152]) ).
tff(161,plain,
h5(op1(e12,e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[160,151]) ).
tff(162,plain,
( ( $false
| ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) ) )
<=> ( ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(163,plain,
( ( op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(h3(e13),h3(e13)) )
<=> ( h1(e13) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(164,plain,
( ( op2(e20,e23) != op2(e23,e23) )
<=> ( op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(h3(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,plain,
( ( op2(e20,e23) != op2(e23,e23) )
<=> ( op2(e20,e23) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(166,plain,
op2(e20,e23) != op2(e23,e23),
inference(and_elim,[status(thm)],[47]) ).
tff(167,plain,
op2(e20,e23) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
op2(op2(h2(e13),h3(e13)),h3(e13)) != op2(h3(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[167,164]) ).
tff(169,plain,
h1(e13) != h3(e13),
inference(modus_ponens,[status(thm)],[168,163]) ).
tff(170,plain,
( ( h1(e13) = h3(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[169]) ).
tff(171,plain,
( ( ( h1(e13) = h3(e13) )
| ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) ) )
<=> ( $false
| ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
( ( ( h1(e13) = h3(e13) )
| ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) ) )
<=> ( ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[171,162]) ).
tff(173,plain,
( ( ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) )
| $false
| ( h1(e13) = h3(e13) ) )
<=> ( ( h1(e13) = h3(e13) )
| ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(174,plain,
( ( op2(h1(e13),h1(e13)) = h3(e13) )
<=> ( h1(e13) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(175,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) != op2(h3(e13),h3(e13)) )
<=> ( h6(op1(e12,e13)) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(176,plain,
( ( op2(e21,e23) != op2(e23,e23) )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) != op2(h3(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(177,plain,
( ( op2(e21,e23) != op2(e23,e23) )
<=> ( op2(e21,e23) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
op2(e21,e23) != op2(e23,e23),
inference(and_elim,[status(thm)],[45]) ).
tff(179,plain,
op2(e21,e23) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) != op2(h3(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[179,176]) ).
tff(181,plain,
h6(op1(e12,e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[180,175]) ).
tff(182,plain,
( ( h6(op1(e12,e13)) = h3(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[181]) ).
tff(183,plain,
( ( ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) )
| ( h6(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e13),h1(e13)) = h3(e13) ) )
<=> ( ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) )
| $false
| ( h1(e13) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[182,174]) ).
tff(184,plain,
( ( ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) )
| ( h6(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e13),h1(e13)) = h3(e13) ) )
<=> ( ( h1(e13) = h3(e13) )
| ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[183,173]) ).
tff(185,plain,
( ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) )
<=> ( ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) )
| ( h6(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e13),h1(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(186,plain,
( ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) )
<=> ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,plain,
( ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) ) )
<=> ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(188,plain,
( ( op2(e21,e23) = e23 )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(189,plain,
( ( op2(e21,e22) = e23 )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(190,plain,
( ( op2(e21,e21) = e23 )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(191,plain,
( ( op2(e21,e20) = e23 )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(192,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[191,190,189,188]) ).
tff(193,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[192,187]) ).
tff(194,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(196,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 ) )
<=> ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(197,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ) ),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ) ),
inference(transitivity,[status(thm)],[197,195]) ).
tff(199,plain,
( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ),
inference(and_elim,[status(thm)],[130]) ).
tff(200,plain,
( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[200,194]) ).
tff(202,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[201,193]) ).
tff(203,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[202,186]) ).
tff(204,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(h2(e13),h3(e13))) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[203,186]) ).
tff(205,plain,
( ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) )
| ( h6(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e13),h1(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[204,185]) ).
tff(206,plain,
( ( h1(e13) = h3(e13) )
| ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[205,184]) ).
tff(207,plain,
( ( h4(op1(e12,e13)) = h3(e13) )
| ( h5(op1(e12,e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[206,172]) ).
tff(208,plain,
h4(op1(e12,e13)) = h3(e13),
inference(unit_resolution,[status(thm)],[207,161]) ).
tff(209,plain,
h3(e13) = h4(op1(e12,e13)),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
( ( h9(e13) = e23 )
<=> ( h9(e13) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(211,plain,
( ( h9(e13) = e23 )
<=> ( h9(e13) = e23 ) ),
inference(rewrite,[status(thm)],]) ).
tff(212,axiom,
( ( h9(e12) = e22 )
& ( h9(e13) = e23 )
& ( h9(e10) = op2(e22,e23) )
& ( h9(e11) = op2(op2(e22,e23),e23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
tff(213,plain,
( ( h9(e12) = e22 )
& ( h9(e13) = e23 )
& ( h9(e10) = op2(e22,e23) ) ),
inference(and_elim,[status(thm)],[212]) ).
tff(214,plain,
( ( h9(e12) = e22 )
& ( h9(e13) = e23 ) ),
inference(and_elim,[status(thm)],[213]) ).
tff(215,plain,
h9(e13) = e23,
inference(and_elim,[status(thm)],[214]) ).
tff(216,plain,
h9(e13) = e23,
inference(modus_ponens,[status(thm)],[215,211]) ).
tff(217,plain,
h9(e13) = h3(e13),
inference(modus_ponens,[status(thm)],[216,210]) ).
tff(218,plain,
( ( op1(e12,e13) = e13 )
<=> ( e13 = op1(e12,e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(219,plain,
( ( op1(e12,e13) = op1(op1(op1(e12,e13),e13),op1(e12,e13)) )
<=> ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(220,plain,
( ( op1(e12,e13) != op1(op1(op1(e12,e13),e13),op1(e12,e13)) )
<=> ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) != op1(e12,e13) ) ),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
( ( op1(op1(e12,e13),op1(e12,e13)) != op1(op1(op1(e12,e13),e13),op1(e12,e13)) )
<=> ( op1(e12,e13) != op1(op1(op1(e12,e13),e13),op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(222,plain,
( ( op1(e10,e10) != op1(e11,e10) )
<=> ( op1(op1(e12,e13),op1(e12,e13)) != op1(op1(op1(e12,e13),e13),op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(223,plain,
( ( op1(e10,e10) != op1(e11,e10) )
<=> ( op1(e10,e10) != op1(e11,e10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(224,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/sandbox/benchmark/theBenchmark.p',ax5) ).
tff(225,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)],[224]) ).
tff(226,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)],[225]) ).
tff(227,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)],[226]) ).
tff(228,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)],[227]) ).
tff(229,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)],[228]) ).
tff(230,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)],[229]) ).
tff(231,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)],[230]) ).
tff(232,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)],[231]) ).
tff(233,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)],[232]) ).
tff(234,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)],[233]) ).
tff(235,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)],[234]) ).
tff(236,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)],[235]) ).
tff(237,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)],[236]) ).
tff(238,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)],[237]) ).
tff(239,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)],[238]) ).
tff(240,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)],[239]) ).
tff(241,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)],[240]) ).
tff(242,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)],[241]) ).
tff(243,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)],[242]) ).
tff(244,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)],[243]) ).
tff(245,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)],[244]) ).
tff(246,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)],[245]) ).
tff(247,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)],[246]) ).
tff(248,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)],[247]) ).
tff(249,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)],[248]) ).
tff(250,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)],[249]) ).
tff(251,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)],[250]) ).
tff(252,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)],[251]) ).
tff(253,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)],[252]) ).
tff(254,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)],[253]) ).
tff(255,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)],[254]) ).
tff(256,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)],[255]) ).
tff(257,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)],[256]) ).
tff(258,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)],[257]) ).
tff(259,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)],[258]) ).
tff(260,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)],[259]) ).
tff(261,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)],[260]) ).
tff(262,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)],[261]) ).
tff(263,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)],[262]) ).
tff(264,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)],[263]) ).
tff(265,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)],[264]) ).
tff(266,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)],[265]) ).
tff(267,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)],[266]) ).
tff(268,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)],[267]) ).
tff(269,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) ) ),
inference(and_elim,[status(thm)],[268]) ).
tff(270,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) ) ),
inference(and_elim,[status(thm)],[269]) ).
tff(271,plain,
op1(e10,e10) != op1(e11,e10),
inference(and_elim,[status(thm)],[270]) ).
tff(272,plain,
op1(e10,e10) != op1(e11,e10),
inference(modus_ponens,[status(thm)],[271,223]) ).
tff(273,plain,
op1(op1(e12,e13),op1(e12,e13)) != op1(op1(op1(e12,e13),e13),op1(e12,e13)),
inference(modus_ponens,[status(thm)],[272,222]) ).
tff(274,plain,
op1(e12,e13) != op1(op1(op1(e12,e13),e13),op1(e12,e13)),
inference(modus_ponens,[status(thm)],[273,221]) ).
tff(275,plain,
op1(op1(op1(e12,e13),e13),op1(e12,e13)) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[274,220]) ).
tff(276,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(277,plain,
( ( $false
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(278,plain,
( ( op1(e10,e13) != op1(e12,e13) )
<=> ( op1(op1(e12,e13),e13) != op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(279,plain,
( ( op1(e10,e13) != op1(e12,e13) )
<=> ( op1(e10,e13) != op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(280,plain,
op1(e10,e13) != op1(e12,e13),
inference(and_elim,[status(thm)],[252]) ).
tff(281,plain,
op1(e10,e13) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[280,279]) ).
tff(282,plain,
op1(op1(e12,e13),e13) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[281,278]) ).
tff(283,plain,
( ( op1(op1(e12,e13),e13) = op1(e12,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[282]) ).
tff(284,plain,
( ( ( op1(op1(e12,e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) )
<=> ( $false
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ) ),
inference(monotonicity,[status(thm)],[283]) ).
tff(285,plain,
( ( ( op1(op1(e12,e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ) ),
inference(transitivity,[status(thm)],[284,277]) ).
tff(286,plain,
( ( ( op1(op1(e12,e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) )
<=> ( ( op1(op1(e12,e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(287,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| $false
| ( op1(op1(e12,e13),e13) = op1(e12,e13) ) )
<=> ( ( op1(op1(e12,e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(288,plain,
( ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) )
<=> ( op1(op1(e12,e13),e13) = op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(289,plain,
( ( op1(e11,e13) != op1(e12,e13) )
<=> ( op1(op1(op1(e12,e13),e13),e13) != op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(290,plain,
( ( op1(e11,e13) != op1(e12,e13) )
<=> ( op1(e11,e13) != op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(291,plain,
op1(e11,e13) != op1(e12,e13),
inference(and_elim,[status(thm)],[250]) ).
tff(292,plain,
op1(e11,e13) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[291,290]) ).
tff(293,plain,
op1(op1(op1(e12,e13),e13),e13) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[292,289]) ).
tff(294,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[293]) ).
tff(295,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| $false
| ( op1(op1(e12,e13),e13) = op1(e12,e13) ) ) ),
inference(monotonicity,[status(thm)],[294,288]) ).
tff(296,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) ) )
<=> ( ( op1(op1(e12,e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ) ),
inference(transitivity,[status(thm)],[295,287]) ).
tff(297,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(298,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(299,plain,
( ( op1(e11,e13) = e10 )
<=> ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(300,plain,
( ( op1(e11,e12) = e10 )
<=> ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(301,plain,
( ( op1(e11,e11) = e10 )
<=> ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(302,plain,
( ( op1(e11,e10) = e10 )
<=> ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(303,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) ) ) ),
inference(monotonicity,[status(thm)],[302,301,300,299]) ).
tff(304,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) ) ) ),
inference(transitivity,[status(thm)],[303,298]) ).
tff(305,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(306,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(307,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(308,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ) ),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ) ),
inference(transitivity,[status(thm)],[308,306]) ).
tff(310,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/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(311,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)],[310]) ).
tff(312,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)],[311]) ).
tff(313,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)],[312]) ).
tff(314,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)],[313]) ).
tff(315,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)],[314]) ).
tff(316,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)],[315]) ).
tff(317,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)],[316]) ).
tff(318,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)],[317]) ).
tff(319,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)],[318]) ).
tff(320,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)],[319]) ).
tff(321,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)],[320]) ).
tff(322,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)],[321]) ).
tff(323,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)],[322]) ).
tff(324,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)],[323]) ).
tff(325,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)],[324]) ).
tff(326,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)],[325]) ).
tff(327,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)],[326]) ).
tff(328,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)],[327]) ).
tff(329,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)],[328]) ).
tff(330,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)],[329]) ).
tff(331,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)],[330]) ).
tff(332,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)],[331]) ).
tff(333,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)],[332]) ).
tff(334,plain,
( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ),
inference(and_elim,[status(thm)],[333]) ).
tff(335,plain,
( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[334,309]) ).
tff(336,plain,
( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[335,305]) ).
tff(337,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[336,304]) ).
tff(338,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[337,297]) ).
tff(339,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[338,297]) ).
tff(340,plain,
( ( op1(op1(e12,e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[339,296]) ).
tff(341,plain,
( ( op1(op1(e12,e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[340,286]) ).
tff(342,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[341,285]) ).
tff(343,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[342,276]) ).
tff(344,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[343,276]) ).
tff(345,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[344,276]) ).
tff(346,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[345,276]) ).
tff(347,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[346,276]) ).
tff(348,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13) ) ),
inference(modus_ponens,[status(thm)],[347,276]) ).
tff(349,plain,
op1(op1(op1(e12,e13),e13),e12) = op1(e12,e13),
inference(unit_resolution,[status(thm)],[348,275]) ).
tff(350,plain,
( ( op1(op1(op1(e12,e13),e13),e12) = e13 )
<=> ( op1(e12,e13) = e13 ) ),
inference(monotonicity,[status(thm)],[349]) ).
tff(351,plain,
( ( op1(op1(op1(e12,e13),e13),e12) = e13 )
<=> ( e13 = op1(e12,e13) ) ),
inference(transitivity,[status(thm)],[350,218]) ).
tff(352,plain,
( ( e13 = op1(e12,e13) )
<=> ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ),
inference(symmetry,[status(thm)],[351]) ).
tff(353,plain,
( ( e13 != op1(e12,e13) )
<=> ( op1(op1(op1(e12,e13),e13),e12) != e13 ) ),
inference(monotonicity,[status(thm)],[352]) ).
tff(354,plain,
( ( op1(e12,e13) != e13 )
<=> ( e13 != op1(e12,e13) ) ),
inference(monotonicity,[status(thm)],[218]) ).
tff(355,plain,
( ( op1(e12,e13) != op1(e13,e13) )
<=> ( op1(e12,e13) != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(356,plain,
( ( op1(e12,e13) != op1(e13,e13) )
<=> ( op1(e12,e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(357,plain,
op1(e12,e13) != op1(e13,e13),
inference(and_elim,[status(thm)],[248]) ).
tff(358,plain,
op1(e12,e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[357,356]) ).
tff(359,plain,
op1(e12,e13) != e13,
inference(modus_ponens,[status(thm)],[358,355]) ).
tff(360,plain,
e13 != op1(e12,e13),
inference(modus_ponens,[status(thm)],[359,354]) ).
tff(361,plain,
op1(op1(op1(e12,e13),e13),e12) != e13,
inference(modus_ponens,[status(thm)],[360,353]) ).
tff(362,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(363,plain,
( ( $false
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(364,plain,
( ( op1(op1(e12,e13),e13) != op1(e13,e13) )
<=> ( op1(op1(e12,e13),e13) != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(365,plain,
( ( op1(e10,e13) != op1(e13,e13) )
<=> ( op1(op1(e12,e13),e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(366,plain,
( ( op1(e10,e13) != op1(e13,e13) )
<=> ( op1(e10,e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(367,plain,
op1(e10,e13) != op1(e13,e13),
inference(and_elim,[status(thm)],[251]) ).
tff(368,plain,
op1(e10,e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[367,366]) ).
tff(369,plain,
op1(op1(e12,e13),e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[368,365]) ).
tff(370,plain,
op1(op1(e12,e13),e13) != e13,
inference(modus_ponens,[status(thm)],[369,364]) ).
tff(371,plain,
( ( op1(op1(e12,e13),e13) = e13 )
<=> $false ),
inference(iff_false,[status(thm)],[370]) ).
tff(372,plain,
( ( ( op1(op1(e12,e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) )
<=> ( $false
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ) ),
inference(monotonicity,[status(thm)],[371]) ).
tff(373,plain,
( ( ( op1(op1(e12,e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ) ),
inference(transitivity,[status(thm)],[372,363]) ).
tff(374,plain,
( ( ( op1(op1(e12,e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) )
<=> ( ( op1(op1(e12,e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(375,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| $false
| ( op1(op1(e12,e13),e13) = e13 ) )
<=> ( ( op1(op1(e12,e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(376,plain,
( ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 )
<=> ( op1(op1(e12,e13),e13) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(377,plain,
( ( op1(op1(op1(e12,e13),e13),e13) != op1(e13,e13) )
<=> ( op1(op1(op1(e12,e13),e13),e13) != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(378,plain,
( ( op1(e11,e13) != op1(e13,e13) )
<=> ( op1(op1(op1(e12,e13),e13),e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(379,plain,
( ( op1(e11,e13) != op1(e13,e13) )
<=> ( op1(e11,e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(380,plain,
op1(e11,e13) != op1(e13,e13),
inference(and_elim,[status(thm)],[249]) ).
tff(381,plain,
op1(e11,e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[380,379]) ).
tff(382,plain,
op1(op1(op1(e12,e13),e13),e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[381,378]) ).
tff(383,plain,
op1(op1(op1(e12,e13),e13),e13) != e13,
inference(modus_ponens,[status(thm)],[382,377]) ).
tff(384,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = e13 )
<=> $false ),
inference(iff_false,[status(thm)],[383]) ).
tff(385,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| $false
| ( op1(op1(e12,e13),e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[384,376]) ).
tff(386,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 ) )
<=> ( ( op1(op1(e12,e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ) ),
inference(transitivity,[status(thm)],[385,375]) ).
tff(387,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(388,plain,
( ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(389,plain,
( ( op1(e11,e13) = e13 )
<=> ( op1(op1(op1(e12,e13),e13),e13) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(390,plain,
( ( op1(e11,e12) = e13 )
<=> ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(391,plain,
( ( op1(e11,e11) = e13 )
<=> ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(392,plain,
( ( op1(e11,e10) = e13 )
<=> ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(393,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[392,391,390,389]) ).
tff(394,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(transitivity,[status(thm)],[393,388]) ).
tff(395,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(396,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(397,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 ) )
<=> ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(398,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[397]) ).
tff(399,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[398,396]) ).
tff(400,plain,
( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ),
inference(and_elim,[status(thm)],[327]) ).
tff(401,plain,
( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[400,399]) ).
tff(402,plain,
( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[401,395]) ).
tff(403,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[402,394]) ).
tff(404,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[403,387]) ).
tff(405,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[404,387]) ).
tff(406,plain,
( ( op1(op1(e12,e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[405,386]) ).
tff(407,plain,
( ( op1(op1(e12,e13),e13) = e13 )
| ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[406,374]) ).
tff(408,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[407,373]) ).
tff(409,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[408,362]) ).
tff(410,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[409,362]) ).
tff(411,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[410,362]) ).
tff(412,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[411,362]) ).
tff(413,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[412,362]) ).
tff(414,plain,
( ( op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13 )
| ( op1(op1(op1(e12,e13),e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[413,362]) ).
tff(415,plain,
op1(op1(op1(e12,e13),e13),op1(e12,e13)) = e13,
inference(unit_resolution,[status(thm)],[414,361]) ).
tff(416,plain,
h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = h9(e13),
inference(monotonicity,[status(thm)],[415]) ).
tff(417,plain,
h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)),
inference(transitivity,[status(thm)],[416,217,209,11]) ).
tff(418,plain,
( ( h1(e13) = op2(h1(e13),h2(e13)) )
<=> ( op2(h1(e13),h2(e13)) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(419,plain,
( ( h1(e13) != op2(h1(e13),h2(e13)) )
<=> ( op2(h1(e13),h2(e13)) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[418]) ).
tff(420,plain,
( ( h1(e13) != h5(op1(e12,e13)) )
<=> ( h1(e13) != op2(h1(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(421,plain,
( ( op2(h1(e13),h1(e13)) != h5(op1(e12,e13)) )
<=> ( h1(e13) != h5(op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(422,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) )
<=> ( op2(h1(e13),h1(e13)) != h5(op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(423,plain,
( ( op2(e21,e21) != op2(e21,e22) )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(424,plain,
( ( op2(e21,e21) != op2(e21,e22) )
<=> ( op2(e21,e21) != op2(e21,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(425,plain,
op2(e21,e21) != op2(e21,e22),
inference(and_elim,[status(thm)],[34]) ).
tff(426,plain,
op2(e21,e21) != op2(e21,e22),
inference(modus_ponens,[status(thm)],[425,424]) ).
tff(427,plain,
op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)),
inference(modus_ponens,[status(thm)],[426,423]) ).
tff(428,plain,
op2(h1(e13),h1(e13)) != h5(op1(e12,e13)),
inference(modus_ponens,[status(thm)],[427,422]) ).
tff(429,plain,
h1(e13) != h5(op1(e12,e13)),
inference(modus_ponens,[status(thm)],[428,421]) ).
tff(430,plain,
h1(e13) != op2(h1(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[429,420]) ).
tff(431,plain,
op2(h1(e13),h2(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[430,419]) ).
tff(432,plain,
( ( ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) )
<=> ( ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(433,plain,
( ( $false
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) )
<=> ( ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(434,plain,
( ( op2(h1(e12),h1(e13)) != h1(e13) )
<=> ( h2(e13) != h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(435,plain,
( ( h1(op1(e12,e13)) != h1(e13) )
<=> ( op2(h1(e12),h1(e13)) != h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(436,plain,
( ( h1(op1(e12,e13)) != op2(h1(e13),h1(e13)) )
<=> ( h1(op1(e12,e13)) != h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(437,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) )
<=> ( h1(op1(e12,e13)) != op2(h1(e13),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(438,plain,
( ( op2(e20,e21) != op2(e21,e21) )
<=> ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(439,plain,
( ( op2(e20,e21) != op2(e21,e21) )
<=> ( op2(e20,e21) != op2(e21,e21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(440,plain,
op2(e20,e21) != op2(e21,e21),
inference(and_elim,[status(thm)],[61]) ).
tff(441,plain,
op2(e20,e21) != op2(e21,e21),
inference(modus_ponens,[status(thm)],[440,439]) ).
tff(442,plain,
op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))),
inference(modus_ponens,[status(thm)],[441,438]) ).
tff(443,plain,
h1(op1(e12,e13)) != op2(h1(e13),h1(e13)),
inference(modus_ponens,[status(thm)],[442,437]) ).
tff(444,plain,
h1(op1(e12,e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[443,436]) ).
tff(445,plain,
op2(h1(e12),h1(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[444,435]) ).
tff(446,plain,
h2(e13) != h1(e13),
inference(modus_ponens,[status(thm)],[445,434]) ).
tff(447,plain,
( ( h2(e13) = h1(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[446]) ).
tff(448,plain,
( ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) )
<=> ( $false
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[447]) ).
tff(449,plain,
( ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) )
<=> ( ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[448,433]) ).
tff(450,plain,
( ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(451,plain,
( ( ( h2(e13) = h1(e13) )
| $false
| ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(452,plain,
( ( h5(op1(e12,e13)) = h1(e13) )
<=> ( op2(h1(e13),h2(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(453,plain,
( ( h2(op1(e12,e13)) != h1(e13) )
<=> ( op2(h1(e12),h2(e13)) != h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(454,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) != op2(op2(h2(e13),h3(e13)),h3(e13)) )
<=> ( h2(op1(e12,e13)) != h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(455,plain,
( ( op2(e20,e22) != op2(e20,e23) )
<=> ( op2(op2(h2(e13),h3(e13)),h2(e13)) != op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(456,plain,
( ( op2(e20,e22) != op2(e20,e23) )
<=> ( op2(e20,e22) != op2(e20,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(457,plain,
op2(e20,e22) != op2(e20,e23),
inference(and_elim,[status(thm)],[38]) ).
tff(458,plain,
op2(e20,e22) != op2(e20,e23),
inference(modus_ponens,[status(thm)],[457,456]) ).
tff(459,plain,
op2(op2(h2(e13),h3(e13)),h2(e13)) != op2(op2(h2(e13),h3(e13)),h3(e13)),
inference(modus_ponens,[status(thm)],[458,455]) ).
tff(460,plain,
h2(op1(e12,e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[459,454]) ).
tff(461,plain,
op2(h1(e12),h2(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[460,453]) ).
tff(462,plain,
( ( op2(h1(e12),h2(e13)) = h1(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[461]) ).
tff(463,plain,
( ( ( h2(e13) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| $false
| ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[462,452]) ).
tff(464,plain,
( ( ( h2(e13) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[463,451]) ).
tff(465,plain,
( ( ( h2(e13) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(466,plain,
( ( h2(op1(e12,e13)) = h1(e13) )
<=> ( op2(h1(e12),h2(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(467,plain,
( ( ( h2(e13) = h1(e13) )
| ( h2(op1(e12,e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[466]) ).
tff(468,plain,
( ( ( h2(e13) = h1(e13) )
| ( h2(op1(e12,e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[467,465]) ).
tff(469,plain,
( ( ( h2(op1(e12,e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( h2(e13) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h2(op1(e12,e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(470,plain,
( ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
<=> ( h2(e13) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(471,plain,
( ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
<=> ( op2(h3(e13),h2(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(472,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
<=> ( h5(op1(e12,e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(473,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
<=> ( h2(op1(e12,e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(474,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) )
<=> ( ( h2(op1(e12,e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( h2(e13) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[473,472,471,470]) ).
tff(475,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h2(op1(e12,e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[474,469]) ).
tff(476,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(477,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(478,plain,
( ( op2(e23,e22) = e21 )
<=> ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(479,plain,
( ( op2(e22,e22) = e21 )
<=> ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(480,plain,
( ( op2(e21,e22) = e21 )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(481,plain,
( ( op2(e20,e22) = e21 )
<=> ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(482,plain,
( ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ),
inference(monotonicity,[status(thm)],[481,480,479,478]) ).
tff(483,plain,
( ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[482,477]) ).
tff(484,plain,
( ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
<=> ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(485,plain,
( ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
<=> ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(486,plain,
( ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 ) )
<=> ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(487,plain,
( ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
<=> ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ) ),
inference(monotonicity,[status(thm)],[486]) ).
tff(488,plain,
( ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
<=> ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ) ),
inference(transitivity,[status(thm)],[487,485]) ).
tff(489,plain,
( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ),
inference(and_elim,[status(thm)],[125]) ).
tff(490,plain,
( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ),
inference(modus_ponens,[status(thm)],[489,488]) ).
tff(491,plain,
( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ),
inference(modus_ponens,[status(thm)],[490,484]) ).
tff(492,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[491,483]) ).
tff(493,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[492,476]) ).
tff(494,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h3(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[493,476]) ).
tff(495,plain,
( ( h2(e13) = h1(e13) )
| ( h2(op1(e12,e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[494,475]) ).
tff(496,plain,
( ( h2(e13) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[495,468]) ).
tff(497,plain,
( ( h2(e13) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( h5(op1(e12,e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[496,465]) ).
tff(498,plain,
( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[497,464]) ).
tff(499,plain,
( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[498,450]) ).
tff(500,plain,
( ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[499,449]) ).
tff(501,plain,
( ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[500,432]) ).
tff(502,plain,
( ( op2(h3(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[501,432]) ).
tff(503,plain,
op2(h3(e13),h2(e13)) = h1(e13),
inference(unit_resolution,[status(thm)],[502,431]) ).
tff(504,plain,
h1(e13) = op2(h3(e13),h2(e13)),
inference(symmetry,[status(thm)],[503]) ).
tff(505,plain,
( ( h9(op1(op1(e12,e13),e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
<=> ( h9(op1(op1(e12,e13),e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(506,plain,
( ( h9(e11) = op2(op2(e22,e23),e23) )
<=> ( h9(op1(op1(e12,e13),e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(507,plain,
( ( h9(e11) = op2(op2(e22,e23),e23) )
<=> ( h9(e11) = op2(op2(e22,e23),e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(508,plain,
h9(e11) = op2(op2(e22,e23),e23),
inference(and_elim,[status(thm)],[212]) ).
tff(509,plain,
h9(e11) = op2(op2(e22,e23),e23),
inference(modus_ponens,[status(thm)],[508,507]) ).
tff(510,plain,
h9(op1(op1(e12,e13),e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)),
inference(modus_ponens,[status(thm)],[509,506]) ).
tff(511,plain,
h9(op1(op1(e12,e13),e13)) = h1(e13),
inference(modus_ponens,[status(thm)],[510,505]) ).
tff(512,plain,
( ( op1(op1(e12,e13),e13) = op1(op1(op1(e12,e13),e13),e12) )
<=> ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(513,plain,
( ( op1(op1(e12,e13),e13) != op1(op1(op1(e12,e13),e13),e12) )
<=> ( op1(op1(op1(e12,e13),e13),e12) != op1(op1(e12,e13),e13) ) ),
inference(monotonicity,[status(thm)],[512]) ).
tff(514,plain,
( ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(op1(op1(e12,e13),e13),e12) )
<=> ( op1(op1(e12,e13),e13) != op1(op1(op1(e12,e13),e13),e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(515,plain,
( ( op1(e11,e11) != op1(e11,e12) )
<=> ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(op1(op1(e12,e13),e13),e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(516,plain,
( ( op1(e11,e11) != op1(e11,e12) )
<=> ( op1(e11,e11) != op1(e11,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(517,plain,
op1(e11,e11) != op1(e11,e12),
inference(and_elim,[status(thm)],[238]) ).
tff(518,plain,
op1(e11,e11) != op1(e11,e12),
inference(modus_ponens,[status(thm)],[517,516]) ).
tff(519,plain,
op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(op1(op1(e12,e13),e13),e12),
inference(modus_ponens,[status(thm)],[518,515]) ).
tff(520,plain,
op1(op1(e12,e13),e13) != op1(op1(op1(e12,e13),e13),e12),
inference(modus_ponens,[status(thm)],[519,514]) ).
tff(521,plain,
op1(op1(op1(e12,e13),e13),e12) != op1(op1(e12,e13),e13),
inference(modus_ponens,[status(thm)],[520,513]) ).
tff(522,plain,
( ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(523,plain,
( ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| $false )
<=> ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(524,plain,
( ( op1(op1(e12,e13),op1(op1(e12,e13),e13)) != op1(op1(e12,e13),e13) )
<=> ( e12 != op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(525,plain,
( ( op1(op1(e12,e13),op1(op1(e12,e13),e13)) != op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) )
<=> ( op1(op1(e12,e13),op1(op1(e12,e13),e13)) != op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(526,plain,
( ( op1(e10,e11) != op1(e11,e11) )
<=> ( op1(op1(e12,e13),op1(op1(e12,e13),e13)) != op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(527,plain,
( ( op1(e10,e11) != op1(e11,e11) )
<=> ( op1(e10,e11) != op1(e11,e11) ) ),
inference(rewrite,[status(thm)],]) ).
tff(528,plain,
op1(e10,e11) != op1(e11,e11),
inference(and_elim,[status(thm)],[265]) ).
tff(529,plain,
op1(e10,e11) != op1(e11,e11),
inference(modus_ponens,[status(thm)],[528,527]) ).
tff(530,plain,
op1(op1(e12,e13),op1(op1(e12,e13),e13)) != op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)),
inference(modus_ponens,[status(thm)],[529,526]) ).
tff(531,plain,
op1(op1(e12,e13),op1(op1(e12,e13),e13)) != op1(op1(e12,e13),e13),
inference(modus_ponens,[status(thm)],[530,525]) ).
tff(532,plain,
e12 != op1(op1(e12,e13),e13),
inference(modus_ponens,[status(thm)],[531,524]) ).
tff(533,plain,
( ( e12 = op1(op1(e12,e13),e13) )
<=> $false ),
inference(iff_false,[status(thm)],[532]) ).
tff(534,plain,
( ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| $false ) ),
inference(monotonicity,[status(thm)],[533]) ).
tff(535,plain,
( ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[534,523]) ).
tff(536,plain,
( ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(537,plain,
( ( $false
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(538,plain,
( ( op1(e12,e12) = op1(op1(e12,e13),e13) )
<=> ( e12 = op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(539,plain,
( ( op1(e10,e12) != op1(e10,e13) )
<=> ( op1(op1(e12,e13),e12) != op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(540,plain,
( ( op1(e10,e12) != op1(e10,e13) )
<=> ( op1(e10,e12) != op1(e10,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(541,plain,
op1(e10,e12) != op1(e10,e13),
inference(and_elim,[status(thm)],[242]) ).
tff(542,plain,
op1(e10,e12) != op1(e10,e13),
inference(modus_ponens,[status(thm)],[541,540]) ).
tff(543,plain,
op1(op1(e12,e13),e12) != op1(op1(e12,e13),e13),
inference(modus_ponens,[status(thm)],[542,539]) ).
tff(544,plain,
( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
<=> $false ),
inference(iff_false,[status(thm)],[543]) ).
tff(545,plain,
( ( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) )
<=> ( $false
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ) ),
inference(monotonicity,[status(thm)],[544,538]) ).
tff(546,plain,
( ( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[545,537]) ).
tff(547,plain,
( ( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(548,plain,
( ( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(549,plain,
( ( op1(e13,e12) = e11 )
<=> ( op1(e13,e12) = op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(550,plain,
( ( op1(e12,e12) = e11 )
<=> ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(551,plain,
( ( op1(e11,e12) = e11 )
<=> ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(552,plain,
( ( op1(e10,e12) = e11 )
<=> ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(553,plain,
( ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
<=> ( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) ) ) ),
inference(monotonicity,[status(thm)],[552,551,550,549]) ).
tff(554,plain,
( ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
<=> ( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[553,548]) ).
tff(555,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(556,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(557,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(558,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)],[557]) ).
tff(559,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)],[558,556]) ).
tff(560,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(and_elim,[status(thm)],[322]) ).
tff(561,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(modus_ponens,[status(thm)],[560,559]) ).
tff(562,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(modus_ponens,[status(thm)],[561,555]) ).
tff(563,plain,
( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[562,554]) ).
tff(564,plain,
( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[563,547]) ).
tff(565,plain,
( ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[564,547]) ).
tff(566,plain,
( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[565,546]) ).
tff(567,plain,
( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[566,536]) ).
tff(568,plain,
( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[567,536]) ).
tff(569,plain,
( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[568,536]) ).
tff(570,plain,
( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[569,535]) ).
tff(571,plain,
( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[570,522]) ).
tff(572,plain,
( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[571,522]) ).
tff(573,plain,
( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[572,522]) ).
tff(574,plain,
( ( op1(op1(op1(e12,e13),e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(e13,e12) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[573,522]) ).
tff(575,plain,
op1(e13,e12) = op1(op1(e12,e13),e13),
inference(unit_resolution,[status(thm)],[574,521]) ).
tff(576,plain,
h9(op1(e13,e12)) = h9(op1(op1(e12,e13),e13)),
inference(monotonicity,[status(thm)],[575]) ).
tff(577,plain,
h9(op1(e13,e12)) = op2(h3(e13),h2(e13)),
inference(transitivity,[status(thm)],[576,511,504]) ).
tff(578,plain,
( ( h11(op1(e12,e13)) = op2(h3(e13),op2(h1(e12),h3(e13))) )
<=> ( h11(op1(e12,e13)) = op2(h3(e13),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(579,plain,
( ( h11(op1(e12,e13)) = op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) )
<=> ( h11(op1(e12,e13)) = op2(h3(e13),op2(h1(e12),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(580,plain,
( ( h11(e10) = op2(e23,e21) )
<=> ( h11(op1(e12,e13)) = op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(581,plain,
( ( h11(e10) = op2(e23,e21) )
<=> ( h11(e10) = op2(e23,e21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(582,axiom,
( ( h11(e12) = e23 )
& ( h11(e13) = e21 )
& ( h11(e10) = op2(e23,e21) )
& ( h11(e11) = op2(op2(e23,e21),e21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
tff(583,plain,
( ( h11(e12) = e23 )
& ( h11(e13) = e21 )
& ( h11(e10) = op2(e23,e21) ) ),
inference(and_elim,[status(thm)],[582]) ).
tff(584,plain,
h11(e10) = op2(e23,e21),
inference(and_elim,[status(thm)],[583]) ).
tff(585,plain,
h11(e10) = op2(e23,e21),
inference(modus_ponens,[status(thm)],[584,581]) ).
tff(586,plain,
h11(op1(e12,e13)) = op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))),
inference(modus_ponens,[status(thm)],[585,580]) ).
tff(587,plain,
h11(op1(e12,e13)) = op2(h3(e13),op2(h1(e12),h3(e13))),
inference(modus_ponens,[status(thm)],[586,579]) ).
tff(588,plain,
h11(op1(e12,e13)) = op2(h3(e13),h1(e13)),
inference(modus_ponens,[status(thm)],[587,578]) ).
tff(589,plain,
( ( $false
| ( h11(op1(e12,e13)) = h1(e12) ) )
<=> ( h11(op1(e12,e13)) = h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(590,plain,
( ( op2(h2(e13),h2(e13)) != op2(h2(e13),h3(e13)) )
<=> ( h2(e13) != h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(591,plain,
( ( op2(e22,e22) != op2(e22,e23) )
<=> ( op2(h2(e13),h2(e13)) != op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(592,plain,
( ( op2(e22,e22) != op2(e22,e23) )
<=> ( op2(e22,e22) != op2(e22,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(593,plain,
op2(e22,e22) != op2(e22,e23),
inference(and_elim,[status(thm)],[26]) ).
tff(594,plain,
op2(e22,e22) != op2(e22,e23),
inference(modus_ponens,[status(thm)],[593,592]) ).
tff(595,plain,
op2(h2(e13),h2(e13)) != op2(h2(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[594,591]) ).
tff(596,plain,
h2(e13) != h1(e12),
inference(modus_ponens,[status(thm)],[595,590]) ).
tff(597,plain,
( ( h2(e13) = h1(e12) )
<=> $false ),
inference(iff_false,[status(thm)],[596]) ).
tff(598,plain,
( ( ( h2(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) )
<=> ( $false
| ( h11(op1(e12,e13)) = h1(e12) ) ) ),
inference(monotonicity,[status(thm)],[597]) ).
tff(599,plain,
( ( ( h2(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) )
<=> ( h11(op1(e12,e13)) = h1(e12) ) ),
inference(transitivity,[status(thm)],[598,589]) ).
tff(600,plain,
( ( ( h11(op1(e12,e13)) = h1(e12) )
| ( h2(e13) = h1(e12) ) )
<=> ( ( h2(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(601,plain,
( ( op2(h1(e12),h1(e13)) = h1(e12) )
<=> ( h2(e13) = h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(602,plain,
( ( ( h11(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e12),h1(e13)) = h1(e12) ) )
<=> ( ( h11(op1(e12,e13)) = h1(e12) )
| ( h2(e13) = h1(e12) ) ) ),
inference(monotonicity,[status(thm)],[601]) ).
tff(603,plain,
( ( ( h11(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e12),h1(e13)) = h1(e12) ) )
<=> ( ( h2(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ) ),
inference(transitivity,[status(thm)],[602,600]) ).
tff(604,plain,
( ( ( op2(h1(e12),h1(e13)) = h1(e12) )
| $false
| ( h11(op1(e12,e13)) = h1(e12) ) )
<=> ( ( h11(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e12),h1(e13)) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(605,plain,
( ( h1(op1(e12,e13)) = h1(e12) )
<=> ( op2(h1(e12),h1(e13)) = h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(606,plain,
( ( ( h1(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) )
<=> ( ( op2(h1(e12),h1(e13)) = h1(e12) )
| $false
| ( h11(op1(e12,e13)) = h1(e12) ) ) ),
inference(monotonicity,[status(thm)],[605,82]) ).
tff(607,plain,
( ( ( h1(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) )
<=> ( ( h11(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e12),h1(e13)) = h1(e12) ) ) ),
inference(transitivity,[status(thm)],[606,604]) ).
tff(608,plain,
( ( ( h1(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) )
<=> ( ( h1(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(609,plain,
( ( ( h1(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) )
| $false
| ( h11(op1(e12,e13)) = h1(e12) ) )
<=> ( ( h1(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(610,plain,
( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(h2(e13),h3(e13)) )
<=> ( h8(op1(e12,e13)) != h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(611,plain,
( ( op2(e22,e21) != op2(e22,e23) )
<=> ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(612,plain,
( ( op2(e22,e21) != op2(e22,e23) )
<=> ( op2(e22,e21) != op2(e22,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(613,plain,
op2(e22,e21) != op2(e22,e23),
inference(and_elim,[status(thm)],[27]) ).
tff(614,plain,
op2(e22,e21) != op2(e22,e23),
inference(modus_ponens,[status(thm)],[613,612]) ).
tff(615,plain,
op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(h2(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[614,611]) ).
tff(616,plain,
h8(op1(e12,e13)) != h1(e12),
inference(modus_ponens,[status(thm)],[615,610]) ).
tff(617,plain,
( ( h8(op1(e12,e13)) = h1(e12) )
<=> $false ),
inference(iff_false,[status(thm)],[616]) ).
tff(618,plain,
( ( ( h1(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) )
<=> ( ( h1(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) )
| $false
| ( h11(op1(e12,e13)) = h1(e12) ) ) ),
inference(monotonicity,[status(thm)],[88,617]) ).
tff(619,plain,
( ( ( h1(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) )
<=> ( ( h1(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ) ),
inference(transitivity,[status(thm)],[618,609]) ).
tff(620,plain,
( ( ( h1(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) )
<=> ( ( h1(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(621,plain,
( ( ( h1(op1(e12,e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) ) )
<=> ( ( h1(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(622,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
<=> ( op2(h1(e13),h1(e13)) = h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(623,plain,
( ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
<=> ( h11(op1(e12,e13)) = h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(624,plain,
( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
<=> ( h8(op1(e12,e13)) = h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(625,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
<=> ( h1(op1(e12,e13)) = h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(626,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) )
<=> ( ( h1(op1(e12,e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) ) ) ),
inference(monotonicity,[status(thm)],[625,624,623,622]) ).
tff(627,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) )
<=> ( ( h1(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ) ),
inference(transitivity,[status(thm)],[626,621]) ).
tff(628,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(629,plain,
( ( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(630,plain,
( ( op2(e23,e21) = e20 )
<=> ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(631,plain,
( ( op2(e22,e21) = e20 )
<=> ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(632,plain,
( ( op2(e20,e21) = e20 )
<=> ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(633,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ) ),
inference(monotonicity,[status(thm)],[632,104,631,630]) ).
tff(634,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[633,629]) ).
tff(635,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
<=> ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(636,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
<=> ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(637,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 ) )
<=> ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(638,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
<=> ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ) ),
inference(monotonicity,[status(thm)],[637]) ).
tff(639,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
<=> ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ) ),
inference(transitivity,[status(thm)],[638,636]) ).
tff(640,plain,
( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ),
inference(and_elim,[status(thm)],[135]) ).
tff(641,plain,
( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ),
inference(modus_ponens,[status(thm)],[640,639]) ).
tff(642,plain,
( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ),
inference(modus_ponens,[status(thm)],[641,635]) ).
tff(643,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[642,634]) ).
tff(644,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[643,628]) ).
tff(645,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[644,628]) ).
tff(646,plain,
( ( h1(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[645,627]) ).
tff(647,plain,
( ( h1(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e13),h1(e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[646,620]) ).
tff(648,plain,
( ( h1(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[647,619]) ).
tff(649,plain,
( ( h1(op1(e12,e13)) = h1(e12) )
| ( h1(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[648,608]) ).
tff(650,plain,
( ( h11(op1(e12,e13)) = h1(e12) )
| ( op2(h1(e12),h1(e13)) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[649,607]) ).
tff(651,plain,
( ( h2(e13) = h1(e12) )
| ( h11(op1(e12,e13)) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[650,603]) ).
tff(652,plain,
h11(op1(e12,e13)) = h1(e12),
inference(modus_ponens,[status(thm)],[651,599]) ).
tff(653,plain,
h1(e12) = h11(op1(e12,e13)),
inference(symmetry,[status(thm)],[652]) ).
tff(654,plain,
( ( h9(op1(e12,e13)) = op2(h2(e13),h3(e13)) )
<=> ( h9(op1(e12,e13)) = h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(655,plain,
( ( h9(e10) = op2(e22,e23) )
<=> ( h9(op1(e12,e13)) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(656,plain,
( ( h9(e10) = op2(e22,e23) )
<=> ( h9(e10) = op2(e22,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(657,plain,
h9(e10) = op2(e22,e23),
inference(and_elim,[status(thm)],[213]) ).
tff(658,plain,
h9(e10) = op2(e22,e23),
inference(modus_ponens,[status(thm)],[657,656]) ).
tff(659,plain,
h9(op1(e12,e13)) = op2(h2(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[658,655]) ).
tff(660,plain,
h9(op1(e12,e13)) = h1(e12),
inference(modus_ponens,[status(thm)],[659,654]) ).
tff(661,plain,
( ( e12 = op1(e13,op1(op1(e12,e13),e13)) )
<=> ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(commutativity,[status(thm)],]) ).
tff(662,plain,
( ( e12 != op1(e13,op1(op1(e12,e13),e13)) )
<=> ( op1(e13,op1(op1(e12,e13),e13)) != e12 ) ),
inference(monotonicity,[status(thm)],[661]) ).
tff(663,plain,
( ( op1(op1(e12,e13),op1(op1(e12,e13),e13)) != op1(e13,op1(op1(e12,e13),e13)) )
<=> ( e12 != op1(e13,op1(op1(e12,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(664,plain,
( ( op1(e10,e11) != op1(e13,e11) )
<=> ( op1(op1(e12,e13),op1(op1(e12,e13),e13)) != op1(e13,op1(op1(e12,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(665,plain,
( ( op1(e10,e11) != op1(e13,e11) )
<=> ( op1(e10,e11) != op1(e13,e11) ) ),
inference(rewrite,[status(thm)],]) ).
tff(666,plain,
op1(e10,e11) != op1(e13,e11),
inference(and_elim,[status(thm)],[263]) ).
tff(667,plain,
op1(e10,e11) != op1(e13,e11),
inference(modus_ponens,[status(thm)],[666,665]) ).
tff(668,plain,
op1(op1(e12,e13),op1(op1(e12,e13),e13)) != op1(e13,op1(op1(e12,e13),e13)),
inference(modus_ponens,[status(thm)],[667,664]) ).
tff(669,plain,
e12 != op1(e13,op1(op1(e12,e13),e13)),
inference(modus_ponens,[status(thm)],[668,663]) ).
tff(670,plain,
op1(e13,op1(op1(e12,e13),e13)) != e12,
inference(modus_ponens,[status(thm)],[669,662]) ).
tff(671,plain,
( ( op1(op1(e12,e13),e13) = op1(e13,op1(op1(e12,e13),e13)) )
<=> ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(672,plain,
( ( op1(op1(e12,e13),e13) != op1(e13,op1(op1(e12,e13),e13)) )
<=> ( op1(e13,op1(op1(e12,e13),e13)) != op1(op1(e12,e13),e13) ) ),
inference(monotonicity,[status(thm)],[671]) ).
tff(673,plain,
( ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(e13,op1(op1(e12,e13),e13)) )
<=> ( op1(op1(e12,e13),e13) != op1(e13,op1(op1(e12,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(674,plain,
( ( op1(e11,e11) != op1(e13,e11) )
<=> ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(e13,op1(op1(e12,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(675,plain,
( ( op1(e11,e11) != op1(e13,e11) )
<=> ( op1(e11,e11) != op1(e13,e11) ) ),
inference(rewrite,[status(thm)],]) ).
tff(676,plain,
op1(e11,e11) != op1(e13,e11),
inference(and_elim,[status(thm)],[261]) ).
tff(677,plain,
op1(e11,e11) != op1(e13,e11),
inference(modus_ponens,[status(thm)],[676,675]) ).
tff(678,plain,
op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(e13,op1(op1(e12,e13),e13)),
inference(modus_ponens,[status(thm)],[677,674]) ).
tff(679,plain,
op1(op1(e12,e13),e13) != op1(e13,op1(op1(e12,e13),e13)),
inference(modus_ponens,[status(thm)],[678,673]) ).
tff(680,plain,
op1(e13,op1(op1(e12,e13),e13)) != op1(op1(e12,e13),e13),
inference(modus_ponens,[status(thm)],[679,672]) ).
tff(681,plain,
( ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) )
<=> ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(682,plain,
( ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| $false )
<=> ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(683,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) != op1(e13,e13) )
<=> ( op1(e13,op1(op1(e12,e13),e13)) != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(684,plain,
( ( op1(e13,e11) != op1(e13,e13) )
<=> ( op1(e13,op1(op1(e12,e13),e13)) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(685,plain,
( ( op1(e13,e11) != op1(e13,e13) )
<=> ( op1(e13,e11) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(686,plain,
op1(e13,e11) != op1(e13,e13),
inference(and_elim,[status(thm)],[225]) ).
tff(687,plain,
op1(e13,e11) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[686,685]) ).
tff(688,plain,
op1(e13,op1(op1(e12,e13),e13)) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[687,684]) ).
tff(689,plain,
op1(e13,op1(op1(e12,e13),e13)) != e13,
inference(modus_ponens,[status(thm)],[688,683]) ).
tff(690,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = e13 )
<=> $false ),
inference(iff_false,[status(thm)],[689]) ).
tff(691,plain,
( ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e13 ) )
<=> ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| $false ) ),
inference(monotonicity,[status(thm)],[690]) ).
tff(692,plain,
( ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e13 ) )
<=> ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ) ),
inference(transitivity,[status(thm)],[691,682]) ).
tff(693,plain,
( ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e13 ) )
<=> ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(694,plain,
( ( op1(e13,e11) = e13 )
<=> ( op1(e13,op1(op1(e12,e13),e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(695,plain,
( ( op1(e13,e11) = e12 )
<=> ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(rewrite,[status(thm)],]) ).
tff(696,plain,
( ( op1(e13,e11) = e11 )
<=> ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(697,plain,
( ( op1(e13,e11) = e10 )
<=> ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(698,plain,
( ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) )
<=> ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(monotonicity,[status(thm)],[697,696,695,694]) ).
tff(699,plain,
( ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) )
<=> ( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(transitivity,[status(thm)],[698,693]) ).
tff(700,plain,
( ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) )
<=> ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(701,plain,
( ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) )
<=> ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(702,plain,
( ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 ) )
<=> ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(703,plain,
( ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) )
<=> ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) ) ),
inference(monotonicity,[status(thm)],[702]) ).
tff(704,plain,
( ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) )
<=> ( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) ) ),
inference(transitivity,[status(thm)],[703,701]) ).
tff(705,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/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(706,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)],[705]) ).
tff(707,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)],[706]) ).
tff(708,plain,
( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) ),
inference(and_elim,[status(thm)],[707]) ).
tff(709,plain,
( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) ),
inference(modus_ponens,[status(thm)],[708,704]) ).
tff(710,plain,
( ( op1(e13,e11) = e10 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e11) = e13 ) ),
inference(modus_ponens,[status(thm)],[709,700]) ).
tff(711,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[710,699]) ).
tff(712,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[711,693]) ).
tff(713,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[712,693]) ).
tff(714,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(modus_ponens,[status(thm)],[713,692]) ).
tff(715,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(modus_ponens,[status(thm)],[714,681]) ).
tff(716,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(modus_ponens,[status(thm)],[715,681]) ).
tff(717,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(modus_ponens,[status(thm)],[716,681]) ).
tff(718,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(modus_ponens,[status(thm)],[717,681]) ).
tff(719,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(modus_ponens,[status(thm)],[718,681]) ).
tff(720,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(modus_ponens,[status(thm)],[719,681]) ).
tff(721,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(modus_ponens,[status(thm)],[720,681]) ).
tff(722,plain,
( ( op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(modus_ponens,[status(thm)],[721,681]) ).
tff(723,plain,
op1(e13,op1(op1(e12,e13),e13)) = op1(e12,e13),
inference(unit_resolution,[status(thm)],[722,680,670]) ).
tff(724,plain,
h9(op1(e13,op1(op1(e12,e13),e13))) = h9(op1(e12,e13)),
inference(monotonicity,[status(thm)],[723]) ).
tff(725,plain,
h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)),
inference(transitivity,[status(thm)],[724,660,653,588]) ).
tff(726,plain,
( ( h10(op1(e12,e13)) = op2(h3(e13),op2(h2(e13),h3(e13))) )
<=> ( h10(op1(e12,e13)) = op2(h3(e13),h1(e12)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(727,plain,
( ( h10(e10) = op2(e23,e20) )
<=> ( h10(op1(e12,e13)) = op2(h3(e13),op2(h2(e13),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(728,plain,
( ( h10(e10) = op2(e23,e20) )
<=> ( h10(e10) = op2(e23,e20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(729,axiom,
( ( h10(e12) = e23 )
& ( h10(e13) = e20 )
& ( h10(e10) = op2(e23,e20) )
& ( h10(e11) = op2(op2(e23,e20),e20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
tff(730,plain,
( ( h10(e12) = e23 )
& ( h10(e13) = e20 )
& ( h10(e10) = op2(e23,e20) ) ),
inference(and_elim,[status(thm)],[729]) ).
tff(731,plain,
h10(e10) = op2(e23,e20),
inference(and_elim,[status(thm)],[730]) ).
tff(732,plain,
h10(e10) = op2(e23,e20),
inference(modus_ponens,[status(thm)],[731,728]) ).
tff(733,plain,
h10(op1(e12,e13)) = op2(h3(e13),op2(h2(e13),h3(e13))),
inference(modus_ponens,[status(thm)],[732,727]) ).
tff(734,plain,
h10(op1(e12,e13)) = op2(h3(e13),h1(e12)),
inference(modus_ponens,[status(thm)],[733,726]) ).
tff(735,plain,
( ( h2(e13) = h3(e13) )
<=> ( h3(e13) = h2(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(736,plain,
( ( h2(e13) != h3(e13) )
<=> ( h3(e13) != h2(e13) ) ),
inference(monotonicity,[status(thm)],[735]) ).
tff(737,plain,
( ( e22 != e23 )
<=> ( h2(e13) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(738,plain,
( ( e22 != e23 )
<=> ( e22 != e23 ) ),
inference(rewrite,[status(thm)],]) ).
tff(739,axiom,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 )
& ( e21 != e23 )
& ( e22 != e23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
tff(740,plain,
e22 != e23,
inference(and_elim,[status(thm)],[739]) ).
tff(741,plain,
e22 != e23,
inference(modus_ponens,[status(thm)],[740,738]) ).
tff(742,plain,
h2(e13) != h3(e13),
inference(modus_ponens,[status(thm)],[741,737]) ).
tff(743,plain,
h3(e13) != h2(e13),
inference(modus_ponens,[status(thm)],[742,736]) ).
tff(744,plain,
( ( h2(e13) = op2(h3(e13),h2(e13)) )
<=> ( op2(h3(e13),h2(e13)) = h2(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(745,plain,
( ( h2(e13) != op2(h3(e13),h2(e13)) )
<=> ( op2(h3(e13),h2(e13)) != h2(e13) ) ),
inference(monotonicity,[status(thm)],[744]) ).
tff(746,plain,
( ( op2(h2(e13),h2(e13)) != op2(h3(e13),h2(e13)) )
<=> ( h2(e13) != op2(h3(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(747,plain,
( ( op2(e22,e22) != op2(e23,e22) )
<=> ( op2(h2(e13),h2(e13)) != op2(h3(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(748,plain,
( ( op2(e22,e22) != op2(e23,e22) )
<=> ( op2(e22,e22) != op2(e23,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(749,plain,
op2(e22,e22) != op2(e23,e22),
inference(and_elim,[status(thm)],[50]) ).
tff(750,plain,
op2(e22,e22) != op2(e23,e22),
inference(modus_ponens,[status(thm)],[749,748]) ).
tff(751,plain,
op2(h2(e13),h2(e13)) != op2(h3(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[750,747]) ).
tff(752,plain,
h2(e13) != op2(h3(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[751,746]) ).
tff(753,plain,
op2(h3(e13),h2(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[752,745]) ).
tff(754,plain,
( ( h11(op1(e12,e13)) = h2(e13) )
<=> ( h1(e12) = h2(e13) ) ),
inference(monotonicity,[status(thm)],[652]) ).
tff(755,plain,
( ( h1(e12) = h2(e13) )
<=> ( h11(op1(e12,e13)) = h2(e13) ) ),
inference(symmetry,[status(thm)],[754]) ).
tff(756,plain,
( ( h1(e12) != h2(e13) )
<=> ( h11(op1(e12,e13)) != h2(e13) ) ),
inference(monotonicity,[status(thm)],[755]) ).
tff(757,plain,
( ( h1(e12) != op2(h1(e12),h1(e13)) )
<=> ( h1(e12) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(758,plain,
( ( h1(e12) != h1(op1(e12,e13)) )
<=> ( h1(e12) != op2(h1(e12),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(759,plain,
( ( op2(h1(e12),h1(e12)) != h1(op1(e12,e13)) )
<=> ( h1(e12) != h1(op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(760,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) )
<=> ( op2(h1(e12),h1(e12)) != h1(op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(761,plain,
( ( op2(e20,e20) != op2(e20,e21) )
<=> ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(762,plain,
( ( op2(e20,e20) != op2(e20,e21) )
<=> ( op2(e20,e20) != op2(e20,e21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(763,plain,
op2(e20,e20) != op2(e20,e21),
inference(and_elim,[status(thm)],[43]) ).
tff(764,plain,
op2(e20,e20) != op2(e20,e21),
inference(modus_ponens,[status(thm)],[763,762]) ).
tff(765,plain,
op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(h2(e13),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))),
inference(modus_ponens,[status(thm)],[764,761]) ).
tff(766,plain,
op2(h1(e12),h1(e12)) != h1(op1(e12,e13)),
inference(modus_ponens,[status(thm)],[765,760]) ).
tff(767,plain,
h1(e12) != h1(op1(e12,e13)),
inference(modus_ponens,[status(thm)],[766,759]) ).
tff(768,plain,
h1(e12) != op2(h1(e12),h1(e13)),
inference(modus_ponens,[status(thm)],[767,758]) ).
tff(769,plain,
h1(e12) != h2(e13),
inference(modus_ponens,[status(thm)],[768,757]) ).
tff(770,plain,
h11(op1(e12,e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[769,756]) ).
tff(771,plain,
( ( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) )
<=> ( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(772,plain,
( ( ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) ) )
<=> ( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(773,plain,
( ( op2(h3(e13),h3(e13)) = h2(e13) )
<=> ( h3(e13) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(774,plain,
( ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
<=> ( h11(op1(e12,e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(775,plain,
( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h2(e13) )
<=> ( h10(op1(e12,e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(776,plain,
( ( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) ) )
<=> ( ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[775,774,773]) ).
tff(777,plain,
( ( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[776,772]) ).
tff(778,plain,
( ( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(779,plain,
( ( op2(e23,e23) = e22 )
<=> ( op2(h3(e13),h3(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(780,plain,
( ( op2(e23,e22) = e22 )
<=> ( op2(h3(e13),h2(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(781,plain,
( ( op2(e23,e21) = e22 )
<=> ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(782,plain,
( ( op2(e23,e20) = e22 )
<=> ( op2(h3(e13),op2(h2(e13),h3(e13))) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(783,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[782,781,780,779]) ).
tff(784,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[783,778]) ).
tff(785,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(786,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(787,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(788,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)],[787]) ).
tff(789,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)],[788,786]) ).
tff(790,plain,
( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(and_elim,[status(thm)],[116]) ).
tff(791,plain,
( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[790,789]) ).
tff(792,plain,
( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[791,785]) ).
tff(793,plain,
( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[792,784]) ).
tff(794,plain,
( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[793,778]) ).
tff(795,plain,
( ( op2(h3(e13),op2(h2(e13),h3(e13))) = h2(e13) )
| ( op2(h3(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[794,778]) ).
tff(796,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[795,777]) ).
tff(797,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[796,771]) ).
tff(798,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[797,771]) ).
tff(799,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[798,771]) ).
tff(800,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[799,771]) ).
tff(801,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[800,771]) ).
tff(802,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[801,771]) ).
tff(803,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[802,771]) ).
tff(804,plain,
( ( op2(h3(e13),h2(e13)) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( h10(op1(e12,e13)) = h2(e13) )
| ( h11(op1(e12,e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[803,771]) ).
tff(805,plain,
h10(op1(e12,e13)) = h2(e13),
inference(unit_resolution,[status(thm)],[804,770,753,743]) ).
tff(806,plain,
h2(e13) = h10(op1(e12,e13)),
inference(symmetry,[status(thm)],[805]) ).
tff(807,plain,
( ( h9(e12) = e22 )
<=> ( h9(e12) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(808,plain,
( ( h9(e12) = e22 )
<=> ( h9(e12) = e22 ) ),
inference(rewrite,[status(thm)],]) ).
tff(809,plain,
h9(e12) = e22,
inference(and_elim,[status(thm)],[214]) ).
tff(810,plain,
h9(e12) = e22,
inference(modus_ponens,[status(thm)],[809,808]) ).
tff(811,plain,
h9(e12) = h2(e13),
inference(modus_ponens,[status(thm)],[810,807]) ).
tff(812,plain,
( ( e12 = e13 )
<=> ( e13 = e12 ) ),
inference(commutativity,[status(thm)],]) ).
tff(813,plain,
( ( e12 != e13 )
<=> ( e13 != e12 ) ),
inference(monotonicity,[status(thm)],[812]) ).
tff(814,plain,
( ( e12 != e13 )
<=> ( e12 != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(815,axiom,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 )
& ( e11 != e13 )
& ( e12 != e13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
tff(816,plain,
e12 != e13,
inference(and_elim,[status(thm)],[815]) ).
tff(817,plain,
e12 != e13,
inference(modus_ponens,[status(thm)],[816,814]) ).
tff(818,plain,
e13 != e12,
inference(modus_ponens,[status(thm)],[817,813]) ).
tff(819,plain,
( ( e12 = op1(e13,e12) )
<=> ( op1(e13,e12) = e12 ) ),
inference(commutativity,[status(thm)],]) ).
tff(820,plain,
( ( e12 != op1(e13,e12) )
<=> ( op1(e13,e12) != e12 ) ),
inference(monotonicity,[status(thm)],[819]) ).
tff(821,plain,
( ( op1(e12,e12) != op1(e13,e12) )
<=> ( e12 != op1(e13,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(822,plain,
( ( op1(e12,e12) != op1(e13,e12) )
<=> ( op1(e12,e12) != op1(e13,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(823,plain,
op1(e12,e12) != op1(e13,e12),
inference(and_elim,[status(thm)],[254]) ).
tff(824,plain,
op1(e12,e12) != op1(e13,e12),
inference(modus_ponens,[status(thm)],[823,822]) ).
tff(825,plain,
e12 != op1(e13,e12),
inference(modus_ponens,[status(thm)],[824,821]) ).
tff(826,plain,
op1(e13,e12) != e12,
inference(modus_ponens,[status(thm)],[825,820]) ).
tff(827,plain,
( ( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) )
<=> ( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(828,plain,
( ( ( op1(e13,e12) = e12 )
| ( e13 = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) )
<=> ( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(829,plain,
( ( op1(e13,e13) = e12 )
<=> ( e13 = e12 ) ),
inference(rewrite,[status(thm)],]) ).
tff(830,plain,
( ( ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) )
<=> ( ( op1(e13,e12) = e12 )
| ( e13 = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ) ),
inference(monotonicity,[status(thm)],[829]) ).
tff(831,plain,
( ( ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) )
<=> ( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ) ),
inference(transitivity,[status(thm)],[830,828]) ).
tff(832,plain,
( ( ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(833,plain,
( ( op1(e13,e10) = e12 )
<=> ( op1(e13,op1(e12,e13)) = e12 ) ),
inference(rewrite,[status(thm)],]) ).
tff(834,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(monotonicity,[status(thm)],[833,695]) ).
tff(835,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ) ),
inference(transitivity,[status(thm)],[834,832]) ).
tff(836,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(837,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(838,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 ) )
<=> ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(839,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(monotonicity,[status(thm)],[838]) ).
tff(840,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(transitivity,[status(thm)],[839,837]) ).
tff(841,plain,
( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ),
inference(and_elim,[status(thm)],[313]) ).
tff(842,plain,
( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[841,840]) ).
tff(843,plain,
( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[842,836]) ).
tff(844,plain,
( ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 ) ),
inference(modus_ponens,[status(thm)],[843,835]) ).
tff(845,plain,
( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ),
inference(modus_ponens,[status(thm)],[844,831]) ).
tff(846,plain,
( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ),
inference(modus_ponens,[status(thm)],[845,827]) ).
tff(847,plain,
( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ),
inference(modus_ponens,[status(thm)],[846,827]) ).
tff(848,plain,
( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ),
inference(modus_ponens,[status(thm)],[847,827]) ).
tff(849,plain,
( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ),
inference(modus_ponens,[status(thm)],[848,827]) ).
tff(850,plain,
( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ),
inference(modus_ponens,[status(thm)],[849,827]) ).
tff(851,plain,
( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ),
inference(modus_ponens,[status(thm)],[850,827]) ).
tff(852,plain,
( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ),
inference(modus_ponens,[status(thm)],[851,827]) ).
tff(853,plain,
( ( op1(e13,e12) = e12 )
| ( op1(e13,op1(e12,e13)) = e12 )
| ( op1(e13,op1(op1(e12,e13),e13)) = e12 )
| ( e13 = e12 ) ),
inference(modus_ponens,[status(thm)],[852,827]) ).
tff(854,plain,
op1(e13,op1(e12,e13)) = e12,
inference(unit_resolution,[status(thm)],[853,670,826,818]) ).
tff(855,plain,
h9(op1(e13,op1(e12,e13))) = h9(e12),
inference(monotonicity,[status(thm)],[854]) ).
tff(856,plain,
h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)),
inference(transitivity,[status(thm)],[855,811,806,734]) ).
tff(857,plain,
( ( h8(op1(e12,e13)) = op2(h2(e13),op2(h1(e12),h3(e13))) )
<=> ( h8(op1(e12,e13)) = op2(h2(e13),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(858,plain,
( ( h8(op1(e12,e13)) = op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) )
<=> ( h8(op1(e12,e13)) = op2(h2(e13),op2(h1(e12),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(859,plain,
( ( h8(e10) = op2(e22,e21) )
<=> ( h8(op1(e12,e13)) = op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(860,plain,
( ( h8(e10) = op2(e22,e21) )
<=> ( h8(e10) = op2(e22,e21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(861,axiom,
( ( h8(e12) = e22 )
& ( h8(e13) = e21 )
& ( h8(e10) = op2(e22,e21) )
& ( h8(e11) = op2(op2(e22,e21),e21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
tff(862,plain,
( ( h8(e12) = e22 )
& ( h8(e13) = e21 )
& ( h8(e10) = op2(e22,e21) ) ),
inference(and_elim,[status(thm)],[861]) ).
tff(863,plain,
h8(e10) = op2(e22,e21),
inference(and_elim,[status(thm)],[862]) ).
tff(864,plain,
h8(e10) = op2(e22,e21),
inference(modus_ponens,[status(thm)],[863,860]) ).
tff(865,plain,
h8(op1(e12,e13)) = op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))),
inference(modus_ponens,[status(thm)],[864,859]) ).
tff(866,plain,
h8(op1(e12,e13)) = op2(h2(e13),op2(h1(e12),h3(e13))),
inference(modus_ponens,[status(thm)],[865,858]) ).
tff(867,plain,
h8(op1(e12,e13)) = op2(h2(e13),h1(e13)),
inference(modus_ponens,[status(thm)],[866,857]) ).
tff(868,plain,
( ( h1(e13) = op2(h2(e13),h1(e13)) )
<=> ( op2(h2(e13),h1(e13)) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(869,plain,
( ( h1(e13) != op2(h2(e13),h1(e13)) )
<=> ( op2(h2(e13),h1(e13)) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[868]) ).
tff(870,plain,
( ( h1(e13) != h8(op1(e12,e13)) )
<=> ( h1(e13) != op2(h2(e13),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(871,plain,
( ( op2(h1(e13),h1(e13)) != h8(op1(e12,e13)) )
<=> ( h1(e13) != h8(op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(872,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) )
<=> ( op2(h1(e13),h1(e13)) != h8(op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(873,plain,
( ( op2(e21,e21) != op2(e22,e21) )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(874,plain,
( ( op2(e21,e21) != op2(e22,e21) )
<=> ( op2(e21,e21) != op2(e22,e21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(875,plain,
op2(e21,e21) != op2(e22,e21),
inference(and_elim,[status(thm)],[58]) ).
tff(876,plain,
op2(e21,e21) != op2(e22,e21),
inference(modus_ponens,[status(thm)],[875,874]) ).
tff(877,plain,
op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))),
inference(modus_ponens,[status(thm)],[876,873]) ).
tff(878,plain,
op2(h1(e13),h1(e13)) != h8(op1(e12,e13)),
inference(modus_ponens,[status(thm)],[877,872]) ).
tff(879,plain,
h1(e13) != h8(op1(e12,e13)),
inference(modus_ponens,[status(thm)],[878,871]) ).
tff(880,plain,
h1(e13) != op2(h2(e13),h1(e13)),
inference(modus_ponens,[status(thm)],[879,870]) ).
tff(881,plain,
op2(h2(e13),h1(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[880,869]) ).
tff(882,plain,
( ( ( h8(op1(e12,e13)) = h3(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) )
<=> ( ( h8(op1(e12,e13)) = h3(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(883,plain,
( ( ( h8(op1(e12,e13)) = h3(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) )
<=> ( ( h8(op1(e12,e13)) = h3(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(884,plain,
( ( $false
| ( h8(op1(e12,e13)) = h1(e13) )
| $false
| ( h8(op1(e12,e13)) = h3(e13) ) )
<=> ( ( h8(op1(e12,e13)) = h3(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(885,plain,
( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(h2(e13),h2(e13)) )
<=> ( h8(op1(e12,e13)) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(886,plain,
( ( op2(e22,e21) != op2(e22,e22) )
<=> ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(h2(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(887,plain,
( ( op2(e22,e21) != op2(e22,e22) )
<=> ( op2(e22,e21) != op2(e22,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(888,plain,
op2(e22,e21) != op2(e22,e22),
inference(and_elim,[status(thm)],[28]) ).
tff(889,plain,
op2(e22,e21) != op2(e22,e22),
inference(modus_ponens,[status(thm)],[888,887]) ).
tff(890,plain,
op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(h2(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[889,886]) ).
tff(891,plain,
h8(op1(e12,e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[890,885]) ).
tff(892,plain,
( ( h8(op1(e12,e13)) = h2(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[891]) ).
tff(893,plain,
( ( ( h8(op1(e12,e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h2(e13) )
| ( h8(op1(e12,e13)) = h3(e13) ) )
<=> ( $false
| ( h8(op1(e12,e13)) = h1(e13) )
| $false
| ( h8(op1(e12,e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[617,892]) ).
tff(894,plain,
( ( ( h8(op1(e12,e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h2(e13) )
| ( h8(op1(e12,e13)) = h3(e13) ) )
<=> ( ( h8(op1(e12,e13)) = h3(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[893,884]) ).
tff(895,plain,
( ( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) )
<=> ( ( h8(op1(e12,e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h2(e13) )
| ( h8(op1(e12,e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(896,plain,
( ( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) )
<=> ( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(897,plain,
( ( op2(e22,e21) = e23 )
<=> ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(898,plain,
( ( op2(e22,e21) = e22 )
<=> ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(899,plain,
( ( op2(e22,e21) = e21 )
<=> ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(900,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
<=> ( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[631,899,898,897]) ).
tff(901,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
<=> ( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[900,896]) ).
tff(902,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
<=> ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(903,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
<=> ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(904,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 ) )
<=> ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(905,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
<=> ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ) ),
inference(monotonicity,[status(thm)],[904]) ).
tff(906,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
<=> ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ) ),
inference(transitivity,[status(thm)],[905,903]) ).
tff(907,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/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(908,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)],[907]) ).
tff(909,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)],[908]) ).
tff(910,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)],[909]) ).
tff(911,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)],[910]) ).
tff(912,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)],[911]) ).
tff(913,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)],[912]) ).
tff(914,plain,
( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ),
inference(and_elim,[status(thm)],[913]) ).
tff(915,plain,
( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ),
inference(modus_ponens,[status(thm)],[914,906]) ).
tff(916,plain,
( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ),
inference(modus_ponens,[status(thm)],[915,902]) ).
tff(917,plain,
( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[916,901]) ).
tff(918,plain,
( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[917,896]) ).
tff(919,plain,
( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(h2(e13),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h2(e13) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[918,896]) ).
tff(920,plain,
( ( h8(op1(e12,e13)) = h1(e12) )
| ( h8(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h2(e13) )
| ( h8(op1(e12,e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[919,895]) ).
tff(921,plain,
( ( h8(op1(e12,e13)) = h3(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[920,894]) ).
tff(922,plain,
( ( h8(op1(e12,e13)) = h3(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[921,883]) ).
tff(923,plain,
( ( h8(op1(e12,e13)) = h3(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[922,882]) ).
tff(924,plain,
h8(op1(e12,e13)) = h3(e13),
inference(unit_resolution,[status(thm)],[923,881]) ).
tff(925,plain,
h3(e13) = h8(op1(e12,e13)),
inference(symmetry,[status(thm)],[924]) ).
tff(926,plain,
( ( op1(op1(e12,e13),e13) = op1(e12,op1(op1(e12,e13),e13)) )
<=> ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(927,plain,
( ( op1(op1(e12,e13),e13) != op1(e12,op1(op1(e12,e13),e13)) )
<=> ( op1(e12,op1(op1(e12,e13),e13)) != op1(op1(e12,e13),e13) ) ),
inference(monotonicity,[status(thm)],[926]) ).
tff(928,plain,
( ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(e12,op1(op1(e12,e13),e13)) )
<=> ( op1(op1(e12,e13),e13) != op1(e12,op1(op1(e12,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(929,plain,
( ( op1(e11,e11) != op1(e12,e11) )
<=> ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(e12,op1(op1(e12,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(930,plain,
( ( op1(e11,e11) != op1(e12,e11) )
<=> ( op1(e11,e11) != op1(e12,e11) ) ),
inference(rewrite,[status(thm)],]) ).
tff(931,plain,
op1(e11,e11) != op1(e12,e11),
inference(and_elim,[status(thm)],[262]) ).
tff(932,plain,
op1(e11,e11) != op1(e12,e11),
inference(modus_ponens,[status(thm)],[931,930]) ).
tff(933,plain,
op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(e12,op1(op1(e12,e13),e13)),
inference(modus_ponens,[status(thm)],[932,929]) ).
tff(934,plain,
op1(op1(e12,e13),e13) != op1(e12,op1(op1(e12,e13),e13)),
inference(modus_ponens,[status(thm)],[933,928]) ).
tff(935,plain,
op1(e12,op1(op1(e12,e13),e13)) != op1(op1(e12,e13),e13),
inference(modus_ponens,[status(thm)],[934,927]) ).
tff(936,plain,
( ( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) )
<=> ( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(937,plain,
( ( $false
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| $false
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) )
<=> ( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(938,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) != op1(e12,e12) )
<=> ( op1(e12,op1(op1(e12,e13),e13)) != e12 ) ),
inference(rewrite,[status(thm)],]) ).
tff(939,plain,
( ( op1(e12,e11) != op1(e12,e12) )
<=> ( op1(e12,op1(op1(e12,e13),e13)) != op1(e12,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(940,plain,
( ( op1(e12,e11) != op1(e12,e12) )
<=> ( op1(e12,e11) != op1(e12,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(941,plain,
op1(e12,e11) != op1(e12,e12),
inference(and_elim,[status(thm)],[232]) ).
tff(942,plain,
op1(e12,e11) != op1(e12,e12),
inference(modus_ponens,[status(thm)],[941,940]) ).
tff(943,plain,
op1(e12,op1(op1(e12,e13),e13)) != op1(e12,e12),
inference(modus_ponens,[status(thm)],[942,939]) ).
tff(944,plain,
op1(e12,op1(op1(e12,e13),e13)) != e12,
inference(modus_ponens,[status(thm)],[943,938]) ).
tff(945,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = e12 )
<=> $false ),
inference(iff_false,[status(thm)],[944]) ).
tff(946,plain,
( ( op1(e12,e11) != op1(e12,e13) )
<=> ( op1(e12,op1(op1(e12,e13),e13)) != op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(947,plain,
( ( op1(e12,e11) != op1(e12,e13) )
<=> ( op1(e12,e11) != op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(948,plain,
op1(e12,e11) != op1(e12,e13),
inference(and_elim,[status(thm)],[231]) ).
tff(949,plain,
op1(e12,e11) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[948,947]) ).
tff(950,plain,
op1(e12,op1(op1(e12,e13),e13)) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[949,946]) ).
tff(951,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(e12,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[950]) ).
tff(952,plain,
( ( ( op1(e12,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) )
<=> ( $false
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| $false
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(monotonicity,[status(thm)],[951,945]) ).
tff(953,plain,
( ( ( op1(e12,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) )
<=> ( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(transitivity,[status(thm)],[952,937]) ).
tff(954,plain,
( ( ( op1(e12,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) )
<=> ( ( op1(e12,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(955,plain,
( ( op1(e12,e11) = e13 )
<=> ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(956,plain,
( ( op1(e12,e11) = e12 )
<=> ( op1(e12,op1(op1(e12,e13),e13)) = e12 ) ),
inference(rewrite,[status(thm)],]) ).
tff(957,plain,
( ( op1(e12,e11) = e11 )
<=> ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(958,plain,
( ( op1(e12,e11) = e10 )
<=> ( op1(e12,op1(op1(e12,e13),e13)) = op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(959,plain,
( ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
<=> ( ( op1(e12,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(monotonicity,[status(thm)],[958,957,956,955]) ).
tff(960,plain,
( ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
<=> ( ( op1(e12,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ) ),
inference(transitivity,[status(thm)],[959,954]) ).
tff(961,plain,
( ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
<=> ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(962,plain,
( ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
<=> ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(963,plain,
( ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 ) )
<=> ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(964,plain,
( ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
<=> ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ) ),
inference(monotonicity,[status(thm)],[963]) ).
tff(965,plain,
( ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) )
<=> ( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ) ),
inference(transitivity,[status(thm)],[964,962]) ).
tff(966,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)],[707]) ).
tff(967,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)],[966]) ).
tff(968,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)],[967]) ).
tff(969,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)],[968]) ).
tff(970,plain,
( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ),
inference(and_elim,[status(thm)],[969]) ).
tff(971,plain,
( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ),
inference(modus_ponens,[status(thm)],[970,965]) ).
tff(972,plain,
( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ),
inference(modus_ponens,[status(thm)],[971,961]) ).
tff(973,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[972,960]) ).
tff(974,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[973,954]) ).
tff(975,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(e12,e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e12 )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[974,954]) ).
tff(976,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[975,953]) ).
tff(977,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[976,936]) ).
tff(978,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[977,936]) ).
tff(979,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[978,936]) ).
tff(980,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[979,936]) ).
tff(981,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[980,936]) ).
tff(982,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[981,936]) ).
tff(983,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[982,936]) ).
tff(984,plain,
( ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[983,936]) ).
tff(985,plain,
op1(e12,op1(op1(e12,e13),e13)) = e13,
inference(unit_resolution,[status(thm)],[984,935]) ).
tff(986,plain,
h9(op1(e12,op1(op1(e12,e13),e13))) = h9(e13),
inference(monotonicity,[status(thm)],[985]) ).
tff(987,plain,
h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)),
inference(transitivity,[status(thm)],[986,217,925,867]) ).
tff(988,plain,
( ( h7(op1(e12,e13)) = op2(h2(e13),op2(h2(e13),h3(e13))) )
<=> ( h7(op1(e12,e13)) = op2(h2(e13),h1(e12)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(989,plain,
( ( h7(e10) = op2(e22,e20) )
<=> ( h7(op1(e12,e13)) = op2(h2(e13),op2(h2(e13),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(990,plain,
( ( h7(e10) = op2(e22,e20) )
<=> ( h7(e10) = op2(e22,e20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(991,axiom,
( ( h7(e12) = e22 )
& ( h7(e13) = e20 )
& ( h7(e10) = op2(e22,e20) )
& ( h7(e11) = op2(op2(e22,e20),e20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
tff(992,plain,
( ( h7(e12) = e22 )
& ( h7(e13) = e20 )
& ( h7(e10) = op2(e22,e20) ) ),
inference(and_elim,[status(thm)],[991]) ).
tff(993,plain,
h7(e10) = op2(e22,e20),
inference(and_elim,[status(thm)],[992]) ).
tff(994,plain,
h7(e10) = op2(e22,e20),
inference(modus_ponens,[status(thm)],[993,990]) ).
tff(995,plain,
h7(op1(e12,e13)) = op2(h2(e13),op2(h2(e13),h3(e13))),
inference(modus_ponens,[status(thm)],[994,989]) ).
tff(996,plain,
h7(op1(e12,e13)) = op2(h2(e13),h1(e12)),
inference(modus_ponens,[status(thm)],[995,988]) ).
tff(997,plain,
( ( $false
| ( h7(op1(e12,e13)) = h1(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) )
<=> ( ( h7(op1(e12,e13)) = h1(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(998,plain,
( ( ( h2(e13) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) )
<=> ( $false
| ( h7(op1(e12,e13)) = h1(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[447]) ).
tff(999,plain,
( ( ( h2(e13) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) )
<=> ( ( h7(op1(e12,e13)) = h1(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[998,997]) ).
tff(1000,plain,
( ( ( h2(e13) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1001,plain,
( ( ( h2(e13) = h1(e13) )
| $false
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1002,plain,
( ( op2(h2(e13),h3(e13)) != op2(op2(h2(e13),h3(e13)),h3(e13)) )
<=> ( h1(e12) != h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1003,plain,
( ( e20 != e21 )
<=> ( op2(h2(e13),h3(e13)) != op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1004,plain,
( ( e20 != e21 )
<=> ( e20 != e21 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1005,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 )
& ( e21 != e23 ) ),
inference(and_elim,[status(thm)],[739]) ).
tff(1006,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 ) ),
inference(and_elim,[status(thm)],[1005]) ).
tff(1007,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 ) ),
inference(and_elim,[status(thm)],[1006]) ).
tff(1008,plain,
( ( e20 != e21 )
& ( e20 != e22 ) ),
inference(and_elim,[status(thm)],[1007]) ).
tff(1009,plain,
e20 != e21,
inference(and_elim,[status(thm)],[1008]) ).
tff(1010,plain,
e20 != e21,
inference(modus_ponens,[status(thm)],[1009,1004]) ).
tff(1011,plain,
op2(h2(e13),h3(e13)) != op2(op2(h2(e13),h3(e13)),h3(e13)),
inference(modus_ponens,[status(thm)],[1010,1003]) ).
tff(1012,plain,
h1(e12) != h1(e13),
inference(modus_ponens,[status(thm)],[1011,1002]) ).
tff(1013,plain,
( ( h1(e12) = h1(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1012]) ).
tff(1014,plain,
( ( ( h2(e13) = h1(e13) )
| ( h1(e12) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| $false
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[1013]) ).
tff(1015,plain,
( ( ( h2(e13) = h1(e13) )
| ( h1(e12) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[1014,1001]) ).
tff(1016,plain,
( ( ( h2(e13) = h1(e13) )
| ( h1(e12) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h1(e12) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1017,plain,
( ( ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) )
| ( h1(e12) = h1(e13) )
| ( h2(e13) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h1(e12) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1018,plain,
( ( op2(h2(e13),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
<=> ( h1(e12) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1019,plain,
( ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
<=> ( h8(op1(e12,e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1020,plain,
( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
<=> ( h7(op1(e12,e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1021,plain,
( ( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(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)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) )
<=> ( ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) )
| ( h1(e12) = h1(e13) )
| ( h2(e13) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[1020,1019,1018,470]) ).
tff(1022,plain,
( ( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(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)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( h1(e12) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[1021,1017]) ).
tff(1023,plain,
( ( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(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)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) )
<=> ( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(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)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1024,plain,
( ( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) )
<=> ( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(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)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1025,plain,
( ( op2(e22,e23) = e21 )
<=> ( op2(h2(e13),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1026,plain,
( ( op2(e22,e20) = e21 )
<=> ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1027,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
<=> ( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(e13),h3(e13)),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ),
inference(monotonicity,[status(thm)],[1026,899,479,1025]) ).
tff(1028,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
<=> ( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(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)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[1027,1024]) ).
tff(1029,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
<=> ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1030,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
<=> ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1031,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 ) )
<=> ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1032,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
<=> ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ) ),
inference(monotonicity,[status(thm)],[1031]) ).
tff(1033,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
<=> ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ) ),
inference(transitivity,[status(thm)],[1032,1030]) ).
tff(1034,plain,
( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ),
inference(and_elim,[status(thm)],[126]) ).
tff(1035,plain,
( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ),
inference(modus_ponens,[status(thm)],[1034,1033]) ).
tff(1036,plain,
( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ),
inference(modus_ponens,[status(thm)],[1035,1029]) ).
tff(1037,plain,
( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(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)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1036,1028]) ).
tff(1038,plain,
( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(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)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1037,1023]) ).
tff(1039,plain,
( ( op2(h2(e13),op2(h2(e13),h3(e13))) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(h2(e13),op2(op2(h2(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)) )
| ( op2(h2(e13),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1038,1023]) ).
tff(1040,plain,
( ( h2(e13) = h1(e13) )
| ( h1(e12) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1039,1022]) ).
tff(1041,plain,
( ( h2(e13) = h1(e13) )
| ( h1(e12) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1040,1016]) ).
tff(1042,plain,
( ( h2(e13) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( h8(op1(e12,e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1041,1015]) ).
tff(1043,plain,
( ( h2(e13) = h1(e13) )
| ( h7(op1(e12,e13)) = h1(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1042,1000]) ).
tff(1044,plain,
( ( h7(op1(e12,e13)) = h1(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1043,999]) ).
tff(1045,plain,
h7(op1(e12,e13)) = h1(e13),
inference(unit_resolution,[status(thm)],[1044,881]) ).
tff(1046,plain,
h1(e13) = h7(op1(e12,e13)),
inference(symmetry,[status(thm)],[1045]) ).
tff(1047,plain,
( ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| $false )
<=> ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1048,plain,
( ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| $false ) ),
inference(monotonicity,[status(thm)],[533]) ).
tff(1049,plain,
( ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[1048,1047]) ).
tff(1050,plain,
( ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1051,plain,
( ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| $false
| ( e12 = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1052,plain,
( ( e10 != e11 )
<=> ( op1(e12,e13) != op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1053,plain,
( ( e10 != e11 )
<=> ( e10 != e11 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1054,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 )
& ( e11 != e13 ) ),
inference(and_elim,[status(thm)],[815]) ).
tff(1055,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 ) ),
inference(and_elim,[status(thm)],[1054]) ).
tff(1056,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 ) ),
inference(and_elim,[status(thm)],[1055]) ).
tff(1057,plain,
( ( e10 != e11 )
& ( e10 != e12 ) ),
inference(and_elim,[status(thm)],[1056]) ).
tff(1058,plain,
e10 != e11,
inference(and_elim,[status(thm)],[1057]) ).
tff(1059,plain,
e10 != e11,
inference(modus_ponens,[status(thm)],[1058,1053]) ).
tff(1060,plain,
op1(e12,e13) != op1(op1(e12,e13),e13),
inference(modus_ponens,[status(thm)],[1059,1052]) ).
tff(1061,plain,
( ( op1(e12,e13) = op1(op1(e12,e13),e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1060]) ).
tff(1062,plain,
( ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,e13) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| $false
| ( e12 = op1(op1(e12,e13),e13) ) ) ),
inference(monotonicity,[status(thm)],[1061,538]) ).
tff(1063,plain,
( ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,e13) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[1062,1051]) ).
tff(1064,plain,
( ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,e13) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,e13) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1065,plain,
( ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e13) = op1(op1(e12,e13),e13) ) )
<=> ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,e13) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1066,plain,
( ( op1(e12,e13) = e11 )
<=> ( op1(e12,e13) = op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1067,plain,
( ( op1(e12,e10) = e11 )
<=> ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1068,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
<=> ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) )
| ( op1(e12,e13) = op1(op1(e12,e13),e13) ) ) ),
inference(monotonicity,[status(thm)],[1067,957,550,1066]) ).
tff(1069,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
<=> ( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,e13) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[1068,1065]) ).
tff(1070,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
<=> ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1071,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
<=> ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1072,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 ) )
<=> ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1073,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
<=> ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ) ),
inference(monotonicity,[status(thm)],[1072]) ).
tff(1074,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
<=> ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ) ),
inference(transitivity,[status(thm)],[1073,1071]) ).
tff(1075,plain,
( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ),
inference(and_elim,[status(thm)],[323]) ).
tff(1076,plain,
( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ),
inference(modus_ponens,[status(thm)],[1075,1074]) ).
tff(1077,plain,
( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ),
inference(modus_ponens,[status(thm)],[1076,1070]) ).
tff(1078,plain,
( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,e13) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1077,1069]) ).
tff(1079,plain,
( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,e13) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1078,1064]) ).
tff(1080,plain,
( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,e13) = op1(op1(e12,e13),e13) )
| ( op1(e12,e12) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1079,1064]) ).
tff(1081,plain,
( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1080,1063]) ).
tff(1082,plain,
( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1081,1050]) ).
tff(1083,plain,
( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1082,1050]) ).
tff(1084,plain,
( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) )
| ( e12 = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1083,1050]) ).
tff(1085,plain,
( ( op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13) )
| ( op1(e12,op1(op1(e12,e13),e13)) = op1(op1(e12,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1084,1049]) ).
tff(1086,plain,
op1(e12,op1(e12,e13)) = op1(op1(e12,e13),e13),
inference(unit_resolution,[status(thm)],[1085,935]) ).
tff(1087,plain,
h9(op1(e12,op1(e12,e13))) = h9(op1(op1(e12,e13),e13)),
inference(monotonicity,[status(thm)],[1086]) ).
tff(1088,plain,
h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)),
inference(transitivity,[status(thm)],[1087,511,1046,996]) ).
tff(1089,plain,
( ( h6(op1(e12,e13)) = op2(op2(h1(e12),h3(e13)),h3(e13)) )
<=> ( h6(op1(e12,e13)) = op2(h1(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1090,plain,
( ( h6(op1(e12,e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) )
<=> ( h6(op1(e12,e13)) = op2(op2(h1(e12),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1091,plain,
( ( h3(op1(op1(e12,e13),e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) )
<=> ( h6(op1(e12,e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1092,plain,
( ( h3(e11) = op2(op2(e20,e23),e23) )
<=> ( h3(op1(op1(e12,e13),e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1093,plain,
( ( h3(e11) = op2(op2(e20,e23),e23) )
<=> ( h3(e11) = op2(op2(e20,e23),e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1094,axiom,
( ( h3(e12) = e20 )
& ( h3(e13) = e23 )
& ( h3(e10) = op2(e20,e23) )
& ( h3(e11) = op2(op2(e20,e23),e23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
tff(1095,plain,
h3(e11) = op2(op2(e20,e23),e23),
inference(and_elim,[status(thm)],[1094]) ).
tff(1096,plain,
h3(e11) = op2(op2(e20,e23),e23),
inference(modus_ponens,[status(thm)],[1095,1093]) ).
tff(1097,plain,
h3(op1(op1(e12,e13),e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)),
inference(modus_ponens,[status(thm)],[1096,1092]) ).
tff(1098,plain,
h6(op1(e12,e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)),
inference(modus_ponens,[status(thm)],[1097,1091]) ).
tff(1099,plain,
h6(op1(e12,e13)) = op2(op2(h1(e12),h3(e13)),h3(e13)),
inference(modus_ponens,[status(thm)],[1098,1090]) ).
tff(1100,plain,
h6(op1(e12,e13)) = op2(h1(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[1099,1089]) ).
tff(1101,plain,
( ( h1(e13) = op2(h1(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1102,plain,
( ( h1(e13) != op2(h1(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[1101]) ).
tff(1103,plain,
( ( h1(e13) != h6(op1(e12,e13)) )
<=> ( h1(e13) != op2(h1(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1104,plain,
( ( op2(h1(e13),h1(e13)) != h6(op1(e12,e13)) )
<=> ( h1(e13) != h6(op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1105,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) )
<=> ( op2(h1(e13),h1(e13)) != h6(op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1106,plain,
( ( op2(e21,e21) != op2(e21,e23) )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1107,plain,
( ( op2(e21,e21) != op2(e21,e23) )
<=> ( op2(e21,e21) != op2(e21,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1108,plain,
op2(e21,e21) != op2(e21,e23),
inference(and_elim,[status(thm)],[33]) ).
tff(1109,plain,
op2(e21,e21) != op2(e21,e23),
inference(modus_ponens,[status(thm)],[1108,1107]) ).
tff(1110,plain,
op2(op2(op2(h2(e13),h3(e13)),h3(e13)),op2(op2(h2(e13),h3(e13)),h3(e13))) != op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)),
inference(modus_ponens,[status(thm)],[1109,1106]) ).
tff(1111,plain,
op2(h1(e13),h1(e13)) != h6(op1(e12,e13)),
inference(modus_ponens,[status(thm)],[1110,1105]) ).
tff(1112,plain,
h1(e13) != h6(op1(e12,e13)),
inference(modus_ponens,[status(thm)],[1111,1104]) ).
tff(1113,plain,
h1(e13) != op2(h1(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[1112,1103]) ).
tff(1114,plain,
op2(h1(e13),h3(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[1113,1102]) ).
tff(1115,plain,
( ( ( h6(op1(e12,e13)) = h2(e13) )
| ( h6(op1(e12,e13)) = h1(e13) ) )
<=> ( ( h6(op1(e12,e13)) = h2(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1116,plain,
( ( ( h6(op1(e12,e13)) = h2(e13) )
| ( h6(op1(e12,e13)) = h1(e13) ) )
<=> ( ( h6(op1(e12,e13)) = h2(e13) )
| ( h6(op1(e12,e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1117,plain,
( ( $false
| ( h6(op1(e12,e13)) = h1(e13) )
| ( h6(op1(e12,e13)) = h2(e13) )
| $false )
<=> ( ( h6(op1(e12,e13)) = h2(e13) )
| ( h6(op1(e12,e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1118,plain,
( ( ( h6(op1(e12,e13)) = h1(e12) )
| ( h6(op1(e12,e13)) = h1(e13) )
| ( h6(op1(e12,e13)) = h2(e13) )
| ( h6(op1(e12,e13)) = h3(e13) ) )
<=> ( $false
| ( h6(op1(e12,e13)) = h1(e13) )
| ( h6(op1(e12,e13)) = h2(e13) )
| $false ) ),
inference(monotonicity,[status(thm)],[96,182]) ).
tff(1119,plain,
( ( ( h6(op1(e12,e13)) = h1(e12) )
| ( h6(op1(e12,e13)) = h1(e13) )
| ( h6(op1(e12,e13)) = h2(e13) )
| ( h6(op1(e12,e13)) = h3(e13) ) )
<=> ( ( h6(op1(e12,e13)) = h2(e13) )
| ( h6(op1(e12,e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[1118,1117]) ).
tff(1120,plain,
( ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h2(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) ) )
<=> ( ( h6(op1(e12,e13)) = h1(e12) )
| ( h6(op1(e12,e13)) = h1(e13) )
| ( h6(op1(e12,e13)) = h2(e13) )
| ( h6(op1(e12,e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1121,plain,
( ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h2(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) ) )
<=> ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h2(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1122,plain,
( ( op2(e21,e23) = e22 )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1123,plain,
( ( op2(e21,e23) = e21 )
<=> ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1124,plain,
( ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h2(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[102,1123,1122,188]) ).
tff(1125,plain,
( ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h2(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[1124,1121]) ).
tff(1126,plain,
( ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1127,plain,
( ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1128,plain,
( ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 ) )
<=> ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1129,plain,
( ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ) ),
inference(monotonicity,[status(thm)],[1128]) ).
tff(1130,plain,
( ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ) ),
inference(transitivity,[status(thm)],[1129,1127]) ).
tff(1131,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)],[913]) ).
tff(1132,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)],[1131]) ).
tff(1133,plain,
( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ),
inference(and_elim,[status(thm)],[1132]) ).
tff(1134,plain,
( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[1133,1130]) ).
tff(1135,plain,
( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[1134,1126]) ).
tff(1136,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h2(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1135,1125]) ).
tff(1137,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h2(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1136,1121]) ).
tff(1138,plain,
( ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h2(e13) )
| ( op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h3(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1137,1121]) ).
tff(1139,plain,
( ( h6(op1(e12,e13)) = h1(e12) )
| ( h6(op1(e12,e13)) = h1(e13) )
| ( h6(op1(e12,e13)) = h2(e13) )
| ( h6(op1(e12,e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1138,1120]) ).
tff(1140,plain,
( ( h6(op1(e12,e13)) = h2(e13) )
| ( h6(op1(e12,e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1139,1119]) ).
tff(1141,plain,
( ( h6(op1(e12,e13)) = h2(e13) )
| ( h6(op1(e12,e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1140,1116]) ).
tff(1142,plain,
( ( h6(op1(e12,e13)) = h2(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1141,1115]) ).
tff(1143,plain,
h6(op1(e12,e13)) = h2(e13),
inference(unit_resolution,[status(thm)],[1142,1114]) ).
tff(1144,plain,
h2(e13) = h6(op1(e12,e13)),
inference(symmetry,[status(thm)],[1143]) ).
tff(1145,plain,
( ( op1(op1(e12,e13),e13) = op1(op1(op1(e12,e13),e13),e13) )
<=> ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1146,plain,
( ( op1(op1(e12,e13),e13) != op1(op1(op1(e12,e13),e13),e13) )
<=> ( op1(op1(op1(e12,e13),e13),e13) != op1(op1(e12,e13),e13) ) ),
inference(monotonicity,[status(thm)],[1145]) ).
tff(1147,plain,
( ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(op1(op1(e12,e13),e13),e13) )
<=> ( op1(op1(e12,e13),e13) != op1(op1(op1(e12,e13),e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1148,plain,
( ( op1(e11,e11) != op1(e11,e13) )
<=> ( op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(op1(op1(e12,e13),e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1149,plain,
( ( op1(e11,e11) != op1(e11,e13) )
<=> ( op1(e11,e11) != op1(e11,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1150,plain,
op1(e11,e11) != op1(e11,e13),
inference(and_elim,[status(thm)],[237]) ).
tff(1151,plain,
op1(e11,e11) != op1(e11,e13),
inference(modus_ponens,[status(thm)],[1150,1149]) ).
tff(1152,plain,
op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13)) != op1(op1(op1(e12,e13),e13),e13),
inference(modus_ponens,[status(thm)],[1151,1148]) ).
tff(1153,plain,
op1(op1(e12,e13),e13) != op1(op1(op1(e12,e13),e13),e13),
inference(modus_ponens,[status(thm)],[1152,1147]) ).
tff(1154,plain,
op1(op1(op1(e12,e13),e13),e13) != op1(op1(e12,e13),e13),
inference(modus_ponens,[status(thm)],[1153,1146]) ).
tff(1155,plain,
( ( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1156,plain,
( ( $false
| ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 )
| $false )
<=> ( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1157,plain,
( ( ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 ) )
<=> ( $false
| ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 )
| $false ) ),
inference(monotonicity,[status(thm)],[294,384]) ).
tff(1158,plain,
( ( ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ) ),
inference(transitivity,[status(thm)],[1157,1156]) ).
tff(1159,plain,
( ( ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1160,plain,
( ( op1(e11,e13) = e12 )
<=> ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1161,plain,
( ( op1(e11,e13) = e11 )
<=> ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1162,plain,
( ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[299,1161,1160,389]) ).
tff(1163,plain,
( ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[1162,1159]) ).
tff(1164,plain,
( ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1165,plain,
( ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1166,plain,
( ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 ) )
<=> ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1167,plain,
( ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1166]) ).
tff(1168,plain,
( ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[1167,1165]) ).
tff(1169,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)],[969]) ).
tff(1170,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)],[1169]) ).
tff(1171,plain,
( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ),
inference(and_elim,[status(thm)],[1170]) ).
tff(1172,plain,
( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1171,1168]) ).
tff(1173,plain,
( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1172,1164]) ).
tff(1174,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1173,1163]) ).
tff(1175,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1174,1159]) ).
tff(1176,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(e12,e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 )
| ( op1(op1(op1(e12,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1175,1159]) ).
tff(1177,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[1176,1158]) ).
tff(1178,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[1177,1155]) ).
tff(1179,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[1178,1155]) ).
tff(1180,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[1179,1155]) ).
tff(1181,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[1180,1155]) ).
tff(1182,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[1181,1155]) ).
tff(1183,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[1182,1155]) ).
tff(1184,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[1183,1155]) ).
tff(1185,plain,
( ( op1(op1(op1(e12,e13),e13),e13) = op1(op1(e12,e13),e13) )
| ( op1(op1(op1(e12,e13),e13),e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[1184,1155]) ).
tff(1186,plain,
op1(op1(op1(e12,e13),e13),e13) = e12,
inference(unit_resolution,[status(thm)],[1185,1154]) ).
tff(1187,plain,
h9(op1(op1(op1(e12,e13),e13),e13)) = h9(e12),
inference(monotonicity,[status(thm)],[1186]) ).
tff(1188,plain,
h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)),
inference(transitivity,[status(thm)],[1187,811,1144,1100]) ).
tff(1189,plain,
( ( h5(op1(e12,e13)) = op2(op2(h1(e12),h3(e13)),h2(e13)) )
<=> ( h5(op1(e12,e13)) = op2(h1(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1190,plain,
( ( h5(op1(e12,e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) )
<=> ( h5(op1(e12,e13)) = op2(op2(h1(e12),h3(e13)),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1191,plain,
( ( h5(e10) = op2(e21,e22) )
<=> ( h5(op1(e12,e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1192,plain,
( ( h5(e10) = op2(e21,e22) )
<=> ( h5(e10) = op2(e21,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1193,axiom,
( ( h5(e12) = e21 )
& ( h5(e13) = e22 )
& ( h5(e10) = op2(e21,e22) )
& ( h5(e11) = op2(op2(e21,e22),e22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
tff(1194,plain,
( ( h5(e12) = e21 )
& ( h5(e13) = e22 )
& ( h5(e10) = op2(e21,e22) ) ),
inference(and_elim,[status(thm)],[1193]) ).
tff(1195,plain,
h5(e10) = op2(e21,e22),
inference(and_elim,[status(thm)],[1194]) ).
tff(1196,plain,
h5(e10) = op2(e21,e22),
inference(modus_ponens,[status(thm)],[1195,1192]) ).
tff(1197,plain,
h5(op1(e12,e13)) = op2(op2(op2(h2(e13),h3(e13)),h3(e13)),h2(e13)),
inference(modus_ponens,[status(thm)],[1196,1191]) ).
tff(1198,plain,
h5(op1(e12,e13)) = op2(op2(h1(e12),h3(e13)),h2(e13)),
inference(modus_ponens,[status(thm)],[1197,1190]) ).
tff(1199,plain,
h5(op1(e12,e13)) = op2(h1(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[1198,1189]) ).
tff(1200,plain,
h1(e12) = h5(op1(e12,e13)),
inference(symmetry,[status(thm)],[147]) ).
tff(1201,plain,
h9(op1(op1(op1(e12,e13),e13),e12)) = h9(op1(e12,e13)),
inference(monotonicity,[status(thm)],[349]) ).
tff(1202,plain,
h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)),
inference(transitivity,[status(thm)],[1201,660,1200,1199]) ).
tff(1203,plain,
( ( h2(op1(e12,e13)) = op2(op2(h2(e13),h3(e13)),h2(e13)) )
<=> ( h2(op1(e12,e13)) = op2(h1(e12),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1204,plain,
( ( h2(e10) = op2(e20,e22) )
<=> ( h2(op1(e12,e13)) = op2(op2(h2(e13),h3(e13)),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1205,plain,
( ( h2(e10) = op2(e20,e22) )
<=> ( h2(e10) = op2(e20,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1206,axiom,
( ( h2(e12) = e20 )
& ( h2(e13) = e22 )
& ( h2(e10) = op2(e20,e22) )
& ( h2(e11) = op2(op2(e20,e22),e22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
tff(1207,plain,
( ( h2(e12) = e20 )
& ( h2(e13) = e22 )
& ( h2(e10) = op2(e20,e22) ) ),
inference(and_elim,[status(thm)],[1206]) ).
tff(1208,plain,
h2(e10) = op2(e20,e22),
inference(and_elim,[status(thm)],[1207]) ).
tff(1209,plain,
h2(e10) = op2(e20,e22),
inference(modus_ponens,[status(thm)],[1208,1205]) ).
tff(1210,plain,
h2(op1(e12,e13)) = op2(op2(h2(e13),h3(e13)),h2(e13)),
inference(modus_ponens,[status(thm)],[1209,1204]) ).
tff(1211,plain,
h2(op1(e12,e13)) = op2(h1(e12),h2(e13)),
inference(modus_ponens,[status(thm)],[1210,1203]) ).
tff(1212,plain,
( ( h1(e12) = op2(h1(e12),h2(e13)) )
<=> ( op2(h1(e12),h2(e13)) = h1(e12) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1213,plain,
( ( h1(e12) != op2(h1(e12),h2(e13)) )
<=> ( op2(h1(e12),h2(e13)) != h1(e12) ) ),
inference(monotonicity,[status(thm)],[1212]) ).
tff(1214,plain,
( ( op2(h1(e12),h1(e12)) != h2(op1(e12,e13)) )
<=> ( h1(e12) != op2(h1(e12),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1215,plain,
( ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(h2(e13),h3(e13)),h2(e13)) )
<=> ( op2(h1(e12),h1(e12)) != h2(op1(e12,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1216,plain,
( ( op2(e20,e20) != op2(e20,e22) )
<=> ( op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(h2(e13),h3(e13)),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1217,plain,
( ( op2(e20,e20) != op2(e20,e22) )
<=> ( op2(e20,e20) != op2(e20,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1218,plain,
op2(e20,e20) != op2(e20,e22),
inference(and_elim,[status(thm)],[42]) ).
tff(1219,plain,
op2(e20,e20) != op2(e20,e22),
inference(modus_ponens,[status(thm)],[1218,1217]) ).
tff(1220,plain,
op2(op2(h2(e13),h3(e13)),op2(h2(e13),h3(e13))) != op2(op2(h2(e13),h3(e13)),h2(e13)),
inference(modus_ponens,[status(thm)],[1219,1216]) ).
tff(1221,plain,
op2(h1(e12),h1(e12)) != h2(op1(e12,e13)),
inference(modus_ponens,[status(thm)],[1220,1215]) ).
tff(1222,plain,
h1(e12) != op2(h1(e12),h2(e13)),
inference(modus_ponens,[status(thm)],[1221,1214]) ).
tff(1223,plain,
op2(h1(e12),h2(e13)) != h1(e12),
inference(modus_ponens,[status(thm)],[1222,1213]) ).
tff(1224,plain,
( ( ( h2(op1(e12,e13)) = h3(e13) )
| $false
| $false
| ( op2(h1(e12),h2(e13)) = h1(e12) ) )
<=> ( ( h2(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1225,plain,
( ( h2(op1(e12,e13)) != h2(e13) )
<=> ( op2(h1(e12),h2(e13)) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1226,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) != op2(h2(e13),h2(e13)) )
<=> ( h2(op1(e12,e13)) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1227,plain,
( ( op2(e20,e22) != op2(e22,e22) )
<=> ( op2(op2(h2(e13),h3(e13)),h2(e13)) != op2(h2(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1228,plain,
( ( op2(e20,e22) != op2(e22,e22) )
<=> ( op2(e20,e22) != op2(e22,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1229,plain,
op2(e20,e22) != op2(e22,e22),
inference(and_elim,[status(thm)],[54]) ).
tff(1230,plain,
op2(e20,e22) != op2(e22,e22),
inference(modus_ponens,[status(thm)],[1229,1228]) ).
tff(1231,plain,
op2(op2(h2(e13),h3(e13)),h2(e13)) != op2(h2(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[1230,1227]) ).
tff(1232,plain,
h2(op1(e12,e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[1231,1226]) ).
tff(1233,plain,
op2(h1(e12),h2(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[1232,1225]) ).
tff(1234,plain,
( ( op2(h1(e12),h2(e13)) = h2(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1233]) ).
tff(1235,plain,
( ( ( h2(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h2(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e12) ) )
<=> ( ( h2(op1(e12,e13)) = h3(e13) )
| $false
| $false
| ( op2(h1(e12),h2(e13)) = h1(e12) ) ) ),
inference(monotonicity,[status(thm)],[462,1234]) ).
tff(1236,plain,
( ( ( h2(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h2(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e12) ) )
<=> ( ( h2(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e12) ) ) ),
inference(transitivity,[status(thm)],[1235,1224]) ).
tff(1237,plain,
( ( ( h2(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h2(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e12) ) )
<=> ( ( h2(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h2(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1238,plain,
( ( ( op2(h1(e12),h2(e13)) = h1(e12) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h2(e13) )
| ( h2(op1(e12,e13)) = h3(e13) ) )
<=> ( ( h2(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h2(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e12) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1239,plain,
( ( h2(op1(e12,e13)) = h2(e13) )
<=> ( op2(h1(e12),h2(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1240,plain,
( ( h2(op1(e12,e13)) = h1(e12) )
<=> ( op2(h1(e12),h2(e13)) = h1(e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1241,plain,
( ( ( h2(op1(e12,e13)) = h1(e12) )
| ( h2(op1(e12,e13)) = h1(e13) )
| ( h2(op1(e12,e13)) = h2(e13) )
| ( h2(op1(e12,e13)) = h3(e13) ) )
<=> ( ( op2(h1(e12),h2(e13)) = h1(e12) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h2(e13) )
| ( h2(op1(e12,e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[1240,466,1239]) ).
tff(1242,plain,
( ( ( h2(op1(e12,e13)) = h1(e12) )
| ( h2(op1(e12,e13)) = h1(e13) )
| ( h2(op1(e12,e13)) = h2(e13) )
| ( h2(op1(e12,e13)) = h3(e13) ) )
<=> ( ( h2(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h2(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e12) ) ) ),
inference(transitivity,[status(thm)],[1241,1238]) ).
tff(1243,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) )
<=> ( ( h2(op1(e12,e13)) = h1(e12) )
| ( h2(op1(e12,e13)) = h1(e13) )
| ( h2(op1(e12,e13)) = h2(e13) )
| ( h2(op1(e12,e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1244,plain,
( ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1245,plain,
( ( op2(e20,e22) = e23 )
<=> ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1246,plain,
( ( op2(e20,e22) = e22 )
<=> ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1247,plain,
( ( op2(e20,e22) = e20 )
<=> ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1248,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[1247,481,1246,1245]) ).
tff(1249,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[1248,1244]) ).
tff(1250,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(1251,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(1252,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(1253,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)],[1252]) ).
tff(1254,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)],[1253,1251]) ).
tff(1255,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)],[1132]) ).
tff(1256,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)],[1255]) ).
tff(1257,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)],[1256]) ).
tff(1258,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)],[1257]) ).
tff(1259,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)],[1258]) ).
tff(1260,plain,
( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ),
inference(and_elim,[status(thm)],[1259]) ).
tff(1261,plain,
( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ),
inference(modus_ponens,[status(thm)],[1260,1254]) ).
tff(1262,plain,
( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ),
inference(modus_ponens,[status(thm)],[1261,1250]) ).
tff(1263,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1262,1249]) ).
tff(1264,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1263,1244]) ).
tff(1265,plain,
( ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(h2(e13),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h2(e13) )
| ( op2(op2(h2(e13),h3(e13)),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1264,1244]) ).
tff(1266,plain,
( ( h2(op1(e12,e13)) = h1(e12) )
| ( h2(op1(e12,e13)) = h1(e13) )
| ( h2(op1(e12,e13)) = h2(e13) )
| ( h2(op1(e12,e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1265,1243]) ).
tff(1267,plain,
( ( h2(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h2(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[1266,1242]) ).
tff(1268,plain,
( ( h2(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e13) )
| ( op2(h1(e12),h2(e13)) = h2(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[1267,1237]) ).
tff(1269,plain,
( ( h2(op1(e12,e13)) = h3(e13) )
| ( op2(h1(e12),h2(e13)) = h1(e12) ) ),
inference(modus_ponens,[status(thm)],[1268,1236]) ).
tff(1270,plain,
h2(op1(e12,e13)) = h3(e13),
inference(unit_resolution,[status(thm)],[1269,1223]) ).
tff(1271,plain,
h3(e13) = h2(op1(e12,e13)),
inference(symmetry,[status(thm)],[1270]) ).
tff(1272,plain,
( ( op1(e12,e13) = op1(op1(e12,e13),e12) )
<=> ( op1(op1(e12,e13),e12) = op1(e12,e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1273,plain,
( ( op1(e12,e13) != op1(op1(e12,e13),e12) )
<=> ( op1(op1(e12,e13),e12) != op1(e12,e13) ) ),
inference(monotonicity,[status(thm)],[1272]) ).
tff(1274,plain,
( ( op1(op1(e12,e13),op1(e12,e13)) != op1(op1(e12,e13),e12) )
<=> ( op1(e12,e13) != op1(op1(e12,e13),e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1275,plain,
( ( op1(e10,e10) != op1(e10,e12) )
<=> ( op1(op1(e12,e13),op1(e12,e13)) != op1(op1(e12,e13),e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1276,plain,
( ( op1(e10,e10) != op1(e10,e12) )
<=> ( op1(e10,e10) != op1(e10,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1277,plain,
op1(e10,e10) != op1(e10,e12),
inference(and_elim,[status(thm)],[246]) ).
tff(1278,plain,
op1(e10,e10) != op1(e10,e12),
inference(modus_ponens,[status(thm)],[1277,1276]) ).
tff(1279,plain,
op1(op1(e12,e13),op1(e12,e13)) != op1(op1(e12,e13),e12),
inference(modus_ponens,[status(thm)],[1278,1275]) ).
tff(1280,plain,
op1(e12,e13) != op1(op1(e12,e13),e12),
inference(modus_ponens,[status(thm)],[1279,1274]) ).
tff(1281,plain,
op1(op1(e12,e13),e12) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[1280,1273]) ).
tff(1282,plain,
( ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) )
<=> ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1283,plain,
( ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| $false
| $false
| ( op1(op1(e12,e13),e12) = e13 ) )
<=> ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1284,plain,
( ( op1(op1(e12,e13),e12) != op1(e12,e12) )
<=> ( op1(op1(e12,e13),e12) != e12 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1285,plain,
( ( op1(e10,e12) != op1(e12,e12) )
<=> ( op1(op1(e12,e13),e12) != op1(e12,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1286,plain,
( ( op1(e10,e12) != op1(e12,e12) )
<=> ( op1(e10,e12) != op1(e12,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1287,plain,
op1(e10,e12) != op1(e12,e12),
inference(and_elim,[status(thm)],[258]) ).
tff(1288,plain,
op1(e10,e12) != op1(e12,e12),
inference(modus_ponens,[status(thm)],[1287,1286]) ).
tff(1289,plain,
op1(op1(e12,e13),e12) != op1(e12,e12),
inference(modus_ponens,[status(thm)],[1288,1285]) ).
tff(1290,plain,
op1(op1(e12,e13),e12) != e12,
inference(modus_ponens,[status(thm)],[1289,1284]) ).
tff(1291,plain,
( ( op1(op1(e12,e13),e12) = e12 )
<=> $false ),
inference(iff_false,[status(thm)],[1290]) ).
tff(1292,plain,
( ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(e12,e13),e12) = e12 )
| ( op1(op1(e12,e13),e12) = e13 ) )
<=> ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| $false
| $false
| ( op1(op1(e12,e13),e12) = e13 ) ) ),
inference(monotonicity,[status(thm)],[544,1291]) ).
tff(1293,plain,
( ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(e12,e13),e12) = e12 )
| ( op1(op1(e12,e13),e12) = e13 ) )
<=> ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ) ),
inference(transitivity,[status(thm)],[1292,1283]) ).
tff(1294,plain,
( ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(e12,e13),e12) = e12 )
| ( op1(op1(e12,e13),e12) = e13 ) )
<=> ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(e12,e13),e12) = e12 )
| ( op1(op1(e12,e13),e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1295,plain,
( ( op1(e10,e12) = e13 )
<=> ( op1(op1(e12,e13),e12) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1296,plain,
( ( op1(e10,e12) = e12 )
<=> ( op1(op1(e12,e13),e12) = e12 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1297,plain,
( ( op1(e10,e12) = e10 )
<=> ( op1(op1(e12,e13),e12) = op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1298,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
<=> ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(e12,e13),e12) = e12 )
| ( op1(op1(e12,e13),e12) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1297,552,1296,1295]) ).
tff(1299,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
<=> ( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(e12,e13),e12) = e12 )
| ( op1(op1(e12,e13),e12) = e13 ) ) ),
inference(transitivity,[status(thm)],[1298,1294]) ).
tff(1300,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
<=> ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1301,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
<=> ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1302,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 ) )
<=> ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1303,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
<=> ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1302]) ).
tff(1304,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
<=> ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ) ),
inference(transitivity,[status(thm)],[1303,1301]) ).
tff(1305,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)],[1170]) ).
tff(1306,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)],[1305]) ).
tff(1307,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)],[1306]) ).
tff(1308,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)],[1307]) ).
tff(1309,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 ) ) ),
inference(and_elim,[status(thm)],[1308]) ).
tff(1310,plain,
( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ),
inference(and_elim,[status(thm)],[1309]) ).
tff(1311,plain,
( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1310,1304]) ).
tff(1312,plain,
( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1311,1300]) ).
tff(1313,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(e12,e13),e12) = e12 )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1312,1299]) ).
tff(1314,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(e12,e13),e12) = e12 )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1313,1294]) ).
tff(1315,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = op1(op1(e12,e13),e13) )
| ( op1(op1(e12,e13),e12) = e12 )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1314,1294]) ).
tff(1316,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1315,1293]) ).
tff(1317,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1316,1282]) ).
tff(1318,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1317,1282]) ).
tff(1319,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1318,1282]) ).
tff(1320,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1319,1282]) ).
tff(1321,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1320,1282]) ).
tff(1322,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1321,1282]) ).
tff(1323,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1322,1282]) ).
tff(1324,plain,
( ( op1(op1(e12,e13),e12) = op1(e12,e13) )
| ( op1(op1(e12,e13),e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[1323,1282]) ).
tff(1325,plain,
op1(op1(e12,e13),e12) = e13,
inference(unit_resolution,[status(thm)],[1324,1281]) ).
tff(1326,plain,
h9(op1(op1(e12,e13),e12)) = h9(e13),
inference(monotonicity,[status(thm)],[1325]) ).
tff(1327,plain,
h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)),
inference(transitivity,[status(thm)],[1326,217,1271,1211]) ).
tff(1328,plain,
( ~ ~ ( ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) != op2(h1(e13),h1(e12)) )
| ( h9(op1(op1(e12,e13),e12)) != op2(h1(e12),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e12)) != op2(h1(e13),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e13)) != op2(h1(e13),h3(e13)) )
| ( h9(op1(e12,op1(e12,e13))) != op2(h2(e13),h1(e12)) )
| ( h9(op1(e12,op1(op1(e12,e13),e13))) != op2(h2(e13),h1(e13)) )
| ( h9(op1(e13,op1(e12,e13))) != op2(h3(e13),h1(e12)) )
| ( h9(op1(e13,op1(op1(e12,e13),e13))) != op2(h3(e13),h1(e13)) )
| ( h9(op1(e13,e12)) != op2(h3(e13),h2(e13)) ) )
<=> ( ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) != op2(h1(e13),h1(e12)) )
| ( h9(op1(op1(e12,e13),e12)) != op2(h1(e12),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e12)) != op2(h1(e13),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e13)) != op2(h1(e13),h3(e13)) )
| ( h9(op1(e12,op1(e12,e13))) != op2(h2(e13),h1(e12)) )
| ( h9(op1(e12,op1(op1(e12,e13),e13))) != op2(h2(e13),h1(e13)) )
| ( h9(op1(e13,op1(e12,e13))) != op2(h3(e13),h1(e12)) )
| ( h9(op1(e13,op1(op1(e12,e13),e13))) != op2(h3(e13),h1(e13)) )
| ( h9(op1(e13,e12)) != op2(h3(e13),h2(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1329,plain,
( ( ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) ) )
<=> ~ ( ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) != op2(h1(e13),h1(e12)) )
| ( h9(op1(op1(e12,e13),e12)) != op2(h1(e12),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e12)) != op2(h1(e13),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e13)) != op2(h1(e13),h3(e13)) )
| ( h9(op1(e12,op1(e12,e13))) != op2(h2(e13),h1(e12)) )
| ( h9(op1(e12,op1(op1(e12,e13),e13))) != op2(h2(e13),h1(e13)) )
| ( h9(op1(e13,op1(e12,e13))) != op2(h3(e13),h1(e12)) )
| ( h9(op1(e13,op1(op1(e12,e13),e13))) != op2(h3(e13),h1(e13)) )
| ( h9(op1(e13,e12)) != op2(h3(e13),h2(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1330,plain,
( ~ ( ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) ) )
<=> ~ ~ ( ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) != op2(h1(e13),h1(e12)) )
| ( h9(op1(op1(e12,e13),e12)) != op2(h1(e12),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e12)) != op2(h1(e13),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e13)) != op2(h1(e13),h3(e13)) )
| ( h9(op1(e12,op1(e12,e13))) != op2(h2(e13),h1(e12)) )
| ( h9(op1(e12,op1(op1(e12,e13),e13))) != op2(h2(e13),h1(e13)) )
| ( h9(op1(e13,op1(e12,e13))) != op2(h3(e13),h1(e12)) )
| ( h9(op1(e13,op1(op1(e12,e13),e13))) != op2(h3(e13),h1(e13)) )
| ( h9(op1(e13,e12)) != op2(h3(e13),h2(e13)) ) ) ),
inference(monotonicity,[status(thm)],[1329]) ).
tff(1331,plain,
( ~ ( ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) ) )
<=> ( ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) != op2(h1(e13),h1(e12)) )
| ( h9(op1(op1(e12,e13),e12)) != op2(h1(e12),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e12)) != op2(h1(e13),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e13)) != op2(h1(e13),h3(e13)) )
| ( h9(op1(e12,op1(e12,e13))) != op2(h2(e13),h1(e12)) )
| ( h9(op1(e12,op1(op1(e12,e13),e13))) != op2(h2(e13),h1(e13)) )
| ( h9(op1(e13,op1(e12,e13))) != op2(h3(e13),h1(e12)) )
| ( h9(op1(e13,op1(op1(e12,e13),e13))) != op2(h3(e13),h1(e13)) )
| ( h9(op1(e13,e12)) != op2(h3(e13),h2(e13)) ) ) ),
inference(transitivity,[status(thm)],[1330,1328]) ).
tff(1332,plain,
( ~ ( ( h9(e12) = op2(h1(e12),h1(e13)) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) ) )
<=> ~ ( ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1333,plain,
( ~ ( ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h1(e12),h1(e13)) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) ) )
<=> ~ ( ( h9(e12) = op2(h1(e12),h1(e13)) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1334,plain,
( ~ ( ( h9(op1(e12,e13)) = op2(h1(e12),h1(e12)) )
& ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h1(e12),h1(e13)) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h1(e13) = op2(h1(e12),h3(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(e12,e13),e13)) = op2(h1(e13),h1(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(e12) = op2(h2(e13),h2(e13)) )
& ( h1(e12) = op2(h2(e13),h3(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) )
& ( h9(e13) = op2(h3(e13),h3(e13)) ) )
<=> ~ ( ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h1(e12),h1(e13)) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1335,plain,
( ~ ( ( h9(op1(op1(e12,e13),op1(e12,e13))) = op2(h9(op1(e12,e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h9(op1(e12,e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h9(op1(e12,e13)),h9(e12)) )
& ( h9(op1(op1(e12,e13),e13)) = op2(h9(op1(e12,e13)),h9(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h9(op1(op1(e12,e13),e13)),h9(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h9(op1(op1(e12,e13),e13)),h9(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h9(e12),h9(op1(e12,e13))) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h9(e12),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h9(e13),h9(op1(e12,e13))) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h9(e13),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(op1(e12,e13)) = op2(h2(e13),h3(e13)) )
| ( h9(op1(op1(e12,e13),e13)) = op2(h2(e13),h3(e13)) )
| ( h9(e12) = op2(h2(e13),h3(e13)) )
| ( h9(e13) = op2(h2(e13),h3(e13)) ) )
& ( ( h9(op1(op1(e12,e13),e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(op1(e12,e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e12) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e13) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) )
<=> ~ ( ( h9(op1(e12,e13)) = op2(h1(e12),h1(e12)) )
& ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h1(e12),h1(e13)) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h1(e13) = op2(h1(e12),h3(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(e12,e13),e13)) = op2(h1(e13),h1(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(e12) = op2(h2(e13),h2(e13)) )
& ( h1(e12) = op2(h2(e13),h3(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) )
& ( h9(e13) = op2(h3(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1336,plain,
( ( ( h9(op1(op1(e12,e13),op1(e12,e13))) = op2(h9(op1(e12,e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h9(op1(e12,e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h9(op1(e12,e13)),h9(e12)) )
& ( h9(op1(op1(e12,e13),e13)) = op2(h9(op1(e12,e13)),h9(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h9(op1(op1(e12,e13),e13)),h9(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h9(op1(op1(e12,e13),e13)),h9(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h9(e12),h9(op1(e12,e13))) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h9(e12),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h9(e13),h9(op1(e12,e13))) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h9(e13),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(op1(e12,e13)) = op2(h2(e13),h3(e13)) )
| ( h9(op1(op1(e12,e13),e13)) = op2(h2(e13),h3(e13)) )
| ( h9(e12) = op2(h2(e13),h3(e13)) )
| ( h9(e13) = op2(h2(e13),h3(e13)) ) )
& ( ( h9(op1(op1(e12,e13),e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(op1(e12,e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e12) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e13) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) )
<=> ( ( h9(op1(op1(e12,e13),op1(e12,e13))) = op2(h9(op1(e12,e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h9(op1(e12,e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h9(op1(e12,e13)),h9(e12)) )
& ( h9(op1(op1(e12,e13),e13)) = op2(h9(op1(e12,e13)),h9(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h9(op1(op1(e12,e13),e13)),h9(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h9(op1(op1(e12,e13),e13)),h9(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h9(e12),h9(op1(e12,e13))) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h9(e12),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h9(e13),h9(op1(e12,e13))) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h9(e13),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(op1(e12,e13)) = op2(h2(e13),h3(e13)) )
| ( h9(op1(op1(e12,e13),e13)) = op2(h2(e13),h3(e13)) )
| ( h9(e12) = op2(h2(e13),h3(e13)) )
| ( h9(e13) = op2(h2(e13),h3(e13)) ) )
& ( ( h9(op1(op1(e12,e13),e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(op1(e12,e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e12) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e13) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1337,plain,
( ~ ( ( h9(op1(op1(e12,e13),op1(e12,e13))) = op2(h9(op1(e12,e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h9(op1(e12,e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h9(op1(e12,e13)),h9(e12)) )
& ( h9(op1(op1(e12,e13),e13)) = op2(h9(op1(e12,e13)),h9(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h9(op1(op1(e12,e13),e13)),h9(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h9(op1(op1(e12,e13),e13)),h9(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h9(e12),h9(op1(e12,e13))) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h9(e12),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h9(e13),h9(op1(e12,e13))) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h9(e13),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(op1(e12,e13)) = op2(h2(e13),h3(e13)) )
| ( h9(op1(op1(e12,e13),e13)) = op2(h2(e13),h3(e13)) )
| ( h9(e12) = op2(h2(e13),h3(e13)) )
| ( h9(e13) = op2(h2(e13),h3(e13)) ) )
& ( ( h9(op1(op1(e12,e13),e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(op1(e12,e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e12) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e13) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) )
<=> ~ ( ( h9(op1(op1(e12,e13),op1(e12,e13))) = op2(h9(op1(e12,e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h9(op1(e12,e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h9(op1(e12,e13)),h9(e12)) )
& ( h9(op1(op1(e12,e13),e13)) = op2(h9(op1(e12,e13)),h9(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h9(op1(op1(e12,e13),e13)),h9(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h9(op1(op1(e12,e13),e13)),h9(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h9(e12),h9(op1(e12,e13))) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h9(e12),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h9(e13),h9(op1(e12,e13))) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h9(e13),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(op1(e12,e13)) = op2(h2(e13),h3(e13)) )
| ( h9(op1(op1(e12,e13),e13)) = op2(h2(e13),h3(e13)) )
| ( h9(e12) = op2(h2(e13),h3(e13)) )
| ( h9(e13) = op2(h2(e13),h3(e13)) ) )
& ( ( h9(op1(op1(e12,e13),e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(op1(e12,e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e12) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e13) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ) ),
inference(monotonicity,[status(thm)],[1336]) ).
tff(1338,plain,
( ~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) ) )
<=> ~ ( ( h9(op1(op1(e12,e13),op1(e12,e13))) = op2(h9(op1(e12,e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h9(op1(e12,e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h9(op1(e12,e13)),h9(e12)) )
& ( h9(op1(op1(e12,e13),e13)) = op2(h9(op1(e12,e13)),h9(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h9(op1(op1(e12,e13),e13)),h9(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h9(op1(op1(e12,e13),e13)),h9(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h9(e12),h9(op1(e12,e13))) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h9(e12),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h9(e13),h9(op1(e12,e13))) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h9(e13),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(op1(e12,e13)) = op2(h2(e13),h3(e13)) )
| ( h9(op1(op1(e12,e13),e13)) = op2(h2(e13),h3(e13)) )
| ( h9(e12) = op2(h2(e13),h3(e13)) )
| ( h9(e13) = op2(h2(e13),h3(e13)) ) )
& ( ( h9(op1(op1(e12,e13),e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(op1(e12,e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e12) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e13) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1339,plain,
( ~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) ) )
<=> ~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1340,plain,
( ~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e12) = e22 )
| ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e13) = e23 )
| ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 ) ) )
<=> ~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1341,plain,
( ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e12) = e22 )
| ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e13) = e23 )
| ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 ) ) )
<=> ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e12) = e22 )
| ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e13) = e23 )
| ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1342,plain,
( ~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e12) = e22 )
| ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e13) = e23 )
| ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 ) ) )
<=> ~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e12) = e22 )
| ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e13) = e23 )
| ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 ) ) ) ),
inference(monotonicity,[status(thm)],[1341]) ).
tff(1343,plain,
( ~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e12) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 )
| ( h9(e13) = e23 ) ) )
<=> ~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e12) = e22 )
| ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e13) = e23 )
| ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1344,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 ) ) )
| ( ( h5(op1(e10,e10)) = op2(h5(e10),h5(e10)) )
& ( h5(op1(e10,e11)) = op2(h5(e10),h5(e11)) )
& ( h5(op1(e10,e12)) = op2(h5(e10),h5(e12)) )
& ( h5(op1(e10,e13)) = op2(h5(e10),h5(e13)) )
& ( h5(op1(e11,e10)) = op2(h5(e11),h5(e10)) )
& ( h5(op1(e11,e11)) = op2(h5(e11),h5(e11)) )
& ( h5(op1(e11,e12)) = op2(h5(e11),h5(e12)) )
& ( h5(op1(e11,e13)) = op2(h5(e11),h5(e13)) )
& ( h5(op1(e12,e10)) = op2(h5(e12),h5(e10)) )
& ( h5(op1(e12,e11)) = op2(h5(e12),h5(e11)) )
& ( h5(op1(e12,e12)) = op2(h5(e12),h5(e12)) )
& ( h5(op1(e12,e13)) = op2(h5(e12),h5(e13)) )
& ( h5(op1(e13,e10)) = op2(h5(e13),h5(e10)) )
& ( h5(op1(e13,e11)) = op2(h5(e13),h5(e11)) )
& ( h5(op1(e13,e12)) = op2(h5(e13),h5(e12)) )
& ( h5(op1(e13,e13)) = op2(h5(e13),h5(e13)) )
& ( ( h5(e10) = e20 )
| ( h5(e11) = e20 )
| ( h5(e12) = e20 )
| ( h5(e13) = e20 ) )
& ( ( h5(e10) = e21 )
| ( h5(e11) = e21 )
| ( h5(e12) = e21 )
| ( h5(e13) = e21 ) )
& ( ( h5(e10) = e22 )
| ( h5(e11) = e22 )
| ( h5(e12) = e22 )
| ( h5(e13) = e22 ) )
& ( ( h5(e10) = e23 )
| ( h5(e11) = e23 )
| ( h5(e12) = e23 )
| ( h5(e13) = e23 ) ) )
| ( ( h6(op1(e10,e10)) = op2(h6(e10),h6(e10)) )
& ( h6(op1(e10,e11)) = op2(h6(e10),h6(e11)) )
& ( h6(op1(e10,e12)) = op2(h6(e10),h6(e12)) )
& ( h6(op1(e10,e13)) = op2(h6(e10),h6(e13)) )
& ( h6(op1(e11,e10)) = op2(h6(e11),h6(e10)) )
& ( h6(op1(e11,e11)) = op2(h6(e11),h6(e11)) )
& ( h6(op1(e11,e12)) = op2(h6(e11),h6(e12)) )
& ( h6(op1(e11,e13)) = op2(h6(e11),h6(e13)) )
& ( h6(op1(e12,e10)) = op2(h6(e12),h6(e10)) )
& ( h6(op1(e12,e11)) = op2(h6(e12),h6(e11)) )
& ( h6(op1(e12,e12)) = op2(h6(e12),h6(e12)) )
& ( h6(op1(e12,e13)) = op2(h6(e12),h6(e13)) )
& ( h6(op1(e13,e10)) = op2(h6(e13),h6(e10)) )
& ( h6(op1(e13,e11)) = op2(h6(e13),h6(e11)) )
& ( h6(op1(e13,e12)) = op2(h6(e13),h6(e12)) )
& ( h6(op1(e13,e13)) = op2(h6(e13),h6(e13)) )
& ( ( h6(e10) = e20 )
| ( h6(e11) = e20 )
| ( h6(e12) = e20 )
| ( h6(e13) = e20 ) )
& ( ( h6(e10) = e21 )
| ( h6(e11) = e21 )
| ( h6(e12) = e21 )
| ( h6(e13) = e21 ) )
& ( ( h6(e10) = e22 )
| ( h6(e11) = e22 )
| ( h6(e12) = e22 )
| ( h6(e13) = e22 ) )
& ( ( h6(e10) = e23 )
| ( h6(e11) = e23 )
| ( h6(e12) = e23 )
| ( h6(e13) = e23 ) ) )
| ( ( h7(op1(e10,e10)) = op2(h7(e10),h7(e10)) )
& ( h7(op1(e10,e11)) = op2(h7(e10),h7(e11)) )
& ( h7(op1(e10,e12)) = op2(h7(e10),h7(e12)) )
& ( h7(op1(e10,e13)) = op2(h7(e10),h7(e13)) )
& ( h7(op1(e11,e10)) = op2(h7(e11),h7(e10)) )
& ( h7(op1(e11,e11)) = op2(h7(e11),h7(e11)) )
& ( h7(op1(e11,e12)) = op2(h7(e11),h7(e12)) )
& ( h7(op1(e11,e13)) = op2(h7(e11),h7(e13)) )
& ( h7(op1(e12,e10)) = op2(h7(e12),h7(e10)) )
& ( h7(op1(e12,e11)) = op2(h7(e12),h7(e11)) )
& ( h7(op1(e12,e12)) = op2(h7(e12),h7(e12)) )
& ( h7(op1(e12,e13)) = op2(h7(e12),h7(e13)) )
& ( h7(op1(e13,e10)) = op2(h7(e13),h7(e10)) )
& ( h7(op1(e13,e11)) = op2(h7(e13),h7(e11)) )
& ( h7(op1(e13,e12)) = op2(h7(e13),h7(e12)) )
& ( h7(op1(e13,e13)) = op2(h7(e13),h7(e13)) )
& ( ( h7(e10) = e20 )
| ( h7(e11) = e20 )
| ( h7(e12) = e20 )
| ( h7(e13) = e20 ) )
& ( ( h7(e10) = e21 )
| ( h7(e11) = e21 )
| ( h7(e12) = e21 )
| ( h7(e13) = e21 ) )
& ( ( h7(e10) = e22 )
| ( h7(e11) = e22 )
| ( h7(e12) = e22 )
| ( h7(e13) = e22 ) )
& ( ( h7(e10) = e23 )
| ( h7(e11) = e23 )
| ( h7(e12) = e23 )
| ( h7(e13) = e23 ) ) )
| ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) = e21 ) )
& ( ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e12) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
| ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e12) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 )
| ( h9(e13) = e23 ) ) )
| ( ( h10(op1(e10,e10)) = op2(h10(e10),h10(e10)) )
& ( h10(op1(e10,e11)) = op2(h10(e10),h10(e11)) )
& ( h10(op1(e10,e12)) = op2(h10(e10),h10(e12)) )
& ( h10(op1(e10,e13)) = op2(h10(e10),h10(e13)) )
& ( h10(op1(e11,e10)) = op2(h10(e11),h10(e10)) )
& ( h10(op1(e11,e11)) = op2(h10(e11),h10(e11)) )
& ( h10(op1(e11,e12)) = op2(h10(e11),h10(e12)) )
& ( h10(op1(e11,e13)) = op2(h10(e11),h10(e13)) )
& ( h10(op1(e12,e10)) = op2(h10(e12),h10(e10)) )
& ( h10(op1(e12,e11)) = op2(h10(e12),h10(e11)) )
& ( h10(op1(e12,e12)) = op2(h10(e12),h10(e12)) )
& ( h10(op1(e12,e13)) = op2(h10(e12),h10(e13)) )
& ( h10(op1(e13,e10)) = op2(h10(e13),h10(e10)) )
& ( h10(op1(e13,e11)) = op2(h10(e13),h10(e11)) )
& ( h10(op1(e13,e12)) = op2(h10(e13),h10(e12)) )
& ( h10(op1(e13,e13)) = op2(h10(e13),h10(e13)) )
& ( ( h10(e10) = e20 )
| ( h10(e11) = e20 )
| ( h10(e12) = e20 )
| ( h10(e13) = e20 ) )
& ( ( h10(e10) = e21 )
| ( h10(e11) = e21 )
| ( h10(e12) = e21 )
| ( h10(e13) = e21 ) )
& ( ( h10(e10) = e22 )
| ( h10(e11) = e22 )
| ( h10(e12) = e22 )
| ( h10(e13) = e22 ) )
& ( ( h10(e10) = e23 )
| ( h10(e11) = e23 )
| ( h10(e12) = e23 )
| ( h10(e13) = e23 ) ) )
| ( ( h11(op1(e10,e10)) = op2(h11(e10),h11(e10)) )
& ( h11(op1(e10,e11)) = op2(h11(e10),h11(e11)) )
& ( h11(op1(e10,e12)) = op2(h11(e10),h11(e12)) )
& ( h11(op1(e10,e13)) = op2(h11(e10),h11(e13)) )
& ( h11(op1(e11,e10)) = op2(h11(e11),h11(e10)) )
& ( h11(op1(e11,e11)) = op2(h11(e11),h11(e11)) )
& ( h11(op1(e11,e12)) = op2(h11(e11),h11(e12)) )
& ( h11(op1(e11,e13)) = op2(h11(e11),h11(e13)) )
& ( h11(op1(e12,e10)) = op2(h11(e12),h11(e10)) )
& ( h11(op1(e12,e11)) = op2(h11(e12),h11(e11)) )
& ( h11(op1(e12,e12)) = op2(h11(e12),h11(e12)) )
& ( h11(op1(e12,e13)) = op2(h11(e12),h11(e13)) )
& ( h11(op1(e13,e10)) = op2(h11(e13),h11(e10)) )
& ( h11(op1(e13,e11)) = op2(h11(e13),h11(e11)) )
& ( h11(op1(e13,e12)) = op2(h11(e13),h11(e12)) )
& ( h11(op1(e13,e13)) = op2(h11(e13),h11(e13)) )
& ( ( h11(e10) = e20 )
| ( h11(e11) = e20 )
| ( h11(e12) = e20 )
| ( h11(e13) = e20 ) )
& ( ( h11(e10) = e21 )
| ( h11(e11) = e21 )
| ( h11(e12) = e21 )
| ( h11(e13) = e21 ) )
& ( ( h11(e10) = e22 )
| ( h11(e11) = e22 )
| ( h11(e12) = e22 )
| ( h11(e13) = e22 ) )
& ( ( h11(e10) = e23 )
| ( h11(e11) = e23 )
| ( h11(e12) = e23 )
| ( h11(e13) = e23 ) ) )
| ( ( h12(op1(e10,e10)) = op2(h12(e10),h12(e10)) )
& ( h12(op1(e10,e11)) = op2(h12(e10),h12(e11)) )
& ( h12(op1(e10,e12)) = op2(h12(e10),h12(e12)) )
& ( h12(op1(e10,e13)) = op2(h12(e10),h12(e13)) )
& ( h12(op1(e11,e10)) = op2(h12(e11),h12(e10)) )
& ( h12(op1(e11,e11)) = op2(h12(e11),h12(e11)) )
& ( h12(op1(e11,e12)) = op2(h12(e11),h12(e12)) )
& ( h12(op1(e11,e13)) = op2(h12(e11),h12(e13)) )
& ( h12(op1(e12,e10)) = op2(h12(e12),h12(e10)) )
& ( h12(op1(e12,e11)) = op2(h12(e12),h12(e11)) )
& ( h12(op1(e12,e12)) = op2(h12(e12),h12(e12)) )
& ( h12(op1(e12,e13)) = op2(h12(e12),h12(e13)) )
& ( h12(op1(e13,e10)) = op2(h12(e13),h12(e10)) )
& ( h12(op1(e13,e11)) = op2(h12(e13),h12(e11)) )
& ( h12(op1(e13,e12)) = op2(h12(e13),h12(e12)) )
& ( h12(op1(e13,e13)) = op2(h12(e13),h12(e13)) )
& ( ( h12(e10) = e20 )
| ( h12(e11) = e20 )
| ( h12(e12) = e20 )
| ( h12(e13) = e20 ) )
& ( ( h12(e10) = e21 )
| ( h12(e11) = e21 )
| ( h12(e12) = e21 )
| ( h12(e13) = e21 ) )
& ( ( h12(e10) = e22 )
| ( h12(e11) = e22 )
| ( h12(e12) = e22 )
| ( h12(e13) = e22 ) )
& ( ( h12(e10) = e23 )
| ( h12(e11) = e23 )
| ( h12(e12) = e23 )
| ( h12(e13) = e23 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(1345,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 ) ) )
| ( ( 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 ) ) )
| ( ( h5(op1(e10,e10)) = op2(h5(e10),h5(e10)) )
& ( h5(op1(e10,e11)) = op2(h5(e10),h5(e11)) )
& ( h5(op1(e10,e12)) = op2(h5(e10),h5(e12)) )
& ( h5(op1(e10,e13)) = op2(h5(e10),h5(e13)) )
& ( h5(op1(e11,e10)) = op2(h5(e11),h5(e10)) )
& ( h5(op1(e11,e11)) = op2(h5(e11),h5(e11)) )
& ( h5(op1(e11,e12)) = op2(h5(e11),h5(e12)) )
& ( h5(op1(e11,e13)) = op2(h5(e11),h5(e13)) )
& ( h5(op1(e12,e10)) = op2(h5(e12),h5(e10)) )
& ( h5(op1(e12,e11)) = op2(h5(e12),h5(e11)) )
& ( h5(op1(e12,e12)) = op2(h5(e12),h5(e12)) )
& ( h5(op1(e12,e13)) = op2(h5(e12),h5(e13)) )
& ( h5(op1(e13,e10)) = op2(h5(e13),h5(e10)) )
& ( h5(op1(e13,e11)) = op2(h5(e13),h5(e11)) )
& ( h5(op1(e13,e12)) = op2(h5(e13),h5(e12)) )
& ( h5(op1(e13,e13)) = op2(h5(e13),h5(e13)) )
& ( ( h5(e10) = e20 )
| ( h5(e11) = e20 )
| ( h5(e12) = e20 )
| ( h5(e13) = e20 ) )
& ( ( h5(e10) = e21 )
| ( h5(e11) = e21 )
| ( h5(e12) = e21 )
| ( h5(e13) = e21 ) )
& ( ( h5(e10) = e22 )
| ( h5(e11) = e22 )
| ( h5(e12) = e22 )
| ( h5(e13) = e22 ) )
& ( ( h5(e10) = e23 )
| ( h5(e11) = e23 )
| ( h5(e12) = e23 )
| ( h5(e13) = e23 ) ) )
| ( ( h6(op1(e10,e10)) = op2(h6(e10),h6(e10)) )
& ( h6(op1(e10,e11)) = op2(h6(e10),h6(e11)) )
& ( h6(op1(e10,e12)) = op2(h6(e10),h6(e12)) )
& ( h6(op1(e10,e13)) = op2(h6(e10),h6(e13)) )
& ( h6(op1(e11,e10)) = op2(h6(e11),h6(e10)) )
& ( h6(op1(e11,e11)) = op2(h6(e11),h6(e11)) )
& ( h6(op1(e11,e12)) = op2(h6(e11),h6(e12)) )
& ( h6(op1(e11,e13)) = op2(h6(e11),h6(e13)) )
& ( h6(op1(e12,e10)) = op2(h6(e12),h6(e10)) )
& ( h6(op1(e12,e11)) = op2(h6(e12),h6(e11)) )
& ( h6(op1(e12,e12)) = op2(h6(e12),h6(e12)) )
& ( h6(op1(e12,e13)) = op2(h6(e12),h6(e13)) )
& ( h6(op1(e13,e10)) = op2(h6(e13),h6(e10)) )
& ( h6(op1(e13,e11)) = op2(h6(e13),h6(e11)) )
& ( h6(op1(e13,e12)) = op2(h6(e13),h6(e12)) )
& ( h6(op1(e13,e13)) = op2(h6(e13),h6(e13)) )
& ( ( h6(e10) = e20 )
| ( h6(e11) = e20 )
| ( h6(e12) = e20 )
| ( h6(e13) = e20 ) )
& ( ( h6(e10) = e21 )
| ( h6(e11) = e21 )
| ( h6(e12) = e21 )
| ( h6(e13) = e21 ) )
& ( ( h6(e10) = e22 )
| ( h6(e11) = e22 )
| ( h6(e12) = e22 )
| ( h6(e13) = e22 ) )
& ( ( h6(e10) = e23 )
| ( h6(e11) = e23 )
| ( h6(e12) = e23 )
| ( h6(e13) = e23 ) ) )
| ( ( h7(op1(e10,e10)) = op2(h7(e10),h7(e10)) )
& ( h7(op1(e10,e11)) = op2(h7(e10),h7(e11)) )
& ( h7(op1(e10,e12)) = op2(h7(e10),h7(e12)) )
& ( h7(op1(e10,e13)) = op2(h7(e10),h7(e13)) )
& ( h7(op1(e11,e10)) = op2(h7(e11),h7(e10)) )
& ( h7(op1(e11,e11)) = op2(h7(e11),h7(e11)) )
& ( h7(op1(e11,e12)) = op2(h7(e11),h7(e12)) )
& ( h7(op1(e11,e13)) = op2(h7(e11),h7(e13)) )
& ( h7(op1(e12,e10)) = op2(h7(e12),h7(e10)) )
& ( h7(op1(e12,e11)) = op2(h7(e12),h7(e11)) )
& ( h7(op1(e12,e12)) = op2(h7(e12),h7(e12)) )
& ( h7(op1(e12,e13)) = op2(h7(e12),h7(e13)) )
& ( h7(op1(e13,e10)) = op2(h7(e13),h7(e10)) )
& ( h7(op1(e13,e11)) = op2(h7(e13),h7(e11)) )
& ( h7(op1(e13,e12)) = op2(h7(e13),h7(e12)) )
& ( h7(op1(e13,e13)) = op2(h7(e13),h7(e13)) )
& ( ( h7(e10) = e20 )
| ( h7(e11) = e20 )
| ( h7(e12) = e20 )
| ( h7(e13) = e20 ) )
& ( ( h7(e10) = e21 )
| ( h7(e11) = e21 )
| ( h7(e12) = e21 )
| ( h7(e13) = e21 ) )
& ( ( h7(e10) = e22 )
| ( h7(e11) = e22 )
| ( h7(e12) = e22 )
| ( h7(e13) = e22 ) )
& ( ( h7(e10) = e23 )
| ( h7(e11) = e23 )
| ( h7(e12) = e23 )
| ( h7(e13) = e23 ) ) )
| ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) = e21 ) )
& ( ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e12) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
| ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e12) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 )
| ( h9(e13) = e23 ) ) )
| ( ( h10(op1(e10,e10)) = op2(h10(e10),h10(e10)) )
& ( h10(op1(e10,e11)) = op2(h10(e10),h10(e11)) )
& ( h10(op1(e10,e12)) = op2(h10(e10),h10(e12)) )
& ( h10(op1(e10,e13)) = op2(h10(e10),h10(e13)) )
& ( h10(op1(e11,e10)) = op2(h10(e11),h10(e10)) )
& ( h10(op1(e11,e11)) = op2(h10(e11),h10(e11)) )
& ( h10(op1(e11,e12)) = op2(h10(e11),h10(e12)) )
& ( h10(op1(e11,e13)) = op2(h10(e11),h10(e13)) )
& ( h10(op1(e12,e10)) = op2(h10(e12),h10(e10)) )
& ( h10(op1(e12,e11)) = op2(h10(e12),h10(e11)) )
& ( h10(op1(e12,e12)) = op2(h10(e12),h10(e12)) )
& ( h10(op1(e12,e13)) = op2(h10(e12),h10(e13)) )
& ( h10(op1(e13,e10)) = op2(h10(e13),h10(e10)) )
& ( h10(op1(e13,e11)) = op2(h10(e13),h10(e11)) )
& ( h10(op1(e13,e12)) = op2(h10(e13),h10(e12)) )
& ( h10(op1(e13,e13)) = op2(h10(e13),h10(e13)) )
& ( ( h10(e10) = e20 )
| ( h10(e11) = e20 )
| ( h10(e12) = e20 )
| ( h10(e13) = e20 ) )
& ( ( h10(e10) = e21 )
| ( h10(e11) = e21 )
| ( h10(e12) = e21 )
| ( h10(e13) = e21 ) )
& ( ( h10(e10) = e22 )
| ( h10(e11) = e22 )
| ( h10(e12) = e22 )
| ( h10(e13) = e22 ) )
& ( ( h10(e10) = e23 )
| ( h10(e11) = e23 )
| ( h10(e12) = e23 )
| ( h10(e13) = e23 ) ) )
| ( ( h11(op1(e10,e10)) = op2(h11(e10),h11(e10)) )
& ( h11(op1(e10,e11)) = op2(h11(e10),h11(e11)) )
& ( h11(op1(e10,e12)) = op2(h11(e10),h11(e12)) )
& ( h11(op1(e10,e13)) = op2(h11(e10),h11(e13)) )
& ( h11(op1(e11,e10)) = op2(h11(e11),h11(e10)) )
& ( h11(op1(e11,e11)) = op2(h11(e11),h11(e11)) )
& ( h11(op1(e11,e12)) = op2(h11(e11),h11(e12)) )
& ( h11(op1(e11,e13)) = op2(h11(e11),h11(e13)) )
& ( h11(op1(e12,e10)) = op2(h11(e12),h11(e10)) )
& ( h11(op1(e12,e11)) = op2(h11(e12),h11(e11)) )
& ( h11(op1(e12,e12)) = op2(h11(e12),h11(e12)) )
& ( h11(op1(e12,e13)) = op2(h11(e12),h11(e13)) )
& ( h11(op1(e13,e10)) = op2(h11(e13),h11(e10)) )
& ( h11(op1(e13,e11)) = op2(h11(e13),h11(e11)) )
& ( h11(op1(e13,e12)) = op2(h11(e13),h11(e12)) )
& ( h11(op1(e13,e13)) = op2(h11(e13),h11(e13)) )
& ( ( h11(e10) = e20 )
| ( h11(e11) = e20 )
| ( h11(e12) = e20 )
| ( h11(e13) = e20 ) )
& ( ( h11(e10) = e21 )
| ( h11(e11) = e21 )
| ( h11(e12) = e21 )
| ( h11(e13) = e21 ) )
& ( ( h11(e10) = e22 )
| ( h11(e11) = e22 )
| ( h11(e12) = e22 )
| ( h11(e13) = e22 ) )
& ( ( h11(e10) = e23 )
| ( h11(e11) = e23 )
| ( h11(e12) = e23 )
| ( h11(e13) = e23 ) ) ) ),
inference(or_elim,[status(thm)],[1344]) ).
tff(1346,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 ) ) )
| ( ( 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 ) ) )
| ( ( h5(op1(e10,e10)) = op2(h5(e10),h5(e10)) )
& ( h5(op1(e10,e11)) = op2(h5(e10),h5(e11)) )
& ( h5(op1(e10,e12)) = op2(h5(e10),h5(e12)) )
& ( h5(op1(e10,e13)) = op2(h5(e10),h5(e13)) )
& ( h5(op1(e11,e10)) = op2(h5(e11),h5(e10)) )
& ( h5(op1(e11,e11)) = op2(h5(e11),h5(e11)) )
& ( h5(op1(e11,e12)) = op2(h5(e11),h5(e12)) )
& ( h5(op1(e11,e13)) = op2(h5(e11),h5(e13)) )
& ( h5(op1(e12,e10)) = op2(h5(e12),h5(e10)) )
& ( h5(op1(e12,e11)) = op2(h5(e12),h5(e11)) )
& ( h5(op1(e12,e12)) = op2(h5(e12),h5(e12)) )
& ( h5(op1(e12,e13)) = op2(h5(e12),h5(e13)) )
& ( h5(op1(e13,e10)) = op2(h5(e13),h5(e10)) )
& ( h5(op1(e13,e11)) = op2(h5(e13),h5(e11)) )
& ( h5(op1(e13,e12)) = op2(h5(e13),h5(e12)) )
& ( h5(op1(e13,e13)) = op2(h5(e13),h5(e13)) )
& ( ( h5(e10) = e20 )
| ( h5(e11) = e20 )
| ( h5(e12) = e20 )
| ( h5(e13) = e20 ) )
& ( ( h5(e10) = e21 )
| ( h5(e11) = e21 )
| ( h5(e12) = e21 )
| ( h5(e13) = e21 ) )
& ( ( h5(e10) = e22 )
| ( h5(e11) = e22 )
| ( h5(e12) = e22 )
| ( h5(e13) = e22 ) )
& ( ( h5(e10) = e23 )
| ( h5(e11) = e23 )
| ( h5(e12) = e23 )
| ( h5(e13) = e23 ) ) )
| ( ( h6(op1(e10,e10)) = op2(h6(e10),h6(e10)) )
& ( h6(op1(e10,e11)) = op2(h6(e10),h6(e11)) )
& ( h6(op1(e10,e12)) = op2(h6(e10),h6(e12)) )
& ( h6(op1(e10,e13)) = op2(h6(e10),h6(e13)) )
& ( h6(op1(e11,e10)) = op2(h6(e11),h6(e10)) )
& ( h6(op1(e11,e11)) = op2(h6(e11),h6(e11)) )
& ( h6(op1(e11,e12)) = op2(h6(e11),h6(e12)) )
& ( h6(op1(e11,e13)) = op2(h6(e11),h6(e13)) )
& ( h6(op1(e12,e10)) = op2(h6(e12),h6(e10)) )
& ( h6(op1(e12,e11)) = op2(h6(e12),h6(e11)) )
& ( h6(op1(e12,e12)) = op2(h6(e12),h6(e12)) )
& ( h6(op1(e12,e13)) = op2(h6(e12),h6(e13)) )
& ( h6(op1(e13,e10)) = op2(h6(e13),h6(e10)) )
& ( h6(op1(e13,e11)) = op2(h6(e13),h6(e11)) )
& ( h6(op1(e13,e12)) = op2(h6(e13),h6(e12)) )
& ( h6(op1(e13,e13)) = op2(h6(e13),h6(e13)) )
& ( ( h6(e10) = e20 )
| ( h6(e11) = e20 )
| ( h6(e12) = e20 )
| ( h6(e13) = e20 ) )
& ( ( h6(e10) = e21 )
| ( h6(e11) = e21 )
| ( h6(e12) = e21 )
| ( h6(e13) = e21 ) )
& ( ( h6(e10) = e22 )
| ( h6(e11) = e22 )
| ( h6(e12) = e22 )
| ( h6(e13) = e22 ) )
& ( ( h6(e10) = e23 )
| ( h6(e11) = e23 )
| ( h6(e12) = e23 )
| ( h6(e13) = e23 ) ) )
| ( ( h7(op1(e10,e10)) = op2(h7(e10),h7(e10)) )
& ( h7(op1(e10,e11)) = op2(h7(e10),h7(e11)) )
& ( h7(op1(e10,e12)) = op2(h7(e10),h7(e12)) )
& ( h7(op1(e10,e13)) = op2(h7(e10),h7(e13)) )
& ( h7(op1(e11,e10)) = op2(h7(e11),h7(e10)) )
& ( h7(op1(e11,e11)) = op2(h7(e11),h7(e11)) )
& ( h7(op1(e11,e12)) = op2(h7(e11),h7(e12)) )
& ( h7(op1(e11,e13)) = op2(h7(e11),h7(e13)) )
& ( h7(op1(e12,e10)) = op2(h7(e12),h7(e10)) )
& ( h7(op1(e12,e11)) = op2(h7(e12),h7(e11)) )
& ( h7(op1(e12,e12)) = op2(h7(e12),h7(e12)) )
& ( h7(op1(e12,e13)) = op2(h7(e12),h7(e13)) )
& ( h7(op1(e13,e10)) = op2(h7(e13),h7(e10)) )
& ( h7(op1(e13,e11)) = op2(h7(e13),h7(e11)) )
& ( h7(op1(e13,e12)) = op2(h7(e13),h7(e12)) )
& ( h7(op1(e13,e13)) = op2(h7(e13),h7(e13)) )
& ( ( h7(e10) = e20 )
| ( h7(e11) = e20 )
| ( h7(e12) = e20 )
| ( h7(e13) = e20 ) )
& ( ( h7(e10) = e21 )
| ( h7(e11) = e21 )
| ( h7(e12) = e21 )
| ( h7(e13) = e21 ) )
& ( ( h7(e10) = e22 )
| ( h7(e11) = e22 )
| ( h7(e12) = e22 )
| ( h7(e13) = e22 ) )
& ( ( h7(e10) = e23 )
| ( h7(e11) = e23 )
| ( h7(e12) = e23 )
| ( h7(e13) = e23 ) ) )
| ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) = e21 ) )
& ( ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e12) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
| ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e12) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 )
| ( h9(e13) = e23 ) ) )
| ( ( h10(op1(e10,e10)) = op2(h10(e10),h10(e10)) )
& ( h10(op1(e10,e11)) = op2(h10(e10),h10(e11)) )
& ( h10(op1(e10,e12)) = op2(h10(e10),h10(e12)) )
& ( h10(op1(e10,e13)) = op2(h10(e10),h10(e13)) )
& ( h10(op1(e11,e10)) = op2(h10(e11),h10(e10)) )
& ( h10(op1(e11,e11)) = op2(h10(e11),h10(e11)) )
& ( h10(op1(e11,e12)) = op2(h10(e11),h10(e12)) )
& ( h10(op1(e11,e13)) = op2(h10(e11),h10(e13)) )
& ( h10(op1(e12,e10)) = op2(h10(e12),h10(e10)) )
& ( h10(op1(e12,e11)) = op2(h10(e12),h10(e11)) )
& ( h10(op1(e12,e12)) = op2(h10(e12),h10(e12)) )
& ( h10(op1(e12,e13)) = op2(h10(e12),h10(e13)) )
& ( h10(op1(e13,e10)) = op2(h10(e13),h10(e10)) )
& ( h10(op1(e13,e11)) = op2(h10(e13),h10(e11)) )
& ( h10(op1(e13,e12)) = op2(h10(e13),h10(e12)) )
& ( h10(op1(e13,e13)) = op2(h10(e13),h10(e13)) )
& ( ( h10(e10) = e20 )
| ( h10(e11) = e20 )
| ( h10(e12) = e20 )
| ( h10(e13) = e20 ) )
& ( ( h10(e10) = e21 )
| ( h10(e11) = e21 )
| ( h10(e12) = e21 )
| ( h10(e13) = e21 ) )
& ( ( h10(e10) = e22 )
| ( h10(e11) = e22 )
| ( h10(e12) = e22 )
| ( h10(e13) = e22 ) )
& ( ( h10(e10) = e23 )
| ( h10(e11) = e23 )
| ( h10(e12) = e23 )
| ( h10(e13) = e23 ) ) ) ),
inference(or_elim,[status(thm)],[1345]) ).
tff(1347,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 ) ) )
| ( ( 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 ) ) )
| ( ( h5(op1(e10,e10)) = op2(h5(e10),h5(e10)) )
& ( h5(op1(e10,e11)) = op2(h5(e10),h5(e11)) )
& ( h5(op1(e10,e12)) = op2(h5(e10),h5(e12)) )
& ( h5(op1(e10,e13)) = op2(h5(e10),h5(e13)) )
& ( h5(op1(e11,e10)) = op2(h5(e11),h5(e10)) )
& ( h5(op1(e11,e11)) = op2(h5(e11),h5(e11)) )
& ( h5(op1(e11,e12)) = op2(h5(e11),h5(e12)) )
& ( h5(op1(e11,e13)) = op2(h5(e11),h5(e13)) )
& ( h5(op1(e12,e10)) = op2(h5(e12),h5(e10)) )
& ( h5(op1(e12,e11)) = op2(h5(e12),h5(e11)) )
& ( h5(op1(e12,e12)) = op2(h5(e12),h5(e12)) )
& ( h5(op1(e12,e13)) = op2(h5(e12),h5(e13)) )
& ( h5(op1(e13,e10)) = op2(h5(e13),h5(e10)) )
& ( h5(op1(e13,e11)) = op2(h5(e13),h5(e11)) )
& ( h5(op1(e13,e12)) = op2(h5(e13),h5(e12)) )
& ( h5(op1(e13,e13)) = op2(h5(e13),h5(e13)) )
& ( ( h5(e10) = e20 )
| ( h5(e11) = e20 )
| ( h5(e12) = e20 )
| ( h5(e13) = e20 ) )
& ( ( h5(e10) = e21 )
| ( h5(e11) = e21 )
| ( h5(e12) = e21 )
| ( h5(e13) = e21 ) )
& ( ( h5(e10) = e22 )
| ( h5(e11) = e22 )
| ( h5(e12) = e22 )
| ( h5(e13) = e22 ) )
& ( ( h5(e10) = e23 )
| ( h5(e11) = e23 )
| ( h5(e12) = e23 )
| ( h5(e13) = e23 ) ) )
| ( ( h6(op1(e10,e10)) = op2(h6(e10),h6(e10)) )
& ( h6(op1(e10,e11)) = op2(h6(e10),h6(e11)) )
& ( h6(op1(e10,e12)) = op2(h6(e10),h6(e12)) )
& ( h6(op1(e10,e13)) = op2(h6(e10),h6(e13)) )
& ( h6(op1(e11,e10)) = op2(h6(e11),h6(e10)) )
& ( h6(op1(e11,e11)) = op2(h6(e11),h6(e11)) )
& ( h6(op1(e11,e12)) = op2(h6(e11),h6(e12)) )
& ( h6(op1(e11,e13)) = op2(h6(e11),h6(e13)) )
& ( h6(op1(e12,e10)) = op2(h6(e12),h6(e10)) )
& ( h6(op1(e12,e11)) = op2(h6(e12),h6(e11)) )
& ( h6(op1(e12,e12)) = op2(h6(e12),h6(e12)) )
& ( h6(op1(e12,e13)) = op2(h6(e12),h6(e13)) )
& ( h6(op1(e13,e10)) = op2(h6(e13),h6(e10)) )
& ( h6(op1(e13,e11)) = op2(h6(e13),h6(e11)) )
& ( h6(op1(e13,e12)) = op2(h6(e13),h6(e12)) )
& ( h6(op1(e13,e13)) = op2(h6(e13),h6(e13)) )
& ( ( h6(e10) = e20 )
| ( h6(e11) = e20 )
| ( h6(e12) = e20 )
| ( h6(e13) = e20 ) )
& ( ( h6(e10) = e21 )
| ( h6(e11) = e21 )
| ( h6(e12) = e21 )
| ( h6(e13) = e21 ) )
& ( ( h6(e10) = e22 )
| ( h6(e11) = e22 )
| ( h6(e12) = e22 )
| ( h6(e13) = e22 ) )
& ( ( h6(e10) = e23 )
| ( h6(e11) = e23 )
| ( h6(e12) = e23 )
| ( h6(e13) = e23 ) ) )
| ( ( h7(op1(e10,e10)) = op2(h7(e10),h7(e10)) )
& ( h7(op1(e10,e11)) = op2(h7(e10),h7(e11)) )
& ( h7(op1(e10,e12)) = op2(h7(e10),h7(e12)) )
& ( h7(op1(e10,e13)) = op2(h7(e10),h7(e13)) )
& ( h7(op1(e11,e10)) = op2(h7(e11),h7(e10)) )
& ( h7(op1(e11,e11)) = op2(h7(e11),h7(e11)) )
& ( h7(op1(e11,e12)) = op2(h7(e11),h7(e12)) )
& ( h7(op1(e11,e13)) = op2(h7(e11),h7(e13)) )
& ( h7(op1(e12,e10)) = op2(h7(e12),h7(e10)) )
& ( h7(op1(e12,e11)) = op2(h7(e12),h7(e11)) )
& ( h7(op1(e12,e12)) = op2(h7(e12),h7(e12)) )
& ( h7(op1(e12,e13)) = op2(h7(e12),h7(e13)) )
& ( h7(op1(e13,e10)) = op2(h7(e13),h7(e10)) )
& ( h7(op1(e13,e11)) = op2(h7(e13),h7(e11)) )
& ( h7(op1(e13,e12)) = op2(h7(e13),h7(e12)) )
& ( h7(op1(e13,e13)) = op2(h7(e13),h7(e13)) )
& ( ( h7(e10) = e20 )
| ( h7(e11) = e20 )
| ( h7(e12) = e20 )
| ( h7(e13) = e20 ) )
& ( ( h7(e10) = e21 )
| ( h7(e11) = e21 )
| ( h7(e12) = e21 )
| ( h7(e13) = e21 ) )
& ( ( h7(e10) = e22 )
| ( h7(e11) = e22 )
| ( h7(e12) = e22 )
| ( h7(e13) = e22 ) )
& ( ( h7(e10) = e23 )
| ( h7(e11) = e23 )
| ( h7(e12) = e23 )
| ( h7(e13) = e23 ) ) )
| ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) = e21 ) )
& ( ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e12) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
| ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e12) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 )
| ( h9(e13) = e23 ) ) ) ),
inference(or_elim,[status(thm)],[1346]) ).
tff(1348,plain,
~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e12) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 )
| ( h9(e13) = e23 ) ) ),
inference(or_elim,[status(thm)],[1347]) ).
tff(1349,plain,
~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e12) = e22 )
| ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e13) = e23 )
| ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[1348,1343]) ).
tff(1350,plain,
~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e12) = e22 )
| ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e13) = e23 )
| ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[1349,1342]) ).
tff(1351,plain,
~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) ) ),
inference(modus_ponens,[status(thm)],[1350,1340]) ).
tff(1352,plain,
~ ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) ) ),
inference(modus_ponens,[status(thm)],[1351,1339]) ).
tff(1353,plain,
~ ( ( h9(op1(op1(e12,e13),op1(e12,e13))) = op2(h9(op1(e12,e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h9(op1(e12,e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h9(op1(e12,e13)),h9(e12)) )
& ( h9(op1(op1(e12,e13),e13)) = op2(h9(op1(e12,e13)),h9(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h9(op1(op1(e12,e13),e13)),h9(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h9(op1(op1(e12,e13),e13)),h9(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h9(e12),h9(op1(e12,e13))) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h9(e12),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h9(e13),h9(op1(e12,e13))) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h9(e13),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(op1(e12,e13)) = op2(h2(e13),h3(e13)) )
| ( h9(op1(op1(e12,e13),e13)) = op2(h2(e13),h3(e13)) )
| ( h9(e12) = op2(h2(e13),h3(e13)) )
| ( h9(e13) = op2(h2(e13),h3(e13)) ) )
& ( ( h9(op1(op1(e12,e13),e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(op1(e12,e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e12) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e13) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ),
inference(modus_ponens,[status(thm)],[1352,1338]) ).
tff(1354,plain,
~ ( ( h9(op1(op1(e12,e13),op1(e12,e13))) = op2(h9(op1(e12,e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h9(op1(e12,e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h9(op1(e12,e13)),h9(e12)) )
& ( h9(op1(op1(e12,e13),e13)) = op2(h9(op1(e12,e13)),h9(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(e12,e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(op1(e12,e13),e13))) = op2(h9(op1(op1(e12,e13),e13)),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h9(op1(op1(e12,e13),e13)),h9(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h9(op1(op1(e12,e13),e13)),h9(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h9(e12),h9(op1(e12,e13))) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h9(e12),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h9(e13),h9(op1(e12,e13))) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h9(e13),h9(op1(op1(e12,e13),e13))) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(op1(e12,e13)) = op2(h2(e13),h3(e13)) )
| ( h9(op1(op1(e12,e13),e13)) = op2(h2(e13),h3(e13)) )
| ( h9(e12) = op2(h2(e13),h3(e13)) )
| ( h9(e13) = op2(h2(e13),h3(e13)) ) )
& ( ( h9(op1(op1(e12,e13),e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(op1(e12,e13)) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e12) = op2(op2(h2(e13),h3(e13)),h3(e13)) )
| ( h9(e13) = op2(op2(h2(e13),h3(e13)),h3(e13)) ) ) ),
inference(modus_ponens,[status(thm)],[1353,1337]) ).
tff(1355,plain,
~ ( ( h9(op1(e12,e13)) = op2(h1(e12),h1(e12)) )
& ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h1(e12),h1(e13)) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h1(e13) = op2(h1(e12),h3(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(e12,e13),e13)) = op2(h1(e13),h1(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(e12) = op2(h2(e13),h2(e13)) )
& ( h1(e12) = op2(h2(e13),h3(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) )
& ( h9(e13) = op2(h3(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1354,1335]) ).
tff(1356,plain,
~ ( ( h9(op1(op1(e12,e13),op1(op1(e12,e13),e13))) = op2(h1(e12),h1(e13)) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) ) ),
inference(modus_ponens,[status(thm)],[1355,1334]) ).
tff(1357,plain,
~ ( ( h9(e12) = op2(h1(e12),h1(e13)) )
& ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) ) ),
inference(modus_ponens,[status(thm)],[1356,1333]) ).
tff(1358,plain,
~ ( ( h9(op1(op1(e12,e13),e12)) = op2(h1(e12),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) = op2(h1(e13),h1(e12)) )
& ( h9(op1(op1(op1(e12,e13),e13),e12)) = op2(h1(e13),h2(e13)) )
& ( h9(op1(op1(op1(e12,e13),e13),e13)) = op2(h1(e13),h3(e13)) )
& ( h9(op1(e12,op1(e12,e13))) = op2(h2(e13),h1(e12)) )
& ( h9(op1(e12,op1(op1(e12,e13),e13))) = op2(h2(e13),h1(e13)) )
& ( h9(op1(e13,op1(e12,e13))) = op2(h3(e13),h1(e12)) )
& ( h9(op1(e13,op1(op1(e12,e13),e13))) = op2(h3(e13),h1(e13)) )
& ( h9(op1(e13,e12)) = op2(h3(e13),h2(e13)) ) ),
inference(modus_ponens,[status(thm)],[1357,1332]) ).
tff(1359,plain,
( ( h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) != op2(h1(e13),h1(e12)) )
| ( h9(op1(op1(e12,e13),e12)) != op2(h1(e12),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e12)) != op2(h1(e13),h2(e13)) )
| ( h9(op1(op1(op1(e12,e13),e13),e13)) != op2(h1(e13),h3(e13)) )
| ( h9(op1(e12,op1(e12,e13))) != op2(h2(e13),h1(e12)) )
| ( h9(op1(e12,op1(op1(e12,e13),e13))) != op2(h2(e13),h1(e13)) )
| ( h9(op1(e13,op1(e12,e13))) != op2(h3(e13),h1(e12)) )
| ( h9(op1(e13,op1(op1(e12,e13),e13))) != op2(h3(e13),h1(e13)) )
| ( h9(op1(e13,e12)) != op2(h3(e13),h2(e13)) ) ),
inference(modus_ponens,[status(thm)],[1358,1331]) ).
tff(1360,plain,
h9(op1(op1(op1(e12,e13),e13),op1(e12,e13))) != op2(h1(e13),h1(e12)),
inference(unit_resolution,[status(thm)],[1359,1327,1202,1188,1088,987,856,725,577]) ).
tff(1361,plain,
$false,
inference(unit_resolution,[status(thm)],[1360,417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.16 % Problem : ALG113+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.18 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.39 % Computer : n010.cluster.edu
% 0.08/0.39 % Model : x86_64 x86_64
% 0.08/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.39 % Memory : 8042.1875MB
% 0.08/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.39 % CPULimit : 300
% 0.08/0.39 % WCLimit : 300
% 0.08/0.39 % DateTime : Mon Aug 29 13:21:59 EDT 2022
% 0.08/0.39 % CPUTime :
% 0.08/0.39 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.39 Usage: tptp [options] [-file:]file
% 0.08/0.39 -h, -? prints this message.
% 0.08/0.39 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.39 -m, -model generate model.
% 0.08/0.39 -p, -proof generate proof.
% 0.08/0.39 -c, -core generate unsat core of named formulas.
% 0.08/0.39 -st, -statistics display statistics.
% 0.08/0.39 -t:timeout set timeout (in second).
% 0.08/0.39 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.39 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.39 -<param>:<value> configuration parameter and value.
% 0.08/0.39 -o:<output-file> file to place output in.
% 0.12/0.48 % SZS status Theorem
% 0.12/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------