TSTP Solution File: ALG117+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG117+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 16:08:13 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 591
% Syntax : Number of formulae : 1765 ( 310 unt; 14 typ; 0 def)
% Number of atoms : 14711 (14593 equ)
% Maximal formula atoms : 128 ( 8 avg)
% Number of connectives : 16870 (3910 ~;7161 |;4907 &)
% ( 892 <=>; 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 : 8 ( 6 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(op2_type,type,
op2: ( $i * $i ) > $i ).
tff(h2_type,type,
h2: $i > $i ).
tff(e13_type,type,
e13: $i ).
tff(h4_type,type,
h4: $i > $i ).
tff(op1_type,type,
op1: ( $i * $i ) > $i ).
tff(h3_type,type,
h3: $i > $i ).
tff(e23_type,type,
e23: $i ).
tff(e22_type,type,
e22: $i ).
tff(e21_type,type,
e21: $i ).
tff(e20_type,type,
e20: $i ).
tff(h1_type,type,
h1: $i > $i ).
tff(e12_type,type,
e12: $i ).
tff(e11_type,type,
e11: $i ).
tff(e10_type,type,
e10: $i ).
tff(1,plain,
( ( h2(e13) = h3(e13) )
<=> ( h3(e13) = h2(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( h2(e13) != h3(e13) )
<=> ( h3(e13) != h2(e13) ) ),
inference(monotonicity,[status(thm)],[1]) ).
tff(3,plain,
( ( op2(h3(e13),h4(e13)) != h3(e13) )
<=> ( h2(e13) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) )
<=> ( op2(h3(e13),h4(e13)) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( op2(e22,e23) != op2(e23,e23) )
<=> ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ( op2(e22,e23) != op2(e23,e23) )
<=> ( op2(e22,e23) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,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(8,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)],[7]) ).
tff(9,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)],[8]) ).
tff(10,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)],[9]) ).
tff(11,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)],[10]) ).
tff(12,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)],[11]) ).
tff(13,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)],[12]) ).
tff(14,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)],[13]) ).
tff(15,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)],[14]) ).
tff(16,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)],[15]) ).
tff(17,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)],[16]) ).
tff(18,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)],[17]) ).
tff(19,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)],[18]) ).
tff(20,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)],[19]) ).
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
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) ) ),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
op2(e22,e23) != op2(e23,e23),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
op2(e22,e23) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[32,6]) ).
tff(34,plain,
op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[33,5]) ).
tff(35,plain,
op2(h3(e13),h4(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[34,4]) ).
tff(36,plain,
h2(e13) != h3(e13),
inference(modus_ponens,[status(thm)],[35,3]) ).
tff(37,plain,
h3(e13) != h2(e13),
inference(modus_ponens,[status(thm)],[36,2]) ).
tff(38,plain,
( ( h2(e13) = op2(h4(e13),h1(e13)) )
<=> ( op2(h4(e13),h1(e13)) = h2(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(39,plain,
( ( h3(e13) != h2(e13) )
| ( op2(h4(e13),h2(e13)) = h4(e13) )
| ( h3(e13) = h2(e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(40,plain,
( ( h3(e13) != h2(e13) )
| ( op2(h4(e13),h2(e13)) = h4(e13) ) ),
inference(unit_resolution,[status(thm)],[39,37]) ).
tff(41,plain,
( ( ( ( h3(e13) = h2(e13) )
& ( op2(h4(e13),h2(e13)) != h4(e13) ) )
| ( ( h1(op1(e13,e13)) = h2(e13) )
& ( op2(h1(e13),h2(e13)) != h1(e13) ) ) )
<=> ( ~ ( ( h3(e13) != h2(e13) )
| ( op2(h4(e13),h2(e13)) = h4(e13) ) )
| ~ ( ( h1(op1(e13,e13)) != h2(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( ( ( h3(e13) = op2(h3(e13),h4(e13)) )
& ( op2(h4(e13),op2(h3(e13),h4(e13))) != h4(e13) ) )
| ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
& ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) != op2(h4(e13),h3(e13)) ) ) )
<=> ( ( ( h3(e13) = h2(e13) )
& ( op2(h4(e13),h2(e13)) != h4(e13) ) )
| ( ( h1(op1(e13,e13)) = h2(e13) )
& ( op2(h1(e13),h2(e13)) != h1(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
& ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) != op2(h4(e13),h3(e13)) ) )
| ( ( h3(e13) = op2(h3(e13),h4(e13)) )
& ( op2(h4(e13),op2(h3(e13),h4(e13))) != h4(e13) ) ) )
<=> ( ( ( h3(e13) = op2(h3(e13),h4(e13)) )
& ( op2(h4(e13),op2(h3(e13),h4(e13))) != h4(e13) ) )
| ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
& ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) != op2(h4(e13),h3(e13)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) )
<=> ( ( h3(e13) = op2(h3(e13),h4(e13)) )
& ( op2(h4(e13),op2(h3(e13),h4(e13))) != h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
& ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) != op2(h4(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) )
<=> ( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
& ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) != op2(h4(e13),h3(e13)) ) )
| ( ( h3(e13) = op2(h3(e13),h4(e13)) )
& ( op2(h4(e13),op2(h3(e13),h4(e13))) != h4(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[45,44]) ).
tff(47,plain,
( ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) )
<=> ( ( ( h3(e13) = op2(h3(e13),h4(e13)) )
& ( op2(h4(e13),op2(h3(e13),h4(e13))) != h4(e13) ) )
| ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
& ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) != op2(h4(e13),h3(e13)) ) ) ) ),
inference(transitivity,[status(thm)],[46,43]) ).
tff(48,plain,
( ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| $false
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) )
<=> ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( $false
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( op2(e22,e22) != op2(e22,e23) )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( op2(e22,e22) != op2(e22,e23) )
<=> ( op2(e22,e22) != op2(e22,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
op2(e22,e22) != op2(e22,e23),
inference(and_elim,[status(thm)],[13]) ).
tff(53,plain,
op2(e22,e22) != op2(e22,e23),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[53,50]) ).
tff(55,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> $false ),
inference(iff_false,[status(thm)],[54]) ).
tff(56,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) )
<=> ( $false
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) )
<=> $false ),
inference(transitivity,[status(thm)],[56,49]) ).
tff(58,plain,
( ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) )
<=> ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| $false
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) )
<=> ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) ) ),
inference(transitivity,[status(thm)],[58,48]) ).
tff(60,plain,
( ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) )
<=> ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) )
<=> ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) )
<=> ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[63,62,61]) ).
tff(65,plain,
( ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) )
<=> ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) ) ),
inference(transitivity,[status(thm)],[64,60]) ).
tff(66,plain,
( ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) )
<=> ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) )
<=> ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e21,e21) = e21 )
& ( op2(e21,e21) != e21 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) ) )
<=> ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e21,e21) = e21 )
& ( op2(e21,e21) != e21 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) )
<=> ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e21,e21) = e21 )
& ( op2(e21,e21) != e21 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) )
<=> ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,axiom,
( ( ( ( op2(e20,e20) = e20 )
& ( op2(e20,e20) != e20 ) )
| ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) )
& ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e21,e21) = e21 )
& ( op2(e21,e21) != e21 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) )
& ( ( ( op2(e20,e20) = e22 )
& ( op2(e20,e22) != e20 ) )
| ( ( op2(e21,e21) = e22 )
& ( op2(e21,e22) != e21 ) )
| ( ( op2(e22,e22) = e22 )
& ( op2(e22,e22) != e22 ) )
| ( ( op2(e23,e23) = e22 )
& ( op2(e23,e22) != e23 ) ) )
& ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) )
| ( ( op2(e23,e23) = e23 )
& ( op2(e23,e23) != e23 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
tff(72,plain,
( ( ( ( op2(e20,e20) = e20 )
& ( op2(e20,e20) != e20 ) )
| ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) )
& ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e21,e21) = e21 )
& ( op2(e21,e21) != e21 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) )
& ( ( ( op2(e20,e20) = e22 )
& ( op2(e20,e22) != e20 ) )
| ( ( op2(e21,e21) = e22 )
& ( op2(e21,e22) != e21 ) )
| ( ( op2(e22,e22) = e22 )
& ( op2(e22,e22) != e22 ) )
| ( ( op2(e23,e23) = e22 )
& ( op2(e23,e22) != e23 ) ) ) ),
inference(and_elim,[status(thm)],[71]) ).
tff(73,plain,
( ( ( ( op2(e20,e20) = e20 )
& ( op2(e20,e20) != e20 ) )
| ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) )
& ( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e21,e21) = e21 )
& ( op2(e21,e21) != e21 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) ) ),
inference(and_elim,[status(thm)],[72]) ).
tff(74,plain,
( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e21,e21) = e21 )
& ( op2(e21,e21) != e21 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) ),
inference(and_elim,[status(thm)],[73]) ).
tff(75,plain,
( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ( ( op2(e20,e20) = e21 )
& ( op2(e20,e21) != e20 ) )
| ( ( op2(e22,e22) = e21 )
& ( op2(e22,e21) != e22 ) )
| ( ( op2(e23,e23) = e21 )
& ( op2(e23,e21) != e23 ) ) ),
inference(modus_ponens,[status(thm)],[75,66]) ).
tff(77,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[76,65]) ).
tff(78,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[77,60]) ).
tff(79,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
& ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) != h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[78,59]) ).
tff(80,plain,
( ( ( h3(e13) = op2(h3(e13),h4(e13)) )
& ( op2(h4(e13),op2(h3(e13),h4(e13))) != h4(e13) ) )
| ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
& ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) != op2(h4(e13),h3(e13)) ) ) ),
inference(modus_ponens,[status(thm)],[79,47]) ).
tff(81,plain,
( ( ( h3(e13) = h2(e13) )
& ( op2(h4(e13),h2(e13)) != h4(e13) ) )
| ( ( h1(op1(e13,e13)) = h2(e13) )
& ( op2(h1(e13),h2(e13)) != h1(e13) ) ) ),
inference(modus_ponens,[status(thm)],[80,42]) ).
tff(82,plain,
( ~ ( ( h3(e13) != h2(e13) )
| ( op2(h4(e13),h2(e13)) = h4(e13) ) )
| ~ ( ( h1(op1(e13,e13)) != h2(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ) ),
inference(modus_ponens,[status(thm)],[81,41]) ).
tff(83,plain,
~ ( ( h1(op1(e13,e13)) != h2(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) ) ),
inference(unit_resolution,[status(thm)],[82,40]) ).
tff(84,plain,
( ( h1(op1(e13,e13)) != h2(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h2(e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
h1(op1(e13,e13)) = h2(e13),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
( ( h1(op1(e13,e13)) = op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) )
<=> ( h1(op1(e13,e13)) = op2(h1(e13),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( h1(op1(e13,e13)) = op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) )
<=> ( h1(op1(e13,e13)) = op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( h1(e12) = op2(e20,e20) )
<=> ( h1(op1(e13,e13)) = op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( h1(e12) = op2(e20,e20) )
<=> ( h1(e12) = op2(e20,e20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,axiom,
( ( h1(e13) = e20 )
& ( h1(e10) = op2(e20,op2(e20,e20)) )
& ( h1(e11) = op2(op2(e20,e20),e20) )
& ( h1(e12) = op2(e20,e20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
tff(91,plain,
h1(e12) = op2(e20,e20),
inference(and_elim,[status(thm)],[90]) ).
tff(92,plain,
h1(e12) = op2(e20,e20),
inference(modus_ponens,[status(thm)],[91,89]) ).
tff(93,plain,
h1(op1(e13,e13)) = op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
h1(op1(e13,e13)) = op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))),
inference(modus_ponens,[status(thm)],[93,87]) ).
tff(95,plain,
h1(op1(e13,e13)) = op2(h1(e13),h1(e13)),
inference(modus_ponens,[status(thm)],[94,86]) ).
tff(96,plain,
op2(h1(e13),h1(e13)) = h1(op1(e13,e13)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
op2(h1(e13),h1(e13)) = h2(e13),
inference(transitivity,[status(thm)],[96,85]) ).
tff(98,plain,
( ( op2(h1(e13),h1(e13)) = op2(h4(e13),h1(e13)) )
<=> ( h2(e13) = op2(h4(e13),h1(e13)) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ( op2(h1(e13),h1(e13)) = op2(h4(e13),h1(e13)) )
<=> ( op2(h4(e13),h1(e13)) = h2(e13) ) ),
inference(transitivity,[status(thm)],[98,38]) ).
tff(100,plain,
( ( op2(h1(e13),h1(e13)) != op2(h4(e13),h1(e13)) )
<=> ( op2(h4(e13),h1(e13)) != h2(e13) ) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ( h1(op1(e13,e13)) != op2(h4(e13),h1(e13)) )
<=> ( op2(h1(e13),h1(e13)) != op2(h4(e13),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) != op2(h4(e13),op2(h4(e13),h3(e13))) )
<=> ( h1(op1(e13,e13)) != op2(h4(e13),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) )
<=> ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) != op2(h4(e13),op2(h4(e13),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( op2(e20,e20) != op2(e23,e20) )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( op2(e20,e20) != op2(e23,e20) )
<=> ( op2(e20,e20) != op2(e23,e20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,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)],[31]) ).
tff(107,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)],[106]) ).
tff(108,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)],[107]) ).
tff(109,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)],[108]) ).
tff(110,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)],[109]) ).
tff(111,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)],[110]) ).
tff(112,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)],[111]) ).
tff(113,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)],[112]) ).
tff(114,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)],[113]) ).
tff(115,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)],[114]) ).
tff(116,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)],[115]) ).
tff(117,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)],[116]) ).
tff(118,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)],[117]) ).
tff(119,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)],[118]) ).
tff(120,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)],[119]) ).
tff(121,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)],[120]) ).
tff(122,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)],[121]) ).
tff(123,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)],[122]) ).
tff(124,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)],[123]) ).
tff(125,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)],[124]) ).
tff(126,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) ) ),
inference(and_elim,[status(thm)],[125]) ).
tff(127,plain,
op2(e20,e20) != op2(e23,e20),
inference(and_elim,[status(thm)],[126]) ).
tff(128,plain,
op2(e20,e20) != op2(e23,e20),
inference(modus_ponens,[status(thm)],[127,105]) ).
tff(129,plain,
op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))),
inference(modus_ponens,[status(thm)],[128,104]) ).
tff(130,plain,
op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) != op2(h4(e13),op2(h4(e13),h3(e13))),
inference(modus_ponens,[status(thm)],[129,103]) ).
tff(131,plain,
h1(op1(e13,e13)) != op2(h4(e13),h1(e13)),
inference(modus_ponens,[status(thm)],[130,102]) ).
tff(132,plain,
op2(h1(e13),h1(e13)) != op2(h4(e13),h1(e13)),
inference(modus_ponens,[status(thm)],[131,101]) ).
tff(133,plain,
op2(h4(e13),h1(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[132,100]) ).
tff(134,plain,
( ( $false
| ( h3(e13) = h2(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) ) )
<=> ( ( h3(e13) = h2(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( op2(h4(e13),h3(e13)) != op2(h3(e13),h4(e13)) )
<=> ( h1(e13) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ( op2(h4(e13),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(h4(e13),h3(e13)) != op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ( e20 != e21 )
<=> ( op2(h4(e13),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,plain,
( ( e20 != e21 )
<=> ( e20 != e21 ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,axiom,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 )
& ( e21 != e23 )
& ( e22 != e23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
tff(140,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 )
& ( e21 != e23 ) ),
inference(and_elim,[status(thm)],[139]) ).
tff(141,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 ) ),
inference(and_elim,[status(thm)],[140]) ).
tff(142,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 ) ),
inference(and_elim,[status(thm)],[141]) ).
tff(143,plain,
( ( e20 != e21 )
& ( e20 != e22 ) ),
inference(and_elim,[status(thm)],[142]) ).
tff(144,plain,
e20 != e21,
inference(and_elim,[status(thm)],[143]) ).
tff(145,plain,
e20 != e21,
inference(modus_ponens,[status(thm)],[144,138]) ).
tff(146,plain,
op2(h4(e13),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[145,137]) ).
tff(147,plain,
op2(h4(e13),h3(e13)) != op2(h3(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[146,136]) ).
tff(148,plain,
h1(e13) != h2(e13),
inference(modus_ponens,[status(thm)],[147,135]) ).
tff(149,plain,
( ( h1(e13) = h2(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[148]) ).
tff(150,plain,
( ( ( h1(e13) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) ) )
<=> ( $false
| ( h3(e13) = h2(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( ( ( h1(e13) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) ) )
<=> ( ( h3(e13) = h2(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[150,134]) ).
tff(152,plain,
( ( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(e13) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h3(e13),h4(e13))) = op2(h3(e13),h4(e13)) ) )
<=> ( ( h1(e13) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,plain,
( ( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(e13) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h3(e13),h4(e13))) = op2(h3(e13),h4(e13)) ) )
<=> ( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(e13) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h3(e13),h4(e13))) = op2(h3(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(154,plain,
( ( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h3(e13),h4(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(e13) = op2(h3(e13),h4(e13)) ) )
<=> ( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(e13) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h3(e13),h4(e13))) = op2(h3(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(155,plain,
( ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( h3(e13) = op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(h4(e13),op2(h3(e13),h4(e13))) = op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
( ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h3(e13),h4(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(e13) = op2(h3(e13),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[158,157,156,155]) ).
tff(160,plain,
( ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(e13) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h3(e13),h4(e13))) = op2(h3(e13),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[159,154]) ).
tff(161,plain,
( ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,plain,
( ( op2(e23,e23) = e21 )
<=> ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(163,plain,
( ( op2(e23,e22) = e21 )
<=> ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(164,plain,
( ( op2(e23,e21) = e21 )
<=> ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,plain,
( ( op2(e23,e20) = e21 )
<=> ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(166,plain,
( ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
<=> ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[165,164,163,162]) ).
tff(167,plain,
( ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
<=> ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[166,161]) ).
tff(168,plain,
( ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
<=> ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
( ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
<=> ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 ) )
<=> ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(171,plain,
( ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
<=> ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) ) ),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
( ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) )
<=> ( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) ) ),
inference(transitivity,[status(thm)],[171,169]) ).
tff(173,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(174,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)],[173]) ).
tff(175,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)],[174]) ).
tff(176,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)],[175]) ).
tff(177,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)],[176]) ).
tff(178,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)],[177]) ).
tff(179,plain,
( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) ),
inference(and_elim,[status(thm)],[178]) ).
tff(180,plain,
( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) ),
inference(modus_ponens,[status(thm)],[179,172]) ).
tff(181,plain,
( ( op2(e23,e20) = e21 )
| ( op2(e23,e21) = e21 )
| ( op2(e23,e22) = e21 )
| ( op2(e23,e23) = e21 ) ),
inference(modus_ponens,[status(thm)],[180,168]) ).
tff(182,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[181,167]) ).
tff(183,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[182,161]) ).
tff(184,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[183,161]) ).
tff(185,plain,
( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(e13) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h3(e13),h4(e13))) = op2(h3(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[184,160]) ).
tff(186,plain,
( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(e13) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h3(e13),h4(e13))) = op2(h3(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[185,153]) ).
tff(187,plain,
( ( h1(e13) = h2(e13) )
| ( h3(e13) = h2(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[186,152]) ).
tff(188,plain,
( ( h3(e13) = h2(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) )
| ( op2(h4(e13),h2(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[187,151]) ).
tff(189,plain,
op2(h4(e13),h2(e13)) = h2(e13),
inference(unit_resolution,[status(thm)],[188,133,37]) ).
tff(190,plain,
h2(e13) = op2(h4(e13),h2(e13)),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ( h4(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( h4(op1(op1(e13,e13),e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(192,plain,
( ( h4(e11) = op2(op2(e23,e23),e23) )
<=> ( h4(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(193,plain,
( ( h4(e11) = op2(op2(e23,e23),e23) )
<=> ( h4(e11) = op2(op2(e23,e23),e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,axiom,
( ( h4(e13) = e23 )
& ( h4(e10) = op2(e23,op2(e23,e23)) )
& ( h4(e11) = op2(op2(e23,e23),e23) )
& ( h4(e12) = op2(e23,e23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
tff(195,plain,
( ( h4(e13) = e23 )
& ( h4(e10) = op2(e23,op2(e23,e23)) )
& ( h4(e11) = op2(op2(e23,e23),e23) ) ),
inference(and_elim,[status(thm)],[194]) ).
tff(196,plain,
h4(e11) = op2(op2(e23,e23),e23),
inference(and_elim,[status(thm)],[195]) ).
tff(197,plain,
h4(e11) = op2(op2(e23,e23),e23),
inference(modus_ponens,[status(thm)],[196,193]) ).
tff(198,plain,
h4(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[197,192]) ).
tff(199,plain,
h4(op1(op1(e13,e13),e13)) = h2(e13),
inference(modus_ponens,[status(thm)],[198,191]) ).
tff(200,plain,
( ( op1(op1(e13,e13),e13) = op1(e13,e13) )
<=> ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(201,plain,
( ( op1(op1(e13,e13),e13) != op1(e13,e13) )
<=> ( op1(e13,e13) != op1(op1(e13,e13),e13) ) ),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
( ( op1(e12,e13) != op1(e13,e13) )
<=> ( op1(op1(e13,e13),e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(203,plain,
( ( op1(e12,e13) != op1(e13,e13) )
<=> ( op1(e12,e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(204,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(205,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)],[204]) ).
tff(206,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)],[205]) ).
tff(207,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)],[206]) ).
tff(208,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)],[207]) ).
tff(209,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)],[208]) ).
tff(210,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)],[209]) ).
tff(211,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)],[210]) ).
tff(212,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)],[211]) ).
tff(213,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)],[212]) ).
tff(214,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)],[213]) ).
tff(215,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)],[214]) ).
tff(216,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)],[215]) ).
tff(217,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)],[216]) ).
tff(218,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)],[217]) ).
tff(219,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)],[218]) ).
tff(220,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)],[219]) ).
tff(221,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)],[220]) ).
tff(222,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)],[221]) ).
tff(223,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)],[222]) ).
tff(224,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)],[223]) ).
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) ) ),
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) ) ),
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) ) ),
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) ) ),
inference(and_elim,[status(thm)],[227]) ).
tff(229,plain,
op1(e12,e13) != op1(e13,e13),
inference(and_elim,[status(thm)],[228]) ).
tff(230,plain,
op1(e12,e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[229,203]) ).
tff(231,plain,
op1(op1(e13,e13),e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[230,202]) ).
tff(232,plain,
op1(e13,e13) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[231,201]) ).
tff(233,plain,
( ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,op1(e13,e13))) )
<=> ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(234,plain,
( ( op1(e13,e13) != op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(235,plain,
( ( op1(e13,e13) != op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ),
inference(unit_resolution,[status(thm)],[234,232]) ).
tff(236,plain,
( ( ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) ) )
| ~ ( ( op1(e13,e13) != op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ) )
<=> ( ~ ( ( op1(e13,e13) != op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) )
| ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(237,plain,
( ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) )
<=> ~ ( ( op1(e13,e13) != op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(238,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
<=> ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(239,plain,
( ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) )
<=> ( ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) ) )
| ~ ( ( op1(e13,e13) != op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) ) ) ),
inference(monotonicity,[status(thm)],[238,237]) ).
tff(240,plain,
( ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) )
<=> ( ~ ( ( op1(e13,e13) != op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) )
| ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) ) ) ) ),
inference(transitivity,[status(thm)],[239,236]) ).
tff(241,plain,
( ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) )
<=> ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(242,plain,
( ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| $false
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) )
<=> ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(243,plain,
( ( $false
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(244,plain,
( ( op1(e12,e12) != op1(e12,e13) )
<=> ( op1(op1(e13,e13),op1(e13,e13)) != op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(245,plain,
( ( op1(e12,e12) != op1(e12,e13) )
<=> ( op1(e12,e12) != op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(246,plain,
op1(e12,e12) != op1(e12,e13),
inference(and_elim,[status(thm)],[210]) ).
tff(247,plain,
op1(e12,e12) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[246,245]) ).
tff(248,plain,
op1(op1(e13,e13),op1(e13,e13)) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[247,244]) ).
tff(249,plain,
( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
<=> $false ),
inference(iff_false,[status(thm)],[248]) ).
tff(250,plain,
( ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) )
<=> ( $false
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) ) ),
inference(monotonicity,[status(thm)],[249]) ).
tff(251,plain,
( ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) )
<=> $false ),
inference(transitivity,[status(thm)],[250,243]) ).
tff(252,plain,
( ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) )
<=> ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| $false
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ) ),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
( ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) )
<=> ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ) ),
inference(transitivity,[status(thm)],[252,242]) ).
tff(254,plain,
( ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) )
<=> ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(255,plain,
( ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) )
<=> ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(256,plain,
( ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
<=> ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(257,plain,
( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(258,plain,
( ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) )
<=> ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ) ),
inference(monotonicity,[status(thm)],[257,256,255]) ).
tff(259,plain,
( ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) )
<=> ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ) ),
inference(transitivity,[status(thm)],[258,254]) ).
tff(260,plain,
( ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) )
<=> ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(261,plain,
( ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) )
<=> ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(262,plain,
( ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e11,e11) = e11 )
& ( op1(e11,e11) != e11 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) ) )
<=> ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(263,plain,
( ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e11,e11) = e11 )
& ( op1(e11,e11) != e11 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) )
<=> ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) ) ),
inference(monotonicity,[status(thm)],[262]) ).
tff(264,plain,
( ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e11,e11) = e11 )
& ( op1(e11,e11) != e11 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) )
<=> ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) ) ),
inference(transitivity,[status(thm)],[263,261]) ).
tff(265,axiom,
( ( ( ( op1(e10,e10) = e10 )
& ( op1(e10,e10) != e10 ) )
| ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) )
& ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e11,e11) = e11 )
& ( op1(e11,e11) != e11 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) )
& ( ( ( op1(e10,e10) = e12 )
& ( op1(e10,e12) != e10 ) )
| ( ( op1(e11,e11) = e12 )
& ( op1(e11,e12) != e11 ) )
| ( ( op1(e12,e12) = e12 )
& ( op1(e12,e12) != e12 ) )
| ( ( op1(e13,e13) = e12 )
& ( op1(e13,e12) != e13 ) ) )
& ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) )
| ( ( op1(e13,e13) = e13 )
& ( op1(e13,e13) != e13 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
tff(266,plain,
( ( ( ( op1(e10,e10) = e10 )
& ( op1(e10,e10) != e10 ) )
| ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) )
& ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e11,e11) = e11 )
& ( op1(e11,e11) != e11 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) )
& ( ( ( op1(e10,e10) = e12 )
& ( op1(e10,e12) != e10 ) )
| ( ( op1(e11,e11) = e12 )
& ( op1(e11,e12) != e11 ) )
| ( ( op1(e12,e12) = e12 )
& ( op1(e12,e12) != e12 ) )
| ( ( op1(e13,e13) = e12 )
& ( op1(e13,e12) != e13 ) ) ) ),
inference(and_elim,[status(thm)],[265]) ).
tff(267,plain,
( ( ( ( op1(e10,e10) = e10 )
& ( op1(e10,e10) != e10 ) )
| ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) )
& ( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e11,e11) = e11 )
& ( op1(e11,e11) != e11 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) ) ),
inference(and_elim,[status(thm)],[266]) ).
tff(268,plain,
( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e11,e11) = e11 )
& ( op1(e11,e11) != e11 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) ),
inference(and_elim,[status(thm)],[267]) ).
tff(269,plain,
( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[268,264]) ).
tff(270,plain,
( ( ( op1(e10,e10) = e11 )
& ( op1(e10,e11) != e10 ) )
| ( ( op1(e12,e12) = e11 )
& ( op1(e12,e11) != e12 ) )
| ( ( op1(e13,e13) = e11 )
& ( op1(e13,e11) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[269,260]) ).
tff(271,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[270,259]) ).
tff(272,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[271,254]) ).
tff(273,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[272,253]) ).
tff(274,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[273,241]) ).
tff(275,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[274,241]) ).
tff(276,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[275,241]) ).
tff(277,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[276,241]) ).
tff(278,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[277,241]) ).
tff(279,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[278,241]) ).
tff(280,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
& ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
& ( op1(e13,op1(op1(e13,e13),e13)) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[279,241]) ).
tff(281,plain,
( ~ ( ( op1(e13,e13) != op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = e13 ) )
| ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) ) ) ),
inference(modus_ponens,[status(thm)],[280,240]) ).
tff(282,plain,
~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) ) ),
inference(unit_resolution,[status(thm)],[281,235]) ).
tff(283,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(284,plain,
op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13),
inference(unit_resolution,[status(thm)],[283,282]) ).
tff(285,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,op1(e13,e13))) )
<=> ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,op1(e13,e13))) ) ),
inference(monotonicity,[status(thm)],[284]) ).
tff(286,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,op1(e13,e13))) )
<=> ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) ),
inference(transitivity,[status(thm)],[285,233]) ).
tff(287,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(e13,op1(e13,op1(e13,e13))) )
<=> ( op1(e13,op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) ),
inference(monotonicity,[status(thm)],[286]) ).
tff(288,plain,
( ( op1(e10,e10) != op1(e13,e10) )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(e13,op1(e13,op1(e13,e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(289,plain,
( ( op1(e10,e10) != op1(e13,e10) )
<=> ( op1(e10,e10) != op1(e13,e10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(290,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)],[228]) ).
tff(291,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)],[290]) ).
tff(292,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)],[291]) ).
tff(293,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)],[292]) ).
tff(294,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)],[293]) ).
tff(295,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)],[294]) ).
tff(296,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)],[295]) ).
tff(297,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)],[296]) ).
tff(298,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)],[297]) ).
tff(299,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)],[298]) ).
tff(300,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)],[299]) ).
tff(301,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)],[300]) ).
tff(302,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)],[301]) ).
tff(303,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)],[302]) ).
tff(304,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)],[303]) ).
tff(305,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)],[304]) ).
tff(306,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)],[305]) ).
tff(307,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)],[306]) ).
tff(308,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)],[307]) ).
tff(309,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)],[308]) ).
tff(310,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) ) ),
inference(and_elim,[status(thm)],[309]) ).
tff(311,plain,
op1(e10,e10) != op1(e13,e10),
inference(and_elim,[status(thm)],[310]) ).
tff(312,plain,
op1(e10,e10) != op1(e13,e10),
inference(modus_ponens,[status(thm)],[311,289]) ).
tff(313,plain,
op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(e13,op1(e13,op1(e13,e13))),
inference(modus_ponens,[status(thm)],[312,288]) ).
tff(314,plain,
op1(e13,op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[313,287]) ).
tff(315,plain,
( ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(316,plain,
( ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| $false
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(317,plain,
( ( e10 != e11 )
<=> ( op1(e13,op1(e13,e13)) != op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(318,plain,
( ( e10 != e11 )
<=> ( e10 != e11 ) ),
inference(rewrite,[status(thm)],]) ).
tff(319,axiom,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 )
& ( e11 != e13 )
& ( e12 != e13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
tff(320,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 )
& ( e11 != e13 ) ),
inference(and_elim,[status(thm)],[319]) ).
tff(321,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 ) ),
inference(and_elim,[status(thm)],[320]) ).
tff(322,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 ) ),
inference(and_elim,[status(thm)],[321]) ).
tff(323,plain,
( ( e10 != e11 )
& ( e10 != e12 ) ),
inference(and_elim,[status(thm)],[322]) ).
tff(324,plain,
e10 != e11,
inference(and_elim,[status(thm)],[323]) ).
tff(325,plain,
e10 != e11,
inference(modus_ponens,[status(thm)],[324,318]) ).
tff(326,plain,
op1(e13,op1(e13,e13)) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[325,317]) ).
tff(327,plain,
( ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) )
<=> $false ),
inference(iff_false,[status(thm)],[326]) ).
tff(328,plain,
( ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| $false
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ) ),
inference(monotonicity,[status(thm)],[327]) ).
tff(329,plain,
( ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[328,316]) ).
tff(330,plain,
( ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(331,plain,
( ( op1(e13,e13) = e11 )
<=> ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(332,plain,
( ( op1(e13,e12) = e11 )
<=> ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(333,plain,
( ( op1(e13,e11) = e11 )
<=> ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(334,plain,
( ( op1(e13,e10) = e11 )
<=> ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(335,plain,
( ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ) ),
inference(monotonicity,[status(thm)],[334,333,332,331]) ).
tff(336,plain,
( ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[335,330]) ).
tff(337,plain,
( ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
<=> ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(338,plain,
( ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
<=> ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(339,plain,
( ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 ) )
<=> ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(340,plain,
( ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
<=> ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) ) ),
inference(monotonicity,[status(thm)],[339]) ).
tff(341,plain,
( ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) )
<=> ( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) ) ),
inference(transitivity,[status(thm)],[340,338]) ).
tff(342,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(343,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)],[342]) ).
tff(344,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)],[343]) ).
tff(345,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)],[344]) ).
tff(346,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)],[345]) ).
tff(347,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)],[346]) ).
tff(348,plain,
( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) ),
inference(and_elim,[status(thm)],[347]) ).
tff(349,plain,
( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) ),
inference(modus_ponens,[status(thm)],[348,341]) ).
tff(350,plain,
( ( op1(e13,e10) = e11 )
| ( op1(e13,e11) = e11 )
| ( op1(e13,e12) = e11 )
| ( op1(e13,e13) = e11 ) ),
inference(modus_ponens,[status(thm)],[349,337]) ).
tff(351,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[350,336]) ).
tff(352,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[351,330]) ).
tff(353,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[352,330]) ).
tff(354,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[353,329]) ).
tff(355,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[354,315]) ).
tff(356,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[355,315]) ).
tff(357,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[356,315]) ).
tff(358,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[357,315]) ).
tff(359,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[358,315]) ).
tff(360,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[359,315]) ).
tff(361,plain,
op1(e13,op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13),
inference(unit_resolution,[status(thm)],[360,314,232]) ).
tff(362,plain,
h4(op1(e13,op1(op1(e13,e13),e13))) = h4(op1(op1(e13,e13),e13)),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h2(e13)),
inference(transitivity,[status(thm)],[362,199,190]) ).
tff(364,plain,
( ( ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) )
<=> ( ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(365,plain,
( ( $false
| $false
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) )
<=> ( ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(366,plain,
( ( op2(h4(e13),op2(h4(e13),h3(e13))) != op2(h4(e13),h3(e13)) )
<=> ( op2(h4(e13),h1(e13)) != h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(367,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(h4(e13),op2(h4(e13),h3(e13))) != op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(368,plain,
( ( op2(e23,e20) != op2(e23,e22) )
<=> ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(369,plain,
( ( op2(e23,e20) != op2(e23,e22) )
<=> ( op2(e23,e20) != op2(e23,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(370,plain,
op2(e23,e20) != op2(e23,e22),
inference(and_elim,[status(thm)],[11]) ).
tff(371,plain,
op2(e23,e20) != op2(e23,e22),
inference(modus_ponens,[status(thm)],[370,369]) ).
tff(372,plain,
op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),op2(h4(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[371,368]) ).
tff(373,plain,
op2(h4(e13),op2(h4(e13),h3(e13))) != op2(h4(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[372,367]) ).
tff(374,plain,
op2(h4(e13),h1(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[373,366]) ).
tff(375,plain,
( ( op2(h4(e13),h1(e13)) = h1(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[374]) ).
tff(376,plain,
( ( op2(h4(e13),op2(h4(e13),h3(e13))) != h3(e13) )
<=> ( op2(h4(e13),h1(e13)) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(377,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) )
<=> ( op2(h4(e13),op2(h4(e13),h3(e13))) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(378,plain,
( ( op2(e23,e20) != op2(e23,e23) )
<=> ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(379,plain,
( ( op2(e23,e20) != op2(e23,e23) )
<=> ( op2(e23,e20) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(380,plain,
op2(e23,e20) != op2(e23,e23),
inference(and_elim,[status(thm)],[10]) ).
tff(381,plain,
op2(e23,e20) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[380,379]) ).
tff(382,plain,
op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[381,378]) ).
tff(383,plain,
op2(h4(e13),op2(h4(e13),h3(e13))) != h3(e13),
inference(modus_ponens,[status(thm)],[382,377]) ).
tff(384,plain,
op2(h4(e13),h1(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[383,376]) ).
tff(385,plain,
( ( op2(h4(e13),h1(e13)) = h3(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[384]) ).
tff(386,plain,
( ( ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) )
<=> ( $false
| $false
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[385,375]) ).
tff(387,plain,
( ( ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) )
<=> ( ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[386,365]) ).
tff(388,plain,
( ( ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) )
<=> ( ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(389,plain,
( ( ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) )
<=> ( ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(390,plain,
( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
<=> ( op2(h4(e13),h1(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(391,plain,
( ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) )
<=> ( op2(h4(e13),h1(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(392,plain,
( ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) )
<=> ( op2(h4(e13),h1(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(393,plain,
( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
<=> ( op2(h4(e13),h1(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(394,plain,
( ( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) ) )
<=> ( ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[393,392,391,390]) ).
tff(395,plain,
( ( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) ) )
<=> ( ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[394,389]) ).
tff(396,plain,
( ( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) ) )
<=> ( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(397,plain,
( ( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) ) )
<=> ( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(398,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
<=> ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(399,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
<=> ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(400,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(401,plain,
( ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) )
<=> ( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[400,158,399,398]) ).
tff(402,plain,
( ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) )
<=> ( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[401,397]) ).
tff(403,plain,
( ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) )
<=> ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(404,plain,
( ( op2(e23,e20) = e23 )
<=> ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(405,plain,
( ( op2(e23,e20) = e22 )
<=> ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(406,plain,
( ( op2(e23,e20) = e20 )
<=> ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(407,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) )
<=> ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[406,165,405,404]) ).
tff(408,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) )
<=> ( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[407,403]) ).
tff(409,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) )
<=> ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(410,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) )
<=> ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(411,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 ) )
<=> ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(412,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) )
<=> ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) ) ),
inference(monotonicity,[status(thm)],[411]) ).
tff(413,plain,
( ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) )
<=> ( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) ) ),
inference(transitivity,[status(thm)],[412,410]) ).
tff(414,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(415,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)],[414]) ).
tff(416,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)],[415]) ).
tff(417,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)],[416]) ).
tff(418,plain,
( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) ),
inference(and_elim,[status(thm)],[417]) ).
tff(419,plain,
( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) ),
inference(modus_ponens,[status(thm)],[418,413]) ).
tff(420,plain,
( ( op2(e23,e20) = e20 )
| ( op2(e23,e20) = e21 )
| ( op2(e23,e20) = e22 )
| ( op2(e23,e20) = e23 ) ),
inference(modus_ponens,[status(thm)],[419,409]) ).
tff(421,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[420,408]) ).
tff(422,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[421,403]) ).
tff(423,plain,
( ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[422,403]) ).
tff(424,plain,
( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[423,402]) ).
tff(425,plain,
( ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(h4(e13),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[424,396]) ).
tff(426,plain,
( ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[425,395]) ).
tff(427,plain,
( ( op2(h4(e13),h1(e13)) = h3(e13) )
| ( op2(h4(e13),h1(e13)) = h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[426,388]) ).
tff(428,plain,
( ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[427,387]) ).
tff(429,plain,
( ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[428,364]) ).
tff(430,plain,
( ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( op2(h4(e13),h1(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[429,364]) ).
tff(431,plain,
op2(h4(e13),h1(e13)) = h4(e13),
inference(unit_resolution,[status(thm)],[430,133]) ).
tff(432,plain,
h4(e13) = op2(h4(e13),h1(e13)),
inference(symmetry,[status(thm)],[431]) ).
tff(433,plain,
( ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(434,plain,
( ( $false
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| $false
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(435,plain,
( ( op1(e13,e10) != op1(e13,e13) )
<=> ( op1(e13,op1(e13,op1(e13,e13))) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(436,plain,
( ( op1(e13,e10) != op1(e13,e13) )
<=> ( op1(e13,e10) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(437,plain,
op1(e13,e10) != op1(e13,e13),
inference(and_elim,[status(thm)],[207]) ).
tff(438,plain,
op1(e13,e10) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[437,436]) ).
tff(439,plain,
op1(e13,op1(e13,op1(e13,e13))) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[438,435]) ).
tff(440,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[439]) ).
tff(441,plain,
( ( op1(e13,e10) != op1(e13,e12) )
<=> ( op1(e13,op1(e13,op1(e13,e13))) != op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(442,plain,
( ( op1(e13,e10) != op1(e13,e12) )
<=> ( op1(e13,e10) != op1(e13,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(443,plain,
op1(e13,e10) != op1(e13,e12),
inference(and_elim,[status(thm)],[208]) ).
tff(444,plain,
op1(e13,e10) != op1(e13,e12),
inference(modus_ponens,[status(thm)],[443,442]) ).
tff(445,plain,
op1(e13,op1(e13,op1(e13,e13))) != op1(e13,op1(e13,e13)),
inference(modus_ponens,[status(thm)],[444,441]) ).
tff(446,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
<=> $false ),
inference(iff_false,[status(thm)],[445]) ).
tff(447,plain,
( ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) )
<=> ( $false
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| $false
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ) ),
inference(monotonicity,[status(thm)],[446,440]) ).
tff(448,plain,
( ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ) ),
inference(transitivity,[status(thm)],[447,434]) ).
tff(449,plain,
( ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(450,plain,
( ( op1(e13,e10) = e13 )
<=> ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(451,plain,
( ( op1(e13,e10) = e12 )
<=> ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(452,plain,
( ( op1(e13,e10) = e10 )
<=> ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(453,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ) ),
inference(monotonicity,[status(thm)],[452,334,451,450]) ).
tff(454,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) )
<=> ( ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ) ),
inference(transitivity,[status(thm)],[453,449]) ).
tff(455,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) )
<=> ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(456,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) )
<=> ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(457,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 ) )
<=> ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(458,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) )
<=> ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) ) ),
inference(monotonicity,[status(thm)],[457]) ).
tff(459,plain,
( ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) )
<=> ( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) ) ),
inference(transitivity,[status(thm)],[458,456]) ).
tff(460,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(461,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)],[460]) ).
tff(462,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)],[461]) ).
tff(463,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)],[462]) ).
tff(464,plain,
( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) ),
inference(and_elim,[status(thm)],[463]) ).
tff(465,plain,
( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) ),
inference(modus_ponens,[status(thm)],[464,459]) ).
tff(466,plain,
( ( op1(e13,e10) = e10 )
| ( op1(e13,e10) = e11 )
| ( op1(e13,e10) = e12 )
| ( op1(e13,e10) = e13 ) ),
inference(modus_ponens,[status(thm)],[465,455]) ).
tff(467,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[466,454]) ).
tff(468,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[467,449]) ).
tff(469,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[468,449]) ).
tff(470,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[469,448]) ).
tff(471,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[470,433]) ).
tff(472,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[471,433]) ).
tff(473,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[472,433]) ).
tff(474,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[473,433]) ).
tff(475,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[474,433]) ).
tff(476,plain,
( ( op1(e13,op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[475,433]) ).
tff(477,plain,
op1(e13,op1(e13,op1(e13,e13))) = e13,
inference(unit_resolution,[status(thm)],[476,314]) ).
tff(478,plain,
h4(op1(e13,op1(e13,op1(e13,e13)))) = h4(e13),
inference(monotonicity,[status(thm)],[477]) ).
tff(479,plain,
h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h1(e13)),
inference(transitivity,[status(thm)],[478,432]) ).
tff(480,plain,
( ( h3(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) )
<=> ( h3(op1(e13,e13)) = op2(h3(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(481,plain,
( ( h3(e12) = op2(e22,e22) )
<=> ( h3(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(482,plain,
( ( h3(e12) = op2(e22,e22) )
<=> ( h3(e12) = op2(e22,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(483,axiom,
( ( h3(e13) = e22 )
& ( h3(e10) = op2(e22,op2(e22,e22)) )
& ( h3(e11) = op2(op2(e22,e22),e22) )
& ( h3(e12) = op2(e22,e22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
tff(484,plain,
h3(e12) = op2(e22,e22),
inference(and_elim,[status(thm)],[483]) ).
tff(485,plain,
h3(e12) = op2(e22,e22),
inference(modus_ponens,[status(thm)],[484,482]) ).
tff(486,plain,
h3(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[485,481]) ).
tff(487,plain,
h3(op1(e13,e13)) = op2(h3(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[486,480]) ).
tff(488,plain,
( ( h1(op1(e13,e13)) = h4(e13) )
<=> ( h2(e13) = h4(e13) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(489,plain,
( ( h2(e13) = h4(e13) )
<=> ( h1(op1(e13,e13)) = h4(e13) ) ),
inference(symmetry,[status(thm)],[488]) ).
tff(490,plain,
( ( h2(e13) != h4(e13) )
<=> ( h1(op1(e13,e13)) != h4(e13) ) ),
inference(monotonicity,[status(thm)],[489]) ).
tff(491,plain,
( ( op2(h3(e13),h4(e13)) != h4(e13) )
<=> ( h2(e13) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(492,plain,
( ( op2(op2(h4(e13),h4(e13)),h4(e13)) != h4(e13) )
<=> ( op2(h3(e13),h4(e13)) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(493,plain,
( ( e21 != e23 )
<=> ( op2(op2(h4(e13),h4(e13)),h4(e13)) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(494,plain,
( ( e21 != e23 )
<=> ( e21 != e23 ) ),
inference(rewrite,[status(thm)],]) ).
tff(495,plain,
e21 != e23,
inference(and_elim,[status(thm)],[140]) ).
tff(496,plain,
e21 != e23,
inference(modus_ponens,[status(thm)],[495,494]) ).
tff(497,plain,
op2(op2(h4(e13),h4(e13)),h4(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[496,493]) ).
tff(498,plain,
op2(h3(e13),h4(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[497,492]) ).
tff(499,plain,
h2(e13) != h4(e13),
inference(modus_ponens,[status(thm)],[498,491]) ).
tff(500,plain,
h1(op1(e13,e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[499,490]) ).
tff(501,plain,
( ( h1(op1(e13,e13)) != h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h4(e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(502,plain,
( ( h1(op1(e13,e13)) != h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ),
inference(unit_resolution,[status(thm)],[501,500]) ).
tff(503,plain,
( ( h1(e13) = h3(e13) )
<=> ( h3(e13) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(504,plain,
( ( h1(e13) != h3(e13) )
<=> ( h3(e13) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[503]) ).
tff(505,plain,
( ( op2(h4(e13),h3(e13)) != h3(e13) )
<=> ( h1(e13) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(506,plain,
( ( op2(h4(e13),op2(h4(e13),h4(e13))) != op2(h4(e13),h4(e13)) )
<=> ( op2(h4(e13),h3(e13)) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(507,plain,
( ( op2(e23,e22) != op2(e23,e23) )
<=> ( op2(h4(e13),op2(h4(e13),h4(e13))) != op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(508,plain,
( ( op2(e23,e22) != op2(e23,e23) )
<=> ( op2(e23,e22) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(509,plain,
op2(e23,e22) != op2(e23,e23),
inference(and_elim,[status(thm)],[7]) ).
tff(510,plain,
op2(e23,e22) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[509,508]) ).
tff(511,plain,
op2(h4(e13),op2(h4(e13),h4(e13))) != op2(h4(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[510,507]) ).
tff(512,plain,
op2(h4(e13),h3(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[511,506]) ).
tff(513,plain,
h1(e13) != h3(e13),
inference(modus_ponens,[status(thm)],[512,505]) ).
tff(514,plain,
h3(e13) != h1(e13),
inference(modus_ponens,[status(thm)],[513,504]) ).
tff(515,plain,
( ( h3(e13) != h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) )
| ( h3(e13) = h1(e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(516,plain,
( ( h3(e13) != h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) ) ),
inference(unit_resolution,[status(thm)],[515,514]) ).
tff(517,plain,
( ( ( ( h3(e13) = h1(e13) )
& ( op2(h4(e13),h1(e13)) != h4(e13) ) )
| ( ( h2(op1(e13,e13)) = h1(e13) )
& ( op2(h2(e13),h1(e13)) != h2(e13) ) ) )
<=> ( ~ ( ( h3(e13) != h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) ) )
| ~ ( ( h2(op1(e13,e13)) != h1(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(518,plain,
( ( ( ( h3(e13) = op2(h4(e13),h3(e13)) )
& ( op2(h4(e13),op2(h4(e13),h3(e13))) != h4(e13) ) )
| ( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
& ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(h3(e13),h4(e13)) ) ) )
<=> ( ( ( h3(e13) = h1(e13) )
& ( op2(h4(e13),h1(e13)) != h4(e13) ) )
| ( ( h2(op1(e13,e13)) = h1(e13) )
& ( op2(h2(e13),h1(e13)) != h2(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(519,plain,
( ( ( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
& ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(h3(e13),h4(e13)) ) )
| ( ( h3(e13) = op2(h4(e13),h3(e13)) )
& ( op2(h4(e13),op2(h4(e13),h3(e13))) != h4(e13) ) ) )
<=> ( ( ( h3(e13) = op2(h4(e13),h3(e13)) )
& ( op2(h4(e13),op2(h4(e13),h3(e13))) != h4(e13) ) )
| ( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
& ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(h3(e13),h4(e13)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(520,plain,
( ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) )
<=> ( ( h3(e13) = op2(h4(e13),h3(e13)) )
& ( op2(h4(e13),op2(h4(e13),h3(e13))) != h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(521,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
& ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(h3(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(522,plain,
( ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) )
<=> ( ( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
& ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(h3(e13),h4(e13)) ) )
| ( ( h3(e13) = op2(h4(e13),h3(e13)) )
& ( op2(h4(e13),op2(h4(e13),h3(e13))) != h4(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[521,520]) ).
tff(523,plain,
( ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) )
<=> ( ( ( h3(e13) = op2(h4(e13),h3(e13)) )
& ( op2(h4(e13),op2(h4(e13),h3(e13))) != h4(e13) ) )
| ( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
& ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(h3(e13),h4(e13)) ) ) ) ),
inference(transitivity,[status(thm)],[522,519]) ).
tff(524,plain,
( ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| $false
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) )
<=> ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(525,plain,
( ( $false
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(526,plain,
( ( op2(e22,e22) != op2(e23,e22) )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(527,plain,
( ( op2(e22,e22) != op2(e23,e22) )
<=> ( op2(e22,e22) != op2(e23,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(528,plain,
op2(e22,e22) != op2(e23,e22),
inference(and_elim,[status(thm)],[111]) ).
tff(529,plain,
op2(e22,e22) != op2(e23,e22),
inference(modus_ponens,[status(thm)],[528,527]) ).
tff(530,plain,
op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[529,526]) ).
tff(531,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> $false ),
inference(iff_false,[status(thm)],[530]) ).
tff(532,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) )
<=> ( $false
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[531]) ).
tff(533,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) )
<=> $false ),
inference(transitivity,[status(thm)],[532,525]) ).
tff(534,plain,
( ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) )
<=> ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| $false
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[533]) ).
tff(535,plain,
( ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) )
<=> ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) ) ),
inference(transitivity,[status(thm)],[534,524]) ).
tff(536,plain,
( ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) )
<=> ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(537,plain,
( ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) )
<=> ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(538,plain,
( ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(539,plain,
( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(540,plain,
( ( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) )
<=> ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[539,538,537]) ).
tff(541,plain,
( ( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) )
<=> ( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) ) ),
inference(transitivity,[status(thm)],[540,536]) ).
tff(542,plain,
( ( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) )
<=> ( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(543,plain,
( ( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) )
<=> ( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(544,plain,
( ( ( ( op2(e20,e20) = e20 )
& ( op2(e20,e20) != e20 ) )
| ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) ) )
<=> ( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(545,plain,
( ( ( ( op2(e20,e20) = e20 )
& ( op2(e20,e20) != e20 ) )
| ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) )
<=> ( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) ) ),
inference(monotonicity,[status(thm)],[544]) ).
tff(546,plain,
( ( ( ( op2(e20,e20) = e20 )
& ( op2(e20,e20) != e20 ) )
| ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) )
<=> ( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) ) ),
inference(transitivity,[status(thm)],[545,543]) ).
tff(547,plain,
( ( ( op2(e20,e20) = e20 )
& ( op2(e20,e20) != e20 ) )
| ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) ),
inference(and_elim,[status(thm)],[73]) ).
tff(548,plain,
( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) ),
inference(modus_ponens,[status(thm)],[547,546]) ).
tff(549,plain,
( ( ( op2(e21,e21) = e20 )
& ( op2(e21,e20) != e21 ) )
| ( ( op2(e22,e22) = e20 )
& ( op2(e22,e20) != e22 ) )
| ( ( op2(e23,e23) = e20 )
& ( op2(e23,e20) != e23 ) ) ),
inference(modus_ponens,[status(thm)],[548,542]) ).
tff(550,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[549,541]) ).
tff(551,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[550,536]) ).
tff(552,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(h4(e13),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
& ( op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) != h4(e13) ) ) ),
inference(modus_ponens,[status(thm)],[551,535]) ).
tff(553,plain,
( ( ( h3(e13) = op2(h4(e13),h3(e13)) )
& ( op2(h4(e13),op2(h4(e13),h3(e13))) != h4(e13) ) )
| ( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
& ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(h3(e13),h4(e13)) ) ) ),
inference(modus_ponens,[status(thm)],[552,523]) ).
tff(554,plain,
( ( ( h3(e13) = h1(e13) )
& ( op2(h4(e13),h1(e13)) != h4(e13) ) )
| ( ( h2(op1(e13,e13)) = h1(e13) )
& ( op2(h2(e13),h1(e13)) != h2(e13) ) ) ),
inference(modus_ponens,[status(thm)],[553,518]) ).
tff(555,plain,
( ~ ( ( h3(e13) != h1(e13) )
| ( op2(h4(e13),h1(e13)) = h4(e13) ) )
| ~ ( ( h2(op1(e13,e13)) != h1(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) ) ) ),
inference(modus_ponens,[status(thm)],[554,517]) ).
tff(556,plain,
~ ( ( h2(op1(e13,e13)) != h1(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) ) ),
inference(unit_resolution,[status(thm)],[555,516]) ).
tff(557,plain,
( ( h2(op1(e13,e13)) != h1(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( h2(op1(e13,e13)) = h1(e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(558,plain,
h2(op1(e13,e13)) = h1(e13),
inference(unit_resolution,[status(thm)],[557,556]) ).
tff(559,plain,
( ( h2(op1(e13,e13)) = h4(e13) )
<=> ( h1(e13) = h4(e13) ) ),
inference(monotonicity,[status(thm)],[558]) ).
tff(560,plain,
( ( h1(e13) = h4(e13) )
<=> ( h2(op1(e13,e13)) = h4(e13) ) ),
inference(symmetry,[status(thm)],[559]) ).
tff(561,plain,
( ( h1(e13) != h4(e13) )
<=> ( h2(op1(e13,e13)) != h4(e13) ) ),
inference(monotonicity,[status(thm)],[560]) ).
tff(562,plain,
( ( op2(h4(e13),h3(e13)) != h4(e13) )
<=> ( h1(e13) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(563,plain,
( ( op2(h4(e13),op2(h4(e13),h4(e13))) != h4(e13) )
<=> ( op2(h4(e13),h3(e13)) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(564,plain,
( ( e20 != e23 )
<=> ( op2(h4(e13),op2(h4(e13),h4(e13))) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(565,plain,
( ( e20 != e23 )
<=> ( e20 != e23 ) ),
inference(rewrite,[status(thm)],]) ).
tff(566,plain,
e20 != e23,
inference(and_elim,[status(thm)],[142]) ).
tff(567,plain,
e20 != e23,
inference(modus_ponens,[status(thm)],[566,565]) ).
tff(568,plain,
op2(h4(e13),op2(h4(e13),h4(e13))) != h4(e13),
inference(modus_ponens,[status(thm)],[567,564]) ).
tff(569,plain,
op2(h4(e13),h3(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[568,563]) ).
tff(570,plain,
h1(e13) != h4(e13),
inference(modus_ponens,[status(thm)],[569,562]) ).
tff(571,plain,
h2(op1(e13,e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[570,561]) ).
tff(572,plain,
( ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ~ ( ( h1(op1(e13,e13)) != h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ) )
<=> ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ~ ( ( h1(op1(e13,e13)) != h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(573,plain,
( ( ( h1(op1(e13,e13)) = h4(e13) )
& ( op2(h1(e13),h4(e13)) != h1(e13) ) )
<=> ~ ( ( h1(op1(e13,e13)) != h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(574,plain,
( ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( ( h1(op1(e13,e13)) = h4(e13) )
& ( op2(h1(e13),h4(e13)) != h1(e13) ) ) )
<=> ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ~ ( ( h1(op1(e13,e13)) != h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ) ) ),
inference(monotonicity,[status(thm)],[573]) ).
tff(575,plain,
( ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( ( h1(op1(e13,e13)) = h4(e13) )
& ( op2(h1(e13),h4(e13)) != h1(e13) ) ) )
<=> ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ~ ( ( h1(op1(e13,e13)) != h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ) ) ),
inference(transitivity,[status(thm)],[574,572]) ).
tff(576,plain,
( ( ( ( h1(op1(e13,e13)) = h4(e13) )
& ( op2(h1(e13),h4(e13)) != h1(e13) ) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) )
<=> ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( ( h1(op1(e13,e13)) = h4(e13) )
& ( op2(h1(e13),h4(e13)) != h1(e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(577,plain,
( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
<=> ( h2(op1(e13,e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(578,plain,
( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) )
<=> ( ( h1(op1(e13,e13)) = h4(e13) )
& ( op2(h1(e13),h4(e13)) != h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(579,plain,
( ( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) )
| ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) )
<=> ( ( ( h1(op1(e13,e13)) = h4(e13) )
& ( op2(h1(e13),h4(e13)) != h1(e13) ) )
| ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[578,577]) ).
tff(580,plain,
( ( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) )
| ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) )
<=> ( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( ( h1(op1(e13,e13)) = h4(e13) )
& ( op2(h1(e13),h4(e13)) != h1(e13) ) ) ) ),
inference(transitivity,[status(thm)],[579,576]) ).
tff(581,plain,
( ( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) )
| ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) )
<=> ( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) )
| ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(582,plain,
( ( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) ) )
<=> ( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) )
| ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(583,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(584,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
<=> ( h3(op1(e13,e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(585,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
<=> ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(586,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) ) )
<=> ( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) ) ) ),
inference(monotonicity,[status(thm)],[585,584,583]) ).
tff(587,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) ) )
<=> ( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) )
| ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[586,582]) ).
tff(588,plain,
( ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(589,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& $true )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(590,plain,
( ~ $false
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(591,plain,
( ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
<=> $false ),
inference(iff_false,[status(thm)],[34]) ).
tff(592,plain,
( ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) )
<=> ~ $false ),
inference(monotonicity,[status(thm)],[591]) ).
tff(593,plain,
( ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) )
<=> $true ),
inference(transitivity,[status(thm)],[592,590]) ).
tff(594,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& $true ) ),
inference(monotonicity,[status(thm)],[593]) ).
tff(595,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) ) ),
inference(transitivity,[status(thm)],[594,589]) ).
tff(596,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& $true )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(597,plain,
( ( op2(e21,e23) != op2(e22,e23) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(598,plain,
( ( op2(e21,e23) != op2(e22,e23) )
<=> ( op2(e21,e23) != op2(e22,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(599,plain,
op2(e21,e23) != op2(e22,e23),
inference(and_elim,[status(thm)],[107]) ).
tff(600,plain,
op2(e21,e23) != op2(e22,e23),
inference(modus_ponens,[status(thm)],[599,598]) ).
tff(601,plain,
op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[600,597]) ).
tff(602,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> $false ),
inference(iff_false,[status(thm)],[601]) ).
tff(603,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ~ $false ),
inference(monotonicity,[status(thm)],[602]) ).
tff(604,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> $true ),
inference(transitivity,[status(thm)],[603,590]) ).
tff(605,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& $true ) ),
inference(monotonicity,[status(thm)],[604]) ).
tff(606,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(transitivity,[status(thm)],[605,596]) ).
tff(607,plain,
( ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ) )
<=> ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[606,595]) ).
tff(608,plain,
( ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) ) ) ),
inference(transitivity,[status(thm)],[607,588]) ).
tff(609,plain,
( ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ) )
<=> ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(610,plain,
( ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(611,plain,
( ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(612,plain,
( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(613,plain,
( ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) ) )
<=> ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ) ) ),
inference(monotonicity,[status(thm)],[612,611,610]) ).
tff(614,plain,
( ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) ) )
<=> ( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ) ) ),
inference(transitivity,[status(thm)],[613,609]) ).
tff(615,plain,
( ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) ) )
<=> ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(616,plain,
( ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) )
| $false )
<=> ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(617,plain,
( ( ( op2(e23,e23) = e23 )
& ( op2(e23,e23) != e23 ) )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(618,plain,
( ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) ) )
<=> ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(619,plain,
( ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) )
| ( ( op2(e23,e23) = e23 )
& ( op2(e23,e23) != e23 ) ) )
<=> ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) )
| $false ) ),
inference(monotonicity,[status(thm)],[618,617]) ).
tff(620,plain,
( ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) )
| ( ( op2(e23,e23) = e23 )
& ( op2(e23,e23) != e23 ) ) )
<=> ( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) ) ) ),
inference(transitivity,[status(thm)],[619,616]) ).
tff(621,plain,
( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) )
| ( ( op2(e23,e23) = e23 )
& ( op2(e23,e23) != e23 ) ) ),
inference(and_elim,[status(thm)],[71]) ).
tff(622,plain,
( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) ) ),
inference(modus_ponens,[status(thm)],[621,620]) ).
tff(623,plain,
( ( ( op2(e20,e20) = e23 )
& ( op2(e20,e23) != e20 ) )
| ( ( op2(e21,e21) = e23 )
& ( op2(e21,e23) != e21 ) )
| ( ( op2(e22,e22) = e23 )
& ( op2(e22,e23) != e22 ) ) ),
inference(modus_ponens,[status(thm)],[622,615]) ).
tff(624,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ) ),
inference(modus_ponens,[status(thm)],[623,614]) ).
tff(625,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) )
| ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
& ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
| ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ) ),
inference(modus_ponens,[status(thm)],[624,609]) ).
tff(626,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = h4(e13) )
| ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
& ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) != op2(h4(e13),op2(h4(e13),h4(e13))) ) ) ),
inference(modus_ponens,[status(thm)],[625,608]) ).
tff(627,plain,
( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) )
| ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[626,587]) ).
tff(628,plain,
( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
& ( op2(op2(h4(e13),h3(e13)),h4(e13)) != op2(h4(e13),h3(e13)) ) )
| ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[627,581]) ).
tff(629,plain,
( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ( ( h1(op1(e13,e13)) = h4(e13) )
& ( op2(h1(e13),h4(e13)) != h1(e13) ) ) ),
inference(modus_ponens,[status(thm)],[628,580]) ).
tff(630,plain,
( ( h2(op1(e13,e13)) = h4(e13) )
| ( h3(op1(e13,e13)) = h4(e13) )
| ~ ( ( h1(op1(e13,e13)) != h4(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) ) ) ),
inference(modus_ponens,[status(thm)],[629,575]) ).
tff(631,plain,
h3(op1(e13,e13)) = h4(e13),
inference(unit_resolution,[status(thm)],[630,571,502]) ).
tff(632,plain,
h4(e13) = h3(op1(e13,e13)),
inference(symmetry,[status(thm)],[631]) ).
tff(633,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
<=> ( op1(op1(e13,e13),e13) = e13 ) ),
inference(monotonicity,[status(thm)],[284]) ).
tff(634,plain,
( ( op1(op1(e13,e13),e13) = e13 )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 ) ),
inference(symmetry,[status(thm)],[633]) ).
tff(635,plain,
( ( op1(op1(e13,e13),e13) != e13 )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != e13 ) ),
inference(monotonicity,[status(thm)],[634]) ).
tff(636,plain,
( ( e11 != e13 )
<=> ( op1(op1(e13,e13),e13) != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(637,plain,
( ( e11 != e13 )
<=> ( e11 != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(638,plain,
e11 != e13,
inference(and_elim,[status(thm)],[320]) ).
tff(639,plain,
e11 != e13,
inference(modus_ponens,[status(thm)],[638,637]) ).
tff(640,plain,
op1(op1(e13,e13),e13) != e13,
inference(modus_ponens,[status(thm)],[639,636]) ).
tff(641,plain,
op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != e13,
inference(modus_ponens,[status(thm)],[640,635]) ).
tff(642,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 ) ),
inference(tautology,[status(thm)],]) ).
tff(643,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(unit_resolution,[status(thm)],[642,641]) ).
tff(644,plain,
( ( op1(e13,op1(e13,e13)) = op1(e13,e13) )
<=> ( op1(e13,e13) = op1(e13,op1(e13,e13)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(645,plain,
( ( op1(e13,op1(e13,e13)) != op1(e13,e13) )
<=> ( op1(e13,e13) != op1(e13,op1(e13,e13)) ) ),
inference(monotonicity,[status(thm)],[644]) ).
tff(646,plain,
( ( op1(e13,e12) != op1(e13,e13) )
<=> ( op1(e13,op1(e13,e13)) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(647,plain,
( ( op1(e13,e12) != op1(e13,e13) )
<=> ( op1(e13,e12) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(648,plain,
op1(e13,e12) != op1(e13,e13),
inference(and_elim,[status(thm)],[204]) ).
tff(649,plain,
op1(e13,e12) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[648,647]) ).
tff(650,plain,
op1(e13,op1(e13,e13)) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[649,646]) ).
tff(651,plain,
op1(e13,e13) != op1(e13,op1(e13,e13)),
inference(modus_ponens,[status(thm)],[650,645]) ).
tff(652,plain,
( ( op1(e13,e13) != op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 )
| ( op1(e13,e13) = op1(e13,op1(e13,e13)) ) ),
inference(tautology,[status(thm)],]) ).
tff(653,plain,
( ( op1(e13,e13) != op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ),
inference(unit_resolution,[status(thm)],[652,651]) ).
tff(654,plain,
( ( ~ ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) )
| ~ ( ( op1(e13,e13) != op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ) )
<=> ( ~ ( ( op1(e13,e13) != op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) )
| ~ ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(655,plain,
( ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) )
<=> ~ ( ( op1(e13,e13) != op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(656,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
<=> ~ ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(657,plain,
( ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) )
<=> ( ~ ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) )
| ~ ( ( op1(e13,e13) != op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) ) ) ),
inference(monotonicity,[status(thm)],[656,655]) ).
tff(658,plain,
( ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) )
<=> ( ~ ( ( op1(e13,e13) != op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) )
| ~ ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) ) ) ),
inference(transitivity,[status(thm)],[657,654]) ).
tff(659,plain,
( ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) )
<=> ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(660,plain,
( ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| $false
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) )
<=> ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(661,plain,
( ( $false
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(662,plain,
( ( op1(e12,e12) != op1(e13,e12) )
<=> ( op1(op1(e13,e13),op1(e13,e13)) != op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(663,plain,
( ( op1(e12,e12) != op1(e13,e12) )
<=> ( op1(e12,e12) != op1(e13,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(664,plain,
op1(e12,e12) != op1(e13,e12),
inference(and_elim,[status(thm)],[295]) ).
tff(665,plain,
op1(e12,e12) != op1(e13,e12),
inference(modus_ponens,[status(thm)],[664,663]) ).
tff(666,plain,
op1(op1(e13,e13),op1(e13,e13)) != op1(e13,op1(e13,e13)),
inference(modus_ponens,[status(thm)],[665,662]) ).
tff(667,plain,
( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
<=> $false ),
inference(iff_false,[status(thm)],[666]) ).
tff(668,plain,
( ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) )
<=> ( $false
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) ) ),
inference(monotonicity,[status(thm)],[667]) ).
tff(669,plain,
( ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) )
<=> $false ),
inference(transitivity,[status(thm)],[668,661]) ).
tff(670,plain,
( ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) )
<=> ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| $false
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ) ),
inference(monotonicity,[status(thm)],[669]) ).
tff(671,plain,
( ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) )
<=> ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ) ),
inference(transitivity,[status(thm)],[670,660]) ).
tff(672,plain,
( ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) )
<=> ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(673,plain,
( ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) )
<=> ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(674,plain,
( ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
<=> ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(675,plain,
( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(676,plain,
( ( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) )
<=> ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ) ),
inference(monotonicity,[status(thm)],[675,674,673]) ).
tff(677,plain,
( ( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) )
<=> ( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ) ),
inference(transitivity,[status(thm)],[676,672]) ).
tff(678,plain,
( ( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) )
<=> ( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(679,plain,
( ( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) )
<=> ( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(680,plain,
( ( ( ( op1(e10,e10) = e10 )
& ( op1(e10,e10) != e10 ) )
| ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) ) )
<=> ( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(681,plain,
( ( ( ( op1(e10,e10) = e10 )
& ( op1(e10,e10) != e10 ) )
| ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) )
<=> ( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) ) ),
inference(monotonicity,[status(thm)],[680]) ).
tff(682,plain,
( ( ( ( op1(e10,e10) = e10 )
& ( op1(e10,e10) != e10 ) )
| ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) )
<=> ( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) ) ),
inference(transitivity,[status(thm)],[681,679]) ).
tff(683,plain,
( ( ( op1(e10,e10) = e10 )
& ( op1(e10,e10) != e10 ) )
| ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) ),
inference(and_elim,[status(thm)],[267]) ).
tff(684,plain,
( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[683,682]) ).
tff(685,plain,
( ( ( op1(e11,e11) = e10 )
& ( op1(e11,e10) != e11 ) )
| ( ( op1(e12,e12) = e10 )
& ( op1(e12,e10) != e12 ) )
| ( ( op1(e13,e13) = e10 )
& ( op1(e13,e10) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[684,678]) ).
tff(686,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[685,677]) ).
tff(687,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) != op1(e13,e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[686,672]) ).
tff(688,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[687,671]) ).
tff(689,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[688,659]) ).
tff(690,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[689,659]) ).
tff(691,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[690,659]) ).
tff(692,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[691,659]) ).
tff(693,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[692,659]) ).
tff(694,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[693,659]) ).
tff(695,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
& ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) )
| ( ( op1(e13,e13) = op1(e13,op1(e13,e13)) )
& ( op1(e13,op1(e13,op1(e13,e13))) != e13 ) ) ),
inference(modus_ponens,[status(thm)],[694,659]) ).
tff(696,plain,
( ~ ( ( op1(e13,e13) != op1(e13,op1(e13,e13)) )
| ( op1(e13,op1(e13,op1(e13,e13))) = e13 ) )
| ~ ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) ) ),
inference(modus_ponens,[status(thm)],[695,658]) ).
tff(697,plain,
~ ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) ),
inference(unit_resolution,[status(thm)],[696,653]) ).
tff(698,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) ) ),
inference(tautology,[status(thm)],]) ).
tff(699,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)),
inference(unit_resolution,[status(thm)],[698,697]) ).
tff(700,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
<=> ( op1(e13,op1(e13,e13)) = e13 ) ),
inference(monotonicity,[status(thm)],[699]) ).
tff(701,plain,
( ( op1(e13,op1(e13,e13)) = e13 )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(symmetry,[status(thm)],[700]) ).
tff(702,plain,
( ( op1(e13,op1(e13,e13)) != e13 )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != e13 ) ),
inference(monotonicity,[status(thm)],[701]) ).
tff(703,plain,
( ( e10 != e13 )
<=> ( op1(e13,op1(e13,e13)) != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(704,plain,
( ( e10 != e13 )
<=> ( e10 != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(705,plain,
e10 != e13,
inference(and_elim,[status(thm)],[322]) ).
tff(706,plain,
e10 != e13,
inference(modus_ponens,[status(thm)],[705,704]) ).
tff(707,plain,
op1(e13,op1(e13,e13)) != e13,
inference(modus_ponens,[status(thm)],[706,703]) ).
tff(708,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != e13,
inference(modus_ponens,[status(thm)],[707,702]) ).
tff(709,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(710,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) )
<=> ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(711,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ) ),
inference(monotonicity,[status(thm)],[710]) ).
tff(712,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ) ),
inference(transitivity,[status(thm)],[711,709]) ).
tff(713,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(714,plain,
( ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(715,plain,
( ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& $true )
<=> ( op1(op1(e13,e13),op1(e13,e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(716,plain,
( ( op1(op1(e13,e13),e13) = op1(e13,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[231]) ).
tff(717,plain,
( ( op1(op1(e13,e13),e13) != op1(e13,e13) )
<=> ~ $false ),
inference(monotonicity,[status(thm)],[716]) ).
tff(718,plain,
( ( op1(op1(e13,e13),e13) != op1(e13,e13) )
<=> $true ),
inference(transitivity,[status(thm)],[717,590]) ).
tff(719,plain,
( ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& ( op1(op1(e13,e13),e13) != op1(e13,e13) ) )
<=> ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& $true ) ),
inference(monotonicity,[status(thm)],[718]) ).
tff(720,plain,
( ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& ( op1(op1(e13,e13),e13) != op1(e13,e13) ) )
<=> ( op1(op1(e13,e13),op1(e13,e13)) = e13 ) ),
inference(transitivity,[status(thm)],[719,715]) ).
tff(721,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& $true )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(722,plain,
( ( op1(e11,e13) != op1(e12,e13) )
<=> ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(723,plain,
( ( op1(e11,e13) != op1(e12,e13) )
<=> ( op1(e11,e13) != op1(e12,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(724,plain,
op1(e11,e13) != op1(e12,e13),
inference(and_elim,[status(thm)],[291]) ).
tff(725,plain,
op1(e11,e13) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[724,723]) ).
tff(726,plain,
op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[725,722]) ).
tff(727,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),e13) )
<=> $false ),
inference(iff_false,[status(thm)],[726]) ).
tff(728,plain,
( ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) )
<=> ~ $false ),
inference(monotonicity,[status(thm)],[727]) ).
tff(729,plain,
( ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) )
<=> $true ),
inference(transitivity,[status(thm)],[728,590]) ).
tff(730,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& $true ) ),
inference(monotonicity,[status(thm)],[729]) ).
tff(731,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(transitivity,[status(thm)],[730,721]) ).
tff(732,plain,
( ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& ( op1(op1(e13,e13),e13) != op1(e13,e13) ) ) )
<=> ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) )
| ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 ) ) ),
inference(monotonicity,[status(thm)],[731,720]) ).
tff(733,plain,
( ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& ( op1(op1(e13,e13),e13) != op1(e13,e13) ) ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ) ),
inference(transitivity,[status(thm)],[732,714]) ).
tff(734,plain,
( ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& ( op1(op1(e13,e13),e13) != op1(e13,e13) ) ) )
<=> ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& ( op1(op1(e13,e13),e13) != op1(e13,e13) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(735,plain,
( ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) )
<=> ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& ( op1(op1(e13,e13),e13) != op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(736,plain,
( ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(737,plain,
( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(738,plain,
( ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) ) )
<=> ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& ( op1(op1(e13,e13),e13) != op1(e13,e13) ) ) ) ),
inference(monotonicity,[status(thm)],[737,736,735]) ).
tff(739,plain,
( ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) ) )
<=> ( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& ( op1(op1(e13,e13),e13) != op1(e13,e13) ) ) ) ),
inference(transitivity,[status(thm)],[738,734]) ).
tff(740,plain,
( ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) ) )
<=> ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(741,plain,
( ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) )
| $false )
<=> ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(742,plain,
( ( ( op1(e13,e13) = e13 )
& ( op1(e13,e13) != e13 ) )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(743,plain,
( ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) ) )
<=> ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(744,plain,
( ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) )
| ( ( op1(e13,e13) = e13 )
& ( op1(e13,e13) != e13 ) ) )
<=> ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) )
| $false ) ),
inference(monotonicity,[status(thm)],[743,742]) ).
tff(745,plain,
( ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) )
| ( ( op1(e13,e13) = e13 )
& ( op1(e13,e13) != e13 ) ) )
<=> ( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) ) ) ),
inference(transitivity,[status(thm)],[744,741]) ).
tff(746,plain,
( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) )
| ( ( op1(e13,e13) = e13 )
& ( op1(e13,e13) != e13 ) ) ),
inference(and_elim,[status(thm)],[265]) ).
tff(747,plain,
( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) ) ),
inference(modus_ponens,[status(thm)],[746,745]) ).
tff(748,plain,
( ( ( op1(e10,e10) = e13 )
& ( op1(e10,e13) != e10 ) )
| ( ( op1(e11,e11) = e13 )
& ( op1(e11,e13) != e11 ) )
| ( ( op1(e12,e12) = e13 )
& ( op1(e12,e13) != e12 ) ) ),
inference(modus_ponens,[status(thm)],[747,740]) ).
tff(749,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& ( op1(op1(e13,e13),e13) != op1(e13,e13) ) ) ),
inference(modus_ponens,[status(thm)],[748,739]) ).
tff(750,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) )
| ( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
& ( op1(op1(op1(e13,e13),e13),e13) != op1(op1(e13,e13),e13) ) )
| ( ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
& ( op1(op1(e13,e13),e13) != op1(e13,e13) ) ) ),
inference(modus_ponens,[status(thm)],[749,734]) ).
tff(751,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ),
inference(modus_ponens,[status(thm)],[750,733]) ).
tff(752,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ),
inference(modus_ponens,[status(thm)],[751,713]) ).
tff(753,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ),
inference(modus_ponens,[status(thm)],[752,713]) ).
tff(754,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ),
inference(modus_ponens,[status(thm)],[753,713]) ).
tff(755,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ),
inference(modus_ponens,[status(thm)],[754,713]) ).
tff(756,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ),
inference(modus_ponens,[status(thm)],[755,713]) ).
tff(757,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ),
inference(modus_ponens,[status(thm)],[756,713]) ).
tff(758,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
& ( op1(op1(e13,op1(e13,e13)),e13) != op1(e13,op1(e13,e13)) ) ) ),
inference(modus_ponens,[status(thm)],[757,713]) ).
tff(759,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,e13),op1(e13,e13)) = e13 )
| ~ ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(modus_ponens,[status(thm)],[758,712]) ).
tff(760,plain,
op1(op1(e13,e13),op1(e13,e13)) = e13,
inference(unit_resolution,[status(thm)],[759,708,643]) ).
tff(761,plain,
h4(op1(op1(e13,e13),op1(e13,e13))) = h4(e13),
inference(monotonicity,[status(thm)],[760]) ).
tff(762,plain,
h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h3(e13),h3(e13)),
inference(transitivity,[status(thm)],[761,632,487]) ).
tff(763,plain,
( ( h4(e13) = h3(e13) )
<=> ( h3(e13) = h4(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(764,plain,
op2(h3(e13),h3(e13)) = h3(op1(e13,e13)),
inference(symmetry,[status(thm)],[487]) ).
tff(765,plain,
op2(h3(e13),h3(e13)) = h4(e13),
inference(transitivity,[status(thm)],[764,631]) ).
tff(766,plain,
( ( op2(h3(e13),h3(e13)) = h3(e13) )
<=> ( h4(e13) = h3(e13) ) ),
inference(monotonicity,[status(thm)],[765]) ).
tff(767,plain,
( ( op2(h3(e13),h3(e13)) = h3(e13) )
<=> ( h3(e13) = h4(e13) ) ),
inference(transitivity,[status(thm)],[766,763]) ).
tff(768,plain,
( ( h3(e13) = h4(e13) )
<=> ( op2(h3(e13),h3(e13)) = h3(e13) ) ),
inference(symmetry,[status(thm)],[767]) ).
tff(769,plain,
( ( h3(e13) != h4(e13) )
<=> ( op2(h3(e13),h3(e13)) != h3(e13) ) ),
inference(monotonicity,[status(thm)],[768]) ).
tff(770,plain,
( ( op2(h4(e13),h4(e13)) != h4(e13) )
<=> ( h3(e13) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(771,plain,
( ( e22 != e23 )
<=> ( op2(h4(e13),h4(e13)) != h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(772,plain,
( ( e22 != e23 )
<=> ( e22 != e23 ) ),
inference(rewrite,[status(thm)],]) ).
tff(773,plain,
e22 != e23,
inference(and_elim,[status(thm)],[139]) ).
tff(774,plain,
e22 != e23,
inference(modus_ponens,[status(thm)],[773,772]) ).
tff(775,plain,
op2(h4(e13),h4(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[774,771]) ).
tff(776,plain,
h3(e13) != h4(e13),
inference(modus_ponens,[status(thm)],[775,770]) ).
tff(777,plain,
op2(h3(e13),h3(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[776,769]) ).
tff(778,plain,
( ( h1(e13) = h2(e13) )
<=> ( h2(e13) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(779,plain,
( ( h1(e13) != h2(e13) )
<=> ( h2(e13) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[778]) ).
tff(780,plain,
h2(e13) != h1(e13),
inference(modus_ponens,[status(thm)],[148,779]) ).
tff(781,plain,
( ( h1(e13) = op2(h3(e13),h2(e13)) )
<=> ( op2(h3(e13),h2(e13)) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(782,plain,
( ( h2(op1(e13,e13)) = op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) )
<=> ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(783,plain,
( ( h2(op1(e13,e13)) = op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( h2(op1(e13,e13)) = op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(784,plain,
( ( h2(e12) = op2(e21,e21) )
<=> ( h2(op1(e13,e13)) = op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(785,plain,
( ( h2(e12) = op2(e21,e21) )
<=> ( h2(e12) = op2(e21,e21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(786,axiom,
( ( h2(e13) = e21 )
& ( h2(e10) = op2(e21,op2(e21,e21)) )
& ( h2(e11) = op2(op2(e21,e21),e21) )
& ( h2(e12) = op2(e21,e21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
tff(787,plain,
h2(e12) = op2(e21,e21),
inference(and_elim,[status(thm)],[786]) ).
tff(788,plain,
h2(e12) = op2(e21,e21),
inference(modus_ponens,[status(thm)],[787,785]) ).
tff(789,plain,
h2(op1(e13,e13)) = op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[788,784]) ).
tff(790,plain,
h2(op1(e13,e13)) = op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[789,783]) ).
tff(791,plain,
h2(op1(e13,e13)) = op2(h2(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[790,782]) ).
tff(792,plain,
op2(h2(e13),h2(e13)) = h2(op1(e13,e13)),
inference(symmetry,[status(thm)],[791]) ).
tff(793,plain,
op2(h2(e13),h2(e13)) = h1(e13),
inference(transitivity,[status(thm)],[792,558]) ).
tff(794,plain,
( ( op2(h2(e13),h2(e13)) = op2(h3(e13),h2(e13)) )
<=> ( h1(e13) = op2(h3(e13),h2(e13)) ) ),
inference(monotonicity,[status(thm)],[793]) ).
tff(795,plain,
( ( op2(h2(e13),h2(e13)) = op2(h3(e13),h2(e13)) )
<=> ( op2(h3(e13),h2(e13)) = h1(e13) ) ),
inference(transitivity,[status(thm)],[794,781]) ).
tff(796,plain,
( ( op2(h2(e13),h2(e13)) != op2(h3(e13),h2(e13)) )
<=> ( op2(h3(e13),h2(e13)) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[795]) ).
tff(797,plain,
( ( h2(op1(e13,e13)) != op2(h3(e13),h2(e13)) )
<=> ( op2(h2(e13),h2(e13)) != op2(h3(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(798,plain,
( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) != op2(h3(e13),op2(h3(e13),h4(e13))) )
<=> ( h2(op1(e13,e13)) != op2(h3(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(799,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) != op2(h3(e13),op2(h3(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(800,plain,
( ( op2(e21,e21) != op2(e22,e21) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(801,plain,
( ( op2(e21,e21) != op2(e22,e21) )
<=> ( op2(e21,e21) != op2(e22,e21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(802,plain,
op2(e21,e21) != op2(e22,e21),
inference(and_elim,[status(thm)],[119]) ).
tff(803,plain,
op2(e21,e21) != op2(e22,e21),
inference(modus_ponens,[status(thm)],[802,801]) ).
tff(804,plain,
op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[803,800]) ).
tff(805,plain,
op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) != op2(h3(e13),op2(h3(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[804,799]) ).
tff(806,plain,
h2(op1(e13,e13)) != op2(h3(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[805,798]) ).
tff(807,plain,
op2(h2(e13),h2(e13)) != op2(h3(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[806,797]) ).
tff(808,plain,
op2(h3(e13),h2(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[807,796]) ).
tff(809,plain,
( ( ( h2(e13) = h1(e13) )
| $false
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(810,plain,
( ( h3(op1(e13,e13)) != op2(h4(e13),h3(e13)) )
<=> ( op2(h3(e13),h3(e13)) != h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(811,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( h3(op1(e13,e13)) != op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(812,plain,
h3(op1(e13,e13)) != op2(h4(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[530,811]) ).
tff(813,plain,
op2(h3(e13),h3(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[812,810]) ).
tff(814,plain,
( ( op2(h3(e13),h3(e13)) = h1(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[813]) ).
tff(815,plain,
( ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h3(e13)) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| $false
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[814]) ).
tff(816,plain,
( ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h3(e13)) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[815,809]) ).
tff(817,plain,
( ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h3(e13)) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h3(e13)) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(818,plain,
( ( ( op2(h3(e13),h3(e13)) = h1(e13) )
| ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h3(e13)) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(819,plain,
( ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
<=> ( op2(h3(e13),h2(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(820,plain,
( ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
<=> ( op2(h3(e13),h1(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(821,plain,
( ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) )
<=> ( h2(e13) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(822,plain,
( ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) )
<=> ( op2(h3(e13),h3(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(823,plain,
( ( ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) ) )
<=> ( ( op2(h3(e13),h3(e13)) = h1(e13) )
| ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[822,821,820,819]) ).
tff(824,plain,
( ( ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) ) )
<=> ( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h3(e13)) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[823,818]) ).
tff(825,plain,
( ( ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) ) )
<=> ( ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(826,plain,
( ( ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) ) )
<=> ( ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(827,plain,
( ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(828,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(829,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(830,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(831,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
<=> ( ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) ) ) ),
inference(monotonicity,[status(thm)],[830,829,828,827]) ).
tff(832,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
<=> ( ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[831,826]) ).
tff(833,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(834,plain,
( ( op2(e22,e23) = e20 )
<=> ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(835,plain,
( ( op2(e22,e22) = e20 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(836,plain,
( ( op2(e22,e21) = e20 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(837,plain,
( ( op2(e22,e20) = e20 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(838,plain,
( ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ) ),
inference(monotonicity,[status(thm)],[837,836,835,834]) ).
tff(839,plain,
( ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ) ),
inference(transitivity,[status(thm)],[838,833]) ).
tff(840,plain,
( ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
<=> ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(841,plain,
( ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
<=> ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(842,plain,
( ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 ) )
<=> ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(843,plain,
( ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
<=> ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) ) ),
inference(monotonicity,[status(thm)],[842]) ).
tff(844,plain,
( ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) )
<=> ( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) ) ),
inference(transitivity,[status(thm)],[843,841]) ).
tff(845,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)],[178]) ).
tff(846,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)],[845]) ).
tff(847,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)],[846]) ).
tff(848,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)],[847]) ).
tff(849,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)],[848]) ).
tff(850,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)],[849]) ).
tff(851,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)],[850]) ).
tff(852,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)],[851]) ).
tff(853,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)],[852]) ).
tff(854,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)],[853]) ).
tff(855,plain,
( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) ),
inference(and_elim,[status(thm)],[854]) ).
tff(856,plain,
( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[855,844]) ).
tff(857,plain,
( ( op2(e22,e20) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e22,e22) = e20 )
| ( op2(e22,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[856,840]) ).
tff(858,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[857,839]) ).
tff(859,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[858,833]) ).
tff(860,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[859,833]) ).
tff(861,plain,
( ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[860,832]) ).
tff(862,plain,
( ( h3(op1(e13,e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[861,825]) ).
tff(863,plain,
( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h3(e13)) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[862,824]) ).
tff(864,plain,
( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h3(e13)) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[863,817]) ).
tff(865,plain,
( ( h2(e13) = h1(e13) )
| ( op2(h3(e13),h1(e13)) = h1(e13) )
| ( op2(h3(e13),h2(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[864,816]) ).
tff(866,plain,
op2(h3(e13),h1(e13)) = h1(e13),
inference(unit_resolution,[status(thm)],[865,808,780]) ).
tff(867,plain,
( ( op2(h3(e13),h1(e13)) = h3(e13) )
<=> ( h1(e13) = h3(e13) ) ),
inference(monotonicity,[status(thm)],[866]) ).
tff(868,plain,
( ( op2(h3(e13),h1(e13)) = h3(e13) )
<=> ( h3(e13) = h1(e13) ) ),
inference(transitivity,[status(thm)],[867,503]) ).
tff(869,plain,
( ( h3(e13) = h1(e13) )
<=> ( op2(h3(e13),h1(e13)) = h3(e13) ) ),
inference(symmetry,[status(thm)],[868]) ).
tff(870,plain,
( ( h3(e13) != h1(e13) )
<=> ( op2(h3(e13),h1(e13)) != h3(e13) ) ),
inference(monotonicity,[status(thm)],[869]) ).
tff(871,plain,
op2(h3(e13),h1(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[514,870]) ).
tff(872,plain,
( ( ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) )
<=> ( ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(873,plain,
( ( $false
| ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) )
<=> ( ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(874,plain,
( ( h2(e13) = h3(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[36]) ).
tff(875,plain,
( ( ( h2(e13) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) )
<=> ( $false
| ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[874]) ).
tff(876,plain,
( ( ( h2(e13) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) )
<=> ( ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[875,873]) ).
tff(877,plain,
( ( ( h2(e13) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) )
<=> ( ( h2(e13) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(878,plain,
( ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) )
<=> ( op2(h3(e13),h2(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(879,plain,
( ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) )
<=> ( op2(h3(e13),h1(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(880,plain,
( ( h3(op1(e13,e13)) = h3(e13) )
<=> ( op2(h3(e13),h3(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(881,plain,
( ( op2(h3(e13),h4(e13)) = h3(e13) )
<=> ( h2(e13) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(882,plain,
( ( ( op2(h3(e13),h4(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) ) )
<=> ( ( h2(e13) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[881,880,879,878]) ).
tff(883,plain,
( ( ( op2(h3(e13),h4(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) ) )
<=> ( ( h2(e13) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[882,877]) ).
tff(884,plain,
( ( ( op2(h3(e13),h4(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) ) )
<=> ( ( op2(h3(e13),h4(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(885,plain,
( ( ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),h4(e13)) = h3(e13) ) )
<=> ( ( op2(h3(e13),h4(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(886,plain,
( ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
<=> ( op2(h3(e13),h4(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(887,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( h3(op1(e13,e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(888,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(889,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
<=> ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(890,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) )
<=> ( ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),h4(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[889,888,887,886]) ).
tff(891,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) )
<=> ( ( op2(h3(e13),h4(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[890,885]) ).
tff(892,plain,
( ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(893,plain,
( ( op2(e22,e23) = e22 )
<=> ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(894,plain,
( ( op2(e22,e22) = e22 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(895,plain,
( ( op2(e22,e21) = e22 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(896,plain,
( ( op2(e22,e20) = e22 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(897,plain,
( ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[896,895,894,893]) ).
tff(898,plain,
( ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
<=> ( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[897,892]) ).
tff(899,plain,
( ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
<=> ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(900,plain,
( ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
<=> ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(901,plain,
( ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 ) )
<=> ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(902,plain,
( ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
<=> ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) ) ),
inference(monotonicity,[status(thm)],[901]) ).
tff(903,plain,
( ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) )
<=> ( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) ) ),
inference(transitivity,[status(thm)],[902,900]) ).
tff(904,plain,
( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) ),
inference(and_elim,[status(thm)],[850]) ).
tff(905,plain,
( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[904,903]) ).
tff(906,plain,
( ( op2(e22,e20) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e22,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[905,899]) ).
tff(907,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[906,898]) ).
tff(908,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[907,892]) ).
tff(909,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[908,892]) ).
tff(910,plain,
( ( op2(h3(e13),h4(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[909,891]) ).
tff(911,plain,
( ( op2(h3(e13),h4(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h3(e13),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(h3(e13),op2(h3(e13),h4(e13))) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[910,884]) ).
tff(912,plain,
( ( h2(e13) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[911,883]) ).
tff(913,plain,
( ( h2(e13) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[912,877]) ).
tff(914,plain,
( ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[913,876]) ).
tff(915,plain,
( ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[914,872]) ).
tff(916,plain,
( ( op2(h3(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h1(e13)) = h3(e13) )
| ( op2(h3(e13),h2(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[915,872]) ).
tff(917,plain,
op2(h3(e13),h2(e13)) = h3(e13),
inference(unit_resolution,[status(thm)],[916,871,777]) ).
tff(918,plain,
h3(e13) = op2(h3(e13),h2(e13)),
inference(symmetry,[status(thm)],[917]) ).
tff(919,plain,
( ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
<=> ( h4(op1(e13,e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(920,plain,
( ( h4(e12) = op2(e23,e23) )
<=> ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(921,plain,
( ( h4(e12) = op2(e23,e23) )
<=> ( h4(e12) = op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(922,plain,
h4(e12) = op2(e23,e23),
inference(and_elim,[status(thm)],[194]) ).
tff(923,plain,
h4(e12) = op2(e23,e23),
inference(modus_ponens,[status(thm)],[922,921]) ).
tff(924,plain,
h4(op1(e13,e13)) = op2(h4(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[923,920]) ).
tff(925,plain,
h4(op1(e13,e13)) = h3(e13),
inference(modus_ponens,[status(thm)],[924,919]) ).
tff(926,plain,
( ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(927,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
<=> ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(monotonicity,[status(thm)],[699]) ).
tff(928,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) ) ),
inference(transitivity,[status(thm)],[927,926]) ).
tff(929,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) ),
inference(monotonicity,[status(thm)],[928]) ).
tff(930,plain,
( ( op1(e11,e11) != op1(e12,e11) )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(931,plain,
( ( op1(e11,e11) != op1(e12,e11) )
<=> ( op1(e11,e11) != op1(e12,e11) ) ),
inference(rewrite,[status(thm)],]) ).
tff(932,plain,
op1(e11,e11) != op1(e12,e11),
inference(and_elim,[status(thm)],[303]) ).
tff(933,plain,
op1(e11,e11) != op1(e12,e11),
inference(modus_ponens,[status(thm)],[932,931]) ).
tff(934,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[933,930]) ).
tff(935,plain,
op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)),
inference(modus_ponens,[status(thm)],[934,929]) ).
tff(936,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),op1(e13,e13)) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(monotonicity,[status(thm)],[760]) ).
tff(937,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),op1(e13,e13)) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != e13 ) ),
inference(monotonicity,[status(thm)],[936]) ).
tff(938,plain,
( ( op1(e12,e11) != op1(e12,e12) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(939,plain,
( ( op1(e12,e11) != op1(e12,e12) )
<=> ( op1(e12,e11) != op1(e12,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(940,plain,
op1(e12,e11) != op1(e12,e12),
inference(and_elim,[status(thm)],[212]) ).
tff(941,plain,
op1(e12,e11) != op1(e12,e12),
inference(modus_ponens,[status(thm)],[940,939]) ).
tff(942,plain,
op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),op1(e13,e13)),
inference(modus_ponens,[status(thm)],[941,938]) ).
tff(943,plain,
op1(op1(e13,e13),op1(op1(e13,e13),e13)) != e13,
inference(modus_ponens,[status(thm)],[942,937]) ).
tff(944,plain,
( ( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(945,plain,
( ( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| $false
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(946,plain,
( ( op1(e12,e11) != op1(e12,e13) )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),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)],[211]) ).
tff(949,plain,
op1(e12,e11) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[948,947]) ).
tff(950,plain,
op1(op1(e13,e13),op1(op1(e13,e13),e13)) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[949,946]) ).
tff(951,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
<=> $false ),
inference(iff_false,[status(thm)],[950]) ).
tff(952,plain,
( ( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| $false
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(monotonicity,[status(thm)],[951]) ).
tff(953,plain,
( ( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(transitivity,[status(thm)],[952,945]) ).
tff(954,plain,
( ( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) )
<=> ( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(955,plain,
( ( op1(e12,e11) = e13 )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(956,plain,
( ( op1(e12,e11) = e12 )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(957,plain,
( ( op1(e12,e11) = e11 )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(958,plain,
( ( op1(e12,e11) = e10 )
<=> ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,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(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,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(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,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 ) ) ),
inference(and_elim,[status(thm)],[463]) ).
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 ) ) ),
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 ) ) ),
inference(and_elim,[status(thm)],[967]) ).
tff(969,plain,
( ( 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(modus_ponens,[status(thm)],[969,965]) ).
tff(971,plain,
( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ),
inference(modus_ponens,[status(thm)],[970,961]) ).
tff(972,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[971,960]) ).
tff(973,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[972,954]) ).
tff(974,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[973,954]) ).
tff(975,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[974,953]) ).
tff(976,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[975,944]) ).
tff(977,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[976,944]) ).
tff(978,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[977,944]) ).
tff(979,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[978,944]) ).
tff(980,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[979,944]) ).
tff(981,plain,
( ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = e13 ) ),
inference(modus_ponens,[status(thm)],[980,944]) ).
tff(982,plain,
op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,e13),
inference(unit_resolution,[status(thm)],[981,943,935]) ).
tff(983,plain,
h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = h4(op1(e13,e13)),
inference(monotonicity,[status(thm)],[982]) ).
tff(984,plain,
h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h3(e13),h2(e13)),
inference(transitivity,[status(thm)],[983,925,918]) ).
tff(985,plain,
h1(e13) = op2(h3(e13),h1(e13)),
inference(symmetry,[status(thm)],[866]) ).
tff(986,plain,
( ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( h4(op1(e13,op1(e13,e13))) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(987,plain,
( ( h4(e10) = op2(e23,op2(e23,e23)) )
<=> ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(988,plain,
( ( h4(e10) = op2(e23,op2(e23,e23)) )
<=> ( h4(e10) = op2(e23,op2(e23,e23)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(989,plain,
( ( h4(e13) = e23 )
& ( h4(e10) = op2(e23,op2(e23,e23)) ) ),
inference(and_elim,[status(thm)],[195]) ).
tff(990,plain,
h4(e10) = op2(e23,op2(e23,e23)),
inference(and_elim,[status(thm)],[989]) ).
tff(991,plain,
h4(e10) = op2(e23,op2(e23,e23)),
inference(modus_ponens,[status(thm)],[990,988]) ).
tff(992,plain,
h4(op1(e13,op1(e13,e13))) = op2(h4(e13),op2(h4(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[991,987]) ).
tff(993,plain,
h4(op1(e13,op1(e13,e13))) = h1(e13),
inference(modus_ponens,[status(thm)],[992,986]) ).
tff(994,plain,
( ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) )
<=> ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(995,plain,
( ( op1(e13,op1(e13,e13)) != op1(op1(e13,e13),e13) )
<=> ( op1(op1(e13,e13),e13) != op1(e13,op1(e13,e13)) ) ),
inference(monotonicity,[status(thm)],[994]) ).
tff(996,plain,
op1(op1(e13,e13),e13) != op1(e13,op1(e13,e13)),
inference(modus_ponens,[status(thm)],[326,995]) ).
tff(997,plain,
( ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) )
<=> ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(998,plain,
( ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| $false
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) )
<=> ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(999,plain,
( ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) )
<=> ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| $false
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(monotonicity,[status(thm)],[667]) ).
tff(1000,plain,
( ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) )
<=> ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(transitivity,[status(thm)],[999,998]) ).
tff(1001,plain,
( ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) )
<=> ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1002,plain,
( ( op1(e12,e13) = e10 )
<=> ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1003,plain,
( ( op1(e12,e12) = e10 )
<=> ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1004,plain,
( ( op1(e12,e10) = e10 )
<=> ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1005,plain,
( ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
<=> ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(monotonicity,[status(thm)],[1004,958,1003,1002]) ).
tff(1006,plain,
( ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
<=> ( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(transitivity,[status(thm)],[1005,1001]) ).
tff(1007,plain,
( ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
<=> ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1008,plain,
( ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
<=> ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1009,plain,
( ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 ) )
<=> ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1010,plain,
( ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
<=> ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) ) ),
inference(monotonicity,[status(thm)],[1009]) ).
tff(1011,plain,
( ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) )
<=> ( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) ) ),
inference(transitivity,[status(thm)],[1010,1008]) ).
tff(1012,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)],[347]) ).
tff(1013,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)],[1012]) ).
tff(1014,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)],[1013]) ).
tff(1015,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)],[1014]) ).
tff(1016,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)],[1015]) ).
tff(1017,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)],[1016]) ).
tff(1018,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)],[1017]) ).
tff(1019,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)],[1018]) ).
tff(1020,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)],[1019]) ).
tff(1021,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)],[1020]) ).
tff(1022,plain,
( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) ),
inference(and_elim,[status(thm)],[1021]) ).
tff(1023,plain,
( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[1022,1011]) ).
tff(1024,plain,
( ( op1(e12,e10) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e12,e12) = e10 )
| ( op1(e12,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[1023,1007]) ).
tff(1025,plain,
( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1024,1006]) ).
tff(1026,plain,
( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1025,1001]) ).
tff(1027,plain,
( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1026,1001]) ).
tff(1028,plain,
( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1027,1000]) ).
tff(1029,plain,
( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1028,997]) ).
tff(1030,plain,
( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1029,997]) ).
tff(1031,plain,
( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1030,997]) ).
tff(1032,plain,
( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1031,997]) ).
tff(1033,plain,
( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1032,997]) ).
tff(1034,plain,
( ( op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1033,997]) ).
tff(1035,plain,
op1(op1(e13,e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)),
inference(unit_resolution,[status(thm)],[1034,935,996]) ).
tff(1036,plain,
h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = h4(op1(e13,op1(e13,e13))),
inference(monotonicity,[status(thm)],[1035]) ).
tff(1037,plain,
h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h3(e13),h1(e13)),
inference(transitivity,[status(thm)],[1036,993,985]) ).
tff(1038,plain,
( ( h1(e13) = op2(h2(e13),h4(e13)) )
<=> ( op2(h2(e13),h4(e13)) = h1(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1039,plain,
( ( op2(h2(e13),h2(e13)) = op2(h2(e13),h4(e13)) )
<=> ( h1(e13) = op2(h2(e13),h4(e13)) ) ),
inference(monotonicity,[status(thm)],[793]) ).
tff(1040,plain,
( ( op2(h2(e13),h2(e13)) = op2(h2(e13),h4(e13)) )
<=> ( op2(h2(e13),h4(e13)) = h1(e13) ) ),
inference(transitivity,[status(thm)],[1039,1038]) ).
tff(1041,plain,
( ( op2(h2(e13),h2(e13)) != op2(h2(e13),h4(e13)) )
<=> ( op2(h2(e13),h4(e13)) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[1040]) ).
tff(1042,plain,
( ( h2(op1(e13,e13)) != op2(h2(e13),h4(e13)) )
<=> ( op2(h2(e13),h2(e13)) != op2(h2(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1043,plain,
( ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) != op2(op2(h3(e13),h4(e13)),h4(e13)) )
<=> ( h2(op1(e13,e13)) != op2(h2(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1044,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) )
<=> ( op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) != op2(op2(h3(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1045,plain,
( ( op2(e21,e21) != op2(e21,e23) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1046,plain,
( ( op2(e21,e21) != op2(e21,e23) )
<=> ( op2(e21,e21) != op2(e21,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1047,plain,
op2(e21,e21) != op2(e21,e23),
inference(and_elim,[status(thm)],[20]) ).
tff(1048,plain,
op2(e21,e21) != op2(e21,e23),
inference(modus_ponens,[status(thm)],[1047,1046]) ).
tff(1049,plain,
op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[1048,1045]) ).
tff(1050,plain,
op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) != op2(op2(h3(e13),h4(e13)),h4(e13)),
inference(modus_ponens,[status(thm)],[1049,1044]) ).
tff(1051,plain,
h2(op1(e13,e13)) != op2(h2(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[1050,1043]) ).
tff(1052,plain,
op2(h2(e13),h2(e13)) != op2(h2(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[1051,1042]) ).
tff(1053,plain,
op2(h2(e13),h4(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[1052,1041]) ).
tff(1054,plain,
( ( ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) )
<=> ( ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1055,plain,
( ( $false
| $false
| ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) )
<=> ( ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1056,plain,
( ( op2(op2(h3(e13),h4(e13)),h4(e13)) != op2(h3(e13),h4(e13)) )
<=> ( op2(h2(e13),h4(e13)) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1057,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(op2(h3(e13),h4(e13)),h4(e13)) != op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1058,plain,
op2(op2(h3(e13),h4(e13)),h4(e13)) != op2(h3(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[601,1057]) ).
tff(1059,plain,
op2(h2(e13),h4(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[1058,1056]) ).
tff(1060,plain,
( ( op2(h2(e13),h4(e13)) = h2(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1059]) ).
tff(1061,plain,
( ( op2(op2(h3(e13),h4(e13)),h4(e13)) != h3(e13) )
<=> ( op2(h2(e13),h4(e13)) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1062,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) )
<=> ( op2(op2(h3(e13),h4(e13)),h4(e13)) != h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1063,plain,
( ( op2(e21,e23) != op2(e23,e23) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1064,plain,
( ( op2(e21,e23) != op2(e23,e23) )
<=> ( op2(e21,e23) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1065,plain,
op2(e21,e23) != op2(e23,e23),
inference(and_elim,[status(thm)],[106]) ).
tff(1066,plain,
op2(e21,e23) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[1065,1064]) ).
tff(1067,plain,
op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) != op2(h4(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[1066,1063]) ).
tff(1068,plain,
op2(op2(h3(e13),h4(e13)),h4(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[1067,1062]) ).
tff(1069,plain,
op2(h2(e13),h4(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[1068,1061]) ).
tff(1070,plain,
( ( op2(h2(e13),h4(e13)) = h3(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1069]) ).
tff(1071,plain,
( ( ( op2(h2(e13),h4(e13)) = h3(e13) )
| ( op2(h2(e13),h4(e13)) = h2(e13) )
| ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) )
<=> ( $false
| $false
| ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[1070,1060]) ).
tff(1072,plain,
( ( ( op2(h2(e13),h4(e13)) = h3(e13) )
| ( op2(h2(e13),h4(e13)) = h2(e13) )
| ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) )
<=> ( ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[1071,1055]) ).
tff(1073,plain,
( ( ( op2(h2(e13),h4(e13)) = h3(e13) )
| ( op2(h2(e13),h4(e13)) = h2(e13) )
| ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) )
<=> ( ( op2(h2(e13),h4(e13)) = h3(e13) )
| ( op2(h2(e13),h4(e13)) = h2(e13) )
| ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1074,plain,
( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
<=> ( op2(h2(e13),h4(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1075,plain,
( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) )
<=> ( op2(h2(e13),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1076,plain,
( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) )
<=> ( op2(h2(e13),h4(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1077,plain,
( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) )
<=> ( op2(h2(e13),h4(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1078,plain,
( ( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) )
<=> ( ( op2(h2(e13),h4(e13)) = h3(e13) )
| ( op2(h2(e13),h4(e13)) = h2(e13) )
| ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[1077,1076,1075,1074]) ).
tff(1079,plain,
( ( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) )
<=> ( ( op2(h2(e13),h4(e13)) = h3(e13) )
| ( op2(h2(e13),h4(e13)) = h2(e13) )
| ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[1078,1073]) ).
tff(1080,plain,
( ( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) )
<=> ( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1081,plain,
( ( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1082,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) )
<=> ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1083,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
<=> ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1084,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1085,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1086,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[1085,1084,1083,1082]) ).
tff(1087,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[1086,1081]) ).
tff(1088,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1089,plain,
( ( op2(e21,e23) = e23 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1090,plain,
( ( op2(e21,e23) = e22 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1091,plain,
( ( op2(e21,e23) = e21 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1092,plain,
( ( op2(e21,e23) = e20 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1093,plain,
( ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[1092,1091,1090,1089]) ).
tff(1094,plain,
( ( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[1093,1088]) ).
tff(1095,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(1096,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(1097,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(1098,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)],[1097]) ).
tff(1099,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)],[1098,1096]) ).
tff(1100,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)],[417]) ).
tff(1101,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)],[1100]) ).
tff(1102,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)],[1101]) ).
tff(1103,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)],[1102]) ).
tff(1104,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)],[1103]) ).
tff(1105,plain,
( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ),
inference(and_elim,[status(thm)],[1104]) ).
tff(1106,plain,
( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[1105,1099]) ).
tff(1107,plain,
( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[1106,1095]) ).
tff(1108,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1107,1094]) ).
tff(1109,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1108,1088]) ).
tff(1110,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1109,1088]) ).
tff(1111,plain,
( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1110,1087]) ).
tff(1112,plain,
( ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1111,1080]) ).
tff(1113,plain,
( ( op2(h2(e13),h4(e13)) = h3(e13) )
| ( op2(h2(e13),h4(e13)) = h2(e13) )
| ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1112,1079]) ).
tff(1114,plain,
( ( op2(h2(e13),h4(e13)) = h3(e13) )
| ( op2(h2(e13),h4(e13)) = h2(e13) )
| ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1113,1073]) ).
tff(1115,plain,
( ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1114,1072]) ).
tff(1116,plain,
( ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1115,1054]) ).
tff(1117,plain,
( ( op2(h2(e13),h4(e13)) = h4(e13) )
| ( op2(h2(e13),h4(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1116,1054]) ).
tff(1118,plain,
op2(h2(e13),h4(e13)) = h4(e13),
inference(unit_resolution,[status(thm)],[1117,1053]) ).
tff(1119,plain,
h4(e13) = op2(h2(e13),h4(e13)),
inference(symmetry,[status(thm)],[1118]) ).
tff(1120,plain,
( ( op1(e13,op1(e13,e13)) = op1(op1(op1(e13,e13),e13),e13) )
<=> ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1121,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(op1(e13,e13),e13),e13) )
<=> ( op1(e13,op1(e13,e13)) = op1(op1(op1(e13,e13),e13),e13) ) ),
inference(monotonicity,[status(thm)],[699]) ).
tff(1122,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) = op1(op1(op1(e13,e13),e13),e13) )
<=> ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(transitivity,[status(thm)],[1121,1120]) ).
tff(1123,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(op1(op1(e13,e13),e13),e13) )
<=> ( op1(op1(op1(e13,e13),e13),e13) != op1(e13,op1(e13,e13)) ) ),
inference(monotonicity,[status(thm)],[1122]) ).
tff(1124,plain,
( ( op1(e11,e11) != op1(e11,e13) )
<=> ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(op1(op1(e13,e13),e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1125,plain,
( ( op1(e11,e11) != op1(e11,e13) )
<=> ( op1(e11,e11) != op1(e11,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1126,plain,
op1(e11,e11) != op1(e11,e13),
inference(and_elim,[status(thm)],[217]) ).
tff(1127,plain,
op1(e11,e11) != op1(e11,e13),
inference(modus_ponens,[status(thm)],[1126,1125]) ).
tff(1128,plain,
op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(op1(op1(e13,e13),e13),e13),
inference(modus_ponens,[status(thm)],[1127,1124]) ).
tff(1129,plain,
op1(op1(op1(e13,e13),e13),e13) != op1(e13,op1(e13,e13)),
inference(modus_ponens,[status(thm)],[1128,1123]) ).
tff(1130,plain,
( ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1131,plain,
( ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| $false
| $false
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1132,plain,
( ( op1(e11,e13) != op1(e13,e13) )
<=> ( op1(op1(op1(e13,e13),e13),e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1133,plain,
( ( op1(e11,e13) != op1(e13,e13) )
<=> ( op1(e11,e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1134,plain,
op1(e11,e13) != op1(e13,e13),
inference(and_elim,[status(thm)],[290]) ).
tff(1135,plain,
op1(e11,e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1134,1133]) ).
tff(1136,plain,
op1(op1(op1(e13,e13),e13),e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1135,1132]) ).
tff(1137,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1136]) ).
tff(1138,plain,
( ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| $false
| $false
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[727,1137]) ).
tff(1139,plain,
( ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[1138,1131]) ).
tff(1140,plain,
( ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1141,plain,
( ( op1(e11,e13) = e13 )
<=> ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1142,plain,
( ( op1(e11,e13) = e12 )
<=> ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1143,plain,
( ( op1(e11,e13) = e11 )
<=> ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1144,plain,
( ( op1(e11,e13) = e10 )
<=> ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1145,plain,
( ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1144,1143,1142,1141]) ).
tff(1146,plain,
( ( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[1145,1140]) ).
tff(1147,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(1148,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(1149,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(1150,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)],[1149]) ).
tff(1151,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)],[1150,1148]) ).
tff(1152,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)],[968]) ).
tff(1153,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)],[1152]) ).
tff(1154,plain,
( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ),
inference(and_elim,[status(thm)],[1153]) ).
tff(1155,plain,
( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1154,1151]) ).
tff(1156,plain,
( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1155,1147]) ).
tff(1157,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1156,1146]) ).
tff(1158,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1157,1140]) ).
tff(1159,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1158,1140]) ).
tff(1160,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1159,1139]) ).
tff(1161,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1160,1130]) ).
tff(1162,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1161,1130]) ).
tff(1163,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1162,1130]) ).
tff(1164,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1163,1130]) ).
tff(1165,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1164,1130]) ).
tff(1166,plain,
( ( op1(op1(op1(e13,e13),e13),e13) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1165,1130]) ).
tff(1167,plain,
op1(op1(op1(e13,e13),e13),e13) = e13,
inference(unit_resolution,[status(thm)],[1166,1129]) ).
tff(1168,plain,
h4(op1(op1(op1(e13,e13),e13),e13)) = h4(e13),
inference(monotonicity,[status(thm)],[1167]) ).
tff(1169,plain,
h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(e13),h4(e13)),
inference(transitivity,[status(thm)],[1168,1119]) ).
tff(1170,plain,
( ( h2(e13) = op2(h1(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) = h2(e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1171,plain,
( ( op2(h1(e13),h1(e13)) = op2(h1(e13),h3(e13)) )
<=> ( h2(e13) = op2(h1(e13),h3(e13)) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(1172,plain,
( ( op2(h1(e13),h1(e13)) = op2(h1(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) = h2(e13) ) ),
inference(transitivity,[status(thm)],[1171,1170]) ).
tff(1173,plain,
( ( op2(h1(e13),h1(e13)) != op2(h1(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) != h2(e13) ) ),
inference(monotonicity,[status(thm)],[1172]) ).
tff(1174,plain,
( ( h1(op1(e13,e13)) != op2(h1(e13),h3(e13)) )
<=> ( op2(h1(e13),h1(e13)) != op2(h1(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1175,plain,
( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) != op2(op2(h4(e13),h3(e13)),h3(e13)) )
<=> ( h1(op1(e13,e13)) != op2(h1(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1176,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) )
<=> ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) != op2(op2(h4(e13),h3(e13)),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1177,plain,
( ( op2(e20,e20) != op2(e20,e22) )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1178,plain,
( ( op2(e20,e20) != op2(e20,e22) )
<=> ( op2(e20,e20) != op2(e20,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1179,plain,
op2(e20,e20) != op2(e20,e22),
inference(and_elim,[status(thm)],[29]) ).
tff(1180,plain,
op2(e20,e20) != op2(e20,e22),
inference(modus_ponens,[status(thm)],[1179,1178]) ).
tff(1181,plain,
op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[1180,1177]) ).
tff(1182,plain,
op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) != op2(op2(h4(e13),h3(e13)),h3(e13)),
inference(modus_ponens,[status(thm)],[1181,1176]) ).
tff(1183,plain,
h1(op1(e13,e13)) != op2(h1(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[1182,1175]) ).
tff(1184,plain,
op2(h1(e13),h1(e13)) != op2(h1(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[1183,1174]) ).
tff(1185,plain,
op2(h1(e13),h3(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[1184,1173]) ).
tff(1186,plain,
( ( $false
| $false
| ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1187,plain,
( ( h3(op1(e13,e13)) != op2(h3(e13),h4(e13)) )
<=> ( op2(h3(e13),h3(e13)) != h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1188,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( h3(op1(e13,e13)) != op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1189,plain,
h3(op1(e13,e13)) != op2(h3(e13),h4(e13)),
inference(modus_ponens,[status(thm)],[54,1188]) ).
tff(1190,plain,
op2(h3(e13),h3(e13)) != h2(e13),
inference(modus_ponens,[status(thm)],[1189,1187]) ).
tff(1191,plain,
( ( op2(h3(e13),h3(e13)) = h2(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1190]) ).
tff(1192,plain,
( ( ( h1(e13) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) )
<=> ( $false
| $false
| ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[149,1191]) ).
tff(1193,plain,
( ( ( h1(e13) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) )
<=> ( ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[1192,1186]) ).
tff(1194,plain,
( ( ( h1(e13) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) )
<=> ( ( h1(e13) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1195,plain,
( ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
<=> ( op2(h2(e13),h3(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1196,plain,
( ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
<=> ( op2(h1(e13),h3(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1197,plain,
( ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) )
<=> ( op2(h3(e13),h3(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1198,plain,
( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
<=> ( h1(e13) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1199,plain,
( ( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) ) )
<=> ( ( h1(e13) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ) ),
inference(monotonicity,[status(thm)],[1198,1197,1196,1195]) ).
tff(1200,plain,
( ( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) ) )
<=> ( ( h1(e13) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ) ),
inference(transitivity,[status(thm)],[1199,1194]) ).
tff(1201,plain,
( ( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) ) )
<=> ( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1202,plain,
( ( ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) ) )
<=> ( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1203,plain,
( ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1204,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1205,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1206,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) )
| ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[1205,1204,1203,156]) ).
tff(1207,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[1206,1202]) ).
tff(1208,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1209,plain,
( ( op2(e22,e22) = e21 )
<=> ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1210,plain,
( ( op2(e21,e22) = e21 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1211,plain,
( ( op2(e20,e22) = e21 )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1212,plain,
( ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[1211,1210,1209,163]) ).
tff(1213,plain,
( ( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[1212,1208]) ).
tff(1214,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(1215,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(1216,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(1217,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)],[1216]) ).
tff(1218,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)],[1217,1215]) ).
tff(1219,plain,
( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ),
inference(and_elim,[status(thm)],[851]) ).
tff(1220,plain,
( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ),
inference(modus_ponens,[status(thm)],[1219,1218]) ).
tff(1221,plain,
( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ),
inference(modus_ponens,[status(thm)],[1220,1214]) ).
tff(1222,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1221,1213]) ).
tff(1223,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1222,1208]) ).
tff(1224,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1223,1208]) ).
tff(1225,plain,
( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1224,1207]) ).
tff(1226,plain,
( ( op2(h4(e13),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( h3(op1(e13,e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = op2(h3(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1225,1201]) ).
tff(1227,plain,
( ( h1(e13) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1226,1200]) ).
tff(1228,plain,
( ( h1(e13) = h2(e13) )
| ( op2(h3(e13),h3(e13)) = h2(e13) )
| ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1227,1194]) ).
tff(1229,plain,
( ( op2(h1(e13),h3(e13)) = h2(e13) )
| ( op2(h2(e13),h3(e13)) = h2(e13) ) ),
inference(modus_ponens,[status(thm)],[1228,1193]) ).
tff(1230,plain,
op2(h2(e13),h3(e13)) = h2(e13),
inference(unit_resolution,[status(thm)],[1229,1185]) ).
tff(1231,plain,
h2(e13) = op2(h2(e13),h3(e13)),
inference(symmetry,[status(thm)],[1230]) ).
tff(1232,plain,
( ( op1(op1(e13,e13),e13) = op1(op1(e13,op1(e13,e13)),op1(e13,e13)) )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(commutativity,[status(thm)],]) ).
tff(1233,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,op1(e13,e13)),op1(e13,e13)) )
<=> ( op1(op1(e13,e13),e13) = op1(op1(e13,op1(e13,e13)),op1(e13,e13)) ) ),
inference(monotonicity,[status(thm)],[284]) ).
tff(1234,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(op1(e13,op1(e13,e13)),op1(e13,e13)) )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(transitivity,[status(thm)],[1233,1232]) ).
tff(1235,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,op1(e13,e13)),op1(e13,e13)) )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) != op1(op1(e13,e13),e13) ) ),
inference(monotonicity,[status(thm)],[1234]) ).
tff(1236,plain,
( ( op1(e10,e10) != op1(e10,e12) )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,op1(e13,e13)),op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1237,plain,
( ( op1(e10,e10) != op1(e10,e12) )
<=> ( op1(e10,e10) != op1(e10,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1238,plain,
op1(e10,e10) != op1(e10,e12),
inference(and_elim,[status(thm)],[226]) ).
tff(1239,plain,
op1(e10,e10) != op1(e10,e12),
inference(modus_ponens,[status(thm)],[1238,1237]) ).
tff(1240,plain,
op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,op1(e13,e13)),op1(e13,e13)),
inference(modus_ponens,[status(thm)],[1239,1236]) ).
tff(1241,plain,
op1(op1(e13,op1(e13,e13)),op1(e13,e13)) != op1(op1(e13,e13),e13),
inference(modus_ponens,[status(thm)],[1240,1235]) ).
tff(1242,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| $false
| $false )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1243,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[249,327]) ).
tff(1244,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[1243,1242]) ).
tff(1245,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1246,plain,
( ( op1(e12,e12) = e11 )
<=> ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1247,plain,
( ( op1(e11,e12) = e11 )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1248,plain,
( ( op1(e10,e12) = e11 )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1249,plain,
( ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) ) ) ),
inference(monotonicity,[status(thm)],[1248,1247,1246,332]) ).
tff(1250,plain,
( ( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) ) ) ),
inference(transitivity,[status(thm)],[1249,1245]) ).
tff(1251,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(1252,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(1253,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(1254,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)],[1253]) ).
tff(1255,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)],[1254,1252]) ).
tff(1256,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(and_elim,[status(thm)],[1018]) ).
tff(1257,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(modus_ponens,[status(thm)],[1256,1255]) ).
tff(1258,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(modus_ponens,[status(thm)],[1257,1251]) ).
tff(1259,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1258,1250]) ).
tff(1260,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1259,1245]) ).
tff(1261,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(e13,op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1260,1245]) ).
tff(1262,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13) ) ),
inference(modus_ponens,[status(thm)],[1261,1244]) ).
tff(1263,plain,
op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(op1(e13,e13),e13),
inference(unit_resolution,[status(thm)],[1262,1241]) ).
tff(1264,plain,
h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = h4(op1(op1(e13,e13),e13)),
inference(monotonicity,[status(thm)],[1263]) ).
tff(1265,plain,
h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(e13),h3(e13)),
inference(transitivity,[status(thm)],[1264,199,1231]) ).
tff(1266,plain,
( ( h1(op1(e13,e13)) != h2(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) != h1(e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(1267,plain,
op2(h1(e13),h2(e13)) != h1(e13),
inference(unit_resolution,[status(thm)],[1266,83]) ).
tff(1268,plain,
( ( op2(h1(e13),h1(e13)) = h1(e13) )
<=> ( h2(e13) = h1(e13) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(1269,plain,
( ( h2(e13) = h1(e13) )
<=> ( op2(h1(e13),h1(e13)) = h1(e13) ) ),
inference(symmetry,[status(thm)],[1268]) ).
tff(1270,plain,
( ( h2(e13) != h1(e13) )
<=> ( op2(h1(e13),h1(e13)) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[1269]) ).
tff(1271,plain,
op2(h1(e13),h1(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[780,1270]) ).
tff(1272,plain,
( ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h1(e13)) = h1(e13) ) )
<=> ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h1(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1273,plain,
( ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| $false
| ( op2(h1(e13),h1(e13)) = h1(e13) ) )
<=> ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h1(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1274,plain,
( ( h1(op1(e13,e13)) = h1(e13) )
<=> ( op2(h1(e13),h1(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1275,plain,
( ( op2(op2(h4(e13),h3(e13)),h3(e13)) != op2(h4(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) != h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1276,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(op2(h4(e13),h3(e13)),h3(e13)) != op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1277,plain,
( ( op2(e20,e22) != op2(e23,e22) )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1278,plain,
( ( op2(e20,e22) != op2(e23,e22) )
<=> ( op2(e20,e22) != op2(e23,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1279,plain,
op2(e20,e22) != op2(e23,e22),
inference(and_elim,[status(thm)],[114]) ).
tff(1280,plain,
op2(e20,e22) != op2(e23,e22),
inference(modus_ponens,[status(thm)],[1279,1278]) ).
tff(1281,plain,
op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) != op2(h4(e13),op2(h4(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[1280,1277]) ).
tff(1282,plain,
op2(op2(h4(e13),h3(e13)),h3(e13)) != op2(h4(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[1281,1276]) ).
tff(1283,plain,
op2(h1(e13),h3(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[1282,1275]) ).
tff(1284,plain,
( ( op2(h1(e13),h3(e13)) = h1(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[1283]) ).
tff(1285,plain,
( ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) )
<=> ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| $false
| ( op2(h1(e13),h1(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[1284,1274]) ).
tff(1286,plain,
( ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) )
<=> ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h1(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[1285,1273]) ).
tff(1287,plain,
( ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) )
<=> ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1288,plain,
( ( ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) )
<=> ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1289,plain,
( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
<=> ( h1(op1(e13,e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1290,plain,
( ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1291,plain,
( ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
<=> ( op2(h1(e13),h2(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1292,plain,
( ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
<=> ( op2(h1(e13),h4(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1293,plain,
( ( ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) )
<=> ( ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[1292,1291,1290,1289]) ).
tff(1294,plain,
( ( ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) )
<=> ( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[1293,1288]) ).
tff(1295,plain,
( ( ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1296,plain,
( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1297,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1298,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1299,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1300,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1301,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) ) ) ),
inference(monotonicity,[status(thm)],[1300,1299,1298,1297]) ).
tff(1302,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[1301,1296]) ).
tff(1303,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1304,plain,
( ( op2(e20,e23) = e20 )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1305,plain,
( ( op2(e20,e22) = e20 )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1306,plain,
( ( op2(e20,e21) = e20 )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1307,plain,
( ( op2(e20,e20) = e20 )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1308,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ) ),
inference(monotonicity,[status(thm)],[1307,1306,1305,1304]) ).
tff(1309,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ) ),
inference(transitivity,[status(thm)],[1308,1303]) ).
tff(1310,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
<=> ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1311,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
<=> ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1312,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 ) )
<=> ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1313,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
<=> ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) ) ),
inference(monotonicity,[status(thm)],[1312]) ).
tff(1314,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
<=> ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) ) ),
inference(transitivity,[status(thm)],[1313,1311]) ).
tff(1315,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)],[854]) ).
tff(1316,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)],[1315]) ).
tff(1317,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)],[1316]) ).
tff(1318,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)],[1317]) ).
tff(1319,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)],[1318]) ).
tff(1320,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)],[1319]) ).
tff(1321,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)],[1320]) ).
tff(1322,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)],[1321]) ).
tff(1323,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) ) ),
inference(and_elim,[status(thm)],[1322]) ).
tff(1324,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) ) ),
inference(and_elim,[status(thm)],[1323]) ).
tff(1325,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) ) ),
inference(and_elim,[status(thm)],[1324]) ).
tff(1326,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ) ),
inference(and_elim,[status(thm)],[1325]) ).
tff(1327,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 ) ) ),
inference(and_elim,[status(thm)],[1326]) ).
tff(1328,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 ) ) ),
inference(and_elim,[status(thm)],[1327]) ).
tff(1329,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 ) ) ),
inference(and_elim,[status(thm)],[1328]) ).
tff(1330,plain,
( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) ),
inference(and_elim,[status(thm)],[1329]) ).
tff(1331,plain,
( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[1330,1314]) ).
tff(1332,plain,
( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[1331,1310]) ).
tff(1333,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[1332,1309]) ).
tff(1334,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[1333,1303]) ).
tff(1335,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(modus_ponens,[status(thm)],[1334,1303]) ).
tff(1336,plain,
( ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1335,1302]) ).
tff(1337,plain,
( ( op2(op2(h4(e13),h3(e13)),h4(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1336,1295]) ).
tff(1338,plain,
( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1337,1294]) ).
tff(1339,plain,
( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h3(e13)) = h1(e13) )
| ( h1(op1(e13,e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1338,1287]) ).
tff(1340,plain,
( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1339,1286]) ).
tff(1341,plain,
( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1340,1272]) ).
tff(1342,plain,
( ( op2(h1(e13),h2(e13)) = h1(e13) )
| ( op2(h1(e13),h4(e13)) = h1(e13) )
| ( op2(h1(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1341,1272]) ).
tff(1343,plain,
op2(h1(e13),h4(e13)) = h1(e13),
inference(unit_resolution,[status(thm)],[1342,1271,1267]) ).
tff(1344,plain,
h1(e13) = op2(h1(e13),h4(e13)),
inference(symmetry,[status(thm)],[1343]) ).
tff(1345,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) ) ),
inference(tautology,[status(thm)],]) ).
tff(1346,plain,
op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)),
inference(unit_resolution,[status(thm)],[1345,282]) ).
tff(1347,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
<=> ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) ) ),
inference(monotonicity,[status(thm)],[284]) ).
tff(1348,plain,
( ( op1(op1(e13,e13),e13) = op1(e13,op1(e13,e13)) )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) ) ),
inference(symmetry,[status(thm)],[1347]) ).
tff(1349,plain,
( ( op1(op1(e13,e13),e13) != op1(e13,op1(e13,e13)) )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(e13,op1(e13,e13)) ) ),
inference(monotonicity,[status(thm)],[1348]) ).
tff(1350,plain,
op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) != op1(e13,op1(e13,e13)),
inference(modus_ponens,[status(thm)],[996,1349]) ).
tff(1351,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1352,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| $false
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1353,plain,
( ( op1(e10,e12) != op1(e13,e12) )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) != op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1354,plain,
( ( op1(e10,e12) != op1(e13,e12) )
<=> ( op1(e10,e12) != op1(e13,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1355,plain,
op1(e10,e12) != op1(e13,e12),
inference(and_elim,[status(thm)],[298]) ).
tff(1356,plain,
op1(e10,e12) != op1(e13,e12),
inference(modus_ponens,[status(thm)],[1355,1354]) ).
tff(1357,plain,
op1(op1(e13,op1(e13,e13)),op1(e13,e13)) != op1(e13,op1(e13,e13)),
inference(modus_ponens,[status(thm)],[1356,1353]) ).
tff(1358,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
<=> $false ),
inference(iff_false,[status(thm)],[1357]) ).
tff(1359,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| $false
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(monotonicity,[status(thm)],[1358]) ).
tff(1360,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(transitivity,[status(thm)],[1359,1352]) ).
tff(1361,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1362,plain,
( ( op1(e10,e13) = e10 )
<=> ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1363,plain,
( ( op1(e10,e12) = e10 )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1364,plain,
( ( op1(e10,e11) = e10 )
<=> ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1365,plain,
( ( op1(e10,e10) = e10 )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1366,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(monotonicity,[status(thm)],[1365,1364,1363,1362]) ).
tff(1367,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ) ),
inference(transitivity,[status(thm)],[1366,1361]) ).
tff(1368,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
<=> ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1369,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
<=> ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1370,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 ) )
<=> ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1371,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
<=> ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) ) ),
inference(monotonicity,[status(thm)],[1370]) ).
tff(1372,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
<=> ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) ) ),
inference(transitivity,[status(thm)],[1371,1369]) ).
tff(1373,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)],[1021]) ).
tff(1374,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)],[1373]) ).
tff(1375,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)],[1374]) ).
tff(1376,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)],[1375]) ).
tff(1377,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)],[1376]) ).
tff(1378,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)],[1377]) ).
tff(1379,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)],[1378]) ).
tff(1380,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)],[1379]) ).
tff(1381,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e11,e10) = e13 )
| ( op1(e12,e10) = e13 )
| ( op1(e13,e10) = e13 ) ) ),
inference(and_elim,[status(thm)],[1380]) ).
tff(1382,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) )
& ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) ) ),
inference(and_elim,[status(thm)],[1381]) ).
tff(1383,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e11,e10) = e12 )
| ( op1(e12,e10) = e12 )
| ( op1(e13,e10) = e12 ) ) ),
inference(and_elim,[status(thm)],[1382]) ).
tff(1384,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) )
& ( ( op1(e10,e10) = e10 )
| ( op1(e11,e10) = e10 )
| ( op1(e12,e10) = e10 )
| ( op1(e13,e10) = e10 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e13) = e11 ) )
& ( ( op1(e10,e10) = e11 )
| ( op1(e11,e10) = e11 )
| ( op1(e12,e10) = e11 )
| ( op1(e13,e10) = e11 ) )
& ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ) ),
inference(and_elim,[status(thm)],[1383]) ).
tff(1385,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 ) ) ),
inference(and_elim,[status(thm)],[1384]) ).
tff(1386,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 ) ) ),
inference(and_elim,[status(thm)],[1385]) ).
tff(1387,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 ) ) ),
inference(and_elim,[status(thm)],[1386]) ).
tff(1388,plain,
( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) ),
inference(and_elim,[status(thm)],[1387]) ).
tff(1389,plain,
( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[1388,1372]) ).
tff(1390,plain,
( ( op1(e10,e10) = e10 )
| ( op1(e10,e11) = e10 )
| ( op1(e10,e12) = e10 )
| ( op1(e10,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[1389,1368]) ).
tff(1391,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1390,1367]) ).
tff(1392,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1391,1361]) ).
tff(1393,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1392,1361]) ).
tff(1394,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1393,1360]) ).
tff(1395,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1394,1351]) ).
tff(1396,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1395,1351]) ).
tff(1397,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1396,1351]) ).
tff(1398,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1397,1351]) ).
tff(1399,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1398,1351]) ).
tff(1400,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = op1(e13,op1(e13,e13)) )
| ( op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)) ) ),
inference(modus_ponens,[status(thm)],[1399,1351]) ).
tff(1401,plain,
op1(op1(e13,op1(e13,e13)),e13) = op1(e13,op1(e13,e13)),
inference(unit_resolution,[status(thm)],[1400,1350,1346]) ).
tff(1402,plain,
h4(op1(op1(e13,op1(e13,e13)),e13)) = h4(op1(e13,op1(e13,e13))),
inference(monotonicity,[status(thm)],[1401]) ).
tff(1403,plain,
h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h1(e13),h4(e13)),
inference(transitivity,[status(thm)],[1402,993,1344]) ).
tff(1404,plain,
( ( op2(h1(e13),h4(e13)) = h4(e13) )
<=> ( h1(e13) = h4(e13) ) ),
inference(monotonicity,[status(thm)],[1343]) ).
tff(1405,plain,
( ( h1(e13) = h4(e13) )
<=> ( op2(h1(e13),h4(e13)) = h4(e13) ) ),
inference(symmetry,[status(thm)],[1404]) ).
tff(1406,plain,
( ( h1(e13) != h4(e13) )
<=> ( op2(h1(e13),h4(e13)) != h4(e13) ) ),
inference(monotonicity,[status(thm)],[1405]) ).
tff(1407,plain,
op2(h1(e13),h4(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[570,1406]) ).
tff(1408,plain,
( ( op2(h1(e13),h3(e13)) = op2(h3(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) = h4(e13) ) ),
inference(monotonicity,[status(thm)],[765]) ).
tff(1409,plain,
( ( op2(h1(e13),h3(e13)) != op2(h3(e13),h3(e13)) )
<=> ( op2(h1(e13),h3(e13)) != h4(e13) ) ),
inference(monotonicity,[status(thm)],[1408]) ).
tff(1410,plain,
( ( op2(op2(h4(e13),h3(e13)),h3(e13)) != h3(op1(e13,e13)) )
<=> ( op2(h1(e13),h3(e13)) != op2(h3(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1411,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) )
<=> ( op2(op2(h4(e13),h3(e13)),h3(e13)) != h3(op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1412,plain,
( ( op2(e20,e22) != op2(e22,e22) )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1413,plain,
( ( op2(e20,e22) != op2(e22,e22) )
<=> ( op2(e20,e22) != op2(e22,e22) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1414,plain,
op2(e20,e22) != op2(e22,e22),
inference(and_elim,[status(thm)],[115]) ).
tff(1415,plain,
op2(e20,e22) != op2(e22,e22),
inference(modus_ponens,[status(thm)],[1414,1413]) ).
tff(1416,plain,
op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) != op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[1415,1412]) ).
tff(1417,plain,
op2(op2(h4(e13),h3(e13)),h3(e13)) != h3(op1(e13,e13)),
inference(modus_ponens,[status(thm)],[1416,1411]) ).
tff(1418,plain,
op2(h1(e13),h3(e13)) != op2(h3(e13),h3(e13)),
inference(modus_ponens,[status(thm)],[1417,1410]) ).
tff(1419,plain,
op2(h1(e13),h3(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[1418,1409]) ).
tff(1420,plain,
( ( ( h1(op1(e13,e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h2(e13)) = h4(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h2(e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1421,plain,
( ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
<=> ( op2(h1(e13),h2(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1422,plain,
( ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) )
<=> ( op2(h1(e13),h3(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1423,plain,
( ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) )
<=> ( op2(h1(e13),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1424,plain,
( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
<=> ( h1(op1(e13,e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1425,plain,
( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h2(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[1424,1423,1422,1421]) ).
tff(1426,plain,
( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) ) )
<=> ( ( h1(op1(e13,e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h2(e13)) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[1425,1420]) ).
tff(1427,plain,
( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1428,plain,
( ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1429,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = h4(e13) )
<=> ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1430,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = h4(e13) )
<=> ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1431,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
<=> ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1432,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
<=> ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1433,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[1432,1431,1430,1429]) ).
tff(1434,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[1433,1428]) ).
tff(1435,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = h4(e13) ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1436,plain,
( ( op2(e20,e23) = e23 )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1437,plain,
( ( op2(e20,e22) = e23 )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1438,plain,
( ( op2(e20,e21) = e23 )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1439,plain,
( ( op2(e20,e20) = e23 )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1440,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[1439,1438,1437,1436]) ).
tff(1441,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[1440,1435]) ).
tff(1442,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1443,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1444,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1445,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) ) ),
inference(monotonicity,[status(thm)],[1444]) ).
tff(1446,plain,
( ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
<=> ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) ) ),
inference(transitivity,[status(thm)],[1445,1443]) ).
tff(1447,plain,
( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) ),
inference(and_elim,[status(thm)],[1324]) ).
tff(1448,plain,
( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[1447,1446]) ).
tff(1449,plain,
( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[1448,1442]) ).
tff(1450,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1449,1441]) ).
tff(1451,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1450,1435]) ).
tff(1452,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(op2(h4(e13),h4(e13)),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = h4(e13) )
| ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),h4(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1451,1435]) ).
tff(1453,plain,
( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1452,1434]) ).
tff(1454,plain,
( ( op2(op2(h4(e13),h3(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h4(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h4(e13) )
| ( op2(op2(h4(e13),h3(e13)),op2(h3(e13),h4(e13))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1453,1427]) ).
tff(1455,plain,
( ( h1(op1(e13,e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h2(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1454,1426]) ).
tff(1456,plain,
( ( h1(op1(e13,e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h2(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1455,1420]) ).
tff(1457,plain,
( ( h1(op1(e13,e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h2(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1456,1420]) ).
tff(1458,plain,
( ( h1(op1(e13,e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h2(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1457,1420]) ).
tff(1459,plain,
( ( h1(op1(e13,e13)) = h4(e13) )
| ( op2(h1(e13),h4(e13)) = h4(e13) )
| ( op2(h1(e13),h3(e13)) = h4(e13) )
| ( op2(h1(e13),h2(e13)) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1458,1420]) ).
tff(1460,plain,
op2(h1(e13),h2(e13)) = h4(e13),
inference(unit_resolution,[status(thm)],[1459,1419,500,1407]) ).
tff(1461,plain,
h4(e13) = op2(h1(e13),h2(e13)),
inference(symmetry,[status(thm)],[1460]) ).
tff(1462,plain,
( ( op1(op1(e13,op1(e13,e13)),e13) = e13 )
<=> ( op1(e13,op1(e13,e13)) = e13 ) ),
inference(monotonicity,[status(thm)],[1401]) ).
tff(1463,plain,
( ( op1(e13,op1(e13,e13)) = e13 )
<=> ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(symmetry,[status(thm)],[1462]) ).
tff(1464,plain,
( ( op1(e13,op1(e13,e13)) != e13 )
<=> ( op1(op1(e13,op1(e13,e13)),e13) != e13 ) ),
inference(monotonicity,[status(thm)],[1463]) ).
tff(1465,plain,
op1(op1(e13,op1(e13,e13)),e13) != e13,
inference(modus_ponens,[status(thm)],[707,1464]) ).
tff(1466,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(op1(e13,e13),op1(e13,e13)) )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 ) ),
inference(monotonicity,[status(thm)],[760]) ).
tff(1467,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) != op1(op1(e13,e13),op1(e13,e13)) )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) != e13 ) ),
inference(monotonicity,[status(thm)],[1466]) ).
tff(1468,plain,
( ( op1(e10,e12) != op1(e12,e12) )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) != op1(op1(e13,e13),op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1469,plain,
( ( op1(e10,e12) != op1(e12,e12) )
<=> ( op1(e10,e12) != op1(e12,e12) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1470,plain,
op1(e10,e12) != op1(e12,e12),
inference(and_elim,[status(thm)],[299]) ).
tff(1471,plain,
op1(e10,e12) != op1(e12,e12),
inference(modus_ponens,[status(thm)],[1470,1469]) ).
tff(1472,plain,
op1(op1(e13,op1(e13,e13)),op1(e13,e13)) != op1(op1(e13,e13),op1(e13,e13)),
inference(modus_ponens,[status(thm)],[1471,1468]) ).
tff(1473,plain,
op1(op1(e13,op1(e13,e13)),op1(e13,e13)) != e13,
inference(modus_ponens,[status(thm)],[1472,1467]) ).
tff(1474,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1475,plain,
( ( op1(e10,e13) = e13 )
<=> ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1476,plain,
( ( op1(e10,e12) = e13 )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1477,plain,
( ( op1(e10,e11) = e13 )
<=> ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1478,plain,
( ( op1(e10,e10) = e13 )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1479,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1478,1477,1476,1475]) ).
tff(1480,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[1479,1474]) ).
tff(1481,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1482,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1483,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 ) )
<=> ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1484,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1483]) ).
tff(1485,plain,
( ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) )
<=> ( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[1484,1482]) ).
tff(1486,plain,
( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) ),
inference(and_elim,[status(thm)],[1382]) ).
tff(1487,plain,
( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1486,1485]) ).
tff(1488,plain,
( ( op1(e10,e10) = e13 )
| ( op1(e10,e11) = e13 )
| ( op1(e10,e12) = e13 )
| ( op1(e10,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1487,1481]) ).
tff(1489,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1488,1480]) ).
tff(1490,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1489,1474]) ).
tff(1491,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1490,1474]) ).
tff(1492,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1491,1474]) ).
tff(1493,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1492,1474]) ).
tff(1494,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1493,1474]) ).
tff(1495,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1494,1474]) ).
tff(1496,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1495,1474]) ).
tff(1497,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1496,1474]) ).
tff(1498,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13))) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = e13 )
| ( op1(op1(e13,op1(e13,e13)),e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[1497,1474]) ).
tff(1499,plain,
op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13)) = e13,
inference(unit_resolution,[status(thm)],[1498,1473,641,1465]) ).
tff(1500,plain,
h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = h4(e13),
inference(monotonicity,[status(thm)],[1499]) ).
tff(1501,plain,
h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h1(e13),h2(e13)),
inference(transitivity,[status(thm)],[1500,1461]) ).
tff(1502,plain,
h1(e13) = h2(op1(e13,e13)),
inference(symmetry,[status(thm)],[558]) ).
tff(1503,plain,
h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = h4(op1(e13,op1(e13,e13))),
inference(monotonicity,[status(thm)],[699]) ).
tff(1504,plain,
h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(e13),h2(e13)),
inference(transitivity,[status(thm)],[1503,993,1502,791]) ).
tff(1505,plain,
h2(e13) = h1(op1(e13,e13)),
inference(symmetry,[status(thm)],[85]) ).
tff(1506,plain,
h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = h4(op1(op1(e13,e13),e13)),
inference(monotonicity,[status(thm)],[284]) ).
tff(1507,plain,
h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h1(e13),h1(e13)),
inference(transitivity,[status(thm)],[1506,199,1505,95]) ).
tff(1508,plain,
( ( op2(h2(e13),h1(e13)) = op2(h2(e13),h2(e13)) )
<=> ( op2(h2(e13),h1(e13)) = h1(e13) ) ),
inference(monotonicity,[status(thm)],[793]) ).
tff(1509,plain,
( ( op2(h2(e13),h1(e13)) != op2(h2(e13),h2(e13)) )
<=> ( op2(h2(e13),h1(e13)) != h1(e13) ) ),
inference(monotonicity,[status(thm)],[1508]) ).
tff(1510,plain,
( ( op2(h2(e13),h1(e13)) != h2(op1(e13,e13)) )
<=> ( op2(h2(e13),h1(e13)) != op2(h2(e13),h2(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1511,plain,
( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) )
<=> ( op2(h2(e13),h1(e13)) != h2(op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1512,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) )
<=> ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1513,plain,
( ( op2(e21,e20) != op2(e21,e21) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1514,plain,
( ( op2(e21,e20) != op2(e21,e21) )
<=> ( op2(e21,e20) != op2(e21,e21) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1515,plain,
op2(e21,e20) != op2(e21,e21),
inference(and_elim,[status(thm)],[24]) ).
tff(1516,plain,
op2(e21,e20) != op2(e21,e21),
inference(modus_ponens,[status(thm)],[1515,1514]) ).
tff(1517,plain,
op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(op2(h4(e13),h4(e13)),h4(e13))),
inference(modus_ponens,[status(thm)],[1516,1513]) ).
tff(1518,plain,
op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(op2(h3(e13),h4(e13)),op2(h3(e13),h4(e13))),
inference(modus_ponens,[status(thm)],[1517,1512]) ).
tff(1519,plain,
op2(h2(e13),h1(e13)) != h2(op1(e13,e13)),
inference(modus_ponens,[status(thm)],[1518,1511]) ).
tff(1520,plain,
op2(h2(e13),h1(e13)) != op2(h2(e13),h2(e13)),
inference(modus_ponens,[status(thm)],[1519,1510]) ).
tff(1521,plain,
op2(h2(e13),h1(e13)) != h1(e13),
inference(modus_ponens,[status(thm)],[1520,1509]) ).
tff(1522,plain,
( ( h2(op1(e13,e13)) != h1(e13) )
| ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) != h2(e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(1523,plain,
op2(h2(e13),h1(e13)) != h2(e13),
inference(unit_resolution,[status(thm)],[1522,556]) ).
tff(1524,plain,
op2(op2(h1(e13),h1(e13)),h1(e13)) = op2(h1(op1(e13,e13)),h1(e13)),
inference(monotonicity,[status(thm)],[96]) ).
tff(1525,plain,
h2(e13) = op2(h1(e13),h1(e13)),
inference(transitivity,[status(thm)],[1505,95]) ).
tff(1526,plain,
op2(h2(e13),h1(e13)) = op2(op2(h1(e13),h1(e13)),h1(e13)),
inference(monotonicity,[status(thm)],[1525]) ).
tff(1527,plain,
op2(h2(e13),h1(e13)) = op2(h1(op1(e13,e13)),h1(e13)),
inference(transitivity,[status(thm)],[1526,1524]) ).
tff(1528,plain,
( ( op2(h2(e13),h1(e13)) = h4(e13) )
<=> ( op2(h1(op1(e13,e13)),h1(e13)) = h4(e13) ) ),
inference(monotonicity,[status(thm)],[1527]) ).
tff(1529,plain,
( ( op2(h1(op1(e13,e13)),h1(e13)) = h4(e13) )
<=> ( op2(h2(e13),h1(e13)) = h4(e13) ) ),
inference(symmetry,[status(thm)],[1528]) ).
tff(1530,plain,
( ( op2(h2(e13),h1(e13)) = op2(h4(e13),h1(e13)) )
<=> ( op2(h1(op1(e13,e13)),h1(e13)) = h4(e13) ) ),
inference(monotonicity,[status(thm)],[1527,431]) ).
tff(1531,plain,
( ( op2(h2(e13),h1(e13)) = op2(h4(e13),h1(e13)) )
<=> ( op2(h2(e13),h1(e13)) = h4(e13) ) ),
inference(transitivity,[status(thm)],[1530,1529]) ).
tff(1532,plain,
( ( op2(h2(e13),h1(e13)) != op2(h4(e13),h1(e13)) )
<=> ( op2(h2(e13),h1(e13)) != h4(e13) ) ),
inference(monotonicity,[status(thm)],[1531]) ).
tff(1533,plain,
( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(h4(e13),op2(h4(e13),h3(e13))) )
<=> ( op2(h2(e13),h1(e13)) != op2(h4(e13),h1(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1534,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) )
<=> ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(h4(e13),op2(h4(e13),h3(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1535,plain,
( ( op2(e21,e20) != op2(e23,e20) )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1536,plain,
( ( op2(e21,e20) != op2(e23,e20) )
<=> ( op2(e21,e20) != op2(e23,e20) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1537,plain,
op2(e21,e20) != op2(e23,e20),
inference(and_elim,[status(thm)],[124]) ).
tff(1538,plain,
op2(e21,e20) != op2(e23,e20),
inference(modus_ponens,[status(thm)],[1537,1536]) ).
tff(1539,plain,
op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) != op2(h4(e13),op2(h4(e13),op2(h4(e13),h4(e13)))),
inference(modus_ponens,[status(thm)],[1538,1535]) ).
tff(1540,plain,
op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) != op2(h4(e13),op2(h4(e13),h3(e13))),
inference(modus_ponens,[status(thm)],[1539,1534]) ).
tff(1541,plain,
op2(h2(e13),h1(e13)) != op2(h4(e13),h1(e13)),
inference(modus_ponens,[status(thm)],[1540,1533]) ).
tff(1542,plain,
op2(h2(e13),h1(e13)) != h4(e13),
inference(modus_ponens,[status(thm)],[1541,1532]) ).
tff(1543,plain,
( ( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h4(e13) )
| ( op2(h2(e13),h1(e13)) = h3(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) )
<=> ( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h4(e13) )
| ( op2(h2(e13),h1(e13)) = h3(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1544,plain,
( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
<=> ( op2(h2(e13),h1(e13)) = h1(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1545,plain,
( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) )
<=> ( op2(h2(e13),h1(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1546,plain,
( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
<=> ( op2(h2(e13),h1(e13)) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1547,plain,
( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
<=> ( op2(h2(e13),h1(e13)) = h2(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1548,plain,
( ( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) )
<=> ( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h4(e13) )
| ( op2(h2(e13),h1(e13)) = h3(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ) ),
inference(monotonicity,[status(thm)],[1547,1546,1545,1544]) ).
tff(1549,plain,
( ( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) )
<=> ( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h4(e13) )
| ( op2(h2(e13),h1(e13)) = h3(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ) ),
inference(transitivity,[status(thm)],[1548,1543]) ).
tff(1550,plain,
( ( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) )
<=> ( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1551,plain,
( ( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) ) )
<=> ( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1552,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) )
<=> ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1553,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
<=> ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1554,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
<=> ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1555,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
<=> ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1556,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) )
<=> ( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[1555,1554,1553,1552]) ).
tff(1557,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) )
<=> ( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ) ),
inference(transitivity,[status(thm)],[1556,1551]) ).
tff(1558,plain,
( ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1559,plain,
( ( op2(e21,e20) = e23 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1560,plain,
( ( op2(e21,e20) = e22 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1561,plain,
( ( op2(e21,e20) = e21 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1562,plain,
( ( op2(e21,e20) = e20 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1563,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ) ),
inference(monotonicity,[status(thm)],[1562,1561,1560,1559]) ).
tff(1564,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
<=> ( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ) ),
inference(transitivity,[status(thm)],[1563,1558]) ).
tff(1565,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1566,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1567,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1568,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) ) ),
inference(monotonicity,[status(thm)],[1567]) ).
tff(1569,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) ) ),
inference(transitivity,[status(thm)],[1568,1566]) ).
tff(1570,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)],[1104]) ).
tff(1571,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)],[1570]) ).
tff(1572,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)],[1571]) ).
tff(1573,plain,
( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) ),
inference(and_elim,[status(thm)],[1572]) ).
tff(1574,plain,
( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) ),
inference(modus_ponens,[status(thm)],[1573,1569]) ).
tff(1575,plain,
( ( op2(e21,e20) = e20 )
| ( op2(e21,e20) = e21 )
| ( op2(e21,e20) = e22 )
| ( op2(e21,e20) = e23 ) ),
inference(modus_ponens,[status(thm)],[1574,1565]) ).
tff(1576,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1575,1564]) ).
tff(1577,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1576,1558]) ).
tff(1578,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),op2(h4(e13),h4(e13)))) = h4(e13) ) ),
inference(modus_ponens,[status(thm)],[1577,1558]) ).
tff(1579,plain,
( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1578,1557]) ).
tff(1580,plain,
( ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h3(e13),h4(e13)) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h4(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),op2(h4(e13),h3(e13))) = op2(h4(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1579,1550]) ).
tff(1581,plain,
( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h4(e13) )
| ( op2(h2(e13),h1(e13)) = h3(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1580,1549]) ).
tff(1582,plain,
( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h4(e13) )
| ( op2(h2(e13),h1(e13)) = h3(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1581,1543]) ).
tff(1583,plain,
( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h4(e13) )
| ( op2(h2(e13),h1(e13)) = h3(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1582,1543]) ).
tff(1584,plain,
( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h4(e13) )
| ( op2(h2(e13),h1(e13)) = h3(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1583,1543]) ).
tff(1585,plain,
( ( op2(h2(e13),h1(e13)) = h2(e13) )
| ( op2(h2(e13),h1(e13)) = h4(e13) )
| ( op2(h2(e13),h1(e13)) = h3(e13) )
| ( op2(h2(e13),h1(e13)) = h1(e13) ) ),
inference(modus_ponens,[status(thm)],[1584,1543]) ).
tff(1586,plain,
op2(h2(e13),h1(e13)) = h3(e13),
inference(unit_resolution,[status(thm)],[1585,1542,1523,1521]) ).
tff(1587,plain,
h3(e13) = op2(h2(e13),h1(e13)),
inference(symmetry,[status(thm)],[1586]) ).
tff(1588,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) ) ),
inference(monotonicity,[status(thm)],[699]) ).
tff(1589,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(e13,op1(e13,e13)) ) ),
inference(monotonicity,[status(thm)],[1588]) ).
tff(1590,plain,
( ( op1(e11,e10) != op1(e11,e11) )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1591,plain,
( ( op1(e11,e10) != op1(e11,e11) )
<=> ( op1(e11,e10) != op1(e11,e11) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1592,plain,
op1(e11,e10) != op1(e11,e11),
inference(and_elim,[status(thm)],[221]) ).
tff(1593,plain,
op1(e11,e10) != op1(e11,e11),
inference(modus_ponens,[status(thm)],[1592,1591]) ).
tff(1594,plain,
op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)),
inference(modus_ponens,[status(thm)],[1593,1590]) ).
tff(1595,plain,
op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(e13,op1(e13,e13)),
inference(modus_ponens,[status(thm)],[1594,1589]) ).
tff(1596,plain,
( ( op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13)) != op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13) ) ),
inference(tautology,[status(thm)],]) ).
tff(1597,plain,
op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(op1(e13,e13),e13),
inference(unit_resolution,[status(thm)],[1596,697]) ).
tff(1598,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,op1(e13,e13))) )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(monotonicity,[status(thm)],[477]) ).
tff(1599,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(e13,op1(e13,op1(e13,e13))) )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != e13 ) ),
inference(monotonicity,[status(thm)],[1598]) ).
tff(1600,plain,
( ( op1(e11,e10) != op1(e13,e10) )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(e13,op1(e13,op1(e13,e13))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1601,plain,
( ( op1(e11,e10) != op1(e13,e10) )
<=> ( op1(e11,e10) != op1(e13,e10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1602,plain,
op1(e11,e10) != op1(e13,e10),
inference(and_elim,[status(thm)],[308]) ).
tff(1603,plain,
op1(e11,e10) != op1(e13,e10),
inference(modus_ponens,[status(thm)],[1602,1601]) ).
tff(1604,plain,
op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != op1(e13,op1(e13,op1(e13,e13))),
inference(modus_ponens,[status(thm)],[1603,1600]) ).
tff(1605,plain,
op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) != e13,
inference(modus_ponens,[status(thm)],[1604,1599]) ).
tff(1606,plain,
( ( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1607,plain,
( ( op1(e11,e10) = e13 )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1608,plain,
( ( op1(e11,e10) = e12 )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1609,plain,
( ( op1(e11,e10) = e11 )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1610,plain,
( ( op1(e11,e10) = e10 )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1611,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1610,1609,1608,1607]) ).
tff(1612,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
<=> ( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ) ),
inference(transitivity,[status(thm)],[1611,1606]) ).
tff(1613,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1614,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1615,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1616,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) ) ),
inference(monotonicity,[status(thm)],[1615]) ).
tff(1617,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) ) ),
inference(transitivity,[status(thm)],[1616,1614]) ).
tff(1618,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)],[1153]) ).
tff(1619,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)],[1618]) ).
tff(1620,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)],[1619]) ).
tff(1621,plain,
( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) ),
inference(and_elim,[status(thm)],[1620]) ).
tff(1622,plain,
( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) ),
inference(modus_ponens,[status(thm)],[1621,1617]) ).
tff(1623,plain,
( ( op1(e11,e10) = e10 )
| ( op1(e11,e10) = e11 )
| ( op1(e11,e10) = e12 )
| ( op1(e11,e10) = e13 ) ),
inference(modus_ponens,[status(thm)],[1622,1613]) ).
tff(1624,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[1623,1612]) ).
tff(1625,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[1624,1606]) ).
tff(1626,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[1625,1606]) ).
tff(1627,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[1626,1606]) ).
tff(1628,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[1627,1606]) ).
tff(1629,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[1628,1606]) ).
tff(1630,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[1629,1606]) ).
tff(1631,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[1630,1606]) ).
tff(1632,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[1631,1606]) ).
tff(1633,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,op1(e13,e13)) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(op1(e13,e13),e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = e13 ) ),
inference(modus_ponens,[status(thm)],[1632,1606]) ).
tff(1634,plain,
op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13))) = op1(e13,e13),
inference(unit_resolution,[status(thm)],[1633,1605,1597,1595]) ).
tff(1635,plain,
h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = h4(op1(e13,e13)),
inference(monotonicity,[status(thm)],[1634]) ).
tff(1636,plain,
h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h2(e13),h1(e13)),
inference(transitivity,[status(thm)],[1635,925,1587]) ).
tff(1637,plain,
( ( op2(h2(e13),h3(e13)) = h3(e13) )
<=> ( h2(e13) = h3(e13) ) ),
inference(monotonicity,[status(thm)],[1230]) ).
tff(1638,plain,
( ( op2(h2(e13),h3(e13)) = h3(e13) )
<=> ( h3(e13) = h2(e13) ) ),
inference(transitivity,[status(thm)],[1637,1]) ).
tff(1639,plain,
( ( h3(e13) = h2(e13) )
<=> ( op2(h2(e13),h3(e13)) = h3(e13) ) ),
inference(symmetry,[status(thm)],[1638]) ).
tff(1640,plain,
( ( h3(e13) != h2(e13) )
<=> ( op2(h2(e13),h3(e13)) != h3(e13) ) ),
inference(monotonicity,[status(thm)],[1639]) ).
tff(1641,plain,
op2(h2(e13),h3(e13)) != h3(e13),
inference(modus_ponens,[status(thm)],[37,1640]) ).
tff(1642,plain,
( ( $false
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h2(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) )
<=> ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h2(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1643,plain,
( ( h1(e13) = h3(e13) )
<=> $false ),
inference(iff_false,[status(thm)],[513]) ).
tff(1644,plain,
( ( ( h1(e13) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h2(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) )
<=> ( $false
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h2(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[1643]) ).
tff(1645,plain,
( ( ( h1(e13) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h2(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) )
<=> ( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h2(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[1644,1642]) ).
tff(1646,plain,
( ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) ) )
<=> ( ( h1(e13) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h2(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1647,plain,
( ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1648,plain,
( ( ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1649,plain,
( ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( op2(h4(e13),h3(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1650,plain,
( ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( op2(op2(h3(e13),h4(e13)),h3(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1651,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
<=> ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h3(e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1652,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) )
<=> ( ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) )
| ( op2(h4(e13),h3(e13)) = h3(e13) ) ) ),
inference(monotonicity,[status(thm)],[1651,1650,887,1649]) ).
tff(1653,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) )
<=> ( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) ) ) ),
inference(transitivity,[status(thm)],[1652,1648]) ).
tff(1654,plain,
( ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1655,plain,
( ( op2(e23,e22) = e22 )
<=> ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1656,plain,
( ( op2(e21,e22) = e22 )
<=> ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1657,plain,
( ( op2(e20,e22) = e22 )
<=> ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1658,plain,
( ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ) ),
inference(monotonicity,[status(thm)],[1657,1656,894,1655]) ).
tff(1659,plain,
( ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
<=> ( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ) ),
inference(transitivity,[status(thm)],[1658,1654]) ).
tff(1660,plain,
( ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
<=> ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1661,plain,
( ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
<=> ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1662,plain,
( ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 ) )
<=> ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1663,plain,
( ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
<=> ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) ) ),
inference(monotonicity,[status(thm)],[1662]) ).
tff(1664,plain,
( ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) )
<=> ( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) ) ),
inference(transitivity,[status(thm)],[1663,1661]) ).
tff(1665,plain,
( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) ),
inference(and_elim,[status(thm)],[849]) ).
tff(1666,plain,
( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) ),
inference(modus_ponens,[status(thm)],[1665,1664]) ).
tff(1667,plain,
( ( op2(e20,e22) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e22,e22) = e22 )
| ( op2(e23,e22) = e22 ) ),
inference(modus_ponens,[status(thm)],[1666,1660]) ).
tff(1668,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1667,1659]) ).
tff(1669,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1668,1654]) ).
tff(1670,plain,
( ( op2(op2(h4(e13),op2(h4(e13),h4(e13))),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(op2(h4(e13),h4(e13)),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(op2(h4(e13),h4(e13)),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) )
| ( op2(h4(e13),op2(h4(e13),h4(e13))) = op2(h4(e13),h4(e13)) ) ),
inference(modus_ponens,[status(thm)],[1669,1654]) ).
tff(1671,plain,
( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1670,1653]) ).
tff(1672,plain,
( ( op2(h4(e13),h3(e13)) = h3(e13) )
| ( op2(op2(h4(e13),h3(e13)),h3(e13)) = h3(e13) )
| ( op2(op2(h3(e13),h4(e13)),h3(e13)) = h3(e13) )
| ( h3(op1(e13,e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1671,1647]) ).
tff(1673,plain,
( ( h1(e13) = h3(e13) )
| ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h2(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1672,1646]) ).
tff(1674,plain,
( ( op2(h1(e13),h3(e13)) = h3(e13) )
| ( op2(h2(e13),h3(e13)) = h3(e13) )
| ( op2(h3(e13),h3(e13)) = h3(e13) ) ),
inference(modus_ponens,[status(thm)],[1673,1645]) ).
tff(1675,plain,
op2(h1(e13),h3(e13)) = h3(e13),
inference(unit_resolution,[status(thm)],[1674,1641,777]) ).
tff(1676,plain,
h3(e13) = op2(h1(e13),h3(e13)),
inference(symmetry,[status(thm)],[1675]) ).
tff(1677,plain,
( ( e13 = op1(e13,e13) )
<=> ( op1(e13,e13) = e13 ) ),
inference(commutativity,[status(thm)],]) ).
tff(1678,plain,
( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
<=> ( e13 = op1(e13,e13) ) ),
inference(monotonicity,[status(thm)],[760]) ).
tff(1679,plain,
( ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
<=> ( op1(e13,e13) = e13 ) ),
inference(transitivity,[status(thm)],[1678,1677]) ).
tff(1680,plain,
( ( op1(e13,e13) = e13 )
<=> ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(symmetry,[status(thm)],[1679]) ).
tff(1681,plain,
( ( op1(e13,e13) != e13 )
<=> ( op1(op1(e13,e13),op1(e13,e13)) != op1(e13,e13) ) ),
inference(monotonicity,[status(thm)],[1680]) ).
tff(1682,plain,
( ( e12 != e13 )
<=> ( op1(e13,e13) != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1683,plain,
( ( e12 != e13 )
<=> ( e12 != e13 ) ),
inference(rewrite,[status(thm)],]) ).
tff(1684,plain,
e12 != e13,
inference(and_elim,[status(thm)],[319]) ).
tff(1685,plain,
e12 != e13,
inference(modus_ponens,[status(thm)],[1684,1683]) ).
tff(1686,plain,
op1(e13,e13) != e13,
inference(modus_ponens,[status(thm)],[1685,1682]) ).
tff(1687,plain,
op1(op1(e13,e13),op1(e13,e13)) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[1686,1681]) ).
tff(1688,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
<=> ( op1(op1(e13,e13),e13) = op1(e13,e13) ) ),
inference(monotonicity,[status(thm)],[1263]) ).
tff(1689,plain,
( ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
<=> ( op1(e13,e13) = op1(op1(e13,e13),e13) ) ),
inference(transitivity,[status(thm)],[1688,200]) ).
tff(1690,plain,
( ( op1(e13,e13) = op1(op1(e13,e13),e13) )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(symmetry,[status(thm)],[1689]) ).
tff(1691,plain,
( ( op1(e13,e13) != op1(op1(e13,e13),e13) )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) != op1(e13,e13) ) ),
inference(monotonicity,[status(thm)],[1690]) ).
tff(1692,plain,
op1(op1(op1(e13,e13),e13),op1(e13,e13)) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[232,1691]) ).
tff(1693,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1694,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| $false )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1695,plain,
( ( op1(e13,op1(e13,e13)) = op1(e13,e13) )
<=> $false ),
inference(iff_false,[status(thm)],[650]) ).
tff(1696,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| $false ) ),
inference(monotonicity,[status(thm)],[1695]) ).
tff(1697,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(transitivity,[status(thm)],[1696,1694]) ).
tff(1698,plain,
( ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1699,plain,
( ( op1(e13,e12) = e12 )
<=> ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1700,plain,
( ( op1(e12,e12) = e12 )
<=> ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1701,plain,
( ( op1(e11,e12) = e12 )
<=> ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1702,plain,
( ( op1(e10,e12) = e12 )
<=> ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1703,plain,
( ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(monotonicity,[status(thm)],[1702,1701,1700,1699]) ).
tff(1704,plain,
( ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
<=> ( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ) ),
inference(transitivity,[status(thm)],[1703,1698]) ).
tff(1705,plain,
( ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
<=> ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1706,plain,
( ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
<=> ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1707,plain,
( ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 ) )
<=> ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1708,plain,
( ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
<=> ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) ) ),
inference(monotonicity,[status(thm)],[1707]) ).
tff(1709,plain,
( ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) )
<=> ( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) ) ),
inference(transitivity,[status(thm)],[1708,1706]) ).
tff(1710,plain,
( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) ),
inference(and_elim,[status(thm)],[1016]) ).
tff(1711,plain,
( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) ),
inference(modus_ponens,[status(thm)],[1710,1709]) ).
tff(1712,plain,
( ( op1(e10,e12) = e12 )
| ( op1(e11,e12) = e12 )
| ( op1(e12,e12) = e12 )
| ( op1(e13,e12) = e12 ) ),
inference(modus_ponens,[status(thm)],[1711,1705]) ).
tff(1713,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1712,1704]) ).
tff(1714,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1713,1698]) ).
tff(1715,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(e13,op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1714,1698]) ).
tff(1716,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1715,1697]) ).
tff(1717,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1716,1693]) ).
tff(1718,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1717,1693]) ).
tff(1719,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1718,1693]) ).
tff(1720,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1719,1693]) ).
tff(1721,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1720,1693]) ).
tff(1722,plain,
( ( op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(op1(e13,e13),e13),op1(e13,e13)) = op1(e13,e13) )
| ( op1(op1(e13,e13),op1(e13,e13)) = op1(e13,e13) ) ),
inference(modus_ponens,[status(thm)],[1721,1693]) ).
tff(1723,plain,
op1(op1(e13,op1(e13,e13)),op1(e13,e13)) = op1(e13,e13),
inference(unit_resolution,[status(thm)],[1722,1692,1687]) ).
tff(1724,plain,
h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = h4(op1(e13,e13)),
inference(monotonicity,[status(thm)],[1723]) ).
tff(1725,plain,
h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h1(e13),h3(e13)),
inference(transitivity,[status(thm)],[1724,925,1676]) ).
tff(1726,plain,
( ~ ~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) != op2(h1(e13),h3(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) != op2(h1(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) != op2(h2(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(h2(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) != op2(h1(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),e13)) != op2(h1(e13),h4(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(h2(e13),h3(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),e13)) != op2(h2(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) != op2(h3(e13),h1(e13)) )
| ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op2(h3(e13),h2(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,e13))) != op2(h3(e13),h3(e13)) )
| ( h4(op1(e13,op1(e13,op1(e13,e13)))) != op2(h4(e13),h1(e13)) )
| ( h4(op1(e13,op1(op1(e13,e13),e13))) != op2(h4(e13),h2(e13)) ) )
<=> ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) != op2(h1(e13),h3(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) != op2(h1(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) != op2(h2(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(h2(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) != op2(h1(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),e13)) != op2(h1(e13),h4(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(h2(e13),h3(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),e13)) != op2(h2(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) != op2(h3(e13),h1(e13)) )
| ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op2(h3(e13),h2(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,e13))) != op2(h3(e13),h3(e13)) )
| ( h4(op1(e13,op1(e13,op1(e13,e13)))) != op2(h4(e13),h1(e13)) )
| ( h4(op1(e13,op1(op1(e13,e13),e13))) != op2(h4(e13),h2(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1727,plain,
( ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h1(e13),h1(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h1(e13),h2(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h1(e13),h3(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h1(e13),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h2(e13),h1(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(e13),h2(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(e13),h3(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(e13),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h3(e13),h1(e13)) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h3(e13),h2(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h3(e13),h3(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h1(e13)) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h2(e13)) ) )
<=> ~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) != op2(h1(e13),h3(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) != op2(h1(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) != op2(h2(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(h2(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) != op2(h1(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),e13)) != op2(h1(e13),h4(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(h2(e13),h3(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),e13)) != op2(h2(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) != op2(h3(e13),h1(e13)) )
| ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op2(h3(e13),h2(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,e13))) != op2(h3(e13),h3(e13)) )
| ( h4(op1(e13,op1(e13,op1(e13,e13)))) != op2(h4(e13),h1(e13)) )
| ( h4(op1(e13,op1(op1(e13,e13),e13))) != op2(h4(e13),h2(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1728,plain,
( ~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h1(e13),h1(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h1(e13),h2(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h1(e13),h3(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h1(e13),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h2(e13),h1(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(e13),h2(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(e13),h3(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(e13),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h3(e13),h1(e13)) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h3(e13),h2(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h3(e13),h3(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h1(e13)) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h2(e13)) ) )
<=> ~ ~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) != op2(h1(e13),h3(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) != op2(h1(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) != op2(h2(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(h2(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) != op2(h1(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),e13)) != op2(h1(e13),h4(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(h2(e13),h3(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),e13)) != op2(h2(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) != op2(h3(e13),h1(e13)) )
| ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op2(h3(e13),h2(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,e13))) != op2(h3(e13),h3(e13)) )
| ( h4(op1(e13,op1(e13,op1(e13,e13)))) != op2(h4(e13),h1(e13)) )
| ( h4(op1(e13,op1(op1(e13,e13),e13))) != op2(h4(e13),h2(e13)) ) ) ),
inference(monotonicity,[status(thm)],[1727]) ).
tff(1729,plain,
( ~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h1(e13),h1(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h1(e13),h2(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h1(e13),h3(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h1(e13),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h2(e13),h1(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(e13),h2(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(e13),h3(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(e13),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h3(e13),h1(e13)) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h3(e13),h2(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h3(e13),h3(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h1(e13)) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h2(e13)) ) )
<=> ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) != op2(h1(e13),h3(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) != op2(h1(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) != op2(h2(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(h2(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) != op2(h1(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),e13)) != op2(h1(e13),h4(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(h2(e13),h3(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),e13)) != op2(h2(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) != op2(h3(e13),h1(e13)) )
| ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op2(h3(e13),h2(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,e13))) != op2(h3(e13),h3(e13)) )
| ( h4(op1(e13,op1(e13,op1(e13,e13)))) != op2(h4(e13),h1(e13)) )
| ( h4(op1(e13,op1(op1(e13,e13),e13))) != op2(h4(e13),h2(e13)) ) ) ),
inference(transitivity,[status(thm)],[1728,1726]) ).
tff(1730,plain,
( ~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h1(e13),h1(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h1(e13),h2(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h1(e13),h3(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h1(e13),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h2(e13),h1(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(e13),h2(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(e13),h3(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(e13),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h3(e13),h1(e13)) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h3(e13),h2(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h3(e13),h3(e13)) )
& ( h2(e13) = op2(h3(e13),h4(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h1(e13)) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h2(e13)) )
& ( h1(e13) = op2(h4(e13),h3(e13)) ) )
<=> ~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h1(e13),h1(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h1(e13),h2(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h1(e13),h3(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h1(e13),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h2(e13),h1(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(e13),h2(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(e13),h3(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(e13),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h3(e13),h1(e13)) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h3(e13),h2(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h3(e13),h3(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h1(e13)) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h2(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1731,plain,
( ~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h4(op1(e13,op1(e13,e13))),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h4(op1(op1(e13,e13),e13)),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h4(op1(e13,e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,e13),e13)) = op2(h4(op1(e13,e13)),h4(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(op1(e13,e13))) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(e13,e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(e13) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
& ( ( h4(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),h4(e13)) )
| ( h4(e13) = op2(h4(e13),h4(e13)) ) ) )
<=> ~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h1(e13),h1(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h1(e13),h2(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h1(e13),h3(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h1(e13),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h2(e13),h1(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(e13),h2(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(e13),h3(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(e13),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h3(e13),h1(e13)) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h3(e13),h2(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h3(e13),h3(e13)) )
& ( h2(e13) = op2(h3(e13),h4(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h1(e13)) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h2(e13)) )
& ( h1(e13) = op2(h4(e13),h3(e13)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1732,plain,
( ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h4(op1(e13,op1(e13,e13))),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h4(op1(op1(e13,e13),e13)),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h4(op1(e13,e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,e13),e13)) = op2(h4(op1(e13,e13)),h4(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(op1(e13,e13))) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(e13,e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(e13) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
& ( ( h4(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),h4(e13)) )
| ( h4(e13) = op2(h4(e13),h4(e13)) ) ) )
<=> ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h4(op1(e13,op1(e13,e13))),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h4(op1(op1(e13,e13),e13)),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h4(op1(e13,e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,e13),e13)) = op2(h4(op1(e13,e13)),h4(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(op1(e13,e13))) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(e13,e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(e13) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
& ( ( h4(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),h4(e13)) )
| ( h4(e13) = op2(h4(e13),h4(e13)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1733,plain,
( ~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h4(op1(e13,op1(e13,e13))),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h4(op1(op1(e13,e13),e13)),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h4(op1(e13,e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,e13),e13)) = op2(h4(op1(e13,e13)),h4(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(op1(e13,e13))) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(e13,e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(e13) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
& ( ( h4(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),h4(e13)) )
| ( h4(e13) = op2(h4(e13),h4(e13)) ) ) )
<=> ~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h4(op1(e13,op1(e13,e13))),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h4(op1(op1(e13,e13),e13)),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h4(op1(e13,e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,e13),e13)) = op2(h4(op1(e13,e13)),h4(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(op1(e13,e13))) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(e13,e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(e13) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
& ( ( h4(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),h4(e13)) )
| ( h4(e13) = op2(h4(e13),h4(e13)) ) ) ) ),
inference(monotonicity,[status(thm)],[1732]) ).
tff(1734,plain,
( ~ ( ( 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(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h4(op1(e13,op1(e13,e13))),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h4(op1(op1(e13,e13),e13)),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h4(op1(e13,e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,e13),e13)) = op2(h4(op1(e13,e13)),h4(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(op1(e13,e13))) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(e13,e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(e13) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
& ( ( h4(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),h4(e13)) )
| ( h4(e13) = op2(h4(e13),h4(e13)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1735,plain,
( ~ ( ( 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(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 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1736,plain,
( ~ ( ( 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(e13) = e23 )
| ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = 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 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1737,plain,
( ( ( 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(e13) = e23 )
| ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = 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(e13) = e23 )
| ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1738,plain,
( ~ ( ( 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(e13) = e23 )
| ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = 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(e13) = e23 )
| ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 ) ) ) ),
inference(monotonicity,[status(thm)],[1737]) ).
tff(1739,plain,
( ~ ( ( 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 ) ) )
<=> ~ ( ( 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(e13) = e23 )
| ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(1740,axiom,
~ ( ( ( h1(op1(e10,e10)) = op2(h1(e10),h1(e10)) )
& ( h1(op1(e10,e11)) = op2(h1(e10),h1(e11)) )
& ( h1(op1(e10,e12)) = op2(h1(e10),h1(e12)) )
& ( h1(op1(e10,e13)) = op2(h1(e10),h1(e13)) )
& ( h1(op1(e11,e10)) = op2(h1(e11),h1(e10)) )
& ( h1(op1(e11,e11)) = op2(h1(e11),h1(e11)) )
& ( h1(op1(e11,e12)) = op2(h1(e11),h1(e12)) )
& ( h1(op1(e11,e13)) = op2(h1(e11),h1(e13)) )
& ( h1(op1(e12,e10)) = op2(h1(e12),h1(e10)) )
& ( h1(op1(e12,e11)) = op2(h1(e12),h1(e11)) )
& ( h1(op1(e12,e12)) = op2(h1(e12),h1(e12)) )
& ( h1(op1(e12,e13)) = op2(h1(e12),h1(e13)) )
& ( h1(op1(e13,e10)) = op2(h1(e13),h1(e10)) )
& ( h1(op1(e13,e11)) = op2(h1(e13),h1(e11)) )
& ( h1(op1(e13,e12)) = op2(h1(e13),h1(e12)) )
& ( h1(op1(e13,e13)) = op2(h1(e13),h1(e13)) )
& ( ( h1(e10) = e20 )
| ( h1(e11) = e20 )
| ( h1(e12) = e20 )
| ( h1(e13) = e20 ) )
& ( ( h1(e10) = e21 )
| ( h1(e11) = e21 )
| ( h1(e12) = e21 )
| ( h1(e13) = e21 ) )
& ( ( h1(e10) = e22 )
| ( h1(e11) = e22 )
| ( h1(e12) = e22 )
| ( h1(e13) = e22 ) )
& ( ( h1(e10) = e23 )
| ( h1(e11) = e23 )
| ( h1(e12) = e23 )
| ( h1(e13) = e23 ) ) )
| ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 )
| ( h2(e13) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
| ( ( h3(op1(e10,e10)) = op2(h3(e10),h3(e10)) )
& ( h3(op1(e10,e11)) = op2(h3(e10),h3(e11)) )
& ( h3(op1(e10,e12)) = op2(h3(e10),h3(e12)) )
& ( h3(op1(e10,e13)) = op2(h3(e10),h3(e13)) )
& ( h3(op1(e11,e10)) = op2(h3(e11),h3(e10)) )
& ( h3(op1(e11,e11)) = op2(h3(e11),h3(e11)) )
& ( h3(op1(e11,e12)) = op2(h3(e11),h3(e12)) )
& ( h3(op1(e11,e13)) = op2(h3(e11),h3(e13)) )
& ( h3(op1(e12,e10)) = op2(h3(e12),h3(e10)) )
& ( h3(op1(e12,e11)) = op2(h3(e12),h3(e11)) )
& ( h3(op1(e12,e12)) = op2(h3(e12),h3(e12)) )
& ( h3(op1(e12,e13)) = op2(h3(e12),h3(e13)) )
& ( h3(op1(e13,e10)) = op2(h3(e13),h3(e10)) )
& ( h3(op1(e13,e11)) = op2(h3(e13),h3(e11)) )
& ( h3(op1(e13,e12)) = op2(h3(e13),h3(e12)) )
& ( h3(op1(e13,e13)) = op2(h3(e13),h3(e13)) )
& ( ( h3(e10) = e20 )
| ( h3(e11) = e20 )
| ( h3(e12) = e20 )
| ( h3(e13) = e20 ) )
& ( ( h3(e10) = e21 )
| ( h3(e11) = e21 )
| ( h3(e12) = e21 )
| ( h3(e13) = e21 ) )
& ( ( h3(e10) = e22 )
| ( h3(e11) = e22 )
| ( h3(e12) = e22 )
| ( h3(e13) = e22 ) )
& ( ( h3(e10) = e23 )
| ( h3(e11) = e23 )
| ( h3(e12) = e23 )
| ( h3(e13) = e23 ) ) )
| ( ( h4(op1(e10,e10)) = op2(h4(e10),h4(e10)) )
& ( h4(op1(e10,e11)) = op2(h4(e10),h4(e11)) )
& ( h4(op1(e10,e12)) = op2(h4(e10),h4(e12)) )
& ( h4(op1(e10,e13)) = op2(h4(e10),h4(e13)) )
& ( h4(op1(e11,e10)) = op2(h4(e11),h4(e10)) )
& ( h4(op1(e11,e11)) = op2(h4(e11),h4(e11)) )
& ( h4(op1(e11,e12)) = op2(h4(e11),h4(e12)) )
& ( h4(op1(e11,e13)) = op2(h4(e11),h4(e13)) )
& ( h4(op1(e12,e10)) = op2(h4(e12),h4(e10)) )
& ( h4(op1(e12,e11)) = op2(h4(e12),h4(e11)) )
& ( h4(op1(e12,e12)) = op2(h4(e12),h4(e12)) )
& ( h4(op1(e12,e13)) = op2(h4(e12),h4(e13)) )
& ( h4(op1(e13,e10)) = op2(h4(e13),h4(e10)) )
& ( h4(op1(e13,e11)) = op2(h4(e13),h4(e11)) )
& ( h4(op1(e13,e12)) = op2(h4(e13),h4(e12)) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(e10) = e20 )
| ( h4(e11) = e20 )
| ( h4(e12) = e20 )
| ( h4(e13) = e20 ) )
& ( ( h4(e10) = e21 )
| ( h4(e11) = e21 )
| ( h4(e12) = e21 )
| ( h4(e13) = e21 ) )
& ( ( h4(e10) = e22 )
| ( h4(e11) = e22 )
| ( h4(e12) = e22 )
| ( h4(e13) = e22 ) )
& ( ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 )
| ( h4(e13) = e23 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(1741,plain,
~ ( ( 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 ) ) ),
inference(or_elim,[status(thm)],[1740]) ).
tff(1742,plain,
~ ( ( 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(e13) = e23 )
| ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[1741,1739]) ).
tff(1743,plain,
~ ( ( 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(e13) = e23 )
| ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[1742,1738]) ).
tff(1744,plain,
~ ( ( 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 ) ) ),
inference(modus_ponens,[status(thm)],[1743,1736]) ).
tff(1745,plain,
~ ( ( 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 ) ) ),
inference(modus_ponens,[status(thm)],[1744,1735]) ).
tff(1746,plain,
~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h4(op1(e13,op1(e13,e13))),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h4(op1(op1(e13,e13),e13)),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h4(op1(e13,e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,e13),e13)) = op2(h4(op1(e13,e13)),h4(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(op1(e13,e13))) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(e13,e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(e13) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
& ( ( h4(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),h4(e13)) )
| ( h4(e13) = op2(h4(e13),h4(e13)) ) ) ),
inference(modus_ponens,[status(thm)],[1745,1734]) ).
tff(1747,plain,
~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h4(op1(e13,op1(e13,e13))),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h4(op1(e13,op1(e13,e13))),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h4(op1(op1(e13,e13),e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h4(op1(op1(e13,e13),e13)),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h4(op1(e13,e13)),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h4(op1(e13,e13)),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h4(op1(e13,e13)),h4(op1(e13,e13))) )
& ( h4(op1(op1(e13,e13),e13)) = op2(h4(op1(e13,e13)),h4(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h4(op1(e13,op1(e13,e13)))) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h4(op1(op1(e13,e13),e13))) )
& ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(op1(e13,e13))) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(op1(e13,e13)) = op2(h4(e13),op2(h4(e13),h4(e13))) )
| ( h4(e13) = op2(h4(e13),op2(h4(e13),h4(e13))) ) )
& ( ( h4(op1(op1(e13,e13),e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(op1(e13,e13)) = op2(op2(h4(e13),h4(e13)),h4(e13)) )
| ( h4(e13) = op2(op2(h4(e13),h4(e13)),h4(e13)) ) )
& ( ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
| ( h4(op1(e13,op1(e13,e13))) = op2(h4(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),e13)) = op2(h4(e13),h4(e13)) )
| ( h4(e13) = op2(h4(e13),h4(e13)) ) ) ),
inference(modus_ponens,[status(thm)],[1746,1733]) ).
tff(1748,plain,
~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h1(e13),h1(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h1(e13),h2(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h1(e13),h3(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h1(e13),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h2(e13),h1(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(e13),h2(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(e13),h3(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(e13),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h3(e13),h1(e13)) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h3(e13),h2(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h3(e13),h3(e13)) )
& ( h2(e13) = op2(h3(e13),h4(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h1(e13)) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h2(e13)) )
& ( h1(e13) = op2(h4(e13),h3(e13)) ) ),
inference(modus_ponens,[status(thm)],[1747,1731]) ).
tff(1749,plain,
~ ( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) = op2(h1(e13),h1(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) = op2(h1(e13),h2(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) = op2(h1(e13),h3(e13)) )
& ( h4(op1(op1(e13,op1(e13,e13)),e13)) = op2(h1(e13),h4(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) = op2(h2(e13),h1(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) = op2(h2(e13),h2(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) = op2(h2(e13),h3(e13)) )
& ( h4(op1(op1(op1(e13,e13),e13),e13)) = op2(h2(e13),h4(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) = op2(h3(e13),h1(e13)) )
& ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) = op2(h3(e13),h2(e13)) )
& ( h4(op1(op1(e13,e13),op1(e13,e13))) = op2(h3(e13),h3(e13)) )
& ( h4(op1(e13,op1(e13,op1(e13,e13)))) = op2(h4(e13),h1(e13)) )
& ( h4(op1(e13,op1(op1(e13,e13),e13))) = op2(h4(e13),h2(e13)) ) ),
inference(modus_ponens,[status(thm)],[1748,1730]) ).
tff(1750,plain,
( ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,e13))) != op2(h1(e13),h3(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(e13,op1(e13,e13)))) != op2(h1(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,op1(e13,e13)))) != op2(h2(e13),h1(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(op1(e13,e13),e13))) != op2(h2(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),op1(op1(e13,e13),e13))) != op2(h1(e13),h2(e13)) )
| ( h4(op1(op1(e13,op1(e13,e13)),e13)) != op2(h1(e13),h4(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),op1(e13,e13))) != op2(h2(e13),h3(e13)) )
| ( h4(op1(op1(op1(e13,e13),e13),e13)) != op2(h2(e13),h4(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,op1(e13,e13)))) != op2(h3(e13),h1(e13)) )
| ( h4(op1(op1(e13,e13),op1(op1(e13,e13),e13))) != op2(h3(e13),h2(e13)) )
| ( h4(op1(op1(e13,e13),op1(e13,e13))) != op2(h3(e13),h3(e13)) )
| ( h4(op1(e13,op1(e13,op1(e13,e13)))) != op2(h4(e13),h1(e13)) )
| ( h4(op1(e13,op1(op1(e13,e13),e13))) != op2(h4(e13),h2(e13)) ) ),
inference(modus_ponens,[status(thm)],[1749,1729]) ).
tff(1751,plain,
$false,
inference(unit_resolution,[status(thm)],[1750,1725,1636,1507,1504,1501,1403,1265,1169,1037,984,762,479,363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG117+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 13:23:59 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------