%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG113+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 04:58:15 AM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 165
% Syntax : Number of formulae : 869 ( 264 unt; 0 typ; 0 def)
% Number of atoms : 11829 (11828 equ)
% Maximal formula atoms : 384 ( 13 avg)
% Number of connectives : 13828 (2868 ~;5799 |;4835 &)
% ( 326 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(e23_type,type,
e23: $i ).
tff(h8_type,type,
h8: $i > $i ).
tff(e13_type,type,
e13: $i ).
tff(e12_type,type,
e12: $i ).
tff(e11_type,type,
e11: $i ).
tff(e10_type,type,
e10: $i ).
tff(op2_type,type,
op2: ( $i * $i ) > $i ).
tff(e21_type,type,
e21: $i ).
tff(e22_type,type,
e22: $i ).
tff(e20_type,type,
e20: $i ).
tff(op1_type,type,
op1: ( $i * $i ) > $i ).
tff(h7_type,type,
h7: $i > $i ).
tff(h6_type,type,
h6: $i > $i ).
tff(h5_type,type,
h5: $i > $i ).
tff(h4_type,type,
h4: $i > $i ).
tff(h3_type,type,
h3: $i > $i ).
tff(h2_type,type,
h2: $i > $i ).
tff(h1_type,type,
h1: $i > $i ).
tff(h9_type,type,
h9: $i > $i ).
tff(h10_type,type,
h10: $i > $i ).
tff(h11_type,type,
h11: $i > $i ).
tff(h12_type,type,
h12: $i > $i ).
tff(1,plain,
( ( h8(e10) = op2(e22,e21) )
<=> ( h8(e10) = op2(e22,e21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( ( h8(e12) = e22 )
& ( h8(e13) = e21 )
& ( h8(e10) = op2(e22,e21) )
& ( h8(e11) = op2(op2(e22,e21),e21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
tff(3,plain,
( ( h8(e12) = e22 )
& ( h8(e13) = e21 )
& ( h8(e10) = op2(e22,e21) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
h8(e10) = op2(e22,e21),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
h8(e10) = op2(e22,e21),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( ( h8(e10) = e23 )
<=> ( op2(e22,e21) = e23 ) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( ( op2(e22,e21) = e23 )
<=> ( h8(e10) = e23 ) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( ( e21 = op2(e22,e21) )
<=> ( op2(e22,e21) = e21 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(9,plain,
( ( op2(e21,e21) = e21 )
<=> ( op2(e21,e21) = e21 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
( ( op2(e20,e20) = e20 )
& ( op2(e21,e21) = e21 )
& ( op2(e22,e22) = e22 )
& ( op2(e23,e23) = e23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
tff(11,plain,
( ( op2(e20,e20) = e20 )
& ( op2(e21,e21) = e21 )
& ( op2(e22,e22) = e22 ) ),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
( ( op2(e20,e20) = e20 )
& ( op2(e21,e21) = e21 ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
op2(e21,e21) = e21,
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
op2(e21,e21) = e21,
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( op2(e21,e21) = op2(e22,e21) )
<=> ( e21 = op2(e22,e21) ) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ( op2(e21,e21) = op2(e22,e21) )
<=> ( op2(e22,e21) = e21 ) ),
inference(transitivity,[status(thm)],[15,8]) ).
tff(17,plain,
( ( op2(e21,e21) != op2(e22,e21) )
<=> ( op2(e22,e21) != e21 ) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ( op2(e21,e21) != op2(e22,e21) )
<=> ( op2(e21,e21) != op2(e22,e21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,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(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) )
& ( 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)],[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) )
& ( 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)],[20]) ).
tff(22,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) )
& ( op2(e22,e22) != op2(e22,e23) )
& ( op2(e23,e20) != op2(e23,e21) )
& ( op2(e23,e20) != op2(e23,e22) )
& ( op2(e23,e20) != op2(e23,e23) ) ),
inference(and_elim,[status(thm)],[21]) ).
tff(23,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) )
& ( op2(e22,e22) != op2(e22,e23) )
& ( op2(e23,e20) != op2(e23,e21) )
& ( op2(e23,e20) != op2(e23,e22) ) ),
inference(and_elim,[status(thm)],[22]) ).
tff(24,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) )
& ( op2(e22,e22) != op2(e22,e23) )
& ( op2(e23,e20) != op2(e23,e21) ) ),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) )
& ( op2(e22,e22) != op2(e22,e23) ) ),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) )
& ( op2(e22,e21) != op2(e22,e23) ) ),
inference(and_elim,[status(thm)],[25]) ).
tff(27,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) )
& ( op2(e22,e21) != op2(e22,e22) ) ),
inference(and_elim,[status(thm)],[26]) ).
tff(28,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) )
& ( op2(e22,e20) != op2(e22,e23) ) ),
inference(and_elim,[status(thm)],[27]) ).
tff(29,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) )
& ( op2(e22,e20) != op2(e22,e22) ) ),
inference(and_elim,[status(thm)],[28]) ).
tff(30,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) )
& ( op2(e22,e20) != op2(e22,e21) ) ),
inference(and_elim,[status(thm)],[29]) ).
tff(31,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) )
& ( op2(e21,e22) != op2(e21,e23) ) ),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) )
& ( op2(e21,e21) != op2(e21,e23) ) ),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) )
& ( op2(e21,e21) != op2(e21,e22) ) ),
inference(and_elim,[status(thm)],[32]) ).
tff(34,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) )
& ( op2(e21,e20) != op2(e21,e23) ) ),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) )
& ( op2(e21,e20) != op2(e21,e22) ) ),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) )
& ( op2(e21,e20) != op2(e21,e21) ) ),
inference(and_elim,[status(thm)],[35]) ).
tff(37,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) )
& ( op2(e20,e22) != op2(e20,e23) ) ),
inference(and_elim,[status(thm)],[36]) ).
tff(38,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) )
& ( op2(e20,e21) != op2(e20,e23) ) ),
inference(and_elim,[status(thm)],[37]) ).
tff(39,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) )
& ( op2(e20,e21) != op2(e20,e22) ) ),
inference(and_elim,[status(thm)],[38]) ).
tff(40,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) )
& ( op2(e20,e20) != op2(e20,e23) ) ),
inference(and_elim,[status(thm)],[39]) ).
tff(41,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) )
& ( op2(e20,e20) != op2(e20,e22) ) ),
inference(and_elim,[status(thm)],[40]) ).
tff(42,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) )
& ( op2(e20,e20) != op2(e20,e21) ) ),
inference(and_elim,[status(thm)],[41]) ).
tff(43,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) )
& ( op2(e22,e23) != op2(e23,e23) ) ),
inference(and_elim,[status(thm)],[42]) ).
tff(44,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) )
& ( op2(e21,e23) != op2(e23,e23) ) ),
inference(and_elim,[status(thm)],[43]) ).
tff(45,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) )
& ( op2(e21,e23) != op2(e22,e23) ) ),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) )
& ( op2(e20,e23) != op2(e23,e23) ) ),
inference(and_elim,[status(thm)],[45]) ).
tff(47,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) )
& ( op2(e20,e23) != op2(e22,e23) ) ),
inference(and_elim,[status(thm)],[46]) ).
tff(48,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) )
& ( op2(e20,e23) != op2(e21,e23) ) ),
inference(and_elim,[status(thm)],[47]) ).
tff(49,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) )
& ( op2(e22,e22) != op2(e23,e22) ) ),
inference(and_elim,[status(thm)],[48]) ).
tff(50,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) )
& ( op2(e21,e22) != op2(e23,e22) ) ),
inference(and_elim,[status(thm)],[49]) ).
tff(51,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) )
& ( op2(e21,e22) != op2(e22,e22) ) ),
inference(and_elim,[status(thm)],[50]) ).
tff(52,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) )
& ( op2(e20,e22) != op2(e23,e22) ) ),
inference(and_elim,[status(thm)],[51]) ).
tff(53,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) )
& ( op2(e20,e22) != op2(e22,e22) ) ),
inference(and_elim,[status(thm)],[52]) ).
tff(54,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) )
& ( op2(e20,e22) != op2(e21,e22) ) ),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) )
& ( op2(e22,e21) != op2(e23,e21) ) ),
inference(and_elim,[status(thm)],[54]) ).
tff(56,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) )
& ( op2(e21,e21) != op2(e23,e21) ) ),
inference(and_elim,[status(thm)],[55]) ).
tff(57,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) )
& ( op2(e21,e20) != op2(e22,e20) )
& ( op2(e21,e20) != op2(e23,e20) )
& ( op2(e22,e20) != op2(e23,e20) )
& ( op2(e20,e21) != op2(e21,e21) )
& ( op2(e20,e21) != op2(e22,e21) )
& ( op2(e20,e21) != op2(e23,e21) )
& ( op2(e21,e21) != op2(e22,e21) ) ),
inference(and_elim,[status(thm)],[56]) ).
tff(58,plain,
op2(e21,e21) != op2(e22,e21),
inference(and_elim,[status(thm)],[57]) ).
tff(59,plain,
op2(e21,e21) != op2(e22,e21),
inference(modus_ponens,[status(thm)],[58,18]) ).
tff(60,plain,
op2(e22,e21) != e21,
inference(modus_ponens,[status(thm)],[59,17]) ).
tff(61,plain,
( ( op2(e22,e22) = e22 )
<=> ( op2(e22,e22) = e22 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
op2(e22,e22) = e22,
inference(and_elim,[status(thm)],[11]) ).
tff(63,plain,
op2(e22,e22) = e22,
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ( op2(e22,e21) = op2(e22,e22) )
<=> ( op2(e22,e21) = e22 ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( op2(e22,e21) != op2(e22,e22) )
<=> ( op2(e22,e21) != e22 ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( op2(e22,e21) != op2(e22,e22) )
<=> ( op2(e22,e21) != op2(e22,e22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
op2(e22,e21) != op2(e22,e22),
inference(and_elim,[status(thm)],[27]) ).
tff(68,plain,
op2(e22,e21) != op2(e22,e22),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
op2(e22,e21) != e22,
inference(modus_ponens,[status(thm)],[68,65]) ).
tff(70,plain,
( ( e20 = op2(e22,e23) )
<=> ( e20 = op2(e22,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
( ( e20 = op2(e22,e23) )
& ( e21 = op2(op2(e22,e23),e23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
tff(72,plain,
e20 = op2(e22,e23),
inference(and_elim,[status(thm)],[71]) ).
tff(73,plain,
e20 = op2(e22,e23),
inference(modus_ponens,[status(thm)],[72,70]) ).
tff(74,plain,
op2(e22,e23) = e20,
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ( op2(e22,e21) = op2(e22,e23) )
<=> ( op2(e22,e21) = e20 ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( op2(e22,e21) != op2(e22,e23) )
<=> ( op2(e22,e21) != e20 ) ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ( op2(e22,e21) != op2(e22,e23) )
<=> ( op2(e22,e21) != op2(e22,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
op2(e22,e21) != op2(e22,e23),
inference(and_elim,[status(thm)],[26]) ).
tff(79,plain,
op2(e22,e21) != op2(e22,e23),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
op2(e22,e21) != e20,
inference(modus_ponens,[status(thm)],[79,76]) ).
tff(81,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
<=> ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
<=> ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 ) )
<=> ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
<=> ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) )
<=> ( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,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(87,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)],[86]) ).
tff(88,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)],[87]) ).
tff(89,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)],[88]) ).
tff(90,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)],[89]) ).
tff(91,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)],[90]) ).
tff(92,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)],[91]) ).
tff(93,plain,
( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ),
inference(and_elim,[status(thm)],[92]) ).
tff(94,plain,
( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ),
inference(modus_ponens,[status(thm)],[93,85]) ).
tff(95,plain,
( ( op2(e22,e21) = e20 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e21) = e22 )
| ( op2(e22,e21) = e23 ) ),
inference(modus_ponens,[status(thm)],[94,81]) ).
tff(96,plain,
op2(e22,e21) = e23,
inference(unit_resolution,[status(thm)],[95,80,69,60]) ).
tff(97,plain,
h8(e10) = e23,
inference(modus_ponens,[status(thm)],[96,7]) ).
tff(98,plain,
( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 )
| ( h8(e10) != e23 ) ),
inference(tautology,[status(thm)],[]) ).
tff(99,plain,
( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
( ( e20 = op2(e20,e21) )
<=> ( op2(e20,e21) = e20 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(101,plain,
( ( op2(e20,e20) = e20 )
<=> ( op2(e20,e20) = e20 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
op2(e20,e20) = e20,
inference(and_elim,[status(thm)],[12]) ).
tff(103,plain,
op2(e20,e20) = e20,
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
( ( op2(e20,e20) = op2(e20,e21) )
<=> ( e20 = op2(e20,e21) ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( ( op2(e20,e20) = op2(e20,e21) )
<=> ( op2(e20,e21) = e20 ) ),
inference(transitivity,[status(thm)],[104,100]) ).
tff(106,plain,
( ( op2(e20,e20) != op2(e20,e21) )
<=> ( op2(e20,e21) != e20 ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( op2(e20,e20) != op2(e20,e21) )
<=> ( op2(e20,e20) != op2(e20,e21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
op2(e20,e20) != op2(e20,e21),
inference(and_elim,[status(thm)],[42]) ).
tff(109,plain,
op2(e20,e20) != op2(e20,e21),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
op2(e20,e21) != e20,
inference(modus_ponens,[status(thm)],[109,106]) ).
tff(111,plain,
( ( e21 = e20 )
<=> ( e20 = e21 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(112,plain,
( ( op2(e21,e21) = e20 )
<=> ( e21 = e20 ) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(113,plain,
( ( op2(e21,e21) = e20 )
<=> ( e20 = e21 ) ),
inference(transitivity,[status(thm)],[112,111]) ).
tff(114,plain,
( ( e20 = e21 )
<=> ( op2(e21,e21) = e20 ) ),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
( ( e20 != e21 )
<=> ( op2(e21,e21) != e20 ) ),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ( e20 != e21 )
<=> ( e20 != e21 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,axiom,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 )
& ( e21 != e23 )
& ( e22 != e23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
tff(118,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 )
& ( e21 != e23 ) ),
inference(and_elim,[status(thm)],[117]) ).
tff(119,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 ) ),
inference(and_elim,[status(thm)],[118]) ).
tff(120,plain,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 ) ),
inference(and_elim,[status(thm)],[119]) ).
tff(121,plain,
( ( e20 != e21 )
& ( e20 != e22 ) ),
inference(and_elim,[status(thm)],[120]) ).
tff(122,plain,
e20 != e21,
inference(and_elim,[status(thm)],[121]) ).
tff(123,plain,
e20 != e21,
inference(modus_ponens,[status(thm)],[122,116]) ).
tff(124,plain,
op2(e21,e21) != e20,
inference(modus_ponens,[status(thm)],[123,115]) ).
tff(125,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
<=> ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
<=> ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 ) )
<=> ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
<=> ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
<=> ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ) ),
inference(transitivity,[status(thm)],[128,126]) ).
tff(130,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(131,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( op2(e20,e21) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e22,e21) = e22 )
| ( op2(e23,e21) = e22 ) )
& ( ( 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)],[130]) ).
tff(132,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( op2(e21,e20) = e22 )
| ( op2(e21,e21) = e22 )
| ( op2(e21,e22) = e22 )
| ( op2(e21,e23) = e22 ) )
& ( ( 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)],[131]) ).
tff(133,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( op2(e20,e21) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e23,e21) = e21 ) )
& ( ( 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)],[132]) ).
tff(134,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( op2(e21,e20) = e21 )
| ( op2(e21,e21) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e21,e23) = e21 ) )
& ( ( 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)],[133]) ).
tff(135,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) )
& ( ( 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)],[134]) ).
tff(136,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e21) = e20 )
| ( op2(e20,e22) = e20 )
| ( op2(e20,e23) = e20 ) )
& ( ( op2(e20,e20) = e20 )
| ( op2(e21,e20) = e20 )
| ( op2(e22,e20) = e20 )
| ( op2(e23,e20) = e20 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e23) = e21 ) )
& ( ( op2(e20,e20) = e21 )
| ( op2(e21,e20) = e21 )
| ( op2(e22,e20) = e21 )
| ( op2(e23,e20) = e21 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
& ( ( op2(e20,e20) = e22 )
| ( op2(e21,e20) = e22 )
| ( op2(e22,e20) = e22 )
| ( op2(e23,e20) = e22 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e20,e21) = e23 )
| ( op2(e20,e22) = e23 )
| ( op2(e20,e23) = e23 ) )
& ( ( op2(e20,e20) = e23 )
| ( op2(e21,e20) = e23 )
| ( op2(e22,e20) = e23 )
| ( op2(e23,e20) = e23 ) )
& ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
& ( ( 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)],[135]) ).
tff(137,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)],[136]) ).
tff(138,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)],[137]) ).
tff(139,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)],[138]) ).
tff(140,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)],[139]) ).
tff(141,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)],[140]) ).
tff(142,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)],[141]) ).
tff(143,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)],[142]) ).
tff(144,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)],[143]) ).
tff(145,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)],[144]) ).
tff(146,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)],[145]) ).
tff(147,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)],[146]) ).
tff(148,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)],[147]) ).
tff(149,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)],[148]) ).
tff(150,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)],[149]) ).
tff(151,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)],[150]) ).
tff(152,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)],[151]) ).
tff(153,plain,
( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ),
inference(and_elim,[status(thm)],[152]) ).
tff(154,plain,
( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ),
inference(modus_ponens,[status(thm)],[153,129]) ).
tff(155,plain,
( ( op2(e20,e21) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e22,e21) = e20 )
| ( op2(e23,e21) = e20 ) ),
inference(modus_ponens,[status(thm)],[154,125]) ).
tff(156,plain,
op2(e23,e21) = e20,
inference(unit_resolution,[status(thm)],[155,124,80,110]) ).
tff(157,plain,
op2(op2(e22,e21),e21) = op2(e23,e21),
inference(monotonicity,[status(thm)],[96]) ).
tff(158,plain,
( ( h8(e11) = op2(op2(e22,e21),e21) )
<=> ( h8(e11) = op2(op2(e22,e21),e21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,plain,
h8(e11) = op2(op2(e22,e21),e21),
inference(and_elim,[status(thm)],[2]) ).
tff(160,plain,
h8(e11) = op2(op2(e22,e21),e21),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
h8(e11) = e20,
inference(transitivity,[status(thm)],[160,157,156]) ).
tff(162,plain,
( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 )
| ( h8(e11) != e20 ) ),
inference(tautology,[status(thm)],[]) ).
tff(163,plain,
( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) ),
inference(unit_resolution,[status(thm)],[162,161]) ).
tff(164,plain,
( ( h8(e13) = e21 )
<=> ( h8(e13) = e21 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,plain,
( ( h8(e12) = e22 )
& ( h8(e13) = e21 ) ),
inference(and_elim,[status(thm)],[3]) ).
tff(166,plain,
h8(e13) = e21,
inference(and_elim,[status(thm)],[165]) ).
tff(167,plain,
h8(e13) = e21,
inference(modus_ponens,[status(thm)],[166,164]) ).
tff(168,plain,
op2(h8(e13),h8(e13)) = op2(e21,e21),
inference(monotonicity,[status(thm)],[167,167]) ).
tff(169,plain,
op2(e21,e21) = op2(h8(e13),h8(e13)),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
e21 = op2(e21,e21),
inference(symmetry,[status(thm)],[14]) ).
tff(171,plain,
( ( op1(e13,e13) = e13 )
<=> ( op1(e13,e13) = e13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,axiom,
( ( op1(e10,e10) = e10 )
& ( op1(e11,e11) = e11 )
& ( op1(e12,e12) = e12 )
& ( op1(e13,e13) = e13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
tff(173,plain,
op1(e13,e13) = e13,
inference(and_elim,[status(thm)],[172]) ).
tff(174,plain,
op1(e13,e13) = e13,
inference(modus_ponens,[status(thm)],[173,171]) ).
tff(175,plain,
h8(op1(e13,e13)) = h8(e13),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
h8(op1(e13,e13)) = op2(h8(e13),h8(e13)),
inference(transitivity,[status(thm)],[175,167,170,169]) ).
tff(177,plain,
( ( h8(e12) = e22 )
<=> ( h8(e12) = e22 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,plain,
h8(e12) = e22,
inference(and_elim,[status(thm)],[165]) ).
tff(179,plain,
h8(e12) = e22,
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
op2(h8(e13),h8(e12)) = op2(e21,e22),
inference(monotonicity,[status(thm)],[167,179]) ).
tff(181,plain,
op2(e21,e22) = op2(h8(e13),h8(e12)),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
( ( op2(e21,e23) = op2(e22,e23) )
<=> ( op2(e21,e23) = e20 ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(183,plain,
( ( op2(e21,e23) != op2(e22,e23) )
<=> ( op2(e21,e23) != e20 ) ),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
( ( op2(e21,e23) != op2(e22,e23) )
<=> ( op2(e21,e23) != op2(e22,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(185,plain,
op2(e21,e23) != op2(e22,e23),
inference(and_elim,[status(thm)],[45]) ).
tff(186,plain,
op2(e21,e23) != op2(e22,e23),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
op2(e21,e23) != e20,
inference(modus_ponens,[status(thm)],[186,183]) ).
tff(188,plain,
( ( e20 = op2(e21,e20) )
<=> ( op2(e21,e20) = e20 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(189,plain,
( ( op2(e20,e20) = op2(e21,e20) )
<=> ( e20 = op2(e21,e20) ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(190,plain,
( ( op2(e20,e20) = op2(e21,e20) )
<=> ( op2(e21,e20) = e20 ) ),
inference(transitivity,[status(thm)],[189,188]) ).
tff(191,plain,
( ( op2(e20,e20) != op2(e21,e20) )
<=> ( op2(e21,e20) != e20 ) ),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
( ( op2(e20,e20) != op2(e21,e20) )
<=> ( op2(e20,e20) != op2(e21,e20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(193,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)],[57]) ).
tff(194,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)],[193]) ).
tff(195,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)],[194]) ).
tff(196,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)],[195]) ).
tff(197,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)],[196]) ).
tff(198,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)],[197]) ).
tff(199,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) )
& ( op2(e20,e20) != op2(e23,e20) ) ),
inference(and_elim,[status(thm)],[198]) ).
tff(200,plain,
( ( op2(e20,e20) != op2(e21,e20) )
& ( op2(e20,e20) != op2(e22,e20) ) ),
inference(and_elim,[status(thm)],[199]) ).
tff(201,plain,
op2(e20,e20) != op2(e21,e20),
inference(and_elim,[status(thm)],[200]) ).
tff(202,plain,
op2(e20,e20) != op2(e21,e20),
inference(modus_ponens,[status(thm)],[201,192]) ).
tff(203,plain,
op2(e21,e20) != e20,
inference(modus_ponens,[status(thm)],[202,191]) ).
tff(204,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(206,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ) ),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
( ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) )
<=> ( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ) ),
inference(transitivity,[status(thm)],[207,205]) ).
tff(209,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)],[152]) ).
tff(210,plain,
( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ),
inference(and_elim,[status(thm)],[209]) ).
tff(211,plain,
( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[210,208]) ).
tff(212,plain,
( ( op2(e21,e20) = e20 )
| ( op2(e21,e21) = e20 )
| ( op2(e21,e22) = e20 )
| ( op2(e21,e23) = e20 ) ),
inference(modus_ponens,[status(thm)],[211,204]) ).
tff(213,plain,
op2(e21,e22) = e20,
inference(unit_resolution,[status(thm)],[212,124,203,187]) ).
tff(214,plain,
e20 = op2(e21,e22),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
( ( e11 = op1(e11,e12) )
<=> ( op1(e11,e12) = e11 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(216,plain,
( ( op1(e11,e11) = e11 )
<=> ( op1(e11,e11) = e11 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(217,plain,
( ( op1(e10,e10) = e10 )
& ( op1(e11,e11) = e11 )
& ( op1(e12,e12) = e12 ) ),
inference(and_elim,[status(thm)],[172]) ).
tff(218,plain,
( ( op1(e10,e10) = e10 )
& ( op1(e11,e11) = e11 ) ),
inference(and_elim,[status(thm)],[217]) ).
tff(219,plain,
op1(e11,e11) = e11,
inference(and_elim,[status(thm)],[218]) ).
tff(220,plain,
op1(e11,e11) = e11,
inference(modus_ponens,[status(thm)],[219,216]) ).
tff(221,plain,
( ( op1(e11,e11) = op1(e11,e12) )
<=> ( e11 = op1(e11,e12) ) ),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
( ( op1(e11,e11) = op1(e11,e12) )
<=> ( op1(e11,e12) = e11 ) ),
inference(transitivity,[status(thm)],[221,215]) ).
tff(223,plain,
( ( op1(e11,e11) != op1(e11,e12) )
<=> ( op1(e11,e12) != e11 ) ),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
( ( op1(e11,e11) != op1(e11,e12) )
<=> ( op1(e11,e11) != op1(e11,e12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(225,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(226,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) )
& ( op1(e13,e10) != op1(e13,e11) )
& ( op1(e13,e10) != op1(e13,e12) )
& ( op1(e13,e10) != op1(e13,e13) )
& ( op1(e13,e11) != op1(e13,e12) )
& ( op1(e13,e11) != op1(e13,e13) ) ),
inference(and_elim,[status(thm)],[225]) ).
tff(227,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) )
& ( op1(e13,e10) != op1(e13,e11) )
& ( op1(e13,e10) != op1(e13,e12) )
& ( op1(e13,e10) != op1(e13,e13) )
& ( op1(e13,e11) != op1(e13,e12) ) ),
inference(and_elim,[status(thm)],[226]) ).
tff(228,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) )
& ( op1(e13,e10) != op1(e13,e11) )
& ( op1(e13,e10) != op1(e13,e12) )
& ( op1(e13,e10) != op1(e13,e13) ) ),
inference(and_elim,[status(thm)],[227]) ).
tff(229,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) )
& ( op1(e13,e10) != op1(e13,e11) )
& ( op1(e13,e10) != op1(e13,e12) ) ),
inference(and_elim,[status(thm)],[228]) ).
tff(230,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) )
& ( op1(e13,e10) != op1(e13,e11) ) ),
inference(and_elim,[status(thm)],[229]) ).
tff(231,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) )
& ( op1(e12,e12) != op1(e12,e13) ) ),
inference(and_elim,[status(thm)],[230]) ).
tff(232,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) )
& ( op1(e12,e11) != op1(e12,e13) ) ),
inference(and_elim,[status(thm)],[231]) ).
tff(233,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) )
& ( op1(e12,e11) != op1(e12,e12) ) ),
inference(and_elim,[status(thm)],[232]) ).
tff(234,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) )
& ( op1(e12,e10) != op1(e12,e13) ) ),
inference(and_elim,[status(thm)],[233]) ).
tff(235,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) )
& ( op1(e12,e10) != op1(e12,e12) ) ),
inference(and_elim,[status(thm)],[234]) ).
tff(236,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) )
& ( op1(e12,e10) != op1(e12,e11) ) ),
inference(and_elim,[status(thm)],[235]) ).
tff(237,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) )
& ( op1(e11,e12) != op1(e11,e13) ) ),
inference(and_elim,[status(thm)],[236]) ).
tff(238,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) )
& ( op1(e11,e11) != op1(e11,e13) ) ),
inference(and_elim,[status(thm)],[237]) ).
tff(239,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) )
& ( op1(e11,e10) != op1(e12,e10) )
& ( op1(e11,e10) != op1(e13,e10) )
& ( op1(e12,e10) != op1(e13,e10) )
& ( op1(e10,e11) != op1(e11,e11) )
& ( op1(e10,e11) != op1(e12,e11) )
& ( op1(e10,e11) != op1(e13,e11) )
& ( op1(e11,e11) != op1(e12,e11) )
& ( op1(e11,e11) != op1(e13,e11) )
& ( op1(e12,e11) != op1(e13,e11) )
& ( op1(e10,e12) != op1(e11,e12) )
& ( op1(e10,e12) != op1(e12,e12) )
& ( op1(e10,e12) != op1(e13,e12) )
& ( op1(e11,e12) != op1(e12,e12) )
& ( op1(e11,e12) != op1(e13,e12) )
& ( op1(e12,e12) != op1(e13,e12) )
& ( op1(e10,e13) != op1(e11,e13) )
& ( op1(e10,e13) != op1(e12,e13) )
& ( op1(e10,e13) != op1(e13,e13) )
& ( op1(e11,e13) != op1(e12,e13) )
& ( op1(e11,e13) != op1(e13,e13) )
& ( op1(e12,e13) != op1(e13,e13) )
& ( op1(e10,e10) != op1(e10,e11) )
& ( op1(e10,e10) != op1(e10,e12) )
& ( op1(e10,e10) != op1(e10,e13) )
& ( op1(e10,e11) != op1(e10,e12) )
& ( op1(e10,e11) != op1(e10,e13) )
& ( op1(e10,e12) != op1(e10,e13) )
& ( op1(e11,e10) != op1(e11,e11) )
& ( op1(e11,e10) != op1(e11,e12) )
& ( op1(e11,e10) != op1(e11,e13) )
& ( op1(e11,e11) != op1(e11,e12) ) ),
inference(and_elim,[status(thm)],[238]) ).
tff(240,plain,
op1(e11,e11) != op1(e11,e12),
inference(and_elim,[status(thm)],[239]) ).
tff(241,plain,
op1(e11,e11) != op1(e11,e12),
inference(modus_ponens,[status(thm)],[240,224]) ).
tff(242,plain,
op1(e11,e12) != e11,
inference(modus_ponens,[status(thm)],[241,223]) ).
tff(243,plain,
( ( e12 = e11 )
<=> ( e11 = e12 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(244,plain,
( ( op1(e12,e12) = e12 )
<=> ( op1(e12,e12) = e12 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(245,plain,
op1(e12,e12) = e12,
inference(and_elim,[status(thm)],[217]) ).
tff(246,plain,
op1(e12,e12) = e12,
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
( ( op1(e12,e12) = e11 )
<=> ( e12 = e11 ) ),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
( ( op1(e12,e12) = e11 )
<=> ( e11 = e12 ) ),
inference(transitivity,[status(thm)],[247,243]) ).
tff(249,plain,
( ( e11 = e12 )
<=> ( op1(e12,e12) = e11 ) ),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
( ( e11 != e12 )
<=> ( op1(e12,e12) != e11 ) ),
inference(monotonicity,[status(thm)],[249]) ).
tff(251,plain,
( ( e11 != e12 )
<=> ( e11 != e12 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(252,axiom,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 )
& ( e11 != e13 )
& ( e12 != e13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
tff(253,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 )
& ( e11 != e13 ) ),
inference(and_elim,[status(thm)],[252]) ).
tff(254,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 )
& ( e11 != e12 ) ),
inference(and_elim,[status(thm)],[253]) ).
tff(255,plain,
e11 != e12,
inference(and_elim,[status(thm)],[254]) ).
tff(256,plain,
e11 != e12,
inference(modus_ponens,[status(thm)],[255,251]) ).
tff(257,plain,
op1(e12,e12) != e11,
inference(modus_ponens,[status(thm)],[256,250]) ).
tff(258,plain,
( ( e11 = op1(op1(e12,e13),e13) )
<=> ( e11 = op1(op1(e12,e13),e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(259,axiom,
( ( e10 = op1(e12,e13) )
& ( e11 = op1(op1(e12,e13),e13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).
tff(260,plain,
e11 = op1(op1(e12,e13),e13),
inference(and_elim,[status(thm)],[259]) ).
tff(261,plain,
e11 = op1(op1(e12,e13),e13),
inference(modus_ponens,[status(thm)],[260,258]) ).
tff(262,plain,
op1(op1(e12,e13),e13) = e11,
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
( ( e10 = op1(e12,e13) )
<=> ( e10 = op1(e12,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(264,plain,
e10 = op1(e12,e13),
inference(and_elim,[status(thm)],[259]) ).
tff(265,plain,
e10 = op1(e12,e13),
inference(modus_ponens,[status(thm)],[264,263]) ).
tff(266,plain,
op1(e10,e13) = op1(op1(e12,e13),e13),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
op1(e10,e13) = e11,
inference(transitivity,[status(thm)],[266,262]) ).
tff(268,plain,
( ( op1(e10,e12) = op1(e10,e13) )
<=> ( op1(e10,e12) = e11 ) ),
inference(monotonicity,[status(thm)],[267]) ).
tff(269,plain,
( ( op1(e10,e12) != op1(e10,e13) )
<=> ( op1(e10,e12) != e11 ) ),
inference(monotonicity,[status(thm)],[268]) ).
tff(270,plain,
( ( op1(e10,e12) != op1(e10,e13) )
<=> ( op1(e10,e12) != op1(e10,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(271,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)],[239]) ).
tff(272,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)],[271]) ).
tff(273,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)],[272]) ).
tff(274,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)],[273]) ).
tff(275,plain,
op1(e10,e12) != op1(e10,e13),
inference(and_elim,[status(thm)],[274]) ).
tff(276,plain,
op1(e10,e12) != op1(e10,e13),
inference(modus_ponens,[status(thm)],[275,270]) ).
tff(277,plain,
op1(e10,e12) != e11,
inference(modus_ponens,[status(thm)],[276,269]) ).
tff(278,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(279,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(280,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(281,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)],[280]) ).
tff(282,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)],[281,279]) ).
tff(283,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(284,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)],[283]) ).
tff(285,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)],[284]) ).
tff(286,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)],[285]) ).
tff(287,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)],[286]) ).
tff(288,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)],[287]) ).
tff(289,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)],[288]) ).
tff(290,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)],[289]) ).
tff(291,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)],[290]) ).
tff(292,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)],[291]) ).
tff(293,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)],[292]) ).
tff(294,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)],[293]) ).
tff(295,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)],[294]) ).
tff(296,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(and_elim,[status(thm)],[295]) ).
tff(297,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(modus_ponens,[status(thm)],[296,282]) ).
tff(298,plain,
( ( op1(e10,e12) = e11 )
| ( op1(e11,e12) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e13,e12) = e11 ) ),
inference(modus_ponens,[status(thm)],[297,278]) ).
tff(299,plain,
op1(e13,e12) = e11,
inference(unit_resolution,[status(thm)],[298,277,257,242]) ).
tff(300,plain,
h8(op1(e13,e12)) = h8(e11),
inference(monotonicity,[status(thm)],[299]) ).
tff(301,plain,
h8(op1(e13,e12)) = op2(h8(e13),h8(e12)),
inference(transitivity,[status(thm)],[300,160,157,156,214,181]) ).
tff(302,plain,
( ( e23 = op2(e21,e20) )
<=> ( op2(e21,e20) = e23 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(303,plain,
op2(h8(e13),h8(e11)) = op2(e21,e20),
inference(monotonicity,[status(thm)],[167,161]) ).
tff(304,plain,
( ( e10 = op1(e10,e11) )
<=> ( op1(e10,e11) = e10 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(305,plain,
( ( op1(e10,e10) = e10 )
<=> ( op1(e10,e10) = e10 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(306,plain,
op1(e10,e10) = e10,
inference(and_elim,[status(thm)],[218]) ).
tff(307,plain,
op1(e10,e10) = e10,
inference(modus_ponens,[status(thm)],[306,305]) ).
tff(308,plain,
( ( op1(e10,e10) = op1(e10,e11) )
<=> ( e10 = op1(e10,e11) ) ),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
( ( op1(e10,e10) = op1(e10,e11) )
<=> ( op1(e10,e11) = e10 ) ),
inference(transitivity,[status(thm)],[308,304]) ).
tff(310,plain,
( ( op1(e10,e10) != op1(e10,e11) )
<=> ( op1(e10,e11) != e10 ) ),
inference(monotonicity,[status(thm)],[309]) ).
tff(311,plain,
( ( op1(e10,e10) != op1(e10,e11) )
<=> ( op1(e10,e10) != op1(e10,e11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(312,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)],[274]) ).
tff(313,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)],[312]) ).
tff(314,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)],[313]) ).
tff(315,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)],[314]) ).
tff(316,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)],[315]) ).
tff(317,plain,
op1(e10,e10) != op1(e10,e11),
inference(and_elim,[status(thm)],[316]) ).
tff(318,plain,
op1(e10,e10) != op1(e10,e11),
inference(modus_ponens,[status(thm)],[317,311]) ).
tff(319,plain,
op1(e10,e11) != e10,
inference(modus_ponens,[status(thm)],[318,310]) ).
tff(320,plain,
op1(e12,e13) = e10,
inference(symmetry,[status(thm)],[265]) ).
tff(321,plain,
( ( op1(e12,e11) = op1(e12,e13) )
<=> ( op1(e12,e11) = e10 ) ),
inference(monotonicity,[status(thm)],[320]) ).
tff(322,plain,
( ( op1(e12,e11) != op1(e12,e13) )
<=> ( op1(e12,e11) != e10 ) ),
inference(monotonicity,[status(thm)],[321]) ).
tff(323,plain,
( ( op1(e12,e11) != op1(e12,e13) )
<=> ( op1(e12,e11) != op1(e12,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(324,plain,
op1(e12,e11) != op1(e12,e13),
inference(and_elim,[status(thm)],[232]) ).
tff(325,plain,
op1(e12,e11) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[324,323]) ).
tff(326,plain,
op1(e12,e11) != e10,
inference(modus_ponens,[status(thm)],[325,322]) ).
tff(327,plain,
( ( e11 = e10 )
<=> ( e10 = e11 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(328,plain,
( ( op1(e11,e11) = e10 )
<=> ( e11 = e10 ) ),
inference(monotonicity,[status(thm)],[220]) ).
tff(329,plain,
( ( op1(e11,e11) = e10 )
<=> ( e10 = e11 ) ),
inference(transitivity,[status(thm)],[328,327]) ).
tff(330,plain,
( ( e10 = e11 )
<=> ( op1(e11,e11) = e10 ) ),
inference(symmetry,[status(thm)],[329]) ).
tff(331,plain,
( ( e10 != e11 )
<=> ( op1(e11,e11) != e10 ) ),
inference(monotonicity,[status(thm)],[330]) ).
tff(332,plain,
( ( e10 != e11 )
<=> ( e10 != e11 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(333,plain,
( ( e10 != e11 )
& ( e10 != e12 )
& ( e10 != e13 ) ),
inference(and_elim,[status(thm)],[254]) ).
tff(334,plain,
( ( e10 != e11 )
& ( e10 != e12 ) ),
inference(and_elim,[status(thm)],[333]) ).
tff(335,plain,
e10 != e11,
inference(and_elim,[status(thm)],[334]) ).
tff(336,plain,
e10 != e11,
inference(modus_ponens,[status(thm)],[335,332]) ).
tff(337,plain,
op1(e11,e11) != e10,
inference(modus_ponens,[status(thm)],[336,331]) ).
tff(338,plain,
( ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
<=> ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(339,plain,
( ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
<=> ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(340,plain,
( ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 ) )
<=> ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(341,plain,
( ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
<=> ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) ) ),
inference(monotonicity,[status(thm)],[340]) ).
tff(342,plain,
( ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) )
<=> ( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) ) ),
inference(transitivity,[status(thm)],[341,339]) ).
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 ) ) ),
inference(and_elim,[status(thm)],[295]) ).
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 ) ) ),
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 ) ) ),
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 ) ) ),
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 ) ) ),
inference(and_elim,[status(thm)],[346]) ).
tff(348,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)],[347]) ).
tff(349,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)],[348]) ).
tff(350,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)],[349]) ).
tff(351,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)],[350]) ).
tff(352,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)],[351]) ).
tff(353,plain,
( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) ),
inference(and_elim,[status(thm)],[352]) ).
tff(354,plain,
( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) ),
inference(modus_ponens,[status(thm)],[353,342]) ).
tff(355,plain,
( ( op1(e10,e11) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e12,e11) = e10 )
| ( op1(e13,e11) = e10 ) ),
inference(modus_ponens,[status(thm)],[354,338]) ).
tff(356,plain,
op1(e13,e11) = e10,
inference(unit_resolution,[status(thm)],[355,337,326,319]) ).
tff(357,plain,
h8(op1(e13,e11)) = h8(e10),
inference(monotonicity,[status(thm)],[356]) ).
tff(358,plain,
h8(op1(e13,e11)) = e23,
inference(transitivity,[status(thm)],[357,5,96]) ).
tff(359,plain,
( ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
<=> ( e23 = op2(e21,e20) ) ),
inference(monotonicity,[status(thm)],[358,303]) ).
tff(360,plain,
( ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
<=> ( op2(e21,e20) = e23 ) ),
inference(transitivity,[status(thm)],[359,302]) ).
tff(361,plain,
( ( op2(e21,e20) = e23 )
<=> ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) ) ),
inference(symmetry,[status(thm)],[360]) ).
tff(362,plain,
( ( op2(e23,e23) = e23 )
<=> ( op2(e23,e23) = e23 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(363,plain,
op2(e23,e23) = e23,
inference(and_elim,[status(thm)],[10]) ).
tff(364,plain,
op2(e23,e23) = e23,
inference(modus_ponens,[status(thm)],[363,362]) ).
tff(365,plain,
( ( op2(e21,e23) = op2(e23,e23) )
<=> ( op2(e21,e23) = e23 ) ),
inference(monotonicity,[status(thm)],[364]) ).
tff(366,plain,
( ( op2(e21,e23) != op2(e23,e23) )
<=> ( op2(e21,e23) != e23 ) ),
inference(monotonicity,[status(thm)],[365]) ).
tff(367,plain,
( ( op2(e21,e23) != op2(e23,e23) )
<=> ( op2(e21,e23) != op2(e23,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(368,plain,
op2(e21,e23) != op2(e23,e23),
inference(and_elim,[status(thm)],[44]) ).
tff(369,plain,
op2(e21,e23) != op2(e23,e23),
inference(modus_ponens,[status(thm)],[368,367]) ).
tff(370,plain,
op2(e21,e23) != e23,
inference(modus_ponens,[status(thm)],[369,366]) ).
tff(371,plain,
( ( op2(e21,e21) = e23 )
<=> ( e21 = e23 ) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(372,plain,
( ( e21 = e23 )
<=> ( op2(e21,e21) = e23 ) ),
inference(symmetry,[status(thm)],[371]) ).
tff(373,plain,
( ( e21 != e23 )
<=> ( op2(e21,e21) != e23 ) ),
inference(monotonicity,[status(thm)],[372]) ).
tff(374,plain,
( ( e21 != e23 )
<=> ( e21 != e23 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(375,plain,
e21 != e23,
inference(and_elim,[status(thm)],[118]) ).
tff(376,plain,
e21 != e23,
inference(modus_ponens,[status(thm)],[375,374]) ).
tff(377,plain,
op2(e21,e21) != e23,
inference(modus_ponens,[status(thm)],[376,373]) ).
tff(378,plain,
( ( op2(e21,e22) = e23 )
<=> ( e20 = e23 ) ),
inference(monotonicity,[status(thm)],[213]) ).
tff(379,plain,
( ( e20 = e23 )
<=> ( op2(e21,e22) = e23 ) ),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
( ( e20 != e23 )
<=> ( op2(e21,e22) != e23 ) ),
inference(monotonicity,[status(thm)],[379]) ).
tff(381,plain,
( ( e20 != e23 )
<=> ( e20 != e23 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(382,plain,
e20 != e23,
inference(and_elim,[status(thm)],[120]) ).
tff(383,plain,
e20 != e23,
inference(modus_ponens,[status(thm)],[382,381]) ).
tff(384,plain,
op2(e21,e22) != e23,
inference(modus_ponens,[status(thm)],[383,380]) ).
tff(385,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(386,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(387,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 ) )
<=> ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(388,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ) ),
inference(monotonicity,[status(thm)],[387]) ).
tff(389,plain,
( ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) )
<=> ( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ) ),
inference(transitivity,[status(thm)],[388,386]) ).
tff(390,plain,
( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ),
inference(and_elim,[status(thm)],[147]) ).
tff(391,plain,
( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[390,389]) ).
tff(392,plain,
( ( op2(e21,e20) = e23 )
| ( op2(e21,e21) = e23 )
| ( op2(e21,e22) = e23 )
| ( op2(e21,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[391,385]) ).
tff(393,plain,
op2(e21,e20) = e23,
inference(unit_resolution,[status(thm)],[392,384,377,370]) ).
tff(394,plain,
h8(op1(e13,e11)) = op2(h8(e13),h8(e11)),
inference(modus_ponens,[status(thm)],[393,361]) ).
tff(395,plain,
h8(e10) = e23,
inference(transitivity,[status(thm)],[5,96]) ).
tff(396,plain,
op2(h8(e13),h8(e10)) = op2(e21,e23),
inference(monotonicity,[status(thm)],[167,395]) ).
tff(397,plain,
op2(e21,e23) = op2(h8(e13),h8(e10)),
inference(symmetry,[status(thm)],[396]) ).
tff(398,plain,
( ( e21 = op2(e21,e23) )
<=> ( op2(e21,e23) = e21 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(399,plain,
( ( op2(e21,e21) = op2(e21,e23) )
<=> ( e21 = op2(e21,e23) ) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(400,plain,
( ( op2(e21,e21) = op2(e21,e23) )
<=> ( op2(e21,e23) = e21 ) ),
inference(transitivity,[status(thm)],[399,398]) ).
tff(401,plain,
( ( op2(e21,e21) != op2(e21,e23) )
<=> ( op2(e21,e23) != e21 ) ),
inference(monotonicity,[status(thm)],[400]) ).
tff(402,plain,
( ( op2(e21,e21) != op2(e21,e23) )
<=> ( op2(e21,e21) != op2(e21,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(403,plain,
op2(e21,e21) != op2(e21,e23),
inference(and_elim,[status(thm)],[32]) ).
tff(404,plain,
op2(e21,e21) != op2(e21,e23),
inference(modus_ponens,[status(thm)],[403,402]) ).
tff(405,plain,
op2(e21,e23) != e21,
inference(modus_ponens,[status(thm)],[404,401]) ).
tff(406,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(407,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(408,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(409,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)],[408]) ).
tff(410,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)],[409,407]) ).
tff(411,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)],[92]) ).
tff(412,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)],[411]) ).
tff(413,plain,
( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ),
inference(and_elim,[status(thm)],[412]) ).
tff(414,plain,
( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[413,410]) ).
tff(415,plain,
( ( op2(e21,e23) = e20 )
| ( op2(e21,e23) = e21 )
| ( op2(e21,e23) = e22 )
| ( op2(e21,e23) = e23 ) ),
inference(modus_ponens,[status(thm)],[414,406]) ).
tff(416,plain,
op2(e21,e23) = e22,
inference(unit_resolution,[status(thm)],[415,187,405,370]) ).
tff(417,plain,
e22 = op2(e21,e23),
inference(symmetry,[status(thm)],[416]) ).
tff(418,plain,
( ( e13 = e12 )
<=> ( e12 = e13 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(419,plain,
( ( op1(e13,e13) = e12 )
<=> ( e13 = e12 ) ),
inference(monotonicity,[status(thm)],[174]) ).
tff(420,plain,
( ( op1(e13,e13) = e12 )
<=> ( e12 = e13 ) ),
inference(transitivity,[status(thm)],[419,418]) ).
tff(421,plain,
( ( e12 = e13 )
<=> ( op1(e13,e13) = e12 ) ),
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
( ( e12 != e13 )
<=> ( op1(e13,e13) != e12 ) ),
inference(monotonicity,[status(thm)],[421]) ).
tff(423,plain,
( ( e12 != e13 )
<=> ( e12 != e13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(424,plain,
e12 != e13,
inference(and_elim,[status(thm)],[252]) ).
tff(425,plain,
e12 != e13,
inference(modus_ponens,[status(thm)],[424,423]) ).
tff(426,plain,
op1(e13,e13) != e12,
inference(modus_ponens,[status(thm)],[425,422]) ).
tff(427,plain,
( ( e12 = op1(e13,e12) )
<=> ( op1(e13,e12) = e12 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(428,plain,
( ( op1(e12,e12) = op1(e13,e12) )
<=> ( e12 = op1(e13,e12) ) ),
inference(monotonicity,[status(thm)],[246]) ).
tff(429,plain,
( ( op1(e12,e12) = op1(e13,e12) )
<=> ( op1(e13,e12) = e12 ) ),
inference(transitivity,[status(thm)],[428,427]) ).
tff(430,plain,
( ( op1(e12,e12) != op1(e13,e12) )
<=> ( op1(e13,e12) != e12 ) ),
inference(monotonicity,[status(thm)],[429]) ).
tff(431,plain,
( ( op1(e12,e12) != op1(e13,e12) )
<=> ( op1(e12,e12) != op1(e13,e12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(432,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)],[316]) ).
tff(433,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)],[432]) ).
tff(434,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)],[433]) ).
tff(435,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)],[434]) ).
tff(436,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)],[435]) ).
tff(437,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)],[436]) ).
tff(438,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)],[437]) ).
tff(439,plain,
op1(e12,e12) != op1(e13,e12),
inference(and_elim,[status(thm)],[438]) ).
tff(440,plain,
op1(e12,e12) != op1(e13,e12),
inference(modus_ponens,[status(thm)],[439,431]) ).
tff(441,plain,
op1(e13,e12) != e12,
inference(modus_ponens,[status(thm)],[440,430]) ).
tff(442,plain,
( ( e12 = op1(e13,e11) )
<=> ( op1(e13,e11) = e12 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(443,plain,
( ( op1(e10,e13) = e12 )
<=> ( e11 = e12 ) ),
inference(monotonicity,[status(thm)],[267]) ).
tff(444,plain,
( ( e11 = e12 )
<=> ( op1(e10,e13) = e12 ) ),
inference(symmetry,[status(thm)],[443]) ).
tff(445,plain,
( ( e11 != e12 )
<=> ( op1(e10,e13) != e12 ) ),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
op1(e10,e13) != e12,
inference(modus_ponens,[status(thm)],[256,445]) ).
tff(447,plain,
( ( op1(e10,e12) = op1(e12,e12) )
<=> ( op1(e10,e12) = e12 ) ),
inference(monotonicity,[status(thm)],[246]) ).
tff(448,plain,
( ( op1(e10,e12) != op1(e12,e12) )
<=> ( op1(e10,e12) != e12 ) ),
inference(monotonicity,[status(thm)],[447]) ).
tff(449,plain,
( ( op1(e10,e12) != op1(e12,e12) )
<=> ( op1(e10,e12) != op1(e12,e12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(450,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)],[438]) ).
tff(451,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)],[450]) ).
tff(452,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)],[451]) ).
tff(453,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)],[452]) ).
tff(454,plain,
op1(e10,e12) != op1(e12,e12),
inference(and_elim,[status(thm)],[453]) ).
tff(455,plain,
op1(e10,e12) != op1(e12,e12),
inference(modus_ponens,[status(thm)],[454,449]) ).
tff(456,plain,
op1(e10,e12) != e12,
inference(modus_ponens,[status(thm)],[455,448]) ).
tff(457,plain,
( ( op1(e10,e10) = e12 )
<=> ( e10 = e12 ) ),
inference(monotonicity,[status(thm)],[307]) ).
tff(458,plain,
( ( e10 = e12 )
<=> ( op1(e10,e10) = e12 ) ),
inference(symmetry,[status(thm)],[457]) ).
tff(459,plain,
( ( e10 != e12 )
<=> ( op1(e10,e10) != e12 ) ),
inference(monotonicity,[status(thm)],[458]) ).
tff(460,plain,
( ( e10 != e12 )
<=> ( e10 != e12 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(461,plain,
e10 != e12,
inference(and_elim,[status(thm)],[334]) ).
tff(462,plain,
e10 != e12,
inference(modus_ponens,[status(thm)],[461,460]) ).
tff(463,plain,
op1(e10,e10) != e12,
inference(modus_ponens,[status(thm)],[462,459]) ).
tff(464,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(465,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(466,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(467,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ) ),
inference(monotonicity,[status(thm)],[466]) ).
tff(468,plain,
( ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) )
<=> ( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ) ),
inference(transitivity,[status(thm)],[467,465]) ).
tff(469,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)],[352]) ).
tff(470,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)],[469]) ).
tff(471,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)],[470]) ).
tff(472,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)],[471]) ).
tff(473,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)],[472]) ).
tff(474,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ),
inference(and_elim,[status(thm)],[473]) ).
tff(475,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[474,468]) ).
tff(476,plain,
( ( op1(e10,e10) = e12 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[475,464]) ).
tff(477,plain,
op1(e10,e11) = e12,
inference(unit_resolution,[status(thm)],[476,463,456,446]) ).
tff(478,plain,
( ( op1(e10,e11) = op1(e13,e11) )
<=> ( e12 = op1(e13,e11) ) ),
inference(monotonicity,[status(thm)],[477]) ).
tff(479,plain,
( ( op1(e10,e11) = op1(e13,e11) )
<=> ( op1(e13,e11) = e12 ) ),
inference(transitivity,[status(thm)],[478,442]) ).
tff(480,plain,
( ( op1(e10,e11) != op1(e13,e11) )
<=> ( op1(e13,e11) != e12 ) ),
inference(monotonicity,[status(thm)],[479]) ).
tff(481,plain,
( ( op1(e10,e11) != op1(e13,e11) )
<=> ( op1(e10,e11) != op1(e13,e11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(482,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)],[453]) ).
tff(483,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)],[482]) ).
tff(484,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)],[483]) ).
tff(485,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)],[484]) ).
tff(486,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)],[485]) ).
tff(487,plain,
op1(e10,e11) != op1(e13,e11),
inference(and_elim,[status(thm)],[486]) ).
tff(488,plain,
op1(e10,e11) != op1(e13,e11),
inference(modus_ponens,[status(thm)],[487,481]) ).
tff(489,plain,
op1(e13,e11) != e12,
inference(modus_ponens,[status(thm)],[488,480]) ).
tff(490,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(491,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(492,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 ) )
<=> ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(493,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(monotonicity,[status(thm)],[492]) ).
tff(494,plain,
( ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) )
<=> ( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ) ),
inference(transitivity,[status(thm)],[493,491]) ).
tff(495,plain,
( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ),
inference(and_elim,[status(thm)],[286]) ).
tff(496,plain,
( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[495,494]) ).
tff(497,plain,
( ( op1(e13,e10) = e12 )
| ( op1(e13,e11) = e12 )
| ( op1(e13,e12) = e12 )
| ( op1(e13,e13) = e12 ) ),
inference(modus_ponens,[status(thm)],[496,490]) ).
tff(498,plain,
op1(e13,e10) = e12,
inference(unit_resolution,[status(thm)],[497,489,441,426]) ).
tff(499,plain,
h8(op1(e13,e10)) = h8(e12),
inference(monotonicity,[status(thm)],[498]) ).
tff(500,plain,
h8(op1(e13,e10)) = op2(h8(e13),h8(e10)),
inference(transitivity,[status(thm)],[499,179,417,397]) ).
tff(501,plain,
op2(h8(e12),h8(e13)) = op2(e22,e21),
inference(monotonicity,[status(thm)],[179,167]) ).
tff(502,plain,
op2(e22,e21) = op2(h8(e12),h8(e13)),
inference(symmetry,[status(thm)],[501]) ).
tff(503,plain,
h8(op1(e12,e13)) = h8(e10),
inference(monotonicity,[status(thm)],[320]) ).
tff(504,plain,
h8(op1(e12,e13)) = op2(h8(e12),h8(e13)),
inference(transitivity,[status(thm)],[503,5,502]) ).
tff(505,plain,
op2(h8(e12),h8(e12)) = op2(e22,e22),
inference(monotonicity,[status(thm)],[179,179]) ).
tff(506,plain,
op2(e22,e22) = op2(h8(e12),h8(e12)),
inference(symmetry,[status(thm)],[505]) ).
tff(507,plain,
e22 = op2(e22,e22),
inference(symmetry,[status(thm)],[63]) ).
tff(508,plain,
h8(op1(e12,e12)) = h8(e12),
inference(monotonicity,[status(thm)],[246]) ).
tff(509,plain,
h8(op1(e12,e12)) = op2(h8(e12),h8(e12)),
inference(transitivity,[status(thm)],[508,179,507,506]) ).
tff(510,plain,
op2(h8(e12),h8(e11)) = op2(e22,e20),
inference(monotonicity,[status(thm)],[179,161]) ).
tff(511,plain,
op2(e22,e20) = op2(h8(e12),h8(e11)),
inference(symmetry,[status(thm)],[510]) ).
tff(512,plain,
( ( op2(e22,e23) = e21 )
<=> ( e20 = e21 ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(513,plain,
( ( e20 = e21 )
<=> ( op2(e22,e23) = e21 ) ),
inference(symmetry,[status(thm)],[512]) ).
tff(514,plain,
( ( e20 != e21 )
<=> ( op2(e22,e23) != e21 ) ),
inference(monotonicity,[status(thm)],[513]) ).
tff(515,plain,
op2(e22,e23) != e21,
inference(modus_ponens,[status(thm)],[123,514]) ).
tff(516,plain,
( ( e22 = e21 )
<=> ( e21 = e22 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(517,plain,
( ( op2(e22,e22) = e21 )
<=> ( e22 = e21 ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(518,plain,
( ( op2(e22,e22) = e21 )
<=> ( e21 = e22 ) ),
inference(transitivity,[status(thm)],[517,516]) ).
tff(519,plain,
( ( e21 = e22 )
<=> ( op2(e22,e22) = e21 ) ),
inference(symmetry,[status(thm)],[518]) ).
tff(520,plain,
( ( e21 != e22 )
<=> ( op2(e22,e22) != e21 ) ),
inference(monotonicity,[status(thm)],[519]) ).
tff(521,plain,
( ( e21 != e22 )
<=> ( e21 != e22 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(522,plain,
e21 != e22,
inference(and_elim,[status(thm)],[119]) ).
tff(523,plain,
e21 != e22,
inference(modus_ponens,[status(thm)],[522,521]) ).
tff(524,plain,
op2(e22,e22) != e21,
inference(modus_ponens,[status(thm)],[523,520]) ).
tff(525,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
<=> ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(526,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
<=> ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(527,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 ) )
<=> ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(528,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
<=> ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ) ),
inference(monotonicity,[status(thm)],[527]) ).
tff(529,plain,
( ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) )
<=> ( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ) ),
inference(transitivity,[status(thm)],[528,526]) ).
tff(530,plain,
( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ),
inference(and_elim,[status(thm)],[143]) ).
tff(531,plain,
( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ),
inference(modus_ponens,[status(thm)],[530,529]) ).
tff(532,plain,
( ( op2(e22,e20) = e21 )
| ( op2(e22,e21) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e22,e23) = e21 ) ),
inference(modus_ponens,[status(thm)],[531,525]) ).
tff(533,plain,
op2(e22,e20) = e21,
inference(unit_resolution,[status(thm)],[532,60,524,515]) ).
tff(534,plain,
e21 = op2(e22,e20),
inference(symmetry,[status(thm)],[533]) ).
tff(535,plain,
( ( e11 = op1(e12,e11) )
<=> ( op1(e12,e11) = e11 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(536,plain,
( ( op1(e11,e11) = op1(e12,e11) )
<=> ( e11 = op1(e12,e11) ) ),
inference(monotonicity,[status(thm)],[220]) ).
tff(537,plain,
( ( op1(e11,e11) = op1(e12,e11) )
<=> ( op1(e12,e11) = e11 ) ),
inference(transitivity,[status(thm)],[536,535]) ).
tff(538,plain,
( ( op1(e11,e11) != op1(e12,e11) )
<=> ( op1(e12,e11) != e11 ) ),
inference(monotonicity,[status(thm)],[537]) ).
tff(539,plain,
( ( op1(e11,e11) != op1(e12,e11) )
<=> ( op1(e11,e11) != op1(e12,e11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(540,plain,
op1(e11,e11) != op1(e12,e11),
inference(and_elim,[status(thm)],[485]) ).
tff(541,plain,
op1(e11,e11) != op1(e12,e11),
inference(modus_ponens,[status(thm)],[540,539]) ).
tff(542,plain,
op1(e12,e11) != e11,
inference(modus_ponens,[status(thm)],[541,538]) ).
tff(543,plain,
( ( op1(e12,e11) = op1(e12,e12) )
<=> ( op1(e12,e11) = e12 ) ),
inference(monotonicity,[status(thm)],[246]) ).
tff(544,plain,
( ( op1(e12,e11) != op1(e12,e12) )
<=> ( op1(e12,e11) != e12 ) ),
inference(monotonicity,[status(thm)],[543]) ).
tff(545,plain,
( ( op1(e12,e11) != op1(e12,e12) )
<=> ( op1(e12,e11) != op1(e12,e12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(546,plain,
op1(e12,e11) != op1(e12,e12),
inference(and_elim,[status(thm)],[233]) ).
tff(547,plain,
op1(e12,e11) != op1(e12,e12),
inference(modus_ponens,[status(thm)],[546,545]) ).
tff(548,plain,
op1(e12,e11) != e12,
inference(modus_ponens,[status(thm)],[547,544]) ).
tff(549,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(550,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(551,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(552,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)],[551]) ).
tff(553,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)],[552,550]) ).
tff(554,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(555,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)],[554]) ).
tff(556,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)],[555]) ).
tff(557,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)],[556]) ).
tff(558,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)],[557]) ).
tff(559,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)],[558]) ).
tff(560,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)],[559]) ).
tff(561,plain,
( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ),
inference(and_elim,[status(thm)],[560]) ).
tff(562,plain,
( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ),
inference(modus_ponens,[status(thm)],[561,553]) ).
tff(563,plain,
( ( op1(e12,e11) = e10 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e11) = e12 )
| ( op1(e12,e11) = e13 ) ),
inference(modus_ponens,[status(thm)],[562,549]) ).
tff(564,plain,
op1(e12,e11) = e13,
inference(unit_resolution,[status(thm)],[563,326,548,542]) ).
tff(565,plain,
h8(op1(e12,e11)) = h8(e13),
inference(monotonicity,[status(thm)],[564]) ).
tff(566,plain,
h8(op1(e12,e11)) = op2(h8(e12),h8(e11)),
inference(transitivity,[status(thm)],[565,167,534,511]) ).
tff(567,plain,
op2(h8(e12),h8(e10)) = op2(e22,e23),
inference(monotonicity,[status(thm)],[179,395]) ).
tff(568,plain,
op2(e22,e23) = op2(h8(e12),h8(e10)),
inference(symmetry,[status(thm)],[567]) ).
tff(569,plain,
( ( op1(e12,e13) = e11 )
<=> ( e10 = e11 ) ),
inference(monotonicity,[status(thm)],[320]) ).
tff(570,plain,
( ( e10 = e11 )
<=> ( op1(e12,e13) = e11 ) ),
inference(symmetry,[status(thm)],[569]) ).
tff(571,plain,
( ( e10 != e11 )
<=> ( op1(e12,e13) != e11 ) ),
inference(monotonicity,[status(thm)],[570]) ).
tff(572,plain,
op1(e12,e13) != e11,
inference(modus_ponens,[status(thm)],[336,571]) ).
tff(573,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
<=> ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(574,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
<=> ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(575,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 ) )
<=> ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(576,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
<=> ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ) ),
inference(monotonicity,[status(thm)],[575]) ).
tff(577,plain,
( ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) )
<=> ( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ) ),
inference(transitivity,[status(thm)],[576,574]) ).
tff(578,plain,
( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ),
inference(and_elim,[status(thm)],[343]) ).
tff(579,plain,
( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ),
inference(modus_ponens,[status(thm)],[578,577]) ).
tff(580,plain,
( ( op1(e12,e10) = e11 )
| ( op1(e12,e11) = e11 )
| ( op1(e12,e12) = e11 )
| ( op1(e12,e13) = e11 ) ),
inference(modus_ponens,[status(thm)],[579,573]) ).
tff(581,plain,
op1(e12,e10) = e11,
inference(unit_resolution,[status(thm)],[580,542,257,572]) ).
tff(582,plain,
h8(op1(e12,e10)) = h8(e11),
inference(monotonicity,[status(thm)],[581]) ).
tff(583,plain,
h8(op1(e12,e10)) = op2(h8(e12),h8(e10)),
inference(transitivity,[status(thm)],[582,160,157,156,73,568]) ).
tff(584,plain,
op2(h8(e11),h8(e13)) = op2(e20,e21),
inference(monotonicity,[status(thm)],[161,167]) ).
tff(585,plain,
op2(e20,e21) = op2(h8(e11),h8(e13)),
inference(symmetry,[status(thm)],[584]) ).
tff(586,plain,
( ( e21 = op2(op2(e22,e23),e23) )
<=> ( e21 = op2(op2(e22,e23),e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(587,plain,
e21 = op2(op2(e22,e23),e23),
inference(and_elim,[status(thm)],[71]) ).
tff(588,plain,
e21 = op2(op2(e22,e23),e23),
inference(modus_ponens,[status(thm)],[587,586]) ).
tff(589,plain,
op2(op2(e22,e23),e23) = e21,
inference(symmetry,[status(thm)],[588]) ).
tff(590,plain,
op2(e20,e23) = op2(op2(e22,e23),e23),
inference(monotonicity,[status(thm)],[73]) ).
tff(591,plain,
op2(e20,e23) = e21,
inference(transitivity,[status(thm)],[590,589]) ).
tff(592,plain,
( ( op2(e20,e23) = e22 )
<=> ( e21 = e22 ) ),
inference(monotonicity,[status(thm)],[591]) ).
tff(593,plain,
( ( e21 = e22 )
<=> ( op2(e20,e23) = e22 ) ),
inference(symmetry,[status(thm)],[592]) ).
tff(594,plain,
( ( e21 != e22 )
<=> ( op2(e20,e23) != e22 ) ),
inference(monotonicity,[status(thm)],[593]) ).
tff(595,plain,
op2(e20,e23) != e22,
inference(modus_ponens,[status(thm)],[523,594]) ).
tff(596,plain,
( ( op2(e20,e22) = op2(e22,e22) )
<=> ( op2(e20,e22) = e22 ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(597,plain,
( ( op2(e20,e22) != op2(e22,e22) )
<=> ( op2(e20,e22) != e22 ) ),
inference(monotonicity,[status(thm)],[596]) ).
tff(598,plain,
( ( op2(e20,e22) != op2(e22,e22) )
<=> ( op2(e20,e22) != op2(e22,e22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(599,plain,
op2(e20,e22) != op2(e22,e22),
inference(and_elim,[status(thm)],[53]) ).
tff(600,plain,
op2(e20,e22) != op2(e22,e22),
inference(modus_ponens,[status(thm)],[599,598]) ).
tff(601,plain,
op2(e20,e22) != e22,
inference(modus_ponens,[status(thm)],[600,597]) ).
tff(602,plain,
( ( op2(e20,e20) = e22 )
<=> ( e20 = e22 ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(603,plain,
( ( e20 = e22 )
<=> ( op2(e20,e20) = e22 ) ),
inference(symmetry,[status(thm)],[602]) ).
tff(604,plain,
( ( e20 != e22 )
<=> ( op2(e20,e20) != e22 ) ),
inference(monotonicity,[status(thm)],[603]) ).
tff(605,plain,
( ( e20 != e22 )
<=> ( e20 != e22 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(606,plain,
e20 != e22,
inference(and_elim,[status(thm)],[121]) ).
tff(607,plain,
e20 != e22,
inference(modus_ponens,[status(thm)],[606,605]) ).
tff(608,plain,
op2(e20,e20) != e22,
inference(modus_ponens,[status(thm)],[607,604]) ).
tff(609,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(610,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(611,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(612,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ) ),
inference(monotonicity,[status(thm)],[611]) ).
tff(613,plain,
( ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) )
<=> ( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ) ),
inference(transitivity,[status(thm)],[612,610]) ).
tff(614,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)],[209]) ).
tff(615,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)],[614]) ).
tff(616,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)],[615]) ).
tff(617,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)],[616]) ).
tff(618,plain,
( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ),
inference(and_elim,[status(thm)],[617]) ).
tff(619,plain,
( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[618,613]) ).
tff(620,plain,
( ( op2(e20,e20) = e22 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[619,609]) ).
tff(621,plain,
op2(e20,e21) = e22,
inference(unit_resolution,[status(thm)],[620,608,601,595]) ).
tff(622,plain,
e22 = op2(e20,e21),
inference(symmetry,[status(thm)],[621]) ).
tff(623,plain,
( ( op1(e11,e13) = op1(e13,e13) )
<=> ( op1(e11,e13) = e13 ) ),
inference(monotonicity,[status(thm)],[174]) ).
tff(624,plain,
( ( op1(e11,e13) != op1(e13,e13) )
<=> ( op1(e11,e13) != e13 ) ),
inference(monotonicity,[status(thm)],[623]) ).
tff(625,plain,
( ( op1(e11,e13) != op1(e13,e13) )
<=> ( op1(e11,e13) != op1(e13,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(626,plain,
op1(e11,e13) != op1(e13,e13),
inference(and_elim,[status(thm)],[433]) ).
tff(627,plain,
op1(e11,e13) != op1(e13,e13),
inference(modus_ponens,[status(thm)],[626,625]) ).
tff(628,plain,
op1(e11,e13) != e13,
inference(modus_ponens,[status(thm)],[627,624]) ).
tff(629,plain,
( ( e11 = op1(e11,e13) )
<=> ( op1(e11,e13) = e11 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(630,plain,
( ( op1(e11,e11) = op1(e11,e13) )
<=> ( e11 = op1(e11,e13) ) ),
inference(monotonicity,[status(thm)],[220]) ).
tff(631,plain,
( ( op1(e11,e11) = op1(e11,e13) )
<=> ( op1(e11,e13) = e11 ) ),
inference(transitivity,[status(thm)],[630,629]) ).
tff(632,plain,
( ( op1(e11,e11) != op1(e11,e13) )
<=> ( op1(e11,e13) != e11 ) ),
inference(monotonicity,[status(thm)],[631]) ).
tff(633,plain,
( ( op1(e11,e11) != op1(e11,e13) )
<=> ( op1(e11,e11) != op1(e11,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(634,plain,
op1(e11,e11) != op1(e11,e13),
inference(and_elim,[status(thm)],[238]) ).
tff(635,plain,
op1(e11,e11) != op1(e11,e13),
inference(modus_ponens,[status(thm)],[634,633]) ).
tff(636,plain,
op1(e11,e13) != e11,
inference(modus_ponens,[status(thm)],[635,632]) ).
tff(637,plain,
( ( op1(e11,e13) = op1(e12,e13) )
<=> ( op1(e11,e13) = e10 ) ),
inference(monotonicity,[status(thm)],[320]) ).
tff(638,plain,
( ( op1(e11,e13) != op1(e12,e13) )
<=> ( op1(e11,e13) != e10 ) ),
inference(monotonicity,[status(thm)],[637]) ).
tff(639,plain,
( ( op1(e11,e13) != op1(e12,e13) )
<=> ( op1(e11,e13) != op1(e12,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(640,plain,
op1(e11,e13) != op1(e12,e13),
inference(and_elim,[status(thm)],[434]) ).
tff(641,plain,
op1(e11,e13) != op1(e12,e13),
inference(modus_ponens,[status(thm)],[640,639]) ).
tff(642,plain,
op1(e11,e13) != e10,
inference(modus_ponens,[status(thm)],[641,638]) ).
tff(643,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(644,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(645,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(646,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)],[645]) ).
tff(647,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)],[646,644]) ).
tff(648,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)],[560]) ).
tff(649,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)],[648]) ).
tff(650,plain,
( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ),
inference(and_elim,[status(thm)],[649]) ).
tff(651,plain,
( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[650,647]) ).
tff(652,plain,
( ( op1(e11,e13) = e10 )
| ( op1(e11,e13) = e11 )
| ( op1(e11,e13) = e12 )
| ( op1(e11,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[651,643]) ).
tff(653,plain,
op1(e11,e13) = e12,
inference(unit_resolution,[status(thm)],[652,642,636,628]) ).
tff(654,plain,
h8(op1(e11,e13)) = h8(e12),
inference(monotonicity,[status(thm)],[653]) ).
tff(655,plain,
h8(op1(e11,e13)) = op2(h8(e11),h8(e13)),
inference(transitivity,[status(thm)],[654,179,622,585]) ).
tff(656,plain,
op2(h8(e11),h8(e12)) = op2(e20,e22),
inference(monotonicity,[status(thm)],[161,179]) ).
tff(657,plain,
op2(e20,e22) = op2(h8(e11),h8(e12)),
inference(symmetry,[status(thm)],[656]) ).
tff(658,plain,
( ( e20 = op2(e20,e22) )
<=> ( op2(e20,e22) = e20 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(659,plain,
( ( op2(e20,e20) = op2(e20,e22) )
<=> ( e20 = op2(e20,e22) ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(660,plain,
( ( op2(e20,e20) = op2(e20,e22) )
<=> ( op2(e20,e22) = e20 ) ),
inference(transitivity,[status(thm)],[659,658]) ).
tff(661,plain,
( ( op2(e20,e20) != op2(e20,e22) )
<=> ( op2(e20,e22) != e20 ) ),
inference(monotonicity,[status(thm)],[660]) ).
tff(662,plain,
( ( op2(e20,e20) != op2(e20,e22) )
<=> ( op2(e20,e20) != op2(e20,e22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(663,plain,
op2(e20,e20) != op2(e20,e22),
inference(and_elim,[status(thm)],[41]) ).
tff(664,plain,
op2(e20,e20) != op2(e20,e22),
inference(modus_ponens,[status(thm)],[663,662]) ).
tff(665,plain,
op2(e20,e22) != e20,
inference(modus_ponens,[status(thm)],[664,661]) ).
tff(666,plain,
( ( op2(e20,e22) = op2(e20,e23) )
<=> ( op2(e20,e22) = e21 ) ),
inference(monotonicity,[status(thm)],[591]) ).
tff(667,plain,
( ( op2(e20,e22) != op2(e20,e23) )
<=> ( op2(e20,e22) != e21 ) ),
inference(monotonicity,[status(thm)],[666]) ).
tff(668,plain,
( ( op2(e20,e22) != op2(e20,e23) )
<=> ( op2(e20,e22) != op2(e20,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(669,plain,
op2(e20,e22) != op2(e20,e23),
inference(and_elim,[status(thm)],[37]) ).
tff(670,plain,
op2(e20,e22) != op2(e20,e23),
inference(modus_ponens,[status(thm)],[669,668]) ).
tff(671,plain,
op2(e20,e22) != e21,
inference(modus_ponens,[status(thm)],[670,667]) ).
tff(672,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(673,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(674,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 ) )
<=> ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(675,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ) ),
inference(monotonicity,[status(thm)],[674]) ).
tff(676,plain,
( ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
<=> ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ) ),
inference(transitivity,[status(thm)],[675,673]) ).
tff(677,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)],[412]) ).
tff(678,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)],[677]) ).
tff(679,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)],[678]) ).
tff(680,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) )
& ( ( op2(e20,e23) = e20 )
| ( op2(e20,e23) = e21 )
| ( op2(e20,e23) = e22 )
| ( op2(e20,e23) = e23 ) ) ),
inference(and_elim,[status(thm)],[679]) ).
tff(681,plain,
( ( ( op2(e20,e20) = e20 )
| ( op2(e20,e20) = e21 )
| ( op2(e20,e20) = e22 )
| ( op2(e20,e20) = e23 ) )
& ( ( op2(e20,e21) = e20 )
| ( op2(e20,e21) = e21 )
| ( op2(e20,e21) = e22 )
| ( op2(e20,e21) = e23 ) )
& ( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ) ),
inference(and_elim,[status(thm)],[680]) ).
tff(682,plain,
( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ),
inference(and_elim,[status(thm)],[681]) ).
tff(683,plain,
( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ),
inference(modus_ponens,[status(thm)],[682,676]) ).
tff(684,plain,
( ( op2(e20,e22) = e20 )
| ( op2(e20,e22) = e21 )
| ( op2(e20,e22) = e22 )
| ( op2(e20,e22) = e23 ) ),
inference(modus_ponens,[status(thm)],[683,672]) ).
tff(685,plain,
op2(e20,e22) = e23,
inference(unit_resolution,[status(thm)],[684,671,601,665]) ).
tff(686,plain,
e23 = op2(e20,e22),
inference(symmetry,[status(thm)],[685]) ).
tff(687,plain,
( ( e10 = op1(e11,e10) )
<=> ( op1(e11,e10) = e10 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(688,plain,
( ( op1(e10,e10) = op1(e11,e10) )
<=> ( e10 = op1(e11,e10) ) ),
inference(monotonicity,[status(thm)],[307]) ).
tff(689,plain,
( ( op1(e10,e10) = op1(e11,e10) )
<=> ( op1(e11,e10) = e10 ) ),
inference(transitivity,[status(thm)],[688,687]) ).
tff(690,plain,
( ( op1(e10,e10) != op1(e11,e10) )
<=> ( op1(e11,e10) != e10 ) ),
inference(monotonicity,[status(thm)],[689]) ).
tff(691,plain,
( ( op1(e10,e10) != op1(e11,e10) )
<=> ( op1(e10,e10) != op1(e11,e10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(692,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)],[486]) ).
tff(693,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)],[692]) ).
tff(694,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)],[693]) ).
tff(695,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)],[694]) ).
tff(696,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)],[695]) ).
tff(697,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) )
& ( op1(e10,e10) != op1(e13,e10) ) ),
inference(and_elim,[status(thm)],[696]) ).
tff(698,plain,
( ( op1(e10,e10) != op1(e11,e10) )
& ( op1(e10,e10) != op1(e12,e10) ) ),
inference(and_elim,[status(thm)],[697]) ).
tff(699,plain,
op1(e10,e10) != op1(e11,e10),
inference(and_elim,[status(thm)],[698]) ).
tff(700,plain,
op1(e10,e10) != op1(e11,e10),
inference(modus_ponens,[status(thm)],[699,691]) ).
tff(701,plain,
op1(e11,e10) != e10,
inference(modus_ponens,[status(thm)],[700,690]) ).
tff(702,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(703,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(704,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(705,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ) ),
inference(monotonicity,[status(thm)],[704]) ).
tff(706,plain,
( ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) )
<=> ( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ) ),
inference(transitivity,[status(thm)],[705,703]) ).
tff(707,plain,
( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ),
inference(and_elim,[status(thm)],[469]) ).
tff(708,plain,
( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[707,706]) ).
tff(709,plain,
( ( op1(e11,e10) = e10 )
| ( op1(e11,e11) = e10 )
| ( op1(e11,e12) = e10 )
| ( op1(e11,e13) = e10 ) ),
inference(modus_ponens,[status(thm)],[708,702]) ).
tff(710,plain,
op1(e11,e12) = e10,
inference(unit_resolution,[status(thm)],[709,337,701,642]) ).
tff(711,plain,
h8(op1(e11,e12)) = h8(e10),
inference(monotonicity,[status(thm)],[710]) ).
tff(712,plain,
h8(op1(e11,e12)) = op2(h8(e11),h8(e12)),
inference(transitivity,[status(thm)],[711,5,96,686,657]) ).
tff(713,plain,
op2(h8(e11),h8(e11)) = op2(e20,e20),
inference(monotonicity,[status(thm)],[161,161]) ).
tff(714,plain,
op2(e20,e20) = op2(h8(e11),h8(e11)),
inference(symmetry,[status(thm)],[713]) ).
tff(715,plain,
e20 = op2(e20,e20),
inference(symmetry,[status(thm)],[103]) ).
tff(716,plain,
h8(op1(e11,e11)) = h8(e11),
inference(monotonicity,[status(thm)],[220]) ).
tff(717,plain,
h8(op1(e11,e11)) = op2(h8(e11),h8(e11)),
inference(transitivity,[status(thm)],[716,160,157,156,715,714]) ).
tff(718,plain,
op2(h8(e10),h8(e10)) = op2(e23,e23),
inference(monotonicity,[status(thm)],[395,395]) ).
tff(719,plain,
op2(e23,e23) = op2(h8(e10),h8(e10)),
inference(symmetry,[status(thm)],[718]) ).
tff(720,plain,
e23 = op2(e23,e23),
inference(symmetry,[status(thm)],[364]) ).
tff(721,plain,
h8(op1(e10,e10)) = h8(e10),
inference(monotonicity,[status(thm)],[307]) ).
tff(722,plain,
h8(op1(e10,e10)) = op2(h8(e10),h8(e10)),
inference(transitivity,[status(thm)],[721,5,96,720,719]) ).
tff(723,plain,
op2(h8(e10),h8(e13)) = op2(op2(e22,e21),e21),
inference(monotonicity,[status(thm)],[5,167]) ).
tff(724,plain,
op2(op2(e22,e21),e21) = op2(h8(e10),h8(e13)),
inference(symmetry,[status(thm)],[723]) ).
tff(725,plain,
h8(op1(e10,e13)) = h8(e11),
inference(monotonicity,[status(thm)],[267]) ).
tff(726,plain,
h8(op1(e10,e13)) = op2(h8(e10),h8(e13)),
inference(transitivity,[status(thm)],[725,160,724]) ).
tff(727,plain,
op2(h8(e10),h8(e12)) = op2(e23,e22),
inference(monotonicity,[status(thm)],[395,179]) ).
tff(728,plain,
op2(e23,e22) = op2(h8(e10),h8(e12)),
inference(symmetry,[status(thm)],[727]) ).
tff(729,plain,
( ( e21 = op2(e21,e22) )
<=> ( op2(e21,e22) = e21 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(730,plain,
( ( op2(e21,e21) = op2(e21,e22) )
<=> ( e21 = op2(e21,e22) ) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(731,plain,
( ( op2(e21,e21) = op2(e21,e22) )
<=> ( op2(e21,e22) = e21 ) ),
inference(transitivity,[status(thm)],[730,729]) ).
tff(732,plain,
( ( op2(e21,e21) != op2(e21,e22) )
<=> ( op2(e21,e22) != e21 ) ),
inference(monotonicity,[status(thm)],[731]) ).
tff(733,plain,
( ( op2(e21,e21) != op2(e21,e22) )
<=> ( op2(e21,e21) != op2(e21,e22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(734,plain,
op2(e21,e21) != op2(e21,e22),
inference(and_elim,[status(thm)],[33]) ).
tff(735,plain,
op2(e21,e21) != op2(e21,e22),
inference(modus_ponens,[status(thm)],[734,733]) ).
tff(736,plain,
op2(e21,e22) != e21,
inference(modus_ponens,[status(thm)],[735,732]) ).
tff(737,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(738,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(739,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(740,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)],[739]) ).
tff(741,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)],[740,738]) ).
tff(742,plain,
( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ),
inference(and_elim,[status(thm)],[142]) ).
tff(743,plain,
( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ),
inference(modus_ponens,[status(thm)],[742,741]) ).
tff(744,plain,
( ( op2(e20,e22) = e21 )
| ( op2(e21,e22) = e21 )
| ( op2(e22,e22) = e21 )
| ( op2(e23,e22) = e21 ) ),
inference(modus_ponens,[status(thm)],[743,737]) ).
tff(745,plain,
op2(e23,e22) = e21,
inference(unit_resolution,[status(thm)],[744,671,524,736]) ).
tff(746,plain,
e21 = op2(e23,e22),
inference(symmetry,[status(thm)],[745]) ).
tff(747,plain,
( ( e10 = op1(e10,e12) )
<=> ( op1(e10,e12) = e10 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(748,plain,
( ( op1(e10,e10) = op1(e10,e12) )
<=> ( e10 = op1(e10,e12) ) ),
inference(monotonicity,[status(thm)],[307]) ).
tff(749,plain,
( ( op1(e10,e10) = op1(e10,e12) )
<=> ( op1(e10,e12) = e10 ) ),
inference(transitivity,[status(thm)],[748,747]) ).
tff(750,plain,
( ( op1(e10,e10) != op1(e10,e12) )
<=> ( op1(e10,e12) != e10 ) ),
inference(monotonicity,[status(thm)],[749]) ).
tff(751,plain,
( ( op1(e10,e10) != op1(e10,e12) )
<=> ( op1(e10,e10) != op1(e10,e12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(752,plain,
op1(e10,e10) != op1(e10,e12),
inference(and_elim,[status(thm)],[315]) ).
tff(753,plain,
op1(e10,e10) != op1(e10,e12),
inference(modus_ponens,[status(thm)],[752,751]) ).
tff(754,plain,
op1(e10,e12) != e10,
inference(modus_ponens,[status(thm)],[753,750]) ).
tff(755,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
<=> ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(756,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
<=> ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(757,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 ) )
<=> ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(758,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
<=> ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ) ),
inference(monotonicity,[status(thm)],[757]) ).
tff(759,plain,
( ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
<=> ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ) ),
inference(transitivity,[status(thm)],[758,756]) ).
tff(760,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)],[649]) ).
tff(761,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)],[760]) ).
tff(762,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)],[761]) ).
tff(763,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) )
& ( ( op1(e10,e13) = e10 )
| ( op1(e10,e13) = e11 )
| ( op1(e10,e13) = e12 )
| ( op1(e10,e13) = e13 ) ) ),
inference(and_elim,[status(thm)],[762]) ).
tff(764,plain,
( ( ( op1(e10,e10) = e10 )
| ( op1(e10,e10) = e11 )
| ( op1(e10,e10) = e12 )
| ( op1(e10,e10) = e13 ) )
& ( ( op1(e10,e11) = e10 )
| ( op1(e10,e11) = e11 )
| ( op1(e10,e11) = e12 )
| ( op1(e10,e11) = e13 ) )
& ( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ) ),
inference(and_elim,[status(thm)],[763]) ).
tff(765,plain,
( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ),
inference(and_elim,[status(thm)],[764]) ).
tff(766,plain,
( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[765,759]) ).
tff(767,plain,
( ( op1(e10,e12) = e10 )
| ( op1(e10,e12) = e11 )
| ( op1(e10,e12) = e12 )
| ( op1(e10,e12) = e13 ) ),
inference(modus_ponens,[status(thm)],[766,755]) ).
tff(768,plain,
op1(e10,e12) = e13,
inference(unit_resolution,[status(thm)],[767,277,456,754]) ).
tff(769,plain,
h8(op1(e10,e12)) = h8(e13),
inference(monotonicity,[status(thm)],[768]) ).
tff(770,plain,
h8(op1(e10,e12)) = op2(h8(e10),h8(e12)),
inference(transitivity,[status(thm)],[769,167,746,728]) ).
tff(771,plain,
( ( e22 = op2(e23,e20) )
<=> ( op2(e23,e20) = e22 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(772,plain,
op2(h8(e10),h8(e11)) = op2(e23,e20),
inference(monotonicity,[status(thm)],[395,161]) ).
tff(773,plain,
h8(op1(e10,e11)) = h8(e12),
inference(monotonicity,[status(thm)],[477]) ).
tff(774,plain,
h8(op1(e10,e11)) = e22,
inference(transitivity,[status(thm)],[773,179]) ).
tff(775,plain,
( ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
<=> ( e22 = op2(e23,e20) ) ),
inference(monotonicity,[status(thm)],[774,772]) ).
tff(776,plain,
( ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
<=> ( op2(e23,e20) = e22 ) ),
inference(transitivity,[status(thm)],[775,771]) ).
tff(777,plain,
( ( op2(e23,e20) = e22 )
<=> ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) ) ),
inference(symmetry,[status(thm)],[776]) ).
tff(778,plain,
( ( e23 = e22 )
<=> ( e22 = e23 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(779,plain,
( ( op2(e23,e23) = e22 )
<=> ( e23 = e22 ) ),
inference(monotonicity,[status(thm)],[364]) ).
tff(780,plain,
( ( op2(e23,e23) = e22 )
<=> ( e22 = e23 ) ),
inference(transitivity,[status(thm)],[779,778]) ).
tff(781,plain,
( ( e22 = e23 )
<=> ( op2(e23,e23) = e22 ) ),
inference(symmetry,[status(thm)],[780]) ).
tff(782,plain,
( ( e22 != e23 )
<=> ( op2(e23,e23) != e22 ) ),
inference(monotonicity,[status(thm)],[781]) ).
tff(783,plain,
( ( e22 != e23 )
<=> ( e22 != e23 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(784,plain,
e22 != e23,
inference(and_elim,[status(thm)],[117]) ).
tff(785,plain,
e22 != e23,
inference(modus_ponens,[status(thm)],[784,783]) ).
tff(786,plain,
op2(e23,e23) != e22,
inference(modus_ponens,[status(thm)],[785,782]) ).
tff(787,plain,
( ( e22 = op2(e23,e22) )
<=> ( op2(e23,e22) = e22 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(788,plain,
( ( op2(e22,e22) = op2(e23,e22) )
<=> ( e22 = op2(e23,e22) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(789,plain,
( ( op2(e22,e22) = op2(e23,e22) )
<=> ( op2(e23,e22) = e22 ) ),
inference(transitivity,[status(thm)],[788,787]) ).
tff(790,plain,
( ( op2(e22,e22) != op2(e23,e22) )
<=> ( op2(e23,e22) != e22 ) ),
inference(monotonicity,[status(thm)],[789]) ).
tff(791,plain,
( ( op2(e22,e22) != op2(e23,e22) )
<=> ( op2(e22,e22) != op2(e23,e22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(792,plain,
op2(e22,e22) != op2(e23,e22),
inference(and_elim,[status(thm)],[49]) ).
tff(793,plain,
op2(e22,e22) != op2(e23,e22),
inference(modus_ponens,[status(thm)],[792,791]) ).
tff(794,plain,
op2(e23,e22) != e22,
inference(modus_ponens,[status(thm)],[793,790]) ).
tff(795,plain,
( ( e22 = op2(e23,e21) )
<=> ( op2(e23,e21) = e22 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(796,plain,
( ( op2(e20,e21) = op2(e23,e21) )
<=> ( e22 = op2(e23,e21) ) ),
inference(monotonicity,[status(thm)],[621]) ).
tff(797,plain,
( ( op2(e20,e21) = op2(e23,e21) )
<=> ( op2(e23,e21) = e22 ) ),
inference(transitivity,[status(thm)],[796,795]) ).
tff(798,plain,
( ( op2(e20,e21) != op2(e23,e21) )
<=> ( op2(e23,e21) != e22 ) ),
inference(monotonicity,[status(thm)],[797]) ).
tff(799,plain,
( ( op2(e20,e21) != op2(e23,e21) )
<=> ( op2(e20,e21) != op2(e23,e21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(800,plain,
op2(e20,e21) != op2(e23,e21),
inference(and_elim,[status(thm)],[193]) ).
tff(801,plain,
op2(e20,e21) != op2(e23,e21),
inference(modus_ponens,[status(thm)],[800,799]) ).
tff(802,plain,
op2(e23,e21) != e22,
inference(modus_ponens,[status(thm)],[801,798]) ).
tff(803,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(804,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(805,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 ) )
<=> ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(806,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(monotonicity,[status(thm)],[805]) ).
tff(807,plain,
( ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) )
<=> ( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ) ),
inference(transitivity,[status(thm)],[806,804]) ).
tff(808,plain,
( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(and_elim,[status(thm)],[133]) ).
tff(809,plain,
( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[808,807]) ).
tff(810,plain,
( ( op2(e23,e20) = e22 )
| ( op2(e23,e21) = e22 )
| ( op2(e23,e22) = e22 )
| ( op2(e23,e23) = e22 ) ),
inference(modus_ponens,[status(thm)],[809,803]) ).
tff(811,plain,
op2(e23,e20) = e22,
inference(unit_resolution,[status(thm)],[810,802,794,786]) ).
tff(812,plain,
h8(op1(e10,e11)) = op2(h8(e10),h8(e11)),
inference(modus_ponens,[status(thm)],[811,777]) ).
tff(813,plain,
op2(h8(e11),h8(e10)) = op2(e20,e23),
inference(monotonicity,[status(thm)],[161,395]) ).
tff(814,plain,
op2(e20,e23) = op2(h8(e11),h8(e10)),
inference(symmetry,[status(thm)],[813]) ).
tff(815,plain,
op2(op2(e22,e23),e23) = op2(e20,e23),
inference(symmetry,[status(thm)],[590]) ).
tff(816,plain,
( ( op1(e11,e11) = e13 )
<=> ( e11 = e13 ) ),
inference(monotonicity,[status(thm)],[220]) ).
tff(817,plain,
( ( e11 = e13 )
<=> ( op1(e11,e11) = e13 ) ),
inference(symmetry,[status(thm)],[816]) ).
tff(818,plain,
( ( e11 != e13 )
<=> ( op1(e11,e11) != e13 ) ),
inference(monotonicity,[status(thm)],[817]) ).
tff(819,plain,
( ( e11 != e13 )
<=> ( e11 != e13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(820,plain,
e11 != e13,
inference(and_elim,[status(thm)],[253]) ).
tff(821,plain,
e11 != e13,
inference(modus_ponens,[status(thm)],[820,819]) ).
tff(822,plain,
op1(e11,e11) != e13,
inference(modus_ponens,[status(thm)],[821,818]) ).
tff(823,plain,
( ( op1(e11,e12) = e13 )
<=> ( e10 = e13 ) ),
inference(monotonicity,[status(thm)],[710]) ).
tff(824,plain,
( ( e10 = e13 )
<=> ( op1(e11,e12) = e13 ) ),
inference(symmetry,[status(thm)],[823]) ).
tff(825,plain,
( ( e10 != e13 )
<=> ( op1(e11,e12) != e13 ) ),
inference(monotonicity,[status(thm)],[824]) ).
tff(826,plain,
( ( e10 != e13 )
<=> ( e10 != e13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(827,plain,
e10 != e13,
inference(and_elim,[status(thm)],[333]) ).
tff(828,plain,
e10 != e13,
inference(modus_ponens,[status(thm)],[827,826]) ).
tff(829,plain,
op1(e11,e12) != e13,
inference(modus_ponens,[status(thm)],[828,825]) ).
tff(830,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(831,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(832,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 ) )
<=> ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(833,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ) ),
inference(monotonicity,[status(thm)],[832]) ).
tff(834,plain,
( ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) )
<=> ( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ) ),
inference(transitivity,[status(thm)],[833,831]) ).
tff(835,plain,
( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ),
inference(and_elim,[status(thm)],[347]) ).
tff(836,plain,
( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[835,834]) ).
tff(837,plain,
( ( op1(e11,e10) = e13 )
| ( op1(e11,e11) = e13 )
| ( op1(e11,e12) = e13 )
| ( op1(e11,e13) = e13 ) ),
inference(modus_ponens,[status(thm)],[836,830]) ).
tff(838,plain,
op1(e11,e10) = e13,
inference(unit_resolution,[status(thm)],[837,829,822,628]) ).
tff(839,plain,
h8(op1(e11,e10)) = h8(e13),
inference(monotonicity,[status(thm)],[838]) ).
tff(840,plain,
h8(op1(e11,e10)) = op2(h8(e11),h8(e10)),
inference(transitivity,[status(thm)],[839,167,588,815,814]) ).
tff(841,plain,
( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 )
| ( h8(e12) != e22 ) ),
inference(tautology,[status(thm)],[]) ).
tff(842,plain,
( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) ),
inference(unit_resolution,[status(thm)],[841,179]) ).
tff(843,plain,
( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) != e21 ) ),
inference(tautology,[status(thm)],[]) ).
tff(844,plain,
( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) ),
inference(unit_resolution,[status(thm)],[843,167]) ).
tff(845,plain,
( ~ ~ ( ( h8(op1(e10,e10)) != op2(h8(e10),h8(e10)) )
| ( h8(op1(e10,e11)) != op2(h8(e10),h8(e11)) )
| ( h8(op1(e10,e12)) != op2(h8(e10),h8(e12)) )
| ( h8(op1(e10,e13)) != op2(h8(e10),h8(e13)) )
| ( h8(op1(e11,e10)) != op2(h8(e11),h8(e10)) )
| ( h8(op1(e11,e11)) != op2(h8(e11),h8(e11)) )
| ( h8(op1(e11,e12)) != op2(h8(e11),h8(e12)) )
| ( h8(op1(e11,e13)) != op2(h8(e11),h8(e13)) )
| ( h8(op1(e12,e10)) != op2(h8(e12),h8(e10)) )
| ( h8(op1(e12,e11)) != op2(h8(e12),h8(e11)) )
| ( h8(op1(e12,e12)) != op2(h8(e12),h8(e12)) )
| ( h8(op1(e12,e13)) != op2(h8(e12),h8(e13)) )
| ( h8(op1(e13,e10)) != op2(h8(e13),h8(e10)) )
| ( h8(op1(e13,e11)) != op2(h8(e13),h8(e11)) )
| ( h8(op1(e13,e12)) != op2(h8(e13),h8(e12)) )
| ( h8(op1(e13,e13)) != op2(h8(e13),h8(e13)) )
| ~ ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
| ~ ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
| ~ ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
| ~ ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
<=> ( ( h8(op1(e10,e10)) != op2(h8(e10),h8(e10)) )
| ( h8(op1(e10,e11)) != op2(h8(e10),h8(e11)) )
| ( h8(op1(e10,e12)) != op2(h8(e10),h8(e12)) )
| ( h8(op1(e10,e13)) != op2(h8(e10),h8(e13)) )
| ( h8(op1(e11,e10)) != op2(h8(e11),h8(e10)) )
| ( h8(op1(e11,e11)) != op2(h8(e11),h8(e11)) )
| ( h8(op1(e11,e12)) != op2(h8(e11),h8(e12)) )
| ( h8(op1(e11,e13)) != op2(h8(e11),h8(e13)) )
| ( h8(op1(e12,e10)) != op2(h8(e12),h8(e10)) )
| ( h8(op1(e12,e11)) != op2(h8(e12),h8(e11)) )
| ( h8(op1(e12,e12)) != op2(h8(e12),h8(e12)) )
| ( h8(op1(e12,e13)) != op2(h8(e12),h8(e13)) )
| ( h8(op1(e13,e10)) != op2(h8(e13),h8(e10)) )
| ( h8(op1(e13,e11)) != op2(h8(e13),h8(e11)) )
| ( h8(op1(e13,e12)) != op2(h8(e13),h8(e12)) )
| ( h8(op1(e13,e13)) != op2(h8(e13),h8(e13)) )
| ~ ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
| ~ ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
| ~ ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
| ~ ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(846,plain,
( ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
<=> ~ ( ( h8(op1(e10,e10)) != op2(h8(e10),h8(e10)) )
| ( h8(op1(e10,e11)) != op2(h8(e10),h8(e11)) )
| ( h8(op1(e10,e12)) != op2(h8(e10),h8(e12)) )
| ( h8(op1(e10,e13)) != op2(h8(e10),h8(e13)) )
| ( h8(op1(e11,e10)) != op2(h8(e11),h8(e10)) )
| ( h8(op1(e11,e11)) != op2(h8(e11),h8(e11)) )
| ( h8(op1(e11,e12)) != op2(h8(e11),h8(e12)) )
| ( h8(op1(e11,e13)) != op2(h8(e11),h8(e13)) )
| ( h8(op1(e12,e10)) != op2(h8(e12),h8(e10)) )
| ( h8(op1(e12,e11)) != op2(h8(e12),h8(e11)) )
| ( h8(op1(e12,e12)) != op2(h8(e12),h8(e12)) )
| ( h8(op1(e12,e13)) != op2(h8(e12),h8(e13)) )
| ( h8(op1(e13,e10)) != op2(h8(e13),h8(e10)) )
| ( h8(op1(e13,e11)) != op2(h8(e13),h8(e11)) )
| ( h8(op1(e13,e12)) != op2(h8(e13),h8(e12)) )
| ( h8(op1(e13,e13)) != op2(h8(e13),h8(e13)) )
| ~ ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
| ~ ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
| ~ ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
| ~ ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(847,plain,
( ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
<=> ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(848,plain,
( ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
<=> ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(849,plain,
( ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
<=> ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ) ),
inference(monotonicity,[status(thm)],[848,847]) ).
tff(850,plain,
( ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
<=> ~ ( ( h8(op1(e10,e10)) != op2(h8(e10),h8(e10)) )
| ( h8(op1(e10,e11)) != op2(h8(e10),h8(e11)) )
| ( h8(op1(e10,e12)) != op2(h8(e10),h8(e12)) )
| ( h8(op1(e10,e13)) != op2(h8(e10),h8(e13)) )
| ( h8(op1(e11,e10)) != op2(h8(e11),h8(e10)) )
| ( h8(op1(e11,e11)) != op2(h8(e11),h8(e11)) )
| ( h8(op1(e11,e12)) != op2(h8(e11),h8(e12)) )
| ( h8(op1(e11,e13)) != op2(h8(e11),h8(e13)) )
| ( h8(op1(e12,e10)) != op2(h8(e12),h8(e10)) )
| ( h8(op1(e12,e11)) != op2(h8(e12),h8(e11)) )
| ( h8(op1(e12,e12)) != op2(h8(e12),h8(e12)) )
| ( h8(op1(e12,e13)) != op2(h8(e12),h8(e13)) )
| ( h8(op1(e13,e10)) != op2(h8(e13),h8(e10)) )
| ( h8(op1(e13,e11)) != op2(h8(e13),h8(e11)) )
| ( h8(op1(e13,e12)) != op2(h8(e13),h8(e12)) )
| ( h8(op1(e13,e13)) != op2(h8(e13),h8(e13)) )
| ~ ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
| ~ ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
| ~ ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
| ~ ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ) ),
inference(transitivity,[status(thm)],[849,846]) ).
tff(851,plain,
( ~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
<=> ~ ~ ( ( h8(op1(e10,e10)) != op2(h8(e10),h8(e10)) )
| ( h8(op1(e10,e11)) != op2(h8(e10),h8(e11)) )
| ( h8(op1(e10,e12)) != op2(h8(e10),h8(e12)) )
| ( h8(op1(e10,e13)) != op2(h8(e10),h8(e13)) )
| ( h8(op1(e11,e10)) != op2(h8(e11),h8(e10)) )
| ( h8(op1(e11,e11)) != op2(h8(e11),h8(e11)) )
| ( h8(op1(e11,e12)) != op2(h8(e11),h8(e12)) )
| ( h8(op1(e11,e13)) != op2(h8(e11),h8(e13)) )
| ( h8(op1(e12,e10)) != op2(h8(e12),h8(e10)) )
| ( h8(op1(e12,e11)) != op2(h8(e12),h8(e11)) )
| ( h8(op1(e12,e12)) != op2(h8(e12),h8(e12)) )
| ( h8(op1(e12,e13)) != op2(h8(e12),h8(e13)) )
| ( h8(op1(e13,e10)) != op2(h8(e13),h8(e10)) )
| ( h8(op1(e13,e11)) != op2(h8(e13),h8(e11)) )
| ( h8(op1(e13,e12)) != op2(h8(e13),h8(e12)) )
| ( h8(op1(e13,e13)) != op2(h8(e13),h8(e13)) )
| ~ ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
| ~ ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
| ~ ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
| ~ ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ) ),
inference(monotonicity,[status(thm)],[850]) ).
tff(852,plain,
( ~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
<=> ( ( h8(op1(e10,e10)) != op2(h8(e10),h8(e10)) )
| ( h8(op1(e10,e11)) != op2(h8(e10),h8(e11)) )
| ( h8(op1(e10,e12)) != op2(h8(e10),h8(e12)) )
| ( h8(op1(e10,e13)) != op2(h8(e10),h8(e13)) )
| ( h8(op1(e11,e10)) != op2(h8(e11),h8(e10)) )
| ( h8(op1(e11,e11)) != op2(h8(e11),h8(e11)) )
| ( h8(op1(e11,e12)) != op2(h8(e11),h8(e12)) )
| ( h8(op1(e11,e13)) != op2(h8(e11),h8(e13)) )
| ( h8(op1(e12,e10)) != op2(h8(e12),h8(e10)) )
| ( h8(op1(e12,e11)) != op2(h8(e12),h8(e11)) )
| ( h8(op1(e12,e12)) != op2(h8(e12),h8(e12)) )
| ( h8(op1(e12,e13)) != op2(h8(e12),h8(e13)) )
| ( h8(op1(e13,e10)) != op2(h8(e13),h8(e10)) )
| ( h8(op1(e13,e11)) != op2(h8(e13),h8(e11)) )
| ( h8(op1(e13,e12)) != op2(h8(e13),h8(e12)) )
| ( h8(op1(e13,e13)) != op2(h8(e13),h8(e13)) )
| ~ ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
| ~ ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
| ~ ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
| ~ ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ) ),
inference(transitivity,[status(thm)],[851,845]) ).
tff(853,plain,
( ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
<=> ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(854,plain,
( ~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
<=> ~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ) ),
inference(monotonicity,[status(thm)],[853]) ).
tff(855,plain,
( ~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
<=> ~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(856,plain,
( ~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) = e21 ) )
& ( ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e12) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
<=> ~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(857,axiom,
~ ( ( ( h1(op1(e10,e10)) = op2(h1(e10),h1(e10)) )
& ( h1(op1(e10,e11)) = op2(h1(e10),h1(e11)) )
& ( h1(op1(e10,e12)) = op2(h1(e10),h1(e12)) )
& ( h1(op1(e10,e13)) = op2(h1(e10),h1(e13)) )
& ( h1(op1(e11,e10)) = op2(h1(e11),h1(e10)) )
& ( h1(op1(e11,e11)) = op2(h1(e11),h1(e11)) )
& ( h1(op1(e11,e12)) = op2(h1(e11),h1(e12)) )
& ( h1(op1(e11,e13)) = op2(h1(e11),h1(e13)) )
& ( h1(op1(e12,e10)) = op2(h1(e12),h1(e10)) )
& ( h1(op1(e12,e11)) = op2(h1(e12),h1(e11)) )
& ( h1(op1(e12,e12)) = op2(h1(e12),h1(e12)) )
& ( h1(op1(e12,e13)) = op2(h1(e12),h1(e13)) )
& ( h1(op1(e13,e10)) = op2(h1(e13),h1(e10)) )
& ( h1(op1(e13,e11)) = op2(h1(e13),h1(e11)) )
& ( h1(op1(e13,e12)) = op2(h1(e13),h1(e12)) )
& ( h1(op1(e13,e13)) = op2(h1(e13),h1(e13)) )
& ( ( h1(e10) = e20 )
| ( h1(e11) = e20 )
| ( h1(e12) = e20 )
| ( h1(e13) = e20 ) )
& ( ( h1(e10) = e21 )
| ( h1(e11) = e21 )
| ( h1(e12) = e21 )
| ( h1(e13) = e21 ) )
& ( ( h1(e10) = e22 )
| ( h1(e11) = e22 )
| ( h1(e12) = e22 )
| ( h1(e13) = e22 ) )
& ( ( h1(e10) = e23 )
| ( h1(e11) = e23 )
| ( h1(e12) = e23 )
| ( h1(e13) = e23 ) ) )
| ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 )
| ( h2(e13) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
| ( ( h3(op1(e10,e10)) = op2(h3(e10),h3(e10)) )
& ( h3(op1(e10,e11)) = op2(h3(e10),h3(e11)) )
& ( h3(op1(e10,e12)) = op2(h3(e10),h3(e12)) )
& ( h3(op1(e10,e13)) = op2(h3(e10),h3(e13)) )
& ( h3(op1(e11,e10)) = op2(h3(e11),h3(e10)) )
& ( h3(op1(e11,e11)) = op2(h3(e11),h3(e11)) )
& ( h3(op1(e11,e12)) = op2(h3(e11),h3(e12)) )
& ( h3(op1(e11,e13)) = op2(h3(e11),h3(e13)) )
& ( h3(op1(e12,e10)) = op2(h3(e12),h3(e10)) )
& ( h3(op1(e12,e11)) = op2(h3(e12),h3(e11)) )
& ( h3(op1(e12,e12)) = op2(h3(e12),h3(e12)) )
& ( h3(op1(e12,e13)) = op2(h3(e12),h3(e13)) )
& ( h3(op1(e13,e10)) = op2(h3(e13),h3(e10)) )
& ( h3(op1(e13,e11)) = op2(h3(e13),h3(e11)) )
& ( h3(op1(e13,e12)) = op2(h3(e13),h3(e12)) )
& ( h3(op1(e13,e13)) = op2(h3(e13),h3(e13)) )
& ( ( h3(e10) = e20 )
| ( h3(e11) = e20 )
| ( h3(e12) = e20 )
| ( h3(e13) = e20 ) )
& ( ( h3(e10) = e21 )
| ( h3(e11) = e21 )
| ( h3(e12) = e21 )
| ( h3(e13) = e21 ) )
& ( ( h3(e10) = e22 )
| ( h3(e11) = e22 )
| ( h3(e12) = e22 )
| ( h3(e13) = e22 ) )
& ( ( h3(e10) = e23 )
| ( h3(e11) = e23 )
| ( h3(e12) = e23 )
| ( h3(e13) = e23 ) ) )
| ( ( h4(op1(e10,e10)) = op2(h4(e10),h4(e10)) )
& ( h4(op1(e10,e11)) = op2(h4(e10),h4(e11)) )
& ( h4(op1(e10,e12)) = op2(h4(e10),h4(e12)) )
& ( h4(op1(e10,e13)) = op2(h4(e10),h4(e13)) )
& ( h4(op1(e11,e10)) = op2(h4(e11),h4(e10)) )
& ( h4(op1(e11,e11)) = op2(h4(e11),h4(e11)) )
& ( h4(op1(e11,e12)) = op2(h4(e11),h4(e12)) )
& ( h4(op1(e11,e13)) = op2(h4(e11),h4(e13)) )
& ( h4(op1(e12,e10)) = op2(h4(e12),h4(e10)) )
& ( h4(op1(e12,e11)) = op2(h4(e12),h4(e11)) )
& ( h4(op1(e12,e12)) = op2(h4(e12),h4(e12)) )
& ( h4(op1(e12,e13)) = op2(h4(e12),h4(e13)) )
& ( h4(op1(e13,e10)) = op2(h4(e13),h4(e10)) )
& ( h4(op1(e13,e11)) = op2(h4(e13),h4(e11)) )
& ( h4(op1(e13,e12)) = op2(h4(e13),h4(e12)) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(e10) = e20 )
| ( h4(e11) = e20 )
| ( h4(e12) = e20 )
| ( h4(e13) = e20 ) )
& ( ( h4(e10) = e21 )
| ( h4(e11) = e21 )
| ( h4(e12) = e21 )
| ( h4(e13) = e21 ) )
& ( ( h4(e10) = e22 )
| ( h4(e11) = e22 )
| ( h4(e12) = e22 )
| ( h4(e13) = e22 ) )
& ( ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 )
| ( h4(e13) = e23 ) ) )
| ( ( h5(op1(e10,e10)) = op2(h5(e10),h5(e10)) )
& ( h5(op1(e10,e11)) = op2(h5(e10),h5(e11)) )
& ( h5(op1(e10,e12)) = op2(h5(e10),h5(e12)) )
& ( h5(op1(e10,e13)) = op2(h5(e10),h5(e13)) )
& ( h5(op1(e11,e10)) = op2(h5(e11),h5(e10)) )
& ( h5(op1(e11,e11)) = op2(h5(e11),h5(e11)) )
& ( h5(op1(e11,e12)) = op2(h5(e11),h5(e12)) )
& ( h5(op1(e11,e13)) = op2(h5(e11),h5(e13)) )
& ( h5(op1(e12,e10)) = op2(h5(e12),h5(e10)) )
& ( h5(op1(e12,e11)) = op2(h5(e12),h5(e11)) )
& ( h5(op1(e12,e12)) = op2(h5(e12),h5(e12)) )
& ( h5(op1(e12,e13)) = op2(h5(e12),h5(e13)) )
& ( h5(op1(e13,e10)) = op2(h5(e13),h5(e10)) )
& ( h5(op1(e13,e11)) = op2(h5(e13),h5(e11)) )
& ( h5(op1(e13,e12)) = op2(h5(e13),h5(e12)) )
& ( h5(op1(e13,e13)) = op2(h5(e13),h5(e13)) )
& ( ( h5(e10) = e20 )
| ( h5(e11) = e20 )
| ( h5(e12) = e20 )
| ( h5(e13) = e20 ) )
& ( ( h5(e10) = e21 )
| ( h5(e11) = e21 )
| ( h5(e12) = e21 )
| ( h5(e13) = e21 ) )
& ( ( h5(e10) = e22 )
| ( h5(e11) = e22 )
| ( h5(e12) = e22 )
| ( h5(e13) = e22 ) )
& ( ( h5(e10) = e23 )
| ( h5(e11) = e23 )
| ( h5(e12) = e23 )
| ( h5(e13) = e23 ) ) )
| ( ( h6(op1(e10,e10)) = op2(h6(e10),h6(e10)) )
& ( h6(op1(e10,e11)) = op2(h6(e10),h6(e11)) )
& ( h6(op1(e10,e12)) = op2(h6(e10),h6(e12)) )
& ( h6(op1(e10,e13)) = op2(h6(e10),h6(e13)) )
& ( h6(op1(e11,e10)) = op2(h6(e11),h6(e10)) )
& ( h6(op1(e11,e11)) = op2(h6(e11),h6(e11)) )
& ( h6(op1(e11,e12)) = op2(h6(e11),h6(e12)) )
& ( h6(op1(e11,e13)) = op2(h6(e11),h6(e13)) )
& ( h6(op1(e12,e10)) = op2(h6(e12),h6(e10)) )
& ( h6(op1(e12,e11)) = op2(h6(e12),h6(e11)) )
& ( h6(op1(e12,e12)) = op2(h6(e12),h6(e12)) )
& ( h6(op1(e12,e13)) = op2(h6(e12),h6(e13)) )
& ( h6(op1(e13,e10)) = op2(h6(e13),h6(e10)) )
& ( h6(op1(e13,e11)) = op2(h6(e13),h6(e11)) )
& ( h6(op1(e13,e12)) = op2(h6(e13),h6(e12)) )
& ( h6(op1(e13,e13)) = op2(h6(e13),h6(e13)) )
& ( ( h6(e10) = e20 )
| ( h6(e11) = e20 )
| ( h6(e12) = e20 )
| ( h6(e13) = e20 ) )
& ( ( h6(e10) = e21 )
| ( h6(e11) = e21 )
| ( h6(e12) = e21 )
| ( h6(e13) = e21 ) )
& ( ( h6(e10) = e22 )
| ( h6(e11) = e22 )
| ( h6(e12) = e22 )
| ( h6(e13) = e22 ) )
& ( ( h6(e10) = e23 )
| ( h6(e11) = e23 )
| ( h6(e12) = e23 )
| ( h6(e13) = e23 ) ) )
| ( ( h7(op1(e10,e10)) = op2(h7(e10),h7(e10)) )
& ( h7(op1(e10,e11)) = op2(h7(e10),h7(e11)) )
& ( h7(op1(e10,e12)) = op2(h7(e10),h7(e12)) )
& ( h7(op1(e10,e13)) = op2(h7(e10),h7(e13)) )
& ( h7(op1(e11,e10)) = op2(h7(e11),h7(e10)) )
& ( h7(op1(e11,e11)) = op2(h7(e11),h7(e11)) )
& ( h7(op1(e11,e12)) = op2(h7(e11),h7(e12)) )
& ( h7(op1(e11,e13)) = op2(h7(e11),h7(e13)) )
& ( h7(op1(e12,e10)) = op2(h7(e12),h7(e10)) )
& ( h7(op1(e12,e11)) = op2(h7(e12),h7(e11)) )
& ( h7(op1(e12,e12)) = op2(h7(e12),h7(e12)) )
& ( h7(op1(e12,e13)) = op2(h7(e12),h7(e13)) )
& ( h7(op1(e13,e10)) = op2(h7(e13),h7(e10)) )
& ( h7(op1(e13,e11)) = op2(h7(e13),h7(e11)) )
& ( h7(op1(e13,e12)) = op2(h7(e13),h7(e12)) )
& ( h7(op1(e13,e13)) = op2(h7(e13),h7(e13)) )
& ( ( h7(e10) = e20 )
| ( h7(e11) = e20 )
| ( h7(e12) = e20 )
| ( h7(e13) = e20 ) )
& ( ( h7(e10) = e21 )
| ( h7(e11) = e21 )
| ( h7(e12) = e21 )
| ( h7(e13) = e21 ) )
& ( ( h7(e10) = e22 )
| ( h7(e11) = e22 )
| ( h7(e12) = e22 )
| ( h7(e13) = e22 ) )
& ( ( h7(e10) = e23 )
| ( h7(e11) = e23 )
| ( h7(e12) = e23 )
| ( h7(e13) = e23 ) ) )
| ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) = e21 ) )
& ( ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e12) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
| ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e12) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 )
| ( h9(e13) = e23 ) ) )
| ( ( h10(op1(e10,e10)) = op2(h10(e10),h10(e10)) )
& ( h10(op1(e10,e11)) = op2(h10(e10),h10(e11)) )
& ( h10(op1(e10,e12)) = op2(h10(e10),h10(e12)) )
& ( h10(op1(e10,e13)) = op2(h10(e10),h10(e13)) )
& ( h10(op1(e11,e10)) = op2(h10(e11),h10(e10)) )
& ( h10(op1(e11,e11)) = op2(h10(e11),h10(e11)) )
& ( h10(op1(e11,e12)) = op2(h10(e11),h10(e12)) )
& ( h10(op1(e11,e13)) = op2(h10(e11),h10(e13)) )
& ( h10(op1(e12,e10)) = op2(h10(e12),h10(e10)) )
& ( h10(op1(e12,e11)) = op2(h10(e12),h10(e11)) )
& ( h10(op1(e12,e12)) = op2(h10(e12),h10(e12)) )
& ( h10(op1(e12,e13)) = op2(h10(e12),h10(e13)) )
& ( h10(op1(e13,e10)) = op2(h10(e13),h10(e10)) )
& ( h10(op1(e13,e11)) = op2(h10(e13),h10(e11)) )
& ( h10(op1(e13,e12)) = op2(h10(e13),h10(e12)) )
& ( h10(op1(e13,e13)) = op2(h10(e13),h10(e13)) )
& ( ( h10(e10) = e20 )
| ( h10(e11) = e20 )
| ( h10(e12) = e20 )
| ( h10(e13) = e20 ) )
& ( ( h10(e10) = e21 )
| ( h10(e11) = e21 )
| ( h10(e12) = e21 )
| ( h10(e13) = e21 ) )
& ( ( h10(e10) = e22 )
| ( h10(e11) = e22 )
| ( h10(e12) = e22 )
| ( h10(e13) = e22 ) )
& ( ( h10(e10) = e23 )
| ( h10(e11) = e23 )
| ( h10(e12) = e23 )
| ( h10(e13) = e23 ) ) )
| ( ( h11(op1(e10,e10)) = op2(h11(e10),h11(e10)) )
& ( h11(op1(e10,e11)) = op2(h11(e10),h11(e11)) )
& ( h11(op1(e10,e12)) = op2(h11(e10),h11(e12)) )
& ( h11(op1(e10,e13)) = op2(h11(e10),h11(e13)) )
& ( h11(op1(e11,e10)) = op2(h11(e11),h11(e10)) )
& ( h11(op1(e11,e11)) = op2(h11(e11),h11(e11)) )
& ( h11(op1(e11,e12)) = op2(h11(e11),h11(e12)) )
& ( h11(op1(e11,e13)) = op2(h11(e11),h11(e13)) )
& ( h11(op1(e12,e10)) = op2(h11(e12),h11(e10)) )
& ( h11(op1(e12,e11)) = op2(h11(e12),h11(e11)) )
& ( h11(op1(e12,e12)) = op2(h11(e12),h11(e12)) )
& ( h11(op1(e12,e13)) = op2(h11(e12),h11(e13)) )
& ( h11(op1(e13,e10)) = op2(h11(e13),h11(e10)) )
& ( h11(op1(e13,e11)) = op2(h11(e13),h11(e11)) )
& ( h11(op1(e13,e12)) = op2(h11(e13),h11(e12)) )
& ( h11(op1(e13,e13)) = op2(h11(e13),h11(e13)) )
& ( ( h11(e10) = e20 )
| ( h11(e11) = e20 )
| ( h11(e12) = e20 )
| ( h11(e13) = e20 ) )
& ( ( h11(e10) = e21 )
| ( h11(e11) = e21 )
| ( h11(e12) = e21 )
| ( h11(e13) = e21 ) )
& ( ( h11(e10) = e22 )
| ( h11(e11) = e22 )
| ( h11(e12) = e22 )
| ( h11(e13) = e22 ) )
& ( ( h11(e10) = e23 )
| ( h11(e11) = e23 )
| ( h11(e12) = e23 )
| ( h11(e13) = e23 ) ) )
| ( ( h12(op1(e10,e10)) = op2(h12(e10),h12(e10)) )
& ( h12(op1(e10,e11)) = op2(h12(e10),h12(e11)) )
& ( h12(op1(e10,e12)) = op2(h12(e10),h12(e12)) )
& ( h12(op1(e10,e13)) = op2(h12(e10),h12(e13)) )
& ( h12(op1(e11,e10)) = op2(h12(e11),h12(e10)) )
& ( h12(op1(e11,e11)) = op2(h12(e11),h12(e11)) )
& ( h12(op1(e11,e12)) = op2(h12(e11),h12(e12)) )
& ( h12(op1(e11,e13)) = op2(h12(e11),h12(e13)) )
& ( h12(op1(e12,e10)) = op2(h12(e12),h12(e10)) )
& ( h12(op1(e12,e11)) = op2(h12(e12),h12(e11)) )
& ( h12(op1(e12,e12)) = op2(h12(e12),h12(e12)) )
& ( h12(op1(e12,e13)) = op2(h12(e12),h12(e13)) )
& ( h12(op1(e13,e10)) = op2(h12(e13),h12(e10)) )
& ( h12(op1(e13,e11)) = op2(h12(e13),h12(e11)) )
& ( h12(op1(e13,e12)) = op2(h12(e13),h12(e12)) )
& ( h12(op1(e13,e13)) = op2(h12(e13),h12(e13)) )
& ( ( h12(e10) = e20 )
| ( h12(e11) = e20 )
| ( h12(e12) = e20 )
| ( h12(e13) = e20 ) )
& ( ( h12(e10) = e21 )
| ( h12(e11) = e21 )
| ( h12(e12) = e21 )
| ( h12(e13) = e21 ) )
& ( ( h12(e10) = e22 )
| ( h12(e11) = e22 )
| ( h12(e12) = e22 )
| ( h12(e13) = e22 ) )
& ( ( h12(e10) = e23 )
| ( h12(e11) = e23 )
| ( h12(e12) = e23 )
| ( h12(e13) = e23 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(858,plain,
~ ( ( ( h1(op1(e10,e10)) = op2(h1(e10),h1(e10)) )
& ( h1(op1(e10,e11)) = op2(h1(e10),h1(e11)) )
& ( h1(op1(e10,e12)) = op2(h1(e10),h1(e12)) )
& ( h1(op1(e10,e13)) = op2(h1(e10),h1(e13)) )
& ( h1(op1(e11,e10)) = op2(h1(e11),h1(e10)) )
& ( h1(op1(e11,e11)) = op2(h1(e11),h1(e11)) )
& ( h1(op1(e11,e12)) = op2(h1(e11),h1(e12)) )
& ( h1(op1(e11,e13)) = op2(h1(e11),h1(e13)) )
& ( h1(op1(e12,e10)) = op2(h1(e12),h1(e10)) )
& ( h1(op1(e12,e11)) = op2(h1(e12),h1(e11)) )
& ( h1(op1(e12,e12)) = op2(h1(e12),h1(e12)) )
& ( h1(op1(e12,e13)) = op2(h1(e12),h1(e13)) )
& ( h1(op1(e13,e10)) = op2(h1(e13),h1(e10)) )
& ( h1(op1(e13,e11)) = op2(h1(e13),h1(e11)) )
& ( h1(op1(e13,e12)) = op2(h1(e13),h1(e12)) )
& ( h1(op1(e13,e13)) = op2(h1(e13),h1(e13)) )
& ( ( h1(e10) = e20 )
| ( h1(e11) = e20 )
| ( h1(e12) = e20 )
| ( h1(e13) = e20 ) )
& ( ( h1(e10) = e21 )
| ( h1(e11) = e21 )
| ( h1(e12) = e21 )
| ( h1(e13) = e21 ) )
& ( ( h1(e10) = e22 )
| ( h1(e11) = e22 )
| ( h1(e12) = e22 )
| ( h1(e13) = e22 ) )
& ( ( h1(e10) = e23 )
| ( h1(e11) = e23 )
| ( h1(e12) = e23 )
| ( h1(e13) = e23 ) ) )
| ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 )
| ( h2(e13) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
| ( ( h3(op1(e10,e10)) = op2(h3(e10),h3(e10)) )
& ( h3(op1(e10,e11)) = op2(h3(e10),h3(e11)) )
& ( h3(op1(e10,e12)) = op2(h3(e10),h3(e12)) )
& ( h3(op1(e10,e13)) = op2(h3(e10),h3(e13)) )
& ( h3(op1(e11,e10)) = op2(h3(e11),h3(e10)) )
& ( h3(op1(e11,e11)) = op2(h3(e11),h3(e11)) )
& ( h3(op1(e11,e12)) = op2(h3(e11),h3(e12)) )
& ( h3(op1(e11,e13)) = op2(h3(e11),h3(e13)) )
& ( h3(op1(e12,e10)) = op2(h3(e12),h3(e10)) )
& ( h3(op1(e12,e11)) = op2(h3(e12),h3(e11)) )
& ( h3(op1(e12,e12)) = op2(h3(e12),h3(e12)) )
& ( h3(op1(e12,e13)) = op2(h3(e12),h3(e13)) )
& ( h3(op1(e13,e10)) = op2(h3(e13),h3(e10)) )
& ( h3(op1(e13,e11)) = op2(h3(e13),h3(e11)) )
& ( h3(op1(e13,e12)) = op2(h3(e13),h3(e12)) )
& ( h3(op1(e13,e13)) = op2(h3(e13),h3(e13)) )
& ( ( h3(e10) = e20 )
| ( h3(e11) = e20 )
| ( h3(e12) = e20 )
| ( h3(e13) = e20 ) )
& ( ( h3(e10) = e21 )
| ( h3(e11) = e21 )
| ( h3(e12) = e21 )
| ( h3(e13) = e21 ) )
& ( ( h3(e10) = e22 )
| ( h3(e11) = e22 )
| ( h3(e12) = e22 )
| ( h3(e13) = e22 ) )
& ( ( h3(e10) = e23 )
| ( h3(e11) = e23 )
| ( h3(e12) = e23 )
| ( h3(e13) = e23 ) ) )
| ( ( h4(op1(e10,e10)) = op2(h4(e10),h4(e10)) )
& ( h4(op1(e10,e11)) = op2(h4(e10),h4(e11)) )
& ( h4(op1(e10,e12)) = op2(h4(e10),h4(e12)) )
& ( h4(op1(e10,e13)) = op2(h4(e10),h4(e13)) )
& ( h4(op1(e11,e10)) = op2(h4(e11),h4(e10)) )
& ( h4(op1(e11,e11)) = op2(h4(e11),h4(e11)) )
& ( h4(op1(e11,e12)) = op2(h4(e11),h4(e12)) )
& ( h4(op1(e11,e13)) = op2(h4(e11),h4(e13)) )
& ( h4(op1(e12,e10)) = op2(h4(e12),h4(e10)) )
& ( h4(op1(e12,e11)) = op2(h4(e12),h4(e11)) )
& ( h4(op1(e12,e12)) = op2(h4(e12),h4(e12)) )
& ( h4(op1(e12,e13)) = op2(h4(e12),h4(e13)) )
& ( h4(op1(e13,e10)) = op2(h4(e13),h4(e10)) )
& ( h4(op1(e13,e11)) = op2(h4(e13),h4(e11)) )
& ( h4(op1(e13,e12)) = op2(h4(e13),h4(e12)) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(e10) = e20 )
| ( h4(e11) = e20 )
| ( h4(e12) = e20 )
| ( h4(e13) = e20 ) )
& ( ( h4(e10) = e21 )
| ( h4(e11) = e21 )
| ( h4(e12) = e21 )
| ( h4(e13) = e21 ) )
& ( ( h4(e10) = e22 )
| ( h4(e11) = e22 )
| ( h4(e12) = e22 )
| ( h4(e13) = e22 ) )
& ( ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 )
| ( h4(e13) = e23 ) ) )
| ( ( h5(op1(e10,e10)) = op2(h5(e10),h5(e10)) )
& ( h5(op1(e10,e11)) = op2(h5(e10),h5(e11)) )
& ( h5(op1(e10,e12)) = op2(h5(e10),h5(e12)) )
& ( h5(op1(e10,e13)) = op2(h5(e10),h5(e13)) )
& ( h5(op1(e11,e10)) = op2(h5(e11),h5(e10)) )
& ( h5(op1(e11,e11)) = op2(h5(e11),h5(e11)) )
& ( h5(op1(e11,e12)) = op2(h5(e11),h5(e12)) )
& ( h5(op1(e11,e13)) = op2(h5(e11),h5(e13)) )
& ( h5(op1(e12,e10)) = op2(h5(e12),h5(e10)) )
& ( h5(op1(e12,e11)) = op2(h5(e12),h5(e11)) )
& ( h5(op1(e12,e12)) = op2(h5(e12),h5(e12)) )
& ( h5(op1(e12,e13)) = op2(h5(e12),h5(e13)) )
& ( h5(op1(e13,e10)) = op2(h5(e13),h5(e10)) )
& ( h5(op1(e13,e11)) = op2(h5(e13),h5(e11)) )
& ( h5(op1(e13,e12)) = op2(h5(e13),h5(e12)) )
& ( h5(op1(e13,e13)) = op2(h5(e13),h5(e13)) )
& ( ( h5(e10) = e20 )
| ( h5(e11) = e20 )
| ( h5(e12) = e20 )
| ( h5(e13) = e20 ) )
& ( ( h5(e10) = e21 )
| ( h5(e11) = e21 )
| ( h5(e12) = e21 )
| ( h5(e13) = e21 ) )
& ( ( h5(e10) = e22 )
| ( h5(e11) = e22 )
| ( h5(e12) = e22 )
| ( h5(e13) = e22 ) )
& ( ( h5(e10) = e23 )
| ( h5(e11) = e23 )
| ( h5(e12) = e23 )
| ( h5(e13) = e23 ) ) )
| ( ( h6(op1(e10,e10)) = op2(h6(e10),h6(e10)) )
& ( h6(op1(e10,e11)) = op2(h6(e10),h6(e11)) )
& ( h6(op1(e10,e12)) = op2(h6(e10),h6(e12)) )
& ( h6(op1(e10,e13)) = op2(h6(e10),h6(e13)) )
& ( h6(op1(e11,e10)) = op2(h6(e11),h6(e10)) )
& ( h6(op1(e11,e11)) = op2(h6(e11),h6(e11)) )
& ( h6(op1(e11,e12)) = op2(h6(e11),h6(e12)) )
& ( h6(op1(e11,e13)) = op2(h6(e11),h6(e13)) )
& ( h6(op1(e12,e10)) = op2(h6(e12),h6(e10)) )
& ( h6(op1(e12,e11)) = op2(h6(e12),h6(e11)) )
& ( h6(op1(e12,e12)) = op2(h6(e12),h6(e12)) )
& ( h6(op1(e12,e13)) = op2(h6(e12),h6(e13)) )
& ( h6(op1(e13,e10)) = op2(h6(e13),h6(e10)) )
& ( h6(op1(e13,e11)) = op2(h6(e13),h6(e11)) )
& ( h6(op1(e13,e12)) = op2(h6(e13),h6(e12)) )
& ( h6(op1(e13,e13)) = op2(h6(e13),h6(e13)) )
& ( ( h6(e10) = e20 )
| ( h6(e11) = e20 )
| ( h6(e12) = e20 )
| ( h6(e13) = e20 ) )
& ( ( h6(e10) = e21 )
| ( h6(e11) = e21 )
| ( h6(e12) = e21 )
| ( h6(e13) = e21 ) )
& ( ( h6(e10) = e22 )
| ( h6(e11) = e22 )
| ( h6(e12) = e22 )
| ( h6(e13) = e22 ) )
& ( ( h6(e10) = e23 )
| ( h6(e11) = e23 )
| ( h6(e12) = e23 )
| ( h6(e13) = e23 ) ) )
| ( ( h7(op1(e10,e10)) = op2(h7(e10),h7(e10)) )
& ( h7(op1(e10,e11)) = op2(h7(e10),h7(e11)) )
& ( h7(op1(e10,e12)) = op2(h7(e10),h7(e12)) )
& ( h7(op1(e10,e13)) = op2(h7(e10),h7(e13)) )
& ( h7(op1(e11,e10)) = op2(h7(e11),h7(e10)) )
& ( h7(op1(e11,e11)) = op2(h7(e11),h7(e11)) )
& ( h7(op1(e11,e12)) = op2(h7(e11),h7(e12)) )
& ( h7(op1(e11,e13)) = op2(h7(e11),h7(e13)) )
& ( h7(op1(e12,e10)) = op2(h7(e12),h7(e10)) )
& ( h7(op1(e12,e11)) = op2(h7(e12),h7(e11)) )
& ( h7(op1(e12,e12)) = op2(h7(e12),h7(e12)) )
& ( h7(op1(e12,e13)) = op2(h7(e12),h7(e13)) )
& ( h7(op1(e13,e10)) = op2(h7(e13),h7(e10)) )
& ( h7(op1(e13,e11)) = op2(h7(e13),h7(e11)) )
& ( h7(op1(e13,e12)) = op2(h7(e13),h7(e12)) )
& ( h7(op1(e13,e13)) = op2(h7(e13),h7(e13)) )
& ( ( h7(e10) = e20 )
| ( h7(e11) = e20 )
| ( h7(e12) = e20 )
| ( h7(e13) = e20 ) )
& ( ( h7(e10) = e21 )
| ( h7(e11) = e21 )
| ( h7(e12) = e21 )
| ( h7(e13) = e21 ) )
& ( ( h7(e10) = e22 )
| ( h7(e11) = e22 )
| ( h7(e12) = e22 )
| ( h7(e13) = e22 ) )
& ( ( h7(e10) = e23 )
| ( h7(e11) = e23 )
| ( h7(e12) = e23 )
| ( h7(e13) = e23 ) ) )
| ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) = e21 ) )
& ( ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e12) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
| ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e12) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 )
| ( h9(e13) = e23 ) ) )
| ( ( h10(op1(e10,e10)) = op2(h10(e10),h10(e10)) )
& ( h10(op1(e10,e11)) = op2(h10(e10),h10(e11)) )
& ( h10(op1(e10,e12)) = op2(h10(e10),h10(e12)) )
& ( h10(op1(e10,e13)) = op2(h10(e10),h10(e13)) )
& ( h10(op1(e11,e10)) = op2(h10(e11),h10(e10)) )
& ( h10(op1(e11,e11)) = op2(h10(e11),h10(e11)) )
& ( h10(op1(e11,e12)) = op2(h10(e11),h10(e12)) )
& ( h10(op1(e11,e13)) = op2(h10(e11),h10(e13)) )
& ( h10(op1(e12,e10)) = op2(h10(e12),h10(e10)) )
& ( h10(op1(e12,e11)) = op2(h10(e12),h10(e11)) )
& ( h10(op1(e12,e12)) = op2(h10(e12),h10(e12)) )
& ( h10(op1(e12,e13)) = op2(h10(e12),h10(e13)) )
& ( h10(op1(e13,e10)) = op2(h10(e13),h10(e10)) )
& ( h10(op1(e13,e11)) = op2(h10(e13),h10(e11)) )
& ( h10(op1(e13,e12)) = op2(h10(e13),h10(e12)) )
& ( h10(op1(e13,e13)) = op2(h10(e13),h10(e13)) )
& ( ( h10(e10) = e20 )
| ( h10(e11) = e20 )
| ( h10(e12) = e20 )
| ( h10(e13) = e20 ) )
& ( ( h10(e10) = e21 )
| ( h10(e11) = e21 )
| ( h10(e12) = e21 )
| ( h10(e13) = e21 ) )
& ( ( h10(e10) = e22 )
| ( h10(e11) = e22 )
| ( h10(e12) = e22 )
| ( h10(e13) = e22 ) )
& ( ( h10(e10) = e23 )
| ( h10(e11) = e23 )
| ( h10(e12) = e23 )
| ( h10(e13) = e23 ) ) )
| ( ( h11(op1(e10,e10)) = op2(h11(e10),h11(e10)) )
& ( h11(op1(e10,e11)) = op2(h11(e10),h11(e11)) )
& ( h11(op1(e10,e12)) = op2(h11(e10),h11(e12)) )
& ( h11(op1(e10,e13)) = op2(h11(e10),h11(e13)) )
& ( h11(op1(e11,e10)) = op2(h11(e11),h11(e10)) )
& ( h11(op1(e11,e11)) = op2(h11(e11),h11(e11)) )
& ( h11(op1(e11,e12)) = op2(h11(e11),h11(e12)) )
& ( h11(op1(e11,e13)) = op2(h11(e11),h11(e13)) )
& ( h11(op1(e12,e10)) = op2(h11(e12),h11(e10)) )
& ( h11(op1(e12,e11)) = op2(h11(e12),h11(e11)) )
& ( h11(op1(e12,e12)) = op2(h11(e12),h11(e12)) )
& ( h11(op1(e12,e13)) = op2(h11(e12),h11(e13)) )
& ( h11(op1(e13,e10)) = op2(h11(e13),h11(e10)) )
& ( h11(op1(e13,e11)) = op2(h11(e13),h11(e11)) )
& ( h11(op1(e13,e12)) = op2(h11(e13),h11(e12)) )
& ( h11(op1(e13,e13)) = op2(h11(e13),h11(e13)) )
& ( ( h11(e10) = e20 )
| ( h11(e11) = e20 )
| ( h11(e12) = e20 )
| ( h11(e13) = e20 ) )
& ( ( h11(e10) = e21 )
| ( h11(e11) = e21 )
| ( h11(e12) = e21 )
| ( h11(e13) = e21 ) )
& ( ( h11(e10) = e22 )
| ( h11(e11) = e22 )
| ( h11(e12) = e22 )
| ( h11(e13) = e22 ) )
& ( ( h11(e10) = e23 )
| ( h11(e11) = e23 )
| ( h11(e12) = e23 )
| ( h11(e13) = e23 ) ) ) ),
inference(or_elim,[status(thm)],[857]) ).
tff(859,plain,
~ ( ( ( h1(op1(e10,e10)) = op2(h1(e10),h1(e10)) )
& ( h1(op1(e10,e11)) = op2(h1(e10),h1(e11)) )
& ( h1(op1(e10,e12)) = op2(h1(e10),h1(e12)) )
& ( h1(op1(e10,e13)) = op2(h1(e10),h1(e13)) )
& ( h1(op1(e11,e10)) = op2(h1(e11),h1(e10)) )
& ( h1(op1(e11,e11)) = op2(h1(e11),h1(e11)) )
& ( h1(op1(e11,e12)) = op2(h1(e11),h1(e12)) )
& ( h1(op1(e11,e13)) = op2(h1(e11),h1(e13)) )
& ( h1(op1(e12,e10)) = op2(h1(e12),h1(e10)) )
& ( h1(op1(e12,e11)) = op2(h1(e12),h1(e11)) )
& ( h1(op1(e12,e12)) = op2(h1(e12),h1(e12)) )
& ( h1(op1(e12,e13)) = op2(h1(e12),h1(e13)) )
& ( h1(op1(e13,e10)) = op2(h1(e13),h1(e10)) )
& ( h1(op1(e13,e11)) = op2(h1(e13),h1(e11)) )
& ( h1(op1(e13,e12)) = op2(h1(e13),h1(e12)) )
& ( h1(op1(e13,e13)) = op2(h1(e13),h1(e13)) )
& ( ( h1(e10) = e20 )
| ( h1(e11) = e20 )
| ( h1(e12) = e20 )
| ( h1(e13) = e20 ) )
& ( ( h1(e10) = e21 )
| ( h1(e11) = e21 )
| ( h1(e12) = e21 )
| ( h1(e13) = e21 ) )
& ( ( h1(e10) = e22 )
| ( h1(e11) = e22 )
| ( h1(e12) = e22 )
| ( h1(e13) = e22 ) )
& ( ( h1(e10) = e23 )
| ( h1(e11) = e23 )
| ( h1(e12) = e23 )
| ( h1(e13) = e23 ) ) )
| ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 )
| ( h2(e13) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
| ( ( h3(op1(e10,e10)) = op2(h3(e10),h3(e10)) )
& ( h3(op1(e10,e11)) = op2(h3(e10),h3(e11)) )
& ( h3(op1(e10,e12)) = op2(h3(e10),h3(e12)) )
& ( h3(op1(e10,e13)) = op2(h3(e10),h3(e13)) )
& ( h3(op1(e11,e10)) = op2(h3(e11),h3(e10)) )
& ( h3(op1(e11,e11)) = op2(h3(e11),h3(e11)) )
& ( h3(op1(e11,e12)) = op2(h3(e11),h3(e12)) )
& ( h3(op1(e11,e13)) = op2(h3(e11),h3(e13)) )
& ( h3(op1(e12,e10)) = op2(h3(e12),h3(e10)) )
& ( h3(op1(e12,e11)) = op2(h3(e12),h3(e11)) )
& ( h3(op1(e12,e12)) = op2(h3(e12),h3(e12)) )
& ( h3(op1(e12,e13)) = op2(h3(e12),h3(e13)) )
& ( h3(op1(e13,e10)) = op2(h3(e13),h3(e10)) )
& ( h3(op1(e13,e11)) = op2(h3(e13),h3(e11)) )
& ( h3(op1(e13,e12)) = op2(h3(e13),h3(e12)) )
& ( h3(op1(e13,e13)) = op2(h3(e13),h3(e13)) )
& ( ( h3(e10) = e20 )
| ( h3(e11) = e20 )
| ( h3(e12) = e20 )
| ( h3(e13) = e20 ) )
& ( ( h3(e10) = e21 )
| ( h3(e11) = e21 )
| ( h3(e12) = e21 )
| ( h3(e13) = e21 ) )
& ( ( h3(e10) = e22 )
| ( h3(e11) = e22 )
| ( h3(e12) = e22 )
| ( h3(e13) = e22 ) )
& ( ( h3(e10) = e23 )
| ( h3(e11) = e23 )
| ( h3(e12) = e23 )
| ( h3(e13) = e23 ) ) )
| ( ( h4(op1(e10,e10)) = op2(h4(e10),h4(e10)) )
& ( h4(op1(e10,e11)) = op2(h4(e10),h4(e11)) )
& ( h4(op1(e10,e12)) = op2(h4(e10),h4(e12)) )
& ( h4(op1(e10,e13)) = op2(h4(e10),h4(e13)) )
& ( h4(op1(e11,e10)) = op2(h4(e11),h4(e10)) )
& ( h4(op1(e11,e11)) = op2(h4(e11),h4(e11)) )
& ( h4(op1(e11,e12)) = op2(h4(e11),h4(e12)) )
& ( h4(op1(e11,e13)) = op2(h4(e11),h4(e13)) )
& ( h4(op1(e12,e10)) = op2(h4(e12),h4(e10)) )
& ( h4(op1(e12,e11)) = op2(h4(e12),h4(e11)) )
& ( h4(op1(e12,e12)) = op2(h4(e12),h4(e12)) )
& ( h4(op1(e12,e13)) = op2(h4(e12),h4(e13)) )
& ( h4(op1(e13,e10)) = op2(h4(e13),h4(e10)) )
& ( h4(op1(e13,e11)) = op2(h4(e13),h4(e11)) )
& ( h4(op1(e13,e12)) = op2(h4(e13),h4(e12)) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(e10) = e20 )
| ( h4(e11) = e20 )
| ( h4(e12) = e20 )
| ( h4(e13) = e20 ) )
& ( ( h4(e10) = e21 )
| ( h4(e11) = e21 )
| ( h4(e12) = e21 )
| ( h4(e13) = e21 ) )
& ( ( h4(e10) = e22 )
| ( h4(e11) = e22 )
| ( h4(e12) = e22 )
| ( h4(e13) = e22 ) )
& ( ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 )
| ( h4(e13) = e23 ) ) )
| ( ( h5(op1(e10,e10)) = op2(h5(e10),h5(e10)) )
& ( h5(op1(e10,e11)) = op2(h5(e10),h5(e11)) )
& ( h5(op1(e10,e12)) = op2(h5(e10),h5(e12)) )
& ( h5(op1(e10,e13)) = op2(h5(e10),h5(e13)) )
& ( h5(op1(e11,e10)) = op2(h5(e11),h5(e10)) )
& ( h5(op1(e11,e11)) = op2(h5(e11),h5(e11)) )
& ( h5(op1(e11,e12)) = op2(h5(e11),h5(e12)) )
& ( h5(op1(e11,e13)) = op2(h5(e11),h5(e13)) )
& ( h5(op1(e12,e10)) = op2(h5(e12),h5(e10)) )
& ( h5(op1(e12,e11)) = op2(h5(e12),h5(e11)) )
& ( h5(op1(e12,e12)) = op2(h5(e12),h5(e12)) )
& ( h5(op1(e12,e13)) = op2(h5(e12),h5(e13)) )
& ( h5(op1(e13,e10)) = op2(h5(e13),h5(e10)) )
& ( h5(op1(e13,e11)) = op2(h5(e13),h5(e11)) )
& ( h5(op1(e13,e12)) = op2(h5(e13),h5(e12)) )
& ( h5(op1(e13,e13)) = op2(h5(e13),h5(e13)) )
& ( ( h5(e10) = e20 )
| ( h5(e11) = e20 )
| ( h5(e12) = e20 )
| ( h5(e13) = e20 ) )
& ( ( h5(e10) = e21 )
| ( h5(e11) = e21 )
| ( h5(e12) = e21 )
| ( h5(e13) = e21 ) )
& ( ( h5(e10) = e22 )
| ( h5(e11) = e22 )
| ( h5(e12) = e22 )
| ( h5(e13) = e22 ) )
& ( ( h5(e10) = e23 )
| ( h5(e11) = e23 )
| ( h5(e12) = e23 )
| ( h5(e13) = e23 ) ) )
| ( ( h6(op1(e10,e10)) = op2(h6(e10),h6(e10)) )
& ( h6(op1(e10,e11)) = op2(h6(e10),h6(e11)) )
& ( h6(op1(e10,e12)) = op2(h6(e10),h6(e12)) )
& ( h6(op1(e10,e13)) = op2(h6(e10),h6(e13)) )
& ( h6(op1(e11,e10)) = op2(h6(e11),h6(e10)) )
& ( h6(op1(e11,e11)) = op2(h6(e11),h6(e11)) )
& ( h6(op1(e11,e12)) = op2(h6(e11),h6(e12)) )
& ( h6(op1(e11,e13)) = op2(h6(e11),h6(e13)) )
& ( h6(op1(e12,e10)) = op2(h6(e12),h6(e10)) )
& ( h6(op1(e12,e11)) = op2(h6(e12),h6(e11)) )
& ( h6(op1(e12,e12)) = op2(h6(e12),h6(e12)) )
& ( h6(op1(e12,e13)) = op2(h6(e12),h6(e13)) )
& ( h6(op1(e13,e10)) = op2(h6(e13),h6(e10)) )
& ( h6(op1(e13,e11)) = op2(h6(e13),h6(e11)) )
& ( h6(op1(e13,e12)) = op2(h6(e13),h6(e12)) )
& ( h6(op1(e13,e13)) = op2(h6(e13),h6(e13)) )
& ( ( h6(e10) = e20 )
| ( h6(e11) = e20 )
| ( h6(e12) = e20 )
| ( h6(e13) = e20 ) )
& ( ( h6(e10) = e21 )
| ( h6(e11) = e21 )
| ( h6(e12) = e21 )
| ( h6(e13) = e21 ) )
& ( ( h6(e10) = e22 )
| ( h6(e11) = e22 )
| ( h6(e12) = e22 )
| ( h6(e13) = e22 ) )
& ( ( h6(e10) = e23 )
| ( h6(e11) = e23 )
| ( h6(e12) = e23 )
| ( h6(e13) = e23 ) ) )
| ( ( h7(op1(e10,e10)) = op2(h7(e10),h7(e10)) )
& ( h7(op1(e10,e11)) = op2(h7(e10),h7(e11)) )
& ( h7(op1(e10,e12)) = op2(h7(e10),h7(e12)) )
& ( h7(op1(e10,e13)) = op2(h7(e10),h7(e13)) )
& ( h7(op1(e11,e10)) = op2(h7(e11),h7(e10)) )
& ( h7(op1(e11,e11)) = op2(h7(e11),h7(e11)) )
& ( h7(op1(e11,e12)) = op2(h7(e11),h7(e12)) )
& ( h7(op1(e11,e13)) = op2(h7(e11),h7(e13)) )
& ( h7(op1(e12,e10)) = op2(h7(e12),h7(e10)) )
& ( h7(op1(e12,e11)) = op2(h7(e12),h7(e11)) )
& ( h7(op1(e12,e12)) = op2(h7(e12),h7(e12)) )
& ( h7(op1(e12,e13)) = op2(h7(e12),h7(e13)) )
& ( h7(op1(e13,e10)) = op2(h7(e13),h7(e10)) )
& ( h7(op1(e13,e11)) = op2(h7(e13),h7(e11)) )
& ( h7(op1(e13,e12)) = op2(h7(e13),h7(e12)) )
& ( h7(op1(e13,e13)) = op2(h7(e13),h7(e13)) )
& ( ( h7(e10) = e20 )
| ( h7(e11) = e20 )
| ( h7(e12) = e20 )
| ( h7(e13) = e20 ) )
& ( ( h7(e10) = e21 )
| ( h7(e11) = e21 )
| ( h7(e12) = e21 )
| ( h7(e13) = e21 ) )
& ( ( h7(e10) = e22 )
| ( h7(e11) = e22 )
| ( h7(e12) = e22 )
| ( h7(e13) = e22 ) )
& ( ( h7(e10) = e23 )
| ( h7(e11) = e23 )
| ( h7(e12) = e23 )
| ( h7(e13) = e23 ) ) )
| ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) = e21 ) )
& ( ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e12) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
| ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e12) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 )
| ( h9(e13) = e23 ) ) )
| ( ( h10(op1(e10,e10)) = op2(h10(e10),h10(e10)) )
& ( h10(op1(e10,e11)) = op2(h10(e10),h10(e11)) )
& ( h10(op1(e10,e12)) = op2(h10(e10),h10(e12)) )
& ( h10(op1(e10,e13)) = op2(h10(e10),h10(e13)) )
& ( h10(op1(e11,e10)) = op2(h10(e11),h10(e10)) )
& ( h10(op1(e11,e11)) = op2(h10(e11),h10(e11)) )
& ( h10(op1(e11,e12)) = op2(h10(e11),h10(e12)) )
& ( h10(op1(e11,e13)) = op2(h10(e11),h10(e13)) )
& ( h10(op1(e12,e10)) = op2(h10(e12),h10(e10)) )
& ( h10(op1(e12,e11)) = op2(h10(e12),h10(e11)) )
& ( h10(op1(e12,e12)) = op2(h10(e12),h10(e12)) )
& ( h10(op1(e12,e13)) = op2(h10(e12),h10(e13)) )
& ( h10(op1(e13,e10)) = op2(h10(e13),h10(e10)) )
& ( h10(op1(e13,e11)) = op2(h10(e13),h10(e11)) )
& ( h10(op1(e13,e12)) = op2(h10(e13),h10(e12)) )
& ( h10(op1(e13,e13)) = op2(h10(e13),h10(e13)) )
& ( ( h10(e10) = e20 )
| ( h10(e11) = e20 )
| ( h10(e12) = e20 )
| ( h10(e13) = e20 ) )
& ( ( h10(e10) = e21 )
| ( h10(e11) = e21 )
| ( h10(e12) = e21 )
| ( h10(e13) = e21 ) )
& ( ( h10(e10) = e22 )
| ( h10(e11) = e22 )
| ( h10(e12) = e22 )
| ( h10(e13) = e22 ) )
& ( ( h10(e10) = e23 )
| ( h10(e11) = e23 )
| ( h10(e12) = e23 )
| ( h10(e13) = e23 ) ) ) ),
inference(or_elim,[status(thm)],[858]) ).
tff(860,plain,
~ ( ( ( h1(op1(e10,e10)) = op2(h1(e10),h1(e10)) )
& ( h1(op1(e10,e11)) = op2(h1(e10),h1(e11)) )
& ( h1(op1(e10,e12)) = op2(h1(e10),h1(e12)) )
& ( h1(op1(e10,e13)) = op2(h1(e10),h1(e13)) )
& ( h1(op1(e11,e10)) = op2(h1(e11),h1(e10)) )
& ( h1(op1(e11,e11)) = op2(h1(e11),h1(e11)) )
& ( h1(op1(e11,e12)) = op2(h1(e11),h1(e12)) )
& ( h1(op1(e11,e13)) = op2(h1(e11),h1(e13)) )
& ( h1(op1(e12,e10)) = op2(h1(e12),h1(e10)) )
& ( h1(op1(e12,e11)) = op2(h1(e12),h1(e11)) )
& ( h1(op1(e12,e12)) = op2(h1(e12),h1(e12)) )
& ( h1(op1(e12,e13)) = op2(h1(e12),h1(e13)) )
& ( h1(op1(e13,e10)) = op2(h1(e13),h1(e10)) )
& ( h1(op1(e13,e11)) = op2(h1(e13),h1(e11)) )
& ( h1(op1(e13,e12)) = op2(h1(e13),h1(e12)) )
& ( h1(op1(e13,e13)) = op2(h1(e13),h1(e13)) )
& ( ( h1(e10) = e20 )
| ( h1(e11) = e20 )
| ( h1(e12) = e20 )
| ( h1(e13) = e20 ) )
& ( ( h1(e10) = e21 )
| ( h1(e11) = e21 )
| ( h1(e12) = e21 )
| ( h1(e13) = e21 ) )
& ( ( h1(e10) = e22 )
| ( h1(e11) = e22 )
| ( h1(e12) = e22 )
| ( h1(e13) = e22 ) )
& ( ( h1(e10) = e23 )
| ( h1(e11) = e23 )
| ( h1(e12) = e23 )
| ( h1(e13) = e23 ) ) )
| ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 )
| ( h2(e13) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
| ( ( h3(op1(e10,e10)) = op2(h3(e10),h3(e10)) )
& ( h3(op1(e10,e11)) = op2(h3(e10),h3(e11)) )
& ( h3(op1(e10,e12)) = op2(h3(e10),h3(e12)) )
& ( h3(op1(e10,e13)) = op2(h3(e10),h3(e13)) )
& ( h3(op1(e11,e10)) = op2(h3(e11),h3(e10)) )
& ( h3(op1(e11,e11)) = op2(h3(e11),h3(e11)) )
& ( h3(op1(e11,e12)) = op2(h3(e11),h3(e12)) )
& ( h3(op1(e11,e13)) = op2(h3(e11),h3(e13)) )
& ( h3(op1(e12,e10)) = op2(h3(e12),h3(e10)) )
& ( h3(op1(e12,e11)) = op2(h3(e12),h3(e11)) )
& ( h3(op1(e12,e12)) = op2(h3(e12),h3(e12)) )
& ( h3(op1(e12,e13)) = op2(h3(e12),h3(e13)) )
& ( h3(op1(e13,e10)) = op2(h3(e13),h3(e10)) )
& ( h3(op1(e13,e11)) = op2(h3(e13),h3(e11)) )
& ( h3(op1(e13,e12)) = op2(h3(e13),h3(e12)) )
& ( h3(op1(e13,e13)) = op2(h3(e13),h3(e13)) )
& ( ( h3(e10) = e20 )
| ( h3(e11) = e20 )
| ( h3(e12) = e20 )
| ( h3(e13) = e20 ) )
& ( ( h3(e10) = e21 )
| ( h3(e11) = e21 )
| ( h3(e12) = e21 )
| ( h3(e13) = e21 ) )
& ( ( h3(e10) = e22 )
| ( h3(e11) = e22 )
| ( h3(e12) = e22 )
| ( h3(e13) = e22 ) )
& ( ( h3(e10) = e23 )
| ( h3(e11) = e23 )
| ( h3(e12) = e23 )
| ( h3(e13) = e23 ) ) )
| ( ( h4(op1(e10,e10)) = op2(h4(e10),h4(e10)) )
& ( h4(op1(e10,e11)) = op2(h4(e10),h4(e11)) )
& ( h4(op1(e10,e12)) = op2(h4(e10),h4(e12)) )
& ( h4(op1(e10,e13)) = op2(h4(e10),h4(e13)) )
& ( h4(op1(e11,e10)) = op2(h4(e11),h4(e10)) )
& ( h4(op1(e11,e11)) = op2(h4(e11),h4(e11)) )
& ( h4(op1(e11,e12)) = op2(h4(e11),h4(e12)) )
& ( h4(op1(e11,e13)) = op2(h4(e11),h4(e13)) )
& ( h4(op1(e12,e10)) = op2(h4(e12),h4(e10)) )
& ( h4(op1(e12,e11)) = op2(h4(e12),h4(e11)) )
& ( h4(op1(e12,e12)) = op2(h4(e12),h4(e12)) )
& ( h4(op1(e12,e13)) = op2(h4(e12),h4(e13)) )
& ( h4(op1(e13,e10)) = op2(h4(e13),h4(e10)) )
& ( h4(op1(e13,e11)) = op2(h4(e13),h4(e11)) )
& ( h4(op1(e13,e12)) = op2(h4(e13),h4(e12)) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(e10) = e20 )
| ( h4(e11) = e20 )
| ( h4(e12) = e20 )
| ( h4(e13) = e20 ) )
& ( ( h4(e10) = e21 )
| ( h4(e11) = e21 )
| ( h4(e12) = e21 )
| ( h4(e13) = e21 ) )
& ( ( h4(e10) = e22 )
| ( h4(e11) = e22 )
| ( h4(e12) = e22 )
| ( h4(e13) = e22 ) )
& ( ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 )
| ( h4(e13) = e23 ) ) )
| ( ( h5(op1(e10,e10)) = op2(h5(e10),h5(e10)) )
& ( h5(op1(e10,e11)) = op2(h5(e10),h5(e11)) )
& ( h5(op1(e10,e12)) = op2(h5(e10),h5(e12)) )
& ( h5(op1(e10,e13)) = op2(h5(e10),h5(e13)) )
& ( h5(op1(e11,e10)) = op2(h5(e11),h5(e10)) )
& ( h5(op1(e11,e11)) = op2(h5(e11),h5(e11)) )
& ( h5(op1(e11,e12)) = op2(h5(e11),h5(e12)) )
& ( h5(op1(e11,e13)) = op2(h5(e11),h5(e13)) )
& ( h5(op1(e12,e10)) = op2(h5(e12),h5(e10)) )
& ( h5(op1(e12,e11)) = op2(h5(e12),h5(e11)) )
& ( h5(op1(e12,e12)) = op2(h5(e12),h5(e12)) )
& ( h5(op1(e12,e13)) = op2(h5(e12),h5(e13)) )
& ( h5(op1(e13,e10)) = op2(h5(e13),h5(e10)) )
& ( h5(op1(e13,e11)) = op2(h5(e13),h5(e11)) )
& ( h5(op1(e13,e12)) = op2(h5(e13),h5(e12)) )
& ( h5(op1(e13,e13)) = op2(h5(e13),h5(e13)) )
& ( ( h5(e10) = e20 )
| ( h5(e11) = e20 )
| ( h5(e12) = e20 )
| ( h5(e13) = e20 ) )
& ( ( h5(e10) = e21 )
| ( h5(e11) = e21 )
| ( h5(e12) = e21 )
| ( h5(e13) = e21 ) )
& ( ( h5(e10) = e22 )
| ( h5(e11) = e22 )
| ( h5(e12) = e22 )
| ( h5(e13) = e22 ) )
& ( ( h5(e10) = e23 )
| ( h5(e11) = e23 )
| ( h5(e12) = e23 )
| ( h5(e13) = e23 ) ) )
| ( ( h6(op1(e10,e10)) = op2(h6(e10),h6(e10)) )
& ( h6(op1(e10,e11)) = op2(h6(e10),h6(e11)) )
& ( h6(op1(e10,e12)) = op2(h6(e10),h6(e12)) )
& ( h6(op1(e10,e13)) = op2(h6(e10),h6(e13)) )
& ( h6(op1(e11,e10)) = op2(h6(e11),h6(e10)) )
& ( h6(op1(e11,e11)) = op2(h6(e11),h6(e11)) )
& ( h6(op1(e11,e12)) = op2(h6(e11),h6(e12)) )
& ( h6(op1(e11,e13)) = op2(h6(e11),h6(e13)) )
& ( h6(op1(e12,e10)) = op2(h6(e12),h6(e10)) )
& ( h6(op1(e12,e11)) = op2(h6(e12),h6(e11)) )
& ( h6(op1(e12,e12)) = op2(h6(e12),h6(e12)) )
& ( h6(op1(e12,e13)) = op2(h6(e12),h6(e13)) )
& ( h6(op1(e13,e10)) = op2(h6(e13),h6(e10)) )
& ( h6(op1(e13,e11)) = op2(h6(e13),h6(e11)) )
& ( h6(op1(e13,e12)) = op2(h6(e13),h6(e12)) )
& ( h6(op1(e13,e13)) = op2(h6(e13),h6(e13)) )
& ( ( h6(e10) = e20 )
| ( h6(e11) = e20 )
| ( h6(e12) = e20 )
| ( h6(e13) = e20 ) )
& ( ( h6(e10) = e21 )
| ( h6(e11) = e21 )
| ( h6(e12) = e21 )
| ( h6(e13) = e21 ) )
& ( ( h6(e10) = e22 )
| ( h6(e11) = e22 )
| ( h6(e12) = e22 )
| ( h6(e13) = e22 ) )
& ( ( h6(e10) = e23 )
| ( h6(e11) = e23 )
| ( h6(e12) = e23 )
| ( h6(e13) = e23 ) ) )
| ( ( h7(op1(e10,e10)) = op2(h7(e10),h7(e10)) )
& ( h7(op1(e10,e11)) = op2(h7(e10),h7(e11)) )
& ( h7(op1(e10,e12)) = op2(h7(e10),h7(e12)) )
& ( h7(op1(e10,e13)) = op2(h7(e10),h7(e13)) )
& ( h7(op1(e11,e10)) = op2(h7(e11),h7(e10)) )
& ( h7(op1(e11,e11)) = op2(h7(e11),h7(e11)) )
& ( h7(op1(e11,e12)) = op2(h7(e11),h7(e12)) )
& ( h7(op1(e11,e13)) = op2(h7(e11),h7(e13)) )
& ( h7(op1(e12,e10)) = op2(h7(e12),h7(e10)) )
& ( h7(op1(e12,e11)) = op2(h7(e12),h7(e11)) )
& ( h7(op1(e12,e12)) = op2(h7(e12),h7(e12)) )
& ( h7(op1(e12,e13)) = op2(h7(e12),h7(e13)) )
& ( h7(op1(e13,e10)) = op2(h7(e13),h7(e10)) )
& ( h7(op1(e13,e11)) = op2(h7(e13),h7(e11)) )
& ( h7(op1(e13,e12)) = op2(h7(e13),h7(e12)) )
& ( h7(op1(e13,e13)) = op2(h7(e13),h7(e13)) )
& ( ( h7(e10) = e20 )
| ( h7(e11) = e20 )
| ( h7(e12) = e20 )
| ( h7(e13) = e20 ) )
& ( ( h7(e10) = e21 )
| ( h7(e11) = e21 )
| ( h7(e12) = e21 )
| ( h7(e13) = e21 ) )
& ( ( h7(e10) = e22 )
| ( h7(e11) = e22 )
| ( h7(e12) = e22 )
| ( h7(e13) = e22 ) )
& ( ( h7(e10) = e23 )
| ( h7(e11) = e23 )
| ( h7(e12) = e23 )
| ( h7(e13) = e23 ) ) )
| ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) = e21 ) )
& ( ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e12) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) )
| ( ( h9(op1(e10,e10)) = op2(h9(e10),h9(e10)) )
& ( h9(op1(e10,e11)) = op2(h9(e10),h9(e11)) )
& ( h9(op1(e10,e12)) = op2(h9(e10),h9(e12)) )
& ( h9(op1(e10,e13)) = op2(h9(e10),h9(e13)) )
& ( h9(op1(e11,e10)) = op2(h9(e11),h9(e10)) )
& ( h9(op1(e11,e11)) = op2(h9(e11),h9(e11)) )
& ( h9(op1(e11,e12)) = op2(h9(e11),h9(e12)) )
& ( h9(op1(e11,e13)) = op2(h9(e11),h9(e13)) )
& ( h9(op1(e12,e10)) = op2(h9(e12),h9(e10)) )
& ( h9(op1(e12,e11)) = op2(h9(e12),h9(e11)) )
& ( h9(op1(e12,e12)) = op2(h9(e12),h9(e12)) )
& ( h9(op1(e12,e13)) = op2(h9(e12),h9(e13)) )
& ( h9(op1(e13,e10)) = op2(h9(e13),h9(e10)) )
& ( h9(op1(e13,e11)) = op2(h9(e13),h9(e11)) )
& ( h9(op1(e13,e12)) = op2(h9(e13),h9(e12)) )
& ( h9(op1(e13,e13)) = op2(h9(e13),h9(e13)) )
& ( ( h9(e10) = e20 )
| ( h9(e11) = e20 )
| ( h9(e12) = e20 )
| ( h9(e13) = e20 ) )
& ( ( h9(e10) = e21 )
| ( h9(e11) = e21 )
| ( h9(e12) = e21 )
| ( h9(e13) = e21 ) )
& ( ( h9(e10) = e22 )
| ( h9(e11) = e22 )
| ( h9(e12) = e22 )
| ( h9(e13) = e22 ) )
& ( ( h9(e10) = e23 )
| ( h9(e11) = e23 )
| ( h9(e12) = e23 )
| ( h9(e13) = e23 ) ) ) ),
inference(or_elim,[status(thm)],[859]) ).
tff(861,plain,
~ ( ( ( h1(op1(e10,e10)) = op2(h1(e10),h1(e10)) )
& ( h1(op1(e10,e11)) = op2(h1(e10),h1(e11)) )
& ( h1(op1(e10,e12)) = op2(h1(e10),h1(e12)) )
& ( h1(op1(e10,e13)) = op2(h1(e10),h1(e13)) )
& ( h1(op1(e11,e10)) = op2(h1(e11),h1(e10)) )
& ( h1(op1(e11,e11)) = op2(h1(e11),h1(e11)) )
& ( h1(op1(e11,e12)) = op2(h1(e11),h1(e12)) )
& ( h1(op1(e11,e13)) = op2(h1(e11),h1(e13)) )
& ( h1(op1(e12,e10)) = op2(h1(e12),h1(e10)) )
& ( h1(op1(e12,e11)) = op2(h1(e12),h1(e11)) )
& ( h1(op1(e12,e12)) = op2(h1(e12),h1(e12)) )
& ( h1(op1(e12,e13)) = op2(h1(e12),h1(e13)) )
& ( h1(op1(e13,e10)) = op2(h1(e13),h1(e10)) )
& ( h1(op1(e13,e11)) = op2(h1(e13),h1(e11)) )
& ( h1(op1(e13,e12)) = op2(h1(e13),h1(e12)) )
& ( h1(op1(e13,e13)) = op2(h1(e13),h1(e13)) )
& ( ( h1(e10) = e20 )
| ( h1(e11) = e20 )
| ( h1(e12) = e20 )
| ( h1(e13) = e20 ) )
& ( ( h1(e10) = e21 )
| ( h1(e11) = e21 )
| ( h1(e12) = e21 )
| ( h1(e13) = e21 ) )
& ( ( h1(e10) = e22 )
| ( h1(e11) = e22 )
| ( h1(e12) = e22 )
| ( h1(e13) = e22 ) )
& ( ( h1(e10) = e23 )
| ( h1(e11) = e23 )
| ( h1(e12) = e23 )
| ( h1(e13) = e23 ) ) )
| ( ( h2(op1(e10,e10)) = op2(h2(e10),h2(e10)) )
& ( h2(op1(e10,e11)) = op2(h2(e10),h2(e11)) )
& ( h2(op1(e10,e12)) = op2(h2(e10),h2(e12)) )
& ( h2(op1(e10,e13)) = op2(h2(e10),h2(e13)) )
& ( h2(op1(e11,e10)) = op2(h2(e11),h2(e10)) )
& ( h2(op1(e11,e11)) = op2(h2(e11),h2(e11)) )
& ( h2(op1(e11,e12)) = op2(h2(e11),h2(e12)) )
& ( h2(op1(e11,e13)) = op2(h2(e11),h2(e13)) )
& ( h2(op1(e12,e10)) = op2(h2(e12),h2(e10)) )
& ( h2(op1(e12,e11)) = op2(h2(e12),h2(e11)) )
& ( h2(op1(e12,e12)) = op2(h2(e12),h2(e12)) )
& ( h2(op1(e12,e13)) = op2(h2(e12),h2(e13)) )
& ( h2(op1(e13,e10)) = op2(h2(e13),h2(e10)) )
& ( h2(op1(e13,e11)) = op2(h2(e13),h2(e11)) )
& ( h2(op1(e13,e12)) = op2(h2(e13),h2(e12)) )
& ( h2(op1(e13,e13)) = op2(h2(e13),h2(e13)) )
& ( ( h2(e10) = e20 )
| ( h2(e11) = e20 )
| ( h2(e12) = e20 )
| ( h2(e13) = e20 ) )
& ( ( h2(e10) = e21 )
| ( h2(e11) = e21 )
| ( h2(e12) = e21 )
| ( h2(e13) = e21 ) )
& ( ( h2(e10) = e22 )
| ( h2(e11) = e22 )
| ( h2(e12) = e22 )
| ( h2(e13) = e22 ) )
& ( ( h2(e10) = e23 )
| ( h2(e11) = e23 )
| ( h2(e12) = e23 )
| ( h2(e13) = e23 ) ) )
| ( ( h3(op1(e10,e10)) = op2(h3(e10),h3(e10)) )
& ( h3(op1(e10,e11)) = op2(h3(e10),h3(e11)) )
& ( h3(op1(e10,e12)) = op2(h3(e10),h3(e12)) )
& ( h3(op1(e10,e13)) = op2(h3(e10),h3(e13)) )
& ( h3(op1(e11,e10)) = op2(h3(e11),h3(e10)) )
& ( h3(op1(e11,e11)) = op2(h3(e11),h3(e11)) )
& ( h3(op1(e11,e12)) = op2(h3(e11),h3(e12)) )
& ( h3(op1(e11,e13)) = op2(h3(e11),h3(e13)) )
& ( h3(op1(e12,e10)) = op2(h3(e12),h3(e10)) )
& ( h3(op1(e12,e11)) = op2(h3(e12),h3(e11)) )
& ( h3(op1(e12,e12)) = op2(h3(e12),h3(e12)) )
& ( h3(op1(e12,e13)) = op2(h3(e12),h3(e13)) )
& ( h3(op1(e13,e10)) = op2(h3(e13),h3(e10)) )
& ( h3(op1(e13,e11)) = op2(h3(e13),h3(e11)) )
& ( h3(op1(e13,e12)) = op2(h3(e13),h3(e12)) )
& ( h3(op1(e13,e13)) = op2(h3(e13),h3(e13)) )
& ( ( h3(e10) = e20 )
| ( h3(e11) = e20 )
| ( h3(e12) = e20 )
| ( h3(e13) = e20 ) )
& ( ( h3(e10) = e21 )
| ( h3(e11) = e21 )
| ( h3(e12) = e21 )
| ( h3(e13) = e21 ) )
& ( ( h3(e10) = e22 )
| ( h3(e11) = e22 )
| ( h3(e12) = e22 )
| ( h3(e13) = e22 ) )
& ( ( h3(e10) = e23 )
| ( h3(e11) = e23 )
| ( h3(e12) = e23 )
| ( h3(e13) = e23 ) ) )
| ( ( h4(op1(e10,e10)) = op2(h4(e10),h4(e10)) )
& ( h4(op1(e10,e11)) = op2(h4(e10),h4(e11)) )
& ( h4(op1(e10,e12)) = op2(h4(e10),h4(e12)) )
& ( h4(op1(e10,e13)) = op2(h4(e10),h4(e13)) )
& ( h4(op1(e11,e10)) = op2(h4(e11),h4(e10)) )
& ( h4(op1(e11,e11)) = op2(h4(e11),h4(e11)) )
& ( h4(op1(e11,e12)) = op2(h4(e11),h4(e12)) )
& ( h4(op1(e11,e13)) = op2(h4(e11),h4(e13)) )
& ( h4(op1(e12,e10)) = op2(h4(e12),h4(e10)) )
& ( h4(op1(e12,e11)) = op2(h4(e12),h4(e11)) )
& ( h4(op1(e12,e12)) = op2(h4(e12),h4(e12)) )
& ( h4(op1(e12,e13)) = op2(h4(e12),h4(e13)) )
& ( h4(op1(e13,e10)) = op2(h4(e13),h4(e10)) )
& ( h4(op1(e13,e11)) = op2(h4(e13),h4(e11)) )
& ( h4(op1(e13,e12)) = op2(h4(e13),h4(e12)) )
& ( h4(op1(e13,e13)) = op2(h4(e13),h4(e13)) )
& ( ( h4(e10) = e20 )
| ( h4(e11) = e20 )
| ( h4(e12) = e20 )
| ( h4(e13) = e20 ) )
& ( ( h4(e10) = e21 )
| ( h4(e11) = e21 )
| ( h4(e12) = e21 )
| ( h4(e13) = e21 ) )
& ( ( h4(e10) = e22 )
| ( h4(e11) = e22 )
| ( h4(e12) = e22 )
| ( h4(e13) = e22 ) )
& ( ( h4(e10) = e23 )
| ( h4(e11) = e23 )
| ( h4(e12) = e23 )
| ( h4(e13) = e23 ) ) )
| ( ( h5(op1(e10,e10)) = op2(h5(e10),h5(e10)) )
& ( h5(op1(e10,e11)) = op2(h5(e10),h5(e11)) )
& ( h5(op1(e10,e12)) = op2(h5(e10),h5(e12)) )
& ( h5(op1(e10,e13)) = op2(h5(e10),h5(e13)) )
& ( h5(op1(e11,e10)) = op2(h5(e11),h5(e10)) )
& ( h5(op1(e11,e11)) = op2(h5(e11),h5(e11)) )
& ( h5(op1(e11,e12)) = op2(h5(e11),h5(e12)) )
& ( h5(op1(e11,e13)) = op2(h5(e11),h5(e13)) )
& ( h5(op1(e12,e10)) = op2(h5(e12),h5(e10)) )
& ( h5(op1(e12,e11)) = op2(h5(e12),h5(e11)) )
& ( h5(op1(e12,e12)) = op2(h5(e12),h5(e12)) )
& ( h5(op1(e12,e13)) = op2(h5(e12),h5(e13)) )
& ( h5(op1(e13,e10)) = op2(h5(e13),h5(e10)) )
& ( h5(op1(e13,e11)) = op2(h5(e13),h5(e11)) )
& ( h5(op1(e13,e12)) = op2(h5(e13),h5(e12)) )
& ( h5(op1(e13,e13)) = op2(h5(e13),h5(e13)) )
& ( ( h5(e10) = e20 )
| ( h5(e11) = e20 )
| ( h5(e12) = e20 )
| ( h5(e13) = e20 ) )
& ( ( h5(e10) = e21 )
| ( h5(e11) = e21 )
| ( h5(e12) = e21 )
| ( h5(e13) = e21 ) )
& ( ( h5(e10) = e22 )
| ( h5(e11) = e22 )
| ( h5(e12) = e22 )
| ( h5(e13) = e22 ) )
& ( ( h5(e10) = e23 )
| ( h5(e11) = e23 )
| ( h5(e12) = e23 )
| ( h5(e13) = e23 ) ) )
| ( ( h6(op1(e10,e10)) = op2(h6(e10),h6(e10)) )
& ( h6(op1(e10,e11)) = op2(h6(e10),h6(e11)) )
& ( h6(op1(e10,e12)) = op2(h6(e10),h6(e12)) )
& ( h6(op1(e10,e13)) = op2(h6(e10),h6(e13)) )
& ( h6(op1(e11,e10)) = op2(h6(e11),h6(e10)) )
& ( h6(op1(e11,e11)) = op2(h6(e11),h6(e11)) )
& ( h6(op1(e11,e12)) = op2(h6(e11),h6(e12)) )
& ( h6(op1(e11,e13)) = op2(h6(e11),h6(e13)) )
& ( h6(op1(e12,e10)) = op2(h6(e12),h6(e10)) )
& ( h6(op1(e12,e11)) = op2(h6(e12),h6(e11)) )
& ( h6(op1(e12,e12)) = op2(h6(e12),h6(e12)) )
& ( h6(op1(e12,e13)) = op2(h6(e12),h6(e13)) )
& ( h6(op1(e13,e10)) = op2(h6(e13),h6(e10)) )
& ( h6(op1(e13,e11)) = op2(h6(e13),h6(e11)) )
& ( h6(op1(e13,e12)) = op2(h6(e13),h6(e12)) )
& ( h6(op1(e13,e13)) = op2(h6(e13),h6(e13)) )
& ( ( h6(e10) = e20 )
| ( h6(e11) = e20 )
| ( h6(e12) = e20 )
| ( h6(e13) = e20 ) )
& ( ( h6(e10) = e21 )
| ( h6(e11) = e21 )
| ( h6(e12) = e21 )
| ( h6(e13) = e21 ) )
& ( ( h6(e10) = e22 )
| ( h6(e11) = e22 )
| ( h6(e12) = e22 )
| ( h6(e13) = e22 ) )
& ( ( h6(e10) = e23 )
| ( h6(e11) = e23 )
| ( h6(e12) = e23 )
| ( h6(e13) = e23 ) ) )
| ( ( h7(op1(e10,e10)) = op2(h7(e10),h7(e10)) )
& ( h7(op1(e10,e11)) = op2(h7(e10),h7(e11)) )
& ( h7(op1(e10,e12)) = op2(h7(e10),h7(e12)) )
& ( h7(op1(e10,e13)) = op2(h7(e10),h7(e13)) )
& ( h7(op1(e11,e10)) = op2(h7(e11),h7(e10)) )
& ( h7(op1(e11,e11)) = op2(h7(e11),h7(e11)) )
& ( h7(op1(e11,e12)) = op2(h7(e11),h7(e12)) )
& ( h7(op1(e11,e13)) = op2(h7(e11),h7(e13)) )
& ( h7(op1(e12,e10)) = op2(h7(e12),h7(e10)) )
& ( h7(op1(e12,e11)) = op2(h7(e12),h7(e11)) )
& ( h7(op1(e12,e12)) = op2(h7(e12),h7(e12)) )
& ( h7(op1(e12,e13)) = op2(h7(e12),h7(e13)) )
& ( h7(op1(e13,e10)) = op2(h7(e13),h7(e10)) )
& ( h7(op1(e13,e11)) = op2(h7(e13),h7(e11)) )
& ( h7(op1(e13,e12)) = op2(h7(e13),h7(e12)) )
& ( h7(op1(e13,e13)) = op2(h7(e13),h7(e13)) )
& ( ( h7(e10) = e20 )
| ( h7(e11) = e20 )
| ( h7(e12) = e20 )
| ( h7(e13) = e20 ) )
& ( ( h7(e10) = e21 )
| ( h7(e11) = e21 )
| ( h7(e12) = e21 )
| ( h7(e13) = e21 ) )
& ( ( h7(e10) = e22 )
| ( h7(e11) = e22 )
| ( h7(e12) = e22 )
| ( h7(e13) = e22 ) )
& ( ( h7(e10) = e23 )
| ( h7(e11) = e23 )
| ( h7(e12) = e23 )
| ( h7(e13) = e23 ) ) )
| ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) = e21 ) )
& ( ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e12) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ) ),
inference(or_elim,[status(thm)],[860]) ).
tff(862,plain,
~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 )
| ( h8(e13) = e21 ) )
& ( ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e12) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ),
inference(or_elim,[status(thm)],[861]) ).
tff(863,plain,
~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[862,856]) ).
tff(864,plain,
~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[863,854]) ).
tff(865,plain,
~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[864,855]) ).
tff(866,plain,
~ ( ( h8(op1(e10,e10)) = op2(h8(e10),h8(e10)) )
& ( h8(op1(e10,e11)) = op2(h8(e10),h8(e11)) )
& ( h8(op1(e10,e12)) = op2(h8(e10),h8(e12)) )
& ( h8(op1(e10,e13)) = op2(h8(e10),h8(e13)) )
& ( h8(op1(e11,e10)) = op2(h8(e11),h8(e10)) )
& ( h8(op1(e11,e11)) = op2(h8(e11),h8(e11)) )
& ( h8(op1(e11,e12)) = op2(h8(e11),h8(e12)) )
& ( h8(op1(e11,e13)) = op2(h8(e11),h8(e13)) )
& ( h8(op1(e12,e10)) = op2(h8(e12),h8(e10)) )
& ( h8(op1(e12,e11)) = op2(h8(e12),h8(e11)) )
& ( h8(op1(e12,e12)) = op2(h8(e12),h8(e12)) )
& ( h8(op1(e12,e13)) = op2(h8(e12),h8(e13)) )
& ( h8(op1(e13,e10)) = op2(h8(e13),h8(e10)) )
& ( h8(op1(e13,e11)) = op2(h8(e13),h8(e11)) )
& ( h8(op1(e13,e12)) = op2(h8(e13),h8(e12)) )
& ( h8(op1(e13,e13)) = op2(h8(e13),h8(e13)) )
& ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
& ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
& ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
& ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[865,854]) ).
tff(867,plain,
( ( h8(op1(e10,e10)) != op2(h8(e10),h8(e10)) )
| ( h8(op1(e10,e11)) != op2(h8(e10),h8(e11)) )
| ( h8(op1(e10,e12)) != op2(h8(e10),h8(e12)) )
| ( h8(op1(e10,e13)) != op2(h8(e10),h8(e13)) )
| ( h8(op1(e11,e10)) != op2(h8(e11),h8(e10)) )
| ( h8(op1(e11,e11)) != op2(h8(e11),h8(e11)) )
| ( h8(op1(e11,e12)) != op2(h8(e11),h8(e12)) )
| ( h8(op1(e11,e13)) != op2(h8(e11),h8(e13)) )
| ( h8(op1(e12,e10)) != op2(h8(e12),h8(e10)) )
| ( h8(op1(e12,e11)) != op2(h8(e12),h8(e11)) )
| ( h8(op1(e12,e12)) != op2(h8(e12),h8(e12)) )
| ( h8(op1(e12,e13)) != op2(h8(e12),h8(e13)) )
| ( h8(op1(e13,e10)) != op2(h8(e13),h8(e10)) )
| ( h8(op1(e13,e11)) != op2(h8(e13),h8(e11)) )
| ( h8(op1(e13,e12)) != op2(h8(e13),h8(e12)) )
| ( h8(op1(e13,e13)) != op2(h8(e13),h8(e13)) )
| ~ ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
| ~ ( ( h8(e13) = e21 )
| ( h8(e10) = e21 )
| ( h8(e11) = e21 )
| ( h8(e12) = e21 ) )
| ~ ( ( h8(e12) = e22 )
| ( h8(e10) = e22 )
| ( h8(e11) = e22 )
| ( h8(e13) = e22 ) )
| ~ ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ),
inference(modus_ponens,[status(thm)],[866,852]) ).
tff(868,plain,
( ( h8(op1(e10,e10)) != op2(h8(e10),h8(e10)) )
| ( h8(op1(e10,e11)) != op2(h8(e10),h8(e11)) )
| ( h8(op1(e10,e12)) != op2(h8(e10),h8(e12)) )
| ( h8(op1(e10,e13)) != op2(h8(e10),h8(e13)) )
| ( h8(op1(e11,e10)) != op2(h8(e11),h8(e10)) )
| ( h8(op1(e11,e11)) != op2(h8(e11),h8(e11)) )
| ( h8(op1(e11,e12)) != op2(h8(e11),h8(e12)) )
| ( h8(op1(e11,e13)) != op2(h8(e11),h8(e13)) )
| ( h8(op1(e12,e10)) != op2(h8(e12),h8(e10)) )
| ( h8(op1(e12,e11)) != op2(h8(e12),h8(e11)) )
| ( h8(op1(e12,e12)) != op2(h8(e12),h8(e12)) )
| ( h8(op1(e12,e13)) != op2(h8(e12),h8(e13)) )
| ( h8(op1(e13,e10)) != op2(h8(e13),h8(e10)) )
| ( h8(op1(e13,e11)) != op2(h8(e13),h8(e11)) )
| ( h8(op1(e13,e12)) != op2(h8(e13),h8(e12)) )
| ( h8(op1(e13,e13)) != op2(h8(e13),h8(e13)) )
| ~ ( ( h8(e10) = e20 )
| ( h8(e11) = e20 )
| ( h8(e12) = e20 )
| ( h8(e13) = e20 ) )
| ~ ( ( h8(e10) = e23 )
| ( h8(e11) = e23 )
| ( h8(e12) = e23 )
| ( h8(e13) = e23 ) ) ),
inference(unit_resolution,[status(thm)],[867,844,842]) ).
tff(869,plain,
$false,
inference(unit_resolution,[status(thm)],[868,840,812,770,726,722,717,712,655,583,566,509,504,500,394,301,176,163,99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG113+1 : TPTP v9.0.0. Released v2.7.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 10:47:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% See solution above
% 0.61/0.82 % E exiting
%------------------------------------------------------------------------------