TSTP Solution File: ANA126^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ANA126^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:27:55 EDT 2024
% Result : Theorem 45.89s 9.62s
% Output : Refutation 45.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of formulae : 269 ( 88 unt; 14 typ; 0 def)
% Number of atoms : 523 ( 385 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 3310 ( 316 ~; 225 |; 0 &;2766 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 623 ( 68 ^ 555 !; 0 ?; 623 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
'\'type/realax/real\'': $tType ).
thf('\'type/nums/num\'_type',type,
'\'type/nums/num\'': $tType ).
thf('\'const/realax/real_of_num\'_type',type,
'\'const/realax/real_of_num\'': '\'type/nums/num\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_neg\'_type',type,
'\'const/realax/real_neg\'': '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_mul\'_type',type,
'\'const/realax/real_mul\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/nums/NUMERAL\'_type',type,
'\'const/nums/NUMERAL\'': '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/nums/BIT1\'_type',type,
'\'const/nums/BIT1\'': '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/nums/_0\'_type',type,
'\'const/nums/_0\'': '\'type/nums/num\'' ).
thf('\'const/iterate/polynomial_function\'_type',type,
'\'const/iterate/polynomial_function\'': ( '\'type/realax/real\'' > '\'type/realax/real\'' ) > $o ).
thf(sk1_type,type,
sk1: '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf(sk2_type,type,
sk2: '\'type/realax/real\'' ).
thf(sk3_type,type,
sk3: '\'type/realax/real\'' > ( '\'type/realax/real\'' > '\'type/realax/real\'' ) > '\'type/realax/real\'' ).
thf(sk4_type,type,
sk4: '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf(sk14_type,type,
sk14: '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf(4,axiom,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/calc_int/REAL_MUL_LNEG_') ).
thf(13,plain,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(6,axiom,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/calc_int/REAL_NEG_NEG_') ).
thf(19,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
= A ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(44,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ A @ C )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
!= ( '\'const/realax/real_neg\'' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,15]) ).
thf(45,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ B @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ B ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( D )),bind(B,$thf( '\'const/realax/real_neg\'' @ D ))]]) ).
thf(52,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ B @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ B ) @ A ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(53,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) ) )
= ( '\'const/realax/real_mul\'' @ B @ A ) ),
inference(rewrite,[status(thm)],[52,15]) ).
thf(63,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) @ D )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ C ) ) ),
inference(paramod_ordered,[status(thm)],[53,15]) ).
thf(64,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ F @ G ) )),bind(D,$thf( D ))]]) ).
thf(72,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) ) @ A ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(96,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A ) ),
inference(rewrite,[status(thm)],[72,15]) ).
thf(101,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A ) @ E )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ D ) ) ),
inference(paramod_ordered,[status(thm)],[96,15]) ).
thf(102,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ I @ J ) @ H ) )),bind(E,$thf( E ))]]) ).
thf(129,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) ) @ A ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(150,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A ) ),
inference(rewrite,[status(thm)],[129,15]) ).
thf(163,plain,
! [F: '\'type/realax/real\'',E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) @ D ) @ C ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,150]) ).
thf(193,plain,
! [F: '\'type/realax/real\'',E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) @ D ) @ C ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) @ D ) )
| ( B != C ) ),
inference(simp,[status(thm)],[163]) ).
thf(195,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(3172,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) ) ),
inference(rewrite,[status(thm)],[195,21]) ).
thf(3,axiom,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_MUL_LID_') ).
thf(10,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\''
@ ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( A @ B ) ) )
= ( '\'const/iterate/polynomial_function\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_NEG_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\''
@ ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( A @ B ) ) )
= ( '\'const/iterate/polynomial_function\'' @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\''
@ ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( A @ B ) ) )
= ( '\'const/iterate/polynomial_function\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( '\'const/iterate/polynomial_function\''
@ ^ [A: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ A ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( '\'const/iterate/polynomial_function\''
@ ^ [A: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ A ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(22,plain,
( ( ^ [A: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ A ) ) )
!= sk1 ),
inference(simp,[status(thm)],[9]) ).
thf(25,plain,
( ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) )
!= ( sk1 @ sk2 ) ),
inference(func_ext,[status(esa)],[22]) ).
thf(106,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[96,25]) ).
thf(121,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A ) )
!= ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(11,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
= A ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
= A ),
inference(lifteq,[status(thm)],[11]) ).
thf(46,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
= C )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,12]) ).
thf(48,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
= C )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( B != C ) ),
inference(simp,[status(thm)],[46]) ).
thf(50,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
= B )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(277,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ B @ A )
= D )
| ( ( '\'const/realax/real_neg\'' @ C )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,50]) ).
thf(293,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ B @ A )
= D )
| ( ( '\'const/realax/real_neg\'' @ C )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) )
!= ( '\'const/realax/real_mul\'' @ C @ D ) ) ),
inference(simp,[status(thm)],[277]) ).
thf(160,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,150]) ).
thf(190,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) )
| ( ( '\'const/realax/real_mul\'' @ D @ E )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[160]) ).
thf(200,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) ) ) )
| ( ( '\'const/realax/real_mul\'' @ C @ D )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(5658,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A )
= ( '\'const/realax/real_mul\'' @ B @ A ) )
| ( ( '\'const/realax/real_mul\'' @ C @ D )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(rewrite,[status(thm)],[200,21]) ).
thf(67,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,25]) ).
thf(70,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) )
!= ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(80,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ C @ B )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
!= ( '\'const/realax/real_mul\'' @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,70]) ).
thf(81,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ))]]) ).
thf(201,plain,
! [A: '\'type/realax/real\''] :
( ( A
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[81,12]) ).
thf(207,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( C
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ C ) ) ),
inference(paramod_ordered,[status(thm)],[53,201]) ).
thf(208,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ A @ B )
!= ( sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) ))]]) ).
thf(213,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ A @ B )
!= ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(1815,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( A
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ B @ C )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,213]) ).
thf(1836,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ A @ B )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ A @ B )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[1815]) ).
thf(1844,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ A @ B )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ A @ B )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[1836]) ).
thf(265,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( B
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[50,25]) ).
thf(289,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ sk2 ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(1441,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ ( sk1 @ sk2 ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
!= ( '\'const/realax/real_neg\'' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,289]) ).
thf(1442,plain,
! [A: '\'type/realax/real\''] :
( ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ ( sk1 @ sk2 ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[1441:[bind(A,$thf( C )),bind(B,$thf( '\'const/realax/real_neg\'' @ C ))]]) ).
thf(1462,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( sk1 @ sk2 ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[1442]) ).
thf(1475,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( sk1 @ sk2 ) ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[1462,15]) ).
thf(1484,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( sk1 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,1475]) ).
thf(1512,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[1484]) ).
thf(6799,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[1512,12]) ).
thf(272,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) )
= C )
| ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
!= ( '\'const/realax/real_neg\'' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,50]) ).
thf(273,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ B ) @ A ) )
= A )
| ( B
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( D )),bind(B,$thf( '\'const/realax/real_neg\'' @ D ))]]) ).
thf(304,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) )
= A ),
inference(simp,[status(thm)],[273]) ).
thf(310,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A ) ) )
= A ),
inference(rewrite,[status(thm)],[304,15]) ).
thf(318,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) )
= C )
| ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[310,50]) ).
thf(319,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ B ) ) @ A ) )
= A )
| ( B
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( F )),bind(B,$thf( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ F ) )),bind(C,$thf( C ))]]) ).
thf(376,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) @ A ) )
= A ),
inference(simp,[status(thm)],[319]) ).
thf(489,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) ) )
= A ),
inference(rewrite,[status(thm)],[376,15]) ).
thf(496,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) )
= C )
| ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[489,50]) ).
thf(497,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ B ) ) @ A ) )
= A )
| ( B
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(pattern_uni,[status(thm)],[496:[bind(A,$thf( F )),bind(B,$thf( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ F ) )),bind(C,$thf( C ))]]) ).
thf(576,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) @ A ) )
= A ),
inference(simp,[status(thm)],[497]) ).
thf(1011,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) ) )
= A ),
inference(rewrite,[status(thm)],[576,15]) ).
thf(1038,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( A
= ( '\'const/realax/real_mul\'' @ C @ B ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ C @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1011,53]) ).
thf(1039,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[1038:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ))]]) ).
thf(1158,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A )
= A ),
inference(rewrite,[status(thm)],[1039,12]) ).
thf(290,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ sk2 ) )
!= ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(390,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ B )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( A
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
!= ( '\'const/realax/real_mul\'' @ B @ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,290]) ).
thf(391,plain,
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( sk1 @ sk2 )
!= ( sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[390:[bind(A,$thf( sk1 @ sk2 )),bind(B,$thf( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ))]]) ).
thf(399,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ),
inference(simp,[status(thm)],[391]) ).
thf(494,plain,
! [A: '\'type/realax/real\''] :
( ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[489,399]) ).
thf(560,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(simp,[status(thm)],[494]) ).
thf(1406,plain,
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(rewrite,[status(thm)],[560,53]) ).
thf(82,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ D @ C ) )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
!= ( '\'const/realax/real_mul\'' @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,70]) ).
thf(83,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ B ) @ A ) )
!= ( sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( '\'const/realax/real_neg\'' @ E ))]]) ).
thf(91,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ B ) @ A ) )
!= ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(683,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) ) )
!= ( sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[91,15]) ).
thf(275,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ B )
= ( '\'const/realax/real_mul\'' @ D @ C ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[50,53]) ).
thf(276,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_mul\'' @ A @ B )
= ( '\'const/realax/real_neg\'' @ B ) ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(284,plain,
! [F: '\'type/realax/real\'',E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( B
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) @ D ) @ C ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) @ D ) @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[50,150]) ).
thf(288,plain,
! [F: '\'type/realax/real\'',E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( B
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) @ D ) @ C ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_mul\'' @ A @ B )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) @ D ) @ C ) ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(24,plain,
( ( '\'const/iterate/polynomial_function\''
@ ^ [A: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ A ) ) )
| ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(5,axiom,
! [A: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ A )
=> ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_LMUL_') ).
thf(16,plain,
! [A: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ A )
=> ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
! [A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ A )
=> ! [B: '\'type/realax/real\''] :
( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) ) ),
inference(miniscope,[status(thm)],[16]) ).
thf(18,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(137,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ A ) ) ),
inference(paramod_ordered,[status(thm)],[24,18]) ).
thf(138,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( '\'const/iterate/polynomial_function\''
@ ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) )),bind(B,$thf( B ))]]) ).
thf(144,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( '\'const/iterate/polynomial_function\''
@ ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ B ) ) ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(235,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ B ) ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[144]) ).
thf(239,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ B ) ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[235]) ).
thf(241,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk4 @ A ) ) ) )
!= ( sk1 @ ( sk4 @ A ) ) )
| ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(func_ext,[status(esa)],[239]) ).
thf(938,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( A
!= ( sk1 @ ( sk4 @ B ) ) )
| ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
!= ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk4 @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,241]) ).
thf(939,plain,
( ( ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk4 @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) )
!= ( sk1 @ ( sk4 @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) )
| ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(pattern_uni,[status(thm)],[938:[bind(A,$thf( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk4 @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) )),bind(B,$thf( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ))]]) ).
thf(23,plain,
( ~ ( '\'const/iterate/polynomial_function\''
@ ^ [A: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ A ) ) )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(135,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
!= ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,23]) ).
thf(140,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
!= ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(217,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ B @ ( A @ ( sk3 @ B @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk3 @ B @ A ) ) ) )
| ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(func_ext,[status(esa)],[140]) ).
thf(6462,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ B @ ( A @ ( sk3 @ B @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk3 @ B @ A ) ) ) )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( '\'const/iterate/polynomial_function\'' @ A )
!= ( '\'const/iterate/polynomial_function\'' @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[217]) ).
thf(6504,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ ( sk3 @ A @ sk1 ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk3 @ A @ sk1 ) ) ) )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(pattern_uni,[status(thm)],[6462:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(6536,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ ( sk3 @ A @ sk1 ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk3 @ A @ sk1 ) ) ) )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(simp,[status(thm)],[6504]) ).
thf(8108,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ B )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk3 @ C @ sk1 ) ) ) )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( '\'const/realax/real_mul\'' @ A @ B )
!= ( '\'const/realax/real_mul\'' @ C @ ( sk1 @ ( sk3 @ C @ sk1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[276,6536]) ).
thf(8109,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk3 @ A @ sk1 ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk3 @ A @ sk1 ) ) ) )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8108:[bind(A,$thf( E )),bind(B,$thf( sk1 @ ( sk3 @ E @ sk1 ) )),bind(C,$thf( E ))]]) ).
thf(8149,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(simp,[status(thm)],[8109]) ).
thf(8160,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
!= ( '\'const/realax/real_neg\'' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,8149]) ).
thf(8161,plain,
! [A: '\'type/realax/real\''] :
( ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ~ ( '\'const/iterate/polynomial_function\'' @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8160:[bind(A,$thf( C )),bind(B,$thf( '\'const/realax/real_neg\'' @ C ))]]) ).
thf(8195,plain,
~ ( '\'const/iterate/polynomial_function\'' @ sk1 ),
inference(simp,[status(thm)],[8161]) ).
thf(8471,plain,
( ( ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk4 @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) )
!= ( sk1 @ ( sk4 @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) )
| $false ),
inference(rewrite,[status(thm)],[939,8195]) ).
thf(8472,plain,
( ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk4 @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) )
!= ( sk1 @ ( sk4 @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) ),
inference(simp,[status(thm)],[8471]) ).
thf(233,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'' > '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( '\'const/iterate/polynomial_function\''
@ ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ C @ ( B @ D ) ) )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[144,18]) ).
thf(234,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[233:[bind(A,$thf( A )),bind(B,$thf( ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) )),bind(C,$thf( C ))]]) ).
thf(240,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(428,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[240]) ).
thf(431,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[428]) ).
thf(8467,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( $false
| ( ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) )
!= sk1 ) ),
inference(rewrite,[status(thm)],[431,8195]) ).
thf(8468,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[8467]) ).
thf(157,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,150]) ).
thf(183,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[157]) ).
thf(198,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(4368,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A )
= A )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(rewrite,[status(thm)],[198,21]) ).
thf(255,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( B
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[50,96]) ).
thf(292,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( B
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_mul\'' @ A @ B )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(384,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ C )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
!= ( '\'const/realax/real_mul\'' @ C @ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,290]) ).
thf(385,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ sk2 ) ) )
!= ( sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[384:[bind(A,$thf( D )),bind(B,$thf( sk1 @ sk2 )),bind(C,$thf( '\'const/realax/real_neg\'' @ D ))]]) ).
thf(396,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ sk2 ) ) )
!= ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[385]) ).
thf(2164,plain,
! [A: '\'type/realax/real\''] :
( ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ ( sk1 @ sk2 ) ) )
!= ( sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[396,21]) ).
thf(511,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
= B )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[489,21]) ).
thf(512,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) )
= ( '\'const/realax/real_neg\'' @ A ) ),
inference(pattern_uni,[status(thm)],[511:[bind(A,$thf( E )),bind(B,$thf( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ E ) ))]]) ).
thf(569,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) )
= ( '\'const/realax/real_neg\'' @ A ) ),
inference(simp,[status(thm)],[512]) ).
thf(778,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A ) )
= ( '\'const/realax/real_neg\'' @ A ) ),
inference(rewrite,[status(thm)],[569,12]) ).
thf(8475,plain,
! [A: '\'type/realax/real\''] :
( $false
| ( ( ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ B ) ) ) )
!= sk1 ) ),
inference(rewrite,[status(thm)],[239,8195]) ).
thf(8476,plain,
! [A: '\'type/realax/real\''] :
( ( ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ B ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[8475]) ).
thf(168,plain,
! [F: '\'type/realax/real\'',E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ F @ E )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ F @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[150,70]) ).
thf(192,plain,
! [F: '\'type/realax/real\'',E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ F @ E )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A ) )
!= ( '\'const/realax/real_mul\'' @ F @ E ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(136,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ~ ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[18,23]) ).
thf(142,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ~ ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) )
| ( ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[136]) ).
thf(665,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ( ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
!= sk1 )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) )
!= ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,142]) ).
thf(666,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ( ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[665:[]]) ).
thf(8450,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( $false
| ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ( ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
!= sk1 ) ),
inference(rewrite,[status(thm)],[666,8195]) ).
thf(8451,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ( ( ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ C ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[8450]) ).
thf(561,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ),
inference(simp,[status(thm)],[494]) ).
thf(869,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ),
inference(rewrite,[status(thm)],[561,12]) ).
thf(8516,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk14 @ A ) ) ) )
!= ( sk1 @ ( sk14 @ A ) ) ),
inference(func_ext,[status(esa)],[8476]) ).
thf(9259,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( A
!= ( sk1 @ ( sk14 @ B ) ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
!= ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk14 @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,8516]) ).
thf(9260,plain,
( ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk14 @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) )
!= ( sk1 @ ( sk14 @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[9259:[bind(A,$thf( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk14 @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) )),bind(B,$thf( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ))]]) ).
thf(238,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ B ) ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ sk1 ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(8454,plain,
! [A: '\'type/realax/real\''] :
( $false
| ( '\'const/iterate/polynomial_function\''
@ ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ B ) ) ) ) ),
inference(rewrite,[status(thm)],[238,8195]) ).
thf(8455,plain,
! [A: '\'type/realax/real\''] :
( '\'const/iterate/polynomial_function\''
@ ^ [B: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ B ) ) ) ),
inference(simp,[status(thm)],[8454]) ).
thf(1024,plain,
! [A: '\'type/realax/real\''] :
( ( A
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1011,25]) ).
thf(1084,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( sk1 @ sk2 ) ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[1024]) ).
thf(2121,plain,
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( sk1 @ sk2 ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[1084,53]) ).
thf(8469,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk4 @ A ) ) ) )
!= ( sk1 @ ( sk4 @ A ) ) )
| $false ),
inference(rewrite,[status(thm)],[241,8195]) ).
thf(8470,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ ( sk4 @ A ) ) ) )
!= ( sk1 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[8469]) ).
thf(256,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A )
= E )
| ( ( '\'const/realax/real_neg\'' @ D )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[96,50]) ).
thf(291,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A )
= E )
| ( ( '\'const/realax/real_neg\'' @ D )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A ) )
!= ( '\'const/realax/real_mul\'' @ D @ E ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(323,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ A @ C )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[310,15]) ).
thf(324,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ B @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ B ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[323:[bind(A,$thf( F )),bind(B,$thf( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ F ) )),bind(C,$thf( C ))]]) ).
thf(368,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ B @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ B ) ) @ A ) ) ),
inference(simp,[status(thm)],[324]) ).
thf(2202,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ B @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ B ) @ A ) ) ) ),
inference(rewrite,[status(thm)],[368,15]) ).
thf(386,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_mul\'' @ B @ ( sk1 @ sk2 ) )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
!= ( '\'const/realax/real_neg\'' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,290]) ).
thf(387,plain,
! [A: '\'type/realax/real\''] :
( ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ ( sk1 @ sk2 ) )
!= ( sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[386:[bind(A,$thf( C )),bind(B,$thf( '\'const/realax/real_neg\'' @ C ))]]) ).
thf(397,plain,
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( sk1 @ sk2 ) )
!= ( sk1 @ sk2 ) ),
inference(simp,[status(thm)],[387]) ).
thf(434,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( sk1 @ sk2 ) ) )
!= ( sk1 @ sk2 ) ),
inference(rewrite,[status(thm)],[397,15]) ).
thf(493,plain,
! [A: '\'type/realax/real\''] :
( ( A
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( sk1 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[489,434]) ).
thf(553,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( sk1 @ sk2 ) ) ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[493]) ).
thf(2081,plain,
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( sk1 @ sk2 ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[553,53,778]) ).
thf(2333,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ B ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) )
| ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2202,2081]) ).
thf(2334,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) @ ( sk1 @ sk2 ) ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[2333:[bind(A,$thf( sk1 @ sk2 )),bind(B,$thf( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ))]]) ).
thf(6091,plain,
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) @ ( sk1 @ sk2 ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[2334,53]) ).
thf(167,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[150,25]) ).
thf(187,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A ) )
!= ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(709,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ C @ B ) ) )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
!= ( '\'const/realax/real_mul\'' @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,683]) ).
thf(710,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A ) ) )
!= ( sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[709:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ))]]) ).
thf(5584,plain,
! [A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
!= ( sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[710,21]) ).
thf(2256,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ B ) @ A ) ) ) )
= ( '\'const/realax/real_neg\'' @ C ) )
| ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2202,778]) ).
thf(2257,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) ) ) )
= ( '\'const/realax/real_neg\'' @ A ) ),
inference(pattern_uni,[status(thm)],[2256:[bind(A,$thf( A )),bind(B,$thf( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) )),bind(C,$thf( A ))]]) ).
thf(3027,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ A ) )
= ( '\'const/realax/real_neg\'' @ A ) ),
inference(rewrite,[status(thm)],[2257,21]) ).
thf(2375,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ B ) @ A ) ) )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) ) )
| ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2202,15]) ).
thf(2376,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_neg\'' @ B ) ) @ A ) ) )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[2375:[bind(A,$thf( A )),bind(B,$thf( '\'const/realax/real_neg\'' @ E )),bind(C,$thf( E )),bind(D,$thf( A ))]]) ).
thf(2467,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_neg\'' @ B ) ) @ A ) ) )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) ) ),
inference(simp,[status(thm)],[2376]) ).
thf(7603,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_neg\'' @ B ) ) @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) ) ),
inference(rewrite,[status(thm)],[2467,53]) ).
thf(856,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( ^ [E: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ D @ ( C @ E ) ) )
!= sk1 )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [E: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ E ) ) ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ C ) ) ),
inference(paramod_ordered,[status(thm)],[240,666]) ).
thf(857,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ C @ ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) ) ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[856:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [E: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ E ) ) ) ) )),bind(D,$thf( D ))]]) ).
thf(862,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ C @ ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[857]) ).
thf(8456,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( $false
| ( ( ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ C @ ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) ) ) )
!= sk1 ) ),
inference(rewrite,[status(thm)],[862,8195]) ).
thf(8457,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ C @ ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[8456]) ).
thf(394,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_mul\'' @ B @ ( sk1 @ sk2 ) )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ B ) ) ),
inference(paramod_ordered,[status(thm)],[310,290]) ).
thf(395,plain,
! [A: '\'type/realax/real\''] :
( ( A
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A ) ) @ ( sk1 @ sk2 ) )
!= ( sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[394:[bind(A,$thf( E )),bind(B,$thf( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ E ) ))]]) ).
thf(401,plain,
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) @ ( sk1 @ sk2 ) )
!= ( sk1 @ sk2 ) ),
inference(simp,[status(thm)],[395]) ).
thf(461,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( sk1 @ sk2 ) ) )
!= ( sk1 @ sk2 ) ),
inference(rewrite,[status(thm)],[401,15]) ).
thf(467,plain,
! [A: '\'type/realax/real\''] :
( ( A
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( sk1 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,461]) ).
thf(477,plain,
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( sk1 @ sk2 ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[467]) ).
thf(648,plain,
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( sk1 @ sk2 ) )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[477,12]) ).
thf(166,plain,
! [F: '\'type/realax/real\'',E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) @ C ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) @ D ) @ C ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15,150]) ).
thf(186,plain,
! [F: '\'type/realax/real\'',E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) @ C ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) @ D ) @ C ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_mul\'' @ E @ F ) )
| ( B != D ) ),
inference(simp,[status(thm)],[166]) ).
thf(199,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ C ) ) @ B ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_mul\'' @ D @ E ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(4768,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ C ) ) @ B )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_mul\'' @ D @ E ) ) ),
inference(rewrite,[status(thm)],[199,21]) ).
thf(554,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ ( sk1 @ sk2 ) ) )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[493]) ).
thf(951,plain,
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( sk1 @ sk2 ) ) )
!= ( sk1 @ sk2 ) ),
inference(rewrite,[status(thm)],[554,12]) ).
thf(426,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( '\'const/iterate/polynomial_function\''
@ ^ [E: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ D @ ( C @ E ) ) )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [E: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ E ) ) ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ C ) ) ),
inference(paramod_ordered,[status(thm)],[240,18]) ).
thf(427,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( '\'const/iterate/polynomial_function\''
@ ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ C @ ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[426:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [E: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ E ) ) ) ) )),bind(D,$thf( D ))]]) ).
thf(433,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( '\'const/iterate/polynomial_function\''
@ ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ C @ ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) ) ) ) ),
inference(simp,[status(thm)],[427]) ).
thf(910,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ C @ ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[433]) ).
thf(911,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ C @ ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ sk1 ) ) ),
inference(simp,[status(thm)],[910]) ).
thf(8448,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( $false
| ( '\'const/iterate/polynomial_function\''
@ ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ C @ ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[911,8195]) ).
thf(8449,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( '\'const/iterate/polynomial_function\''
@ ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ C @ ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[8448]) ).
thf(3081,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ B ) @ A ) ) ) )
= ( '\'const/realax/real_neg\'' @ C ) )
| ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2202,3027]) ).
thf(3082,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) @ A ) ) ) )
= ( '\'const/realax/real_neg\'' @ A ) ),
inference(pattern_uni,[status(thm)],[3081:[bind(A,$thf( A )),bind(B,$thf( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )),bind(C,$thf( A ))]]) ).
thf(6960,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) @ A ) )
= ( '\'const/realax/real_neg\'' @ A ) ),
inference(rewrite,[status(thm)],[3082,21]) ).
thf(133,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\'' > '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ A )
| ( '\'const/iterate/polynomial_function\''
@ ^ [E: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ D @ ( C @ E ) ) )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [E: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( A @ E ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,18]) ).
thf(134,plain,
! [C: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ C )
| ( '\'const/iterate/polynomial_function\''
@ ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( C @ D ) ) ) ) ),
inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( ^ [F: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( F @ F ) ) )),bind(D,$thf( D ))]]) ).
thf(143,plain,
! [C: '\'type/realax/real\'' > '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ~ ( '\'const/iterate/polynomial_function\'' @ C )
| ( '\'const/iterate/polynomial_function\''
@ ^ [D: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( C @ D ) ) ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(2219,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ B ) @ A ) ) )
= C )
| ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2202,1158]) ).
thf(2220,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) @ A ) ) )
= A ),
inference(pattern_uni,[status(thm)],[2219:[bind(A,$thf( A )),bind(B,$thf( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )),bind(C,$thf( A ))]]) ).
thf(4014,plain,
! [A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ) @ A )
= A ),
inference(rewrite,[status(thm)],[2220,96]) ).
thf(107,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ E @ D )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ E @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[96,70]) ).
thf(126,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ E @ D )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A ) )
!= ( '\'const/realax/real_mul\'' @ E @ D ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(86,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ C @ B )
!= ( sk1 @ sk2 ) )
| ( A
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,70]) ).
thf(89,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(94,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( '\'const/realax/real_neg\'' @ ( sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(430,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/iterate/polynomial_function\'' @ sk1 )
| ( ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) )
!= ( '\'const/iterate/polynomial_function\'' @ sk1 ) ) ),
inference(simp,[status(thm)],[428]) ).
thf(8459,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( $false
| ( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) ) ),
inference(rewrite,[status(thm)],[430,8195]) ).
thf(8460,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( '\'const/iterate/polynomial_function\''
@ ^ [C: '\'type/realax/real\''] : ( '\'const/realax/real_mul\'' @ B @ ( '\'const/realax/real_mul\'' @ A @ ( '\'const/realax/real_neg\'' @ ( sk1 @ C ) ) ) ) ),
inference(simp,[status(thm)],[8459]) ).
thf(105,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ A ) @ B )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,96]) ).
thf(123,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_mul\'' @ D @ E ) )
| ( B != C ) ),
inference(simp,[status(thm)],[105]) ).
thf(131,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_mul\'' @ C @ D ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(1532,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ A @ B ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) )
| ( ( '\'const/realax/real_neg\'' @ A )
!= ( '\'const/realax/real_mul\'' @ C @ D ) ) ),
inference(rewrite,[status(thm)],[131,21]) ).
thf(8452,plain,
( ( '\'const/iterate/polynomial_function\''
@ ^ [A: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ A ) ) )
| $false ),
inference(rewrite,[status(thm)],[24,8195]) ).
thf(8453,plain,
( '\'const/iterate/polynomial_function\''
@ ^ [A: '\'type/realax/real\''] : ( '\'const/realax/real_neg\'' @ ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[8452]) ).
thf(161,plain,
! [F: '\'type/realax/real\'',E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A ) @ F )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ E @ F ) ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ E ) ) ),
inference(paramod_ordered,[status(thm)],[150,15]) ).
thf(162,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( M )),bind(E,$thf( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ L @ M ) @ K ) @ I ) )),bind(F,$thf( F ))]]) ).
thf(196,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) ) @ A ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(3740,plain,
! [E: '\'type/realax/real\'',D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) @ A ) ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ D @ E ) @ C ) @ B ) @ A ) ),
inference(rewrite,[status(thm)],[196,15]) ).
thf(87,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ D @ C )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) ) )
!= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,70]) ).
thf(90,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ D @ C )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_mul\'' @ B @ A )
!= ( sk1 @ sk2 ) )
| ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_mul\'' @ B @ A ) )
!= ( '\'const/realax/real_mul\'' @ D @ C ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(100,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,96]) ).
thf(127,plain,
! [D: '\'type/realax/real\'',C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ C @ D ) @ B ) )
| ( ( '\'const/realax/real_mul\'' @ C @ D )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) )
| ( A != B ) ),
inference(simp,[status(thm)],[100]) ).
thf(132,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A )
= ( '\'const/realax/real_neg\'' @ ( '\'const/realax/real_neg\'' @ A ) ) )
| ( ( '\'const/realax/real_mul\'' @ B @ C )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(1848,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_mul\'' @ B @ C ) @ A )
= A )
| ( ( '\'const/realax/real_mul\'' @ B @ C )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ ( '\'const/nums/BIT1\'' @ '\'const/nums/_0\'' ) ) ) ) ),
inference(rewrite,[status(thm)],[132,21]) ).
thf(9601,plain,
$false,
inference(e,[status(thm)],[3172,10,121,293,5658,1844,6799,1158,1406,683,276,288,8472,1475,25,8468,4368,289,292,201,2164,778,8476,70,192,21,8451,53,869,96,9260,13,8455,2121,8195,22,8470,291,12,6091,187,7,5584,3027,213,7603,399,8457,648,2202,18,150,50,16,4768,951,8449,6960,143,2081,290,4014,19,126,8516,94,8460,1532,15,8453,3740,90,1848]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA126^1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n015.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 12:44:24 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.95/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.00 % [INFO] Parsing done (119ms).
% 1.23/1.01 % [INFO] Running in sequential loop mode.
% 1.58/1.23 % [INFO] eprover registered as external prover.
% 1.58/1.23 % [INFO] cvc4 registered as external prover.
% 1.72/1.23 % [INFO] Scanning for conjecture ...
% 1.80/1.29 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.80/1.32 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.80/1.32 % [INFO] Problem is higher-order (TPTP THF).
% 1.96/1.33 % [INFO] Type checking passed.
% 1.96/1.33 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 45.89/9.61 % External prover 'e' found a proof!
% 45.89/9.61 % [INFO] Killing All external provers ...
% 45.89/9.61 % Time passed: 9085ms (effective reasoning time: 8604ms)
% 45.89/9.61 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 45.89/9.61 % Axioms used in derivation (4): thm/calc_int/REAL_MUL_LNEG_, thm/calc_int/REAL_NEG_NEG_, thm/realax/REAL_MUL_LID_, thm/iterate/POLYNOMIAL_FUNCTION_LMUL_
% 45.89/9.61 % No. of inferences in proof: 255
% 45.89/9.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9085 ms resp. 8604 ms w/o parsing
% 45.89/9.74 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 45.89/9.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------