SET007 Axioms: SET007+591.ax
%------------------------------------------------------------------------------
% File : SET007+591 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Definition of the Riemann Definite Integral and Related Lemmas
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : integra1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 117 ( 2 unt; 0 def)
% Number of atoms : 904 ( 81 equ)
% Maximal formula atoms : 17 ( 7 avg)
% Number of connectives : 892 ( 105 ~; 1 |; 394 &)
% ( 20 <=>; 372 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 1 prp; 0-4 aty)
% Number of functors : 52 ( 52 usr; 4 con; 0-5 aty)
% Number of variables : 371 ( 360 !; 11 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_integra1,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_membered(A)
& v2_membered(A)
& v1_integra1(A) ) ).
fof(cc1_integra1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ( v1_integra1(A)
=> ( ~ v1_xboole_0(A)
& v1_membered(A)
& v2_membered(A)
& v1_rcomp_1(A) ) ) ) ).
fof(cc2_integra1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ( v1_integra1(A)
=> ( v1_membered(A)
& v2_membered(A)
& v3_seq_4(A) ) ) ) ).
fof(rc2_integra1,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& ~ v1_xboole_0(A)
& v1_membered(A)
& v2_membered(A)
& v3_seq_4(A)
& v1_rcomp_1(A)
& v1_integra1(A) ) ).
fof(fc1_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ~ v1_xboole_0(k1_integra1(A)) ) ).
fof(rc3_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ? [B] :
( m2_integra1(B,A)
& ~ v1_xboole_0(B) ) ) ).
fof(d1_integra1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ( v1_integra1(A)
<=> ? [B] :
( m1_subset_1(B,k1_numbers)
& ? [C] :
( m1_subset_1(C,k1_numbers)
& r1_xreal_0(B,C)
& A = k1_rcomp_1(B,C) ) ) ) ) ).
fof(t1_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> v1_rcomp_1(A) ) ).
fof(t2_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ~ v1_xboole_0(A) ) ).
fof(t3_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ( v2_seq_4(A)
& v1_seq_4(A) ) ) ).
fof(t4_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ? [B] :
( m1_subset_1(B,k1_numbers)
& ? [C] :
( m1_subset_1(C,k1_numbers)
& r1_xreal_0(B,C)
& B = k4_pscomp_1(A)
& C = k3_pscomp_1(A) ) ) ) ).
fof(t5_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> A = k1_rcomp_1(k4_pscomp_1(A),k3_pscomp_1(A)) ) ).
fof(t6_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( v1_xreal_0(E)
=> ( ( A = k1_rcomp_1(B,D)
& A = k1_rcomp_1(C,E) )
=> ( B = C
& D = E ) ) ) ) ) ) ) ).
fof(d2_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_goboard1(B)
& m2_finseq_1(B,k1_numbers) )
=> ( m1_integra1(B,A)
<=> ( r1_tarski(k5_relset_1(k5_numbers,k1_numbers,B),A)
& k1_goboard1(B,k3_finseq_1(B)) = k3_pscomp_1(A) ) ) ) ) ).
fof(d3_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( B = k1_integra1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> m1_integra1(C,A) ) ) ) ).
fof(d4_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ( m2_integra1(B,A)
<=> ! [C] :
( r2_hidden(C,B)
<=> m1_integra1(C,A) ) ) ) ) ).
fof(t7_integra1,axiom,
$true ).
fof(t8_integra1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_integra1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,B) )
=> ! [D] :
( m3_integra1(D,B,C)
=> ( r2_hidden(A,k4_finseq_1(D))
=> r2_hidden(k1_goboard1(D,A),B) ) ) ) ) ) ).
fof(t9_integra1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_integra1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,B) )
=> ! [D] :
( m3_integra1(D,B,C)
=> ( r2_hidden(A,k4_finseq_1(D))
=> ( A = np__1
| ( r2_hidden(k10_binop_2(A,np__1),k4_finseq_1(D))
& r2_hidden(k2_seq_1(k5_numbers,k1_numbers,D,k10_binop_2(A,np__1)),B)
& r2_hidden(k10_binop_2(A,np__1),k5_numbers) ) ) ) ) ) ) ) ).
fof(d5_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ! [C] :
( m3_integra1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k4_finseq_1(C))
=> ! [E] :
( ( v1_integra1(E)
& m1_subset_1(E,k1_zfmisc_1(k1_numbers)) )
=> ( ( D = np__1
=> ( E = k2_integra1(A,B,C,D)
<=> ( k4_pscomp_1(E) = k4_pscomp_1(A)
& k3_pscomp_1(E) = k1_goboard1(C,D) ) ) )
& ( D != np__1
=> ( E = k2_integra1(A,B,C,D)
<=> ( k4_pscomp_1(E) = k2_seq_1(k5_numbers,k1_numbers,C,k10_binop_2(D,np__1))
& k3_pscomp_1(E) = k1_goboard1(C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t10_integra1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_integra1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,B) )
=> ! [D] :
( m3_integra1(D,B,C)
=> ( r2_hidden(A,k4_finseq_1(D))
=> r1_tarski(k2_integra1(B,C,D,A),B) ) ) ) ) ) ).
fof(d6_integra1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> k3_integra1(A) = k10_binop_2(k3_pscomp_1(A),k4_pscomp_1(A)) ) ).
fof(t11_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v3_seq_4(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> r1_xreal_0(np__0,k3_integra1(A)) ) ).
fof(d7_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m2_finseq_1(E,k1_numbers)
=> ( E = k4_integra1(A,B,C,D)
<=> ( k3_finseq_1(E) = k3_finseq_1(D)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,k2_finseq_1(k3_finseq_1(D)))
=> k1_goboard1(E,F) = k11_binop_2(k3_pscomp_1(k5_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_integra1(A,C,D,F)))),k3_integra1(k2_integra1(A,C,D,F))) ) ) ) ) ) ) ) ) ) ).
fof(d8_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m2_finseq_1(E,k1_numbers)
=> ( E = k5_integra1(A,B,C,D)
<=> ( k3_finseq_1(E) = k3_finseq_1(D)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,k2_finseq_1(k3_finseq_1(D)))
=> k1_goboard1(E,F) = k11_binop_2(k4_pscomp_1(k5_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_integra1(A,C,D,F)))),k3_integra1(k2_integra1(A,C,D,F))) ) ) ) ) ) ) ) ) ) ).
fof(d9_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> k6_integra1(A,B,C,D) = k15_rvsum_1(k4_integra1(A,B,C,D)) ) ) ) ) ).
fof(d10_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> k7_integra1(A,B,C,D) = k15_rvsum_1(k5_integra1(A,B,C,D)) ) ) ) ) ).
fof(d11_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k8_integra1(A),k1_numbers) )
=> ( C = k9_integra1(A,B)
<=> ( k4_relset_1(k8_integra1(A),k1_numbers,C) = k8_integra1(A)
& ! [D] :
( m3_integra1(D,A,k8_integra1(A))
=> ( r2_hidden(D,k4_relset_1(k8_integra1(A),k1_numbers,C))
=> k2_seq_1(k8_integra1(A),k1_numbers,C,D) = k6_integra1(A,B,k8_integra1(A),D) ) ) ) ) ) ) ) ).
fof(d12_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k8_integra1(A),k1_numbers) )
=> ( C = k10_integra1(A,B)
<=> ( k4_relset_1(k8_integra1(A),k1_numbers,C) = k8_integra1(A)
& ! [D] :
( m3_integra1(D,A,k8_integra1(A))
=> ( r2_hidden(D,k4_relset_1(k8_integra1(A),k1_numbers,C))
=> k2_seq_1(k8_integra1(A),k1_numbers,C,D) = k7_integra1(A,B,k8_integra1(A),D) ) ) ) ) ) ) ) ).
fof(d13_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ( r1_integra1(A,B)
<=> v2_seq_4(k5_relset_1(k8_integra1(A),k1_numbers,k9_integra1(A,B))) ) ) ) ).
fof(d14_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ( r2_integra1(A,B)
<=> v1_seq_4(k5_relset_1(k8_integra1(A),k1_numbers,k10_integra1(A,B))) ) ) ) ).
fof(d15_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> k11_integra1(A,B) = k4_pscomp_1(k5_relset_1(k8_integra1(A),k1_numbers,k9_integra1(A,B))) ) ) ).
fof(d16_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> k12_integra1(A,B) = k3_pscomp_1(k5_relset_1(k8_integra1(A),k1_numbers,k10_integra1(A,B))) ) ) ).
fof(d17_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ( r3_integra1(A,B)
<=> ( r1_integra1(A,B)
& r2_integra1(A,B)
& k11_integra1(A,B) = k12_integra1(A,B) ) ) ) ) ).
fof(d18_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> k13_integra1(A,B) = k11_integra1(A,B) ) ) ).
fof(t12_integra1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> r1_tarski(k5_relset_1(A,k1_numbers,k6_seq_1(A,k1_numbers,B,C)),k21_complsp1(k5_relset_1(A,k1_numbers,B),k5_relset_1(A,k1_numbers,C))) ) ) ) ).
fof(t13_integra1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ( r2_rfunct_1(B,A)
=> v2_seq_4(k5_relset_1(A,k1_numbers,B)) ) ) ) ).
fof(t14_integra1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ( v2_seq_4(k5_relset_1(A,k1_numbers,B))
=> r2_rfunct_1(B,A) ) ) ) ).
fof(t15_integra1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ( r1_rfunct_1(B,A)
=> v1_seq_4(k5_relset_1(A,k1_numbers,B)) ) ) ) ).
fof(t16_integra1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ( v1_seq_4(k5_relset_1(A,k1_numbers,B))
=> r1_rfunct_1(B,A) ) ) ) ).
fof(t17_integra1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ( r3_rfunct_1(B,A)
=> v3_seq_4(k5_relset_1(A,k1_numbers,B)) ) ) ) ).
fof(t18_integra1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> r1_partfun2(A,k1_numbers,k5_rfunct_1(A,A),A) ) ).
fof(t19_integra1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> k5_relset_1(B,k1_numbers,k5_rfunct_1(B,B)) = k1_seq_4(np__1) ) ) ).
fof(t20_integra1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ~ r1_xboole_0(C,k4_relset_1(B,k1_numbers,k5_rfunct_1(B,B)))
=> k5_relset_1(B,k1_numbers,k2_partfun1(B,k1_numbers,k5_rfunct_1(B,B),C)) = k1_seq_4(np__1) ) ) ) ).
fof(t21_integra1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_integra1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,B) )
=> ! [D] :
( m3_integra1(D,B,C)
=> ( r2_hidden(A,k2_finseq_1(k3_finseq_1(D)))
=> k3_integra1(k2_integra1(B,C,D,A)) = k1_goboard1(k5_integra1(B,k5_rfunct_1(B,B),C,D),A) ) ) ) ) ) ).
fof(t22_integra1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_integra1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,B) )
=> ! [D] :
( m3_integra1(D,B,C)
=> ( r2_hidden(A,k2_finseq_1(k3_finseq_1(D)))
=> k3_integra1(k2_integra1(B,C,D,A)) = k1_goboard1(k4_integra1(B,k5_rfunct_1(B,B),C,D),A) ) ) ) ) ) ).
fof(t23_integra1,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ! [B] :
( m2_finseq_1(B,k1_numbers)
=> ! [C] :
( m2_finseq_1(C,k1_numbers)
=> ( ( k3_finseq_1(A) = k3_finseq_1(B)
& k3_finseq_1(A) = k3_finseq_1(C)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k4_finseq_1(A))
=> k1_goboard1(C,D) = k9_binop_2(k4_finseq_4(k5_numbers,k1_numbers,A,D),k4_finseq_4(k5_numbers,k1_numbers,B,D)) ) ) )
=> k15_rvsum_1(C) = k9_binop_2(k15_rvsum_1(A),k15_rvsum_1(B)) ) ) ) ) ).
fof(t24_integra1,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ! [B] :
( m2_finseq_1(B,k1_numbers)
=> ! [C] :
( m2_finseq_1(C,k1_numbers)
=> ( ( k3_finseq_1(A) = k3_finseq_1(B)
& k3_finseq_1(A) = k3_finseq_1(C)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k4_finseq_1(A))
=> k1_goboard1(C,D) = k10_binop_2(k4_finseq_4(k5_numbers,k1_numbers,A,D),k4_finseq_4(k5_numbers,k1_numbers,B,D)) ) ) )
=> k15_rvsum_1(C) = k10_binop_2(k15_rvsum_1(A),k15_rvsum_1(B)) ) ) ) ) ).
fof(t25_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ! [C] :
( m3_integra1(C,A,B)
=> k15_rvsum_1(k5_integra1(A,k5_rfunct_1(A,A),B,C)) = k3_integra1(A) ) ) ) ).
fof(t26_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ! [C] :
( m3_integra1(C,A,B)
=> k15_rvsum_1(k4_integra1(A,k5_rfunct_1(A,A),B,C)) = k3_integra1(A) ) ) ) ).
fof(t27_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ( r2_rfunct_1(B,A)
=> r1_xreal_0(k11_binop_2(k4_pscomp_1(k1_pscomp_1(A,k1_numbers,B)),k3_integra1(A)),k7_integra1(A,B,C,D)) ) ) ) ) ) ).
fof(t28_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_rfunct_1(B,A)
& r2_hidden(E,k2_finseq_1(k3_finseq_1(D))) )
=> r1_xreal_0(k11_binop_2(k3_pscomp_1(k5_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_integra1(A,C,D,E)))),k3_integra1(k2_integra1(A,C,D,E))),k11_binop_2(k3_pscomp_1(k1_pscomp_1(A,k1_numbers,B)),k3_integra1(k2_integra1(A,C,D,E)))) ) ) ) ) ) ) ).
fof(t29_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ( r1_rfunct_1(B,A)
=> r1_xreal_0(k6_integra1(A,B,C,D),k11_binop_2(k3_pscomp_1(k1_pscomp_1(A,k1_numbers,B)),k3_integra1(A))) ) ) ) ) ) ).
fof(t30_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ( r3_rfunct_1(B,A)
=> r1_xreal_0(k7_integra1(A,B,C,D),k6_integra1(A,B,C,D)) ) ) ) ) ) ).
fof(d19_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( m3_integra1(B,A,k8_integra1(A))
=> k17_integra1(A,B) = k2_seq_4(k16_integra1(k14_integra1(A,k5_rfunct_1(A,A),k8_integra1(A),B))) ) ) ).
fof(d20_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ! [C] :
( m3_integra1(C,A,B)
=> ! [D] :
( m3_integra1(D,A,B)
=> ( r4_integra1(A,B,C,D)
<=> ( r1_xreal_0(k3_finseq_1(C),k3_finseq_1(D))
& r1_tarski(k16_integra1(C),k16_integra1(D)) ) ) ) ) ) ) ).
fof(t31_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ! [C] :
( m3_integra1(C,A,B)
=> ! [D] :
( m3_integra1(D,A,B)
=> ( k3_finseq_1(C) = np__1
=> r4_integra1(A,B,C,D) ) ) ) ) ) ).
fof(t32_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m3_integra1(E,A,C)
=> ( ( r1_rfunct_1(B,A)
& k3_finseq_1(D) = np__1 )
=> r1_xreal_0(k6_integra1(A,B,C,E),k6_integra1(A,B,C,D)) ) ) ) ) ) ) ).
fof(t33_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m3_integra1(E,A,C)
=> ( ( r2_rfunct_1(B,A)
& k3_finseq_1(D) = np__1 )
=> r1_xreal_0(k7_integra1(A,B,C,D),k7_integra1(A,B,C,E)) ) ) ) ) ) ) ).
fof(t34_integra1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_integra1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,B) )
=> ! [D] :
( m3_integra1(D,B,C)
=> ~ ( r2_hidden(A,k4_finseq_1(D))
& ! [E] :
( ( v1_integra1(E)
& m1_subset_1(E,k1_zfmisc_1(k1_numbers)) )
=> ! [F] :
( ( v1_integra1(F)
& m1_subset_1(F,k1_zfmisc_1(k1_numbers)) )
=> ~ ( E = k1_rcomp_1(k4_pscomp_1(B),k1_goboard1(D,A))
& F = k1_rcomp_1(k1_goboard1(D,A),k3_pscomp_1(B))
& B = k4_subset_1(k1_numbers,E,F) ) ) ) ) ) ) ) ) ).
fof(t35_integra1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_integra1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,B) )
=> ! [D] :
( m3_integra1(D,B,C)
=> ! [E] :
( m3_integra1(E,B,C)
=> ~ ( r2_hidden(A,k4_finseq_1(D))
& r4_integra1(B,C,D,E)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(F,k4_finseq_1(E))
& k1_goboard1(D,A) = k1_goboard1(E,F) ) ) ) ) ) ) ) ) ).
fof(d21_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ! [C] :
( m3_integra1(C,A,B)
=> ! [D] :
( m3_integra1(D,A,B)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r4_integra1(A,B,C,D)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r2_hidden(E,k4_finseq_1(C))
=> ( F = k18_integra1(A,B,C,D,E)
<=> ( r2_hidden(F,k4_finseq_1(D))
& k1_goboard1(C,E) = k1_goboard1(D,F) ) ) )
& ( ~ r2_hidden(E,k4_finseq_1(C))
=> ( F = k18_integra1(A,B,C,D,E)
<=> F = np__0 ) ) ) ) ) ) ) ) ) ) ).
fof(t36_integra1,axiom,
! [A] :
( ( v1_goboard1(A)
& m2_finseq_1(A,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,k3_finseq_1(A))
=> ( v1_goboard1(k1_rfinseq(k1_numbers,A,B))
& m2_finseq_1(k1_rfinseq(k1_numbers,A,B),k1_numbers) ) ) ) ) ).
fof(t37_integra1,axiom,
! [A] :
( ( v1_goboard1(A)
& m2_finseq_1(A,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(C,k4_finseq_1(A))
& r1_xreal_0(B,C) )
=> ( v1_goboard1(k1_jordan3(k1_numbers,A,B,C))
& m2_finseq_1(k1_jordan3(k1_numbers,A,B,C),k1_numbers) ) ) ) ) ) ).
fof(t38_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ! [C] :
( m3_integra1(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k4_finseq_1(C))
& r2_hidden(E,k4_finseq_1(C))
& r1_xreal_0(D,E)
& ! [F] :
( ( v1_integra1(F)
& m1_subset_1(F,k1_zfmisc_1(k1_numbers)) )
=> ~ ( k4_pscomp_1(F) = k1_goboard1(k1_jordan3(k1_numbers,C,D,E),np__1)
& k3_pscomp_1(F) = k1_goboard1(k1_jordan3(k1_numbers,C,D,E),k3_finseq_1(k1_jordan3(k1_numbers,C,D,E)))
& k3_finseq_1(k1_jordan3(k1_numbers,C,D,E)) = k9_binop_2(k10_binop_2(E,D),np__1)
& m1_integra1(k1_jordan3(k1_numbers,C,D,E),F) ) ) ) ) ) ) ) ) ).
fof(t39_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_integra1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m2_integra1(D,B) )
=> ! [E] :
( m3_integra1(E,A,C)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r2_hidden(F,k4_finseq_1(E))
& r2_hidden(G,k4_finseq_1(E))
& r1_xreal_0(F,G)
& r1_xreal_0(k4_pscomp_1(B),k1_goboard1(E,F))
& k1_goboard1(E,G) = k3_pscomp_1(B) )
=> m3_integra1(k1_jordan3(k1_numbers,E,F,G),B,D) ) ) ) ) ) ) ) ) ).
fof(d22_integra1,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ! [B] :
( m2_finseq_1(B,k1_numbers)
=> ( B = k19_integra1(A)
<=> ( k3_finseq_1(B) = k3_finseq_1(A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k2_finseq_1(k3_finseq_1(A)))
=> k1_goboard1(B,C) = k15_rvsum_1(k16_finseq_1(k1_numbers,A,C)) ) ) ) ) ) ) ).
fof(t40_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m3_integra1(E,A,C)
=> ( ( r4_integra1(A,C,D,E)
& r1_rfunct_1(B,A) )
=> ! [F] :
( ( ~ v1_xboole_0(F)
& m2_subset_1(F,k1_numbers,k5_numbers) )
=> ( r2_hidden(F,k4_finseq_1(D))
=> r1_xreal_0(k15_rvsum_1(k16_finseq_1(k1_numbers,k14_integra1(A,B,C,E),k18_integra1(A,C,D,E,F))),k15_rvsum_1(k16_finseq_1(k1_numbers,k14_integra1(A,B,C,D),F))) ) ) ) ) ) ) ) ) ).
fof(t41_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m3_integra1(E,A,C)
=> ( ( r4_integra1(A,C,D,E)
& r2_rfunct_1(B,A) )
=> ! [F] :
( ( ~ v1_xboole_0(F)
& m2_subset_1(F,k1_numbers,k5_numbers) )
=> ( r2_hidden(F,k4_finseq_1(D))
=> r1_xreal_0(k15_rvsum_1(k16_finseq_1(k1_numbers,k15_integra1(A,B,C,D),F)),k15_rvsum_1(k16_finseq_1(k1_numbers,k15_integra1(A,B,C,E),k18_integra1(A,C,D,E,F)))) ) ) ) ) ) ) ) ) ).
fof(t42_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m3_integra1(E,A,C)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r4_integra1(A,C,D,E)
& r2_hidden(F,k4_finseq_1(D))
& r1_rfunct_1(B,A) )
=> r1_xreal_0(k1_goboard1(k19_integra1(k14_integra1(A,B,C,E)),k18_integra1(A,C,D,E,F)),k1_goboard1(k19_integra1(k14_integra1(A,B,C,D)),F)) ) ) ) ) ) ) ) ).
fof(t43_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m3_integra1(E,A,C)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r4_integra1(A,C,D,E)
& r2_hidden(F,k4_finseq_1(D))
& r2_rfunct_1(B,A) )
=> r1_xreal_0(k1_goboard1(k19_integra1(k15_integra1(A,B,C,D)),F),k1_goboard1(k19_integra1(k15_integra1(A,B,C,E)),k18_integra1(A,C,D,E,F))) ) ) ) ) ) ) ) ).
fof(t44_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> k1_goboard1(k19_integra1(k14_integra1(A,B,C,D)),k3_finseq_1(D)) = k6_integra1(A,B,C,D) ) ) ) ) ).
fof(t45_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> k1_goboard1(k19_integra1(k15_integra1(A,B,C,D)),k3_finseq_1(D)) = k7_integra1(A,B,C,D) ) ) ) ) ).
fof(t46_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ! [C] :
( m3_integra1(C,A,B)
=> ! [D] :
( m3_integra1(D,A,B)
=> ( r4_integra1(A,B,C,D)
=> k18_integra1(A,B,C,D,k3_finseq_1(C)) = k3_finseq_1(D) ) ) ) ) ) ).
fof(t47_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m3_integra1(E,A,C)
=> ( ( r4_integra1(A,C,D,E)
& r1_rfunct_1(B,A) )
=> r1_xreal_0(k6_integra1(A,B,C,E),k6_integra1(A,B,C,D)) ) ) ) ) ) ) ).
fof(t48_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m3_integra1(E,A,C)
=> ( ( r4_integra1(A,C,D,E)
& r2_rfunct_1(B,A) )
=> r1_xreal_0(k7_integra1(A,B,C,D),k7_integra1(A,B,C,E)) ) ) ) ) ) ) ).
fof(t49_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ! [C] :
( m3_integra1(C,A,B)
=> ! [D] :
( m3_integra1(D,A,B)
=> ? [E] :
( m3_integra1(E,A,B)
& r4_integra1(A,B,C,E)
& r4_integra1(A,B,D,E) ) ) ) ) ) ).
fof(t50_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_integra1(C,A) )
=> ! [D] :
( m3_integra1(D,A,C)
=> ! [E] :
( m3_integra1(E,A,C)
=> ( r3_rfunct_1(B,A)
=> r1_xreal_0(k7_integra1(A,B,C,D),k6_integra1(A,B,C,E)) ) ) ) ) ) ) ).
fof(t51_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ( r3_rfunct_1(B,A)
=> r1_xreal_0(k12_integra1(A,B),k11_integra1(A,B)) ) ) ) ).
fof(t52_integra1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> k21_complsp1(k5_pscomp_1(A),k5_pscomp_1(B)) = k5_pscomp_1(k21_complsp1(A,B)) ) ) ).
fof(t53_integra1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( ( v1_seq_4(A)
& v1_seq_4(B) )
=> v1_seq_4(k21_complsp1(A,B)) ) ) ) ).
fof(t54_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ( ( v1_seq_4(A)
& v1_seq_4(B) )
=> k3_pscomp_1(k21_complsp1(A,B)) = k9_binop_2(k3_pscomp_1(A),k3_pscomp_1(B)) ) ) ) ).
fof(t55_integra1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_integra1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,k1_numbers)
& m2_relset_1(C,B,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,k1_numbers)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( ~ v1_xboole_0(E)
& m2_integra1(E,B) )
=> ! [F] :
( m3_integra1(F,B,E)
=> ( ( r2_hidden(A,k2_finseq_1(k3_finseq_1(F)))
& r1_rfunct_1(C,B)
& r1_rfunct_1(D,B) )
=> r1_xreal_0(k1_goboard1(k14_integra1(B,k6_seq_1(B,k1_numbers,C,D),E,F),A),k9_binop_2(k1_goboard1(k14_integra1(B,C,E,F),A),k1_goboard1(k14_integra1(B,D,E,F),A))) ) ) ) ) ) ) ) ).
fof(t56_integra1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_integra1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,k1_numbers)
& m2_relset_1(C,B,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,k1_numbers)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( ~ v1_xboole_0(E)
& m2_integra1(E,B) )
=> ! [F] :
( m3_integra1(F,B,E)
=> ( ( r2_hidden(A,k2_finseq_1(k3_finseq_1(F)))
& r2_rfunct_1(C,B)
& r2_rfunct_1(D,B) )
=> r1_xreal_0(k9_binop_2(k1_goboard1(k15_integra1(B,C,E,F),A),k1_goboard1(k15_integra1(B,D,E,F),A)),k1_goboard1(k15_integra1(B,k6_seq_1(B,k1_numbers,C,D),E,F),A)) ) ) ) ) ) ) ) ).
fof(t57_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m2_integra1(D,A) )
=> ! [E] :
( m3_integra1(E,A,D)
=> ( ( r1_rfunct_1(B,A)
& r1_rfunct_1(C,A) )
=> r1_xreal_0(k6_integra1(A,k6_seq_1(A,k1_numbers,B,C),D,E),k9_binop_2(k6_integra1(A,B,D,E),k6_integra1(A,C,D,E))) ) ) ) ) ) ) ).
fof(t58_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m2_integra1(D,A) )
=> ! [E] :
( m3_integra1(E,A,D)
=> ( ( r2_rfunct_1(B,A)
& r2_rfunct_1(C,A) )
=> r1_xreal_0(k9_binop_2(k7_integra1(A,B,D,E),k7_integra1(A,C,D,E)),k7_integra1(A,k6_seq_1(A,k1_numbers,B,C),D,E)) ) ) ) ) ) ) ).
fof(t59_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m2_relset_1(C,A,k1_numbers) )
=> ( ( r3_rfunct_1(B,A)
& r3_rfunct_1(C,A)
& r3_integra1(A,B)
& r3_integra1(A,C) )
=> ( r3_integra1(A,k6_seq_1(A,k1_numbers,B,C))
& k13_integra1(A,k6_seq_1(A,k1_numbers,B,C)) = k9_binop_2(k13_integra1(A,B),k13_integra1(A,C)) ) ) ) ) ) ).
fof(dt_m1_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( m1_integra1(B,A)
=> ( ~ v1_xboole_0(B)
& v1_goboard1(B)
& m2_finseq_1(B,k1_numbers) ) ) ) ).
fof(existence_m1_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ? [B] : m1_integra1(B,A) ) ).
fof(dt_m2_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( m2_integra1(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(existence_m2_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ? [B] : m2_integra1(B,A) ) ).
fof(dt_m3_integra1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ! [C] :
( m3_integra1(C,A,B)
=> m1_integra1(C,A) ) ) ).
fof(existence_m3_integra1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ? [C] : m3_integra1(C,A,B) ) ).
fof(redefinition_m3_integra1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& ~ v1_xboole_0(B)
& m2_integra1(B,A) )
=> ! [C] :
( m3_integra1(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_k1_integra1,axiom,
$true ).
fof(dt_k2_integra1,axiom,
! [A,B,C,D] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& ~ v1_xboole_0(B)
& m2_integra1(B,A)
& m1_subset_1(C,B)
& m1_subset_1(D,k5_numbers) )
=> ( v1_integra1(k2_integra1(A,B,C,D))
& m1_subset_1(k2_integra1(A,B,C,D),k1_zfmisc_1(k1_numbers)) ) ) ).
fof(dt_k3_integra1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> m1_subset_1(k3_integra1(A),k1_numbers) ) ).
fof(dt_k4_integra1,axiom,
! [A,B,C,D] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers)
& ~ v1_xboole_0(C)
& m2_integra1(C,A)
& m1_subset_1(D,C) )
=> m2_finseq_1(k4_integra1(A,B,C,D),k1_numbers) ) ).
fof(dt_k5_integra1,axiom,
! [A,B,C,D] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers)
& ~ v1_xboole_0(C)
& m2_integra1(C,A)
& m1_subset_1(D,C) )
=> m2_finseq_1(k5_integra1(A,B,C,D),k1_numbers) ) ).
fof(dt_k6_integra1,axiom,
! [A,B,C,D] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers)
& ~ v1_xboole_0(C)
& m2_integra1(C,A)
& m1_subset_1(D,C) )
=> m1_subset_1(k6_integra1(A,B,C,D),k1_numbers) ) ).
fof(dt_k7_integra1,axiom,
! [A,B,C,D] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers)
& ~ v1_xboole_0(C)
& m2_integra1(C,A)
& m1_subset_1(D,C) )
=> m1_subset_1(k7_integra1(A,B,C,D),k1_numbers) ) ).
fof(dt_k8_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> m2_integra1(k8_integra1(A),A) ) ).
fof(redefinition_k8_integra1,axiom,
! [A] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> k8_integra1(A) = k1_integra1(A) ) ).
fof(dt_k9_integra1,axiom,
! [A,B] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers) )
=> ( v1_funct_1(k9_integra1(A,B))
& m2_relset_1(k9_integra1(A,B),k8_integra1(A),k1_numbers) ) ) ).
fof(dt_k10_integra1,axiom,
! [A,B] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers) )
=> ( v1_funct_1(k10_integra1(A,B))
& m2_relset_1(k10_integra1(A,B),k8_integra1(A),k1_numbers) ) ) ).
fof(dt_k11_integra1,axiom,
! [A,B] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers) )
=> m1_subset_1(k11_integra1(A,B),k1_numbers) ) ).
fof(dt_k12_integra1,axiom,
! [A,B] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers) )
=> m1_subset_1(k12_integra1(A,B),k1_numbers) ) ).
fof(dt_k13_integra1,axiom,
! [A,B] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers) )
=> m1_subset_1(k13_integra1(A,B),k1_numbers) ) ).
fof(dt_k14_integra1,axiom,
! [A,B,C,D] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers)
& ~ v1_xboole_0(C)
& m2_integra1(C,A)
& m1_subset_1(D,C) )
=> ( ~ v1_xboole_0(k14_integra1(A,B,C,D))
& m2_finseq_1(k14_integra1(A,B,C,D),k1_numbers) ) ) ).
fof(redefinition_k14_integra1,axiom,
! [A,B,C,D] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers)
& ~ v1_xboole_0(C)
& m2_integra1(C,A)
& m1_subset_1(D,C) )
=> k14_integra1(A,B,C,D) = k4_integra1(A,B,C,D) ) ).
fof(dt_k15_integra1,axiom,
! [A,B,C,D] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers)
& ~ v1_xboole_0(C)
& m2_integra1(C,A)
& m1_subset_1(D,C) )
=> ( ~ v1_xboole_0(k15_integra1(A,B,C,D))
& m2_finseq_1(k15_integra1(A,B,C,D),k1_numbers) ) ) ).
fof(redefinition_k15_integra1,axiom,
! [A,B,C,D] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& v1_funct_1(B)
& m1_relset_1(B,A,k1_numbers)
& ~ v1_xboole_0(C)
& m2_integra1(C,A)
& m1_subset_1(D,C) )
=> k15_integra1(A,B,C,D) = k5_integra1(A,B,C,D) ) ).
fof(dt_k16_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k1_numbers) )
=> ( ~ v1_xboole_0(k16_integra1(A))
& v1_finset_1(k16_integra1(A))
& m1_subset_1(k16_integra1(A),k1_zfmisc_1(k1_numbers)) ) ) ).
fof(redefinition_k16_integra1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k1_numbers) )
=> k16_integra1(A) = k2_relat_1(A) ) ).
fof(dt_k17_integra1,axiom,
! [A,B] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& m1_subset_1(B,k8_integra1(A)) )
=> m1_subset_1(k17_integra1(A,B),k1_numbers) ) ).
fof(dt_k18_integra1,axiom,
! [A,B,C,D,E] :
( ( v1_integra1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& ~ v1_xboole_0(B)
& m2_integra1(B,A)
& m1_subset_1(C,B)
& m1_subset_1(D,B)
& m1_subset_1(E,k5_numbers) )
=> m2_subset_1(k18_integra1(A,B,C,D,E),k1_numbers,k5_numbers) ) ).
fof(dt_k19_integra1,axiom,
! [A] :
( m1_finseq_1(A,k1_numbers)
=> m2_finseq_1(k19_integra1(A),k1_numbers) ) ).
%------------------------------------------------------------------------------