SET007 Axioms: SET007+533.ax
%------------------------------------------------------------------------------
% File : SET007+533 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Order on a Special Polygon
% 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 : sprect_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 90 ( 7 unt; 0 def)
% Number of atoms : 767 ( 81 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 835 ( 158 ~; 22 |; 444 &)
% ( 6 <=>; 205 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 35 ( 33 usr; 1 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 6 con; 0-4 aty)
% Number of variables : 187 ( 185 !; 2 ?)
% 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(fc1_sprect_2,axiom,
( ~ v1_xboole_0(k2_topreal1)
& ~ v1_realset1(k2_topreal1)
& ~ v1_sppol_1(k2_topreal1)
& ~ v2_sppol_1(k2_topreal1)
& v1_topreal4(k2_topreal1)
& v6_compts_1(k2_topreal1,k15_euclid(np__2)) ) ).
fof(fc2_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k1_sprect_1(A))
& v1_relat_1(k1_sprect_1(A))
& v1_funct_1(k1_sprect_1(A))
& v1_finset_1(k1_sprect_1(A))
& v1_finseq_1(k1_sprect_1(A))
& v1_topreal1(k1_sprect_1(A))
& v2_topreal1(k1_sprect_1(A))
& v1_finseq_6(k1_sprect_1(A),u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(k1_sprect_1(A))
& v2_goboard5(k1_sprect_1(A))
& ~ v1_realset1(k1_sprect_1(A))
& ~ v5_seqm_3(k1_sprect_1(A))
& v1_sprect_1(k1_sprect_1(A))
& v1_sprect_2(k1_sprect_1(A)) ) ) ).
fof(rc1_sprect_2,axiom,
? [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v1_realset1(A)
& ~ v5_seqm_3(A)
& v1_sprect_2(A) ) ).
fof(fc3_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( ~ v1_xboole_0(k5_topreal1(np__2,A))
& v1_topreal2(k5_topreal1(np__2,A))
& v6_compts_1(k5_topreal1(np__2,A),k15_euclid(np__2)) ) ) ).
fof(t1_sprect_2,axiom,
! [A,B,C,D] :
( ( r1_tarski(k3_xboole_0(A,B),k1_tarski(D))
& r2_hidden(D,C)
& r1_xboole_0(C,B) )
=> r1_xboole_0(k2_xboole_0(A,C),B) ) ).
fof(t2_sprect_2,axiom,
! [A,B,C,D] :
( ( k3_xboole_0(A,C) = k1_tarski(D)
& r2_hidden(D,B)
& r1_tarski(B,C) )
=> k3_xboole_0(A,B) = k1_tarski(D) ) ).
fof(t3_sprect_2,axiom,
$true ).
fof(t4_sprect_2,axiom,
! [A,B] :
( ! [C,D] :
( ( r2_hidden(C,A)
& r2_hidden(D,B) )
=> r1_xboole_0(C,D) )
=> r1_xboole_0(k3_tarski(A),k3_tarski(B)) ) ).
fof(t5_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m2_finseq_1(E,D)
=> ( ( r1_xreal_0(A,B)
& r2_hidden(A,k4_finseq_1(E))
& r2_hidden(B,k4_finseq_1(E))
& r2_hidden(C,k4_finseq_1(k1_jordan3(D,E,A,B))) )
=> r2_hidden(k5_binarith(k1_nat_1(C,A),np__1),k4_finseq_1(E)) ) ) ) ) ) ) ).
fof(t6_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m2_finseq_1(E,D)
=> ( ( r2_hidden(A,k4_finseq_1(E))
& r2_hidden(B,k4_finseq_1(E))
& r2_hidden(C,k4_finseq_1(k1_jordan3(D,E,A,B))) )
=> ( r1_xreal_0(A,B)
| r2_hidden(k1_nat_1(k5_binarith(A,C),np__1),k4_finseq_1(E)) ) ) ) ) ) ) ) ).
fof(t7_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m2_finseq_1(E,D)
=> ( ( r1_xreal_0(A,B)
& r2_hidden(A,k4_finseq_1(E))
& r2_hidden(B,k4_finseq_1(E))
& r2_hidden(C,k4_finseq_1(k1_jordan3(D,E,A,B))) )
=> k4_finseq_4(k5_numbers,D,k1_jordan3(D,E,A,B),C) = k4_finseq_4(k5_numbers,D,E,k5_binarith(k1_nat_1(C,A),np__1)) ) ) ) ) ) ) ).
fof(t8_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m2_finseq_1(E,D)
=> ( ( r2_hidden(A,k4_finseq_1(E))
& r2_hidden(B,k4_finseq_1(E))
& r2_hidden(C,k4_finseq_1(k1_jordan3(D,E,A,B))) )
=> ( r1_xreal_0(A,B)
| k4_finseq_4(k5_numbers,D,k1_jordan3(D,E,A,B),C) = k4_finseq_4(k5_numbers,D,E,k1_nat_1(k5_binarith(A,C),np__1)) ) ) ) ) ) ) ) ).
fof(t9_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m2_finseq_1(D,C)
=> ( ( r2_hidden(A,k4_finseq_1(D))
& r2_hidden(B,k4_finseq_1(D)) )
=> r1_xreal_0(np__1,k3_finseq_1(k1_jordan3(C,D,A,B))) ) ) ) ) ) ).
fof(t10_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m2_finseq_1(D,C)
=> ( ( r2_hidden(A,k4_finseq_1(D))
& r2_hidden(B,k4_finseq_1(D))
& k3_finseq_1(k1_jordan3(C,D,A,B)) = np__1 )
=> A = B ) ) ) ) ) ).
fof(t11_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m2_finseq_1(D,C)
=> ~ ( r2_hidden(A,k4_finseq_1(D))
& r2_hidden(B,k4_finseq_1(D))
& v1_xboole_0(k1_jordan3(C,D,A,B)) ) ) ) ) ) ).
fof(t12_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m2_finseq_1(D,C)
=> ( ( r2_hidden(A,k4_finseq_1(D))
& r2_hidden(B,k4_finseq_1(D)) )
=> k4_finseq_4(k5_numbers,C,k1_jordan3(C,D,A,B),np__1) = k4_finseq_4(k5_numbers,C,D,A) ) ) ) ) ) ).
fof(t13_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m2_finseq_1(D,C)
=> ( ( r2_hidden(A,k4_finseq_1(D))
& r2_hidden(B,k4_finseq_1(D)) )
=> k4_finseq_4(k5_numbers,C,k1_jordan3(C,D,A,B),k3_finseq_1(k1_jordan3(C,D,A,B))) = k4_finseq_4(k5_numbers,C,D,B) ) ) ) ) ) ).
fof(t14_sprect_2,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,A)
& k22_euclid(B) = k19_pscomp_1(A) )
=> r2_hidden(B,k27_pscomp_1(A)) ) ) ) ).
fof(t15_sprect_2,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,A)
& k22_euclid(B) = k21_pscomp_1(A) )
=> r2_hidden(B,k29_pscomp_1(A)) ) ) ) ).
fof(t16_sprect_2,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,A)
& k21_euclid(B) = k18_pscomp_1(A) )
=> r2_hidden(B,k26_pscomp_1(A)) ) ) ) ).
fof(t17_sprect_2,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,A)
& k21_euclid(B) = k20_pscomp_1(A) )
=> r2_hidden(B,k28_pscomp_1(A)) ) ) ) ).
fof(t19_sprect_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> k4_finseq_1(k2_goboard1(A)) = k4_finseq_1(A) ) ).
fof(t20_sprect_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> k4_finseq_1(k3_goboard1(A)) = k4_finseq_1(A) ) ).
fof(t21_sprect_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(B,k3_topreal1(np__2,A,C))
& r1_xreal_0(k21_euclid(A),k21_euclid(B))
& r1_xreal_0(k21_euclid(C),k21_euclid(B))
& A != B
& B != C
& ~ ( k21_euclid(A) = k21_euclid(B)
& k21_euclid(C) = k21_euclid(B) ) ) ) ) ) ).
fof(t22_sprect_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(B,k3_topreal1(np__2,A,C))
& r1_xreal_0(k22_euclid(A),k22_euclid(B))
& r1_xreal_0(k22_euclid(C),k22_euclid(B))
& A != B
& B != C
& ~ ( k22_euclid(A) = k22_euclid(B)
& k22_euclid(C) = k22_euclid(B) ) ) ) ) ) ).
fof(t23_sprect_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(B,k3_topreal1(np__2,A,C))
& r1_xreal_0(k21_euclid(B),k21_euclid(A))
& r1_xreal_0(k21_euclid(B),k21_euclid(C))
& A != B
& B != C
& ~ ( k21_euclid(A) = k21_euclid(B)
& k21_euclid(C) = k21_euclid(B) ) ) ) ) ) ).
fof(t24_sprect_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(B,k3_topreal1(np__2,A,C))
& r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),k22_euclid(C))
& A != B
& B != C
& ~ ( k22_euclid(A) = k22_euclid(B)
& k22_euclid(C) = k22_euclid(B) ) ) ) ) ) ).
fof(d1_sprect_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_sprect_2(A,B)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(B))
=> ( r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,A)),k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C)))
& r1_xreal_0(k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C)),k20_pscomp_1(k5_topreal1(np__2,A)))
& r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,A)),k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C)))
& r1_xreal_0(k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C)),k19_pscomp_1(k5_topreal1(np__2,A))) ) ) ) ) ) ) ).
fof(t25_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r1_sprect_2(A,A) ) ).
fof(t26_sprect_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_sprect_2(A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(C,k4_finseq_1(B))
& r2_hidden(D,k4_finseq_1(B)) )
=> r1_sprect_2(A,k1_jordan3(u1_struct_0(k15_euclid(np__2)),B,C,D)) ) ) ) ) ) ) ).
fof(t27_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A)) )
=> r1_sprect_2(A,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)) ) ) ) ) ).
fof(t28_sprect_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_sprect_2(A,B)
& r1_sprect_2(A,C) )
=> r1_sprect_2(A,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),B,C)) ) ) ) ) ).
fof(t29_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r1_sprect_2(A,k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))) ) ).
fof(t30_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r1_sprect_2(A,k13_binarith(u1_struct_0(k15_euclid(np__2)),k23_pscomp_1(k5_topreal1(np__2,A)))) ) ).
fof(t31_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r1_sprect_2(A,k13_binarith(u1_struct_0(k15_euclid(np__2)),k25_pscomp_1(k5_topreal1(np__2,A)))) ) ).
fof(t32_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r1_sprect_2(A,k13_binarith(u1_struct_0(k15_euclid(np__2)),k22_pscomp_1(k5_topreal1(np__2,A)))) ) ).
fof(d2_sprect_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_sprect_2(A,B)
<=> ( r1_sprect_2(A,B)
& k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) = k18_pscomp_1(k5_topreal1(np__2,A))
& k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))) = k20_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) ).
fof(d3_sprect_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r3_sprect_2(A,B)
<=> ( r1_sprect_2(A,B)
& k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) = k21_pscomp_1(k5_topreal1(np__2,A))
& k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))) = k19_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) ).
fof(t33_sprect_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v2_funct_1(B)
& v1_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( ( v2_funct_1(C)
& v1_topreal1(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__2,k3_finseq_1(B))
& r1_xreal_0(np__2,k3_finseq_1(C))
& r2_sprect_2(A,B)
& r3_sprect_2(A,C)
& r1_xboole_0(k5_topreal1(np__2,B),k5_topreal1(np__2,C)) ) ) ) ) ).
fof(d4_sprect_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v1_sprect_2(A)
<=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,k32_pscomp_1(k5_topreal1(np__2,A))),np__2),k27_pscomp_1(k5_topreal1(np__2,A))) ) ) ).
fof(t34_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
=> ( v1_sprect_2(A)
<=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__2),k27_pscomp_1(k5_topreal1(np__2,A))) ) ) ) ).
fof(t35_sprect_2,axiom,
k19_pscomp_1(k2_topreal1) = np__1 ).
fof(t36_sprect_2,axiom,
k18_pscomp_1(k2_topreal1) = np__0 ).
fof(t37_sprect_2,axiom,
k20_pscomp_1(k2_topreal1) = np__1 ).
fof(t38_sprect_2,axiom,
k21_pscomp_1(k2_topreal1) = np__0 ).
fof(t39_sprect_2,axiom,
k27_pscomp_1(k2_topreal1) = k3_topreal1(np__2,k23_euclid(np__0,np__1),k23_euclid(np__1,np__1)) ).
fof(t40_sprect_2,axiom,
k32_pscomp_1(k2_topreal1) = k23_euclid(np__0,np__1) ).
fof(t41_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,C)
& ( ( ~ r1_xreal_0(C,np__1)
& r1_xreal_0(B,k3_finseq_1(A)) )
| ( r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(A),B) ) )
& ~ ( v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
& m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ).
fof(t42_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,B)
& ( ( ~ r1_xreal_0(B,np__1)
& r1_xreal_0(C,k3_finseq_1(A)) )
| ( r1_xreal_0(np__1,B)
& ~ r1_xreal_0(k3_finseq_1(A),C) ) )
& ~ ( v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
& m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ).
fof(t43_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r2_hidden(k32_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) ).
fof(t44_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r2_hidden(k33_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) ).
fof(t45_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r2_hidden(k37_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) ).
fof(t46_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r2_hidden(k36_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) ).
fof(t47_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r2_hidden(k30_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) ).
fof(t48_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r2_hidden(k31_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) ).
fof(t49_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r2_hidden(k35_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) ).
fof(t50_sprect_2,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r2_hidden(k34_pscomp_1(k5_topreal1(np__2,A)),k2_relat_1(A)) ) ).
fof(t51_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v1_topreal1(E)
& v2_topreal1(E)
& v1_finseq_6(E,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(E)
& v2_goboard5(E)
& ~ v5_seqm_3(E)
& m2_finseq_1(E,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B)
& r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(E)) )
=> ( r1_xreal_0(C,B)
| ( r1_xreal_0(A,np__1)
& r1_xreal_0(k3_finseq_1(E),D) )
| r1_xboole_0(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,A,B)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,C,D))) ) ) ) ) ) ) ) ).
fof(t52_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v1_topreal1(E)
& v2_topreal1(E)
& v1_finseq_6(E,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(E)
& v2_goboard5(E)
& ~ v5_seqm_3(E)
& m2_finseq_1(E,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B)
& r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(E)) )
=> ( r1_xreal_0(C,B)
| ( r1_xreal_0(A,np__1)
& r1_xreal_0(k3_finseq_1(E),D) )
| r1_xboole_0(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,A,B)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,D,C))) ) ) ) ) ) ) ) ).
fof(t53_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v1_topreal1(E)
& v2_topreal1(E)
& v1_finseq_6(E,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(E)
& v2_goboard5(E)
& ~ v5_seqm_3(E)
& m2_finseq_1(E,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B)
& r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(E)) )
=> ( r1_xreal_0(C,B)
| ( r1_xreal_0(A,np__1)
& r1_xreal_0(k3_finseq_1(E),D) )
| r1_xboole_0(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,B,A)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,D,C))) ) ) ) ) ) ) ) ).
fof(t54_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v1_topreal1(E)
& v2_topreal1(E)
& v1_finseq_6(E,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(E)
& v2_goboard5(E)
& ~ v5_seqm_3(E)
& m2_finseq_1(E,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B)
& r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(E)) )
=> ( r1_xreal_0(C,B)
| ( r1_xreal_0(A,np__1)
& r1_xreal_0(k3_finseq_1(E),D) )
| r1_xboole_0(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,B,A)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),E,C,D))) ) ) ) ) ) ) ) ).
fof(t55_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ r1_xreal_0(k21_euclid(k33_pscomp_1(k5_topreal1(np__2,A))),k21_euclid(k32_pscomp_1(k5_topreal1(np__2,A)))) ) ).
fof(t56_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k32_pscomp_1(k5_topreal1(np__2,A)) != k33_pscomp_1(k5_topreal1(np__2,A)) ) ).
fof(t57_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ r1_xreal_0(k22_euclid(k34_pscomp_1(k5_topreal1(np__2,A))),k22_euclid(k35_pscomp_1(k5_topreal1(np__2,A)))) ) ).
fof(t58_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k35_pscomp_1(k5_topreal1(np__2,A)) != k34_pscomp_1(k5_topreal1(np__2,A)) ) ).
fof(t59_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ r1_xreal_0(k21_euclid(k36_pscomp_1(k5_topreal1(np__2,A))),k21_euclid(k37_pscomp_1(k5_topreal1(np__2,A)))) ) ).
fof(t60_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k37_pscomp_1(k5_topreal1(np__2,A)) != k36_pscomp_1(k5_topreal1(np__2,A)) ) ).
fof(t61_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ r1_xreal_0(k22_euclid(k31_pscomp_1(k5_topreal1(np__2,A))),k22_euclid(k30_pscomp_1(k5_topreal1(np__2,A)))) ) ).
fof(t62_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k30_pscomp_1(k5_topreal1(np__2,A)) != k31_pscomp_1(k5_topreal1(np__2,A)) ) ).
fof(t63_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r1_subset_1(k3_topreal1(np__2,k23_pscomp_1(k5_topreal1(np__2,A)),k32_pscomp_1(k5_topreal1(np__2,A))),k3_topreal1(np__2,k33_pscomp_1(k5_topreal1(np__2,A)),k24_pscomp_1(k5_topreal1(np__2,A)))) ) ).
fof(t64_sprect_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)),k5_topreal1(np__2,A)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) )
=> ( B = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)
| ( k21_euclid(B) != k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1))
& k22_euclid(B) != k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) )
| ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),B),A))
& m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),B),A),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ).
fof(t65_sprect_2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))),k5_topreal1(np__2,A)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) )
=> ( B = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))
| ( k21_euclid(B) != k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)))
& k22_euclid(B) != k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) )
| ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,k13_binarith(u1_struct_0(k15_euclid(np__2)),B)))
& m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,k13_binarith(u1_struct_0(k15_euclid(np__2)),B)),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ).
fof(t66_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A))
& v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
& m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k33_pscomp_1(k5_topreal1(np__2,A)) )
=> ( k33_pscomp_1(k5_topreal1(np__2,A)) = k24_pscomp_1(k5_topreal1(np__2,A))
| ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))))
& m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) ).
fof(t67_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A))
& v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
& m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k34_pscomp_1(k5_topreal1(np__2,A)) )
=> ( k34_pscomp_1(k5_topreal1(np__2,A)) = k24_pscomp_1(k5_topreal1(np__2,A))
| ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))))
& m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) ).
fof(t68_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A))
& v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
& m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k36_pscomp_1(k5_topreal1(np__2,A)) )
=> ( k36_pscomp_1(k5_topreal1(np__2,A)) = k25_pscomp_1(k5_topreal1(np__2,A))
| ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k25_pscomp_1(k5_topreal1(np__2,A)))))
& m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k25_pscomp_1(k5_topreal1(np__2,A)))),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) ).
fof(t69_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A))
& v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
& m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k34_pscomp_1(k5_topreal1(np__2,A)) )
=> ( k34_pscomp_1(k5_topreal1(np__2,A)) = k24_pscomp_1(k5_topreal1(np__2,A))
| ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))))
& m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),k13_binarith(u1_struct_0(k15_euclid(np__2)),k24_pscomp_1(k5_topreal1(np__2,A)))),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) ).
fof(t70_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A))
& v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
& m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k32_pscomp_1(k5_topreal1(np__2,A)) )
=> ( k32_pscomp_1(k5_topreal1(np__2,A)) = k23_pscomp_1(k5_topreal1(np__2,A))
| ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),k23_pscomp_1(k5_topreal1(np__2,A))),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)))
& m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),k23_pscomp_1(k5_topreal1(np__2,A))),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) ).
fof(t71_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A))
& v4_topreal1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C))
& m2_finseq_1(k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C),u1_struct_0(k15_euclid(np__2)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k30_pscomp_1(k5_topreal1(np__2,A)) )
=> ( k30_pscomp_1(k5_topreal1(np__2,A)) = k22_pscomp_1(k5_topreal1(np__2,A))
| ( v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),k22_pscomp_1(k5_topreal1(np__2,A))),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)))
& m2_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k13_binarith(u1_struct_0(k15_euclid(np__2)),k22_pscomp_1(k5_topreal1(np__2,A))),k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,B,C)),u1_struct_0(k15_euclid(np__2))) ) ) ) ) ) ) ).
fof(t72_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
& r1_xreal_0(k5_finseq_4(A,k33_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k32_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t73_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
& r1_xreal_0(k5_finseq_4(A,k33_pscomp_1(k5_topreal1(np__2,A))),np__1) ) ) ).
fof(t74_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
& k33_pscomp_1(k5_topreal1(np__2,A)) != k34_pscomp_1(k5_topreal1(np__2,A))
& r1_xreal_0(k5_finseq_4(A,k34_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k33_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t75_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
& r1_xreal_0(k5_finseq_4(A,k35_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k34_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t76_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
& k35_pscomp_1(k5_topreal1(np__2,A)) != k36_pscomp_1(k5_topreal1(np__2,A))
& r1_xreal_0(k5_finseq_4(A,k36_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k35_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t77_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
& r1_xreal_0(k5_finseq_4(A,k37_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k36_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t78_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
& k37_pscomp_1(k5_topreal1(np__2,A)) != k30_pscomp_1(k5_topreal1(np__2,A))
& r1_xreal_0(k5_finseq_4(A,k30_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k37_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t79_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
& k32_pscomp_1(k5_topreal1(np__2,A)) != k31_pscomp_1(k5_topreal1(np__2,A))
& r1_xreal_0(k5_finseq_4(A,k31_pscomp_1(k5_topreal1(np__2,A))),k5_finseq_4(A,k30_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t80_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
& r1_xreal_0(k3_finseq_1(A),k5_finseq_4(A,k30_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t81_sprect_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
& r1_xreal_0(k3_finseq_1(A),k5_finseq_4(A,k31_pscomp_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t18_sprect_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B)
& r1_xreal_0(B,k3_finseq_1(C)) )
=> k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,B)) = k3_tarski(a_3_0_sprect_2(A,B,C)) ) ) ) ) ).
fof(fraenkel_a_3_0_sprect_2,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,a_3_0_sprect_2(B,C,D))
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& A = k4_topreal1(np__2,D,E)
& r1_xreal_0(B,E)
& ~ r1_xreal_0(C,E) ) ) ) ).
%------------------------------------------------------------------------------