SET007 Axioms: SET007+769.ax
%------------------------------------------------------------------------------
% File : SET007+769 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Dijkstra's Shortest Path Algorithm
% 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 : graphsp [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 108 ( 4 unt; 0 def)
% Number of atoms : 830 ( 141 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 760 ( 38 ~; 18 |; 307 &)
% ( 23 <=>; 374 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 10 avg)
% Maximal term depth : 10 ( 1 avg)
% Number of predicates : 46 ( 44 usr; 1 prp; 0-6 aty)
% Number of functors : 67 ( 67 usr; 8 con; 0-4 aty)
% Number of variables : 404 ( 395 !; 9 ?)
% 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_graphsp,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
& m1_subset_1(B,k5_numbers) )
=> ( v1_finset_1(k15_graphsp(A,B))
& v1_membered(k15_graphsp(A,B))
& v2_membered(k15_graphsp(A,B))
& v3_membered(k15_graphsp(A,B))
& v4_membered(k15_graphsp(A,B))
& v5_membered(k15_graphsp(A,B)) ) ) ).
fof(fc2_graphsp,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
& m1_subset_1(B,k5_numbers) )
=> ( v1_finset_1(k9_graphsp(A,B))
& v1_membered(k9_graphsp(A,B))
& v2_membered(k9_graphsp(A,B))
& v3_membered(k9_graphsp(A,B))
& v4_membered(k9_graphsp(A,B))
& v5_membered(k9_graphsp(A,B)) ) ) ).
fof(t1_graphsp,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( ~ r2_hidden(B,k2_relat_1(A))
& v2_funct_1(A) )
<=> v2_funct_1(k7_finseq_1(A,k9_finseq_1(B))) ) ) ).
fof(t2_graphsp,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( v1_int_1(C)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> r2_hidden(k1_funct_1(B,C),A) ) ) ) ).
fof(t3_graphsp,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( v1_int_1(C)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> k4_finseq_4(k5_numbers,A,B,C) = k1_funct_1(B,C) ) ) ) ).
fof(t4_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( m2_finseq_1(B,u2_graph_1(A))
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r6_graph_5(A,C)
& k3_finseq_1(B) = np__1 )
=> k10_graph_5(A,B,C) = k1_funct_1(C,k1_funct_1(B,np__1)) ) ) ) ) ).
fof(t5_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( r2_hidden(B,u2_graph_1(A))
=> ( v8_graph_1(k9_finseq_1(B),A)
& v1_graph_4(k9_finseq_1(B),A)
& m2_graph_1(k9_finseq_1(B),A) ) ) ) ).
fof(t6_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( m2_finseq_1(B,u2_graph_1(A))
=> ! [C] :
( m2_finseq_1(C,u2_graph_1(A))
=> ! [D] :
( ( v8_graph_1(D,A)
& v1_graph_4(D,A)
& m2_graph_1(D,A) )
=> ( ( D = k8_finseq_1(u2_graph_1(A),B,C)
& r1_xreal_0(np__1,k3_finseq_1(B))
& r1_xreal_0(np__1,k3_finseq_1(C)) )
=> ( k1_funct_1(u4_graph_1(A),k1_funct_1(D,k3_finseq_1(D))) != k1_funct_1(u4_graph_1(A),k1_funct_1(B,k3_finseq_1(B)))
& k1_funct_1(u3_graph_1(A),k1_funct_1(D,np__1)) != k1_funct_1(u3_graph_1(A),k1_funct_1(C,np__1)) ) ) ) ) ) ) ).
fof(t7_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( ( v8_graph_1(B,A)
& m2_graph_1(B,A) )
=> ! [C,D] :
( m1_subset_1(D,u1_graph_1(A))
=> ! [E] :
( m1_subset_1(E,u1_graph_1(A))
=> ( r2_graph_5(A,D,E,B,C)
<=> r2_graph_5(A,D,E,B,k2_xboole_0(C,k1_tarski(E))) ) ) ) ) ) ).
fof(t8_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( ( v8_graph_1(B,A)
& m2_graph_1(B,A) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D,E] :
( m1_subset_1(E,u1_graph_1(A))
=> ! [F] :
( m1_subset_1(F,u1_graph_1(A))
=> ( r8_graph_5(A,E,F,B,D,C)
<=> r8_graph_5(A,E,F,B,k2_xboole_0(D,k1_tarski(F)),C) ) ) ) ) ) ) ).
fof(t9_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( ( v8_graph_1(B,A)
& m2_graph_1(B,A) )
=> ! [C] :
( ( v8_graph_1(C,A)
& m2_graph_1(C,A) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E,F] :
( m1_subset_1(F,u1_graph_1(A))
=> ! [G] :
( m1_subset_1(G,u1_graph_1(A))
=> ( ( r8_graph_5(A,F,G,B,E,D)
& r8_graph_5(A,F,G,C,E,D) )
=> k10_graph_5(A,B,D) = k10_graph_5(A,C,D) ) ) ) ) ) ) ) ).
fof(t10_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& v3_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_graph_1(A))
=> ! [C] :
( m1_subset_1(C,u1_graph_1(A))
=> ! [D,E] :
( ( r2_hidden(D,u2_graph_1(A))
& r2_hidden(E,u2_graph_1(A))
& r1_graph_4(A,B,C,D)
& r1_graph_4(A,B,C,E) )
=> D = E ) ) ) ) ).
fof(t11_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& l1_graph_1(A) )
=> ! [B,C,D] :
( m1_subset_1(D,u1_graph_1(A))
=> ! [E] :
( m1_subset_1(E,u1_graph_1(A))
=> ( ( u1_graph_1(A) = k2_xboole_0(B,C)
& r2_hidden(D,B)
& r2_hidden(E,C)
& ! [F] :
( m1_subset_1(F,u1_graph_1(A))
=> ! [G] :
( m1_subset_1(G,u1_graph_1(A))
=> ( ( r2_hidden(F,B)
& r2_hidden(G,C) )
=> ! [H] :
~ ( r2_hidden(H,u2_graph_1(A))
& r1_graph_4(A,F,G,H) ) ) ) ) )
=> ! [F] :
( ( v8_graph_1(F,A)
& m2_graph_1(F,A) )
=> ~ r1_graph_5(A,F,D,E) ) ) ) ) ) ).
fof(t12_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( ( v8_graph_1(B,A)
& m2_graph_1(B,A) )
=> ! [C,D,E] :
( m1_subset_1(E,u1_graph_1(A))
=> ! [F] :
( m1_subset_1(F,u1_graph_1(A))
=> ( ( u1_graph_1(A) = k2_xboole_0(C,D)
& r2_hidden(E,C)
& ! [G] :
( m1_subset_1(G,u1_graph_1(A))
=> ! [H] :
( m1_subset_1(H,u1_graph_1(A))
=> ( ( r2_hidden(G,C)
& r2_hidden(H,D) )
=> ! [I] :
~ ( r2_hidden(I,u2_graph_1(A))
& r1_graph_4(A,G,H,I) ) ) ) )
& r1_graph_5(A,B,E,F) )
=> r2_graph_5(A,E,F,B,C) ) ) ) ) ) ).
fof(t13_graphsp,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( ( v2_graph_1(C)
& v7_graph_1(C)
& l1_graph_1(C) )
=> ! [D] :
( ( v8_graph_1(D,C)
& m2_graph_1(D,C) )
=> ! [E] :
( ( v8_graph_1(E,C)
& m2_graph_1(E,C) )
=> ! [F] :
( m1_subset_1(F,u1_graph_1(C))
=> ! [G] :
( m1_subset_1(G,u1_graph_1(C))
=> ! [H] :
( m1_subset_1(H,u1_graph_1(C))
=> ( ( r5_graph_5(C,A)
& r8_graph_5(C,F,G,D,B,A)
& r8_graph_5(C,F,H,E,B,A)
& ! [I] :
~ ( r2_hidden(I,u2_graph_1(C))
& r1_graph_4(C,G,H,I) )
& r9_graph_5(C,D,B,F,A) )
=> ( F = G
| F = H
| r8_graph_5(C,F,H,E,k2_xboole_0(B,k1_tarski(G)),A) ) ) ) ) ) ) ) ) ) ).
fof(t14_graphsp,axiom,
! [A,B] :
( ( v2_graph_1(B)
& v3_graph_1(B)
& v7_graph_1(B)
& l1_graph_1(B) )
=> ! [C] :
( ( v8_graph_1(C,B)
& m2_graph_1(C,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u2_graph_1(B),k8_graph_5)
& m2_relset_1(D,u2_graph_1(B),k8_graph_5) )
=> ! [E] :
( m1_subset_1(E,u1_graph_1(B))
=> ! [F] :
( m1_subset_1(F,u1_graph_1(B))
=> ( ( r2_hidden(A,u2_graph_1(B))
& C = k9_finseq_1(A)
& r1_graph_4(B,E,F,A) )
=> ( E = F
| r8_graph_5(B,E,F,C,k1_tarski(E),D) ) ) ) ) ) ) ) ).
fof(t15_graphsp,axiom,
! [A,B,C] :
( ( v2_graph_1(C)
& v3_graph_1(C)
& v7_graph_1(C)
& l1_graph_1(C) )
=> ! [D] :
( ( v8_graph_1(D,C)
& m2_graph_1(D,C) )
=> ! [E] :
( ( v8_graph_1(E,C)
& m2_graph_1(E,C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u2_graph_1(C),k8_graph_5)
& m2_relset_1(F,u2_graph_1(C),k8_graph_5) )
=> ! [G] :
( m1_subset_1(G,u1_graph_1(C))
=> ! [H] :
( m1_subset_1(H,u1_graph_1(C))
=> ! [I] :
( m1_subset_1(I,u1_graph_1(C))
=> ( ( r2_hidden(A,u2_graph_1(C))
& r8_graph_5(C,G,H,D,B,F)
& E = k7_finseq_1(D,k9_finseq_1(A))
& r1_graph_4(C,H,I,A)
& r2_hidden(G,B)
& ! [J] :
( m1_subset_1(J,u1_graph_1(C))
=> ( r2_hidden(J,B)
=> ! [K] :
~ ( r2_hidden(K,u2_graph_1(C))
& r1_graph_4(C,J,I,K) ) ) ) )
=> ( G = I
| r8_graph_5(C,G,I,E,k2_xboole_0(B,k1_tarski(H)),F) ) ) ) ) ) ) ) ) ) ).
fof(t16_graphsp,axiom,
! [A,B,C] :
( ( v2_graph_1(C)
& v3_graph_1(C)
& v7_graph_1(C)
& l1_graph_1(C) )
=> ! [D] :
( ( v8_graph_1(D,C)
& m2_graph_1(D,C) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u2_graph_1(C),k8_graph_5)
& m2_relset_1(E,u2_graph_1(C),k8_graph_5) )
=> ! [F] :
( m1_subset_1(F,u1_graph_1(C))
=> ! [G] :
( m1_subset_1(G,u1_graph_1(C))
=> ( ( u1_graph_1(C) = k2_xboole_0(A,B)
& r2_hidden(F,A)
& ! [H] :
( m1_subset_1(H,u1_graph_1(C))
=> ! [I] :
( m1_subset_1(I,u1_graph_1(C))
=> ( ( r2_hidden(H,A)
& r2_hidden(I,B) )
=> ! [J] :
~ ( r2_hidden(J,u2_graph_1(C))
& r1_graph_4(C,H,I,J) ) ) ) ) )
=> ( r8_graph_5(C,F,G,D,A,E)
<=> r7_graph_5(C,F,G,D,E) ) ) ) ) ) ) ) ).
fof(t17_graphsp,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> r1_tarski(k2_relat_1(k2_funct_7(C,A,B)),k2_xboole_0(k2_relat_1(C),k1_tarski(B))) ) ).
fof(d1_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> k2_graphsp(A,B,C,D) = k1_graphsp(k1_graphsp(C,A,B),B,D) ) ) ) ) ).
fof(t18_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(A,k4_finseq_1(C))
=> ( A = B
| k1_goboard1(k2_graphsp(A,B,C,D),A) = B ) ) ) ) ) ) ).
fof(t19_graphsp,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_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(A,k4_finseq_1(D))
=> ( A = B
| A = C
| k1_goboard1(k2_graphsp(B,C,D,E),A) = k1_goboard1(D,A) ) ) ) ) ) ) ) ).
fof(t20_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(A,k4_finseq_1(C))
=> k1_goboard1(k2_graphsp(B,A,C,D),A) = D ) ) ) ) ) ).
fof(t21_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> k4_finseq_1(k2_graphsp(A,B,C,D)) = k4_finseq_1(C) ) ) ) ) ).
fof(d2_graphsp,axiom,
! [A,B] :
( m1_subset_1(B,k1_funct_2(A,A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_funct_2(A,A))
& m2_relset_1(C,k5_numbers,k1_funct_2(A,A)) )
=> ( C = k7_graphsp(A,B)
<=> ( k8_funct_2(k5_numbers,k1_funct_2(A,A),C,np__0) = k3_graphsp(A)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k1_funct_2(A,A),C,k1_nat_1(D,np__1)) = k5_graphsp(A,k8_funct_2(k5_numbers,k1_funct_2(A,A),C,D),B) ) ) ) ) ) ).
fof(t22_graphsp,axiom,
! [A] :
( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k6_graphsp(k3_finseq_2(k1_numbers),k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),np__0),B) = B ) ) ) ) ).
fof(t23_graphsp,axiom,
! [A] :
( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
=> ! [B] :
( m1_subset_1(B,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k6_graphsp(k3_finseq_2(k1_numbers),k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),B,A)),k1_nat_1(D,np__1)),C) = k6_graphsp(k3_finseq_2(k1_numbers),A,k6_graphsp(k3_finseq_2(k1_numbers),B,k6_graphsp(k3_finseq_2(k1_numbers),k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),B,A)),D),C))) ) ) ) ) ).
fof(d4_graphsp,axiom,
! [A] :
( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),D),B),C) = k1_xboole_0 )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( D = k10_graphsp(A,B,C)
<=> ( k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),D),B),C) = k1_xboole_0
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),E),B),C) = k1_xboole_0
=> r1_xreal_0(D,E) ) ) ) ) ) ) ) ) ) ).
fof(d5_graphsp,axiom,
! [A] :
( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
=> ( C = k11_graphsp(A,B)
<=> ( k1_relat_1(C) = k3_finseq_2(k1_numbers)
& ! [D] :
( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
=> k8_graphsp(C,D) = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),k10_graphsp(A,D,B)),D) ) ) ) ) ) ) ).
fof(d6_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& v3_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_graph_1(A))
=> ! [C] :
( m1_subset_1(C,u1_graph_1(A))
=> ( ? [D] :
( r2_hidden(D,u2_graph_1(A))
& r1_graph_4(A,B,C,D) )
=> ! [D] :
( D = k12_graphsp(A,B,C)
<=> ? [E] :
( D = E
& r2_hidden(E,u2_graph_1(A))
& r1_graph_4(A,B,C,E) ) ) ) ) ) ) ).
fof(d7_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& v3_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_graph_1(A))
=> ! [C] :
( m1_subset_1(C,u1_graph_1(A))
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( ? [E] :
( r2_hidden(E,u2_graph_1(A))
& r1_graph_4(A,B,C,E) )
=> k13_graphsp(A,B,C,D) = k1_funct_1(D,k12_graphsp(A,B,C)) )
& ( ! [E] :
~ ( r2_hidden(E,u2_graph_1(A))
& r1_graph_4(A,B,C,E) )
=> k13_graphsp(A,B,C,D) = k1_real_1(np__1) ) ) ) ) ) ) ).
fof(t24_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& v3_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_graph_1(A))
=> ! [C] :
( m1_subset_1(C,u1_graph_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u2_graph_1(A),k8_graph_5)
& m2_relset_1(D,u2_graph_1(A),k8_graph_5) )
=> ( r1_xreal_0(np__0,k14_graphsp(A,B,C,D))
<=> ? [E] :
( r2_hidden(E,u2_graph_1(A))
& r1_graph_4(A,B,C,E) ) ) ) ) ) ) ).
fof(t25_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& v3_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_graph_1(A))
=> ! [C] :
( m1_subset_1(C,u1_graph_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u2_graph_1(A),k8_graph_5)
& m2_relset_1(D,u2_graph_1(A),k8_graph_5) )
=> ( k14_graphsp(A,B,C,D) = k1_real_1(np__1)
<=> ! [E] :
~ ( r2_hidden(E,u2_graph_1(A))
& r1_graph_4(A,B,C,E) ) ) ) ) ) ) ).
fof(t26_graphsp,axiom,
! [A,B] :
( ( v2_graph_1(B)
& v3_graph_1(B)
& l1_graph_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_graph_1(B))
=> ! [D] :
( m1_subset_1(D,u1_graph_1(B))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u2_graph_1(B),k8_graph_5)
& m2_relset_1(E,u2_graph_1(B),k8_graph_5) )
=> ( ( r2_hidden(A,u2_graph_1(B))
& r1_graph_4(B,C,D,A) )
=> k14_graphsp(B,C,D,E) = k1_funct_1(E,A) ) ) ) ) ) ).
fof(t27_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> r1_tarski(k15_graphsp(B,A),k2_finseq_1(A)) ) ) ).
fof(t28_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> r1_tarski(k9_graphsp(B,A),k15_graphsp(B,A)) ) ) ).
fof(t29_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> r1_tarski(k9_graphsp(B,A),k2_finseq_1(A)) ) ) ).
fof(d10_graphsp,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( D = k17_graphsp(A,B,C)
<=> ( ~ ( A != k1_xboole_0
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( E = D
& r2_hidden(E,A)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,A)
=> r1_xreal_0(k4_finseq_4(k5_numbers,k1_numbers,B,k1_nat_1(k2_nat_1(np__2,C),E)),k4_finseq_4(k5_numbers,k1_numbers,B,k1_nat_1(k2_nat_1(np__2,C),F))) ) )
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r2_hidden(F,A)
& k4_finseq_4(k5_numbers,k1_numbers,B,k1_nat_1(k2_nat_1(np__2,C),E)) = k4_finseq_4(k5_numbers,k1_numbers,B,k1_nat_1(k2_nat_1(np__2,C),F)) )
=> r1_xreal_0(E,F) ) ) ) ) )
& ( A = k1_xboole_0
=> D = np__0 ) ) ) ) ) ) ) ).
fof(t30_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ( B = k17_graphsp(k9_graphsp(C,A),C,A)
=> ( k9_graphsp(C,A) = k1_xboole_0
| ( r2_hidden(B,k4_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,A)
& k1_goboard1(C,B) != k1_real_1(np__1)
& k1_goboard1(C,k1_nat_1(A,B)) != k1_real_1(np__1) ) ) ) ) ) ) ).
fof(t31_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> r1_xreal_0(k17_graphsp(k9_graphsp(B,A),B,A),A) ) ) ).
fof(d11_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
=> ( B = k18_graphsp(A)
<=> ( k1_relat_1(B) = k3_finseq_2(k1_numbers)
& ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> k8_graphsp(B,C) = k2_graphsp(k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(np__3,A)),np__1),k17_graphsp(k9_graphsp(C,A),C,A),C,k1_real_1(np__1)) ) ) ) ) ) ).
fof(t32_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ( r2_hidden(A,k4_finseq_1(C))
=> ( r1_xreal_0(A,B)
| A = k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(np__3,B)),np__1)
| k1_goboard1(k8_graphsp(k18_graphsp(B),C),A) = k1_goboard1(C,A) ) ) ) ) ) ).
fof(t33_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ( ( r2_hidden(A,k4_finseq_1(C))
& k1_goboard1(C,A) = k1_real_1(np__1) )
=> ( A = k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(np__3,B)),np__1)
| k1_goboard1(k8_graphsp(k18_graphsp(B),C),A) = k1_real_1(np__1) ) ) ) ) ) ).
fof(t34_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> k4_finseq_1(k8_graphsp(k18_graphsp(A),B)) = k4_finseq_1(B) ) ) ).
fof(t35_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> ~ ( k9_graphsp(B,A) != k1_xboole_0
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(C,k9_graphsp(B,A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,A)
& k1_goboard1(k8_graphsp(k18_graphsp(A),B),C) = k1_real_1(np__1) ) ) ) ) ) ).
fof(d12_graphsp,axiom,
! [A] :
( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k19_graphsp(A,B,C) = k3_real_1(k4_finseq_4(k5_numbers,k1_numbers,A,k3_real_1(k2_nat_1(np__2,B),k4_finseq_4(k5_numbers,k1_numbers,A,k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(np__3,B)),np__1)))),k4_finseq_4(k5_numbers,k1_numbers,A,k3_real_1(k3_real_1(k2_nat_1(np__2,B),k4_real_1(B,k4_finseq_4(k5_numbers,k1_numbers,A,k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(np__3,B)),np__1)))),C))) ) ) ) ).
fof(d13_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ( r1_graphsp(A,B,C)
<=> ( ~ ( k1_goboard1(C,k1_nat_1(A,B)) != k1_real_1(np__1)
& r1_xreal_0(k4_finseq_4(k5_numbers,k1_numbers,C,k1_nat_1(k2_nat_1(np__2,A),B)),k19_graphsp(C,A,B)) )
& r1_xreal_0(np__0,k4_finseq_4(k5_numbers,k1_numbers,C,k3_real_1(k3_real_1(k2_nat_1(np__2,A),k4_real_1(A,k4_finseq_4(k5_numbers,k1_numbers,C,k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(np__3,A)),np__1)))),B)))
& k1_goboard1(C,B) != k1_real_1(np__1) ) ) ) ) ) ).
fof(d14_graphsp,axiom,
! [A] :
( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ( C = k20_graphsp(A,B)
<=> ( k4_finseq_1(C) = k4_finseq_1(A)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k4_finseq_1(A))
=> ( ( r1_xreal_0(D,k2_nat_1(np__2,B))
=> ( r1_xreal_0(D,B)
| ( ( r1_graphsp(B,k5_binarith(D,B),A)
=> k1_goboard1(C,D) = k4_finseq_4(k5_numbers,k1_numbers,A,k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(np__3,B)),np__1)) )
& ( ~ r1_graphsp(B,k5_binarith(D,B),A)
=> k1_goboard1(C,D) = k1_goboard1(A,D) ) ) ) )
& ( r1_xreal_0(D,k2_nat_1(np__3,B))
=> ( r1_xreal_0(D,k2_nat_1(np__2,B))
| ( ( r1_graphsp(B,k5_binarith(D,k2_nat_1(np__2,B)),A)
=> k1_goboard1(C,D) = k19_graphsp(A,B,k5_binarith(D,k2_nat_1(np__2,B))) )
& ( ~ r1_graphsp(B,k5_binarith(D,k2_nat_1(np__2,B)),A)
=> k1_goboard1(C,D) = k1_goboard1(A,D) ) ) ) )
& ( ~ ( ~ r1_xreal_0(D,B)
& r1_xreal_0(D,k2_nat_1(np__3,B)) )
=> k1_goboard1(C,D) = k1_goboard1(A,D) ) ) ) ) ) ) ) ) ) ).
fof(d15_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
=> ( B = k21_graphsp(A)
<=> ( k1_relat_1(B) = k3_finseq_2(k1_numbers)
& ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> k8_graphsp(B,C) = k20_graphsp(C,A) ) ) ) ) ) ).
fof(t36_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> k4_finseq_1(k8_graphsp(k21_graphsp(A),B)) = k4_finseq_1(B) ) ) ).
fof(t37_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ( r2_hidden(A,k4_finseq_1(C))
=> ( ( ~ r1_xreal_0(A,B)
& r1_xreal_0(A,k2_nat_1(np__3,B)) )
| k1_goboard1(k8_graphsp(k21_graphsp(B),C),A) = k1_goboard1(C,A) ) ) ) ) ) ).
fof(t38_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> k4_finseq_1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C)) = k4_finseq_1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(B,np__1)),C)) ) ) ) ).
fof(t39_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ( k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C),A) != k1_xboole_0
=> r2_xboole_0(k15_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(B,np__1)),C),A),k15_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C),A)) ) ) ) ) ).
fof(t40_graphsp,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_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [E] :
( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [F] :
( m2_finseq_2(F,k1_numbers,k3_finseq_2(k1_numbers))
=> ( ( D = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),E)
& F = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(B,np__1)),E)
& C = k17_graphsp(k9_graphsp(D,A),D,A) )
=> ( k9_graphsp(D,A) = k1_xboole_0
| ( k16_graphsp(F,A) = k4_subset_1(k5_numbers,k16_graphsp(D,A),k6_domain_1(k5_numbers,C))
& ~ r2_hidden(C,k16_graphsp(D,A)) ) ) ) ) ) ) ) ) ) ).
fof(t41_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(C,A)
& k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),C),B),A) = k1_xboole_0 ) ) ) ).
fof(t42_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> k4_finseq_1(C) = k4_finseq_1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C)) ) ) ) ).
fof(d16_graphsp,axiom,
! [A] :
( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_graphsp(A,B,C,D)
<=> ( k4_finseq_1(A) = k4_finseq_1(B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(E,k4_finseq_1(A))
& r1_xreal_0(C,E)
& r1_xreal_0(E,D) )
=> k1_goboard1(A,E) = k1_goboard1(B,E) ) ) ) ) ) ) ) ) ).
fof(t43_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> r2_graphsp(C,C,A,B) ) ) ) ).
fof(t44_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [D] :
( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [E] :
( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers))
=> ( ( r2_graphsp(C,D,A,B)
& r2_graphsp(D,E,A,B) )
=> r2_graphsp(C,E,A,B) ) ) ) ) ) ) ).
fof(t45_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> r2_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C),k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(B,np__1)),C),k1_nat_1(k2_nat_1(np__3,A),np__1),k1_nat_1(k2_nat_1(A,A),k2_nat_1(np__3,A))) ) ) ) ).
fof(t46_graphsp,axiom,
! [A] :
( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(k10_graphsp(A,B,C),D)
& k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),D),B),C) = k1_xboole_0 ) ) ) ) ) ).
fof(t47_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> r2_graphsp(C,k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C),k1_nat_1(k2_nat_1(np__3,A),np__1),k1_nat_1(k2_nat_1(A,A),k2_nat_1(np__3,A))) ) ) ) ).
fof(t48_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> ( ( r1_xreal_0(np__1,A)
& r2_hidden(np__1,k4_finseq_1(B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,A) )
=> k1_goboard1(B,C) = np__1 ) )
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__2,C)
& r1_xreal_0(C,A) )
=> k1_goboard1(B,k1_nat_1(A,C)) = k1_real_1(np__1) ) ) )
=> ( k1_goboard1(B,k1_nat_1(A,np__1)) = k1_real_1(np__1)
| ( np__1 = k17_graphsp(k9_graphsp(B,A),B,A)
& k16_graphsp(B,A) = k1_xboole_0
& k6_domain_1(k5_numbers,np__1) = k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),np__1),B),A) ) ) ) ) ) ).
fof(t49_graphsp,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_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [E] :
( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [F] :
( m2_finseq_2(F,k1_numbers,k3_finseq_2(k1_numbers))
=> ( ( D = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),np__1),E)
& F = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),E)
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k10_graphsp(k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A)),E,A))
& r2_hidden(C,k16_graphsp(D,A)) )
=> r2_hidden(C,k16_graphsp(F,A)) ) ) ) ) ) ) ) ).
fof(d17_graphsp,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r3_graphsp(A,B,C,D)
<=> ( k1_funct_1(A,k3_finseq_1(A)) = C
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,E)
=> ( r1_xreal_0(k3_finseq_1(A),E)
| k1_funct_1(A,k5_real_1(k3_finseq_1(A),E)) = k1_goboard1(B,k1_nat_1(D,k4_finseq_4(k5_numbers,k5_numbers,A,k3_real_1(k5_real_1(k3_finseq_1(A),E),np__1)))) ) ) ) ) ) ) ) ) ) ).
fof(d18_graphsp,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r4_graphsp(A,B,C,D)
<=> ( k1_funct_1(A,np__1) = np__1
& ~ r1_xreal_0(k3_finseq_1(A),np__1)
& r3_graphsp(A,B,C,D)
& v2_funct_1(A) ) ) ) ) ) ) ).
fof(t50_graphsp,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r4_graphsp(A,C,D,E)
& r4_graphsp(B,C,D,E) )
=> A = B ) ) ) ) ) ) ).
fof(d19_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( m2_finseq_1(B,u2_graph_1(A))
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( r5_graphsp(A,B,C)
<=> ( k3_finseq_1(C) = k1_nat_1(k3_finseq_1(B),np__1)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( k1_funct_1(u3_graph_1(A),k1_funct_1(B,D)) = k1_funct_1(C,D)
& k1_funct_1(u4_graph_1(A),k1_funct_1(B,D)) = k1_funct_1(C,k1_nat_1(D,np__1)) ) ) ) ) ) ) ) ) ).
fof(t51_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& v3_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( ( v8_graph_1(C,A)
& m2_graph_1(C,A) )
=> ! [D] :
( ( v8_graph_1(D,A)
& m2_graph_1(D,A) )
=> ( ( r5_graphsp(A,C,B)
& r5_graphsp(A,D,B) )
=> C = D ) ) ) ) ) ).
fof(t52_graphsp,axiom,
! [A] :
( ( v2_graph_1(A)
& l1_graph_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ! [D] :
( ( v8_graph_1(D,A)
& m2_graph_1(D,A) )
=> ( ( r5_graphsp(A,D,B)
& r5_graphsp(A,D,C)
& r1_xreal_0(np__1,k3_finseq_1(D)) )
=> B = C ) ) ) ) ) ).
fof(d20_graphsp,axiom,
! [A] :
( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [B] :
( ( v2_graph_1(B)
& v3_graph_1(B)
& l1_graph_1(B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u2_graph_1(B),k8_graph_5)
& m2_relset_1(D,u2_graph_1(B),k8_graph_5) )
=> ( r6_graphsp(A,B,C,D)
<=> ( k3_finseq_1(A) = k1_nat_1(k1_nat_1(k2_nat_1(C,C),k2_nat_1(np__3,C)),np__1)
& k2_finseq_1(C) = u1_graph_1(B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,C) )
=> ( k1_goboard1(A,E) = np__1
& k1_goboard1(A,k1_nat_1(k2_nat_1(np__2,C),E)) = np__0 ) ) )
& k1_goboard1(A,k1_nat_1(C,np__1)) = np__0
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__2,E)
& r1_xreal_0(E,C) )
=> k1_goboard1(A,k1_nat_1(C,E)) = k1_real_1(np__1) ) )
& ! [E] :
( m1_subset_1(E,u1_graph_1(B))
=> ! [F] :
( m1_subset_1(F,u1_graph_1(B))
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ( G = E
& H = F )
=> k1_goboard1(A,k1_nat_1(k1_nat_1(k2_nat_1(np__2,C),k2_nat_1(C,G)),H)) = k14_graphsp(B,E,F,D) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d21_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k22_graphsp(A) = k11_graphsp(k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A)),A) ) ).
fof(t53_graphsp,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [D] :
( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [E] :
( ( v2_graph_1(E)
& v3_graph_1(E)
& v7_graph_1(E)
& l1_graph_1(E) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u2_graph_1(E),k8_graph_5)
& m2_relset_1(F,u2_graph_1(E),k8_graph_5) )
=> ! [G] :
( m1_subset_1(G,u1_graph_1(E))
=> ! [H] :
( m1_subset_1(H,u1_graph_1(E))
=> ( ( r6_graphsp(C,E,A,F)
& G = np__1
& H = B
& r1_xreal_0(np__1,A)
& D = k8_graphsp(k22_graphsp(A),C) )
=> ( np__1 = H
| ( u1_graph_1(E) = k4_subset_1(k5_numbers,k16_graphsp(D,A),k15_graphsp(D,A))
& ~ ( r2_hidden(H,k16_graphsp(D,A))
& ! [I] :
( m2_finseq_1(I,k5_numbers)
=> ! [J] :
( ( v8_graph_1(J,E)
& m2_graph_1(J,E) )
=> ~ ( r4_graphsp(I,D,B,A)
& r5_graphsp(E,J,I)
& r7_graph_5(E,G,H,J,F)
& k10_graph_5(E,J,F) = k1_goboard1(D,k1_nat_1(k2_nat_1(np__2,A),B)) ) ) ) )
& ( r2_hidden(H,k15_graphsp(D,A))
=> ! [I] :
( ( v8_graph_1(I,E)
& m2_graph_1(I,E) )
=> ~ r1_graph_5(E,I,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_graphsp,axiom,
! [A,B,C] :
( ( m1_finseq_1(A,k1_numbers)
& m1_subset_1(C,k1_numbers) )
=> m2_finseq_1(k1_graphsp(A,B,C),k1_numbers) ) ).
fof(redefinition_k1_graphsp,axiom,
! [A,B,C] :
( ( m1_finseq_1(A,k1_numbers)
& m1_subset_1(C,k1_numbers) )
=> k1_graphsp(A,B,C) = k2_funct_7(A,B,C) ) ).
fof(dt_k2_graphsp,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_finseq_1(C,k1_numbers)
& m1_subset_1(D,k1_numbers) )
=> m2_finseq_1(k2_graphsp(A,B,C,D),k1_numbers) ) ).
fof(dt_k3_graphsp,axiom,
! [A] : m1_subset_1(k3_graphsp(A),k1_funct_2(A,A)) ).
fof(redefinition_k3_graphsp,axiom,
! [A] : k3_graphsp(A) = k6_relat_1(A) ).
fof(dt_k4_graphsp,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> ( v1_funct_1(k4_graphsp(A,B,C))
& v1_funct_2(k4_graphsp(A,B,C),A,A)
& m2_relset_1(k4_graphsp(A,B,C),A,A) ) ) ).
fof(redefinition_k4_graphsp,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> k4_graphsp(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k5_graphsp,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_funct_2(A,A))
& m1_subset_1(C,k1_funct_2(A,A)) )
=> m1_subset_1(k5_graphsp(A,B,C),k1_funct_2(A,A)) ) ).
fof(redefinition_k5_graphsp,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_funct_2(A,A))
& m1_subset_1(C,k1_funct_2(A,A)) )
=> k5_graphsp(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k6_graphsp,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_funct_2(A,A))
& m1_subset_1(C,A) )
=> m1_subset_1(k6_graphsp(A,B,C),A) ) ).
fof(redefinition_k6_graphsp,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_funct_2(A,A))
& m1_subset_1(C,A) )
=> k6_graphsp(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k7_graphsp,axiom,
! [A,B] :
( m1_subset_1(B,k1_funct_2(A,A))
=> ( v1_funct_1(k7_graphsp(A,B))
& v1_funct_2(k7_graphsp(A,B),k5_numbers,k1_funct_2(A,A))
& m2_relset_1(k7_graphsp(A,B),k5_numbers,k1_funct_2(A,A)) ) ) ).
fof(dt_k8_graphsp,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
& m1_subset_1(B,k3_finseq_2(k1_numbers)) )
=> m2_finseq_2(k8_graphsp(A,B),k1_numbers,k3_finseq_2(k1_numbers)) ) ).
fof(redefinition_k8_graphsp,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
& m1_subset_1(B,k3_finseq_2(k1_numbers)) )
=> k8_graphsp(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k9_graphsp,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k9_graphsp(A,B),k1_zfmisc_1(k5_numbers)) ) ).
fof(dt_k10_graphsp,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
& m1_subset_1(B,k3_finseq_2(k1_numbers))
& m1_subset_1(C,k5_numbers) )
=> m2_subset_1(k10_graphsp(A,B,C),k1_numbers,k5_numbers) ) ).
fof(dt_k11_graphsp,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)))
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k11_graphsp(A,B),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) ).
fof(dt_k12_graphsp,axiom,
$true ).
fof(dt_k13_graphsp,axiom,
$true ).
fof(dt_k14_graphsp,axiom,
! [A,B,C,D] :
( ( v2_graph_1(A)
& v3_graph_1(A)
& l1_graph_1(A)
& m1_subset_1(B,u1_graph_1(A))
& m1_subset_1(C,u1_graph_1(A))
& v1_funct_1(D)
& v1_funct_2(D,u2_graph_1(A),k8_graph_5)
& m1_relset_1(D,u2_graph_1(A),k8_graph_5) )
=> m1_subset_1(k14_graphsp(A,B,C,D),k1_numbers) ) ).
fof(redefinition_k14_graphsp,axiom,
! [A,B,C,D] :
( ( v2_graph_1(A)
& v3_graph_1(A)
& l1_graph_1(A)
& m1_subset_1(B,u1_graph_1(A))
& m1_subset_1(C,u1_graph_1(A))
& v1_funct_1(D)
& v1_funct_2(D,u2_graph_1(A),k8_graph_5)
& m1_relset_1(D,u2_graph_1(A),k8_graph_5) )
=> k14_graphsp(A,B,C,D) = k13_graphsp(A,B,C,D) ) ).
fof(dt_k15_graphsp,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k15_graphsp(A,B),k1_zfmisc_1(k5_numbers)) ) ).
fof(dt_k16_graphsp,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k16_graphsp(A,B),k1_zfmisc_1(k5_numbers)) ) ).
fof(dt_k17_graphsp,axiom,
! [A,B,C] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k5_numbers))
& m1_subset_1(B,k3_finseq_2(k1_numbers))
& m1_subset_1(C,k5_numbers) )
=> m2_subset_1(k17_graphsp(A,B,C),k1_numbers,k5_numbers) ) ).
fof(dt_k18_graphsp,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m1_subset_1(k18_graphsp(A),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) ).
fof(dt_k19_graphsp,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k19_graphsp(A,B,C),k1_numbers) ) ).
fof(dt_k20_graphsp,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_finseq_2(k1_numbers))
& m1_subset_1(B,k5_numbers) )
=> m2_finseq_2(k20_graphsp(A,B),k1_numbers,k3_finseq_2(k1_numbers)) ) ).
fof(dt_k21_graphsp,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m1_subset_1(k21_graphsp(A),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) ).
fof(dt_k22_graphsp,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m1_subset_1(k22_graphsp(A),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) ).
fof(d3_graphsp,axiom,
! [A] :
( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k9_graphsp(A,B) = a_2_0_graphsp(A,B) ) ) ).
fof(d8_graphsp,axiom,
! [A] :
( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k15_graphsp(A,B) = a_2_1_graphsp(A,B) ) ) ).
fof(d9_graphsp,axiom,
! [A] :
( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k16_graphsp(A,B) = a_2_2_graphsp(A,B) ) ) ).
fof(fraenkel_a_2_0_graphsp,axiom,
! [A,B,C] :
( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_0_graphsp(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = D
& r2_hidden(D,k4_finseq_1(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,C)
& k1_goboard1(B,D) != k1_real_1(np__1)
& k1_goboard1(B,k1_nat_1(C,D)) != k1_real_1(np__1) ) ) ) ).
fof(fraenkel_a_2_1_graphsp,axiom,
! [A,B,C] :
( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_1_graphsp(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = D
& r2_hidden(D,k4_finseq_1(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,C)
& k1_goboard1(B,D) != k1_real_1(np__1) ) ) ) ).
fof(fraenkel_a_2_2_graphsp,axiom,
! [A,B,C] :
( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers))
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_2_graphsp(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = D
& r2_hidden(D,k4_finseq_1(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,C)
& k1_goboard1(B,D) = k1_real_1(np__1) ) ) ) ).
%------------------------------------------------------------------------------