SET007 Axioms: SET007+582.ax
%------------------------------------------------------------------------------
% File : SET007+582 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Rotating and Reversing
% 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 : revrot_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 51 ( 0 unt; 0 def)
% Number of atoms : 372 ( 37 equ)
% Maximal formula atoms : 23 ( 7 avg)
% Number of connectives : 392 ( 71 ~; 8 |; 170 &)
% ( 5 <=>; 138 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 36 ( 35 usr; 0 prp; 1-3 aty)
% Number of functors : 36 ( 36 usr; 6 con; 0-4 aty)
% Number of variables : 129 ( 127 !; 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_revrot_1,axiom,
! [A] :
( ( ~ v3_realset2(A)
& l1_struct_0(A) )
=> ( ~ v1_xboole_0(u1_struct_0(A))
& ~ v1_realset1(u1_struct_0(A)) ) ) ).
fof(rc1_revrot_1,axiom,
! [A] :
( ~ v1_realset1(A)
=> ? [B] :
( m1_finseq_1(B,A)
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& ~ v5_seqm_3(B)
& v1_finset_1(B)
& v1_finseq_1(B)
& v1_finseq_6(B,A)
& ~ v1_realset1(B) ) ) ).
fof(fc2_revrot_1,axiom,
! [A,B,C] :
( ( ~ v1_realset1(A)
& m1_subset_1(B,A)
& ~ v5_seqm_3(C)
& v1_finseq_6(C,A)
& m1_finseq_1(C,A) )
=> ( ~ v1_xboole_0(k1_finseq_6(A,C,B))
& v1_relat_1(k1_finseq_6(A,C,B))
& v1_funct_1(k1_finseq_6(A,C,B))
& ~ v5_seqm_3(k1_finseq_6(A,C,B))
& v1_finset_1(k1_finseq_6(A,C,B))
& v1_finseq_1(k1_finseq_6(A,C,B))
& v1_finseq_6(k1_finseq_6(A,C,B),A)
& ~ v1_realset1(k1_finseq_6(A,C,B)) ) ) ).
fof(fc3_revrot_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers) )
=> ( ~ v3_struct_0(k15_euclid(A))
& v1_pre_topc(k15_euclid(A))
& v2_pre_topc(k15_euclid(A))
& ~ v3_realset2(k15_euclid(A)) ) ) ).
fof(fc4_revrot_1,axiom,
! [A,B] :
( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
& v1_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& m1_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( v1_relat_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_funct_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finset_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ).
fof(fc5_revrot_1,axiom,
! [A,B] :
( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& m1_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( v1_relat_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_funct_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finset_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ).
fof(fc6_revrot_1,axiom,
! [A,B] :
( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v1_xboole_0(B)
& ~ v5_seqm_3(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& m1_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( ~ v1_xboole_0(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_relat_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_funct_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& ~ v5_seqm_3(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finset_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v2_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finseq_6(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A),u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& ~ v1_realset1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ).
fof(fc7_revrot_1,axiom,
! [A,B] :
( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v1_xboole_0(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v2_goboard5(B)
& m1_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( ~ v1_xboole_0(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_relat_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_funct_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finset_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finseq_6(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A),u1_struct_0(k15_euclid(np__2)))
& v2_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ).
fof(fc8_revrot_1,axiom,
! [A,B] :
( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v1_xboole_0(B)
& ~ v5_seqm_3(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& v1_sprect_2(B)
& m1_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( ~ v1_xboole_0(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_relat_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_funct_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& ~ v5_seqm_3(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finset_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v2_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_finseq_6(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A),u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v2_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& v1_sprect_2(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))
& ~ v1_realset1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ).
fof(d1_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( v5_seqm_3(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)) )
=> k4_finseq_4(k5_numbers,A,B,C) = k4_finseq_4(k5_numbers,A,B,D) ) ) ) ) ) ) ).
fof(t1_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( r2_finseq_4(B,k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B)))
=> k5_finseq_4(B,k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B))) = k3_finseq_1(B) ) ) ) ).
fof(t2_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> k1_rfinseq(A,B,k3_finseq_1(B)) = k1_xboole_0 ) ) ).
fof(t3_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_finseq_1(B,A) )
=> r2_hidden(k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B)),k2_relat_1(B)) ) ) ).
fof(d2_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( r1_revrot_1(A,B,C)
<=> ? [D] :
( r2_hidden(D,k4_finseq_1(B))
& C = k4_finseq_4(k5_numbers,A,B,D)
& ! [E] :
~ ( r2_hidden(E,k4_finseq_1(B))
& E != D
& k4_finseq_4(k5_numbers,A,B,E) = C ) ) ) ) ) ).
fof(t4_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( r1_revrot_1(A,B,k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B)))
=> k1_finseq_5(A,B,k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B))) = B ) ) ) ).
fof(t5_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( r1_revrot_1(A,B,k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B)))
=> k2_finseq_5(A,B,k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B))) = k12_finseq_1(A,k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B))) ) ) ) ).
fof(t6_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> r1_xreal_0(np__1,k3_finseq_1(k2_finseq_5(A,C,B))) ) ) ) ).
fof(t7_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ( r2_hidden(B,k2_relat_1(C))
=> r1_xreal_0(k3_finseq_1(k2_finseq_5(A,C,B)),k3_finseq_1(C)) ) ) ) ) ).
fof(t8_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finseq_6(B,A)
& m2_finseq_1(B,A) )
=> v1_finseq_6(k4_finseq_5(A,B),A) ) ) ).
fof(t9_revrot_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m2_finseq_1(D,B)
=> ( ( r2_hidden(C,k2_relat_1(D))
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k2_finseq_5(B,D,C))) )
=> k4_finseq_4(k5_numbers,B,k1_finseq_6(B,D,C),A) = k4_finseq_4(k5_numbers,B,D,k1_nat_1(k5_binarith(A,np__1),k5_finseq_4(D,C))) ) ) ) ) ) ).
fof(t10_revrot_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m2_finseq_1(D,B)
=> ( ( r2_hidden(C,k2_relat_1(D))
& r1_xreal_0(k5_finseq_4(D,C),A)
& r1_xreal_0(A,k3_finseq_1(D)) )
=> k4_finseq_4(k5_numbers,B,D,A) = k4_finseq_4(k5_numbers,B,k1_finseq_6(B,D,C),k5_binarith(k1_nat_1(A,np__1),k5_finseq_4(D,C))) ) ) ) ) ) ).
fof(t11_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ( r2_hidden(B,k2_relat_1(C))
=> k4_finseq_4(k5_numbers,A,k1_finseq_6(A,C,B),k3_finseq_1(k2_finseq_5(A,C,B))) = k4_finseq_4(k5_numbers,A,C,k3_finseq_1(C)) ) ) ) ) ).
fof(t12_revrot_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m2_finseq_1(D,B)
=> ( ( r2_hidden(C,k2_relat_1(D))
& r1_xreal_0(A,k3_finseq_1(D)) )
=> ( r1_xreal_0(A,k3_finseq_1(k2_finseq_5(B,D,C)))
| k4_finseq_4(k5_numbers,B,k1_finseq_6(B,D,C),A) = k4_finseq_4(k5_numbers,B,D,k5_binarith(k1_nat_1(A,k5_finseq_4(D,C)),k3_finseq_1(D))) ) ) ) ) ) ) ).
fof(t13_revrot_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m2_finseq_1(D,B)
=> ( ( r2_hidden(C,k2_relat_1(D))
& r1_xreal_0(A,k5_finseq_4(D,C)) )
=> ( r1_xreal_0(A,np__1)
| k4_finseq_4(k5_numbers,B,D,A) = k4_finseq_4(k5_numbers,B,k1_finseq_6(B,D,C),k5_binarith(k1_nat_1(A,k3_finseq_1(D)),k5_finseq_4(D,C))) ) ) ) ) ) ) ).
fof(t14_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> k3_finseq_1(k1_finseq_6(A,C,B)) = k3_finseq_1(C) ) ) ) ).
fof(t15_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> k4_finseq_1(k1_finseq_6(A,C,B)) = k4_finseq_1(C) ) ) ) ).
fof(t16_revrot_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_finseq_6(B,A)
& m2_finseq_1(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(D,np__1)
& ~ r1_xreal_0(k3_finseq_1(B),D)
& k4_finseq_4(k5_numbers,A,B,D) = k4_finseq_4(k5_numbers,A,B,np__1) ) )
=> k1_finseq_6(A,k1_finseq_6(A,B,C),k4_finseq_4(k5_numbers,A,B,np__1)) = B ) ) ) ) ).
fof(t17_revrot_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( ( v1_finseq_6(D,B)
& m2_finseq_1(D,B) )
=> ( ( r2_hidden(C,k2_relat_1(D))
& r1_xreal_0(k3_finseq_1(k2_finseq_5(B,D,C)),A)
& r1_xreal_0(A,k3_finseq_1(D)) )
=> k4_finseq_4(k5_numbers,B,k1_finseq_6(B,D,C),A) = k4_finseq_4(k5_numbers,B,D,k5_binarith(k1_nat_1(A,k5_finseq_4(D,C)),k3_finseq_1(D))) ) ) ) ) ) ).
fof(t18_revrot_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( ( v1_finseq_6(D,B)
& m2_finseq_1(D,B) )
=> ( ( r2_hidden(C,k2_relat_1(D))
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k5_finseq_4(D,C)) )
=> k4_finseq_4(k5_numbers,B,D,A) = k4_finseq_4(k5_numbers,B,k1_finseq_6(B,D,C),k5_binarith(k1_nat_1(A,k3_finseq_1(D)),k5_finseq_4(D,C))) ) ) ) ) ) ).
fof(t19_revrot_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> k16_euclid(A) != k5_jordan2c(A) ) ).
fof(t20_revrot_1,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_tarski(k2_relat_1(A),k2_relat_1(B))
=> r1_tarski(k2_relat_1(k2_goboard1(A)),k2_relat_1(k2_goboard1(B))) ) ) ) ).
fof(t21_revrot_1,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)))
=> ( k2_relat_1(A) = k2_relat_1(B)
=> k2_relat_1(k2_goboard1(A)) = k2_relat_1(k2_goboard1(B)) ) ) ) ).
fof(t22_revrot_1,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_tarski(k2_relat_1(A),k2_relat_1(B))
=> r1_tarski(k2_relat_1(k3_goboard1(A)),k2_relat_1(k3_goboard1(B))) ) ) ) ).
fof(t23_revrot_1,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)))
=> ( k2_relat_1(A) = k2_relat_1(B)
=> k2_relat_1(k3_goboard1(A)) = k2_relat_1(k3_goboard1(B)) ) ) ) ).
fof(t24_revrot_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k2_relat_1(C))
& r1_xreal_0(np__1,A) )
=> ( r1_xreal_0(k3_finseq_1(k2_finseq_5(u1_struct_0(k15_euclid(np__2)),C,B)),A)
| k4_topreal1(np__2,k1_finseq_6(u1_struct_0(k15_euclid(np__2)),C,B),A) = k4_topreal1(np__2,C,k1_nat_1(k5_binarith(A,np__1),k5_finseq_4(C,B))) ) ) ) ) ) ).
fof(t25_revrot_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k2_relat_1(C))
& r1_xreal_0(k5_finseq_4(C,B),A) )
=> ( r1_xreal_0(k3_finseq_1(C),A)
| k4_topreal1(np__2,C,A) = k4_topreal1(np__2,k1_finseq_6(u1_struct_0(k15_euclid(np__2)),C,B),k1_nat_1(k5_binarith(A,k5_finseq_4(C,B)),np__1)) ) ) ) ) ) ).
fof(t26_revrot_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> k2_goboard2(k2_goboard1(B)) = k2_goboard2(k2_goboard1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))) ) ) ).
fof(t27_revrot_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> k2_goboard2(k3_goboard1(B)) = k2_goboard2(k3_goboard1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A))) ) ) ).
fof(t28_revrot_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> k3_goboard2(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A)) = k3_goboard2(B) ) ) ).
fof(t29_revrot_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& ~ v5_seqm_3(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> k4_finseq_5(u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A)) = k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_goboard9(B),A) ) ) ).
fof(t30_revrot_1,axiom,
! [A] :
( ( v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( ~ r1_xreal_0(k3_finseq_1(A),np__4)
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,k5_binarith(k3_finseq_1(A),np__1)),k4_topreal1(np__2,A,np__1)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) ) ) ).
fof(t31_revrot_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r2_hidden(B,k2_relat_1(C))
& r1_xreal_0(k3_finseq_1(k2_finseq_5(u1_struct_0(k15_euclid(np__2)),C,B)),A) )
=> ( r1_xreal_0(k3_finseq_1(C),A)
| k4_topreal1(np__2,k1_finseq_6(u1_struct_0(k15_euclid(np__2)),C,B),A) = k4_topreal1(np__2,C,k5_binarith(k1_nat_1(A,k5_finseq_4(C,B)),k3_finseq_1(C))) ) ) ) ) ) ).
fof(t32_revrot_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r2_hidden(B,k2_relat_1(C))
& r1_xreal_0(np__1,A) )
=> ( r1_xreal_0(k5_finseq_4(C,B),A)
| k4_topreal1(np__2,C,A) = k4_topreal1(np__2,k1_finseq_6(u1_struct_0(k15_euclid(np__2)),C,B),k5_binarith(k1_nat_1(A,k3_finseq_1(C)),k5_finseq_4(C,B))) ) ) ) ) ) ).
fof(t33_revrot_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> k5_topreal1(np__2,k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A)) = k5_topreal1(np__2,B) ) ) ).
fof(t34_revrot_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,C)
<=> r1_goboard1(u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A),C) ) ) ) ) ).
fof(t35_revrot_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k2_relat_1(A))
& r1_xreal_0(np__1,C) )
=> ( r1_xreal_0(k5_finseq_4(A,B),C)
| k5_goboard5(A,C) = k5_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,B),k5_binarith(k1_nat_1(C,k3_finseq_1(A)),k5_finseq_4(A,B))) ) ) ) ) ) ).
fof(t36_revrot_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& ~ v5_seqm_3(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> k2_goboard9(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A)) = k2_goboard9(B) ) ) ).
fof(t37_revrot_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& ~ v5_seqm_3(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> k3_goboard9(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),B,A)) = k3_goboard9(B) ) ) ).
fof(t38_revrot_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( v1_sprect_2(A)
| v1_sprect_2(k1_goboard9(A)) ) ) ).
fof(redefinition_v1_revrot_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A) )
=> ( v1_revrot_1(B,A)
<=> v5_seqm_3(B) ) ) ).
fof(redefinition_r1_revrot_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A) )
=> ( r1_revrot_1(A,B,C)
<=> r2_finseq_4(B,C) ) ) ).
%------------------------------------------------------------------------------