SET007 Axioms: SET007+768.ax
%------------------------------------------------------------------------------
% File : SET007+768 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Full Subtracter Circuit. Part II
% 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 : fscirc_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 35 ( 3 unt; 0 def)
% Number of atoms : 357 ( 109 equ)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 369 ( 47 ~; 1 |; 217 &)
% ( 4 <=>; 100 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 12 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 0 prp; 1-3 aty)
% Number of functors : 61 ( 61 usr; 14 con; 0-4 aty)
% Number of variables : 152 ( 141 !; 11 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_fscirc_2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( ~ v1_xboole_0(k3_fscirc_2(A,B,C))
& v1_facirc_1(k3_fscirc_2(A,B,C)) ) ) ).
fof(d1_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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] :
( ( ~ v3_struct_0(D)
& v1_msualg_1(D)
& ~ v2_msualg_1(D)
& v1_circcomb(D)
& v2_circcomb(D)
& v3_circcomb(D)
& l1_msualg_1(D) )
=> ( D = k1_fscirc_2(A,B,C)
<=> ? [E] :
( m1_pboole(E,k5_numbers)
& ? [F] :
( m1_pboole(F,k5_numbers)
& D = k1_funct_1(E,A)
& k1_funct_1(E,np__0) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2)
& k1_funct_1(F,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1))
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( ( ~ v3_struct_0(H)
& l1_msualg_1(H) )
=> ! [I] :
( ( H = k1_funct_1(E,G)
& I = k1_funct_1(F,G) )
=> ( k1_funct_1(E,k1_nat_1(G,np__1)) = k3_circcomb(H,k8_fscirc_1(k1_funct_1(B,k1_nat_1(G,np__1)),k1_funct_1(C,k1_nat_1(G,np__1)),I))
& k1_funct_1(F,k1_nat_1(G,np__1)) = k6_fscirc_1(k1_funct_1(B,k1_nat_1(G,np__1)),k1_funct_1(C,k1_nat_1(G,np__1)),I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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] :
( ( v4_msualg_1(D,k1_fscirc_2(A,B,C))
& v4_msafree2(D,k1_fscirc_2(A,B,C))
& v4_circcomb(D,k1_fscirc_2(A,B,C))
& v6_circcomb(D,k1_fscirc_2(A,B,C))
& l3_msualg_1(D,k1_fscirc_2(A,B,C)) )
=> ( D = k2_fscirc_2(A,B,C)
<=> ? [E] :
( m1_pboole(E,k5_numbers)
& ? [F] :
( m1_pboole(F,k5_numbers)
& ? [G] :
( m1_pboole(G,k5_numbers)
& k1_fscirc_2(A,B,C) = k1_funct_1(E,A)
& D = k1_funct_1(F,A)
& k1_funct_1(E,np__0) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2)
& k1_funct_1(F,np__0) = k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2)
& k1_funct_1(G,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1))
& ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ! [I] :
( ( ~ v3_struct_0(I)
& l1_msualg_1(I) )
=> ! [J] :
( ( v5_msualg_1(J,I)
& l3_msualg_1(J,I) )
=> ! [K] :
( ( I = k1_funct_1(E,H)
& J = k1_funct_1(F,H)
& K = k1_funct_1(G,H) )
=> ( k1_funct_1(E,k1_nat_1(H,np__1)) = k3_circcomb(I,k8_fscirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K))
& k1_funct_1(F,k1_nat_1(H,np__1)) = k4_circcomb(I,k8_fscirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K),J,k9_fscirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K))
& k1_funct_1(G,k1_nat_1(H,np__1)) = k6_fscirc_1(k1_funct_1(B,k1_nat_1(H,np__1)),k1_funct_1(C,k1_nat_1(H,np__1)),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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] :
( m1_struct_0(D,k1_fscirc_2(A,B,C),k4_msafree2(k1_fscirc_2(A,B,C)))
=> ( D = k3_fscirc_2(A,B,C)
<=> ? [E] :
( m1_pboole(E,k5_numbers)
& D = k1_funct_1(E,A)
& k1_funct_1(E,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k1_funct_1(E,k1_nat_1(F,np__1)) = k6_fscirc_1(k1_funct_1(B,k1_nat_1(F,np__1)),k1_funct_1(C,k1_nat_1(F,np__1)),k1_funct_1(E,F)) ) ) ) ) ) ) ) ).
fof(t1_fscirc_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( m1_pboole(C,k5_numbers)
=> ! [D] :
( m1_pboole(D,k5_numbers)
=> ! [E] :
( m1_pboole(E,k5_numbers)
=> ( ( k1_funct_1(C,np__0) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2)
& k1_funct_1(D,np__0) = k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2)
& k1_funct_1(E,np__0) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( ~ v3_struct_0(G)
& l1_msualg_1(G) )
=> ! [H] :
( ( v5_msualg_1(H,G)
& l3_msualg_1(H,G) )
=> ! [I] :
( ( G = k1_funct_1(C,F)
& H = k1_funct_1(D,F)
& I = k1_funct_1(E,F) )
=> ( k1_funct_1(C,k1_nat_1(F,np__1)) = k3_circcomb(G,k8_fscirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I))
& k1_funct_1(D,k1_nat_1(F,np__1)) = k4_circcomb(G,k8_fscirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I),H,k9_fscirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I))
& k1_funct_1(E,k1_nat_1(F,np__1)) = k6_fscirc_1(k1_funct_1(A,k1_nat_1(F,np__1)),k1_funct_1(B,k1_nat_1(F,np__1)),I) ) ) ) ) ) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( k1_fscirc_2(F,A,B) = k1_funct_1(C,F)
& k2_fscirc_2(F,A,B) = k1_funct_1(D,F)
& k3_fscirc_2(F,A,B) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) ).
fof(t2_fscirc_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( k1_fscirc_2(np__0,A,B) = k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2)
& k2_fscirc_2(np__0,A,B) = k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2)
& k3_fscirc_2(np__0,A,B) = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1)) ) ) ) ).
fof(t3_fscirc_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( C = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1))
=> ( k1_fscirc_2(np__1,A,B) = k3_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2),k8_fscirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C))
& k2_fscirc_2(np__1,A,B) = k4_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2),k8_fscirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C),k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2),k9_fscirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C))
& k3_fscirc_2(np__1,A,B) = k6_fscirc_1(k1_funct_1(A,np__1),k1_funct_1(B,np__1),C) ) ) ) ) ).
fof(t4_fscirc_2,axiom,
! [A,B,C] :
( C = k4_tarski(k3_facirc_2,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1))
=> ( k1_fscirc_2(np__1,k5_facirc_1(A),k5_facirc_1(B)) = k3_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2),k8_fscirc_1(A,B,C))
& k2_fscirc_2(np__1,k5_facirc_1(A),k5_facirc_1(B)) = k4_circcomb(k7_circcomb(k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2),k8_fscirc_1(A,B,C),k9_circcomb(np__0,k10_circcomb,k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1),k3_facirc_2),k9_fscirc_1(A,B,C))
& k3_fscirc_2(np__1,k5_facirc_1(A),k5_facirc_1(B)) = k6_fscirc_1(A,B,C) ) ) ).
fof(t5_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_circcomb(B,A)
=> ! [C] :
( m1_circcomb(C,A)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finseq_1(F) )
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G) )
=> ( k1_fscirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k1_fscirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G))
& k2_fscirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k2_fscirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G))
& k3_fscirc_2(A,k7_finseq_1(B,D),k7_finseq_1(C,F)) = k3_fscirc_2(A,k7_finseq_1(B,E),k7_finseq_1(C,G)) ) ) ) ) ) ) ) ) ).
fof(t6_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_circcomb(B,A)
=> ! [C] :
( m1_circcomb(C,A)
=> ! [D,E] :
( k1_fscirc_2(k1_nat_1(A,np__1),k8_facirc_1(A,np__1,B,k5_facirc_1(D)),k8_facirc_1(A,np__1,C,k5_facirc_1(E))) = k3_circcomb(k1_fscirc_2(A,B,C),k8_fscirc_1(D,E,k3_fscirc_2(A,B,C)))
& k2_fscirc_2(k1_nat_1(A,np__1),k8_facirc_1(A,np__1,B,k5_facirc_1(D)),k8_facirc_1(A,np__1,C,k5_facirc_1(E))) = k4_circcomb(k1_fscirc_2(A,B,C),k8_fscirc_1(D,E,k3_fscirc_2(A,B,C)),k2_fscirc_2(A,B,C),k9_fscirc_1(D,E,k3_fscirc_2(A,B,C)))
& k3_fscirc_2(k1_nat_1(A,np__1),k8_facirc_1(A,np__1,B,k5_facirc_1(D)),k8_facirc_1(A,np__1,C,k5_facirc_1(E))) = k6_fscirc_1(D,E,k3_fscirc_2(A,B,C)) ) ) ) ) ).
fof(t7_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> ( k1_fscirc_2(k1_nat_1(A,np__1),B,C) = k3_circcomb(k1_fscirc_2(A,B,C),k8_fscirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k3_fscirc_2(A,B,C)))
& k2_fscirc_2(k1_nat_1(A,np__1),B,C) = k4_circcomb(k1_fscirc_2(A,B,C),k8_fscirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k3_fscirc_2(A,B,C)),k2_fscirc_2(A,B,C),k9_fscirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k3_fscirc_2(A,B,C)))
& k3_fscirc_2(k1_nat_1(A,np__1),B,C) = k6_fscirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k3_fscirc_2(A,B,C)) ) ) ) ) ).
fof(t8_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,B)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> r1_tarski(k4_msafree2(k1_fscirc_2(A,C,D)),k4_msafree2(k1_fscirc_2(B,C,D))) ) ) ) ) ) ).
fof(t9_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> k4_msafree2(k1_fscirc_2(k1_nat_1(A,np__1),B,C)) = k2_xboole_0(k4_msafree2(k1_fscirc_2(A,B,C)),k4_msafree2(k8_fscirc_1(k1_funct_1(B,k1_nat_1(A,np__1)),k1_funct_1(C,k1_nat_1(A,np__1)),k3_fscirc_2(A,B,C)))) ) ) ) ).
fof(d4_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ! [E] :
( m1_struct_0(E,k1_fscirc_2(B,C,D),k4_msafree2(k1_fscirc_2(B,C,D)))
=> ( E = k4_fscirc_2(A,B,C,D)
<=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& A = k1_nat_1(F,np__1)
& E = k1_fscirc_1(k1_funct_1(C,A),k1_funct_1(D,A),k3_fscirc_2(F,C,D)) ) ) ) ) ) ) ) ) ).
fof(t10_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,B)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> k4_fscirc_2(k1_nat_1(B,np__1),A,C,D) = k1_fscirc_1(k1_funct_1(C,k1_nat_1(B,np__1)),k1_funct_1(D,k1_nat_1(B,np__1)),k3_fscirc_2(B,C,D)) ) ) ) ) ) ).
fof(t11_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> v1_relat_1(k4_msafree2(k1_fscirc_2(A,B,C))) ) ) ) ).
fof(t12_fscirc_2,axiom,
! [A,B,C] : k4_msafree2(k3_fscirc_1(A,B,C)) = k1_enumset1(k4_tarski(k6_facirc_1(A,B),k3_twoscomp),k4_tarski(k6_facirc_1(B,C),k2_twoscomp),k4_tarski(k6_facirc_1(A,C),k3_twoscomp)) ).
fof(t13_fscirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
& B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
& C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
& k2_msafree2(k3_fscirc_1(A,B,C)) != k1_enumset1(A,B,C) ) ).
fof(t14_fscirc_2,axiom,
! [A,B,C] : k4_msafree2(k4_fscirc_1(A,B,C)) = k2_xboole_0(k1_enumset1(k4_tarski(k6_facirc_1(A,B),k3_twoscomp),k4_tarski(k6_facirc_1(B,C),k2_twoscomp),k4_tarski(k6_facirc_1(A,C),k3_twoscomp)),k1_struct_0(k4_fscirc_1(A,B,C),k6_fscirc_1(A,B,C))) ).
fof(t15_fscirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
& B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
& C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
& k2_msafree2(k4_fscirc_1(A,B,C)) != k1_enumset1(A,B,C) ) ).
fof(t16_fscirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
& B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
& C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
& C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
& k2_msafree2(k8_fscirc_1(A,B,C)) != k1_enumset1(A,B,C) ) ).
fof(t17_fscirc_2,axiom,
! [A,B,C] : k4_msafree2(k8_fscirc_1(A,B,C)) = k2_xboole_0(k2_xboole_0(k2_tarski(k4_tarski(k6_facirc_1(A,B),k1_facirc_1),k13_facirc_1(A,B,C,k1_facirc_1)),k1_enumset1(k4_tarski(k6_facirc_1(A,B),k3_twoscomp),k4_tarski(k6_facirc_1(B,C),k2_twoscomp),k4_tarski(k6_facirc_1(A,C),k3_twoscomp))),k1_struct_0(k4_fscirc_1(A,B,C),k6_fscirc_1(A,B,C))) ).
fof(t18_fscirc_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( k1_mcart_1(k3_fscirc_2(C,A,B)) = k3_facirc_2
& k2_mcart_1(k3_fscirc_2(C,A,B)) = k5_circcomb(k6_margrel1,k4_finseq_2(np__0,k10_circcomb),k8_margrel1)
& k1_funct_5(k2_mcart_1(k3_fscirc_2(C,A,B))) = k4_finseq_2(np__0,k10_circcomb) )
| ( k1_card_1(k1_mcart_1(k3_fscirc_2(C,A,B))) = np__3
& k2_mcart_1(k3_fscirc_2(C,A,B)) = k4_facirc_1
& k1_funct_5(k2_mcart_1(k3_fscirc_2(C,A,B))) = k4_finseq_2(np__3,k10_circcomb) ) ) ) ) ) ).
fof(t19_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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] :
( k3_fscirc_2(A,B,C) != k4_tarski(D,k2_twoscomp)
& k3_fscirc_2(A,B,C) != k4_tarski(D,k3_twoscomp)
& k3_fscirc_2(A,B,C) != k4_tarski(D,k1_facirc_1) ) ) ) ) ).
fof(t20_fscirc_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v3_facirc_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v3_facirc_1(B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k2_msafree2(k1_fscirc_2(k1_nat_1(C,np__1),A,B)) = k2_xboole_0(k2_msafree2(k1_fscirc_2(C,A,B)),k4_xboole_0(k2_msafree2(k8_fscirc_1(k1_funct_1(A,k1_nat_1(C,np__1)),k1_funct_1(B,k1_nat_1(C,np__1)),k3_fscirc_2(C,A,B))),k1_struct_0(k1_fscirc_2(C,A,B),k3_fscirc_2(C,A,B))))
& v1_relat_1(k4_msafree2(k1_fscirc_2(C,A,B)))
& ~ v2_facirc_1(k2_msafree2(k1_fscirc_2(C,A,B))) ) ) ) ) ).
fof(t21_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v3_facirc_1(B)
& m1_circcomb(B,A) )
=> ! [C] :
( ( v3_facirc_1(C)
& m1_circcomb(C,A) )
=> k2_msafree2(k1_fscirc_2(A,B,C)) = k2_xboole_0(k2_relat_1(B),k2_relat_1(C)) ) ) ) ).
fof(t22_fscirc_2,axiom,
! [A,B,C,D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C))))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
=> ! [G] :
( m2_subset_1(G,k5_numbers,k10_circcomb)
=> ( ( E = k1_funct_1(D,k4_tarski(k6_facirc_1(A,B),k3_twoscomp))
& F = k1_funct_1(D,k4_tarski(k6_facirc_1(B,C),k2_twoscomp))
& G = k1_funct_1(D,k4_tarski(k6_facirc_1(A,C),k3_twoscomp)) )
=> k15_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),k6_circuit2(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D),k6_fscirc_1(A,B,C)) = k3_binarith(k3_binarith(E,F),G) ) ) ) ) ) ).
fof(t23_fscirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
& B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
& C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
& C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
& ~ ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C))))
=> v1_circuit2(k9_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D,np__2),k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)) ) ) ).
fof(t24_fscirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
& B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
& C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
& C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
& ? [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C))))
& ? [E] :
( m2_subset_1(E,k5_numbers,k10_circcomb)
& ? [F] :
( m2_subset_1(F,k5_numbers,k10_circcomb)
& ? [G] :
( m2_subset_1(G,k5_numbers,k10_circcomb)
& E = k1_funct_1(D,A)
& F = k1_funct_1(D,B)
& G = k1_funct_1(D,C)
& ~ ( k1_funct_1(k9_facirc_1(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C),D,np__2),k1_fscirc_1(A,B,C)) = k4_binarith(k4_binarith(E,F),G)
& k1_funct_1(k9_facirc_1(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C),D,np__2),k6_fscirc_1(A,B,C)) = k3_binarith(k3_binarith(k12_margrel1(k11_margrel1(E),F),k12_margrel1(F,G)),k12_margrel1(k11_margrel1(E),G)) ) ) ) ) ) ) ).
fof(t25_fscirc_2,axiom,
! [A,B,C] :
~ ( A != k4_tarski(k6_facirc_1(B,C),k2_twoscomp)
& B != k4_tarski(k6_facirc_1(A,C),k3_twoscomp)
& C != k4_tarski(k6_facirc_1(A,B),k3_twoscomp)
& C != k4_tarski(k6_facirc_1(A,B),k1_facirc_1)
& ~ ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C))))
=> v1_circuit2(k9_facirc_1(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C),D,np__2),k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C)) ) ) ).
fof(t26_fscirc_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v3_facirc_1(B)
& m1_circcomb(B,A) )
=> ! [C] :
( ( v3_facirc_1(C)
& m1_circcomb(C,A) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u4_msualg_1(k1_fscirc_2(A,B,C),k2_fscirc_2(A,B,C))))
=> v1_circuit2(k9_facirc_1(k1_fscirc_2(A,B,C),k2_fscirc_2(A,B,C),D,k1_nat_1(np__1,k2_nat_1(np__2,A))),k1_fscirc_2(A,B,C),k2_fscirc_2(A,B,C)) ) ) ) ) ).
fof(dt_k1_fscirc_2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( ~ v3_struct_0(k1_fscirc_2(A,B,C))
& v1_msualg_1(k1_fscirc_2(A,B,C))
& ~ v2_msualg_1(k1_fscirc_2(A,B,C))
& v1_circcomb(k1_fscirc_2(A,B,C))
& v2_circcomb(k1_fscirc_2(A,B,C))
& v3_circcomb(k1_fscirc_2(A,B,C))
& l1_msualg_1(k1_fscirc_2(A,B,C)) ) ) ).
fof(dt_k2_fscirc_2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( v4_msualg_1(k2_fscirc_2(A,B,C),k1_fscirc_2(A,B,C))
& v4_msafree2(k2_fscirc_2(A,B,C),k1_fscirc_2(A,B,C))
& v4_circcomb(k2_fscirc_2(A,B,C),k1_fscirc_2(A,B,C))
& v6_circcomb(k2_fscirc_2(A,B,C),k1_fscirc_2(A,B,C))
& l3_msualg_1(k2_fscirc_2(A,B,C),k1_fscirc_2(A,B,C)) ) ) ).
fof(dt_k3_fscirc_2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> m1_struct_0(k3_fscirc_2(A,B,C),k1_fscirc_2(A,B,C),k4_msafree2(k1_fscirc_2(A,B,C))) ) ).
fof(dt_k4_fscirc_2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C)
& v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> m1_struct_0(k4_fscirc_2(A,B,C,D),k1_fscirc_2(B,C,D),k4_msafree2(k1_fscirc_2(B,C,D))) ) ).
%------------------------------------------------------------------------------