SET007 Axioms: SET007+624.ax
%------------------------------------------------------------------------------
% File : SET007+624 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Technical Preliminaries to Algebraic Specifications
% 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 : algspec1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 87 ( 4 unt; 0 def)
% Number of atoms : 646 ( 44 equ)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 640 ( 81 ~; 1 |; 288 &)
% ( 9 <=>; 261 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-4 aty)
% Number of functors : 31 ( 31 usr; 1 con; 0-5 aty)
% Number of variables : 246 ( 238 !; 8 ?)
% 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_algspec1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,B,k3_finseq_2(A))
& m1_relset_1(C,B,k3_finseq_2(A))
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A) )
=> ( v1_msualg_1(g1_msualg_1(A,B,C,D))
& ~ v2_msualg_1(g1_msualg_1(A,B,C,D)) ) ) ).
fof(cc1_algspec1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m2_algspec1(B,A)
=> ( ~ v3_struct_0(B)
& v1_instalg1(B) ) ) ) ).
fof(cc2_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m2_algspec1(B,A)
=> ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v1_instalg1(B) ) ) ) ).
fof(rc1_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ? [B] :
( m2_algspec1(B,A)
& ~ v3_struct_0(B)
& v1_msualg_1(B)
& ~ v2_msualg_1(B)
& v1_instalg1(B) ) ) ).
fof(t1_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k3_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(C))
=> k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(k1_funct_4(B,A),C) ) ) ) ) ).
fof(t2_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r1_tarski(A,B)
& r1_tarski(k3_xboole_0(k2_relat_1(C),k1_relat_1(B)),k1_relat_1(A)) )
=> k5_relat_1(C,B) = k5_relat_1(C,A) ) ) ) ) ).
fof(t3_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r1_tarski(k1_relat_1(A),k2_relat_1(B))
& r1_xboole_0(k1_relat_1(A),k2_relat_1(C))
& r1_xboole_0(k9_relat_1(B,k1_relat_1(C)),k1_relat_1(A)) )
=> k5_relat_1(k1_funct_4(B,C),A) = k5_relat_1(B,A) ) ) ) ) ).
fof(t4_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r1_partfun1(A,B)
& r1_partfun1(C,D) )
=> r1_partfun1(k5_relat_1(C,A),k5_relat_1(D,B)) ) ) ) ) ) ).
fof(t5_algspec1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,D)
& m2_relset_1(F,B,D) )
=> ( r1_tarski(E,F)
=> r1_tarski(k16_lang1(A,C,E),k16_lang1(B,D,F)) ) ) ) ) ) ) ) ).
fof(t6_algspec1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,D)
& m2_relset_1(F,B,D) )
=> ( r1_partfun1(E,F)
=> r1_partfun1(k16_lang1(A,C,E),k16_lang1(B,D,F)) ) ) ) ) ) ) ) ).
fof(d1_algspec1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> k1_algspec1(A,B) = k1_funct_4(k6_partfun1(A),k7_relat_1(B,A)) ) ).
fof(t7_algspec1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> k2_relat_1(k1_algspec1(A,B)) = k2_xboole_0(k4_xboole_0(A,k1_relat_1(B)),k9_relat_1(B,A)) ) ).
fof(t8_algspec1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( m1_subset_1(C,A)
=> k1_funct_1(k1_algspec1(A,B),C) = k1_funct_1(k1_funct_4(k6_partfun1(A),B),C) ) ) ) ).
fof(t9_algspec1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r2_hidden(B,A)
=> ( ( r2_hidden(B,k1_relat_1(C))
=> k1_funct_1(k1_algspec1(A,C),B) = k1_funct_1(C,B) )
& ( ~ r2_hidden(B,k1_relat_1(C))
=> k1_funct_1(k1_algspec1(A,C),B) = B ) ) ) ) ).
fof(t10_algspec1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( k1_relat_1(B) = A
=> k1_algspec1(A,B) = B ) ) ).
fof(t11_algspec1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> r6_pboole(A,k1_algspec1(A,k1_algspec1(A,B)),k1_algspec1(A,B)) ) ).
fof(t12_algspec1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> r6_pboole(A,k1_algspec1(A,k1_funct_4(k6_partfun1(A),B)),k1_algspec1(A,B)) ) ).
fof(t13_algspec1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r1_tarski(B,k6_partfun1(A))
=> k1_algspec1(A,B) = k6_partfun1(A) ) ) ).
fof(t14_algspec1,axiom,
! [A] : k1_algspec1(A,k1_xboole_0) = k6_partfun1(A) ).
fof(t15_algspec1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> r6_pboole(A,k1_algspec1(A,k7_relat_1(B,A)),k1_algspec1(A,B)) ) ).
fof(t16_algspec1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r1_tarski(A,k1_relat_1(B))
=> k1_algspec1(A,B) = k7_relat_1(B,A) ) ) ).
fof(t17_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> k1_algspec1(k1_xboole_0,A) = k1_xboole_0 ) ).
fof(t18_algspec1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(A,B)
=> k7_relat_1(k1_algspec1(B,C),A) = k1_algspec1(A,C) ) ) ).
fof(t19_algspec1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> r6_pboole(k2_xboole_0(A,B),k1_algspec1(k2_xboole_0(A,B),C),k1_circcomb(A,B,k1_algspec1(A,C),k1_algspec1(B,C))) ) ).
fof(t20_algspec1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> r1_partfun1(k1_algspec1(A,C),k1_algspec1(B,C)) ) ).
fof(t21_algspec1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> k1_algspec1(k2_xboole_0(A,B),C) = k2_xboole_0(k1_algspec1(A,C),k1_algspec1(B,C)) ) ).
fof(t22_algspec1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k2_relat_1(C),A)
=> k5_relat_1(C,k1_algspec1(A,B)) = k5_relat_1(C,k1_funct_4(k6_partfun1(A),B)) ) ) ) ) ).
fof(t23_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
& r1_xboole_0(k2_relat_1(B),k1_relat_1(A)) )
=> ! [C] : k5_relat_1(k1_algspec1(C,B),A) = k7_relat_1(A,C) ) ) ) ).
fof(d2_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( m1_algspec1(B,A)
<=> ( k1_relat_1(B) = k2_relat_1(A)
& k5_relat_1(B,A) = k6_partfun1(k2_relat_1(A)) ) ) ) ) ).
fof(t24_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( m1_algspec1(B,A)
=> r1_tarski(k2_relat_1(B),k1_relat_1(A)) ) ) ).
fof(t25_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( m1_algspec1(B,A)
=> ! [C] :
( r2_hidden(C,k2_relat_1(A))
=> ( r2_hidden(k1_funct_1(B,C),k1_relat_1(A))
& k1_funct_1(A,k1_funct_1(B,C)) = C ) ) ) ) ).
fof(t26_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v2_funct_1(A)
=> m1_algspec1(k2_funct_1(A),A) ) ) ).
fof(t27_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v2_funct_1(A)
=> ! [B] :
( m1_algspec1(B,A)
=> B = k2_funct_1(A) ) ) ) ).
fof(t28_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r1_partfun1(A,B)
=> ! [C] :
( m1_algspec1(C,A)
=> ! [D] :
( m1_algspec1(D,B)
=> m1_algspec1(k1_funct_4(C,D),k1_funct_4(A,B)) ) ) ) ) ) ).
fof(t29_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r1_tarski(A,B)
=> ! [C] :
( m1_algspec1(C,A)
=> ? [D] :
( m1_algspec1(D,B)
& r1_tarski(C,D) ) ) ) ) ) ).
fof(d3_algspec1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_algspec1(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ( k1_funct_1(k1_funct_4(k6_partfun1(u1_msualg_1(A)),C),D) = k1_funct_1(k1_funct_4(k6_partfun1(u1_msualg_1(A)),C),E)
=> ( k5_relat_1(k1_msualg_1(A,D),k1_funct_4(k6_partfun1(u1_struct_0(A)),B)) = k5_relat_1(k1_msualg_1(A,E),k1_funct_4(k6_partfun1(u1_struct_0(A)),B))
& k1_funct_1(k1_funct_4(k6_partfun1(u1_struct_0(A)),B),k2_msualg_1(A,D)) = k1_funct_1(k1_funct_4(k6_partfun1(u1_struct_0(A)),B),k2_msualg_1(A,E)) ) ) ) ) ) ) ) ) ).
fof(t30_algspec1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_algspec1(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ( k1_funct_1(k1_algspec1(u1_msualg_1(A),C),D) = k1_funct_1(k1_algspec1(u1_msualg_1(A),C),E)
=> ( k5_relat_1(k1_msualg_1(A,D),k1_algspec1(u1_struct_0(A),B)) = k5_relat_1(k1_msualg_1(A,E),k1_algspec1(u1_struct_0(A),B))
& k1_funct_1(k1_algspec1(u1_struct_0(A),B),k2_msualg_1(A,D)) = k1_funct_1(k1_algspec1(u1_struct_0(A),B),k2_msualg_1(A,E)) ) ) ) ) ) ) ) ) ).
fof(t31_algspec1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_algspec1(A,B,C)
<=> r1_algspec1(A,k1_algspec1(u1_struct_0(A),B),k1_algspec1(u1_msualg_1(A),C)) ) ) ) ) ).
fof(t32_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r3_pua2mss1(A,B,C,D)
=> r1_algspec1(A,C,D) ) ) ) ) ) ).
fof(t33_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> r1_algspec1(A,B,k1_xboole_0) ) ) ).
fof(t34_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( v2_funct_1(B)
& r1_tarski(k3_xboole_0(u1_msualg_1(A),k2_relat_1(B)),k1_relat_1(B)) )
=> r1_algspec1(A,C,B) ) ) ) ) ).
fof(t35_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( v2_funct_1(B)
& r1_xboole_0(k2_relat_1(B),u1_msualg_1(A)) )
=> r1_algspec1(A,C,B) ) ) ) ) ).
fof(d4_algspec1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_algspec1(A,B,C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_msualg_1(D)
& ~ v2_msualg_1(D)
& l1_msualg_1(D) )
=> ( D = k2_algspec1(A,B,C)
<=> ( r3_pua2mss1(A,D,k1_algspec1(u1_struct_0(A),B),k1_algspec1(u1_msualg_1(A),C))
& u1_struct_0(D) = k2_relat_1(k1_algspec1(u1_struct_0(A),B))
& u1_msualg_1(D) = k2_relat_1(k1_algspec1(u1_msualg_1(A),C)) ) ) ) ) ) ) ) ).
fof(t36_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r3_pua2mss1(A,B,C,D)
=> k7_funct_2(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(A),k16_lang1(u1_struct_0(A),u1_struct_0(B),C)) = k5_relat_1(D,u2_msualg_1(B)) ) ) ) ) ) ).
fof(t37_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_algspec1(A,B,C)
=> ( v1_funct_1(k1_algspec1(u1_struct_0(A),B))
& v1_funct_2(k1_algspec1(u1_struct_0(A),B),u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C)))
& m2_relset_1(k1_algspec1(u1_struct_0(A),B),u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C))) ) ) ) ) ) ).
fof(t38_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_algspec1(A,B,C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C)))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C))) )
=> ( D = k1_algspec1(u1_struct_0(A),B)
=> ! [E] :
( m1_algspec1(E,k1_algspec1(u1_msualg_1(A),C))
=> u2_msualg_1(k2_algspec1(A,B,C)) = k5_relat_1(E,k7_funct_2(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),k3_finseq_2(u1_struct_0(k2_algspec1(A,B,C))),u2_msualg_1(A),k16_lang1(u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C)),D))) ) ) ) ) ) ) ) ).
fof(t39_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_algspec1(A,B,C)
=> ! [D] :
( m1_algspec1(D,k1_algspec1(u1_msualg_1(A),C))
=> u3_msualg_1(k2_algspec1(A,B,C)) = k5_relat_1(D,k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k1_algspec1(u1_struct_0(A),B))) ) ) ) ) ) ).
fof(t40_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r3_pua2mss1(A,B,C,D)
=> m1_instalg1(k2_algspec1(A,C,D),B) ) ) ) ) ) ).
fof(t41_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_algspec1(A,B,C)
<=> r3_pua2mss1(A,k2_algspec1(A,B,C),k1_algspec1(u1_struct_0(A),B),k1_algspec1(u1_msualg_1(A),C)) ) ) ) ) ).
fof(t42_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r1_tarski(k1_relat_1(B),u1_struct_0(A))
& r1_tarski(k1_relat_1(C),u1_msualg_1(A))
& r1_algspec1(A,B,C) )
=> r3_pua2mss1(A,k2_algspec1(A,B,C),k1_funct_4(k6_partfun1(u1_struct_0(A)),B),k1_funct_4(k6_partfun1(u1_msualg_1(A)),C)) ) ) ) ) ).
fof(t43_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( k1_relat_1(B) = u1_struct_0(A)
& k1_relat_1(C) = u1_msualg_1(A)
& r1_algspec1(A,B,C) )
=> r3_pua2mss1(A,k2_algspec1(A,B,C),B,C) ) ) ) ) ).
fof(t44_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_algspec1(A,B,C)
=> k2_algspec1(A,k1_algspec1(u1_struct_0(A),B),C) = k2_algspec1(A,B,C) ) ) ) ) ).
fof(t45_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_algspec1(A,B,C)
=> k2_algspec1(A,B,k1_algspec1(u1_msualg_1(A),C)) = k2_algspec1(A,B,C) ) ) ) ) ).
fof(d5_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_instalg1(B)
& l1_msualg_1(B) )
=> ( m2_algspec1(B,A)
<=> m1_instalg1(A,B) ) ) ) ).
fof(t46_algspec1,axiom,
$true ).
fof(t47_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> m2_algspec1(A,A) ) ).
fof(t48_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m2_algspec1(B,A)
=> ! [C] :
( m2_algspec1(C,B)
=> m2_algspec1(C,A) ) ) ) ).
fof(t49_algspec1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ( r1_circcomb(A,B)
=> m2_algspec1(k3_circcomb(A,B),A) ) ) ) ).
fof(t50_algspec1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> m2_algspec1(k3_circcomb(A,B),B) ) ) ).
fof(t51_algspec1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_msualg_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ( ( r1_partfun1(D,F)
& r3_pua2mss1(A,C,D,E)
& r3_pua2mss1(B,C,F,G) )
=> r3_pua2mss1(k3_circcomb(A,B),C,k1_funct_4(D,F),k1_funct_4(E,G)) ) ) ) ) ) ) ) ) ).
fof(t52_algspec1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_instalg1(C)
& l1_msualg_1(C) )
=> ( ( ( m2_algspec1(C,A)
& m2_algspec1(C,B) )
=> ( r1_circcomb(A,B)
& m2_algspec1(C,k3_circcomb(A,B)) ) )
& ( ( r1_circcomb(A,B)
& m2_algspec1(C,k3_circcomb(A,B)) )
=> ( m2_algspec1(C,A)
& m2_algspec1(C,B) ) ) ) ) ) ) ).
fof(t53_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_instalg1(B)
& l1_msualg_1(B) )
=> ( v3_struct_0(A)
=> m2_algspec1(B,A) ) ) ) ).
fof(t54_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( ~ v2_msualg_1(C)
& v1_instalg1(C)
& l1_msualg_1(C) )
=> ! [D] :
( m2_algspec1(D,C)
=> ( r1_algspec1(D,A,B)
=> r1_algspec1(C,A,B) ) ) ) ) ) ).
fof(t55_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( ~ v2_msualg_1(C)
& v1_instalg1(C)
& l1_msualg_1(C) )
=> ! [D] :
( m2_algspec1(D,C)
=> ( r1_algspec1(D,A,B)
=> m2_algspec1(k2_algspec1(D,A,B),k2_algspec1(C,A,B)) ) ) ) ) ) ).
fof(t56_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ( r1_circcomb(A,B)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r1_algspec1(k3_circcomb(A,B),C,D)
=> k2_algspec1(k3_circcomb(A,B),C,D) = k3_circcomb(k2_algspec1(A,C,D),k2_algspec1(B,C,D)) ) ) ) ) ) ) ).
fof(d6_algspec1,axiom,
! [A] :
( m3_algspec1(A)
<=> ? [B] :
( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B)
& v1_msualg_6(A,B)
& l3_msualg_1(A,B) ) ) ).
fof(d7_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m3_algspec1(B)
=> ( m4_algspec1(B,A)
<=> ? [C] :
( ~ v2_msualg_1(C)
& m2_algspec1(C,A)
& v1_msualg_6(B,C)
& l3_msualg_1(B,C) ) ) ) ) ).
fof(t57_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_msualg_6(B,A)
& l3_msualg_1(B,A) )
=> m4_algspec1(B,A) ) ) ).
fof(t58_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m2_algspec1(B,A)
=> ! [C] :
( m4_algspec1(C,B)
=> m4_algspec1(C,A) ) ) ) ).
fof(t59_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,B)
=> ( m4_algspec1(C,A)
=> ( r1_tarski(u1_struct_0(A),u1_struct_0(B))
& r1_tarski(u1_msualg_1(A),u1_msualg_1(B)) ) ) ) ) ) ).
fof(t60_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,B)
=> ( m4_algspec1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ( v1_funct_1(k1_funct_1(u5_msualg_1(B,C),D))
& v1_funct_2(k1_funct_1(u5_msualg_1(B,C),D),k1_funct_1(k6_pboole(u1_struct_0(B),u4_msualg_1(B,C)),k1_msualg_1(A,D)),k1_funct_1(u4_msualg_1(B,C),k2_msualg_1(A,D)))
& m2_relset_1(k1_funct_1(u5_msualg_1(B,C),D),k1_funct_1(k6_pboole(u1_struct_0(B),u4_msualg_1(B,C)),k1_msualg_1(A,D)),k1_funct_1(u4_msualg_1(B,C),k2_msualg_1(A,D))) ) ) ) ) ) ) ).
fof(t61_algspec1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m4_algspec1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_msualg_1(C) )
=> ( l3_msualg_1(B,C)
=> l3_msualg_1(B,k3_circcomb(C,A)) ) ) ) ) ).
fof(t62_algspec1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ( l3_msualg_1(C,B)
=> ( u1_struct_0(A) = u1_struct_0(B)
& u1_msualg_1(A) = u1_msualg_1(B) ) ) ) ) ) ).
fof(t63_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v1_msafree1(B,A)
& l3_msualg_1(B,A) )
=> v2_funct_1(u4_msualg_1(A,B)) ) ) ).
fof(t64_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v1_msafree1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B)))
=> ! [D] :
( m1_subset_1(D,k2_relat_1(u4_msualg_1(A,B)))
=> ( C = D
| r1_xboole_0(C,D) ) ) ) ) ) ).
fof(t65_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v1_msafree1(C,A)
& l3_msualg_1(C,A) )
=> ( l3_msualg_1(C,B)
=> g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) = g1_msualg_1(u1_struct_0(B),u1_msualg_1(B),u2_msualg_1(B),u3_msualg_1(B)) ) ) ) ) ).
fof(t66_algspec1,axiom,
! [A] :
( ( ~ v2_msualg_1(A)
& v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v2_msualg_1(B)
& v1_instalg1(B)
& l1_msualg_1(B) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v1_msafree1(C,A)
& l3_msualg_1(C,A) )
=> ( m4_algspec1(C,B)
=> m2_algspec1(A,B) ) ) ) ) ).
fof(dt_m1_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( m1_algspec1(B,A)
=> ( v1_relat_1(B)
& v1_funct_1(B) ) ) ) ).
fof(existence_m1_algspec1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ? [B] : m1_algspec1(B,A) ) ).
fof(dt_m2_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m2_algspec1(B,A)
=> ( v1_instalg1(B)
& l1_msualg_1(B) ) ) ) ).
fof(existence_m2_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ? [B] : m2_algspec1(B,A) ) ).
fof(dt_m3_algspec1,axiom,
$true ).
fof(existence_m3_algspec1,axiom,
? [A] : m3_algspec1(A) ).
fof(dt_m4_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m4_algspec1(B,A)
=> m3_algspec1(B) ) ) ).
fof(existence_m4_algspec1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ? [B] : m4_algspec1(B,A) ) ).
fof(dt_k1_algspec1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> m1_pboole(k1_algspec1(A,B),A) ) ).
fof(dt_k2_algspec1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_relat_1(C)
& v1_funct_1(C) )
=> ( ~ v3_struct_0(k2_algspec1(A,B,C))
& v1_msualg_1(k2_algspec1(A,B,C))
& ~ v2_msualg_1(k2_algspec1(A,B,C))
& l1_msualg_1(k2_algspec1(A,B,C)) ) ) ).
%------------------------------------------------------------------------------