SET007 Axioms: SET007+221.ax
%------------------------------------------------------------------------------
% File : SET007+221 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Fundamental Logic Structure in Quantum Mechanics
% 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 : qmax_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 85 ( 28 unt; 0 def)
% Number of atoms : 352 ( 36 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 281 ( 14 ~; 0 |; 109 &)
% ( 14 <=>; 144 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 36 ( 36 usr; 4 con; 0-4 aty)
% Number of variables : 163 ( 156 !; 7 ?)
% 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_qmax_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_prob_1(B,A) )
=> ~ v1_xboole_0(k1_qmax_1(A,B)) ) ).
fof(rc1_qmax_1,axiom,
? [A] :
( l1_qmax_1(A)
& v1_qmax_1(A) ) ).
fof(fc2_qmax_1,axiom,
! [A] :
( l1_qmax_1(A)
=> ~ v1_xboole_0(k2_qmax_1(A)) ) ).
fof(fc3_qmax_1,axiom,
! [A] :
( l1_qmax_1(A)
=> ~ v1_xboole_0(k3_qmax_1(A)) ) ).
fof(rc2_qmax_1,axiom,
? [A] :
( l1_qmax_1(A)
& v1_qmax_1(A)
& v2_qmax_1(A) ) ).
fof(rc3_qmax_1,axiom,
! [A] :
? [B] :
( l2_qmax_1(B,A)
& v3_qmax_1(B,A) ) ).
fof(fc4_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ~ v1_xboole_0(k5_qmax_1(A)) ) ).
fof(d1_qmax_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_prob_1(B,A)
=> ! [C] :
( C = k1_qmax_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> m4_prob_1(D,A,B) ) ) ) ) ).
fof(d2_qmax_1,axiom,
! [A] :
( l1_qmax_1(A)
=> k2_qmax_1(A) = u1_qmax_1(A) ) ).
fof(d3_qmax_1,axiom,
! [A] :
( l1_qmax_1(A)
=> k3_qmax_1(A) = u2_qmax_1(A) ) ).
fof(d4_qmax_1,axiom,
! [A] :
( l1_qmax_1(A)
=> ! [B] :
( m1_subset_1(B,k2_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k3_qmax_1(A))
=> k4_qmax_1(A,B,C) = k1_funct_1(u3_qmax_1(A),k1_domain_1(k2_qmax_1(A),k3_qmax_1(A),B,C)) ) ) ) ).
fof(d5_qmax_1,axiom,
! [A] :
( l1_qmax_1(A)
=> ( v2_qmax_1(A)
<=> ( ! [B] :
( m1_subset_1(B,k2_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k2_qmax_1(A))
=> ( ! [D] :
( m1_subset_1(D,k3_qmax_1(A))
=> k4_qmax_1(A,B,D) = k4_qmax_1(A,C,D) )
=> B = C ) ) )
& ! [B] :
( m1_subset_1(B,k3_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k3_qmax_1(A))
=> ( ! [D] :
( m1_subset_1(D,k2_qmax_1(A))
=> k4_qmax_1(A,D,B) = k4_qmax_1(A,D,C) )
=> B = C ) ) )
& ! [B] :
( m1_subset_1(B,k3_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k3_qmax_1(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( r1_xreal_0(np__0,D)
& r1_xreal_0(D,np__1)
& ! [E] :
( m1_subset_1(E,k3_qmax_1(A))
=> ~ ! [F] :
( m1_subset_1(F,k2_qmax_1(A))
=> ! [G] :
( m3_prob_1(G,k1_numbers,k14_prob_1)
=> k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,F,E),G) = k2_xcmplx_0(k3_xcmplx_0(D,k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,F,B),G)),k3_xcmplx_0(k6_xcmplx_0(np__1,D),k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,F,C),G))) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_qmax_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ( r1_qmax_1(A,B)
<=> ! [C] :
( m1_subset_1(C,A)
=> k1_funct_1(B,k1_funct_1(B,C)) = C ) ) ) ).
fof(d7_qmax_1,axiom,
! [A,B] :
( l2_qmax_1(B,A)
=> ( r2_qmax_1(A,B)
<=> ? [C] :
( m2_relset_1(C,A,A)
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,A,A)
& m2_relset_1(D,A,A)
& B = g2_qmax_1(A,C,D)
& r2_orders_1(C,A)
& r1_qmax_1(A,D)
& ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(k4_tarski(E,F),C)
=> r2_hidden(k4_tarski(k1_funct_1(D,F),k1_funct_1(D,E)),C) ) ) ) ) ) ) ) ).
fof(d8_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> k5_qmax_1(A) = k2_zfmisc_1(k2_qmax_1(A),k14_prob_1) ) ).
fof(t1_qmax_1,axiom,
$true ).
fof(t2_qmax_1,axiom,
$true ).
fof(t3_qmax_1,axiom,
$true ).
fof(t4_qmax_1,axiom,
$true ).
fof(t5_qmax_1,axiom,
$true ).
fof(t6_qmax_1,axiom,
$true ).
fof(t7_qmax_1,axiom,
$true ).
fof(t8_qmax_1,axiom,
$true ).
fof(t9_qmax_1,axiom,
$true ).
fof(t10_qmax_1,axiom,
$true ).
fof(t11_qmax_1,axiom,
$true ).
fof(t12_qmax_1,axiom,
$true ).
fof(t13_qmax_1,axiom,
$true ).
fof(t14_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> B = k1_domain_1(k2_qmax_1(A),k1_zfmisc_1(k1_numbers),k6_qmax_1(A,B),k7_qmax_1(A,B)) ) ) ).
fof(t15_qmax_1,axiom,
$true ).
fof(t16_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k3_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k5_qmax_1(A))
=> ! [D] :
( m3_prob_1(D,k1_numbers,k14_prob_1)
=> ( D = k3_subset_1(k1_numbers,k7_qmax_1(A,C))
=> k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,C),B),k7_qmax_1(A,C)) = k6_xcmplx_0(np__1,k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,C),B),D)) ) ) ) ) ) ).
fof(d9_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> k8_qmax_1(A,B) = k1_domain_1(k2_qmax_1(A),k1_zfmisc_1(k1_numbers),k6_qmax_1(A,B),k3_subset_1(k1_numbers,k7_qmax_1(A,B))) ) ) ).
fof(d10_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k5_qmax_1(A))
=> ( r3_qmax_1(A,B,C)
<=> ! [D] :
( m1_subset_1(D,k3_qmax_1(A))
=> r1_xreal_0(k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,B),D),k7_qmax_1(A,B)),k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,C),D),k7_qmax_1(A,C))) ) ) ) ) ) ).
fof(d11_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k5_qmax_1(A))
=> ( r4_qmax_1(A,B,C)
<=> ( r3_qmax_1(A,B,C)
& r3_qmax_1(A,C,B) ) ) ) ) ) ).
fof(t17_qmax_1,axiom,
$true ).
fof(t18_qmax_1,axiom,
$true ).
fof(t19_qmax_1,axiom,
$true ).
fof(t20_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k5_qmax_1(A))
=> ( r4_qmax_1(A,B,C)
<=> ! [D] :
( m1_subset_1(D,k3_qmax_1(A))
=> k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,B),D),k7_qmax_1(A,B)) = k10_prob_1(k1_numbers,k14_prob_1,k4_qmax_1(A,k6_qmax_1(A,C),D),k7_qmax_1(A,C)) ) ) ) ) ) ).
fof(t21_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> r3_qmax_1(A,B,B) ) ) ).
fof(t22_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k5_qmax_1(A))
=> ! [D] :
( m1_subset_1(D,k5_qmax_1(A))
=> ( ( r3_qmax_1(A,B,C)
& r3_qmax_1(A,C,D) )
=> r3_qmax_1(A,B,D) ) ) ) ) ) ).
fof(t23_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> r4_qmax_1(A,B,B) ) ) ).
fof(t24_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k5_qmax_1(A))
=> ( r4_qmax_1(A,B,C)
=> r4_qmax_1(A,C,B) ) ) ) ) ).
fof(t25_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k5_qmax_1(A))
=> ! [D] :
( m1_subset_1(D,k5_qmax_1(A))
=> ( ( r4_qmax_1(A,B,C)
& r4_qmax_1(A,C,D) )
=> r4_qmax_1(A,B,D) ) ) ) ) ) ).
fof(t26_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> ( k6_qmax_1(A,k8_qmax_1(A,B)) = k6_qmax_1(A,B)
& k7_qmax_1(A,k8_qmax_1(A,B)) = k3_subset_1(k1_numbers,k7_qmax_1(A,B)) ) ) ) ).
fof(t27_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> k8_qmax_1(A,k8_qmax_1(A,B)) = B ) ) ).
fof(t28_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k5_qmax_1(A))
=> ( r3_qmax_1(A,B,C)
=> r3_qmax_1(A,k8_qmax_1(A,C),k8_qmax_1(A,B)) ) ) ) ) ).
fof(d12_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( ( v3_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k5_qmax_1(A),k5_qmax_1(A))
& m2_relset_1(B,k5_qmax_1(A),k5_qmax_1(A)) )
=> ( B = k9_qmax_1(A)
<=> ! [C] :
( m1_subset_1(C,k5_qmax_1(A))
=> ! [D] :
( m1_subset_1(D,k5_qmax_1(A))
=> ( r2_hidden(k1_domain_1(k5_qmax_1(A),k5_qmax_1(A),C,D),B)
<=> r4_qmax_1(A,C,D) ) ) ) ) ) ) ).
fof(t29_qmax_1,axiom,
$true ).
fof(t30_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_qmax_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k5_qmax_1(A)))
=> ( ( r2_hidden(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
& r2_hidden(C,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) )
=> ! [D] :
( m1_subset_1(D,k5_qmax_1(A))
=> ! [E] :
( m1_subset_1(E,k5_qmax_1(A))
=> ! [F] :
( m1_subset_1(F,k5_qmax_1(A))
=> ! [G] :
( m1_subset_1(G,k5_qmax_1(A))
=> ( ( r2_hidden(D,B)
& r2_hidden(E,B)
& r2_hidden(F,C)
& r2_hidden(G,C)
& r3_qmax_1(A,D,F) )
=> r3_qmax_1(A,E,G) ) ) ) ) ) ) ) ) ) ).
fof(d13_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m2_relset_1(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
=> ( B = k10_qmax_1(A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k5_qmax_1(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k5_qmax_1(A)))
=> ( r2_hidden(k1_domain_1(k1_zfmisc_1(k5_qmax_1(A)),k1_zfmisc_1(k5_qmax_1(A)),C,D),B)
<=> ( r2_hidden(C,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
& r2_hidden(D,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
& ! [E] :
( m1_subset_1(E,k5_qmax_1(A))
=> ! [F] :
( m1_subset_1(F,k5_qmax_1(A))
=> ( ( r2_hidden(E,C)
& r2_hidden(F,D) )
=> r3_qmax_1(A,E,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_qmax_1,axiom,
$true ).
fof(t32_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k5_qmax_1(A))
=> ! [C] :
( m1_subset_1(C,k5_qmax_1(A))
=> ( r3_qmax_1(A,B,C)
<=> r2_hidden(k1_domain_1(k1_zfmisc_1(k5_qmax_1(A)),k1_zfmisc_1(k5_qmax_1(A)),k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),B),k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),C)),k10_qmax_1(A)) ) ) ) ) ).
fof(t33_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_qmax_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k5_qmax_1(A)))
=> ( ( r2_hidden(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
& r2_hidden(C,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) )
=> ! [D] :
( m1_subset_1(D,k5_qmax_1(A))
=> ! [E] :
( m1_subset_1(E,k5_qmax_1(A))
=> ( ( r2_hidden(D,B)
& r2_hidden(E,B)
& r2_hidden(k8_qmax_1(A,D),C) )
=> r2_hidden(k8_qmax_1(A,E),C) ) ) ) ) ) ) ) ).
fof(t34_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_qmax_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k5_qmax_1(A)))
=> ( ( r2_hidden(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
& r2_hidden(C,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) )
=> ! [D] :
( m1_subset_1(D,k5_qmax_1(A))
=> ! [E] :
( m1_subset_1(E,k5_qmax_1(A))
=> ( ( r2_hidden(k8_qmax_1(A,D),C)
& r2_hidden(k8_qmax_1(A,E),C)
& r2_hidden(D,B) )
=> r2_hidden(E,B) ) ) ) ) ) ) ) ).
fof(d14_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
& m2_relset_1(B,k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) )
=> ( B = k11_qmax_1(A)
<=> ! [C] :
( m1_subset_1(C,k5_qmax_1(A))
=> k1_funct_1(B,k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),C)) = k6_eqrel_1(k5_qmax_1(A),k9_qmax_1(A),k8_qmax_1(A,C)) ) ) ) ) ).
fof(t35_qmax_1,axiom,
$true ).
fof(t36_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> r2_qmax_1(k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),g2_qmax_1(k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k10_qmax_1(A),k11_qmax_1(A))) ) ).
fof(dt_l1_qmax_1,axiom,
$true ).
fof(existence_l1_qmax_1,axiom,
? [A] : l1_qmax_1(A) ).
fof(dt_l2_qmax_1,axiom,
$true ).
fof(existence_l2_qmax_1,axiom,
! [A] :
? [B] : l2_qmax_1(B,A) ).
fof(abstractness_v1_qmax_1,axiom,
! [A] :
( l1_qmax_1(A)
=> ( v1_qmax_1(A)
=> A = g1_qmax_1(u1_qmax_1(A),u2_qmax_1(A),u3_qmax_1(A)) ) ) ).
fof(abstractness_v3_qmax_1,axiom,
! [A,B] :
( l2_qmax_1(B,A)
=> ( v3_qmax_1(B,A)
=> B = g2_qmax_1(A,u4_qmax_1(A,B),u5_qmax_1(A,B)) ) ) ).
fof(dt_k1_qmax_1,axiom,
$true ).
fof(dt_k2_qmax_1,axiom,
$true ).
fof(dt_k3_qmax_1,axiom,
$true ).
fof(dt_k4_qmax_1,axiom,
! [A,B,C] :
( ( l1_qmax_1(A)
& m1_subset_1(B,k2_qmax_1(A))
& m1_subset_1(C,k3_qmax_1(A)) )
=> m4_prob_1(k4_qmax_1(A,B,C),k1_numbers,k14_prob_1) ) ).
fof(dt_k5_qmax_1,axiom,
$true ).
fof(dt_k6_qmax_1,axiom,
! [A,B] :
( ( v2_qmax_1(A)
& l1_qmax_1(A)
& m1_subset_1(B,k5_qmax_1(A)) )
=> m1_subset_1(k6_qmax_1(A,B),k2_qmax_1(A)) ) ).
fof(redefinition_k6_qmax_1,axiom,
! [A,B] :
( ( v2_qmax_1(A)
& l1_qmax_1(A)
& m1_subset_1(B,k5_qmax_1(A)) )
=> k6_qmax_1(A,B) = k1_mcart_1(B) ) ).
fof(dt_k7_qmax_1,axiom,
! [A,B] :
( ( v2_qmax_1(A)
& l1_qmax_1(A)
& m1_subset_1(B,k5_qmax_1(A)) )
=> m3_prob_1(k7_qmax_1(A,B),k1_numbers,k14_prob_1) ) ).
fof(redefinition_k7_qmax_1,axiom,
! [A,B] :
( ( v2_qmax_1(A)
& l1_qmax_1(A)
& m1_subset_1(B,k5_qmax_1(A)) )
=> k7_qmax_1(A,B) = k2_mcart_1(B) ) ).
fof(dt_k8_qmax_1,axiom,
! [A,B] :
( ( v2_qmax_1(A)
& l1_qmax_1(A)
& m1_subset_1(B,k5_qmax_1(A)) )
=> m1_subset_1(k8_qmax_1(A,B),k5_qmax_1(A)) ) ).
fof(dt_k9_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ( v3_relat_2(k9_qmax_1(A))
& v8_relat_2(k9_qmax_1(A))
& v1_partfun1(k9_qmax_1(A),k5_qmax_1(A),k5_qmax_1(A))
& m2_relset_1(k9_qmax_1(A),k5_qmax_1(A),k5_qmax_1(A)) ) ) ).
fof(dt_k10_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> m2_relset_1(k10_qmax_1(A),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) ) ).
fof(dt_k11_qmax_1,axiom,
! [A] :
( ( v2_qmax_1(A)
& l1_qmax_1(A) )
=> ( v1_funct_1(k11_qmax_1(A))
& v1_funct_2(k11_qmax_1(A),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)))
& m2_relset_1(k11_qmax_1(A),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A)),k8_eqrel_1(k5_qmax_1(A),k9_qmax_1(A))) ) ) ).
fof(dt_u1_qmax_1,axiom,
! [A] :
( l1_qmax_1(A)
=> ~ v1_xboole_0(u1_qmax_1(A)) ) ).
fof(dt_u2_qmax_1,axiom,
! [A] :
( l1_qmax_1(A)
=> ~ v1_xboole_0(u2_qmax_1(A)) ) ).
fof(dt_u3_qmax_1,axiom,
! [A] :
( l1_qmax_1(A)
=> ( v1_funct_1(u3_qmax_1(A))
& v1_funct_2(u3_qmax_1(A),k2_zfmisc_1(u1_qmax_1(A),u2_qmax_1(A)),k1_qmax_1(k1_numbers,k14_prob_1))
& m2_relset_1(u3_qmax_1(A),k2_zfmisc_1(u1_qmax_1(A),u2_qmax_1(A)),k1_qmax_1(k1_numbers,k14_prob_1)) ) ) ).
fof(dt_u4_qmax_1,axiom,
! [A,B] :
( l2_qmax_1(B,A)
=> m2_relset_1(u4_qmax_1(A,B),A,A) ) ).
fof(dt_u5_qmax_1,axiom,
! [A,B] :
( l2_qmax_1(B,A)
=> ( v1_funct_1(u5_qmax_1(A,B))
& v1_funct_2(u5_qmax_1(A,B),A,A)
& m2_relset_1(u5_qmax_1(A,B),A,A) ) ) ).
fof(dt_g1_qmax_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,B),k1_qmax_1(k1_numbers,k14_prob_1))
& m1_relset_1(C,k2_zfmisc_1(A,B),k1_qmax_1(k1_numbers,k14_prob_1)) )
=> ( v1_qmax_1(g1_qmax_1(A,B,C))
& l1_qmax_1(g1_qmax_1(A,B,C)) ) ) ).
fof(free_g1_qmax_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,B),k1_qmax_1(k1_numbers,k14_prob_1))
& m1_relset_1(C,k2_zfmisc_1(A,B),k1_qmax_1(k1_numbers,k14_prob_1)) )
=> ! [D,E,F] :
( g1_qmax_1(A,B,C) = g1_qmax_1(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(dt_g2_qmax_1,axiom,
! [A,B,C] :
( ( m1_relset_1(B,A,A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> ( v3_qmax_1(g2_qmax_1(A,B,C),A)
& l2_qmax_1(g2_qmax_1(A,B,C),A) ) ) ).
fof(free_g2_qmax_1,axiom,
! [A,B,C] :
( ( m1_relset_1(B,A,A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> ! [D,E,F] :
( g2_qmax_1(A,B,C) = g2_qmax_1(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
%------------------------------------------------------------------------------