fof(t51_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_valuat_1(B,A)
         => r2_valuat_1(A,B,k9_cqc_lang) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_valuat_1,t44_valuat_1]),
    [file(valuat_1,t51_valuat_1),interesting(1.00)]).

fof(t44_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m1_valuat_1(C,A)
             => r1_valuat_1(A,k9_cqc_lang,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_funcop_1,l20_valuat_1,d12_valuat_1]),
    [file(valuat_1,t44_valuat_1),interesting(0.99)]).

fof(t33_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m1_valuat_1(C,A)
             => k12_valuat_1(A,C,k11_cqc_lang(B,B)) = k12_valuat_1(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_valuat_1,t45_margrel1,t51_margrel1,t39_margrel1,t113_funct_2]),
    [file(valuat_1,t33_valuat_1),interesting(0.96)]).

fof(t46_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => r1_valuat_1(A,k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(C),C),C),D,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_qc_lang2,d2_qc_lang2,t20_valuat_1,t22_valuat_1,t20_valuat_1,t33_valuat_1,t20_valuat_1,t40_margrel1,t20_valuat_1,t47_margrel1,d12_valuat_1]),
    [file(valuat_1,t46_valuat_1),interesting(0.95)]).

fof(t53_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m1_valuat_1(C,A)
             => r2_valuat_1(A,C,k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(B),B),B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_valuat_1,t46_valuat_1]),
    [file(valuat_1,t53_valuat_1),interesting(0.94)]).

fof(t57_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => r2_valuat_1(A,D,k12_cqc_lang(k15_cqc_lang(B,C),C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_valuat_1,t50_valuat_1]),
    [file(valuat_1,t57_valuat_1),interesting(0.90)]).

fof(t50_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => r1_valuat_1(A,k12_cqc_lang(k15_cqc_lang(B,D),D),E,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t43_margrel1,d2_qc_lang2,t20_valuat_1,t22_valuat_1,t20_valuat_1,t41_margrel1,t45_margrel1,t41_margrel1,l20_valuat_1,t37_valuat_1,d12_valuat_1]),
    [file(valuat_1,t50_valuat_1),interesting(0.89)]).

fof(t59_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                     => ! [F] : 
                          ( m1_valuat_1(F,A)
                         => ! [G] : 
                              ( m1_subset_1(G,k8_qc_lang1)
                             => ( ( D = k17_cqc_lang(G,B)
                                  & E = k17_cqc_lang(G,C)
                                  & r2_valuat_1(A,F,D) )
                               => ( r2_hidden(B,k24_qc_lang1(G))
                                  | r2_valuat_1(A,F,E) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_valuat_1,t42_valuat_1,d13_valuat_1,d12_valuat_1,t43_valuat_1,t39_valuat_1,d12_valuat_1,d13_valuat_1]),
    [file(valuat_1,t59_valuat_1),interesting(0.88)]).

fof(t13_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_valuat_1(B,A)
         => k12_valuat_1(A,B,k9_cqc_lang) = k1_margrel1(k6_margrel1,k2_valuat_1(A),k8_margrel1) ) ) ),
    inference(mizar_proof,[status(thm)],[l20_valuat_1]),
    [file(valuat_1,t13_valuat_1),interesting(0.87)]).

fof(t56_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => ( ( r2_valuat_1(A,D,B)
                      & r2_valuat_1(A,D,k12_cqc_lang(B,C)) )
                   => r2_valuat_1(A,D,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_valuat_1,t36_valuat_1,d13_valuat_1]),
    [file(valuat_1,t56_valuat_1),interesting(0.87)]).

fof(t14_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m1_valuat_1(C,A)
             => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k9_cqc_lang),B) = k8_margrel1 ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_funcop_1,l20_valuat_1]),
    [file(valuat_1,t14_valuat_1),interesting(0.85)]).

fof(t24_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,k11_cqc_lang(C,k10_cqc_lang(C))),B) = k7_margrel1 ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_valuat_1,t20_valuat_1,t41_margrel1,t45_margrel1,t45_margrel1,t39_margrel1]),
    [file(valuat_1,t24_valuat_1),interesting(0.82)]).

fof(t28_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => ( r1_valuat_1(A,k10_cqc_lang(C),D,B)
                  <=> ~ r1_valuat_1(A,C,D,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_valuat_1,l20_valuat_1,d5_valuat_1,t41_margrel1,d12_valuat_1,d12_valuat_1,t43_margrel1,t41_margrel1,d5_valuat_1,l20_valuat_1,d12_valuat_1]),
    [file(valuat_1,t28_valuat_1),interesting(0.82)]).

fof(t32_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m1_valuat_1(C,A)
             => k12_valuat_1(A,C,k10_cqc_lang(k10_cqc_lang(B))) = k12_valuat_1(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_valuat_1,t20_valuat_1,t40_margrel1,t113_funct_2]),
    [file(valuat_1,t32_valuat_1),interesting(0.80)]).

fof(t54_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => r2_valuat_1(A,D,k12_cqc_lang(B,k12_cqc_lang(k10_cqc_lang(B),C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_valuat_1,t47_valuat_1]),
    [file(valuat_1,t54_valuat_1),interesting(0.80)]).

fof(t19_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m1_valuat_1(C,A)
             => k12_valuat_1(A,C,k10_cqc_lang(B)) = k5_valuat_1(k2_valuat_1(A),k12_valuat_1(A,C,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l20_valuat_1]),
    [file(valuat_1,t19_valuat_1),interesting(0.79)]).

fof(t52_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => r2_valuat_1(A,D,k12_cqc_lang(k11_cqc_lang(B,C),k11_cqc_lang(C,B))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_valuat_1,t45_valuat_1]),
    [file(valuat_1,t52_valuat_1),interesting(0.78)]).

fof(t43_valuat_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m1_subset_1(C,k8_qc_lang1)
             => ~ ( A != B
                  & ~ r2_hidden(A,k24_qc_lang1(C))
                  & r2_hidden(A,k24_qc_lang1(k17_cqc_lang(C,B))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_qc_lang3,t6_qc_lang3,d2_qc_lang3,t29_cqc_lang,d17_qc_lang1,d22_qc_lang1,d8_qc_lang1,d3_cqc_lang,d8_qc_lang1,d21_qc_lang1,d17_qc_lang1,d22_qc_lang1,t6_qc_lang3,d2_qc_lang3,d3_cqc_lang,t11_cqc_lang,t11_cqc_lang,t8_qc_lang3,t28_cqc_lang,t10_qc_lang3,t11_qc_lang3,t31_cqc_lang,t13_qc_lang3,d2_xboole_0,t14_qc_lang3,t33_cqc_lang,t15_qc_lang3,d4_xboole_0,t16_qc_lang3,t36_cqc_lang,t35_cqc_lang,d1_tarski,t16_qc_lang3,d4_xboole_0,t36_cqc_lang,d1_tarski,d4_xboole_0,s2_qc_lang1]),
    [file(valuat_1,t43_valuat_1),interesting(0.74)]).

fof(t23_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => k12_valuat_1(A,D,k15_cqc_lang(B,C)) = k7_valuat_1(A,B,k12_valuat_1(A,D,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l20_valuat_1]),
    [file(valuat_1,t23_valuat_1),interesting(0.72)]).

fof(t25_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,k10_cqc_lang(k11_cqc_lang(C,k10_cqc_lang(C)))),B) = k8_margrel1 ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_valuat_1,t24_valuat_1,t41_margrel1]),
    [file(valuat_1,t25_valuat_1),interesting(0.69)]).

fof(t15_valuat_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_cqc_lang(C,A)
                & m1_qc_lang1(C,A) )
             => ! [D] : 
                  ( m1_valuat_1(D,B)
                 => ! [E] : 
                      ( m2_subset_1(E,k5_qc_lang1,k7_qc_lang1(A))
                     => k12_valuat_1(B,D,k8_cqc_lang(A,E,C)) = k9_valuat_1(B,A,C,k11_valuat_1(B,A,D,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l20_valuat_1]),
    [file(valuat_1,t15_valuat_1),interesting(0.68)]).

fof(t30_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => ( r1_valuat_1(A,k15_cqc_lang(B,D),E,C)
                      <=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k7_valuat_1(A,B,k12_valuat_1(A,E,D)),C) = k8_margrel1 ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_valuat_1,l20_valuat_1,l20_valuat_1,d12_valuat_1]),
    [file(valuat_1,t30_valuat_1),interesting(0.67)]).

fof(t20_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,k10_cqc_lang(C)),B) = k11_margrel1(k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,C),B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l20_valuat_1,d5_valuat_1]),
    [file(valuat_1,t20_valuat_1),interesting(0.66)]).

fof(t39_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => ( ~ r2_hidden(B,k24_qc_lang1(C))
                   => ! [E] : 
                        ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
                       => ! [F] : 
                            ( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A))
                           => ( ! [G] : 
                                  ( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
                                 => ( B != G
                                   => k8_funct_2(k2_qc_lang1,A,F,G) = k8_funct_2(k2_qc_lang1,A,E,G) ) )
                             => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,C),E) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,C),F) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_cqc_lang,t14_valuat_1,l20_valuat_1,d9_valuat_1,d8_valuat_1,d8_valuat_1,d8_qc_lang1,t27_finseq_3,d5_funct_1,t9_qc_lang3,t6_qc_lang3,d2_qc_lang3,d8_valuat_1,t18_finseq_1,d9_valuat_1,l20_valuat_1,l20_valuat_1,d9_valuat_1,d8_valuat_1,d8_valuat_1,d8_qc_lang1,t27_finseq_3,d5_funct_1,t9_qc_lang3,t6_qc_lang3,d2_qc_lang3,d8_valuat_1,t18_finseq_1,d9_valuat_1,l20_valuat_1,t39_margrel1,t20_valuat_1,t41_margrel1,t11_qc_lang3,t41_margrel1,t20_valuat_1,t20_valuat_1,t41_margrel1,t11_qc_lang3,t41_margrel1,t20_valuat_1,t39_margrel1,t14_qc_lang3,t22_valuat_1,t45_margrel1,d2_xboole_0,t45_margrel1,t22_valuat_1,t22_valuat_1,d2_xboole_0,t45_margrel1,t22_valuat_1,d2_xboole_0,t45_margrel1,t22_valuat_1,t45_margrel1,t39_margrel1,t16_qc_lang3,l20_valuat_1,s1_valuat_1,t8_valuat_1,d1_tarski,t8_valuat_1,d4_xboole_0,t8_valuat_1,l20_valuat_1,l20_valuat_1,t7_valuat_1,s1_valuat_1,d1_tarski,d4_xboole_0,t7_valuat_1,l20_valuat_1,t39_margrel1,s1_cqc_lang]),
    [file(valuat_1,t39_valuat_1),interesting(0.62)]).

fof(t2_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_valuat_1(A))
         => ( v1_funct_1(B)
            & v1_funct_2(B,k2_qc_lang1,A)
            & m2_relset_1(B,k2_qc_lang1,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_funct_2,d1_funct_2,t11_relset_1]),
    [file(valuat_1,t2_valuat_1),interesting(0.60)]).

fof(t42_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                     => ! [F] : 
                          ( m1_valuat_1(F,A)
                         => ! [G] : 
                              ( m1_subset_1(G,k8_qc_lang1)
                             => ( ( D = k17_cqc_lang(G,B)
                                  & E = k17_cqc_lang(G,C) )
                               => ( B = C
                                  | ! [H] : 
                                      ( m2_fraenkel(H,k2_qc_lang1,A,k2_valuat_1(A))
                                     => ( k8_funct_2(k2_qc_lang1,A,H,B) = k8_funct_2(k2_qc_lang1,A,H,C)
                                       => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,F,D),H) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,F,E),H) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d17_qc_lang1,t30_cqc_lang,t17_cqc_lang,t17_cqc_lang,t15_cqc_lang,d8_valuat_1,d8_valuat_1,d8_qc_lang1,t11_cqc_lang,d8_valuat_1,t11_cqc_lang,d8_valuat_1,t18_finseq_1,t16_valuat_1,t16_valuat_1,t17_valuat_1,t17_valuat_1,t39_margrel1,t28_cqc_lang,t31_cqc_lang,t18_cqc_lang,t18_cqc_lang,t20_valuat_1,t41_margrel1,t41_margrel1,t20_valuat_1,t20_valuat_1,t41_margrel1,t41_margrel1,t20_valuat_1,t39_margrel1,t33_cqc_lang,t19_cqc_lang,t19_cqc_lang,t22_valuat_1,t45_margrel1,t45_margrel1,t22_valuat_1,t22_valuat_1,t45_margrel1,t22_valuat_1,t45_margrel1,t22_valuat_1,t45_margrel1,t39_margrel1,d20_qc_lang1,d26_qc_lang1,t36_cqc_lang,t23_cqc_lang,t36_cqc_lang,t36_cqc_lang,t23_cqc_lang,t36_cqc_lang,l20_valuat_1,t8_valuat_1,t8_valuat_1,t7_valuat_1,t7_valuat_1,t39_margrel1,t37_cqc_lang,t40_cqc_lang,t37_cqc_lang,t40_cqc_lang,s2_qc_lang1]),
    [file(valuat_1,t42_valuat_1),interesting(0.59)]).

fof(t40_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => ( r1_valuat_1(A,D,E,C)
                       => ( r2_hidden(B,k24_qc_lang1(D))
                          | ! [F] : 
                              ( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A))
                             => ( ! [G] : 
                                    ( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
                                   => ( B != G
                                     => k8_funct_2(k2_qc_lang1,A,F,G) = k8_funct_2(k2_qc_lang1,A,C,G) ) )
                               => r1_valuat_1(A,D,E,F) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_valuat_1,t39_valuat_1,d12_valuat_1]),
    [file(valuat_1,t40_valuat_1),interesting(0.58)]).

fof(t22_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,k11_cqc_lang(C,D)),B) = k12_margrel1(k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,C),B),k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,D),B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l20_valuat_1,d6_valuat_1]),
    [file(valuat_1,t22_valuat_1),interesting(0.53)]).

fof(t31_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => ( r1_valuat_1(A,k15_cqc_lang(B,D),E,C)
                      <=> ! [F] : 
                            ( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A))
                           => ( ! [G] : 
                                  ( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
                                 => ( B != G
                                   => k8_funct_2(k2_qc_lang1,A,F,G) = k8_funct_2(k2_qc_lang1,A,C,G) ) )
                             => k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,D),F) = k8_margrel1 ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_valuat_1,t8_valuat_1,t8_valuat_1,t30_valuat_1]),
    [file(valuat_1,t31_valuat_1),interesting(0.53)]).

fof(t35_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => ( r1_valuat_1(A,k12_cqc_lang(C,D),E,B)
                      <=> ( k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,C),B) = k7_margrel1
                          | k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,D),B) = k8_margrel1 ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_valuat_1,d2_qc_lang2,t20_valuat_1,t41_margrel1,t22_valuat_1,t20_valuat_1,t45_margrel1,t41_margrel1,t45_margrel1,t22_valuat_1,t41_margrel1,t20_valuat_1,d2_qc_lang2,d12_valuat_1,d12_valuat_1,t39_margrel1,d2_qc_lang2,t20_valuat_1,t41_margrel1,t22_valuat_1,t20_valuat_1,t45_margrel1,t41_margrel1]),
    [file(valuat_1,t35_valuat_1),interesting(0.52)]).

fof(t41_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => ( r1_valuat_1(A,k15_cqc_lang(B,D),E,C)
                      <=> ! [F] : 
                            ( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A))
                           => ( ! [G] : 
                                  ( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
                                 => ( B != G
                                   => k8_funct_2(k2_qc_lang1,A,F,G) = k8_funct_2(k2_qc_lang1,A,C,G) ) )
                             => r1_valuat_1(A,D,E,F) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_valuat_1,d12_valuat_1,d12_valuat_1,t31_valuat_1]),
    [file(valuat_1,t41_valuat_1),interesting(0.51)]).

fof(t27_valuat_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] : 
                  ( ( v1_cqc_lang(D,A)
                    & m1_qc_lang1(D,A) )
                 => ! [E] : 
                      ( m1_valuat_1(E,B)
                     => ! [F] : 
                          ( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(A))
                         => ( r1_valuat_1(B,k8_cqc_lang(A,F,D),E,C)
                          <=> k8_funct_2(k2_valuat_1(B),k6_margrel1,k9_valuat_1(B,A,D,k11_valuat_1(B,A,E,F)),C) = k8_margrel1 ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_valuat_1,l20_valuat_1,l20_valuat_1,d12_valuat_1]),
    [file(valuat_1,t27_valuat_1),interesting(0.47)]).

fof(t10_valuat_1,theorem,(
    $true ),
    file(valuat_1,t10_valuat_1),
    [interesting(0.00)]).

fof(t11_valuat_1,theorem,(
    $true ),
    file(valuat_1,t11_valuat_1),
    [interesting(0.00)]).

fof(t12_valuat_1,theorem,(
    $true ),
    file(valuat_1,t12_valuat_1),
    [interesting(0.00)]).

fof(d11_valuat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_valuat_1(B,A)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
                 => ( D = k12_valuat_1(A,B,C)
                  <=> ? [E] : 
                        ( v1_funct_1(E)
                        & v1_funct_2(E,k7_cqc_lang,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
                        & m2_relset_1(E,k7_cqc_lang,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
                        & D = k10_valuat_1(A,E,C)
                        & k10_valuat_1(A,E,k9_cqc_lang) = k1_margrel1(k6_margrel1,k2_valuat_1(A),k8_margrel1)
                        & ! [F] : 
                            ( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
                           => ! [G] : 
                                ( m2_subset_1(G,k8_qc_lang1,k7_cqc_lang)
                               => ! [H] : 
                                    ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                   => ! [I] : 
                                        ( m2_subset_1(I,k1_numbers,k5_numbers)
                                       => ! [J] : 
                                            ( ( v1_cqc_lang(J,I)
                                              & m1_qc_lang1(J,I) )
                                           => ! [K] : 
                                                ( m2_subset_1(K,k5_qc_lang1,k7_qc_lang1(I))
                                               => ( k10_valuat_1(A,E,k8_cqc_lang(I,K,J)) = k9_valuat_1(A,I,J,k11_valuat_1(A,I,B,K))
                                                  & k10_valuat_1(A,E,k10_cqc_lang(F)) = k5_valuat_1(k2_valuat_1(A),k10_valuat_1(A,E,F))
                                                  & k10_valuat_1(A,E,k11_cqc_lang(F,G)) = k6_valuat_1(k2_valuat_1(A),k10_valuat_1(A,E,F),k10_valuat_1(A,E,G))
                                                  & k10_valuat_1(A,E,k15_cqc_lang(H,F)) = k7_valuat_1(A,H,k10_valuat_1(A,E,F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(valuat_1,d11_valuat_1),
    [interesting(0.00)]).

fof(s5_cqc_lang,theorem,
    ( ! [A] : 
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] : 
            ( m1_subset_1(B,f1_s5_cqc_lang)
           => ( B = f2_s5_cqc_lang(A)
            <=> ? [C] : 
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k7_cqc_lang,f1_s5_cqc_lang)
                  & m2_relset_1(C,k7_cqc_lang,f1_s5_cqc_lang)
                  & B = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,A)
                  & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k9_cqc_lang) = f3_s5_cqc_lang
                  & ! [D] : 
                      ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                     => ! [E] : 
                          ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                         => ! [F] : 
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ! [G] : 
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] : 
                                      ( ( v1_cqc_lang(H,G)
                                        & m1_qc_lang1(H,G) )
                                     => ! [I] : 
                                          ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                         => ( k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s5_cqc_lang(G,I,H)
                                            & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k10_cqc_lang(D)) = f5_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D))
                                            & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,E))
                                            & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s5_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
   => f2_s5_cqc_lang(k9_cqc_lang) = f3_s5_cqc_lang ),
    file(cqc_lang,s5_cqc_lang),
    [interesting(0.00)]).

fof(s6_cqc_lang,theorem,
    ( ! [A] : 
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] : 
            ( m1_subset_1(B,f1_s6_cqc_lang)
           => ( B = f3_s6_cqc_lang(A)
            <=> ? [C] : 
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k7_cqc_lang,f1_s6_cqc_lang)
                  & m2_relset_1(C,k7_cqc_lang,f1_s6_cqc_lang)
                  & B = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,A)
                  & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k9_cqc_lang) = f2_s6_cqc_lang
                  & ! [D] : 
                      ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                     => ! [E] : 
                          ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                         => ! [F] : 
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ! [G] : 
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] : 
                                      ( ( v1_cqc_lang(H,G)
                                        & m1_qc_lang1(H,G) )
                                     => ! [I] : 
                                          ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                         => ( k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s6_cqc_lang(G,I,H)
                                            & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k10_cqc_lang(D)) = f8_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D))
                                            & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k11_cqc_lang(D,E)) = f9_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,E))
                                            & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k15_cqc_lang(F,D)) = f10_s6_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
   => f3_s6_cqc_lang(k8_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang)) = f4_s6_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang) ),
    file(cqc_lang,s6_cqc_lang),
    [interesting(0.00)]).

fof(s7_cqc_lang,theorem,
    ( ! [A] : 
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] : 
            ( m1_subset_1(B,f1_s7_cqc_lang)
           => ( B = f2_s7_cqc_lang(A)
            <=> ? [C] : 
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k7_cqc_lang,f1_s7_cqc_lang)
                  & m2_relset_1(C,k7_cqc_lang,f1_s7_cqc_lang)
                  & B = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,A)
                  & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k9_cqc_lang) = f3_s7_cqc_lang
                  & ! [D] : 
                      ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                     => ! [E] : 
                          ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                         => ! [F] : 
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ! [G] : 
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] : 
                                      ( ( v1_cqc_lang(H,G)
                                        & m1_qc_lang1(H,G) )
                                     => ! [I] : 
                                          ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                         => ( k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s7_cqc_lang(G,I,H)
                                            & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k10_cqc_lang(D)) = f5_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D))
                                            & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k11_cqc_lang(D,E)) = f7_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,E))
                                            & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k15_cqc_lang(F,D)) = f8_s7_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
   => f2_s7_cqc_lang(k10_cqc_lang(f6_s7_cqc_lang)) = f5_s7_cqc_lang(f2_s7_cqc_lang(f6_s7_cqc_lang)) ),
    file(cqc_lang,s7_cqc_lang),
    [interesting(0.00)]).

fof(s8_cqc_lang,theorem,
    ( ! [A] : 
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] : 
            ( m1_subset_1(B,f1_s8_cqc_lang)
           => ( B = f2_s8_cqc_lang(A)
            <=> ? [C] : 
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k7_cqc_lang,f1_s8_cqc_lang)
                  & m2_relset_1(C,k7_cqc_lang,f1_s8_cqc_lang)
                  & B = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,A)
                  & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k9_cqc_lang) = f3_s8_cqc_lang
                  & ! [D] : 
                      ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                     => ! [E] : 
                          ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                         => ! [F] : 
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ! [G] : 
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] : 
                                      ( ( v1_cqc_lang(H,G)
                                        & m1_qc_lang1(H,G) )
                                     => ! [I] : 
                                          ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                         => ( k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s8_cqc_lang(G,I,H)
                                            & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k10_cqc_lang(D)) = f5_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D))
                                            & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,E))
                                            & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k15_cqc_lang(F,D)) = f9_s8_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
   => f2_s8_cqc_lang(k11_cqc_lang(f7_s8_cqc_lang,f8_s8_cqc_lang)) = f6_s8_cqc_lang(f2_s8_cqc_lang(f7_s8_cqc_lang),f2_s8_cqc_lang(f8_s8_cqc_lang)) ),
    file(cqc_lang,s8_cqc_lang),
    [interesting(0.00)]).

fof(s9_cqc_lang,theorem,
    ( ! [A] : 
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] : 
            ( m1_subset_1(B,f1_s9_cqc_lang)
           => ( B = f2_s9_cqc_lang(A)
            <=> ? [C] : 
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k7_cqc_lang,f1_s9_cqc_lang)
                  & m2_relset_1(C,k7_cqc_lang,f1_s9_cqc_lang)
                  & B = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,A)
                  & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k9_cqc_lang) = f3_s9_cqc_lang
                  & ! [D] : 
                      ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                     => ! [E] : 
                          ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                         => ! [F] : 
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ! [G] : 
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] : 
                                      ( ( v1_cqc_lang(H,G)
                                        & m1_qc_lang1(H,G) )
                                     => ! [I] : 
                                          ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                         => ( k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s9_cqc_lang(G,I,H)
                                            & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k10_cqc_lang(D)) = f5_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D))
                                            & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,E))
                                            & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s9_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
   => f2_s9_cqc_lang(k15_cqc_lang(f8_s9_cqc_lang,f9_s9_cqc_lang)) = f7_s9_cqc_lang(f8_s9_cqc_lang,f2_s9_cqc_lang(f9_s9_cqc_lang)) ),
    file(cqc_lang,s9_cqc_lang),
    [interesting(0.00)]).

fof(l20_valuat_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_valuat_1(C,B)
             => ( k12_valuat_1(B,C,k9_cqc_lang) = k1_margrel1(k6_margrel1,k2_valuat_1(B),k8_margrel1)
                & ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( ( v1_cqc_lang(E,D)
                          & m1_qc_lang1(E,D) )
                       => ! [F] : 
                            ( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D))
                           => k12_valuat_1(B,C,k8_cqc_lang(D,F,E)) = k9_valuat_1(B,D,E,k11_valuat_1(B,D,C,F)) ) ) )
                & ! [D] : 
                    ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                   => k12_valuat_1(B,C,k10_cqc_lang(D)) = k5_valuat_1(k2_valuat_1(B),k12_valuat_1(B,C,D)) )
                & ! [D] : 
                    ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                   => k12_valuat_1(B,C,k11_cqc_lang(A,D)) = k6_valuat_1(k2_valuat_1(B),k12_valuat_1(B,C,A),k12_valuat_1(B,C,D)) )
                & ! [D] : 
                    ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                   => k12_valuat_1(B,C,k15_cqc_lang(D,A)) = k7_valuat_1(B,D,k12_valuat_1(B,C,A)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_valuat_1,s5_cqc_lang,s6_cqc_lang,s7_cqc_lang,s8_cqc_lang,s9_cqc_lang]),
    [file(valuat_1,l20_valuat_1),interesting(0.00)]).

fof(t18_valuat_1,theorem,(
    $true ),
    file(valuat_1,t18_valuat_1),
    [interesting(0.00)]).

fof(t1_valuat_1,theorem,(
    $true ),
    file(valuat_1,t1_valuat_1),
    [interesting(0.00)]).

fof(t21_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m1_valuat_1(D,A)
                 => k12_valuat_1(A,D,k11_cqc_lang(B,C)) = k6_valuat_1(k2_valuat_1(A),k12_valuat_1(A,D,B),k12_valuat_1(A,D,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l20_valuat_1]),
    [file(valuat_1,t21_valuat_1),interesting(0.00)]).

fof(d5_valuat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( C = k5_valuat_1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => k8_funct_2(A,k6_margrel1,C,D) = k11_margrel1(k8_funct_2(A,k6_margrel1,B,D)) ) ) ) ) ) ),
    file(valuat_1,d5_valuat_1),
    [interesting(0.00)]).

fof(d6_valuat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k6_valuat_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k12_margrel1(k8_funct_2(A,k6_margrel1,B,E),k8_funct_2(A,k6_margrel1,C,E)) ) ) ) ) ) ) ),
    file(valuat_1,d6_valuat_1),
    [interesting(0.00)]).

fof(t41_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( ( A = k7_margrel1
         => k9_margrel1(A) = k8_margrel1 )
        & ( k9_margrel1(A) = k8_margrel1
         => A = k7_margrel1 )
        & ( A = k8_margrel1
         => k9_margrel1(A) = k7_margrel1 )
        & ( k9_margrel1(A) = k7_margrel1
         => A = k8_margrel1 ) ) ) ),
    file(margrel1,t41_margrel1),
    [interesting(0.00)]).

fof(t45_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ( ( k10_margrel1(A,B) = k8_margrel1
             => ( A = k8_margrel1
                & B = k8_margrel1 ) )
            & ( ( A = k8_margrel1
                & B = k8_margrel1 )
             => k10_margrel1(A,B) = k8_margrel1 )
            & ~ ( k10_margrel1(A,B) = k7_margrel1
                & A != k7_margrel1
                & B != k7_margrel1 )
            & ( ( A = k7_margrel1
                | B = k7_margrel1 )
             => k10_margrel1(A,B) = k7_margrel1 ) ) ) ) ),
    file(margrel1,t45_margrel1),
    [interesting(0.00)]).

fof(t39_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( A = k7_margrel1
        | A = k8_margrel1 ) ) ),
    file(margrel1,t39_margrel1),
    [interesting(0.00)]).

fof(t26_valuat_1,theorem,(
    $true ),
    file(valuat_1,t26_valuat_1),
    [interesting(0.00)]).

fof(d12_valuat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m1_valuat_1(C,A)
             => ! [D] : 
                  ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
                 => ( r1_valuat_1(A,B,C,D)
                  <=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,B),D) = k8_margrel1 ) ) ) ) ) ),
    file(valuat_1,d12_valuat_1),
    [interesting(0.00)]).

fof(t43_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( A != k8_margrel1
      <=> A = k7_margrel1 ) ) ),
    file(margrel1,t43_margrel1),
    [interesting(0.00)]).

fof(t29_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => ( r1_valuat_1(A,k11_cqc_lang(C,D),E,B)
                      <=> ( r1_valuat_1(A,C,E,B)
                          & r1_valuat_1(A,D,E,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_valuat_1,l20_valuat_1,d6_valuat_1,t45_margrel1,d12_valuat_1,d12_valuat_1,t45_margrel1,d6_valuat_1,l20_valuat_1,d12_valuat_1]),
    [file(valuat_1,t29_valuat_1),interesting(0.00)]).

fof(d2_funct_2,definition,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    [interesting(0.00)]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.00)]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.00)]).

fof(t40_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,t40_margrel1),
    [interesting(0.00)]).

fof(t113_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( ! [E] : 
                ( m1_subset_1(E,A)
               => k1_funct_1(C,E) = k1_funct_1(D,E) )
           => C = D ) ) ) ),
    file(funct_2,t113_funct_2),
    [interesting(0.00)]).

fof(t34_valuat_1,theorem,(
    $true ),
    file(valuat_1,t34_valuat_1),
    [interesting(0.00)]).

fof(t38_valuat_1,theorem,(
    $true ),
    file(valuat_1,t38_valuat_1),
    [interesting(0.00)]).

fof(t3_valuat_1,theorem,(
    $true ),
    file(valuat_1,t3_valuat_1),
    [interesting(0.00)]).

fof(d2_qc_lang2,definition,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => k2_qc_lang2(A,B) = k12_qc_lang1(k13_qc_lang1(A,k12_qc_lang1(B))) ) ) ),
    file(qc_lang2,d2_qc_lang2),
    [interesting(0.00)]).

fof(t36_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => ( r1_valuat_1(A,k12_cqc_lang(C,D),E,B)
                      <=> ( r1_valuat_1(A,C,E,B)
                         => r1_valuat_1(A,D,E,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t35_valuat_1,d12_valuat_1,d12_valuat_1,t43_margrel1,t35_valuat_1]),
    [file(valuat_1,t36_valuat_1),interesting(0.00)]).

fof(t49_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => ( ( r1_valuat_1(A,C,E,B)
                          & r1_valuat_1(A,k12_cqc_lang(C,D),E,B) )
                       => r1_valuat_1(A,D,E,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_valuat_1]),
    [file(valuat_1,t49_valuat_1),interesting(0.00)]).

fof(t4_valuat_1,theorem,(
    $true ),
    file(valuat_1,t4_valuat_1),
    [interesting(0.00)]).

fof(d13_valuat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_valuat_1(B,A)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( r2_valuat_1(A,B,C)
              <=> ! [D] : 
                    ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
                   => r1_valuat_1(A,C,B,D) ) ) ) ) ) ),
    file(valuat_1,d13_valuat_1),
    [interesting(0.00)]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.00)]).

fof(t45_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => r1_valuat_1(A,k12_cqc_lang(k11_cqc_lang(C,D),k11_cqc_lang(D,C)),E,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t43_margrel1,d2_qc_lang2,t20_valuat_1,t22_valuat_1,t20_valuat_1,t41_margrel1,t45_margrel1,t41_margrel1,t22_valuat_1,d12_valuat_1]),
    [file(valuat_1,t45_valuat_1),interesting(0.00)]).

fof(t51_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( k10_margrel1(A,A) = k7_margrel1
       => A = k7_margrel1 ) ) ),
    file(margrel1,t51_margrel1),
    [interesting(0.00)]).

fof(t47_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k10_margrel1(A,k9_margrel1(A))) = k8_margrel1 ) ),
    file(margrel1,t47_margrel1),
    [interesting(0.00)]).

fof(t52_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k10_margrel1(A,k10_margrel1(B,C)) = k10_margrel1(k10_margrel1(A,B),C) ) ) ) ),
    file(margrel1,t52_margrel1),
    [interesting(0.00)]).

fof(t46_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(A,k9_margrel1(A)) = k7_margrel1 ) ),
    file(margrel1,t46_margrel1),
    [interesting(0.00)]).

fof(t49_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(k7_margrel1,A) = k7_margrel1 ) ),
    file(margrel1,t49_margrel1),
    [interesting(0.00)]).

fof(t47_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => r1_valuat_1(A,k12_cqc_lang(C,k12_cqc_lang(k10_cqc_lang(C),D)),E,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_qc_lang2,d2_qc_lang2,t20_valuat_1,t22_valuat_1,t20_valuat_1,t20_valuat_1,t40_margrel1,t22_valuat_1,t20_valuat_1,t20_valuat_1,t52_margrel1,t46_margrel1,t49_margrel1,t41_margrel1,d12_valuat_1]),
    [file(valuat_1,t47_valuat_1),interesting(0.00)]).

fof(l52_valuat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => ! [B] : 
          ( m1_subset_1(B,k6_margrel1)
         => ! [C] : 
              ( m1_subset_1(C,k6_margrel1)
             => k11_margrel1(k12_margrel1(k11_margrel1(k12_margrel1(A,k11_margrel1(B))),k12_margrel1(k11_margrel1(k12_margrel1(B,C)),k12_margrel1(A,C)))) = k8_margrel1 ) ) ) ),
    inference(mizar_proof,[status(thm)],[t45_margrel1,t41_margrel1,t45_margrel1,t45_margrel1,t41_margrel1,t41_margrel1,t45_margrel1,t41_margrel1,t45_margrel1,t41_margrel1,t45_margrel1,t45_margrel1,t45_margrel1,t41_margrel1,t45_margrel1,t45_margrel1,t45_margrel1,t41_margrel1,t39_margrel1]),
    [file(valuat_1,l52_valuat_1),interesting(0.00)]).

fof(t48_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                     => ! [F] : 
                          ( m1_valuat_1(F,A)
                         => r1_valuat_1(A,k12_cqc_lang(k12_cqc_lang(C,D),k12_cqc_lang(k10_cqc_lang(k11_cqc_lang(D,E)),k10_cqc_lang(k11_cqc_lang(C,E)))),F,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_qc_lang2,d2_qc_lang2,d2_qc_lang2,t20_valuat_1,t22_valuat_1,t20_valuat_1,t22_valuat_1,t20_valuat_1,t20_valuat_1,t20_valuat_1,t40_margrel1,t22_valuat_1,t20_valuat_1,t20_valuat_1,t20_valuat_1,t40_margrel1,t22_valuat_1,t22_valuat_1,l52_valuat_1,d12_valuat_1]),
    [file(valuat_1,t48_valuat_1),interesting(0.00)]).

fof(t55_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => r2_valuat_1(A,E,k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(k10_cqc_lang(k11_cqc_lang(C,D)),k10_cqc_lang(k11_cqc_lang(B,D))))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_valuat_1,t48_valuat_1]),
    [file(valuat_1,t55_valuat_1),interesting(0.00)]).

fof(d7_valuat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_fraenkel(C,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
                 => ( D = k7_valuat_1(A,B,C)
                  <=> ! [E] : 
                        ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
                       => k8_funct_2(k2_valuat_1(A),k6_margrel1,D,E) = k14_margrel1(a_4_0_valuat_1(A,B,C,E)) ) ) ) ) ) ) ),
    file(valuat_1,d7_valuat_1),
    [interesting(0.00)]).

fof(t53_margrel1,theorem,(
    ! [A] : 
      ( ( ~ r2_hidden(k7_margrel1,A)
       => k14_margrel1(A) = k8_margrel1 )
      & ~ ( k14_margrel1(A) = k8_margrel1
          & r2_hidden(k7_margrel1,A) )
      & ( r2_hidden(k7_margrel1,A)
       => k14_margrel1(A) = k7_margrel1 )
      & ( k14_margrel1(A) = k7_margrel1
       => r2_hidden(k7_margrel1,A) ) ) ),
    file(margrel1,t53_margrel1),
    [interesting(0.00)]).

fof(t8_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
             => ! [D] : 
                  ( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
                 => ( k8_funct_2(k2_valuat_1(A),k6_margrel1,k7_valuat_1(A,B,D),C) = k8_margrel1
                  <=> ! [E] : 
                        ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
                       => ( ! [F] : 
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ( B != F
                               => k8_funct_2(k2_qc_lang1,A,E,F) = k8_funct_2(k2_qc_lang1,A,C,F) ) )
                         => k8_funct_2(k2_valuat_1(A),k6_margrel1,D,E) = k8_margrel1 ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_valuat_1,t53_margrel1,t43_margrel1,t53_margrel1,d7_valuat_1]),
    [file(valuat_1,t8_valuat_1),interesting(0.00)]).

fof(t37_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
             => ! [D] : 
                  ( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
                 => ( k8_funct_2(k2_valuat_1(A),k6_margrel1,k7_valuat_1(A,B,D),C) = k8_margrel1
                   => k8_funct_2(k2_valuat_1(A),k6_margrel1,D,C) = k8_margrel1 ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_valuat_1]),
    [file(valuat_1,t37_valuat_1),interesting(0.00)]).

fof(d5_cqc_lang,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_qc_lang1(B,A)
         => ( v1_cqc_lang(B,A)
          <=> r1_tarski(k2_relat_1(B),k2_qc_lang1) ) ) ) ),
    file(cqc_lang,d5_cqc_lang),
    [interesting(0.00)]).

fof(d9_valuat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ( v1_cqc_lang(C,B)
                & m1_qc_lang1(C,B) )
             => ! [D] : 
                  ( m1_subset_1(D,k3_margrel1(A))
                 => ! [E] : 
                      ( m2_fraenkel(E,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
                     => ( E = k9_valuat_1(A,B,C,D)
                      <=> ! [F] : 
                            ( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A))
                           => ( ( r2_hidden(k8_valuat_1(A,B,C,F),D)
                               => k8_funct_2(k2_valuat_1(A),k6_margrel1,E,F) = k8_margrel1 )
                              & ( ~ r2_hidden(k8_valuat_1(A,B,C,F),D)
                               => k8_funct_2(k2_valuat_1(A),k6_margrel1,E,F) = k7_margrel1 ) ) ) ) ) ) ) ) ) ),
    file(valuat_1,d9_valuat_1),
    [interesting(0.00)]).

fof(d8_valuat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ( v1_cqc_lang(C,B)
                & m1_qc_lang1(C,B) )
             => ! [D] : 
                  ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
                 => ! [E] : 
                      ( m2_finseq_1(E,A)
                     => ( E = k8_valuat_1(A,B,C,D)
                      <=> ( k3_finseq_1(E) = B
                          & ! [F] : 
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( ( r1_xreal_0(1,F)
                                  & r1_xreal_0(F,B) )
                               => k1_funct_1(E,F) = k1_funct_1(D,k1_funct_1(C,F)) ) ) ) ) ) ) ) ) ) ),
    file(valuat_1,d8_valuat_1),
    [interesting(0.00)]).

fof(d8_qc_lang1,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_finseq_1(B,k1_qc_lang1)
         => ( m1_qc_lang1(B,A)
          <=> k3_finseq_1(B) = A ) ) ) ),
    file(qc_lang1,d8_qc_lang1),
    [interesting(0.00)]).

fof(t27_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(B,k4_finseq_1(A))
          <=> ( r1_xreal_0(1,B)
              & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ),
    file(finseq_3,t27_finseq_3),
    [interesting(0.00)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.00)]).

fof(t9_qc_lang3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] : 
              ( m1_qc_lang1(C,A)
             => k24_qc_lang1(k9_qc_lang1(B,C)) = k22_qc_lang1(C) ) ) ) ),
    file(qc_lang3,t9_qc_lang3),
    [interesting(0.00)]).

fof(t6_qc_lang3,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k1_qc_lang1)
     => k22_qc_lang1(A) = k1_qc_lang3(A,k2_qc_lang1) ) ),
    file(qc_lang3,t6_qc_lang3),
    [interesting(0.00)]).

fof(d2_qc_lang3,definition,(
    ! [A] : 
      ( m2_finseq_1(A,k1_qc_lang1)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => k1_qc_lang3(A,B) = a_2_0_qc_lang3(A,B) ) ) ),
    file(qc_lang3,d2_qc_lang3),
    [interesting(0.00)]).

fof(t18_finseq_1,theorem,(
    ! [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) )
         => ( ( k3_finseq_1(A) = k3_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(1,C)
                      & r1_xreal_0(C,k3_finseq_1(A)) )
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    file(finseq_1,t18_finseq_1),
    [interesting(0.00)]).

fof(t11_qc_lang3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => k24_qc_lang1(k12_qc_lang1(A)) = k24_qc_lang1(A) ) ),
    file(qc_lang3,t11_qc_lang3),
    [interesting(0.00)]).

fof(t14_qc_lang3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => k24_qc_lang1(k13_qc_lang1(A,B)) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(A),k24_qc_lang1(B)) ) ) ),
    file(qc_lang3,t14_qc_lang3),
    [interesting(0.00)]).

fof(d2_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    [interesting(0.00)]).

fof(t16_qc_lang3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => k24_qc_lang1(k14_qc_lang1(A,B)) = k6_subset_1(k2_qc_lang1,k24_qc_lang1(B),k23_qc_lang1(A)) ) ) ),
    file(qc_lang3,t16_qc_lang3),
    [interesting(0.00)]).

fof(t7_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,A)
       => ( B = k1_xboole_0
          | r2_hidden(k1_funct_1(D,C),B) ) ) ) ),
    file(funct_2,t7_funct_2),
    [interesting(0.00)]).

fof(s9_funct_2,theorem,
    ( ! [A] : 
        ( r2_hidden(A,f1_s9_funct_2)
       => ( ( p1_s9_funct_2(A)
           => r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2) )
          & ( ~ p1_s9_funct_2(A)
           => r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2) ) ) )
   => ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2)
        & m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2)
        & ! [B] : 
            ( r2_hidden(B,f1_s9_funct_2)
           => ( ( p1_s9_funct_2(B)
               => k1_funct_1(A,B) = f3_s9_funct_2(B) )
              & ( ~ p1_s9_funct_2(B)
               => k1_funct_1(A,B) = f4_s9_funct_2(B) ) ) ) ) ),
    file(funct_2,s9_funct_2),
    [interesting(0.00)]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.00)]).

fof(s1_valuat_1,theorem,(
    ? [A] : 
      ( m2_fraenkel(A,k2_qc_lang1,f1_s1_valuat_1,k2_valuat_1(f1_s1_valuat_1))
      & ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( B != f2_s1_valuat_1
           => k8_funct_2(k2_qc_lang1,f1_s1_valuat_1,A,B) = k8_funct_2(k2_qc_lang1,f1_s1_valuat_1,f4_s1_valuat_1,B) ) )
      & k8_funct_2(k2_qc_lang1,f1_s1_valuat_1,A,f2_s1_valuat_1) = k8_funct_2(k2_qc_lang1,f1_s1_valuat_1,f5_s1_valuat_1,f3_s1_valuat_1) ) ),
    inference(mizar_proof,[status(thm)],[t7_funct_2,s9_funct_2,d1_funct_2,t12_relset_1,d2_funct_2]),
    [file(valuat_1,s1_valuat_1),interesting(0.00)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

fof(d4_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    [interesting(0.00)]).

fof(t7_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
             => ! [D] : 
                  ( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
                 => ( k8_funct_2(k2_valuat_1(A),k6_margrel1,k7_valuat_1(A,B,D),C) = k7_margrel1
                  <=> ? [E] : 
                        ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
                        & k8_funct_2(k2_valuat_1(A),k6_margrel1,D,E) = k7_margrel1
                        & ! [F] : 
                            ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                           => ( B != F
                             => k8_funct_2(k2_qc_lang1,A,E,F) = k8_funct_2(k2_qc_lang1,A,C,F) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_valuat_1,t53_margrel1,t53_margrel1,d7_valuat_1]),
    [file(valuat_1,t7_valuat_1),interesting(0.00)]).

fof(s1_cqc_lang,theorem,
    ( ! [A] : 
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] : 
            ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
           => ! [C] : 
                ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( ( v1_cqc_lang(E,D)
                          & m1_qc_lang1(E,D) )
                       => ! [F] : 
                            ( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D))
                           => ( p1_s1_cqc_lang(k9_cqc_lang)
                              & p1_s1_cqc_lang(k8_cqc_lang(D,F,E))
                              & ( p1_s1_cqc_lang(A)
                               => p1_s1_cqc_lang(k10_cqc_lang(A)) )
                              & ( ( p1_s1_cqc_lang(A)
                                  & p1_s1_cqc_lang(B) )
                               => p1_s1_cqc_lang(k11_cqc_lang(A,B)) )
                              & ( p1_s1_cqc_lang(A)
                               => p1_s1_cqc_lang(k15_cqc_lang(C,A)) ) ) ) ) ) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => p1_s1_cqc_lang(A) ) ),
    file(cqc_lang,s1_cqc_lang),
    [interesting(0.00)]).

fof(t58_valuat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] : 
                  ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                 => ! [E] : 
                      ( m1_valuat_1(E,A)
                     => ( r2_valuat_1(A,E,k12_cqc_lang(C,D))
                       => ( r2_hidden(B,k24_qc_lang1(C))
                          | r2_valuat_1(A,E,k12_cqc_lang(C,k15_cqc_lang(B,D))) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_valuat_1,d13_valuat_1,t40_valuat_1,t36_valuat_1,t41_valuat_1,t36_valuat_1]),
    [file(valuat_1,t58_valuat_1),interesting(0.00)]).

fof(d17_qc_lang1,definition,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v2_qc_lang1(A)
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & ? [C] : 
                ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B))
                & ? [D] : 
                    ( m1_qc_lang1(D,B)
                    & A = k9_qc_lang1(C,D) ) ) ) ) ) ),
    file(qc_lang1,d17_qc_lang1),
    [interesting(0.00)]).

fof(t30_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
             => ! [D] : 
                  ( m1_qc_lang1(D,A)
                 => k17_cqc_lang(k9_qc_lang1(C,D),B) = k9_qc_lang1(C,k5_cqc_lang(A,D,k6_cqc_lang(k3_qc_lang3(0),B))) ) ) ) ) ),
    file(cqc_lang,t30_cqc_lang),
    [interesting(0.00)]).

fof(t17_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] : 
              ( m1_qc_lang1(C,A)
             => ( m2_subset_1(k9_qc_lang1(B,C),k8_qc_lang1,k7_cqc_lang)
              <=> ( a_2_0_cqc_lang(A,C) = k1_xboole_0
                  & a_2_1_cqc_lang(A,C) = k1_xboole_0 ) ) ) ) ) ),
    file(cqc_lang,t17_cqc_lang),
    [interesting(0.00)]).

fof(t15_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_qc_lang1(B,A)
         => ( ( v1_cqc_lang(B,A)
              & m1_qc_lang1(B,A) )
          <=> ( a_2_0_cqc_lang(A,B) = k1_xboole_0
              & a_2_1_cqc_lang(A,B) = k1_xboole_0 ) ) ) ) ),
    file(cqc_lang,t15_cqc_lang),
    [interesting(0.00)]).

fof(t11_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] : 
              ( m2_subset_1(C,k1_qc_lang1,k4_qc_lang1)
             => ! [D] : 
                  ( m2_finseq_1(D,k1_qc_lang1)
                 => ! [E] : 
                      ( m2_finseq_1(E,k1_qc_lang1)
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k4_qc_lang1,k1_qc_lang1) )
                         => ( ( F = k6_cqc_lang(C,B)
                              & D = k4_cqc_lang(E,F)
                              & r1_xreal_0(1,A)
                              & r1_xreal_0(A,k3_finseq_1(E)) )
                           => ( ( k1_funct_1(E,A) = C
                               => k1_funct_1(D,A) = B )
                              & ( k1_funct_1(E,A) != C
                               => k1_funct_1(D,A) = k1_funct_1(E,A) ) ) ) ) ) ) ) ) ) ),
    file(cqc_lang,t11_cqc_lang),
    [interesting(0.00)]).

fof(t16_valuat_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] : 
                  ( ( v1_cqc_lang(D,A)
                    & m1_qc_lang1(D,A) )
                 => ! [E] : 
                      ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                     => ! [F] : 
                          ( m1_valuat_1(F,B)
                         => ! [G] : 
                              ( m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,k3_margrel1(B))
                                 => ( ( E = k8_cqc_lang(A,G,D)
                                      & r1_margrel1(B,H,k11_valuat_1(B,A,F,G)) )
                                   => ( r2_hidden(k8_valuat_1(B,A,D,C),H)
                                    <=> k8_funct_2(k2_valuat_1(B),k6_margrel1,k12_valuat_1(B,F,E),C) = k8_margrel1 ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_valuat_1,l20_valuat_1,l20_valuat_1,d9_valuat_1]),
    [file(valuat_1,t16_valuat_1),interesting(0.00)]).

fof(t17_valuat_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] : 
                  ( ( v1_cqc_lang(D,A)
                    & m1_qc_lang1(D,A) )
                 => ! [E] : 
                      ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                     => ! [F] : 
                          ( m1_valuat_1(F,B)
                         => ! [G] : 
                              ( m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,k3_margrel1(B))
                                 => ( ( E = k8_cqc_lang(A,G,D)
                                      & r1_margrel1(B,H,k11_valuat_1(B,A,F,G)) )
                                   => ( ~ r2_hidden(k8_valuat_1(B,A,D,C),H)
                                    <=> k8_funct_2(k2_valuat_1(B),k6_margrel1,k12_valuat_1(B,F,E),C) = k7_margrel1 ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_valuat_1,l20_valuat_1,l20_valuat_1,d9_valuat_1]),
    [file(valuat_1,t17_valuat_1),interesting(0.00)]).

fof(t28_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => k17_cqc_lang(k9_cqc_lang,A) = k9_cqc_lang ) ),
    file(cqc_lang,t28_cqc_lang),
    [interesting(0.00)]).

fof(t31_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v3_qc_lang1(B)
           => k17_cqc_lang(B,A) = k12_qc_lang1(k17_cqc_lang(k17_qc_lang1(B),A)) ) ) ) ),
    file(cqc_lang,t31_cqc_lang),
    [interesting(0.00)]).

fof(t18_cqc_lang,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ( m2_subset_1(k12_qc_lang1(A),k8_qc_lang1,k7_cqc_lang)
      <=> m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) ) ) ),
    file(cqc_lang,t18_cqc_lang),
    [interesting(0.00)]).

fof(t33_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v4_qc_lang1(B)
           => k17_cqc_lang(B,A) = k13_qc_lang1(k17_cqc_lang(k18_qc_lang1(B),A),k17_cqc_lang(k19_qc_lang1(B),A)) ) ) ) ),
    file(cqc_lang,t33_cqc_lang),
    [interesting(0.00)]).

fof(t19_cqc_lang,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ( m2_subset_1(k13_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)
          <=> ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
              & m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) ) ) ) ) ),
    file(cqc_lang,t19_cqc_lang),
    [interesting(0.00)]).

fof(d20_qc_lang1,definition,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v5_qc_lang1(A)
      <=> ? [B] : 
            ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
            & ? [C] : 
                ( m1_subset_1(C,k8_qc_lang1)
                & A = k14_qc_lang1(B,C) ) ) ) ) ),
    file(qc_lang1,d20_qc_lang1),
    [interesting(0.00)]).

fof(d26_qc_lang1,definition,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v5_qc_lang1(A)
       => ! [B] : 
            ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
           => ( B = k20_qc_lang1(A)
            <=> ? [C] : 
                  ( m1_subset_1(C,k8_qc_lang1)
                  & A = k14_qc_lang1(B,C) ) ) ) ) ) ),
    file(qc_lang1,d26_qc_lang1),
    [interesting(0.00)]).

fof(t36_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v5_qc_lang1(B)
           => ( k20_qc_lang1(B) = A
              | k17_cqc_lang(B,A) = k14_qc_lang1(k20_qc_lang1(B),k17_cqc_lang(k21_qc_lang1(B),A)) ) ) ) ) ),
    file(cqc_lang,t36_cqc_lang),
    [interesting(0.00)]).

fof(t23_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ( m2_subset_1(k14_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)
          <=> m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) ) ) ) ),
    file(cqc_lang,t23_cqc_lang),
    [interesting(0.00)]).

fof(t37_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => k17_cqc_lang(k14_qc_lang1(A,B),A) = k14_qc_lang1(A,B) ) ) ),
    file(cqc_lang,t37_cqc_lang),
    [interesting(0.00)]).

fof(t40_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => k17_cqc_lang(B,A) = B ) ) ),
    file(cqc_lang,t40_cqc_lang),
    [interesting(0.00)]).

fof(s2_qc_lang1,theorem,
    ( ! [A] : 
        ( m1_subset_1(A,k8_qc_lang1)
       => ( ( v2_qc_lang1(A)
           => p1_s2_qc_lang1(A) )
          & p1_s2_qc_lang1(k11_qc_lang1)
          & ( ( v3_qc_lang1(A)
              & p1_s2_qc_lang1(k17_qc_lang1(A)) )
           => p1_s2_qc_lang1(A) )
          & ( ( v4_qc_lang1(A)
              & p1_s2_qc_lang1(k18_qc_lang1(A))
              & p1_s2_qc_lang1(k19_qc_lang1(A)) )
           => p1_s2_qc_lang1(A) )
          & ( ( v5_qc_lang1(A)
              & p1_s2_qc_lang1(k21_qc_lang1(A)) )
           => p1_s2_qc_lang1(A) ) ) )
   => ! [A] : 
        ( m1_subset_1(A,k8_qc_lang1)
       => p1_s2_qc_lang1(A) ) ),
    file(qc_lang1,s2_qc_lang1),
    [interesting(0.00)]).

fof(t8_qc_lang3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v2_qc_lang1(A)
       => k24_qc_lang1(A) = k22_qc_lang1(k16_qc_lang1(A)) ) ) ),
    file(qc_lang3,t8_qc_lang3),
    [interesting(0.00)]).

fof(t29_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v2_qc_lang1(B)
           => k17_cqc_lang(B,A) = k9_qc_lang1(k15_qc_lang1(B),k4_cqc_lang(k16_qc_lang1(B),k6_cqc_lang(k3_qc_lang3(0),A))) ) ) ) ),
    file(cqc_lang,t29_cqc_lang),
    [interesting(0.00)]).

fof(d22_qc_lang1,definition,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v2_qc_lang1(A)
       => ! [B] : 
            ( m2_finseq_1(B,k1_qc_lang1)
           => ( B = k16_qc_lang1(A)
            <=> ? [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & ? [D] : 
                      ( m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(C))
                      & ? [E] : 
                          ( m1_qc_lang1(E,C)
                          & B = E
                          & A = k9_qc_lang1(D,E) ) ) ) ) ) ) ) ),
    file(qc_lang1,d22_qc_lang1),
    [interesting(0.00)]).

fof(d3_cqc_lang,definition,(
    ! [A] : 
      ( m2_finseq_1(A,k1_qc_lang1)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k4_qc_lang1,k1_qc_lang1) )
         => ! [C] : 
              ( m2_finseq_1(C,k1_qc_lang1)
             => ( C = k4_cqc_lang(A,B)
              <=> ( k3_finseq_1(C) = k3_finseq_1(A)
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(1,D)
                          & r1_xreal_0(D,k3_finseq_1(A)) )
                       => ( ( r2_hidden(k1_funct_1(A,D),k1_relat_1(B))
                           => k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)) )
                          & ( ~ r2_hidden(k1_funct_1(A,D),k1_relat_1(B))
                           => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ) ),
    file(cqc_lang,d3_cqc_lang),
    [interesting(0.00)]).

fof(d21_qc_lang1,definition,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v2_qc_lang1(A)
       => ! [B] : 
            ( m1_subset_1(B,k5_qc_lang1)
           => ( B = k15_qc_lang1(A)
            <=> ? [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & ? [D] : 
                      ( m1_qc_lang1(D,C)
                      & ? [E] : 
                          ( m2_subset_1(E,k5_qc_lang1,k7_qc_lang1(C))
                          & B = E
                          & A = k9_qc_lang1(E,D) ) ) ) ) ) ) ) ),
    file(qc_lang1,d21_qc_lang1),
    [interesting(0.00)]).

fof(t10_qc_lang3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v3_qc_lang1(A)
       => k24_qc_lang1(A) = k24_qc_lang1(k17_qc_lang1(A)) ) ) ),
    file(qc_lang3,t10_qc_lang3),
    [interesting(0.00)]).

fof(t13_qc_lang3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v4_qc_lang1(A)
       => k24_qc_lang1(A) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(k18_qc_lang1(A)),k24_qc_lang1(k19_qc_lang1(A))) ) ) ),
    file(qc_lang3,t13_qc_lang3),
    [interesting(0.00)]).

fof(t15_qc_lang3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v5_qc_lang1(A)
       => k24_qc_lang1(A) = k6_subset_1(k2_qc_lang1,k24_qc_lang1(k21_qc_lang1(A)),k23_qc_lang1(k20_qc_lang1(A))) ) ) ),
    file(qc_lang3,t15_qc_lang3),
    [interesting(0.00)]).

fof(t35_cqc_lang,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] : 
          ( m1_subset_1(B,k8_qc_lang1)
         => ( ( v5_qc_lang1(B)
              & k20_qc_lang1(B) = A )
           => k17_cqc_lang(B,A) = B ) ) ) ),
    file(cqc_lang,t35_cqc_lang),
    [interesting(0.00)]).

fof(t5_valuat_1,theorem,(
    $true ),
    file(valuat_1,t5_valuat_1),
    [interesting(0.00)]).

fof(t6_valuat_1,theorem,(
    $true ),
    file(valuat_1,t6_valuat_1),
    [interesting(0.00)]).

fof(t9_valuat_1,theorem,(
    $true ),
    file(valuat_1,t9_valuat_1),
    [interesting(0.00)]).