fof(t55_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( ~ v2_msualg_1(C)
                & v1_instalg1(C)
                & l1_msualg_1(C) )
             => ! [D] : 
                  ( m2_algspec1(D,C)
                 => ( r1_algspec1(D,A,B)
                   => m2_algspec1(k2_algspec1(D,A,B),k2_algspec1(C,A,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t54_algspec1,t11_algspec1,t31_algspec1,t31_algspec1,d5_algspec1,t41_algspec1,t19_instalg1,t40_algspec1,t11_instalg1,t18_algspec1,t11_instalg1,t18_algspec1,t44_algspec1,t45_algspec1,d5_algspec1]),
    [file(algspec1,t55_algspec1),interesting(1.00)]).

fof(t21_algspec1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => k1_algspec1(k2_xboole_0(A,B),C) = k2_xboole_0(k1_algspec1(A,C),k1_algspec1(B,C)) ) ),
    inference(mizar_proof,[status(thm)],[t19_algspec1,t20_algspec1,t31_funct_4]),
    [file(algspec1,t21_algspec1),interesting(0.90)]).

fof(t19_algspec1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => r6_pboole(k2_xboole_0(A,B),k1_algspec1(k2_xboole_0(A,B),C),k1_circcomb(A,B,k1_algspec1(A,C),k1_algspec1(B,C))) ) ),
    inference(mizar_proof,[status(thm)],[t88_relat_1,t131_partfun1,t31_funct_4,t90_relat_1,t17_xboole_1,t27_xboole_1,t23_funct_4,t107_relat_1,t15_funct_4,t15_funct_4,t1_algspec1,t15_funct_4,t15_funct_4]),
    [file(algspec1,t19_algspec1),interesting(0.86)]).

fof(t54_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( ~ v2_msualg_1(C)
                & v1_instalg1(C)
                & l1_msualg_1(C) )
             => ! [D] : 
                  ( m2_algspec1(D,C)
                 => ( r1_algspec1(D,A,B)
                   => r1_algspec1(C,A,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_algspec1,t41_algspec1,t19_instalg1,t32_algspec1,t11_instalg1,t18_algspec1,t11_instalg1,t18_algspec1,t31_algspec1]),
    [file(algspec1,t54_algspec1),interesting(0.85)]).

fof(t11_algspec1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r6_pboole(A,k1_algspec1(A,k1_algspec1(A,B)),k1_algspec1(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,t9_algspec1,t3_pboole]),
    [file(algspec1,t11_algspec1),interesting(0.82)]).

fof(t14_algspec1,theorem,(
    ! [A] : k1_algspec1(A,k1_xboole_0) = k6_partfun1(A) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,t13_algspec1]),
    [file(algspec1,t14_algspec1),interesting(0.81)]).

fof(t27_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ! [B] : 
            ( m1_algspec1(B,A)
           => B = k2_funct_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_algspec1,t24_algspec1,d10_xboole_0,d3_tarski,d5_funct_1,t25_algspec1,d8_funct_1,d5_funct_1,t25_algspec1,d5_funct_1,d8_funct_1,t60_funct_1]),
    [file(algspec1,t27_algspec1),interesting(0.81)]).

fof(t13_algspec1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(B,k6_partfun1(A))
       => k1_algspec1(A,B) = k6_partfun1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t71_relat_1,t79_funct_4,t12_algspec1,t10_algspec1]),
    [file(algspec1,t13_algspec1),interesting(0.80)]).

fof(t20_algspec1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => r1_partfun1(k1_algspec1(A,C),k1_algspec1(B,C)) ) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,t18_algspec1,t88_relat_1,t131_partfun1]),
    [file(algspec1,t20_algspec1),interesting(0.79)]).

fof(t47_algspec1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => m2_algspec1(A,A) ) ),
    inference(mizar_proof,[status(thm)],[t16_instalg1,d5_algspec1]),
    [file(algspec1,t47_algspec1),interesting(0.79)]).

fof(t44_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => k2_algspec1(A,k1_algspec1(u1_struct_0(A),B),C) = k2_algspec1(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_algspec1,t11_algspec1,t31_algspec1,d4_algspec1,d4_algspec1]),
    [file(algspec1,t44_algspec1),interesting(0.75)]).

fof(t45_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => k2_algspec1(A,B,k1_algspec1(u1_msualg_1(A),C)) = k2_algspec1(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_algspec1,t11_algspec1,t31_algspec1,d4_algspec1,d4_algspec1]),
    [file(algspec1,t45_algspec1),interesting(0.75)]).

fof(t28_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
           => ! [C] : 
                ( m1_algspec1(C,A)
               => ! [D] : 
                    ( m1_algspec1(D,B)
                   => m1_algspec1(k1_funct_4(C,D),k1_funct_4(A,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_funct_4,d2_algspec1,d1_funct_4,t26_relat_1,d2_algspec1,t24_algspec1,t73_funct_4,d2_algspec1,d2_algspec1,t23_funct_4,t26_relat_1]),
    [file(algspec1,t28_algspec1),interesting(0.74)]).

fof(t12_algspec1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r6_pboole(A,k1_algspec1(A,k1_funct_4(k6_partfun1(A),B)),k1_algspec1(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[t71_relat_1,t75_funct_4,t97_relat_1,t15_funct_4]),
    [file(algspec1,t12_algspec1),interesting(0.73)]).

fof(t24_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( m1_algspec1(B,A)
         => r1_tarski(k2_relat_1(B),k1_relat_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_algspec1,t71_relat_1,t27_funct_1]),
    [file(algspec1,t24_algspec1),interesting(0.73)]).

fof(t16_algspec1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_algspec1(A,B) = k7_relat_1(B,A) ) ) ),
    inference(mizar_proof,[status(thm)],[t91_relat_1,t15_algspec1,t10_algspec1]),
    [file(algspec1,t16_algspec1),interesting(0.72)]).

fof(t29_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
           => ! [C] : 
                ( m1_algspec1(C,A)
               => ? [D] : 
                    ( m1_algspec1(D,B)
                    & r1_tarski(C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t79_funct_4,t131_partfun1,t28_algspec1,t26_funct_4]),
    [file(algspec1,t29_algspec1),interesting(0.72)]).

fof(t10_algspec1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = A
       => k1_algspec1(A,B) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t71_relat_1,t97_relat_1,t20_funct_4]),
    [file(algspec1,t10_algspec1),interesting(0.71)]).

fof(t26_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => m1_algspec1(k2_funct_1(A),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t54_funct_1,t61_funct_1,d2_algspec1]),
    [file(algspec1,t26_algspec1),interesting(0.71)]).

fof(t18_algspec1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(A,B)
       => k7_relat_1(k1_algspec1(B,C),A) = k1_algspec1(A,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t1_funct_3,t103_relat_1,t75_funct_4]),
    [file(algspec1,t18_algspec1),interesting(0.71)]).

fof(t41_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
              <=> r3_pua2mss1(A,k2_algspec1(A,B,C),k1_algspec1(u1_struct_0(A),B),k1_algspec1(u1_msualg_1(A),C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_algspec1,t32_algspec1,t31_algspec1]),
    [file(algspec1,t41_algspec1),interesting(0.70)]).

fof(t15_algspec1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => r6_pboole(A,k1_algspec1(A,k7_relat_1(B,A)),k1_algspec1(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[t101_relat_1]),
    [file(algspec1,t15_algspec1),interesting(0.69)]).

fof(t31_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
              <=> r1_algspec1(A,k1_algspec1(u1_struct_0(A),B),k1_algspec1(u1_msualg_1(A),C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t15_funct_4,t15_funct_4,t30_algspec1,d3_algspec1]),
    [file(algspec1,t31_algspec1),interesting(0.69)]).

fof(t48_algspec1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m2_algspec1(B,A)
         => ! [C] : 
              ( m2_algspec1(C,B)
             => m2_algspec1(C,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_algspec1,t17_instalg1,d5_algspec1]),
    [file(algspec1,t48_algspec1),interesting(0.69)]).

fof(t56_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ( r1_circcomb(A,B)
           => ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C) )
               => ! [D] : 
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D) )
                   => ( r1_algspec1(k3_circcomb(A,B),C,D)
                     => k2_algspec1(k3_circcomb(A,B),C,D) = k3_circcomb(k2_algspec1(A,C,D),k2_algspec1(B,C,D)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_algspec1,t50_algspec1,t54_algspec1,d2_circcomb,t21_algspec1,t26_relat_1,d4_algspec1,d2_circcomb,t21_algspec1,t26_relat_1,d4_algspec1,d2_circcomb,d2_circcomb,t19_algspec1,t20_algspec1,t28_algspec1,t19_algspec1,t20_algspec1,d3_pboole,t24_algspec1,d3_pboole,d3_pboole,d1_circcomb,t4_algspec1,t39_algspec1,t73_funct_4,t73_funct_4,t39_algspec1,t39_algspec1,t37_algspec1,t37_algspec1,t37_algspec1,d1_circcomb,t31_funct_4,t26_relat_1,t13_xboole_1,t7_xboole_1,t18_algspec1,t88_relat_1,t5_algspec1,t30_funct_4,t8_xboole_1,t1_xboole_1,d1_funct_2,d1_funct_4,t17_xboole_1,t1_xboole_1,t6_algspec1,d1_circcomb,t4_algspec1,d1_funct_2,t38_algspec1,t2_algspec1,t73_funct_4,t73_funct_4,t38_algspec1,t38_algspec1,d2_circcomb]),
    [file(algspec1,t56_algspec1),interesting(0.69)]).

fof(t22_algspec1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_tarski(k2_relat_1(C),A)
               => k5_relat_1(C,k1_algspec1(A,B)) = k5_relat_1(C,k1_funct_4(k6_partfun1(A),B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t71_relat_1,d1_funct_4,t7_xboole_1,d3_pboole,t1_xboole_1,t46_relat_1,t23_funct_1,d5_funct_1,t8_algspec1,t9_funct_1]),
    [file(algspec1,t22_algspec1),interesting(0.68)]).

fof(t40_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                   => m1_instalg1(k2_algspec1(A,C,D),B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t32_algspec1,d4_algspec1,d4_algspec1,d4_algspec1,t71_relat_1,d13_pua2mss1,d2_instalg1,d13_pua2mss1,t10_algspec1,t71_relat_1,d13_pua2mss1,d1_funct_2,d13_pua2mss1,t91_relat_1,d1_funct_2,d5_funct_1,d13_pua2mss1,d13_pua2mss1,t23_funct_1,d13_pua2mss1,t23_funct_1,t72_funct_1,t9_funct_1,t79_relat_1,t94_relat_1,d5_funct_1,t7_funct_2,d11_finseq_1,d4_finseq_1,d13_pua2mss1,d13_pua2mss1,t79_relat_1,t35_funct_1]),
    [file(algspec1,t40_algspec1),interesting(0.68)]).

fof(t17_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k1_algspec1(k1_xboole_0,A) = k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,t16_algspec1,t110_relat_1]),
    [file(algspec1,t17_algspec1),interesting(0.67)]).

fof(t50_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => m2_algspec1(k3_circcomb(A,B),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t71_relat_1,d13_pua2mss1,d2_instalg1,d5_algspec1,t71_relat_1,d2_circcomb,t7_xboole_1,d1_funct_2,d2_circcomb,t26_funct_4,t64_grfunc_1,t94_relat_1,t79_relat_1,d1_funct_2,d5_funct_1,d11_finseq_1,d4_finseq_1,t79_relat_1,t14_funct_4,d2_circcomb,t35_funct_1]),
    [file(algspec1,t50_algspec1),interesting(0.67)]).

fof(t23_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
              & r1_xboole_0(k2_relat_1(B),k1_relat_1(A)) )
           => ! [C] : k5_relat_1(k1_algspec1(C,B),A) = k7_relat_1(A,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t88_relat_1,t71_relat_1,t87_relat_1,t89_relat_1,t99_relat_1,t64_xboole_1,d3_tarski,d12_funct_1,t35_funct_1,t64_xboole_1,t144_relat_1,t64_xboole_1,d7_xboole_0,t36_xboole_1,t7_algspec1,t23_xboole_1,t26_xboole_1,t90_relat_1,t2_algspec1,t3_algspec1,t77_relat_1]),
    [file(algspec1,t23_algspec1),interesting(0.66)]).

fof(t25_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( m1_algspec1(B,A)
         => ! [C] : 
              ( r2_hidden(C,k2_relat_1(A))
             => ( r2_hidden(k1_funct_1(B,C),k1_relat_1(A))
                & k1_funct_1(A,k1_funct_1(B,C)) = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_algspec1,t24_algspec1,d5_funct_1,t23_funct_1,d2_algspec1,t35_funct_1]),
    [file(algspec1,t25_algspec1),interesting(0.66)]).

fof(t4_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r1_partfun1(A,B)
                      & r1_partfun1(C,D) )
                   => r1_partfun1(k5_relat_1(C,A),k5_relat_1(D,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_partfun1,d6_partfun1,d3_xboole_0,t21_funct_1,d3_xboole_0,t23_funct_1,d3_xboole_0]),
    [file(algspec1,t4_algspec1),interesting(0.66)]).

fof(t5_algspec1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ~ v1_xboole_0(D)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,C)
                        & m2_relset_1(E,A,C) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,D)
                            & m2_relset_1(F,B,D) )
                         => ( r1_tarski(E,F)
                           => r1_tarski(k16_lang1(A,C,E),k16_lang1(B,D,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t25_relat_1,t83_finseq_1,t17_xboole_1,t1_xboole_1,t2_algspec1,d14_lang1,d14_lang1,t8_grfunc_1]),
    [file(algspec1,t5_algspec1),interesting(0.66)]).

fof(t32_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                   => r1_algspec1(A,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_pua2mss1,t71_relat_1,t20_funct_4,d13_pua2mss1,t71_relat_1,t20_funct_4,t10_instalg1,d3_algspec1,d13_pua2mss1,d13_pua2mss1,t21_funct_2,d13_pua2mss1,t21_funct_2,t21_funct_2,d13_pua2mss1,t21_funct_2]),
    [file(algspec1,t32_algspec1),interesting(0.65)]).

fof(t49_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ( r1_circcomb(A,B)
           => m2_algspec1(k3_circcomb(A,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_circcomb,t71_relat_1,d13_pua2mss1,d2_instalg1,d5_algspec1,t71_relat_1,d2_circcomb,t7_xboole_1,d1_funct_2,d2_circcomb,t29_funct_4,t64_grfunc_1,t94_relat_1,t79_relat_1,d1_funct_2,d5_funct_1,d11_finseq_1,d4_finseq_1,t79_relat_1,t16_funct_4,d2_circcomb,t35_funct_1]),
    [file(algspec1,t49_algspec1),interesting(0.65)]).

fof(t9_algspec1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,A)
       => ( ( r2_hidden(B,k1_relat_1(C))
           => k1_funct_1(k1_algspec1(A,C),B) = k1_funct_1(C,B) )
          & ( ~ r2_hidden(B,k1_relat_1(C))
           => k1_funct_1(k1_algspec1(A,C),B) = B ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_algspec1,t35_funct_1,t71_relat_1,t12_funct_4,t14_funct_4]),
    [file(algspec1,t9_algspec1),interesting(0.64)]).

fof(t63_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & v1_msafree1(B,A)
            & l3_msualg_1(B,A) )
         => v2_funct_1(u4_msualg_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_funct_1,d3_pboole,d2_msafree1,d3_prob_2,t3_xboole_0]),
    [file(algspec1,t63_algspec1),interesting(0.64)]).

fof(t6_algspec1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ~ v1_xboole_0(D)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,C)
                        & m2_relset_1(E,A,C) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,D)
                            & m2_relset_1(F,B,D) )
                         => ( r1_partfun1(E,F)
                           => r1_partfun1(k16_lang1(A,C,E),k16_lang1(B,D,F)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d6_partfun1,d6_partfun1,d3_xboole_0,d14_lang1,t46_relat_1,d5_funct_1,d3_xboole_0,t23_funct_1,t23_funct_1,t9_funct_1]),
    [file(algspec1,t6_algspec1),interesting(0.63)]).

fof(t58_algspec1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m2_algspec1(B,A)
         => ! [C] : 
              ( m4_algspec1(C,B)
             => m4_algspec1(C,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_algspec1,t48_algspec1,d7_algspec1]),
    [file(algspec1,t58_algspec1),interesting(0.63)]).

fof(t7_algspec1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => k2_relat_1(k1_algspec1(A,B)) = k2_xboole_0(k4_xboole_0(A,k1_relat_1(B)),k9_relat_1(B,A)) ) ),
    inference(mizar_proof,[status(thm)],[t36_xboole_1,t71_relat_1,t12_frechet,t148_relat_1,t162_funct_1,t90_relat_1,t47_xboole_1]),
    [file(algspec1,t7_algspec1),interesting(0.62)]).

fof(t53_algspec1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_instalg1(B)
            & l1_msualg_1(B) )
         => ( v3_struct_0(A)
           => m2_algspec1(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_struct_0,d1_instalg1,t57_partfun1,t2_xboole_1,t14_instalg1,d5_algspec1]),
    [file(algspec1,t53_algspec1),interesting(0.62)]).

fof(t57_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_msualg_6(B,A)
            & l3_msualg_1(B,A) )
         => m4_algspec1(B,A) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_algspec1,t47_algspec1,d7_algspec1]),
    [file(algspec1,t57_algspec1),interesting(0.61)]).

fof(t61_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m4_algspec1(B,A)
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l1_msualg_1(C) )
             => ( l3_msualg_1(B,C)
               => l3_msualg_1(B,k3_circcomb(C,A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_circcomb,t59_algspec1,t12_xboole_1,t12_xboole_1,d2_circcomb,t59_algspec1,t12_xboole_1,d1_funct_2,d2_circcomb,t21_funct_2,t21_funct_2,d5_msualg_1,t14_funct_4,t60_algspec1,t12_funct_4,d18_pboole,d18_pboole]),
    [file(algspec1,t61_algspec1),interesting(0.61)]).

fof(t8_algspec1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => k1_funct_1(k1_algspec1(A,B),C) = k1_funct_1(k1_funct_4(k6_partfun1(A),B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t75_funct_4,t71_relat_1,t98_relat_1,t72_funct_1]),
    [file(algspec1,t8_algspec1),interesting(0.60)]).

fof(t33_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_algspec1(A,B,k1_xboole_0) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_algspec1,t22_funct_4,t34_funct_1,t34_funct_1]),
    [file(algspec1,t33_algspec1),interesting(0.58)]).

fof(t66_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & v1_msafree1(C,A)
                & l3_msualg_1(C,A) )
             => ( m4_algspec1(C,B)
               => m2_algspec1(A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_algspec1,d5_algspec1,t65_algspec1,t11_instalg1,t12_instalg1,t14_instalg1,d5_algspec1]),
    [file(algspec1,t66_algspec1),interesting(0.57)]).

fof(t3_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(k1_relat_1(A),k2_relat_1(B))
                  & r1_xboole_0(k1_relat_1(A),k2_relat_1(C))
                  & r1_xboole_0(k9_relat_1(B,k1_relat_1(C)),k1_relat_1(A)) )
               => k5_relat_1(k1_funct_4(B,C),A) = k5_relat_1(B,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_funct_1,d12_funct_1,t3_xboole_0,t12_funct_4,t13_funct_4,t21_funct_1,d3_tarski,d10_xboole_0,d3_tarski,t21_funct_1,t13_funct_4,d5_funct_1,t12_funct_4,t14_funct_4,t21_funct_1,t3_xboole_0,t21_funct_1,d12_funct_1,t3_xboole_0,t12_funct_4,t13_funct_4,t23_funct_1,t23_funct_1,t9_funct_1]),
    [file(algspec1,t3_algspec1),interesting(0.56)]).

fof(t59_algspec1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( l3_msualg_1(C,B)
             => ( m4_algspec1(C,A)
               => ( r1_tarski(u1_struct_0(A),u1_struct_0(B))
                  & r1_tarski(u1_msualg_1(A),u1_msualg_1(B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_algspec1,d5_algspec1,d3_pboole,t11_instalg1,d3_pboole,t11_instalg1]),
    [file(algspec1,t59_algspec1),interesting(0.55)]).

fof(t62_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ( l3_msualg_1(C,B)
               => ( u1_struct_0(A) = u1_struct_0(B)
                  & u1_msualg_1(A) = u1_msualg_1(B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,d3_pboole,d3_pboole,d3_pboole]),
    [file(algspec1,t62_algspec1),interesting(0.55)]).

fof(t34_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( v2_funct_1(B)
                  & r1_tarski(k3_xboole_0(u1_msualg_1(A),k2_relat_1(B)),k1_relat_1(B)) )
               => r1_algspec1(A,C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_algspec1,t35_funct_1,t35_funct_1,d5_funct_1,t14_funct_4,t12_funct_4,d3_xboole_0,t14_funct_4,d8_funct_1,t12_funct_4,d5_funct_1,t14_funct_4,t12_funct_4,d3_xboole_0]),
    [file(algspec1,t34_algspec1),interesting(0.52)]).

fof(t43_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( k1_relat_1(B) = u1_struct_0(A)
                  & k1_relat_1(C) = u1_msualg_1(A)
                  & r1_algspec1(A,B,C) )
               => r3_pua2mss1(A,k2_algspec1(A,B,C),B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t71_relat_1,t20_funct_4,t42_algspec1]),
    [file(algspec1,t43_algspec1),interesting(0.52)]).

fof(t64_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_msafree1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B)))
             => ! [D] : 
                  ( m1_subset_1(D,k2_relat_1(u4_msualg_1(A,B)))
                 => ( C = D
                    | r1_xboole_0(C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,t65_relat_1,d5_funct_1,d5_funct_1,d2_msafree1,d3_prob_2]),
    [file(algspec1,t64_algspec1),interesting(0.51)]).

fof(t42_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(k1_relat_1(B),u1_struct_0(A))
                  & r1_tarski(k1_relat_1(C),u1_msualg_1(A))
                  & r1_algspec1(A,B,C) )
               => r3_pua2mss1(A,k2_algspec1(A,B,C),k1_funct_4(k6_partfun1(u1_struct_0(A)),B),k1_funct_4(k6_partfun1(u1_msualg_1(A)),C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t97_relat_1,t41_algspec1]),
    [file(algspec1,t42_algspec1),interesting(0.48)]).

fof(t65_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & v1_msafree1(C,A)
                & l3_msualg_1(C,A) )
             => ( l3_msualg_1(C,B)
               => g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) = g1_msualg_1(u1_struct_0(B),u1_msualg_1(B),u2_msualg_1(B),u3_msualg_1(B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t62_algspec1,t63_algspec1,d3_pboole,d1_funct_2,t62_algspec1,t6_funct_2,t12_relset_1,t3_xboole_0,t64_algspec1,t21_funct_2,t21_funct_2,d8_funct_1,t9_funct_1,d1_funct_2,t62_algspec1,d1_funct_2,t21_funct_2,d19_pboole,t21_funct_2,d19_pboole,t2_pua2mss1,t46_relat_1,t49_funct_1,t9_funct_1]),
    [file(algspec1,t65_algspec1),interesting(0.48)]).

fof(t35_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( v2_funct_1(B)
                  & r1_xboole_0(k2_relat_1(B),u1_msualg_1(A)) )
               => r1_algspec1(A,C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,t2_xboole_1,t34_algspec1]),
    [file(algspec1,t35_algspec1),interesting(0.45)]).

fof(t37_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => ( v1_funct_1(k1_algspec1(u1_struct_0(A),B))
                  & v1_funct_2(k1_algspec1(u1_struct_0(A),B),u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C)))
                  & m2_relset_1(k1_algspec1(u1_struct_0(A),B),u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_algspec1,t10_instalg1]),
    [file(algspec1,t37_algspec1),interesting(0.40)]).

fof(t30_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => ( k1_funct_1(k1_algspec1(u1_msualg_1(A),C),D) = k1_funct_1(k1_algspec1(u1_msualg_1(A),C),E)
                         => ( k5_relat_1(k1_msualg_1(A,D),k1_algspec1(u1_struct_0(A),B)) = k5_relat_1(k1_msualg_1(A,E),k1_algspec1(u1_struct_0(A),B))
                            & k1_funct_1(k1_algspec1(u1_struct_0(A),B),k2_msualg_1(A,D)) = k1_funct_1(k1_algspec1(u1_struct_0(A),B),k2_msualg_1(A,E)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_algspec1,t8_algspec1,d3_algspec1,t22_algspec1,t22_algspec1,t8_algspec1,d3_algspec1,t8_algspec1,d3_algspec1,t8_algspec1,t8_algspec1,t22_algspec1,t22_algspec1,t8_algspec1,t8_algspec1]),
    [file(algspec1,t30_algspec1),interesting(0.22)]).

fof(t2_xboole_1,theorem,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    [interesting(0.00)]).

fof(t71_relat_1,theorem,(
    ! [A] : 
      ( k1_relat_1(k6_relat_1(A)) = A
      & k2_relat_1(k6_relat_1(A)) = A ) ),
    file(relat_1,t71_relat_1),
    [interesting(0.00)]).

fof(t79_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
           => ( k1_funct_4(A,B) = B
              & k1_funct_4(B,A) = B ) ) ) ) ),
    file(funct_4,t79_funct_4),
    [interesting(0.00)]).

fof(t75_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k7_relat_1(k1_funct_4(A,B),C) = k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C)) ) ) ),
    file(funct_4,t75_funct_4),
    [interesting(0.00)]).

fof(t97_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k7_relat_1(B,A) = B ) ) ),
    file(relat_1,t97_relat_1),
    [interesting(0.00)]).

fof(t15_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,k1_funct_4(B,C)) ) ) ) ),
    file(funct_4,t15_funct_4),
    [interesting(0.00)]).

fof(t20_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
           => k1_funct_4(A,B) = B ) ) ) ),
    file(funct_4,t20_funct_4),
    [interesting(0.00)]).

fof(t91_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    [interesting(0.00)]).

fof(t101_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k7_relat_1(k7_relat_1(B,A),A) = k7_relat_1(B,A) ) ),
    file(relat_1,t101_relat_1),
    [interesting(0.00)]).

fof(t110_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k7_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ),
    file(relat_1,t110_relat_1),
    [interesting(0.00)]).

fof(t88_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k7_relat_1(B,A),B) ) ),
    file(relat_1,t88_relat_1),
    [interesting(0.00)]).

fof(t87_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k1_relat_1(k7_relat_1(B,A)),A) ) ),
    file(relat_1,t87_relat_1),
    [interesting(0.00)]).

fof(t89_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)) ) ),
    file(relat_1,t89_relat_1),
    [interesting(0.00)]).

fof(t99_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) ) ),
    file(relat_1,t99_relat_1),
    [interesting(0.00)]).

fof(t64_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D)
        & r1_xboole_0(B,D) )
     => r1_xboole_0(A,C) ) ),
    file(xboole_1,t64_xboole_1),
    [interesting(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

fof(d12_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    [interesting(0.00)]).

fof(t35_funct_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k6_relat_1(A),B) = B ) ),
    file(funct_1,t35_funct_1),
    [interesting(0.00)]).

fof(t144_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k9_relat_1(B,A),k2_relat_1(B)) ) ),
    file(relat_1,t144_relat_1),
    [interesting(0.00)]).

fof(d7_xboole_0,definition,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    [interesting(0.00)]).

fof(t36_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    [interesting(0.00)]).

fof(t12_frechet,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => k2_relat_1(k1_funct_4(A,B)) = k2_xboole_0(k9_relat_1(A,k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),k2_relat_1(B)) ) ) ),
    file(frechet,t12_frechet),
    [interesting(0.00)]).

fof(t148_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A) ) ),
    file(relat_1,t148_relat_1),
    [interesting(0.00)]).

fof(t162_funct_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k9_relat_1(k6_relat_1(A),B) = B ) ),
    file(funct_1,t162_funct_1),
    [interesting(0.00)]).

fof(t90_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ),
    file(relat_1,t90_relat_1),
    [interesting(0.00)]).

fof(t47_xboole_1,theorem,(
    ! [A,B] : k4_xboole_0(A,k3_xboole_0(A,B)) = k4_xboole_0(A,B) ),
    file(xboole_1,t47_xboole_1),
    [interesting(0.00)]).

fof(t23_xboole_1,theorem,(
    ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ),
    file(xboole_1,t23_xboole_1),
    [interesting(0.00)]).

fof(t26_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)) ) ),
    file(xboole_1,t26_xboole_1),
    [interesting(0.00)]).

fof(t48_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => ( r1_tarski(A,B)
               => r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B)) ) ) ) ) ),
    file(relat_1,t48_relat_1),
    [interesting(0.00)]).

fof(t25_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & r1_tarski(k2_relat_1(A),k2_relat_1(B)) ) ) ) ) ),
    file(relat_1,t25_relat_1),
    [interesting(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(t21_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
          <=> ( r2_hidden(A,k1_relat_1(C))
              & r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) ) ) ) ) ),
    file(funct_1,t21_funct_1),
    [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(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.00)]).

fof(t23_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_1),
    [interesting(0.00)]).

fof(t8_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
          <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ),
    file(grfunc_1,t8_grfunc_1),
    [interesting(0.00)]).

fof(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.00)]).

fof(t2_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(A,B)
                  & r1_tarski(k3_xboole_0(k2_relat_1(C),k1_relat_1(B)),k1_relat_1(A)) )
               => k5_relat_1(C,B) = k5_relat_1(C,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_relat_1,t25_relat_1,d10_xboole_0,d3_tarski,t21_funct_1,d5_funct_1,d3_xboole_0,t21_funct_1,t21_funct_1,t23_funct_1,d5_funct_1,t8_grfunc_1,t9_funct_1]),
    [file(algspec1,t2_algspec1),interesting(0.00)]).

fof(t3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    [interesting(0.00)]).

fof(t12_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ~ r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    [interesting(0.00)]).

fof(t13_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k1_funct_4(B,C)))
          <=> ( r2_hidden(A,k1_relat_1(B))
              | r2_hidden(A,k1_relat_1(C)) ) ) ) ) ),
    file(funct_4,t13_funct_4),
    [interesting(0.00)]).

fof(t14_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    [interesting(0.00)]).

fof(t77_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k5_relat_1(k6_relat_1(A),B) = B ) ) ),
    file(relat_1,t77_relat_1),
    [interesting(0.00)]).

fof(t54_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ( B = k2_funct_1(A)
            <=> ( k1_relat_1(B) = k2_relat_1(A)
                & ! [C,D] : 
                    ( ( ( r2_hidden(C,k2_relat_1(A))
                        & D = k1_funct_1(B,C) )
                     => ( r2_hidden(D,k1_relat_1(A))
                        & C = k1_funct_1(A,D) ) )
                    & ( ( r2_hidden(D,k1_relat_1(A))
                        & C = k1_funct_1(A,D) )
                     => ( r2_hidden(C,k2_relat_1(A))
                        & D = k1_funct_1(B,C) ) ) ) ) ) ) ) ) ),
    file(funct_1,t54_funct_1),
    [interesting(0.00)]).

fof(t61_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ( k5_relat_1(A,k2_funct_1(A)) = k6_relat_1(k1_relat_1(A))
          & k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A)) ) ) ) ),
    file(funct_1,t61_funct_1),
    [interesting(0.00)]).

fof(d2_algspec1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( m1_algspec1(B,A)
          <=> ( k1_relat_1(B) = k2_relat_1(A)
              & k5_relat_1(B,A) = k6_partfun1(k2_relat_1(A)) ) ) ) ) ),
    file(algspec1,d2_algspec1),
    [interesting(0.00)]).

fof(t27_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( k1_relat_1(k5_relat_1(B,A)) = k1_relat_1(B)
           => r1_tarski(k2_relat_1(B),k1_relat_1(A)) ) ) ) ),
    file(funct_1,t27_funct_1),
    [interesting(0.00)]).

fof(d8_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    [interesting(0.00)]).

fof(t60_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v2_funct_1(A)
              & k1_relat_1(A) = k2_relat_1(B)
              & k2_relat_1(A) = k1_relat_1(B)
              & ! [C,D] : 
                  ( ( r2_hidden(C,k1_relat_1(A))
                    & r2_hidden(D,k1_relat_1(B)) )
                 => ( k1_funct_1(A,C) = D
                  <=> k1_funct_1(B,D) = C ) ) )
           => B = k2_funct_1(A) ) ) ) ),
    file(funct_1,t60_funct_1),
    [interesting(0.00)]).

fof(t131_partfun1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & r1_tarski(A,C)
                & r1_tarski(B,C) ) ) ) ) ),
    file(partfun1,t131_partfun1),
    [interesting(0.00)]).

fof(t31_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> k2_xboole_0(A,B) = k1_funct_4(A,B) ) ) ) ),
    file(funct_4,t31_funct_4),
    [interesting(0.00)]).

fof(d1_funct_4,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k1_funct_4(A,B)
              <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => ( ( r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(B,D) )
                        & ( ~ r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ),
    file(funct_4,d1_funct_4),
    [interesting(0.00)]).

fof(t26_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ),
    file(relat_1,t26_relat_1),
    [interesting(0.00)]).

fof(t73_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r1_tarski(k2_relat_1(C),k1_relat_1(A))
                      & r1_tarski(k2_relat_1(D),k1_relat_1(B))
                      & r1_partfun1(A,B) )
                   => k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B)) = k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B)) ) ) ) ) ) ),
    file(funct_4,t73_funct_4),
    [interesting(0.00)]).

fof(t23_funct_4,theorem,(
    ! [A,B] : k1_funct_4(k6_partfun1(A),k6_partfun1(B)) = k6_partfun1(k2_xboole_0(A,B)) ),
    file(funct_4,t23_funct_4),
    [interesting(0.00)]).

fof(t26_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(A,k1_funct_4(B,A)) ) ) ),
    file(funct_4,t26_funct_4),
    [interesting(0.00)]).

fof(d3_algspec1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => ( k1_funct_1(k1_funct_4(k6_partfun1(u1_msualg_1(A)),C),D) = k1_funct_1(k1_funct_4(k6_partfun1(u1_msualg_1(A)),C),E)
                         => ( k5_relat_1(k1_msualg_1(A,D),k1_funct_4(k6_partfun1(u1_struct_0(A)),B)) = k5_relat_1(k1_msualg_1(A,E),k1_funct_4(k6_partfun1(u1_struct_0(A)),B))
                            & k1_funct_1(k1_funct_4(k6_partfun1(u1_struct_0(A)),B),k2_msualg_1(A,D)) = k1_funct_1(k1_funct_4(k6_partfun1(u1_struct_0(A)),B),k2_msualg_1(A,E)) ) ) ) ) ) ) ) ) ),
    file(algspec1,d3_algspec1),
    [interesting(0.00)]).

fof(t22_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k1_funct_4(A,k1_xboole_0) = A ) ),
    file(funct_4,t22_funct_4),
    [interesting(0.00)]).

fof(t34_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( B = k6_relat_1(A)
      <=> ( k1_relat_1(B) = A
          & ! [C] : 
              ( r2_hidden(C,A)
             => k1_funct_1(B,C) = C ) ) ) ) ),
    file(funct_1,t34_funct_1),
    [interesting(0.00)]).

fof(d4_algspec1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => ! [D] : 
                    ( ( ~ v3_struct_0(D)
                      & v1_msualg_1(D)
                      & ~ v2_msualg_1(D)
                      & l1_msualg_1(D) )
                   => ( D = k2_algspec1(A,B,C)
                    <=> ( r3_pua2mss1(A,D,k1_algspec1(u1_struct_0(A),B),k1_algspec1(u1_msualg_1(A),C))
                        & u1_struct_0(D) = k2_relat_1(k1_algspec1(u1_struct_0(A),B))
                        & u1_msualg_1(D) = k2_relat_1(k1_algspec1(u1_msualg_1(A),C)) ) ) ) ) ) ) ) ),
    file(algspec1,d4_algspec1),
    [interesting(0.00)]).

fof(d13_pua2mss1,definition,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ! [B] : 
          ( l1_msualg_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                  <=> ( k1_relat_1(C) = u1_struct_0(A)
                      & k1_relat_1(D) = u1_msualg_1(A)
                      & r1_tarski(k2_relat_1(C),u1_struct_0(B))
                      & r1_tarski(k2_relat_1(D),u1_msualg_1(B))
                      & k5_relat_1(u3_msualg_1(A),C) = k5_relat_1(D,u3_msualg_1(B))
                      & ! [E,F] : 
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ( ( r2_hidden(E,u1_msualg_1(A))
                              & F = k1_funct_1(u2_msualg_1(A),E) )
                           => k5_relat_1(F,C) = k1_funct_1(u2_msualg_1(B),k1_funct_1(D,E)) ) ) ) ) ) ) ) ) ),
    file(pua2mss1,d13_pua2mss1),
    [interesting(0.00)]).

fof(t10_instalg1,theorem,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ! [B] : 
          ( l1_msualg_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                   => ( v1_funct_1(C)
                      & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                      & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
                      & v1_funct_1(D)
                      & v1_funct_2(D,u1_msualg_1(A),u1_msualg_1(B))
                      & m2_relset_1(D,u1_msualg_1(A),u1_msualg_1(B)) ) ) ) ) ) ) ),
    file(instalg1,t10_instalg1),
    [interesting(0.00)]).

fof(t21_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ),
    file(funct_2,t21_funct_2),
    [interesting(0.00)]).

fof(t98_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k7_relat_1(A,k1_relat_1(A)) = A ) ),
    file(relat_1,t98_relat_1),
    [interesting(0.00)]).

fof(t72_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,A)
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t72_funct_1),
    [interesting(0.00)]).

fof(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.00)]).

fof(d3_pboole,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    [interesting(0.00)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.00)]).

fof(t46_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    [interesting(0.00)]).

fof(t46_algspec1,theorem,(
    $true ),
    file(algspec1,t46_algspec1),
    [interesting(0.00)]).

fof(d5_algspec1,definition,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_instalg1(B)
            & l1_msualg_1(B) )
         => ( m2_algspec1(B,A)
          <=> m1_instalg1(A,B) ) ) ) ),
    file(algspec1,d5_algspec1),
    [interesting(0.00)]).

fof(t12_instalg1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_instalg1(B,A)
         => ( r1_tarski(u3_msualg_1(B),u3_msualg_1(A))
            & r1_tarski(u2_msualg_1(B),u2_msualg_1(A)) ) ) ) ),
    file(instalg1,t12_instalg1),
    [interesting(0.00)]).

fof(d1_circcomb,definition,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ! [B] : 
          ( l1_msualg_1(B)
         => ( r1_circcomb(A,B)
          <=> ( r1_partfun1(u2_msualg_1(A),u2_msualg_1(B))
              & r1_partfun1(u3_msualg_1(A),u3_msualg_1(B)) ) ) ) ) ),
    file(circcomb,d1_circcomb),
    [interesting(0.00)]).

fof(t4_funct_4,theorem,(
    ! [A,B] : 
      ( r1_tarski(k6_partfun1(A),k6_partfun1(B))
    <=> r1_tarski(A,B) ) ),
    file(funct_4,t4_funct_4),
    [interesting(0.00)]).

fof(d2_circcomb,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v1_msualg_1(C)
                & l1_msualg_1(C) )
             => ( C = k3_circcomb(A,B)
              <=> ( u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B))
                  & u1_msualg_1(C) = k2_xboole_0(u1_msualg_1(A),u1_msualg_1(B))
                  & u2_msualg_1(C) = k1_funct_4(u2_msualg_1(A),u2_msualg_1(B))
                  & u3_msualg_1(C) = k1_funct_4(u3_msualg_1(A),u3_msualg_1(B)) ) ) ) ) ) ),
    file(circcomb,d2_circcomb),
    [interesting(0.00)]).

fof(d2_instalg1,definition,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l1_msualg_1(B)
         => ( m1_instalg1(B,A)
          <=> r3_pua2mss1(B,A,k6_partfun1(u1_struct_0(B)),k6_partfun1(u1_msualg_1(B))) ) ) ) ),
    file(instalg1,d2_instalg1),
    [interesting(0.00)]).

fof(t18_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))) ) ) ),
    file(funct_4,t18_funct_4),
    [interesting(0.00)]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    [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(t10_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(k2_relat_1(B),k1_relat_1(A))
                  & r1_tarski(k2_relat_1(C),k1_relat_1(A)) )
               => k5_relat_1(k1_funct_4(B,C),A) = k1_funct_4(k5_relat_1(B,A),k5_relat_1(C,A)) ) ) ) ) ),
    file(funct_7,t10_funct_7),
    [interesting(0.00)]).

fof(d11_finseq_1,definition,(
    ! [A,B] : 
      ( B = k13_finseq_1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> m2_finseq_1(C,A) ) ) ),
    file(finseq_1,d11_finseq_1),
    [interesting(0.00)]).

fof(d4_finseq_1,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( m1_finseq_1(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(finseq_1,d4_finseq_1),
    [interesting(0.00)]).

fof(t44_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => r1_tarski(k1_relat_1(k5_relat_1(A,B)),k1_relat_1(A)) ) ) ),
    file(relat_1,t44_relat_1),
    [interesting(0.00)]).

fof(t11_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => k5_relat_1(A,k1_funct_4(B,C)) = k1_funct_4(k5_relat_1(A,B),k5_relat_1(A,C)) ) ) ) ),
    file(funct_7,t11_funct_7),
    [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(t35_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> k1_funct_4(A,B) = k1_funct_4(B,A) ) ) ) ),
    file(funct_4,t35_funct_4),
    [interesting(0.00)]).

fof(t51_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l1_msualg_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] : 
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ! [F] : 
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ! [G] : 
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G) )
                             => ( ( r1_partfun1(D,F)
                                  & r3_pua2mss1(A,C,D,E)
                                  & r3_pua2mss1(B,C,F,G) )
                               => r3_pua2mss1(k3_circcomb(A,B),C,k1_funct_4(D,F),k1_funct_4(E,G)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_pua2mss1,d2_circcomb,d1_funct_4,d13_pua2mss1,d2_circcomb,d1_funct_4,d2_circcomb,t18_funct_4,t8_xboole_1,t1_xboole_1,t18_funct_4,t8_xboole_1,t1_xboole_1,d1_funct_2,t73_funct_4,t10_funct_7,d2_circcomb,d1_funct_2,t14_funct_4,d5_funct_1,d11_finseq_1,d4_finseq_1,t44_relat_1,t46_relat_1,t11_funct_7,t20_funct_4,t14_funct_4,d2_xboole_0,t12_funct_4,d5_funct_1,d11_finseq_1,d4_finseq_1,t44_relat_1,t46_relat_1,t35_funct_4,t11_funct_7,t20_funct_4,t12_funct_4]),
    [file(algspec1,t51_algspec1),interesting(0.00)]).

fof(t29_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> r1_tarski(A,k1_funct_4(A,B)) ) ) ) ),
    file(funct_4,t29_funct_4),
    [interesting(0.00)]).

fof(t64_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
           => k7_relat_1(B,k1_relat_1(A)) = A ) ) ) ),
    file(grfunc_1,t64_grfunc_1),
    [interesting(0.00)]).

fof(t94_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k7_relat_1(B,A) = k5_relat_1(k6_relat_1(A),B) ) ),
    file(relat_1,t94_relat_1),
    [interesting(0.00)]).

fof(t79_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k2_relat_1(B),A)
       => k5_relat_1(B,k6_relat_1(A)) = B ) ) ),
    file(relat_1,t79_relat_1),
    [interesting(0.00)]).

fof(t16_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r1_partfun1(B,C)
              & r2_hidden(A,k1_relat_1(B)) )
           => k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t16_funct_4),
    [interesting(0.00)]).

fof(t17_instalg1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_instalg1(B,A)
         => ! [C] : 
              ( m1_instalg1(C,B)
             => m1_instalg1(C,A) ) ) ) ),
    file(instalg1,t17_instalg1),
    [interesting(0.00)]).

fof(t52_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v1_instalg1(C)
                & l1_msualg_1(C) )
             => ( ( ( m2_algspec1(C,A)
                    & m2_algspec1(C,B) )
                 => ( r1_circcomb(A,B)
                    & m2_algspec1(C,k3_circcomb(A,B)) ) )
                & ( ( r1_circcomb(A,B)
                    & m2_algspec1(C,k3_circcomb(A,B)) )
                 => ( m2_algspec1(C,A)
                    & m2_algspec1(C,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_algspec1,t12_instalg1,t131_partfun1,d1_circcomb,t12_instalg1,t131_partfun1,t7_xboole_1,t4_funct_4,t131_partfun1,d2_circcomb,d2_instalg1,d5_algspec1,t51_algspec1,t23_funct_4,t23_funct_4,d2_instalg1,d5_algspec1,t49_algspec1,t50_algspec1,t48_algspec1]),
    [file(algspec1,t52_algspec1),interesting(0.00)]).

fof(d1_struct_0,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v3_struct_0(A)
      <=> v1_xboole_0(u1_struct_0(A)) ) ) ),
    file(struct_0,d1_struct_0),
    [interesting(0.00)]).

fof(d1_instalg1,definition,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v1_instalg1(A)
      <=> ( u1_struct_0(A) = k1_xboole_0
         => u1_msualg_1(A) = k1_xboole_0 ) ) ) ),
    file(instalg1,d1_instalg1),
    [interesting(0.00)]).

fof(t57_partfun1,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_xboole_0,A) )
     => B = k1_xboole_0 ) ),
    file(partfun1,t57_partfun1),
    [interesting(0.00)]).

fof(t14_instalg1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_instalg1(B)
            & l1_msualg_1(B) )
         => ( ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & r1_tarski(u2_msualg_1(B),u2_msualg_1(A))
              & r1_tarski(u3_msualg_1(B),u3_msualg_1(A)) )
           => m1_instalg1(B,A) ) ) ) ),
    file(instalg1,t14_instalg1),
    [interesting(0.00)]).

fof(t19_instalg1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_instalg1(B,A)
         => ! [C] : 
              ( l1_msualg_1(C)
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] : 
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r3_pua2mss1(A,C,D,E)
                       => r3_pua2mss1(B,C,k7_relat_1(D,u1_struct_0(B)),k7_relat_1(E,u1_msualg_1(B))) ) ) ) ) ) ) ),
    file(instalg1,t19_instalg1),
    [interesting(0.00)]).

fof(t11_instalg1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_instalg1(B,A)
         => ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
            & r1_tarski(u1_msualg_1(B),u1_msualg_1(A)) ) ) ) ),
    file(instalg1,t11_instalg1),
    [interesting(0.00)]).

fof(t1_funct_3,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k6_relat_1(A) = k7_relat_1(k6_relat_1(B),A) ) ),
    file(funct_3,t1_funct_3),
    [interesting(0.00)]).

fof(t103_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A) ) ) ),
    file(relat_1,t103_relat_1),
    [interesting(0.00)]).

fof(t3_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(B,D) = k1_funct_1(C,D) )
           => B = C ) ) ) ),
    file(pboole,t3_pboole),
    [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(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.00)]).

fof(t27_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)) ) ),
    file(xboole_1,t27_xboole_1),
    [interesting(0.00)]).

fof(t107_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => k7_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) ) ),
    file(relat_1,t107_relat_1),
    [interesting(0.00)]).

fof(t1_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_tarski(k3_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(C))
               => k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(k1_funct_4(B,A),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_4,d1_funct_4,d1_funct_4,t14_funct_4,d2_xboole_0,t12_funct_4,d2_xboole_0,d3_xboole_0,t12_funct_4,t14_funct_4,t9_funct_1]),
    [file(algspec1,t1_algspec1),interesting(0.00)]).

fof(d6_partfun1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> ! [C] : 
                ( r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))
               => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ),
    file(partfun1,d6_partfun1),
    [interesting(0.00)]).

fof(t23_funct_2,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C
        & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) ),
    file(funct_2,t23_funct_2),
    [interesting(0.00)]).

fof(t55_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)) ) ) ) ),
    file(relat_1,t55_relat_1),
    [interesting(0.00)]).

fof(t39_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => ! [D] : 
                    ( m1_algspec1(D,k1_algspec1(u1_msualg_1(A),C))
                   => u3_msualg_1(k2_algspec1(A,B,C)) = k5_relat_1(D,k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k1_algspec1(u1_struct_0(A),B))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_algspec1,t23_funct_2,d2_algspec1,t55_relat_1,d13_pua2mss1]),
    [file(algspec1,t39_algspec1),interesting(0.00)]).

fof(t13_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_xboole_1),
    [interesting(0.00)]).

fof(t83_finseq_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k13_finseq_1(A),k13_finseq_1(B)) ) ),
    file(finseq_1,t83_finseq_1),
    [interesting(0.00)]).

fof(d14_lang1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(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,k3_finseq_2(A),k3_finseq_2(B))
                    & m2_relset_1(D,k3_finseq_2(A),k3_finseq_2(B)) )
                 => ( D = k16_lang1(A,B,C)
                  <=> ! [E] : 
                        ( m2_finseq_2(E,A,k3_finseq_2(A))
                       => k8_funct_2(k3_finseq_2(A),k3_finseq_2(B),D,E) = k15_lang1(A,B,E,C) ) ) ) ) ) ) ),
    file(lang1,d14_lang1),
    [interesting(0.00)]).

fof(t30_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)) ) ) ),
    file(funct_4,t30_funct_4),
    [interesting(0.00)]).

fof(t36_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v2_msualg_1(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                   => k7_funct_2(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(A),k16_lang1(u1_struct_0(A),u1_struct_0(B),C)) = k5_relat_1(D,u2_msualg_1(B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_pua2mss1,d1_funct_2,t46_relat_1,d1_funct_2,d5_funct_1,d11_finseq_1,t23_funct_1,d14_lang1,d13_pua2mss1,t23_funct_1,t9_funct_1]),
    [file(algspec1,t36_algspec1),interesting(0.00)]).

fof(t38_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_algspec1(A,B,C)
               => ! [D] : 
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C)))
                      & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C))) )
                   => ( D = k1_algspec1(u1_struct_0(A),B)
                     => ! [E] : 
                          ( m1_algspec1(E,k1_algspec1(u1_msualg_1(A),C))
                         => u2_msualg_1(k2_algspec1(A,B,C)) = k5_relat_1(E,k7_funct_2(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),k3_finseq_2(u1_struct_0(k2_algspec1(A,B,C))),u2_msualg_1(A),k16_lang1(u1_struct_0(A),u1_struct_0(k2_algspec1(A,B,C)),D))) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_algspec1,t23_funct_2,d2_algspec1,t55_relat_1,t36_algspec1]),
    [file(algspec1,t38_algspec1),interesting(0.00)]).

fof(d6_algspec1,definition,(
    ! [A] : 
      ( m3_algspec1(A)
    <=> ? [B] : 
          ( ~ v2_msualg_1(B)
          & v1_instalg1(B)
          & l1_msualg_1(B)
          & v1_msualg_6(A,B)
          & l3_msualg_1(A,B) ) ) ),
    file(algspec1,d6_algspec1),
    [interesting(0.00)]).

fof(t16_instalg1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => m1_instalg1(A,A) ) ),
    file(instalg1,t16_instalg1),
    [interesting(0.00)]).

fof(d7_algspec1,definition,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m3_algspec1(B)
         => ( m4_algspec1(B,A)
          <=> ? [C] : 
                ( ~ v2_msualg_1(C)
                & m2_algspec1(C,A)
                & v1_msualg_6(B,C)
                & l3_msualg_1(B,C) ) ) ) ) ),
    file(algspec1,d7_algspec1),
    [interesting(0.00)]).

fof(t12_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    [interesting(0.00)]).

fof(d5_msualg_1,definition,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v2_msualg_1(A)
      <=> u1_msualg_1(A) = k1_xboole_0 ) ) ),
    file(msualg_1,d5_msualg_1),
    [interesting(0.00)]).

fof(t13_instalg1,theorem,(
    ! [A] : 
      ( ( v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_instalg1(B,A)
         => ( u2_msualg_1(B) = k2_partfun1(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),u1_msualg_1(B))
            & u3_msualg_1(B) = k2_partfun1(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u1_msualg_1(B)) ) ) ) ),
    file(instalg1,t13_instalg1),
    [interesting(0.00)]).

fof(d18_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( m3_pboole(D,A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => ( v1_funct_1(k1_funct_1(D,E))
                      & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))
                      & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ),
    file(pboole,d18_pboole),
    [interesting(0.00)]).

fof(t60_algspec1,theorem,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & v1_instalg1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v1_instalg1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( l3_msualg_1(C,B)
             => ( m4_algspec1(C,A)
               => ! [D] : 
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ( v1_funct_1(k1_funct_1(u5_msualg_1(B,C),D))
                      & v1_funct_2(k1_funct_1(u5_msualg_1(B,C),D),k1_funct_1(k6_pboole(u1_struct_0(B),u4_msualg_1(B,C)),k1_msualg_1(A,D)),k1_funct_1(u4_msualg_1(B,C),k2_msualg_1(A,D)))
                      & m2_relset_1(k1_funct_1(u5_msualg_1(B,C),D),k1_funct_1(k6_pboole(u1_struct_0(B),u4_msualg_1(B,C)),k1_msualg_1(A,D)),k1_funct_1(u4_msualg_1(B,C),k2_msualg_1(A,D))) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_algspec1,d5_algspec1,t13_instalg1,t11_instalg1,d1_funct_2,d3_pboole,t72_funct_1,t23_funct_1,t72_funct_1,t23_funct_1,d18_pboole]),
    [file(algspec1,t60_algspec1),interesting(0.00)]).

fof(d2_msafree1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ( v1_msafree1(B,A)
          <=> v1_prob_2(u4_msualg_1(A,B)) ) ) ) ),
    file(msafree1,d2_msafree1),
    [interesting(0.00)]).

fof(d3_prob_2,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_prob_2(A)
      <=> ! [B,C] : 
            ( B != C
           => r1_xboole_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ),
    file(prob_2,d3_prob_2),
    [interesting(0.00)]).

fof(t6_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),k2_relat_1(D)) ) ) ) ),
    file(funct_2,t6_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(t65_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k1_relat_1(A) = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) ),
    file(relat_1,t65_relat_1),
    [interesting(0.00)]).

fof(d19_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,k3_finseq_2(A))
         => ( C = k6_pboole(A,B)
          <=> ! [D] : 
                ( m2_finseq_2(D,A,k3_finseq_2(A))
               => k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)) ) ) ) ) ),
    file(pboole,d19_pboole),
    [interesting(0.00)]).

fof(t2_pua2mss1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B) )
         => ( k4_card_3(A) = k4_card_3(B)
           => A = B ) ) ) ),
    file(pua2mss1,t2_pua2mss1),
    [interesting(0.00)]).

fof(t49_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C) )
               => ( ( r1_tarski(k2_relat_1(B),k1_relat_1(A))
                    & r1_tarski(k2_relat_1(C),k1_relat_1(A))
                    & k1_relat_1(B) = k1_relat_1(C)
                    & k5_relat_1(B,A) = k5_relat_1(C,A) )
                 => B = C ) ) ) ) ) ),
    file(funct_1,t49_funct_1),
    [interesting(0.00)]).