fof(t58_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v7_rewrite1(A)
      <=> v9_rewrite1(k17_finseq_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_rewrite1,t21_rewrite1,d8_rewrite1,d22_rewrite1,d7_rewrite1,d7_rewrite1,t22_rewrite1,d24_rewrite1,d22_rewrite1,d8_rewrite1,t21_rewrite1,t16_rewrite1,t39_rewrite1,t37_rewrite1,d7_rewrite1,d7_rewrite1,t22_rewrite1]),
    [file(rewrite1,t58_rewrite1),interesting(1.00)]).

fof(t66_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( m2_rewrite1(B,A)
         => ! [C,D] : 
              ( r2_rewrite1(A,C,D)
            <=> k2_rewrite1(B,C) = k2_rewrite1(B,D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d28_rewrite1,t38_rewrite1,d28_rewrite1,t56_rewrite1,t55_rewrite1,d6_rewrite1,d7_rewrite1]),
    [file(rewrite1,t66_rewrite1),interesting(0.94)]).

fof(t59_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v7_rewrite1(A)
      <=> v6_rewrite1(k17_finseq_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_rewrite1,t21_rewrite1,d8_rewrite1,d22_rewrite1,d7_rewrite1,d9_rewrite1,t21_rewrite1,d21_rewrite1,d22_rewrite1,d8_rewrite1,t21_rewrite1,d9_rewrite1,t45_rewrite1,d7_rewrite1,d7_rewrite1,t22_rewrite1]),
    [file(rewrite1,t59_rewrite1),interesting(0.93)]).

fof(t60_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r13_rewrite1(A,B,C)
         => r2_rewrite1(A,B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d27_rewrite1,t46_rewrite1,t38_rewrite1]),
    [file(rewrite1,t60_rewrite1),interesting(0.93)]).

fof(t38_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( ( r5_rewrite1(A,B,C)
            | r6_rewrite1(A,B,C) )
         => r2_rewrite1(A,B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_rewrite1,t26_rewrite1,t26_rewrite1,t31_rewrite1,d8_rewrite1,t26_rewrite1,t26_rewrite1,t31_rewrite1]),
    [file(rewrite1,t38_rewrite1),interesting(0.90)]).

fof(t22_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
        <=> r1_rewrite1(k17_finseq_1(A),B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_rewrite1,t13_rewrite1,t16_rewrite1,d3_rewrite1,l2_rewrite1,l3_rewrite1,t13_rewrite1,l4_rewrite1,d2_rewrite1,l4_rewrite1,t21_rewrite1,t17_rewrite1,t19_nat_1,s1_nat_1,t6_finseq_5]),
    [file(rewrite1,t22_rewrite1),interesting(0.88)]).

fof(t64_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( m2_rewrite1(B,A)
         => r12_rewrite1(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d26_rewrite1,d28_rewrite1,d23_rewrite1,t38_rewrite1]),
    [file(rewrite1,t64_rewrite1),interesting(0.87)]).

fof(t55_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_rewrite1(A)
        & v4_rewrite1(A) )
     => ! [B] : r4_rewrite1(A,B,k2_rewrite1(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[d14_rewrite1,t47_rewrite1,t54_rewrite1,d12_rewrite1]),
    [file(rewrite1,t55_rewrite1),interesting(0.85)]).

fof(t54_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v4_rewrite1(A) )
     => ! [B,C,D] : 
          ( ( r4_rewrite1(A,B,C)
            & r4_rewrite1(A,B,D) )
         => C = D ) ) ),
    inference(mizar_proof,[status(thm)],[d6_rewrite1,d8_rewrite1,t38_rewrite1,d19_rewrite1]),
    [file(rewrite1,t54_rewrite1),interesting(0.84)]).

fof(t56_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_rewrite1(A)
        & v4_rewrite1(A) )
     => ! [B,C] : 
          ( r2_rewrite1(A,B,C)
         => k2_rewrite1(A,B) = k2_rewrite1(A,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_rewrite1,d6_rewrite1,d6_rewrite1,t26_rewrite1,t31_rewrite1,t31_rewrite1,d19_rewrite1]),
    [file(rewrite1,t56_rewrite1),interesting(0.82)]).

fof(t62_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),B)
               => r13_rewrite1(A,C,D) )
           => r12_rewrite1(A,k2_xboole_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,d3_relat_1,d7_relat_1,d7_relat_1,t13_xboole_1,d26_rewrite1,d4_rewrite1,t23_rewrite1,d4_rewrite1,d3_rewrite1,d4_rewrite1,l2_rewrite1,l3_rewrite1,t27_rewrite1,l4_rewrite1,d2_rewrite1,d2_xboole_0,d7_relat_1,d2_xboole_0,t30_rewrite1,t60_rewrite1,l4_rewrite1,l34_rewrite1,t31_rewrite1,t19_nat_1,s1_nat_1,t6_finseq_5]),
    [file(rewrite1,t62_rewrite1),interesting(0.80)]).

fof(t52_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v7_rewrite1(A)
      <=> ! [B,C,D] : 
            ( ( r1_rewrite1(A,B,C)
              & r2_hidden(k4_tarski(B,D),A) )
           => r5_rewrite1(A,C,D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_rewrite1,d8_rewrite1,d22_rewrite1,d22_rewrite1,d8_rewrite1,d3_rewrite1,t6_finseq_5,d3_rewrite1,d2_rewrite1,t6_finseq_5,l2_rewrite1,l2_rewrite1,t6_finseq_5,t29_nat_1,t18_rewrite1,t37_rewrite1,l3_rewrite1,t38_nat_1,l4_rewrite1,d7_rewrite1,l4_rewrite1,d2_rewrite1,t43_rewrite1,t19_nat_1,s1_nat_1,s1_nat_1]),
    [file(rewrite1,t52_rewrite1),interesting(0.79)]).

fof(t27_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : r2_rewrite1(A,B,B) ) ),
    inference(mizar_proof,[status(thm)],[t13_rewrite1,t26_rewrite1]),
    [file(rewrite1,t27_rewrite1),interesting(0.78)]).

fof(t63_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ? [B] : 
          ( v1_relat_1(B)
          & v10_rewrite1(B)
          & r1_tarski(k3_relat_1(B),k3_relat_1(A))
          & ! [C,D] : 
              ( r2_rewrite1(A,C,D)
            <=> r5_rewrite1(B,C,D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,t27_rewrite1,t28_rewrite1,t39_rewrite1,t40_rewrite1,d1_relat_1,t27_rewrite1,l34_rewrite1,t31_rewrite1,s1_eqrel_1,t30_relat_1,d6_eqrel_1,d6_eqrel_1,d5_eqrel_1,t27_wellord2,s1_relat_1,d3_rewrite1,l2_rewrite1,l3_rewrite1,t27_rewrite1,l4_rewrite1,d2_rewrite1,l4_rewrite1,t31_rewrite1,t19_nat_1,s1_nat_1,t6_finseq_5,d15_rewrite1,t12_eqrel_1,t27_eqrel_1,t28_eqrel_1,d5_eqrel_1,d3_xboole_0,d1_tarski,d24_rewrite1,d7_rewrite1,t12_eqrel_1,t27_eqrel_1,d5_eqrel_1,d3_xboole_0,d1_tarski,t13_rewrite1,d3_tarski,d2_xboole_0,d4_relat_1,d5_relat_1,t27_rewrite1,t39_rewrite1,t33_rewrite1,t28_eqrel_1,d5_eqrel_1,d7_rewrite1,d1_tarski,d3_xboole_0,t27_eqrel_1,t12_eqrel_1,t30_eqrel_1,t13_rewrite1,t16_rewrite1,d7_rewrite1,l34_rewrite1,t31_rewrite1]),
    [file(rewrite1,t63_rewrite1),interesting(0.78)]).

fof(t65_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v10_rewrite1(B) )
         => ( r12_rewrite1(A,B)
           => m2_rewrite1(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d26_rewrite1,d28_rewrite1,d23_rewrite1,t38_rewrite1]),
    [file(rewrite1,t65_rewrite1),interesting(0.78)]).

fof(t17_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C,D] : 
          ( ( r1_rewrite1(A,B,C)
            & r1_rewrite1(A,C,D) )
         => r1_rewrite1(A,B,D) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,d3_rewrite1,d2_rewrite1,t9_rewrite1,d3_rewrite1,t63_finseq_1,t2_rewrite1,t35_finseq_1,t19_nat_1,t25_finseq_1,t38_nat_1,t3_finseq_1,t47_finseq_1,t57_finseq_1,d3_finseq_1,d7_finseq_1,t38_nat_1,t3_finseq_1,d3_finseq_1,d7_finseq_1]),
    [file(rewrite1,t17_rewrite1),interesting(0.77)]).

fof(t57_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v8_rewrite1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v8_rewrite1(B) )
         => ( r11_rewrite1(A,B)
           => v8_rewrite1(k2_xboole_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d22_rewrite1,d8_rewrite1,t7_xboole_1,d3_rewrite1,l2_rewrite1,t37_rewrite1,l3_rewrite1,t38_nat_1,l4_rewrite1,d7_rewrite1,l4_rewrite1,d3_rewrite1,d2_rewrite1,d2_xboole_0,l2_rewrite1,l3_rewrite1,t13_rewrite1,t16_rewrite1,l4_rewrite1,d2_rewrite1,d2_xboole_0,l4_rewrite1,d8_rewrite1,d22_rewrite1,d7_rewrite1,t23_rewrite1,t17_rewrite1,d8_rewrite1,d22_rewrite1,d7_rewrite1,t23_rewrite1,t17_rewrite1,d18_rewrite1,t23_rewrite1,t17_rewrite1,d18_rewrite1,t23_rewrite1,t17_rewrite1,t16_rewrite1,t19_nat_1,s1_nat_1,t6_finseq_5,d7_rewrite1,t23_rewrite1,t17_rewrite1,t19_nat_1,s1_nat_1,t6_finseq_5]),
    [file(rewrite1,t57_rewrite1),interesting(0.77)]).

fof(t50_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v6_rewrite1(A)
       => ! [B,C,D] : 
            ( ( r1_rewrite1(A,B,C)
              & r2_hidden(k4_tarski(B,D),A) )
           => r5_rewrite1(A,C,D) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,t6_finseq_5,l2_rewrite1,t13_rewrite1,l3_rewrite1,t38_nat_1,l4_rewrite1,l4_rewrite1,d2_rewrite1,d21_rewrite1,d9_rewrite1,t13_rewrite1,t16_rewrite1,t17_rewrite1,t16_rewrite1,t17_rewrite1,t19_nat_1,s1_nat_1,d7_rewrite1,t13_rewrite1,t16_rewrite1]),
    [file(rewrite1,t50_rewrite1),interesting(0.76)]).

fof(t43_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C,D] : 
          ( ( ( r1_rewrite1(A,B,C)
              & r5_rewrite1(A,C,D) )
            | ( r5_rewrite1(A,B,C)
              & r1_rewrite1(A,D,C) ) )
         => r5_rewrite1(A,B,D) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_rewrite1,t17_rewrite1,d7_rewrite1,d7_rewrite1,t17_rewrite1,d7_rewrite1]),
    [file(rewrite1,t43_rewrite1),interesting(0.76)]).

fof(t31_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C,D] : 
          ( ( r2_rewrite1(A,B,C)
            & r2_rewrite1(A,C,D) )
         => r2_rewrite1(A,B,D) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_rewrite1,t17_rewrite1,d4_rewrite1]),
    [file(rewrite1,t31_rewrite1),interesting(0.76)]).

fof(t24_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C,D] : 
          ( r1_rewrite1(A,C,D)
        <=> r1_rewrite1(k2_xboole_0(A,k6_relat_1(B)),C,D) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,t23_rewrite1,d3_rewrite1,d2_rewrite1,l4_rewrite1,l2_rewrite1,d2_rewrite1,d2_xboole_0,t16_rewrite1,d10_relat_1,t17_rewrite1,l2_rewrite1,l4_rewrite1,t18_nat_1,t38_nat_1,t13_rewrite1,s1_nat_1]),
    [file(rewrite1,t24_rewrite1),interesting(0.74)]).

fof(t30_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r2_hidden(k4_tarski(B,C),A)
         => r2_rewrite1(A,B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_rewrite1,t26_rewrite1]),
    [file(rewrite1,t30_rewrite1),interesting(0.73)]).

fof(l34_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r2_rewrite1(A,B,C)
         => r2_rewrite1(A,C,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_rewrite1,t25_rewrite1,t40_relat_1,d4_rewrite1]),
    [file(rewrite1,l34_rewrite1),interesting(0.72)]).

fof(t45_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r7_rewrite1(A,B,C)
         => r5_rewrite1(A,B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_rewrite1,d7_rewrite1,t13_rewrite1,t16_rewrite1]),
    [file(rewrite1,t45_rewrite1),interesting(0.72)]).

fof(t46_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r8_rewrite1(A,B,C)
         => r6_rewrite1(A,B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_rewrite1,d8_rewrite1,t13_rewrite1,t16_rewrite1]),
    [file(rewrite1,t46_rewrite1),interesting(0.72)]).

fof(t13_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : r1_rewrite1(A,B,B) ) ),
    inference(mizar_proof,[status(thm)],[t7_rewrite1,d3_rewrite1,t57_finseq_1,t57_finseq_1]),
    [file(rewrite1,t13_rewrite1),interesting(0.71)]).

fof(t26_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
         => ( r2_rewrite1(A,B,C)
            & r2_rewrite1(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,d2_rewrite1,d2_rewrite1,d2_rewrite1,d2_xboole_0,d3_rewrite1,d4_rewrite1,l34_rewrite1]),
    [file(rewrite1,t26_rewrite1),interesting(0.71)]).

fof(t25_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
         => r1_rewrite1(k4_relat_1(A),C,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,t10_rewrite1,d3_rewrite1,t6_finseq_5,d3_finseq_5,d3_finseq_5,d3_finseq_5]),
    [file(rewrite1,t25_rewrite1),interesting(0.70)]).

fof(t44_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C,D] : 
          ( ( ( r1_rewrite1(A,C,B)
              & r6_rewrite1(A,C,D) )
            | ( r6_rewrite1(A,B,C)
              & r1_rewrite1(A,C,D) ) )
         => r6_rewrite1(A,B,D) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_rewrite1,t17_rewrite1,d8_rewrite1,d8_rewrite1,t17_rewrite1,d8_rewrite1]),
    [file(rewrite1,t44_rewrite1),interesting(0.69)]).

fof(t39_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r5_rewrite1(A,B,B)
          & r6_rewrite1(A,B,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_rewrite1,d7_rewrite1,d8_rewrite1]),
    [file(rewrite1,t39_rewrite1),interesting(0.69)]).

fof(t14_rewrite1,theorem,(
    ! [A,B] : 
      ( r1_rewrite1(k1_xboole_0,A,B)
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,d2_rewrite1,l4_rewrite1,l5_rewrite1,d2_rewrite1,t38_nat_1,t1_xreal_1]),
    [file(rewrite1,t14_rewrite1),interesting(0.69)]).

fof(t28_rewrite1,theorem,(
    ! [A,B] : 
      ( r2_rewrite1(k1_xboole_0,A,B)
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[d4_rewrite1,t14_rewrite1]),
    [file(rewrite1,t28_rewrite1),interesting(0.69)]).

fof(t7_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : m1_rewrite1(k9_finseq_1(B),A) ) ),
    inference(mizar_proof,[status(thm)],[t4_finseq_1,t55_finseq_1,t57_finseq_1,d2_rewrite1,d1_tarski]),
    [file(rewrite1,t7_rewrite1),interesting(0.68)]).

fof(t21_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
        <=> ( B = C
            | r2_hidden(k4_tarski(B,C),k17_finseq_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,t19_rewrite1,d2_rewrite1,t38_nat_1,l4_rewrite1,l5_rewrite1,d2_rewrite1,d16_finseq_1,t13_rewrite1,d16_finseq_1,d2_rewrite1,l2_rewrite1,l3_rewrite1,d3_rewrite1]),
    [file(rewrite1,t21_rewrite1),interesting(0.68)]).

fof(t16_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r2_hidden(k4_tarski(B,C),A)
         => r1_rewrite1(A,B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_rewrite1,d3_rewrite1,t61_finseq_1,t61_finseq_1]),
    [file(rewrite1,t16_rewrite1),interesting(0.67)]).

fof(t9_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( m1_rewrite1(B,A)
         => ! [C] : 
              ( m1_rewrite1(C,A)
             => ( k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(C,1)
               => m1_rewrite1(k1_rewrite1(B,C),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rewrite1,d2_rewrite1,d2_rewrite1,t63_finseq_1,t2_rewrite1,t35_finseq_1,t18_nat_1,t10_xreal_1,d2_rewrite1,s1_rewrite1]),
    [file(rewrite1,t9_rewrite1),interesting(0.67)]).

fof(t36_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( ~ r2_hidden(B,k3_relat_1(A))
         => r4_rewrite1(A,B,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_rewrite1,t35_rewrite1,d6_rewrite1]),
    [file(rewrite1,t36_rewrite1),interesting(0.67)]).

fof(t47_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( ~ r2_hidden(B,k3_relat_1(A))
         => r9_rewrite1(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_rewrite1,d11_rewrite1]),
    [file(rewrite1,t47_rewrite1),interesting(0.67)]).

fof(t10_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( m1_rewrite1(B,A)
         => m1_rewrite1(k3_finseq_5(B),k4_relat_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rewrite1,d3_finseq_5,d3_finseq_5,d2_rewrite1,d3_finseq_1,d3_finseq_5,l2_rewrite1,t1_finseq_5,t2_finseq_5,d2_rewrite1,d7_relat_1]),
    [file(rewrite1,t10_rewrite1),interesting(0.66)]).

fof(t40_rewrite1,theorem,(
    ! [A,B] : 
      ( ( r5_rewrite1(k1_xboole_0,A,B)
        | r6_rewrite1(k1_xboole_0,A,B) )
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[d7_rewrite1,t14_rewrite1,d8_rewrite1,t14_rewrite1]),
    [file(rewrite1,t40_rewrite1),interesting(0.65)]).

fof(t23_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => ! [C,D] : 
                ( r1_rewrite1(A,C,D)
               => r1_rewrite1(B,C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,t11_rewrite1,d3_rewrite1]),
    [file(rewrite1,t23_rewrite1),interesting(0.64)]).

fof(t15_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
         => ( r2_hidden(B,k3_relat_1(A))
            | B = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,d2_rewrite1,l4_rewrite1,l5_rewrite1,d2_rewrite1,t30_relat_1,t38_nat_1,t1_xreal_1]),
    [file(rewrite1,t15_rewrite1),interesting(0.64)]).

fof(t32_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r2_rewrite1(A,B,C)
         => r2_rewrite1(A,C,B) ) ) ),
    inference(mizar_proof,[status(thm)],[l34_rewrite1]),
    [file(rewrite1,t32_rewrite1),interesting(0.64)]).

fof(t35_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( ~ r2_hidden(B,k3_relat_1(A))
         => r3_rewrite1(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_rewrite1,t30_relat_1]),
    [file(rewrite1,t35_rewrite1),interesting(0.64)]).

fof(t19_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
         => ( B = C
            | ( r2_hidden(B,k3_relat_1(A))
              & r2_hidden(C,k3_relat_1(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,d2_rewrite1,t38_nat_1,d5_real_1,l4_rewrite1,l5_rewrite1,d2_rewrite1,t30_relat_1,l2_rewrite1,l3_rewrite1,t30_relat_1,l4_rewrite1,d2_rewrite1,t30_relat_1,t19_nat_1,s1_nat_1,t6_finseq_5]),
    [file(rewrite1,t19_rewrite1),interesting(0.63)]).

fof(t11_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => ! [C] : 
                ( m1_rewrite1(C,A)
               => m1_rewrite1(C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_rewrite1,d2_rewrite1,d2_rewrite1]),
    [file(rewrite1,t11_rewrite1),interesting(0.63)]).

fof(t8_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r2_hidden(k4_tarski(B,C),A)
         => m1_rewrite1(k10_finseq_1(B,C),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t61_finseq_1,d3_finseq_1,d2_rewrite1,t61_finseq_1,l2_rewrite1,t8_xreal_1,t1_xreal_1,t61_finseq_1]),
    [file(rewrite1,t8_rewrite1),interesting(0.63)]).

fof(t37_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
         => ( r5_rewrite1(A,B,C)
            & r6_rewrite1(A,B,C)
            & r5_rewrite1(A,C,B)
            & r6_rewrite1(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_rewrite1,d7_rewrite1,d8_rewrite1]),
    [file(rewrite1,t37_rewrite1),interesting(0.63)]).

fof(t33_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r2_rewrite1(A,B,C)
         => ( B = C
            | ( r2_hidden(B,k3_relat_1(A))
              & r2_hidden(C,k3_relat_1(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_rewrite1,t33_relat_1,t38_relat_1,t19_rewrite1]),
    [file(rewrite1,t33_rewrite1),interesting(0.63)]).

fof(t51_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v7_rewrite1(A)
      <=> r11_rewrite1(A,A) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_rewrite1,d8_rewrite1,d22_rewrite1,d7_rewrite1,d18_rewrite1,d22_rewrite1,d8_rewrite1,d7_rewrite1]),
    [file(rewrite1,t51_rewrite1),interesting(0.60)]).

fof(t53_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v9_rewrite1(A)
      <=> r10_rewrite1(A,A) ) ) ),
    inference(mizar_proof,[status(thm)],[d17_rewrite1,d24_rewrite1,d7_rewrite1,d17_rewrite1,d24_rewrite1,d7_rewrite1]),
    [file(rewrite1,t53_rewrite1),interesting(0.60)]).

fof(t49_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r11_rewrite1(A,B)
           => r10_rewrite1(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_rewrite1,d17_rewrite1,t16_rewrite1]),
    [file(rewrite1,t49_rewrite1),interesting(0.59)]).

fof(t61_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ! [B,C] : ~ r13_rewrite1(A,B,C)
       => v9_rewrite1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_rewrite1,d10_rewrite1,d27_rewrite1]),
    [file(rewrite1,t61_rewrite1),interesting(0.58)]).

fof(t34_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( ( r3_rewrite1(A,B)
            & r1_rewrite1(A,B,C) )
         => B = C ) ) ),
    inference(mizar_proof,[status(thm)],[d5_rewrite1,t12_rewrite1,l4_rewrite1,l5_rewrite1,t38_nat_1,t1_xreal_1]),
    [file(rewrite1,t34_rewrite1),interesting(0.57)]).

fof(t41_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r5_rewrite1(A,B,C)
         => r5_rewrite1(A,C,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_rewrite1,d7_rewrite1]),
    [file(rewrite1,t41_rewrite1),interesting(0.57)]).

fof(t42_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r6_rewrite1(A,B,C)
         => r6_rewrite1(A,C,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_rewrite1,d8_rewrite1]),
    [file(rewrite1,t42_rewrite1),interesting(0.57)]).

fof(t20_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
         => ( r2_hidden(B,k3_relat_1(A))
          <=> r2_hidden(C,k3_relat_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_rewrite1]),
    [file(rewrite1,t20_rewrite1),interesting(0.56)]).

fof(t29_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r2_rewrite1(A,B,C)
         => ( r2_hidden(B,k3_relat_1(A))
            | B = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_rewrite1,t33_relat_1,t38_relat_1,t15_rewrite1]),
    [file(rewrite1,t29_rewrite1),interesting(0.55)]).

fof(t48_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_rewrite1(A) )
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(B,A)
           => v1_rewrite1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_relat_1,d16_rewrite1,t1_xboole_1,d16_rewrite1]),
    [file(rewrite1,t48_rewrite1),interesting(0.55)]).

fof(t18_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( m1_rewrite1(B,A)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r2_hidden(C,k4_finseq_1(B))
                      & r2_hidden(D,k4_finseq_1(B))
                      & r1_xreal_0(C,D) )
                   => r1_rewrite1(A,k1_funct_1(B,C),k1_funct_1(B,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_rewrite1,l2_rewrite1,t29_nat_1,l3_rewrite1,t2_xreal_1,l4_rewrite1,d2_rewrite1,l4_rewrite1,t16_rewrite1,t17_rewrite1,s1_nat_1,t28_nat_1]),
    [file(rewrite1,t18_rewrite1),interesting(0.55)]).

fof(t2_rewrite1,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) )
         => ! [C] : 
              ( A != k1_xboole_0
             => k1_rewrite1(k7_finseq_1(B,k9_finseq_1(C)),A) = k7_finseq_1(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_rewrite1,t3_trees_1,t57_finseq_1,t35_finseq_1,t29_nat_1,t21_finseq_1,t64_finseq_1,t35_finseq_1,t25_finseq_1,t47_finseq_1]),
    [file(rewrite1,t2_rewrite1),interesting(0.54)]).

fof(t4_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( A != k1_xboole_0
         => k1_rewrite1(k9_finseq_1(B),A) = A ) ) ),
    inference(mizar_proof,[status(thm)],[t47_finseq_1,t2_rewrite1]),
    [file(rewrite1,t4_rewrite1),interesting(0.53)]).

fof(t1_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k1_rewrite1(k1_xboole_0,A) = A
        & k1_rewrite1(A,k1_xboole_0) = A ) ) ),
    inference(mizar_proof,[status(thm)],[t47_finseq_1,d1_rewrite1]),
    [file(rewrite1,t1_rewrite1),interesting(0.46)]).

fof(t3_rewrite1,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) )
         => ! [C,D] : k1_rewrite1(k7_finseq_1(A,k9_finseq_1(C)),k7_finseq_1(k9_finseq_1(D),B)) = k7_finseq_1(k7_finseq_1(A,k9_finseq_1(D)),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t45_finseq_1,t2_rewrite1]),
    [file(rewrite1,t3_rewrite1),interesting(0.44)]).

fof(s2_rewrite1,theorem,
    ( ( v1_rewrite1(f1_s2_rewrite1)
      & ! [A] : 
          ( ! [B] : 
              ( r2_hidden(k4_tarski(A,B),f1_s2_rewrite1)
             => ( A = B
                | p1_s2_rewrite1(B) ) )
         => p1_s2_rewrite1(A) ) )
   => ! [A] : 
        ( r2_hidden(A,k3_relat_1(f1_s2_rewrite1))
       => p1_s2_rewrite1(A) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d16_rewrite1,t30_relat_1]),
    [file(rewrite1,s2_rewrite1),interesting(0.41)]).

fof(l5_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(k3_finseq_1(A),B)
           => r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_nat_1,t38_nat_1,l4_rewrite1]),
    [file(rewrite1,l5_rewrite1),interesting(0.35)]).

fof(l3_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r2_hidden(k1_nat_1(B,1),k4_finseq_1(A))
              & r1_xreal_0(k3_finseq_1(A),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l2_rewrite1,t38_nat_1]),
    [file(rewrite1,l3_rewrite1),interesting(0.35)]).

fof(l4_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ~ ( ~ r1_xreal_0(B,k3_finseq_1(A))
                  & r1_xreal_0(k3_finseq_1(A),B) )
              & ~ ( ~ r1_xreal_0(1,B)
                  & r1_xreal_0(B,0) )
              & ~ r2_hidden(B,k4_finseq_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_nat_1,t3_finseq_1,d3_finseq_1]),
    [file(rewrite1,l4_rewrite1),interesting(0.32)]).

fof(t5_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ~ ( A != k1_xboole_0
          & ! [B,C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ~ ( A = k7_finseq_1(k9_finseq_1(B),C)
                  & k3_finseq_1(A) = k1_nat_1(k3_finseq_1(C),1) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,t63_finseq_1,t35_finseq_1,t56_finseq_1,t47_finseq_1,t47_finseq_1,t35_finseq_1,t45_finseq_1,t56_finseq_1,s1_nat_1]),
    [file(rewrite1,t5_rewrite1),interesting(0.30)]).

fof(l2_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k4_finseq_1(A))
           => ( r1_xreal_0(B,k3_finseq_1(A))
              & r1_xreal_0(k1_nat_1(0,1),B)
              & ~ r1_xreal_0(B,0) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,t3_finseq_1]),
    [file(rewrite1,l2_rewrite1),interesting(0.27)]).

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(d16_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_rewrite1(A)
      <=> ! [B] : ~ ( r1_tarski(B,k3_relat_1(A))
            & B != k1_xboole_0
            & ! [C] : ~ ( r2_hidden(C,B)
                & ! [D] : ~ ( r2_hidden(D,B)
                    & C != D
                    & r2_hidden(k4_tarski(C,D),A) ) ) ) ) ) ),
    file(rewrite1,d16_rewrite1),
    [interesting(0.00)]).

fof(t30_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k3_relat_1(C))
          & r2_hidden(B,k3_relat_1(C)) ) ) ) ),
    file(relat_1,t30_relat_1),
    [interesting(0.00)]).

fof(t47_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k7_finseq_1(A,k1_xboole_0) = A
        & k7_finseq_1(k1_xboole_0,A) = A ) ) ),
    file(finseq_1,t47_finseq_1),
    [interesting(0.00)]).

fof(d1_rewrite1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( ( A = k1_xboole_0
                    | B = k1_xboole_0 )
                 => ( C = k1_rewrite1(A,B)
                  <=> C = k7_finseq_1(A,B) ) )
                & ~ ( A != k1_xboole_0
                    & B != k1_xboole_0
                    & ~ ( C = k1_rewrite1(A,B)
                      <=> ? [D] : 
                            ( m2_subset_1(D,k1_numbers,k5_numbers)
                            & ? [E] : 
                                ( v1_relat_1(E)
                                & v1_funct_1(E)
                                & v1_finseq_1(E)
                                & k3_finseq_1(A) = k1_nat_1(D,1)
                                & E = k7_relat_1(A,k2_finseq_1(D))
                                & C = k7_finseq_1(E,B) ) ) ) ) ) ) ) ) ),
    file(rewrite1,d1_rewrite1),
    [interesting(0.00)]).

fof(d3_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
        <=> ? [D] : 
              ( m1_rewrite1(D,A)
              & k1_funct_1(D,1) = B
              & k1_funct_1(D,k3_finseq_1(D)) = C ) ) ) ),
    file(rewrite1,d3_rewrite1),
    [interesting(0.00)]).

fof(d2_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( m1_rewrite1(B,A)
          <=> ( ~ r1_xreal_0(k3_finseq_1(B),0)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r2_hidden(C,k4_finseq_1(B))
                      & r2_hidden(k1_nat_1(C,1),k4_finseq_1(B)) )
                   => r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,1))),A) ) ) ) ) ) ) ),
    file(rewrite1,d2_rewrite1),
    [interesting(0.00)]).

fof(t38_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A)
          <=> r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,t38_nat_1),
    [interesting(0.00)]).

fof(d5_real_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
          <=> ~ ( r1_xreal_0(B,A)
                & B != A ) ) ) ) ),
    file(real_1,d5_real_1),
    [interesting(0.00)]).

fof(t3_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(A,k2_finseq_1(B))
          <=> ( r1_xreal_0(1,A)
              & r1_xreal_0(A,B) ) ) ) ) ),
    file(finseq_1,t3_finseq_1),
    [interesting(0.00)]).

fof(d3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k3_finseq_1(A)
          <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ),
    file(finseq_1,d3_finseq_1),
    [interesting(0.00)]).

fof(t29_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,t29_nat_1),
    [interesting(0.00)]).

fof(t19_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( 0 != A
          & r1_xreal_0(A,0) ) ) ),
    file(nat_1,t19_nat_1),
    [interesting(0.00)]).

fof(s1_nat_1,theorem,
    ( ( p1_s1_nat_1(0)
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( p1_s1_nat_1(A)
           => p1_s1_nat_1(k1_nat_1(A,1)) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => p1_s1_nat_1(A) ) ),
    file(nat_1,s1_nat_1),
    [interesting(0.00)]).

fof(t6_finseq_5,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( r2_hidden(1,k4_finseq_1(A))
        & r2_hidden(k3_finseq_1(A),k4_finseq_1(A)) ) ) ),
    file(finseq_5,t6_finseq_5),
    [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(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(t61_finseq_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( C = k10_finseq_1(A,B)
      <=> ( k3_finseq_1(C) = 2
          & k1_funct_1(C,1) = A
          & k1_funct_1(C,2) = B ) ) ) ),
    file(finseq_1,t61_finseq_1),
    [interesting(0.00)]).

fof(t8_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,B)
              <=> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t8_xreal_1),
    [interesting(0.00)]).

fof(t1_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & r1_xreal_0(B,A) )
           => A = B ) ) ) ),
    file(xreal_1,t1_xreal_1),
    [interesting(0.00)]).

fof(d10_relat_1,definition,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( B = k6_relat_1(A)
      <=> ! [C,D] : 
            ( r2_hidden(k4_tarski(C,D),B)
          <=> ( r2_hidden(C,A)
              & C = D ) ) ) ) ),
    file(relat_1,d10_relat_1),
    [interesting(0.00)]).

fof(t63_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ~ ( A != k1_xboole_0
          & ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B)
                & v1_finseq_1(B) )
             => ! [C] : A != k7_finseq_1(B,k9_finseq_1(C)) ) ) ) ),
    file(finseq_1,t63_finseq_1),
    [interesting(0.00)]).

fof(t3_trees_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ~ ( C = k7_relat_1(B,k2_finseq_1(A))
                  & ! [D] : 
                      ( ( v1_relat_1(D)
                        & v1_funct_1(D)
                        & v1_finseq_1(D) )
                     => B != k7_finseq_1(C,D) ) ) ) ) ) ),
    file(trees_1,t3_trees_1),
    [interesting(0.00)]).

fof(t57_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k1_funct_1(B,1) = A ) ) ) ),
    file(finseq_1,t57_finseq_1),
    [interesting(0.00)]).

fof(t35_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(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ),
    file(finseq_1,t35_finseq_1),
    [interesting(0.00)]).

fof(t21_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r1_xreal_0(A,k3_finseq_1(B))
                  & C = k7_relat_1(B,k2_finseq_1(A)) )
               => ( k3_finseq_1(C) = A
                  & k4_finseq_1(C) = k2_finseq_1(A) ) ) ) ) ) ),
    file(finseq_1,t21_finseq_1),
    [interesting(0.00)]).

fof(t64_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) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ~ ( k7_finseq_1(A,B) = k7_finseq_1(C,D)
                      & r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C))
                      & ! [E] : 
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => k7_finseq_1(A,E) != C ) ) ) ) ) ) ),
    file(finseq_1,t64_finseq_1),
    [interesting(0.00)]).

fof(t25_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k3_finseq_1(A) = 0
      <=> A = k1_xboole_0 ) ) ),
    file(finseq_1,t25_finseq_1),
    [interesting(0.00)]).

fof(t18_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => r1_xreal_0(0,A) ) ),
    file(nat_1,t18_nat_1),
    [interesting(0.00)]).

fof(t10_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(B,A)
                      & r1_xreal_0(C,D)
                      & r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) ) ) ) ) ) ),
    file(xreal_1,t10_xreal_1),
    [interesting(0.00)]).

fof(d7_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( C = k7_finseq_1(A,B)
              <=> ( k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)))
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(A))
                       => k1_funct_1(C,D) = k1_funct_1(A,D) ) )
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(B))
                       => k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D) ) ) ) ) ) ) ) ),
    file(finseq_1,d7_finseq_1),
    [interesting(0.00)]).

fof(t28_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => B != k2_xcmplx_0(A,C) ) ) ) ) ),
    file(nat_1,t28_nat_1),
    [interesting(0.00)]).

fof(t9_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ),
    file(xreal_1,t9_xreal_1),
    [interesting(0.00)]).

fof(s1_rewrite1,theorem,
    ( ( ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ( r2_hidden(A,k4_finseq_1(f1_s1_rewrite1))
              & r2_hidden(k1_nat_1(A,1),k4_finseq_1(f1_s1_rewrite1)) )
           => p1_s1_rewrite1(k1_funct_1(f1_s1_rewrite1,A),k1_funct_1(f1_s1_rewrite1,k1_nat_1(A,1))) ) )
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ( r2_hidden(A,k4_finseq_1(f2_s1_rewrite1))
              & r2_hidden(k1_nat_1(A,1),k4_finseq_1(f2_s1_rewrite1)) )
           => p1_s1_rewrite1(k1_funct_1(f2_s1_rewrite1,A),k1_funct_1(f2_s1_rewrite1,k1_nat_1(A,1))) ) )
      & ~ r1_xreal_0(k3_finseq_1(f1_s1_rewrite1),0)
      & ~ r1_xreal_0(k3_finseq_1(f2_s1_rewrite1),0)
      & k1_funct_1(f1_s1_rewrite1,k3_finseq_1(f1_s1_rewrite1)) = k1_funct_1(f2_s1_rewrite1,1) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( ( r2_hidden(A,k4_finseq_1(k1_rewrite1(f1_s1_rewrite1,f2_s1_rewrite1)))
            & r2_hidden(k1_nat_1(A,1),k4_finseq_1(k1_rewrite1(f1_s1_rewrite1,f2_s1_rewrite1))) )
         => ! [B,C] : 
              ( ( B = k1_funct_1(k1_rewrite1(f1_s1_rewrite1,f2_s1_rewrite1),A)
                & C = k1_funct_1(k1_rewrite1(f1_s1_rewrite1,f2_s1_rewrite1),k1_nat_1(A,1)) )
             => p1_s1_rewrite1(B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l2_rewrite1,t29_nat_1,t38_nat_1,t3_finseq_1,d3_finseq_1,t25_finseq_1,t63_finseq_1,t2_rewrite1,t35_finseq_1,t57_finseq_1,l4_rewrite1,l5_rewrite1,t38_nat_1,t3_finseq_1,d3_finseq_1,d7_finseq_1,t3_finseq_1,d3_finseq_1,d7_finseq_1,d5_real_1,d7_finseq_1,t38_nat_1,t28_nat_1,l3_rewrite1,t35_finseq_1,t29_nat_1,t9_xreal_1,l4_rewrite1,l5_rewrite1,d7_finseq_1,t19_nat_1]),
    [file(rewrite1,s1_rewrite1),interesting(0.00)]).

fof(t4_finseq_1,theorem,
    ( k2_finseq_1(0) = k1_xboole_0
    & k2_finseq_1(1) = k1_tarski(1)
    & k2_finseq_1(2) = k2_tarski(1,2) ),
    file(finseq_1,t4_finseq_1),
    [interesting(0.00)]).

fof(t55_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k4_finseq_1(B) = k2_finseq_1(1)
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    file(finseq_1,t55_finseq_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_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r2_rewrite1(A,B,C)
        <=> r1_rewrite1(k2_xboole_0(A,k4_relat_1(A)),B,C) ) ) ),
    file(rewrite1,d4_rewrite1),
    [interesting(0.00)]).

fof(t33_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k3_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k3_relat_1(A),k3_relat_1(B)) ) ) ),
    file(relat_1,t33_relat_1),
    [interesting(0.00)]).

fof(t38_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k3_relat_1(A) = k3_relat_1(k4_relat_1(A)) ) ),
    file(relat_1,t38_relat_1),
    [interesting(0.00)]).

fof(d3_finseq_5,definition,(
    ! [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) )
         => ( B = k3_finseq_5(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(A)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => k1_funct_1(B,C) = k1_funct_1(A,k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(A),C),1)) ) ) ) ) ) ) ),
    file(finseq_5,d3_finseq_5),
    [interesting(0.00)]).

fof(t1_finseq_5,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => m2_subset_1(k2_xcmplx_0(k6_xcmplx_0(B,A),1),k1_numbers,k5_numbers) ) ) ) ),
    file(finseq_5,t1_finseq_5),
    [interesting(0.00)]).

fof(t2_finseq_5,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(A,k2_finseq_1(B))
           => r2_hidden(k2_xcmplx_0(k6_xcmplx_0(B,A),1),k2_finseq_1(B)) ) ) ) ),
    file(finseq_5,t2_finseq_5),
    [interesting(0.00)]).

fof(d7_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( B = k4_relat_1(A)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),B)
              <=> r2_hidden(k4_tarski(D,C),A) ) ) ) ) ),
    file(relat_1,d7_relat_1),
    [interesting(0.00)]).

fof(t40_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k4_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k4_relat_1(A),k4_relat_1(B)) ) ) ),
    file(relat_1,t40_relat_1),
    [interesting(0.00)]).

fof(d5_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r3_rewrite1(A,B)
        <=> ! [C] : ~ r2_hidden(k4_tarski(B,C),A) ) ) ),
    file(rewrite1,d5_rewrite1),
    [interesting(0.00)]).

fof(t12_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
        <=> ? [D] : 
              ( v1_relat_1(D)
              & v1_funct_1(D)
              & v1_finseq_1(D)
              & ~ r1_xreal_0(k3_finseq_1(D),0)
              & k1_funct_1(D,1) = B
              & k1_funct_1(D,k3_finseq_1(D)) = C
              & ! [E] : 
                  ( m2_subset_1(E,k1_numbers,k5_numbers)
                 => ( ( r2_hidden(E,k4_finseq_1(D))
                      & r2_hidden(k1_nat_1(E,1),k4_finseq_1(D)) )
                   => r2_hidden(k4_tarski(k1_funct_1(D,E),k1_funct_1(D,k1_nat_1(E,1))),A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,d2_rewrite1,d2_rewrite1,d3_rewrite1]),
    [file(rewrite1,t12_rewrite1),interesting(0.00)]).

fof(t45_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) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)) ) ) ) ),
    file(finseq_1,t45_finseq_1),
    [interesting(0.00)]).

fof(d7_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r5_rewrite1(A,B,C)
        <=> ? [D] : 
              ( r1_rewrite1(A,B,D)
              & r1_rewrite1(A,C,D) ) ) ) ),
    file(rewrite1,d7_rewrite1),
    [interesting(0.00)]).

fof(d8_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r6_rewrite1(A,B,C)
        <=> ? [D] : 
              ( r1_rewrite1(A,D,B)
              & r1_rewrite1(A,D,C) ) ) ) ),
    file(rewrite1,d8_rewrite1),
    [interesting(0.00)]).

fof(t31_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => r1_tarski(k3_relat_1(A),k3_relat_1(B)) ) ) ) ),
    file(relat_1,t31_relat_1),
    [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(d18_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r11_rewrite1(A,B)
          <=> ! [C,D,E] : ~ ( r1_rewrite1(A,C,D)
                & r1_rewrite1(B,C,E)
                & ! [F] : ~ ( r1_rewrite1(B,D,F)
                    & r1_rewrite1(A,E,F) ) ) ) ) ) ),
    file(rewrite1,d18_rewrite1),
    [interesting(0.00)]).

fof(d17_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r10_rewrite1(A,B)
          <=> ! [C,D,E] : ~ ( r2_hidden(k4_tarski(C,D),A)
                & r2_hidden(k4_tarski(C,E),B)
                & ! [F] : ~ ( r1_rewrite1(B,D,F)
                    & r1_rewrite1(A,E,F) ) ) ) ) ) ),
    file(rewrite1,d17_rewrite1),
    [interesting(0.00)]).

fof(d21_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v6_rewrite1(A)
      <=> ! [B,C,D] : 
            ( ( r2_hidden(k4_tarski(B,C),A)
              & r2_hidden(k4_tarski(B,D),A) )
           => r7_rewrite1(A,C,D) ) ) ) ),
    file(rewrite1,d21_rewrite1),
    [interesting(0.00)]).

fof(d9_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r7_rewrite1(A,B,C)
        <=> ? [D] : 
              ( ( r2_hidden(k4_tarski(B,D),A)
                | B = D )
              & ( r2_hidden(k4_tarski(C,D),A)
                | C = D ) ) ) ) ),
    file(rewrite1,d9_rewrite1),
    [interesting(0.00)]).

fof(d22_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v7_rewrite1(A)
      <=> ! [B,C] : 
            ( r6_rewrite1(A,B,C)
           => r5_rewrite1(A,B,C) ) ) ) ),
    file(rewrite1,d22_rewrite1),
    [interesting(0.00)]).

fof(t2_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(B,C) )
               => r1_xreal_0(A,C) ) ) ) ) ),
    file(xreal_1,t2_xreal_1),
    [interesting(0.00)]).

fof(d24_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v9_rewrite1(A)
      <=> ! [B,C,D] : 
            ( ( r2_hidden(k4_tarski(B,C),A)
              & r2_hidden(k4_tarski(B,D),A) )
           => r5_rewrite1(A,C,D) ) ) ) ),
    file(rewrite1,d24_rewrite1),
    [interesting(0.00)]).

fof(d16_finseq_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( B = k17_finseq_1(A)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),B)
              <=> ( r2_hidden(C,k3_relat_1(A))
                  & r2_hidden(D,k3_relat_1(A))
                  & ? [E] : 
                      ( v1_relat_1(E)
                      & v1_funct_1(E)
                      & v1_finseq_1(E)
                      & r1_xreal_0(1,k3_finseq_1(E))
                      & k1_funct_1(E,1) = C
                      & k1_funct_1(E,k3_finseq_1(E)) = D
                      & ! [F] : 
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(1,F)
                           => ( r1_xreal_0(k3_finseq_1(E),F)
                              | r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,k1_nat_1(F,1))),A) ) ) ) ) ) ) ) ) ) ),
    file(finseq_1,d16_finseq_1),
    [interesting(0.00)]).

fof(t56_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    file(finseq_1,t56_finseq_1),
    [interesting(0.00)]).

fof(d10_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r8_rewrite1(A,B,C)
        <=> ? [D] : 
              ( ( r2_hidden(k4_tarski(D,B),A)
                | B = D )
              & ( r2_hidden(k4_tarski(D,C),A)
                | C = D ) ) ) ) ),
    file(rewrite1,d10_rewrite1),
    [interesting(0.00)]).

fof(d27_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r13_rewrite1(A,B,C)
        <=> ( r8_rewrite1(A,B,C)
            & ~ r5_rewrite1(A,B,C) ) ) ) ),
    file(rewrite1,d27_rewrite1),
    [interesting(0.00)]).

fof(d3_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
               => r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d3_relat_1),
    [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(d26_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r12_rewrite1(A,B)
          <=> ! [C,D] : 
                ( r2_rewrite1(A,C,D)
              <=> r2_rewrite1(B,C,D) ) ) ) ) ),
    file(rewrite1,d26_rewrite1),
    [interesting(0.00)]).

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

fof(d1_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
    <=> ! [B] : ~ ( r2_hidden(B,A)
          & ! [C,D] : B != k4_tarski(C,D) ) ) ),
    file(relat_1,d1_relat_1),
    [interesting(0.00)]).

fof(s1_eqrel_1,theorem,
    ( ( ! [A] : 
          ( r2_hidden(A,f1_s1_eqrel_1)
         => p1_s1_eqrel_1(A,A) )
      & ! [A,B] : 
          ( p1_s1_eqrel_1(A,B)
         => p1_s1_eqrel_1(B,A) )
      & ! [A,B,C] : 
          ( ( p1_s1_eqrel_1(A,B)
            & p1_s1_eqrel_1(B,C) )
         => p1_s1_eqrel_1(A,C) ) )
   => ? [A] : 
        ( v3_relat_2(A)
        & v8_relat_2(A)
        & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1)
        & m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1)
        & ! [B,C] : 
            ( r2_hidden(k4_tarski(B,C),A)
          <=> ( r2_hidden(B,f1_s1_eqrel_1)
              & r2_hidden(C,f1_s1_eqrel_1)
              & p1_s1_eqrel_1(B,C) ) ) ) ),
    file(eqrel_1,s1_eqrel_1),
    [interesting(0.00)]).

fof(d6_eqrel_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( A != k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> ( k5_setfam_1(A,B) = A
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(A))
                 => ( r2_hidden(C,B)
                   => ( C != k1_xboole_0
                      & ! [D] : 
                          ( m1_subset_1(D,k1_zfmisc_1(A))
                         => ~ ( r2_hidden(D,B)
                              & C != D
                              & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) )
        & ( A = k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> B = k1_xboole_0 ) ) ) ) ),
    file(eqrel_1,d6_eqrel_1),
    [interesting(0.00)]).

fof(d5_eqrel_1,definition,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( C = k7_eqrel_1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> ? [E] : 
                      ( r2_hidden(E,A)
                      & D = k6_eqrel_1(A,B,E) ) ) ) ) ) ) ),
    file(eqrel_1,d5_eqrel_1),
    [interesting(0.00)]).

fof(t27_wellord2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ~ ( ! [B] : ~ ( r2_hidden(B,A)
              & B = k1_xboole_0 )
          & ! [B,C] : 
              ( ( r2_hidden(B,A)
                & r2_hidden(C,A) )
             => ( B = C
                | r1_xboole_0(B,C) ) )
          & ! [B] : 
            ? [C] : 
              ( r2_hidden(C,A)
              & ! [D] : k3_xboole_0(B,C) != k1_tarski(D) ) ) ) ),
    file(wellord2,t27_wellord2),
    [interesting(0.00)]).

fof(s1_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & ! [B,C] : 
          ( r2_hidden(k4_tarski(B,C),A)
        <=> ( r2_hidden(B,f1_s1_relat_1)
            & r2_hidden(C,f2_s1_relat_1)
            & p1_s1_relat_1(B,C) ) ) ) ),
    file(relat_1,s1_relat_1),
    [interesting(0.00)]).

fof(d15_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v3_rewrite1(A)
      <=> ! [B] : 
            ( m1_pboole(B,k5_numbers)
           => ~ ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,1))),A) ) ) ) ) ),
    file(rewrite1,d15_rewrite1),
    [interesting(0.00)]).

fof(t12_eqrel_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(k4_tarski(B,C),D)
       => r2_hidden(k4_tarski(C,B),D) ) ) ),
    file(eqrel_1,t12_eqrel_1),
    [interesting(0.00)]).

fof(t27_eqrel_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_2(D)
        & v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(B,k6_eqrel_1(A,D,C))
      <=> r2_hidden(k4_tarski(B,C),D) ) ) ),
    file(eqrel_1,t27_eqrel_1),
    [interesting(0.00)]).

fof(t28_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_2(B)
        & v3_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,k6_eqrel_1(A,B,C)) ) ) ),
    file(eqrel_1,t28_eqrel_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(d4_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k1_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) ),
    file(relat_1,d4_relat_1),
    [interesting(0.00)]).

fof(d5_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(D,C),A) ) ) ) ),
    file(relat_1,d5_relat_1),
    [interesting(0.00)]).

fof(t30_eqrel_1,theorem,(
    ! [A,B,C,D,E] : 
      ( ( v1_relat_2(E)
        & v3_relat_2(E)
        & v8_relat_2(E)
        & v1_partfun1(E,A,A)
        & m2_relset_1(E,A,A) )
     => ( ( r2_hidden(B,k6_eqrel_1(A,E,C))
          & r2_hidden(D,k6_eqrel_1(A,E,C)) )
       => r2_hidden(k4_tarski(B,D),E) ) ) ),
    file(eqrel_1,t30_eqrel_1),
    [interesting(0.00)]).

fof(d28_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v10_rewrite1(B) )
         => ( m2_rewrite1(B,A)
          <=> ! [C,D] : 
                ( r2_rewrite1(A,C,D)
              <=> r5_rewrite1(B,C,D) ) ) ) ) ),
    file(rewrite1,d28_rewrite1),
    [interesting(0.00)]).

fof(d23_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v8_rewrite1(A)
      <=> ! [B,C] : 
            ( r2_rewrite1(A,B,C)
           => r5_rewrite1(A,B,C) ) ) ) ),
    file(rewrite1,d23_rewrite1),
    [interesting(0.00)]).

fof(d14_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_rewrite1(A)
      <=> ! [B] : 
            ( r2_hidden(B,k3_relat_1(A))
           => r9_rewrite1(A,B) ) ) ) ),
    file(rewrite1,d14_rewrite1),
    [interesting(0.00)]).

fof(d6_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r4_rewrite1(A,B,C)
        <=> ( r3_rewrite1(A,C)
            & r1_rewrite1(A,B,C) ) ) ) ),
    file(rewrite1,d6_rewrite1),
    [interesting(0.00)]).

fof(d11_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r9_rewrite1(A,B)
        <=> ? [C] : r4_rewrite1(A,B,C) ) ) ),
    file(rewrite1,d11_rewrite1),
    [interesting(0.00)]).

fof(d19_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v4_rewrite1(A)
      <=> ! [B,C] : 
            ( ( r3_rewrite1(A,B)
              & r3_rewrite1(A,C)
              & r2_rewrite1(A,B,C) )
           => B = C ) ) ) ),
    file(rewrite1,d19_rewrite1),
    [interesting(0.00)]).

fof(d12_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( ( r9_rewrite1(A,B)
            & ! [C,D] : 
                ( ( r4_rewrite1(A,B,C)
                  & r4_rewrite1(A,B,D) )
               => C = D ) )
         => ! [C] : 
              ( C = k2_rewrite1(A,B)
            <=> r4_rewrite1(A,B,C) ) ) ) ),
    file(rewrite1,d12_rewrite1),
    [interesting(0.00)]).

fof(t6_rewrite1,theorem,(
    $true ),
    file(rewrite1,t6_rewrite1),
    [interesting(0.00)]).