fof(t44_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k3_newton(2,A) = k15_rvsum_1(k10_newton(A)) ) ),
    inference(mizar_proof,[status(thm)],[t41_newton,t43_newton]),
    [file(newton,t44_newton),interesting(1.00)]).

fof(t41_newton,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => k2_newton(k2_xcmplx_0(A,B),C) = k15_rvsum_1(k9_newton(A,B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_newton,t103_rvsum_1,t38_newton,d1_xreal_0,t11_newton,t117_rvsum_1,t117_rvsum_1,t35_finseq_1,t57_finseq_1,t6_newton,d4_newton,t110_finseq_2,t109_finseq_2,t35_finseq_1,t57_finseq_1,t6_newton,d4_newton,t110_finseq_2,t109_finseq_2,t104_rvsum_1,t106_rvsum_1,t119_rvsum_1,t109_finseq_2,d4_newton,d3_finseq_1,d3_finseq_1,t3_finseq_1,t18_int_1,d3_finseq_1,d3_finseq_1,d3_finseq_1,t37_nat_1,d1_tarski,t8_xreal_1,d4_newton,d3_finseq_1,t7_newton,d4_finseq_4,d4_finseq_4,t39_newton,d4_finseq_4,d4_finseq_4,d7_finseq_1,t66_rvsum_1,t11_newton,d4_finseq_4,d4_finseq_4,t58_finseq_1,t27_rvsum_1,t39_newton,t38_nat_1,d4_newton,d3_finseq_1,t7_newton,t18_int_1,t11_xreal_1,t18_int_1,t38_nat_1,t38_nat_1,t8_xreal_1,d4_newton,d3_finseq_1,t7_newton,t18_int_1,t11_xreal_1,t18_int_1,d4_finseq_4,d4_finseq_4,d4_finseq_4,d4_finseq_4,d7_finseq_1,t66_rvsum_1,t57_finseq_1,d7_finseq_1,t66_rvsum_1,t26_rvsum_1,d4_newton,t11_newton,d4_newton,t11_newton,t32_newton,d4_newton,d1_tarski,d1_tarski,d4_newton,t6_newton,t6_finseq_1,d4_newton,d3_finseq_1,t7_newton,d4_finseq_4,d4_finseq_4,t40_newton,d4_finseq_4,d4_finseq_4,t59_finseq_1,d4_finseq_4,d4_finseq_4,t56_finseq_1,d7_finseq_1,t66_rvsum_1,t11_newton,t27_rvsum_1,t40_newton,d2_xboole_0,d2_xboole_0,t5_newton,d4_newton,t3_newton,s1_nat_1,d21_ordinal2]),
    [file(newton,t41_newton),interesting(0.93)]).

fof(t33_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( r1_xreal_0(1,A)
       => k8_newton(1,A) = A ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t31_newton,t32_newton,t29_newton,s1_int_2]),
    [file(newton,t33_newton),interesting(0.79)]).

fof(t31_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k8_newton(A,A) = 1 ) ),
    inference(mizar_proof,[status(thm)],[t18_int_1,t30_newton,t29_newton]),
    [file(newton,t31_newton),interesting(0.73)]).

fof(t97_newton,theorem,(
    ~ v1_finset_1(k12_newton) ),
    inference(mizar_proof,[status(thm)],[t77_finseq_1,t21_card_1,t76_finseq_1,d11_card_1,t82_newton,t13_finset_1,t80_card_1,d8_newton,t96_newton,t38_nat_1]),
    [file(newton,t97_newton),interesting(0.73)]).

fof(t35_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => m2_subset_1(k8_newton(B,A),k1_numbers,k5_numbers) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_newton,t27_newton,t22_nat_1,t32_newton,t29_newton,s2_nat_1]),
    [file(newton,t35_newton),interesting(0.71)]).

fof(t50_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r1_xreal_0(A,k11_newton(A)) ) ),
    inference(mizar_proof,[status(thm)],[t21_newton,t19_newton,t66_xreal_1,t46_newton,t39_nat_1,s1_nat_1]),
    [file(newton,t50_newton),interesting(0.71)]).

fof(t79_newton,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(A,k6_int_1(B,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_int_1,d7_int_1,t70_xreal_1,t88_xcmplx_1,t170_real_2,d8_int_1]),
    [file(newton,t79_newton),interesting(0.70)]).

fof(t23_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ r1_xreal_0(k6_newton(A),0) ) ),
    inference(mizar_proof,[status(thm)],[t18_newton,t70_xreal_1,t21_newton,s2_nat_1]),
    [file(newton,t23_newton),interesting(0.70)]).

fof(t43_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k10_newton(A) = k9_newton(1,1,A) ) ),
    inference(mizar_proof,[status(thm)],[d5_newton,d4_newton,d3_finseq_1,d5_newton,d4_newton,d3_finseq_1,t3_finseq_1,t18_int_1,t11_xreal_1,t18_int_1,d4_newton,t15_newton,t15_newton,d5_newton,t3_newton]),
    [file(newton,t43_newton),interesting(0.70)]).

fof(t19_newton,theorem,(
    k6_newton(1) = 1 ),
    inference(mizar_proof,[status(thm)],[t59_finseq_2,t125_rvsum_1]),
    [file(newton,t19_newton),interesting(0.69)]).

fof(t29_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k8_newton(0,A) = 1 ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t23_newton,d3_newton,t18_newton,t60_xcmplx_1]),
    [file(newton,t29_newton),interesting(0.68)]).

fof(t15_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k3_newton(1,A) = 1 ) ),
    inference(mizar_proof,[status(thm)],[t9_newton,t11_newton,s2_nat_1]),
    [file(newton,t15_newton),interesting(0.68)]).

fof(t10_newton,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => k2_newton(A,1) = A ) ),
    inference(mizar_proof,[status(thm)],[d1_xreal_0,t73_finseq_2,t125_rvsum_1]),
    [file(newton,t10_newton),interesting(0.67)]).

fof(t78_newton,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( r1_xreal_0(0,A)
           => r1_xreal_0(0,k6_int_1(B,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_int_1,d7_int_1,t66_xreal_1,t88_xcmplx_1,t50_xreal_1,d8_int_1,d8_int_1]),
    [file(newton,t78_newton),interesting(0.67)]).

fof(t27_newton,theorem,(
    k8_newton(0,0) = 1 ),
    inference(mizar_proof,[status(thm)],[d3_newton,t18_newton]),
    [file(newton,t27_newton),interesting(0.67)]).

fof(t18_newton,theorem,(
    k6_newton(0) = 1 ),
    inference(mizar_proof,[status(thm)],[t58_finseq_2,t124_rvsum_1]),
    [file(newton,t18_newton),interesting(0.66)]).

fof(t67_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k6_nat_1(A,k5_nat_1(A,B)) = A ) ) ),
    inference(mizar_proof,[status(thm)],[d4_nat_1,t62_newton]),
    [file(newton,t67_newton),interesting(0.65)]).

fof(t66_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k5_nat_1(k6_nat_1(A,B),B) = B ) ) ),
    inference(mizar_proof,[status(thm)],[d5_nat_1,t57_newton]),
    [file(newton,t66_newton),interesting(0.65)]).

fof(t88_newton,theorem,(
    a_0_0_newton = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[l93_newton,d5_int_2]),
    [file(newton,t88_newton),interesting(0.65)]).

fof(t91_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => v1_finset_1(a_1_2_newton(A)) ) ),
    inference(mizar_proof,[status(thm)],[t90_newton,t13_finset_1]),
    [file(newton,t91_newton),interesting(0.65)]).

fof(t25_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => k3_xcmplx_0(k6_newton(A),k6_newton(B)) != 0 ) ) ),
    inference(mizar_proof,[status(thm)],[t23_newton,t6_xcmplx_1]),
    [file(newton,t25_newton),interesting(0.64)]).

fof(t32_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => k8_newton(k2_xcmplx_0(B,1),k2_xcmplx_0(A,1)) = k2_xcmplx_0(k8_newton(k2_xcmplx_0(B,1),A),k8_newton(B,A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_int_1,t38_nat_1,t18_int_1,d3_newton,t25_newton,t23_newton,t23_newton,d3_newton,t117_xcmplx_1,t21_newton,t92_xcmplx_1,t21_newton,t92_xcmplx_1,t21_newton,t8_xreal_1,t18_int_1,d3_newton,t38_nat_1,t31_newton,d3_newton,t10_xreal_1,d3_newton,d5_real_1]),
    [file(newton,t32_newton),interesting(0.64)]).

fof(t9_newton,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => k2_newton(A,0) = 1 ) ),
    inference(mizar_proof,[status(thm)],[t72_finseq_2,t124_rvsum_1]),
    [file(newton,t9_newton),interesting(0.63)]).

fof(t34_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ( r1_xreal_0(1,A)
              & B = k6_xcmplx_0(A,1) )
           => k8_newton(B,A) = A ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_newton,t33_newton]),
    [file(newton,t34_newton),interesting(0.63)]).

fof(t38_newton,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => k9_newton(A,B,0) = k12_finseq_1(k5_numbers,1) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_newton,t4_finseq_1,d3_finseq_1,d1_tarski,d1_tarski,d1_tarski,t18_int_1,d4_newton,t31_newton,t9_newton,t9_newton,t57_finseq_1]),
    [file(newton,t38_newton),interesting(0.63)]).

fof(t84_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r1_tarski(k13_newton(A),k2_finseq_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d7_newton,d5_int_2]),
    [file(newton,t84_newton),interesting(0.63)]).

fof(t86_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ? [B] : 
          ( v1_int_2(B)
          & m2_subset_1(B,k1_numbers,k5_numbers)
          & v1_int_2(B)
          & ~ r1_xreal_0(B,A) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_int_2,t50_newton,t2_xreal_1,t9_xreal_1,t48_int_2,d5_int_2,d5_int_2,t55_newton,l93_newton]),
    [file(newton,t86_newton),interesting(0.63)]).

fof(t82_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r1_tarski(k13_newton(A),k12_newton) ) ),
    inference(mizar_proof,[status(thm)],[d7_newton,d6_newton,d3_tarski]),
    [file(newton,t82_newton),interesting(0.63)]).

fof(t101_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( k5_int_1(A,B) = k3_nat_1(A,B)
            & k6_int_1(A,B) = k4_nat_1(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_nat_1,t80_newton,t78_newton,t16_int_1,t82_int_1,t16_int_1,t46_nat_1,t79_newton,t43_nat_1,t75_int_1,d1_nat_1,d8_int_1,d2_nat_1]),
    [file(newton,t101_newton),interesting(0.62)]).

fof(t30_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r1_xreal_0(B,A)
           => ! [C] : 
                ( v4_ordinal2(C)
               => ( C = k6_xcmplx_0(A,B)
                 => k8_newton(B,A) = k8_newton(C,A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_xreal_1,t26_xreal_1,d3_newton,d3_newton]),
    [file(newton,t30_newton),interesting(0.62)]).

fof(l107_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( v1_int_2(A)
          & r1_xreal_0(A,0) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_int_2]),
    [file(newton,l107_newton),interesting(0.62)]).

fof(t39_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => k1_funct_1(k9_newton(B,C,A),1) = k2_newton(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_int_1,d4_newton,d3_finseq_1,t8_xreal_1,d4_newton,t29_newton,t9_newton]),
    [file(newton,t39_newton),interesting(0.61)]).

fof(t62_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_nat_1(A,B)
           => k6_nat_1(A,B) = A ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_nat_1,d5_nat_1,t52_nat_1]),
    [file(newton,t62_newton),interesting(0.61)]).

fof(t57_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_nat_1(A,B)
          <=> k5_nat_1(A,B) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_nat_1,d4_nat_1,t52_nat_1,d4_nat_1]),
    [file(newton,t57_newton),interesting(0.61)]).

fof(t60_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r1_nat_1(k5_nat_1(A,B),k2_nat_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t56_nat_1,t56_nat_1,d4_nat_1]),
    [file(newton,t60_newton),interesting(0.61)]).

fof(t90_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r1_tarski(a_1_2_newton(A),k2_finseq_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[d5_int_2,d3_tarski]),
    [file(newton,t90_newton),interesting(0.61)]).

fof(t49_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ r1_xreal_0(1,k7_xcmplx_0(A,k1_nat_1(A,1))) ) ),
    inference(mizar_proof,[status(thm)],[t31_xreal_1,t142_real_2,s1_nat_1]),
    [file(newton,t49_newton),interesting(0.60)]).

fof(t47_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( A != 0
       => r1_nat_1(A,k11_newton(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_nat_1,t21_newton,d3_nat_1]),
    [file(newton,t47_newton),interesting(0.60)]).

fof(t87_newton,theorem,(
    k12_newton != k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d6_newton,t44_int_2]),
    [file(newton,t87_newton),interesting(0.60)]).

fof(t20_newton,theorem,(
    k6_newton(2) = 2 ),
    inference(mizar_proof,[status(thm)],[t61_finseq_2,t129_rvsum_1]),
    [file(newton,t20_newton),interesting(0.59)]).

fof(t6_newton,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( m2_finseq_1(B,k1_numbers)
         => k3_finseq_1(k9_rvsum_1(A,B)) = k3_finseq_1(B) ) ) ),
    inference(mizar_proof,[status(thm)],[t110_finseq_2,t109_finseq_2]),
    [file(newton,t6_newton),interesting(0.59)]).

fof(t40_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => k1_funct_1(k9_newton(B,C,A),k2_xcmplx_0(A,1)) = k2_newton(C,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_nat_1,t18_int_1,t18_int_1,d4_newton,d3_finseq_1,t6_finseq_1,d4_newton,t31_newton,t9_newton]),
    [file(newton,t40_newton),interesting(0.59)]).

fof(t45_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(1,A)
           => r1_xreal_0(B,k2_nat_1(B,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_xreal_1,t9_xreal_1,t2_xreal_1,s1_nat_1]),
    [file(newton,t45_newton),interesting(0.59)]).

fof(t11_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => k2_newton(B,k2_xcmplx_0(A,1)) = k3_xcmplx_0(k2_newton(B,A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xreal_0,t73_finseq_2,t125_rvsum_1,t9_newton,d1_xreal_0,d21_ordinal2,t74_finseq_2,t126_rvsum_1,s2_nat_1]),
    [file(newton,t11_newton),interesting(0.58)]).

fof(t21_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k6_newton(k2_xcmplx_0(A,1)) = k3_xcmplx_0(k6_newton(A),k2_xcmplx_0(A,1)) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t60_finseq_2,t126_rvsum_1]),
    [file(newton,t21_newton),interesting(0.58)]).

fof(t85_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => v1_finset_1(k13_newton(A)) ) ),
    inference(mizar_proof,[status(thm)],[t84_newton,t13_finset_1]),
    [file(newton,t85_newton),interesting(0.58)]).

fof(t96_newton,theorem,(
    ! [A] : 
      ( ( v1_int_2(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => k13_newton(A) = a_1_1_newton(A) ) ),
    inference(mizar_proof,[status(thm)],[d7_newton,d7_newton,t2_tarski]),
    [file(newton,t96_newton),interesting(0.58)]).

fof(t22_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => m2_subset_1(k6_newton(A),k1_numbers,k5_numbers) ) ),
    inference(mizar_proof,[status(thm)],[t58_finseq_2,t124_rvsum_1,t21_newton,d21_ordinal2,s2_nat_1]),
    [file(newton,t22_newton),interesting(0.57)]).

fof(t51_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( A != 1
              & r1_nat_1(A,B)
              & r1_nat_1(A,k1_nat_1(B,1)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_nat_1,d3_nat_1,t90_xcmplx_1,t75_xcmplx_1,t49_newton,t145_real_2,t18_int_1,t40_nat_1]),
    [file(newton,t51_newton),interesting(0.57)]).

fof(t80_newton,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( A != 0
           => B = k2_xcmplx_0(k3_xcmplx_0(k5_int_1(B,A),A),k6_int_1(B,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_int_1]),
    [file(newton,t80_newton),interesting(0.56)]).

fof(t59_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k5_nat_1(A,1) = A ) ),
    inference(mizar_proof,[status(thm)],[d4_nat_1,t53_nat_1,d4_nat_1,t52_nat_1]),
    [file(newton,t59_newton),interesting(0.56)]).

fof(t65_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k6_nat_1(A,0) = A ) ),
    inference(mizar_proof,[status(thm)],[t53_nat_1,d5_nat_1,d5_nat_1,t52_nat_1]),
    [file(newton,t65_newton),interesting(0.56)]).

fof(t76_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r1_nat_1(k6_nat_1(A,B),k5_nat_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_nat_1,d4_nat_1,t51_nat_1]),
    [file(newton,t76_newton),interesting(0.55)]).

fof(t46_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(1,A)
                  & r1_xreal_0(k2_nat_1(C,A),B) )
               => r1_xreal_0(C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t45_newton,t2_xreal_1]),
    [file(newton,t46_newton),interesting(0.55)]).

fof(t53_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B != 0
           => r1_nat_1(B,k11_newton(k1_nat_1(B,A))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_newton,t56_nat_1,t21_newton,s1_nat_1]),
    [file(newton,t53_newton),interesting(0.55)]).

fof(t54_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(B,A)
           => ( B = 0
              | r1_nat_1(B,k11_newton(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t28_nat_1,t53_newton]),
    [file(newton,t54_newton),interesting(0.55)]).

fof(t64_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k6_nat_1(A,1) = 1 ) ),
    inference(mizar_proof,[status(thm)],[d5_nat_1,t53_nat_1,t52_nat_1]),
    [file(newton,t64_newton),interesting(0.54)]).

fof(l93_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( A != 0
          & A != 1
          & ~ r1_xreal_0(2,A) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_cqc_the1,t38_nat_1]),
    [file(newton,l93_newton),interesting(0.54)]).

fof(t16_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( r1_xreal_0(1,A)
       => k3_newton(0,A) = 0 ) ) ),
    inference(mizar_proof,[status(thm)],[d21_ordinal2,t10_newton,t11_newton,s1_int_2]),
    [file(newton,t16_newton),interesting(0.53)]).

fof(t99_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => m2_subset_1(k3_newton(B,A),k1_numbers,k5_numbers) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_newton,t11_newton,s1_nat_1]),
    [file(newton,t99_newton),interesting(0.53)]).

fof(t68_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k6_nat_1(A,k5_nat_1(A,B)) = k5_nat_1(k6_nat_1(B,A),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t67_newton,t66_newton]),
    [file(newton,t68_newton),interesting(0.52)]).

fof(t14_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => k2_newton(k2_newton(C,A),B) = k2_newton(C,k3_xcmplx_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xreal_0,d21_ordinal2,t135_rvsum_1]),
    [file(newton,t14_newton),interesting(0.51)]).

fof(t7_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( m2_finseq_1(C,k1_numbers)
             => ( r2_hidden(A,k4_finseq_1(C))
              <=> r2_hidden(A,k4_finseq_1(k9_rvsum_1(B,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_newton,t31_finseq_3]),
    [file(newton,t7_newton),interesting(0.51)]).

fof(t12_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => k2_newton(k3_xcmplx_0(B,C),A) = k3_xcmplx_0(k2_newton(B,A),k2_newton(C,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xreal_0,d21_ordinal2,t136_rvsum_1]),
    [file(newton,t12_newton),interesting(0.49)]).

fof(t89_newton,theorem,(
    ! [A] : 
      ( ( v1_int_2(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => r1_tarski(a_1_1_newton(A),k5_numbers) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski]),
    [file(newton,t89_newton),interesting(0.49)]).

fof(t98_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( v1_int_2(A)
       => ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ ( r1_nat_1(A,k2_nat_1(B,C))
                    & ~ r1_nat_1(A,B)
                    & ~ r1_nat_1(A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s5_nat_1,s5_nat_1,l107_newton,t46_nat_1,t2_xreal_1,d3_nat_1,t47_nat_1,d3_nat_1,t47_nat_1,t57_nat_1,t55_nat_1,t48_int_2,d5_int_2,d5_int_2,t54_nat_1,t2_xreal_1,d5_int_2,d5_int_2,t54_nat_1,d3_nat_1,t56_nat_1,d3_nat_1,d3_nat_1,d3_nat_1,t54_nat_1,t70_xreal_1,d5_real_1,t5_xcmplx_1,d3_nat_1,t56_nat_1,t38_nat_1,t27_nat_1]),
    [file(newton,t98_newton),interesting(0.49)]).

fof(t100_newton,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( k2_newton(A,2) = k3_xcmplx_0(A,A)
        & k5_square_1(A) = k2_newton(A,2) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_newton,t11_newton]),
    [file(newton,t100_newton),interesting(0.48)]).

fof(t55_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( B != 1
              & B != 0
              & r1_nat_1(B,k1_nat_1(k11_newton(A),1))
              & r1_xreal_0(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t51_newton,t54_newton]),
    [file(newton,t55_newton),interesting(0.48)]).

fof(t13_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => k2_newton(C,k2_xcmplx_0(A,B)) = k3_xcmplx_0(k2_newton(C,A),k2_newton(C,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xreal_0,d21_ordinal2,t134_rvsum_1]),
    [file(newton,t13_newton),interesting(0.47)]).

fof(t5_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(1,A)
       => k2_finseq_1(A) = k2_xboole_0(k2_xboole_0(k1_tarski(1),a_1_0_newton(A)),k1_tarski(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t3_finseq_1,d5_real_1,d1_tarski,d2_xboole_0,d2_xboole_0,t4_finseq_1,d2_xboole_0,d5_real_1,d1_tarski,d1_tarski,t5_finseq_1,d2_xboole_0,d2_xboole_0,d3_tarski,d10_xboole_0]),
    [file(newton,t5_newton),interesting(0.47)]).

fof(t56_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k5_nat_1(A,k5_nat_1(B,C)) = k5_nat_1(k5_nat_1(A,B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_nat_1,d4_nat_1,d4_nat_1,d4_nat_1,t51_nat_1,t51_nat_1,d4_nat_1,d4_nat_1,t51_nat_1,t51_nat_1,d4_nat_1,d4_nat_1,t52_nat_1]),
    [file(newton,t56_newton),interesting(0.47)]).

fof(t58_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_nat_1(A,B)
                  & r1_nat_1(C,B) )
              <=> r1_nat_1(k5_nat_1(A,C),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_nat_1,t51_nat_1,d4_nat_1]),
    [file(newton,t58_newton),interesting(0.47)]).

fof(t61_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k6_nat_1(A,k6_nat_1(B,C)) = k6_nat_1(k6_nat_1(A,B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_nat_1,d5_nat_1,d5_nat_1,d5_nat_1,t51_nat_1,d5_nat_1,t51_nat_1,d5_nat_1,d5_nat_1,t51_nat_1,t51_nat_1,d5_nat_1,d5_nat_1,t52_nat_1]),
    [file(newton,t61_newton),interesting(0.47)]).

fof(t63_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_nat_1(A,B)
                  & r1_nat_1(A,C) )
              <=> r1_nat_1(A,k6_nat_1(B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_nat_1,t51_nat_1,d5_nat_1]),
    [file(newton,t63_newton),interesting(0.47)]).

fof(t69_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_nat_1(A,B)
               => r1_nat_1(k6_nat_1(A,C),k6_nat_1(B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_nat_1,t51_nat_1,d5_nat_1]),
    [file(newton,t69_newton),interesting(0.47)]).

fof(t70_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_nat_1(A,B)
               => r1_nat_1(k6_nat_1(C,A),k6_nat_1(C,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_nat_1,t51_nat_1,d5_nat_1]),
    [file(newton,t70_newton),interesting(0.47)]).

fof(t71_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(k6_nat_1(A,B),0) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_nat_1,d3_nat_1]),
    [file(newton,t71_newton),interesting(0.47)]).

fof(t93_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => v1_finset_1(k2_xboole_0(a_1_2_newton(A),k1_tarski(A))) ) ),
    inference(mizar_proof,[status(thm)],[t91_newton,t14_finset_1]),
    [file(newton,t93_newton),interesting(0.47)]).

fof(t52_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_nat_1(B,A)
              & r1_nat_1(B,k1_nat_1(A,1)) )
          <=> B = 1 ) ) ) ),
    inference(mizar_proof,[status(thm)],[t51_newton,t53_nat_1]),
    [file(newton,t52_newton),interesting(0.46)]).

fof(t73_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ~ r1_xreal_0(A,0)
              & ~ r1_xreal_0(B,0)
              & r1_xreal_0(k5_nat_1(A,B),0) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t60_newton,d3_nat_1,t122_real_2]),
    [file(newton,t73_newton),interesting(0.46)]).

fof(t83_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(B,A)
           => r1_tarski(k13_newton(A),k13_newton(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_newton,t2_xreal_1,d7_newton,d3_tarski]),
    [file(newton,t83_newton),interesting(0.46)]).

fof(t48_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( A != 0
          & r1_xreal_0(k7_xcmplx_0(k1_nat_1(A,1),A),1) ) ) ),
    inference(mizar_proof,[status(thm)],[t63_xcmplx_1,t60_xcmplx_1,t127_real_2,t31_xreal_1]),
    [file(newton,t48_newton),interesting(0.43)]).

fof(t3_newton,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( k3_finseq_1(A) = k3_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(A))
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,d3_finseq_1,t17_finseq_1]),
    [file(newton,t3_newton),interesting(0.37)]).

fof(t94_newton,theorem,(
    ! [A] : 
      ( ( v1_int_2(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] : 
          ( ( v1_int_2(B)
            & m2_subset_1(B,k1_numbers,k5_numbers) )
         => ( ~ r1_xreal_0(B,A)
           => r1_tarski(k2_xboole_0(a_1_1_newton(A),k1_tarski(A)),a_1_1_newton(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_xreal_1,d1_tarski,d2_xboole_0,d3_tarski]),
    [file(newton,t94_newton),interesting(0.32)]).

fof(t81_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ~ ( r1_xreal_0(A,0)
                  & r1_xreal_0(B,0) )
              & ! [C] : 
                  ( v1_int_1(C)
                 => ! [D] : 
                      ( v1_int_1(D)
                     => k2_xcmplx_0(k3_xcmplx_0(C,A),k3_xcmplx_0(D,B)) != k6_nat_1(A,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s5_nat_1,t42_nat_1,d3_nat_1,d3_nat_1,d3_nat_1,d9_int_1,d1_absvalue,t21_int_2,d5_nat_1]),
    [file(newton,t81_newton),interesting(0.28)]).

fof(t77_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(B,0)
           => k4_nat_1(A,B) = k6_xcmplx_0(A,k2_nat_1(B,k3_nat_1(A,B))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_nat_1]),
    [file(newton,t77_newton),interesting(0.26)]).

fof(d1_xreal_0,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
    <=> r2_hidden(A,k1_numbers) ) ),
    file(xreal_0,d1_xreal_0),
    [interesting(0.00)]).

fof(t73_finseq_2,theorem,(
    ! [A] : k2_finseq_2(1,A) = k9_finseq_1(A) ),
    file(finseq_2,t73_finseq_2),
    [interesting(0.00)]).

fof(t125_rvsum_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => k16_rvsum_1(k12_finseq_1(k1_numbers,A)) = A ) ),
    file(rvsum_1,t125_rvsum_1),
    [interesting(0.00)]).

fof(t72_finseq_2,theorem,(
    ! [A] : k2_finseq_2(0,A) = k1_xboole_0 ),
    file(finseq_2,t72_finseq_2),
    [interesting(0.00)]).

fof(t124_rvsum_1,theorem,(
    k16_rvsum_1(k6_finseq_1(k1_numbers)) = 1 ),
    file(rvsum_1,t124_rvsum_1),
    [interesting(0.00)]).

fof(d21_ordinal2,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
    <=> r2_hidden(A,k5_ordinal2) ) ),
    file(ordinal2,d21_ordinal2),
    [interesting(0.00)]).

fof(t74_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : k2_finseq_2(k1_nat_1(A,1),B) = k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B)) ) ),
    file(finseq_2,t74_finseq_2),
    [interesting(0.00)]).

fof(t126_rvsum_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m2_finseq_1(B,k1_numbers)
         => k16_rvsum_1(k8_finseq_1(k1_numbers,B,k12_finseq_1(k1_numbers,A))) = k11_binop_2(k16_rvsum_1(B),A) ) ) ),
    file(rvsum_1,t126_rvsum_1),
    [interesting(0.00)]).

fof(s2_nat_1,theorem,
    ( ( p1_s2_nat_1(0)
      & ! [A] : 
          ( v4_ordinal2(A)
         => ( p1_s2_nat_1(A)
           => p1_s2_nat_1(k2_xcmplx_0(A,1)) ) ) )
   => ! [A] : 
        ( v4_ordinal2(A)
       => p1_s2_nat_1(A) ) ),
    file(nat_1,s2_nat_1),
    [interesting(0.00)]).

fof(t47_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(A,0)
           => B = k2_xcmplx_0(k3_xcmplx_0(A,k3_nat_1(B,A)),k4_nat_1(B,A)) ) ) ) ),
    file(nat_1,t47_nat_1),
    [interesting(0.00)]).

fof(d8_int_1,definition,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( ( B != 0
             => k6_int_1(A,B) = k6_xcmplx_0(A,k3_xcmplx_0(k5_int_1(A,B),B)) )
            & ( B = 0
             => k6_int_1(A,B) = 0 ) ) ) ) ),
    file(int_1,d8_int_1),
    [interesting(0.00)]).

fof(d4_int_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( B = k1_int_1(A)
          <=> ( r1_xreal_0(B,A)
              & ~ r1_xreal_0(B,k6_xcmplx_0(A,1)) ) ) ) ) ),
    file(int_1,d4_int_1),
    [interesting(0.00)]).

fof(d7_int_1,definition,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => k5_int_1(A,B) = k1_int_1(k7_xcmplx_0(A,B)) ) ) ),
    file(int_1,d7_int_1),
    [interesting(0.00)]).

fof(t66_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(0,C) )
               => r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t66_xreal_1),
    [interesting(0.00)]).

fof(t88_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ( A != 0
           => k3_xcmplx_0(k7_xcmplx_0(B,A),A) = B ) ) ) ),
    file(xcmplx_1,t88_xcmplx_1),
    [interesting(0.00)]).

fof(t50_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => r1_xreal_0(0,k6_xcmplx_0(B,A)) ) ) ) ),
    file(xreal_1,t50_xreal_1),
    [interesting(0.00)]).

fof(t16_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( r1_xreal_0(0,A)
       => r2_hidden(A,k5_numbers) ) ) ),
    file(int_1,t16_int_1),
    [interesting(0.00)]).

fof(t82_int_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => r1_xreal_0(0,k5_int_1(A,B)) ) ) ),
    file(int_1,t82_int_1),
    [interesting(0.00)]).

fof(t46_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(A,k4_nat_1(B,A)) ) ) ) ),
    file(nat_1,t46_nat_1),
    [interesting(0.00)]).

fof(t70_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(A,0)
                  & ~ r1_xreal_0(C,B)
                  & r1_xreal_0(k3_xcmplx_0(C,A),k3_xcmplx_0(B,A)) ) ) ) ) ),
    file(xreal_1,t70_xreal_1),
    [interesting(0.00)]).

fof(t170_real_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ( ~ r1_xreal_0(k6_xcmplx_0(C,D),k6_xcmplx_0(A,B))
                   => ( ~ r1_xreal_0(k2_xcmplx_0(C,B),k2_xcmplx_0(A,D))
                      & ~ r1_xreal_0(k6_xcmplx_0(B,D),k6_xcmplx_0(A,C))
                      & ~ r1_xreal_0(k6_xcmplx_0(C,A),k6_xcmplx_0(D,B))
                      & ~ r1_xreal_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C)) ) ) ) ) ) ) ),
    file(real_2,t170_real_2),
    [interesting(0.00)]).

fof(t43_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ! [D] : 
                  ( v4_ordinal2(D)
                 => ! [E] : 
                      ( v4_ordinal2(E)
                     => ! [F] : 
                          ( v4_ordinal2(F)
                         => ( ( A = k2_xcmplx_0(k3_xcmplx_0(B,C),E)
                              & A = k2_xcmplx_0(k3_xcmplx_0(B,D),F) )
                           => ( r1_xreal_0(B,E)
                              | r1_xreal_0(B,F)
                              | ( C = D
                                & E = F ) ) ) ) ) ) ) ) ) ),
    file(nat_1,t43_nat_1),
    [interesting(0.00)]).

fof(t75_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => k5_int_1(A,0) = 0 ) ),
    file(int_1,t75_int_1),
    [interesting(0.00)]).

fof(d1_nat_1,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( C = k3_nat_1(A,B)
              <=> ~ ( ! [D] : 
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ~ ( A = k2_xcmplx_0(k3_xcmplx_0(B,C),D)
                            & ~ r1_xreal_0(B,D) ) )
                    & ~ ( C = 0
                        & B = 0 ) ) ) ) ) ) ),
    file(nat_1,d1_nat_1),
    [interesting(0.00)]).

fof(d2_nat_1,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( C = k4_nat_1(A,B)
              <=> ~ ( ! [D] : 
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ~ ( A = k2_xcmplx_0(k3_xcmplx_0(B,D),C)
                            & ~ r1_xreal_0(B,C) ) )
                    & ~ ( C = 0
                        & B = 0 ) ) ) ) ) ) ),
    file(nat_1,d2_nat_1),
    [interesting(0.00)]).

fof(t136_rvsum_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => k16_rvsum_1(k4_finseqop(k1_numbers,A,k11_binop_2(B,C))) = k11_binop_2(k16_rvsum_1(k4_finseqop(k1_numbers,A,B)),k16_rvsum_1(k4_finseqop(k1_numbers,A,C))) ) ) ) ),
    file(rvsum_1,t136_rvsum_1),
    [interesting(0.00)]).

fof(t134_rvsum_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => k16_rvsum_1(k4_finseqop(k1_numbers,k23_binop_2(A,B),C)) = k11_binop_2(k16_rvsum_1(k4_finseqop(k1_numbers,A,C)),k16_rvsum_1(k4_finseqop(k1_numbers,B,C))) ) ) ) ),
    file(rvsum_1,t134_rvsum_1),
    [interesting(0.00)]).

fof(t135_rvsum_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => k16_rvsum_1(k4_finseqop(k1_numbers,k24_binop_2(A,B),C)) = k16_rvsum_1(k4_finseqop(k1_numbers,B,k16_rvsum_1(k4_finseqop(k1_numbers,A,C)))) ) ) ) ),
    file(rvsum_1,t135_rvsum_1),
    [interesting(0.00)]).

fof(s1_int_2,theorem,
    ( ( p1_s1_int_2(f1_s1_int_2)
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(f1_s1_int_2,A)
              & p1_s1_int_2(A) )
           => p1_s1_int_2(k1_nat_1(A,1)) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r1_xreal_0(f1_s1_int_2,A)
         => p1_s1_int_2(A) ) ) ),
    file(int_2,s1_int_2),
    [interesting(0.00)]).

fof(t17_newton,theorem,(
    $true ),
    file(newton,t17_newton),
    [interesting(0.00)]).

fof(t1_newton,theorem,(
    $true ),
    file(newton,t1_newton),
    [interesting(0.00)]).

fof(t61_finseq_2,theorem,(
    k1_finseq_2(2) = k10_finseq_1(1,2) ),
    file(finseq_2,t61_finseq_2),
    [interesting(0.00)]).

fof(t129_rvsum_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => k16_rvsum_1(k2_finseq_4(k1_numbers,A,B)) = k11_binop_2(A,B) ) ) ),
    file(rvsum_1,t129_rvsum_1),
    [interesting(0.00)]).

fof(t58_finseq_2,theorem,(
    k1_finseq_2(0) = k1_xboole_0 ),
    file(finseq_2,t58_finseq_2),
    [interesting(0.00)]).

fof(t60_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_finseq_2(k1_nat_1(A,1)) = k7_finseq_1(k1_finseq_2(A),k12_finseq_1(k5_numbers,k1_nat_1(A,1))) ) ),
    file(finseq_2,t60_finseq_2),
    [interesting(0.00)]).

fof(t24_newton,theorem,(
    $true ),
    file(newton,t24_newton),
    [interesting(0.00)]).

fof(t26_newton,theorem,(
    $true ),
    file(newton,t26_newton),
    [interesting(0.00)]).

fof(t28_newton,theorem,(
    $true ),
    file(newton,t28_newton),
    [interesting(0.00)]).

fof(t2_newton,theorem,(
    $true ),
    file(newton,t2_newton),
    [interesting(0.00)]).

fof(t11_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(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t11_xreal_1),
    [interesting(0.00)]).

fof(t26_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
          <=> r1_xreal_0(k4_xcmplx_0(B),k4_xcmplx_0(A)) ) ) ) ),
    file(xreal_1,t26_xreal_1),
    [interesting(0.00)]).

fof(d3_newton,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( ( r1_xreal_0(A,B)
               => ( C = k7_newton(A,B)
                <=> ! [D] : 
                      ( v4_ordinal2(D)
                     => ( D = k6_xcmplx_0(B,A)
                       => C = k7_xcmplx_0(k6_newton(B),k3_xcmplx_0(k6_newton(A),k6_newton(D))) ) ) ) )
              & ( ~ r1_xreal_0(A,B)
               => ( C = k7_newton(A,B)
                <=> C = 0 ) ) ) ) ) ),
    file(newton,d3_newton),
    [interesting(0.00)]).

fof(t18_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( r1_xreal_0(A,B)
           => r2_hidden(k6_xcmplx_0(B,A),k5_numbers) ) ) ) ),
    file(int_1,t18_int_1),
    [interesting(0.00)]).

fof(t60_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ( A != 0
       => k7_xcmplx_0(A,A) = 1 ) ) ),
    file(xcmplx_1,t60_xcmplx_1),
    [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(t6_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ~ ( k3_xcmplx_0(A,B) = 0
              & A != 0
              & B != 0 ) ) ) ),
    file(xcmplx_1,t6_xcmplx_1),
    [interesting(0.00)]).

fof(t117_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => ! [D] : 
                  ( v1_xcmplx_0(D)
                 => ~ ( A != 0
                      & B != 0
                      & k2_xcmplx_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) != k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)),k3_xcmplx_0(A,B)) ) ) ) ) ) ),
    file(xcmplx_1,t117_xcmplx_1),
    [interesting(0.00)]).

fof(t92_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => ( A != 0
               => k7_xcmplx_0(B,C) = k7_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)) ) ) ) ) ),
    file(xcmplx_1,t92_xcmplx_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(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(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(t22_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( A != 0
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => A != k1_nat_1(B,1) ) ) ) ),
    file(nat_1,t22_nat_1),
    [interesting(0.00)]).

fof(t22_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_1(B,A)
         => ~ ( k3_finseq_1(B) != 0
              & ! [C] : 
                  ( m2_finseq_1(C,A)
                 => ! [D] : 
                      ( m1_subset_1(D,A)
                     => B != k8_finseq_1(A,C,k12_finseq_1(A,D)) ) ) ) ) ) ),
    file(finseq_2,t22_finseq_2),
    [interesting(0.00)]).

fof(t19_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))) = k1_nat_1(k3_finseq_1(B),1) ) ),
    file(finseq_2,t19_finseq_2),
    [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(d8_finseq_1,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k1_relat_1(B) = k2_finseq_1(1)
          & k1_funct_1(B,1) = A ) ) ) ),
    file(finseq_1,d8_finseq_1),
    [interesting(0.00)]).

fof(t103_rvsum_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => k15_rvsum_1(k12_finseq_1(k1_numbers,A)) = A ) ),
    file(rvsum_1,t103_rvsum_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(t39_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) )
         => r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))) ) ) ),
    file(finseq_1,t39_finseq_1),
    [interesting(0.00)]).

fof(t6_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => r2_hidden(k2_xcmplx_0(A,1),k2_finseq_1(k2_xcmplx_0(A,1))) ) ),
    file(finseq_1,t6_finseq_1),
    [interesting(0.00)]).

fof(t59_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),1)) = A ) ),
    file(finseq_1,t59_finseq_1),
    [interesting(0.00)]).

fof(t104_rvsum_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m2_finseq_1(B,k1_numbers)
         => k15_rvsum_1(k8_finseq_1(k1_numbers,B,k12_finseq_1(k1_numbers,A))) = k9_binop_2(k15_rvsum_1(B),A) ) ) ),
    file(rvsum_1,t104_rvsum_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(t36_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_finseq_1(C,k1_numbers)
             => ( ( k3_finseq_1(C) = B
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r2_hidden(D,k4_finseq_1(C))
                              & E = k6_xcmplx_0(k1_nat_1(A,D),1) )
                           => k1_funct_1(C,D) = k8_newton(A,E) ) ) ) )
               => ( B = 0
                  | k15_rvsum_1(C) = k8_newton(k1_nat_1(A,1),k1_nat_1(A,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_finseq_2,t19_finseq_2,d3_finseq_1,d8_finseq_1,t103_rvsum_1,t31_newton,t31_newton,d7_finseq_1,t39_finseq_1,d3_finseq_1,t6_finseq_1,t59_finseq_1,t104_rvsum_1,t32_newton,s1_nat_1]),
    [file(newton,t36_newton),interesting(0.00)]).

fof(t37_newton,theorem,(
    $true ),
    file(newton,t37_newton),
    [interesting(0.00)]).

fof(t42_newton,theorem,(
    $true ),
    file(newton,t42_newton),
    [interesting(0.00)]).

fof(d4_newton,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ! [D] : 
                  ( m2_finseq_1(D,k1_numbers)
                 => ( D = k9_newton(A,B,C)
                  <=> ( k3_finseq_1(D) = k2_xcmplx_0(C,1)
                      & ! [E] : 
                          ( v4_ordinal2(E)
                         => ! [F] : 
                              ( v4_ordinal2(F)
                             => ! [G] : 
                                  ( v4_ordinal2(G)
                                 => ( ( r2_hidden(E,k4_finseq_1(D))
                                      & G = k6_xcmplx_0(E,1)
                                      & F = k6_xcmplx_0(C,G) )
                                   => k1_funct_1(D,E) = k3_xcmplx_0(k3_xcmplx_0(k8_newton(G,C),k2_newton(A,F)),k2_newton(B,G)) ) ) ) ) ) ) ) ) ) ) ),
    file(newton,d4_newton),
    [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(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [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(t117_rvsum_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m2_finseq_1(B,k1_numbers)
         => k15_rvsum_1(k9_rvsum_1(A,B)) = k11_binop_2(A,k15_rvsum_1(B)) ) ) ),
    file(rvsum_1,t117_rvsum_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(t110_finseq_2,theorem,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => m1_subset_1(B,k4_finseq_2(k3_finseq_1(B),A)) ) ),
    file(finseq_2,t110_finseq_2),
    [interesting(0.00)]).

fof(t109_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => k3_finseq_1(C) = A ) ) ) ),
    file(finseq_2,t109_finseq_2),
    [interesting(0.00)]).

fof(t106_rvsum_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m2_finseq_1(B,k1_numbers)
         => k15_rvsum_1(k8_finseq_1(k1_numbers,k12_finseq_1(k1_numbers,A),B)) = k9_binop_2(A,k15_rvsum_1(B)) ) ) ),
    file(rvsum_1,t106_rvsum_1),
    [interesting(0.00)]).

fof(t119_rvsum_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers))
         => ! [C] : 
              ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers))
             => k15_rvsum_1(k4_rvsum_1(A,B,C)) = k9_binop_2(k15_rvsum_1(B),k15_rvsum_1(C)) ) ) ) ),
    file(rvsum_1,t119_rvsum_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(t37_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( r1_xreal_0(A,B)
               => r1_xreal_0(A,k2_xcmplx_0(B,C)) ) ) ) ) ),
    file(nat_1,t37_nat_1),
    [interesting(0.00)]).

fof(t31_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( k3_finseq_1(A) = k3_finseq_1(B)
          <=> k4_finseq_1(A) = k4_finseq_1(B) ) ) ) ),
    file(finseq_3,t31_finseq_3),
    [interesting(0.00)]).

fof(d4_finseq_4,definition,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( r2_hidden(D,k1_relat_1(C))
         => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ),
    file(finseq_4,d4_finseq_4),
    [interesting(0.00)]).

fof(t66_rvsum_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ! [C] : 
              ( m2_finseq_1(C,k1_numbers)
             => k2_seq_1(k5_numbers,k1_numbers,k9_rvsum_1(B,C),A) = k11_binop_2(B,k2_seq_1(k5_numbers,k1_numbers,C,A)) ) ) ) ),
    file(rvsum_1,t66_rvsum_1),
    [interesting(0.00)]).

fof(t58_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),1) = A ) ),
    file(finseq_1,t58_finseq_1),
    [interesting(0.00)]).

fof(t27_rvsum_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers))
             => ! [D] : 
                  ( m2_finseq_2(D,k1_numbers,k4_finseq_2(A,k1_numbers))
                 => k2_seq_1(k5_numbers,k1_numbers,k4_rvsum_1(A,C,D),B) = k9_binop_2(k2_seq_1(k5_numbers,k1_numbers,C,B),k2_seq_1(k5_numbers,k1_numbers,D,B)) ) ) ) ) ),
    file(rvsum_1,t27_rvsum_1),
    [interesting(0.00)]).

fof(t26_rvsum_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_finseq_1(B,k1_numbers)
         => ! [C] : 
              ( m2_finseq_1(C,k1_numbers)
             => ( r2_hidden(A,k4_finseq_1(k3_rvsum_1(B,C)))
               => k2_seq_1(k5_numbers,k1_numbers,k3_rvsum_1(B,C),A) = k9_binop_2(k2_seq_1(k5_numbers,k1_numbers,B,A),k2_seq_1(k5_numbers,k1_numbers,C,A)) ) ) ) ) ),
    file(rvsum_1,t26_rvsum_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(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(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(t5_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( A = 0
        | r2_hidden(A,k2_finseq_1(A)) ) ) ),
    file(finseq_1,t5_finseq_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(t17_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) )
         => ( ( k4_finseq_1(A) = k4_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(A))
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    file(finseq_1,t17_finseq_1),
    [interesting(0.00)]).

fof(d5_newton,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( m2_finseq_1(B,k1_numbers)
         => ( B = k10_newton(A)
          <=> ( k3_finseq_1(B) = k2_xcmplx_0(A,1)
              & ! [C] : 
                  ( v4_ordinal2(C)
                 => ! [D] : 
                      ( v4_ordinal2(D)
                     => ( ( r2_hidden(C,k4_finseq_1(B))
                          & D = k6_xcmplx_0(C,1) )
                       => k1_funct_1(B,C) = k8_newton(D,A) ) ) ) ) ) ) ) ),
    file(newton,d5_newton),
    [interesting(0.00)]).

fof(t63_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => k2_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,B)) = k7_xcmplx_0(k2_xcmplx_0(A,C),B) ) ) ) ),
    file(xcmplx_1,t63_xcmplx_1),
    [interesting(0.00)]).

fof(t127_real_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ( ( ~ r1_xreal_0(A,0)
                  & ~ r1_xreal_0(B,0) )
                | ( ~ r1_xreal_0(0,A)
                  & ~ r1_xreal_0(0,B) ) )
              & r1_xreal_0(k7_xcmplx_0(A,B),0) ) ) ) ),
    file(real_2,t127_real_2),
    [interesting(0.00)]).

fof(t31_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(k2_xcmplx_0(B,A),B) ) ) ) ),
    file(xreal_1,t31_xreal_1),
    [interesting(0.00)]).

fof(t4_newton,theorem,(
    $true ),
    file(newton,t4_newton),
    [interesting(0.00)]).

fof(d3_nat_1,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r1_nat_1(A,B)
          <=> ? [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & B = k3_xcmplx_0(A,C) ) ) ) ) ),
    file(nat_1,d3_nat_1),
    [interesting(0.00)]).

fof(t90_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ( A != 0
           => B = k7_xcmplx_0(k3_xcmplx_0(B,A),A) ) ) ) ),
    file(xcmplx_1,t90_xcmplx_1),
    [interesting(0.00)]).

fof(t75_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C) ) ) ) ),
    file(xcmplx_1,t75_xcmplx_1),
    [interesting(0.00)]).

fof(t142_real_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( ( ~ r1_xreal_0(A,0)
                & ~ r1_xreal_0(B,A) )
              | ( ~ r1_xreal_0(A,B)
                & ~ r1_xreal_0(0,A) ) )
           => ( ~ r1_xreal_0(1,k7_xcmplx_0(A,B))
              & ~ r1_xreal_0(k7_xcmplx_0(B,A),1) ) ) ) ) ),
    file(real_2,t142_real_2),
    [interesting(0.00)]).

fof(t145_real_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ( ( ~ r1_xreal_0(A,0)
                  & ~ r1_xreal_0(1,B) )
                | ( ~ r1_xreal_0(0,A)
                  & ~ r1_xreal_0(B,1) ) )
              & r1_xreal_0(A,k3_xcmplx_0(A,B)) ) ) ) ),
    file(real_2,t145_real_2),
    [interesting(0.00)]).

fof(t40_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( k3_xcmplx_0(A,B) = 1
           => ( A = 1
              & B = 1 ) ) ) ) ),
    file(nat_1,t40_nat_1),
    [interesting(0.00)]).

fof(t53_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( r1_nat_1(A,0)
        & r1_nat_1(1,A) ) ) ),
    file(nat_1,t53_nat_1),
    [interesting(0.00)]).

fof(d4_nat_1,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( C = k5_nat_1(A,B)
              <=> ( r1_nat_1(A,C)
                  & r1_nat_1(B,C)
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( ( r1_nat_1(A,D)
                          & r1_nat_1(B,D) )
                       => r1_nat_1(C,D) ) ) ) ) ) ) ) ),
    file(nat_1,d4_nat_1),
    [interesting(0.00)]).

fof(t51_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( ( r1_nat_1(A,B)
                  & r1_nat_1(B,C) )
               => r1_nat_1(A,C) ) ) ) ) ),
    file(nat_1,t51_nat_1),
    [interesting(0.00)]).

fof(t52_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ( r1_nat_1(A,B)
              & r1_nat_1(B,A) )
           => A = B ) ) ) ),
    file(nat_1,t52_nat_1),
    [interesting(0.00)]).

fof(d5_nat_1,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( C = k6_nat_1(A,B)
              <=> ( r1_nat_1(C,A)
                  & r1_nat_1(C,B)
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( ( r1_nat_1(D,A)
                          & r1_nat_1(D,B) )
                       => r1_nat_1(D,C) ) ) ) ) ) ) ) ),
    file(nat_1,d5_nat_1),
    [interesting(0.00)]).

fof(t72_newton,theorem,(
    $true ),
    file(newton,t72_newton),
    [interesting(0.00)]).

fof(t56_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( r1_nat_1(A,B)
               => r1_nat_1(A,k3_xcmplx_0(B,C)) ) ) ) ) ),
    file(nat_1,t56_nat_1),
    [interesting(0.00)]).

fof(t122_real_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ( ( ~ r1_xreal_0(0,A)
                  & ~ r1_xreal_0(0,B) )
                | ( ~ r1_xreal_0(A,0)
                  & ~ r1_xreal_0(B,0) ) )
              & r1_xreal_0(k3_xcmplx_0(A,B),0) ) ) ) ),
    file(real_2,t122_real_2),
    [interesting(0.00)]).

fof(t74_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => r1_nat_1(k5_nat_1(k6_nat_1(A,B),k6_nat_1(A,C)),k6_nat_1(A,k5_nat_1(B,C))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_nat_1,d5_nat_1,d5_nat_1,d4_nat_1,t51_nat_1,t51_nat_1,d4_nat_1,d5_nat_1]),
    [file(newton,t74_newton),interesting(0.00)]).

fof(t75_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_nat_1(A,B)
               => r1_nat_1(k5_nat_1(A,k6_nat_1(C,B)),k6_nat_1(k5_nat_1(A,C),B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_nat_1,d5_nat_1,d5_nat_1,t51_nat_1,d5_nat_1,d4_nat_1]),
    [file(newton,t75_newton),interesting(0.00)]).

fof(s5_nat_1,theorem,
    ( ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & p1_s5_nat_1(A) )
   => ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & p1_s5_nat_1(A)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( p1_s5_nat_1(B)
             => r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,s5_nat_1),
    [interesting(0.00)]).

fof(t42_nat_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( ~ r1_xreal_0(A,0)
       => ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ? [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & ? [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & B = k1_nat_1(k2_nat_1(A,C),D)
                    & ~ r1_xreal_0(A,D) ) ) ) ) ) ),
    file(nat_1,t42_nat_1),
    [interesting(0.00)]).

fof(d9_int_1,definition,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( r2_int_1(A,B)
          <=> ? [C] : 
                ( v1_int_1(C)
                & B = k3_xcmplx_0(A,C) ) ) ) ) ),
    file(int_1,d9_int_1),
    [interesting(0.00)]).

fof(d1_absvalue,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ( r1_xreal_0(0,A)
         => k16_complex1(A) = A )
        & ( ~ r1_xreal_0(0,A)
         => k16_complex1(A) = k4_xcmplx_0(A) ) ) ) ),
    file(absvalue,d1_absvalue),
    [interesting(0.00)]).

fof(t21_int_2,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( r2_int_1(A,B)
          <=> r1_nat_1(k1_int_2(A),k1_int_2(B)) ) ) ) ),
    file(int_2,t21_int_2),
    [interesting(0.00)]).

fof(d7_newton,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
         => ( B = k13_newton(A)
          <=> ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r2_hidden(C,B)
                <=> ( ~ r1_xreal_0(A,C)
                    & v1_int_2(C) ) ) ) ) ) ) ),
    file(newton,d7_newton),
    [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(d5_int_2,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( v1_int_2(A)
      <=> ( ~ r1_xreal_0(A,1)
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ~ ( r1_nat_1(B,A)
                  & B != 1
                  & B != A ) ) ) ) ) ),
    file(int_2,d5_int_2),
    [interesting(0.00)]).

fof(t13_finset_1,theorem,(
    ! [A,B] : 
      ( ( r1_tarski(A,B)
        & v1_finset_1(B) )
     => v1_finset_1(A) ) ),
    file(finset_1,t13_finset_1),
    [interesting(0.00)]).

fof(t44_int_2,theorem,(
    v1_int_2(2) ),
    file(int_2,t44_int_2),
    [interesting(0.00)]).

fof(t59_finseq_2,theorem,(
    k1_finseq_2(1) = k12_finseq_1(k5_numbers,1) ),
    file(finseq_2,t59_finseq_2),
    [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(t39_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( ~ r1_xreal_0(1,A)
       => A = 0 ) ) ),
    file(nat_1,t39_nat_1),
    [interesting(0.00)]).

fof(t48_int_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(2,A)
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ~ ( v1_int_2(B)
                  & r1_nat_1(B,A) ) ) ) ) ),
    file(int_2,t48_int_2),
    [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(t2_cqc_the1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,1)
          & A != 0
          & A != 1 ) ) ),
    file(cqc_the1,t2_cqc_the1),
    [interesting(0.00)]).

fof(d6_newton,definition,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( A = k12_newton
      <=> ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,A)
            <=> v1_int_2(B) ) ) ) ) ),
    file(newton,d6_newton),
    [interesting(0.00)]).

fof(t8_newton,theorem,(
    $true ),
    file(newton,t8_newton),
    [interesting(0.00)]).

fof(t92_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ r2_hidden(A,a_1_2_newton(A)) ) ),
    file(newton,t92_newton),
    [interesting(0.00)]).

fof(t14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,t14_finset_1),
    [interesting(0.00)]).

fof(t95_newton,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( ~ r1_xreal_0(B,A)
              & r2_hidden(B,a_1_2_newton(A)) ) ) ) ),
    file(newton,t95_newton),
    [interesting(0.00)]).

fof(t77_finseq_1,theorem,(
    ! [A] : ~ ( v1_finset_1(A)
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ r2_wellord2(A,k2_finseq_1(B)) ) ) ),
    file(finseq_1,t77_finseq_1),
    [interesting(0.00)]).

fof(t21_card_1,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> k1_card_1(A) = k1_card_1(B) ) ),
    file(card_1,t21_card_1),
    [interesting(0.00)]).

fof(t76_finseq_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_card_1(k2_finseq_1(A)) = k1_card_1(A) ) ),
    file(finseq_1,t76_finseq_1),
    [interesting(0.00)]).

fof(d11_card_1,definition,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k4_card_1(A)
          <=> k1_card_1(B) = k1_card_1(A) ) ) ) ),
    file(card_1,d11_card_1),
    [interesting(0.00)]).

fof(t80_card_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( v1_finset_1(B)
         => ( r1_tarski(A,B)
           => r1_xreal_0(k4_card_1(A),k4_card_1(B)) ) ) ) ),
    file(card_1,t80_card_1),
    [interesting(0.00)]).

fof(d8_newton,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_int_2(B)
            & m2_subset_1(B,k1_numbers,k5_numbers) )
         => ( B = k14_newton(A)
          <=> ? [C] : 
                ( v1_finset_1(C)
                & C = a_1_1_newton(B)
                & A = k4_card_1(C) ) ) ) ) ),
    file(newton,d8_newton),
    [interesting(0.00)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.00)]).

fof(t57_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( ( r1_nat_1(A,B)
                  & r1_nat_1(A,k2_xcmplx_0(B,C)) )
               => r1_nat_1(A,C) ) ) ) ) ),
    file(nat_1,t57_nat_1),
    [interesting(0.00)]).

fof(t55_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( ( r1_nat_1(A,B)
                  & r1_nat_1(A,C) )
               => r1_nat_1(A,k2_xcmplx_0(B,C)) ) ) ) ) ),
    file(nat_1,t55_nat_1),
    [interesting(0.00)]).

fof(t54_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r1_nat_1(B,A)
           => ( r1_xreal_0(A,0)
              | r1_xreal_0(B,A) ) ) ) ) ),
    file(nat_1,t54_nat_1),
    [interesting(0.00)]).

fof(t5_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => ( k3_xcmplx_0(B,A) = k3_xcmplx_0(C,A)
               => ( A = 0
                  | B = C ) ) ) ) ) ),
    file(xcmplx_1,t5_xcmplx_1),
    [interesting(0.00)]).

fof(t27_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,B)
              & r1_xreal_0(B,k2_xcmplx_0(A,1))
              & A != B
              & B != k2_xcmplx_0(A,1) ) ) ) ),
    file(nat_1,t27_nat_1),
    [interesting(0.00)]).