fof(t84_square_1,theorem,(
    ~ r1_xreal_0(k9_square_1(2),1) ),
    inference(mizar_proof,[status(thm)],[l98_square_1,t83_square_1]),
    [file(square_1,t84_square_1),interesting(1.00)]).

fof(t86_square_1,theorem,(
    ~ r1_xreal_0(2,k9_square_1(2)) ),
    inference(mizar_proof,[status(thm)],[l98_square_1,t85_square_1]),
    [file(square_1,t86_square_1),interesting(1.00)]).

fof(t56_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => k1_square_1(A,k2_square_1(B,C)) = k2_square_1(k1_square_1(A,B),k1_square_1(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t46_square_1,t2_xreal_1,d1_square_1,t54_square_1,d1_square_1,t39_square_1,d2_square_1,d2_square_1,d1_square_1,t39_square_1,d2_square_1,d2_square_1,d1_square_1,t2_xreal_1]),
    [file(square_1,t56_square_1),interesting(0.93)]).

fof(t78_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(0,A)
              & ~ r1_xreal_0(B,A)
              & r1_xreal_0(k5_square_1(B),k5_square_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t66_xreal_1,t70_xreal_1,t2_xreal_1]),
    [file(square_1,t78_square_1),interesting(0.87)]).

fof(t54_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => k2_square_1(A,k1_square_1(A,B)) = A ) ) ),
    inference(mizar_proof,[status(thm)],[d1_square_1,d1_square_1,d2_square_1]),
    [file(square_1,t54_square_1),interesting(0.87)]).

fof(t55_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => k1_square_1(A,k2_square_1(A,B)) = A ) ) ),
    inference(mizar_proof,[status(thm)],[d2_square_1,d1_square_1,d2_square_1]),
    [file(square_1,t55_square_1),interesting(0.87)]).

fof(t39_square_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(A,C) )
              <=> r1_xreal_0(A,k1_square_1(B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_square_1,t35_square_1,t2_xreal_1]),
    [file(square_1,t39_square_1),interesting(0.86)]).

fof(t46_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => r1_xreal_0(A,k2_square_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_square_1]),
    [file(square_1,t46_square_1),interesting(0.85)]).

fof(t35_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => r1_xreal_0(k1_square_1(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_square_1]),
    [file(square_1,t35_square_1),interesting(0.85)]).

fof(t83_square_1,theorem,(
    k9_square_1(1) = 1 ),
    inference(mizar_proof,[status(thm)],[d4_square_1,t59_square_1]),
    [file(square_1,t83_square_1),interesting(0.83)]).

fof(t57_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => k2_square_1(A,k1_square_1(B,C)) = k1_square_1(k2_square_1(A,B),k2_square_1(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t39_square_1,d2_square_1,d2_square_1,d2_square_1,d1_square_1,d2_square_1,t55_square_1,d2_square_1,d1_square_1,d2_square_1,t55_square_1,d2_square_1,t2_xreal_1]),
    [file(square_1,t57_square_1),interesting(0.82)]).

fof(t85_square_1,theorem,(
    k9_square_1(4) = 2 ),
    inference(mizar_proof,[status(thm)],[d4_square_1,l100_square_1]),
    [file(square_1,t85_square_1),interesting(0.82)]).

fof(l90_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B)
              & k5_square_1(A) = k5_square_1(B) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t78_square_1,t1_xreal_1]),
    [file(square_1,l90_square_1),interesting(0.79)]).

fof(l98_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(0,A)
              & ~ r1_xreal_0(B,A)
              & r1_xreal_0(k8_square_1(B),k8_square_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_square_1,d4_square_1,t77_square_1]),
    [file(square_1,l98_square_1),interesting(0.78)]).

fof(t50_square_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(C,B) )
              <=> r1_xreal_0(k2_square_1(A,C),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_square_1,t46_square_1,t2_xreal_1]),
    [file(square_1,t50_square_1),interesting(0.78)]).

fof(t74_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ~ ( 0 != A
          & r1_xreal_0(k5_square_1(A),0) ) ) ),
    inference(mizar_proof,[status(thm)],[t72_square_1,t73_square_1,d5_real_1]),
    [file(square_1,t74_square_1),interesting(0.77)]).

fof(t77_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(A,B) )
           => r1_xreal_0(k5_square_1(A),k5_square_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t66_xreal_1,t2_xreal_1]),
    [file(square_1,t77_square_1),interesting(0.76)]).

fof(t2_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ~ ( ~ r1_xreal_0(A,1)
          & r1_xreal_0(1,k7_xcmplx_0(1,A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t124_xreal_1,t70_xreal_1,d7_xcmplx_0,d9_xcmplx_0]),
    [file(square_1,t2_square_1),interesting(0.76)]).

fof(t38_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( k1_square_1(A,B) = A
            | k1_square_1(A,B) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_square_1,d1_square_1]),
    [file(square_1,t38_square_1),interesting(0.76)]).

fof(t49_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( k2_square_1(A,B) = A
            | k2_square_1(A,B) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_square_1,d2_square_1]),
    [file(square_1,t49_square_1),interesting(0.76)]).

fof(t73_square_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ( k5_square_1(A) = 0
       => A = 0 ) ) ),
    inference(mizar_proof,[status(thm)],[t6_xcmplx_1]),
    [file(square_1,t73_square_1),interesting(0.76)]).

fof(t82_square_1,theorem,(
    k9_square_1(0) = 0 ),
    inference(mizar_proof,[status(thm)],[d4_square_1,t60_square_1]),
    [file(square_1,t82_square_1),interesting(0.76)]).

fof(t94_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(A,B) )
           => r1_xreal_0(k8_square_1(A),k8_square_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_real_1,l98_square_1]),
    [file(square_1,t94_square_1),interesting(0.76)]).

fof(t72_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => r1_xreal_0(0,k5_square_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t65_xreal_1]),
    [file(square_1,t72_square_1),interesting(0.75)]).

fof(t96_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B)
              & k8_square_1(A) = k8_square_1(B) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t1_xreal_1,l98_square_1]),
    [file(square_1,t96_square_1),interesting(0.74)]).

fof(t40_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => k1_square_1(A,k1_square_1(B,C)) = k1_square_1(k1_square_1(A,B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_square_1,t38_square_1,d1_square_1,d1_square_1,t38_square_1,t2_xreal_1]),
    [file(square_1,t40_square_1),interesting(0.73)]).

fof(t51_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => k2_square_1(A,k2_square_1(B,C)) = k2_square_1(k2_square_1(A,B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_square_1,t49_square_1,d2_square_1,d2_square_1,t49_square_1,t2_xreal_1]),
    [file(square_1,t51_square_1),interesting(0.73)]).

fof(t95_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(0,A)
              & ~ r1_xreal_0(B,A)
              & r1_xreal_0(k8_square_1(B),k8_square_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l98_square_1]),
    [file(square_1,t95_square_1),interesting(0.72)]).

fof(t69_square_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => k5_square_1(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k5_square_1(A),k5_square_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t77_xcmplx_1]),
    [file(square_1,t69_square_1),interesting(0.71)]).

fof(t76_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ~ ( ~ r1_xreal_0(A,1)
          & r1_xreal_0(k5_square_1(A),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t70_xreal_1]),
    [file(square_1,t76_square_1),interesting(0.71)]).

fof(l87_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ~ ( ~ r1_xreal_0(A,0)
          & ! [B] : 
              ( v1_xreal_0(B)
             => ~ ( ~ r1_xreal_0(B,0)
                  & ~ r1_xreal_0(A,k5_square_1(B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_xreal_1,t75_square_1]),
    [file(square_1,l87_square_1),interesting(0.70)]).

fof(l97_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( r1_xreal_0(0,A)
       => k8_square_1(k5_square_1(A)) = A ) ) ),
    inference(mizar_proof,[status(thm)],[t72_square_1,d4_square_1]),
    [file(square_1,l97_square_1),interesting(0.69)]).

fof(t75_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ~ ( ~ r1_xreal_0(A,0)
          & ~ r1_xreal_0(1,A)
          & r1_xreal_0(A,k5_square_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t70_xreal_1]),
    [file(square_1,t75_square_1),interesting(0.68)]).

fof(l31_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B) )
           => r1_xreal_0(0,k7_xcmplx_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t138_xreal_1]),
    [file(square_1,l31_square_1),interesting(0.66)]).

fof(l121_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B)
              & A != B
              & k6_xcmplx_0(k5_square_1(k8_square_1(A)),k5_square_1(k8_square_1(B))) = 0 ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_square_1,t96_square_1,l90_square_1]),
    [file(square_1,l121_square_1),interesting(0.66)]).

fof(l7_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & ~ r1_xreal_0(0,B)
              & r1_xreal_0(0,k3_xcmplx_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t134_xreal_1]),
    [file(square_1,l7_square_1),interesting(0.66)]).

fof(l5_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B) )
           => r1_xreal_0(0,k3_xcmplx_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t129_xreal_1]),
    [file(square_1,l5_square_1),interesting(0.66)]).

fof(t93_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ~ ( ~ r1_xreal_0(A,0)
          & r1_xreal_0(k8_square_1(A),0) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_square_1,t60_square_1]),
    [file(square_1,t93_square_1),interesting(0.64)]).

fof(t53_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => k2_xcmplx_0(k1_square_1(A,B),k2_square_1(A,B)) = k2_xcmplx_0(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_square_1,d2_square_1,d1_square_1,d2_square_1]),
    [file(square_1,t53_square_1),interesting(0.62)]).

fof(t89_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( r1_xreal_0(0,A)
       => k8_square_1(k5_square_1(A)) = A ) ) ),
    inference(mizar_proof,[status(thm)],[l97_square_1]),
    [file(square_1,t89_square_1),interesting(0.61)]).

fof(l32_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(B,k6_xcmplx_0(B,A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t46_xreal_1]),
    [file(square_1,l32_square_1),interesting(0.60)]).

fof(l3_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(B,A)
              & r1_xreal_0(k6_xcmplx_0(B,A),0) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t52_xreal_1]),
    [file(square_1,l3_square_1),interesting(0.60)]).

fof(l4_square_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)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_xreal_1]),
    [file(square_1,l4_square_1),interesting(0.60)]).

fof(t99_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B) )
           => k8_square_1(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k8_square_1(A),k8_square_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_square_1,d4_square_1,t69_square_1,l31_square_1,d4_square_1]),
    [file(square_1,t99_square_1),interesting(0.58)]).

fof(l6_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & ~ r1_xreal_0(B,0)
              & r1_xreal_0(k3_xcmplx_0(A,B),0) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t131_xreal_1]),
    [file(square_1,l6_square_1),interesting(0.54)]).

fof(t90_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( r1_xreal_0(A,0)
       => k8_square_1(k5_square_1(A)) = k4_xcmplx_0(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_xreal_1,l97_square_1]),
    [file(square_1,t90_square_1),interesting(0.54)]).

fof(t103_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ r1_xreal_0(A,0)
       => k7_xcmplx_0(A,k8_square_1(A)) = k8_square_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_square_1,t60_square_1,t92_xcmplx_1,d4_square_1,t92_xcmplx_1]),
    [file(square_1,t103_square_1),interesting(0.52)]).

fof(t97_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B) )
           => k8_square_1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k8_square_1(A),k8_square_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l5_square_1,d4_square_1,d4_square_1,d4_square_1,d4_square_1,d4_square_1,l5_square_1,d4_square_1,l97_square_1]),
    [file(square_1,t97_square_1),interesting(0.52)]).

fof(t101_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ r1_xreal_0(A,0)
       => k8_square_1(k7_xcmplx_0(1,A)) = k7_xcmplx_0(1,k8_square_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t83_square_1,t99_square_1]),
    [file(square_1,t101_square_1),interesting(0.51)]).

fof(t92_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ( r1_xreal_0(0,A)
          & k8_square_1(A) = 0 )
       => A = 0 ) ) ),
    inference(mizar_proof,[status(thm)],[d4_square_1,t60_square_1]),
    [file(square_1,t92_square_1),interesting(0.50)]).

fof(s1_square_1,theorem,
    ( ! [A] : 
        ( v1_xreal_0(A)
       => ! [B] : 
            ( v1_xreal_0(B)
           => ( ( p1_s1_square_1(A)
                & p2_s1_square_1(B) )
             => r1_xreal_0(A,B) ) ) )
   => ? [A] : 
        ( v1_xreal_0(A)
        & ! [B] : 
            ( v1_xreal_0(B)
           => ! [C] : 
                ( v1_xreal_0(C)
               => ( ( p1_s1_square_1(B)
                    & p2_s1_square_1(C) )
                 => ( r1_xreal_0(B,A)
                    & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d3_tarski,t26_axioms,d1_xreal_0]),
    [file(square_1,s1_square_1),interesting(0.49)]).

fof(t25_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(0,k3_xcmplx_0(A,B))
              & ~ ( r1_xreal_0(0,A)
                  & r1_xreal_0(0,B) )
              & ~ ( r1_xreal_0(A,0)
                  & r1_xreal_0(B,0) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l7_square_1]),
    [file(square_1,t25_square_1),interesting(0.45)]).

fof(t106_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(0,A)
           => ( r1_xreal_0(B,A)
              | k7_xcmplx_0(1,k2_xcmplx_0(k8_square_1(B),k8_square_1(A))) = k7_xcmplx_0(k6_xcmplx_0(k8_square_1(B),k8_square_1(A)),k6_xcmplx_0(B,A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l121_square_1,t70_square_1,d4_square_1,d4_square_1]),
    [file(square_1,t106_square_1),interesting(0.36)]).

fof(t108_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(0,A)
           => ( r1_xreal_0(B,A)
              | k7_xcmplx_0(1,k6_xcmplx_0(k8_square_1(B),k8_square_1(A))) = k7_xcmplx_0(k2_xcmplx_0(k8_square_1(B),k8_square_1(A)),k6_xcmplx_0(B,A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l121_square_1,t71_square_1,d4_square_1,d4_square_1]),
    [file(square_1,t108_square_1),interesting(0.36)]).

fof(t102_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ r1_xreal_0(A,0)
       => k7_xcmplx_0(k8_square_1(A),A) = k7_xcmplx_0(1,k8_square_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_square_1,t60_square_1,t92_xcmplx_1,d4_square_1,t92_xcmplx_1]),
    [file(square_1,t102_square_1),interesting(0.34)]).

fof(t107_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B) )
           => k7_xcmplx_0(1,k6_xcmplx_0(k8_square_1(A),k8_square_1(B))) = k7_xcmplx_0(k2_xcmplx_0(k8_square_1(A),k8_square_1(B)),k6_xcmplx_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l121_square_1,t71_square_1,d4_square_1,d4_square_1,t14_xcmplx_1,t49_xcmplx_1]),
    [file(square_1,t107_square_1),interesting(0.34)]).

fof(t105_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B) )
           => ( A = B
              | k7_xcmplx_0(1,k2_xcmplx_0(k8_square_1(A),k8_square_1(B))) = k7_xcmplx_0(k6_xcmplx_0(k8_square_1(A),k8_square_1(B)),k6_xcmplx_0(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l121_square_1,t70_square_1,d4_square_1,d4_square_1]),
    [file(square_1,t105_square_1),interesting(0.28)]).

fof(t70_square_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ( k6_xcmplx_0(k5_square_1(A),k5_square_1(B)) != 0
           => k7_xcmplx_0(1,k2_xcmplx_0(A,B)) = k7_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(k5_square_1(A),k5_square_1(B))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t92_xcmplx_1]),
    [file(square_1,t70_square_1),interesting(0.21)]).

fof(t71_square_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ( k6_xcmplx_0(k5_square_1(A),k5_square_1(B)) != 0
           => k7_xcmplx_0(1,k6_xcmplx_0(A,B)) = k7_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(k5_square_1(A),k5_square_1(B))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t92_xcmplx_1]),
    [file(square_1,t71_square_1),interesting(0.21)]).

fof(t46_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(B,k6_xcmplx_0(B,A)) ) ) ) ),
    file(xreal_1,t46_xreal_1),
    [interesting(0.00)]).

fof(t52_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(B,A)
              & r1_xreal_0(k6_xcmplx_0(B,A),0) ) ) ) ),
    file(xreal_1,t52_xreal_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(t131_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & ~ r1_xreal_0(B,0)
              & r1_xreal_0(k3_xcmplx_0(A,B),0) ) ) ) ),
    file(xreal_1,t131_xreal_1),
    [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(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(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(t26_axioms,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ~ ( ! [C] : 
                  ( v1_xreal_0(C)
                 => ! [D] : 
                      ( v1_xreal_0(D)
                     => ( ( r2_hidden(C,A)
                          & r2_hidden(D,B) )
                       => r1_xreal_0(C,D) ) ) )
              & ! [C] : 
                  ( v1_xreal_0(C)
                 => ? [D] : 
                      ( v1_xreal_0(D)
                      & ? [E] : 
                          ( v1_xreal_0(E)
                          & r2_hidden(D,A)
                          & r2_hidden(E,B)
                          & ~ ( r1_xreal_0(D,C)
                              & r1_xreal_0(C,E) ) ) ) ) ) ) ) ),
    file(axioms,t26_axioms),
    [interesting(0.00)]).

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(t100_square_1,theorem,(
    $true ),
    file(square_1,t100_square_1),
    [interesting(0.00)]).

fof(d4_square_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( r1_xreal_0(0,A)
       => ! [B] : 
            ( v1_xreal_0(B)
           => ( B = k8_square_1(A)
            <=> ( r1_xreal_0(0,B)
                & k5_square_1(B) = A ) ) ) ) ) ),
    file(square_1,d4_square_1),
    [interesting(0.00)]).

fof(t59_square_1,theorem,(
    k7_square_1(1) = 1 ),
    file(square_1,t59_square_1),
    [interesting(0.00)]).

fof(t77_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => ! [D] : 
                  ( v1_xcmplx_0(D)
                 => k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) ) ) ) ) ),
    file(xcmplx_1,t77_xcmplx_1),
    [interesting(0.00)]).

fof(t138_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B) )
           => r1_xreal_0(0,k7_xcmplx_0(A,B)) ) ) ) ),
    file(xreal_1,t138_xreal_1),
    [interesting(0.00)]).

fof(t60_square_1,theorem,(
    k7_square_1(0) = 0 ),
    file(square_1,t60_square_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(t104_square_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B) )
           => k3_xcmplx_0(k6_xcmplx_0(k8_square_1(A),k8_square_1(B)),k2_xcmplx_0(k8_square_1(A),k8_square_1(B))) = k6_xcmplx_0(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_square_1,d4_square_1]),
    [file(square_1,t104_square_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(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(t14_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,A) = 0 ) ),
    file(xcmplx_1,t14_xcmplx_1),
    [interesting(0.00)]).

fof(t49_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(A,0) = 0 ) ),
    file(xcmplx_1,t49_xcmplx_1),
    [interesting(0.00)]).

fof(t10_square_1,theorem,(
    $true ),
    file(square_1,t10_square_1),
    [interesting(0.00)]).

fof(t11_square_1,theorem,(
    $true ),
    file(square_1,t11_square_1),
    [interesting(0.00)]).

fof(t12_square_1,theorem,(
    $true ),
    file(square_1,t12_square_1),
    [interesting(0.00)]).

fof(t13_square_1,theorem,(
    $true ),
    file(square_1,t13_square_1),
    [interesting(0.00)]).

fof(t14_square_1,theorem,(
    $true ),
    file(square_1,t14_square_1),
    [interesting(0.00)]).

fof(t15_square_1,theorem,(
    $true ),
    file(square_1,t15_square_1),
    [interesting(0.00)]).

fof(t16_square_1,theorem,(
    $true ),
    file(square_1,t16_square_1),
    [interesting(0.00)]).

fof(t17_square_1,theorem,(
    $true ),
    file(square_1,t17_square_1),
    [interesting(0.00)]).

fof(t18_square_1,theorem,(
    $true ),
    file(square_1,t18_square_1),
    [interesting(0.00)]).

fof(t19_square_1,theorem,(
    $true ),
    file(square_1,t19_square_1),
    [interesting(0.00)]).

fof(t1_square_1,theorem,(
    $true ),
    file(square_1,t1_square_1),
    [interesting(0.00)]).

fof(t20_square_1,theorem,(
    $true ),
    file(square_1,t20_square_1),
    [interesting(0.00)]).

fof(t21_square_1,theorem,(
    $true ),
    file(square_1,t21_square_1),
    [interesting(0.00)]).

fof(t22_square_1,theorem,(
    $true ),
    file(square_1,t22_square_1),
    [interesting(0.00)]).

fof(t23_square_1,theorem,(
    $true ),
    file(square_1,t23_square_1),
    [interesting(0.00)]).

fof(t24_square_1,theorem,(
    $true ),
    file(square_1,t24_square_1),
    [interesting(0.00)]).

fof(t134_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & ~ r1_xreal_0(0,B)
              & r1_xreal_0(0,k3_xcmplx_0(A,B)) ) ) ) ),
    file(xreal_1,t134_xreal_1),
    [interesting(0.00)]).

fof(t26_square_1,theorem,(
    $true ),
    file(square_1,t26_square_1),
    [interesting(0.00)]).

fof(t27_square_1,theorem,(
    $true ),
    file(square_1,t27_square_1),
    [interesting(0.00)]).

fof(t28_square_1,theorem,(
    $true ),
    file(square_1,t28_square_1),
    [interesting(0.00)]).

fof(t29_square_1,theorem,(
    $true ),
    file(square_1,t29_square_1),
    [interesting(0.00)]).

fof(t124_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ ( ~ r1_xreal_0(A,0)
            & r1_xreal_0(k5_xcmplx_0(A),0) )
        & ~ ( ~ r1_xreal_0(k5_xcmplx_0(A),0)
            & r1_xreal_0(A,0) ) ) ) ),
    file(xreal_1,t124_xreal_1),
    [interesting(0.00)]).

fof(d7_xcmplx_0,definition,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ( ( A != 0
             => ( B = k5_xcmplx_0(A)
              <=> k3_xcmplx_0(A,B) = 1 ) )
            & ( A = 0
             => ( B = k5_xcmplx_0(A)
              <=> B = 0 ) ) ) ) ) ),
    file(xcmplx_0,d7_xcmplx_0),
    [interesting(0.00)]).

fof(d9_xcmplx_0,definition,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => k7_xcmplx_0(A,B) = k3_xcmplx_0(A,k5_xcmplx_0(B)) ) ) ),
    file(xcmplx_0,d9_xcmplx_0),
    [interesting(0.00)]).

fof(t30_square_1,theorem,(
    $true ),
    file(square_1,t30_square_1),
    [interesting(0.00)]).

fof(t31_square_1,theorem,(
    $true ),
    file(square_1,t31_square_1),
    [interesting(0.00)]).

fof(t32_square_1,theorem,(
    $true ),
    file(square_1,t32_square_1),
    [interesting(0.00)]).

fof(t33_square_1,theorem,(
    $true ),
    file(square_1,t33_square_1),
    [interesting(0.00)]).

fof(t34_square_1,theorem,(
    $true ),
    file(square_1,t34_square_1),
    [interesting(0.00)]).

fof(t36_square_1,theorem,(
    $true ),
    file(square_1,t36_square_1),
    [interesting(0.00)]).

fof(t37_square_1,theorem,(
    $true ),
    file(square_1,t37_square_1),
    [interesting(0.00)]).

fof(t3_square_1,theorem,(
    $true ),
    file(square_1,t3_square_1),
    [interesting(0.00)]).

fof(d1_square_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
             => k1_square_1(A,B) = A )
            & ( ~ r1_xreal_0(A,B)
             => k1_square_1(A,B) = B ) ) ) ) ),
    file(square_1,d1_square_1),
    [interesting(0.00)]).

fof(t41_square_1,theorem,(
    $true ),
    file(square_1,t41_square_1),
    [interesting(0.00)]).

fof(t42_square_1,theorem,(
    $true ),
    file(square_1,t42_square_1),
    [interesting(0.00)]).

fof(t43_square_1,theorem,(
    $true ),
    file(square_1,t43_square_1),
    [interesting(0.00)]).

fof(t44_square_1,theorem,(
    $true ),
    file(square_1,t44_square_1),
    [interesting(0.00)]).

fof(t45_square_1,theorem,(
    $true ),
    file(square_1,t45_square_1),
    [interesting(0.00)]).

fof(t47_square_1,theorem,(
    $true ),
    file(square_1,t47_square_1),
    [interesting(0.00)]).

fof(t48_square_1,theorem,(
    $true ),
    file(square_1,t48_square_1),
    [interesting(0.00)]).

fof(t4_square_1,theorem,(
    $true ),
    file(square_1,t4_square_1),
    [interesting(0.00)]).

fof(d2_square_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(B,A)
             => k2_square_1(A,B) = A )
            & ( ~ r1_xreal_0(B,A)
             => k2_square_1(A,B) = B ) ) ) ) ),
    file(square_1,d2_square_1),
    [interesting(0.00)]).

fof(t52_square_1,theorem,(
    $true ),
    file(square_1,t52_square_1),
    [interesting(0.00)]).

fof(t58_square_1,theorem,(
    $true ),
    file(square_1,t58_square_1),
    [interesting(0.00)]).

fof(t5_square_1,theorem,(
    $true ),
    file(square_1,t5_square_1),
    [interesting(0.00)]).

fof(t61_square_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k5_square_1(A) = k5_square_1(k4_xcmplx_0(A)) ) ),
    file(square_1,t61_square_1),
    [interesting(0.00)]).

fof(t62_square_1,theorem,(
    $true ),
    file(square_1,t62_square_1),
    [interesting(0.00)]).

fof(t63_square_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => k5_square_1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k2_xcmplx_0(k5_square_1(A),k3_xcmplx_0(k3_xcmplx_0(2,A),B)),k5_square_1(B)) ) ) ),
    file(square_1,t63_square_1),
    [interesting(0.00)]).

fof(t64_square_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => k5_square_1(k6_xcmplx_0(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k5_square_1(A),k3_xcmplx_0(k3_xcmplx_0(2,A),B)),k5_square_1(B)) ) ) ),
    file(square_1,t64_square_1),
    [interesting(0.00)]).

fof(t65_square_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k5_square_1(k2_xcmplx_0(A,1)) = k2_xcmplx_0(k2_xcmplx_0(k5_square_1(A),k3_xcmplx_0(2,A)),1) ) ),
    file(square_1,t65_square_1),
    [interesting(0.00)]).

fof(t66_square_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k5_square_1(k6_xcmplx_0(A,1)) = k2_xcmplx_0(k6_xcmplx_0(k5_square_1(A),k3_xcmplx_0(2,A)),1) ) ),
    file(square_1,t66_square_1),
    [interesting(0.00)]).

fof(t67_square_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => k3_xcmplx_0(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B)) = k6_xcmplx_0(k5_square_1(A),k5_square_1(B)) ) ) ),
    file(square_1,t67_square_1),
    [interesting(0.00)]).

fof(t68_square_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => k5_square_1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k5_square_1(A),k5_square_1(B)) ) ) ),
    file(square_1,t68_square_1),
    [interesting(0.00)]).

fof(t6_square_1,theorem,(
    $true ),
    file(square_1,t6_square_1),
    [interesting(0.00)]).

fof(t65_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => r1_xreal_0(0,k3_xcmplx_0(A,A)) ) ),
    file(xreal_1,t65_xreal_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(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(t79_square_1,theorem,(
    $true ),
    file(square_1,t79_square_1),
    [interesting(0.00)]).

fof(t7_square_1,theorem,(
    $true ),
    file(square_1,t7_square_1),
    [interesting(0.00)]).

fof(t80_square_1,theorem,(
    $true ),
    file(square_1,t80_square_1),
    [interesting(0.00)]).

fof(t81_square_1,theorem,(
    $true ),
    file(square_1,t81_square_1),
    [interesting(0.00)]).

fof(l100_square_1,theorem,(
    k7_square_1(2) = k3_xcmplx_0(2,2) ),
    file(square_1,l100_square_1),
    [interesting(0.00)]).

fof(t87_square_1,theorem,(
    $true ),
    file(square_1,t87_square_1),
    [interesting(0.00)]).

fof(t88_square_1,theorem,(
    $true ),
    file(square_1,t88_square_1),
    [interesting(0.00)]).

fof(t8_square_1,theorem,(
    $true ),
    file(square_1,t8_square_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(t91_square_1,theorem,(
    $true ),
    file(square_1,t91_square_1),
    [interesting(0.00)]).

fof(t129_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B) )
           => r1_xreal_0(0,k3_xcmplx_0(A,B)) ) ) ) ),
    file(xreal_1,t129_xreal_1),
    [interesting(0.00)]).

fof(t98_square_1,theorem,(
    $true ),
    file(square_1,t98_square_1),
    [interesting(0.00)]).

fof(t9_square_1,theorem,(
    $true ),
    file(square_1,t9_square_1),
    [interesting(0.00)]).