TSTP Solution File: GRP524-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GRP524-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 16 22:27:58 EDT 2022

% Result   : Unsatisfiable 0.54s 0.60s
% Output   : Proof 0.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   50
%            Number of leaves      :   50
% Syntax   : Number of formulae    :  244 ( 198 unt;   5 typ;   0 def)
%            Number of atoms       :  286 ( 282 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   82 (  38   ~;  34   |;   0   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of FOOLs       :    3 (   3 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  164 ( 156   !;   0   ?; 164   :)

% Comments : 
%------------------------------------------------------------------------------
tff(multiply_type,type,
    multiply: ( $i * $i ) > $i ).

tff(a_type,type,
    a: $i ).

tff(b_type,type,
    b: $i ).

tff(divide_type,type,
    divide: ( $i * $i ) > $i ).

tff(inverse_type,type,
    inverse: $i > $i ).

tff(1,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
      <=> ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
  <=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
  <=> ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

tff(5,plain,
    ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = divide(b,divide(b,a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = divide(b,divide(b,a)),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a)))))) = divide(a,divide(divide(b,b),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(11,plain,
    divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a)))))) = divide(a,divide(divide(b,b),b)),
    inference(unit_resolution,[status(thm)],[10,7]) ).

tff(12,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))) = divide(a,divide(divide(b,b),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))) = divide(a,divide(divide(b,b),b)),
    inference(unit_resolution,[status(thm)],[12,7]) ).

tff(14,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(15,plain,
    divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
    inference(unit_resolution,[status(thm)],[14,7]) ).

tff(16,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(b,b),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)))) = divide(a,divide(b,divide(b,a))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(17,plain,
    divide(divide(b,b),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)))) = divide(a,divide(b,divide(b,a))),
    inference(unit_resolution,[status(thm)],[16,7]) ).

tff(18,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
      <=> ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
  <=> ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
    ( ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
  <=> ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).

tff(22,plain,
    ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
    inference(skolemize,[status(sab)],[22]) ).

tff(24,plain,
    ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
    inference(modus_ponens,[status(thm)],[23,19]) ).

tff(25,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
    | ( multiply(divide(a,divide(b,divide(b,a))),b) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(26,plain,
    multiply(divide(a,divide(b,divide(b,a))),b) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
    inference(unit_resolution,[status(thm)],[25,24]) ).

tff(27,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
    | ( multiply(divide(a,divide(b,divide(b,a))),b) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(28,plain,
    multiply(divide(a,divide(b,divide(b,a))),b) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)),
    inference(unit_resolution,[status(thm)],[27,24]) ).

tff(29,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)) = multiply(divide(a,divide(b,divide(b,a))),b),
    inference(symmetry,[status(thm)],[28]) ).

tff(30,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
    inference(transitivity,[status(thm)],[29,26]) ).

tff(31,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
    inference(monotonicity,[status(thm)],[30]) ).

tff(32,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b))),
    inference(symmetry,[status(thm)],[31]) ).

tff(33,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( inverse(A) = divide(divide(B,B),A) )
      <=> ( inverse(A) = divide(divide(B,B),A) ) )),
    inference(bind,[status(th)],]) ).

tff(34,plain,
    ( ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
  <=> ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ) ),
    inference(quant_intro,[status(thm)],[33]) ).

tff(35,plain,
    ( ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
  <=> ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,axiom,
    ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).

tff(37,plain,
    ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
    inference(modus_ponens,[status(thm)],[36,35]) ).

tff(38,plain,
    ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
    inference(skolemize,[status(sab)],[37]) ).

tff(39,plain,
    ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) ),
    inference(modus_ponens,[status(thm)],[38,34]) ).

tff(40,plain,
    ( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
    | ( inverse(b) = divide(divide(divide(b,b),divide(b,b)),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(41,plain,
    inverse(b) = divide(divide(divide(b,b),divide(b,b)),b),
    inference(unit_resolution,[status(thm)],[40,39]) ).

tff(42,plain,
    ( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
    | ( inverse(b) = divide(divide(b,b),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(43,plain,
    inverse(b) = divide(divide(b,b),b),
    inference(unit_resolution,[status(thm)],[42,39]) ).

tff(44,plain,
    divide(divide(b,b),b) = inverse(b),
    inference(symmetry,[status(thm)],[43]) ).

tff(45,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(b,divide(a,divide(b,divide(b,a)))) = b ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(46,plain,
    divide(b,divide(a,divide(b,divide(b,a)))) = b,
    inference(unit_resolution,[status(thm)],[45,7]) ).

tff(47,plain,
    divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(b,b),b),
    inference(monotonicity,[status(thm)],[46]) ).

tff(48,plain,
    divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(divide(b,b),divide(b,b)),b),
    inference(transitivity,[status(thm)],[47,44,41]) ).

tff(49,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
    inference(monotonicity,[status(thm)],[48]) ).

tff(50,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
    inference(monotonicity,[status(thm)],[49]) ).

tff(51,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(b,b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(52,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(b,b),
    inference(unit_resolution,[status(thm)],[51,7]) ).

tff(53,plain,
    divide(b,b) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))))),
    inference(symmetry,[status(thm)],[52]) ).

tff(54,plain,
    divide(b,b) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b))),
    inference(transitivity,[status(thm)],[53,50,32]) ).

tff(55,plain,
    divide(divide(b,b),divide(b,b)) = divide(divide(b,b),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)))),
    inference(monotonicity,[status(thm)],[54]) ).

tff(56,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(divide(b,b),divide(b,b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(57,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(divide(b,b),divide(b,b)),
    inference(unit_resolution,[status(thm)],[56,7]) ).

tff(58,plain,
    divide(divide(b,b),b) = divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))),
    inference(symmetry,[status(thm)],[47]) ).

tff(59,plain,
    divide(divide(divide(b,b),divide(b,b)),b) = inverse(b),
    inference(symmetry,[status(thm)],[41]) ).

tff(60,plain,
    divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(divide(b,b),divide(b,b)),b),
    inference(monotonicity,[status(thm)],[46]) ).

tff(61,plain,
    divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))),
    inference(transitivity,[status(thm)],[60,59,43,58]) ).

tff(62,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
    inference(monotonicity,[status(thm)],[61]) ).

tff(63,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a)))))),
    inference(symmetry,[status(thm)],[62]) ).

tff(64,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
    inference(symmetry,[status(thm)],[49]) ).

tff(65,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a)))))),
    inference(transitivity,[status(thm)],[64,63]) ).

tff(66,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))))),
    inference(monotonicity,[status(thm)],[65]) ).

tff(67,plain,
    ( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
    | ( inverse(b) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(68,plain,
    inverse(b) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),b),
    inference(unit_resolution,[status(thm)],[67,39]) ).

tff(69,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),b) = inverse(b),
    inference(symmetry,[status(thm)],[68]) ).

tff(70,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),b),
    inference(monotonicity,[status(thm)],[46]) ).

tff(71,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))) = divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))),
    inference(transitivity,[status(thm)],[70,69,43,58]) ).

tff(72,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
    inference(monotonicity,[status(thm)],[71]) ).

tff(73,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
    inference(transitivity,[status(thm)],[72,49]) ).

tff(74,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
    inference(monotonicity,[status(thm)],[73]) ).

tff(75,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(76,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),
    inference(unit_resolution,[status(thm)],[75,7]) ).

tff(77,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(b,divide(a,divide(b,divide(b,a))))))),
    inference(symmetry,[status(thm)],[76]) ).

tff(78,plain,
    ( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
    | ( inverse(divide(b,b)) = divide(divide(b,b),divide(b,b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(79,plain,
    inverse(divide(b,b)) = divide(divide(b,b),divide(b,b)),
    inference(unit_resolution,[status(thm)],[78,39]) ).

tff(80,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))))),
    inference(symmetry,[status(thm)],[50]) ).

tff(81,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))))) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
    inference(symmetry,[status(thm)],[66]) ).

tff(82,plain,
    divide(divide(b,b),divide(b,b)) = divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),divide(b,divide(a,divide(b,divide(b,a))))))),
    inference(symmetry,[status(thm)],[57]) ).

tff(83,plain,
    divide(divide(b,b),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)))) = divide(divide(b,b),divide(b,b)),
    inference(symmetry,[status(thm)],[55]) ).

tff(84,plain,
    divide(a,divide(b,divide(b,a))) = divide(divide(b,b),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),b)))),
    inference(symmetry,[status(thm)],[17]) ).

tff(85,plain,
    divide(a,divide(b,divide(b,a))) = divide(b,b),
    inference(transitivity,[status(thm)],[84,83,82,81,80,52]) ).

tff(86,plain,
    inverse(divide(a,divide(b,divide(b,a)))) = inverse(divide(b,b)),
    inference(monotonicity,[status(thm)],[85]) ).

tff(87,plain,
    ( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
    | ( inverse(divide(a,divide(b,divide(b,a)))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(88,plain,
    inverse(divide(a,divide(b,divide(b,a)))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))),
    inference(unit_resolution,[status(thm)],[87,39]) ).

tff(89,plain,
    divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))) = inverse(divide(a,divide(b,divide(b,a)))),
    inference(symmetry,[status(thm)],[88]) ).

tff(90,plain,
    divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))) = divide(a,divide(b,divide(b,a))),
    inference(transitivity,[status(thm)],[89,86,79,55,17]) ).

tff(91,plain,
    divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))),
    inference(monotonicity,[status(thm)],[90]) ).

tff(92,plain,
    divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))) = divide(a,divide(b,divide(b,a))),
    inference(transitivity,[status(thm)],[91,89,86,79,55,17]) ).

tff(93,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),
    inference(monotonicity,[status(thm)],[92]) ).

tff(94,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))))) = divide(a,divide(b,divide(b,a))),
    inference(transitivity,[status(thm)],[93,77,74,66,57,55,17]) ).

tff(95,plain,
    divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))),
    inference(monotonicity,[status(thm)],[94]) ).

tff(96,plain,
    divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a)))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))))),
    inference(symmetry,[status(thm)],[95]) ).

tff(97,plain,
    inverse(divide(b,b)) = inverse(divide(a,divide(b,divide(b,a)))),
    inference(symmetry,[status(thm)],[86]) ).

tff(98,plain,
    divide(divide(b,b),divide(b,b)) = inverse(divide(b,b)),
    inference(symmetry,[status(thm)],[79]) ).

tff(99,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))) = divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),divide(a,divide(b,divide(b,a))))))),
    inference(symmetry,[status(thm)],[15]) ).

tff(100,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))) = divide(a,divide(b,divide(b,a))),
    inference(transitivity,[status(thm)],[99,95,89,86,79,55,17]) ).

tff(101,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))) = divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),
    inference(monotonicity,[status(thm)],[100]) ).

tff(102,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
    inference(transitivity,[status(thm)],[101,77,74,66,57,98,97,88,96,15]) ).

tff(103,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))),
    inference(monotonicity,[status(thm)],[102]) ).

tff(104,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))))),
    inference(symmetry,[status(thm)],[103]) ).

tff(105,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))),
    inference(monotonicity,[status(thm)],[104]) ).

tff(106,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))))),
    inference(symmetry,[status(thm)],[105]) ).

tff(107,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))) = divide(a,divide(b,divide(b,a))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(108,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))) = divide(a,divide(b,divide(b,a))),
    inference(unit_resolution,[status(thm)],[107,7]) ).

tff(109,plain,
    divide(a,divide(b,divide(b,a))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))),
    inference(symmetry,[status(thm)],[108]) ).

tff(110,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))))),
    inference(transitivity,[status(thm)],[99,95,89,86,79,55,17,109,106]) ).

tff(111,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))))),
    inference(monotonicity,[status(thm)],[110]) ).

tff(112,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = b ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(113,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = b,
    inference(unit_resolution,[status(thm)],[112,7]) ).

tff(114,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))) = divide(a,divide(b,divide(b,a))),
    inference(transitivity,[status(thm)],[77,74,66,57,55,17]) ).

tff(115,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))) = divide(b,divide(a,divide(b,divide(b,a)))),
    inference(monotonicity,[status(thm)],[114]) ).

tff(116,plain,
    divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))) = b,
    inference(transitivity,[status(thm)],[115,46]) ).

tff(117,plain,
    divide(a,divide(b,divide(b,a))) = divide(divide(b,b),divide(b,b)),
    inference(transitivity,[status(thm)],[84,83]) ).

tff(118,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))))) = divide(divide(divide(b,b),divide(b,b)),b),
    inference(monotonicity,[status(thm)],[117,116]) ).

tff(119,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))))) = divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))),
    inference(transitivity,[status(thm)],[118,59,43,58]) ).

tff(120,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
    inference(monotonicity,[status(thm)],[119]) ).

tff(121,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))),
    inference(symmetry,[status(thm)],[120]) ).

tff(122,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(b,b),b)) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
    inference(monotonicity,[status(thm)],[114,58]) ).

tff(123,plain,
    ( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
    | ( inverse(divide(divide(b,b),b)) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(b,b),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(124,plain,
    inverse(divide(divide(b,b),b)) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(b,b),b)),
    inference(unit_resolution,[status(thm)],[123,39]) ).

tff(125,plain,
    ( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
    | ( inverse(divide(divide(b,b),b)) = divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(b,b),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(126,plain,
    inverse(divide(divide(b,b),b)) = divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(b,b),b)),
    inference(unit_resolution,[status(thm)],[125,39]) ).

tff(127,plain,
    divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(b,b),b)) = inverse(divide(divide(b,b),b)),
    inference(symmetry,[status(thm)],[126]) ).

tff(128,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)) = b,
    inference(transitivity,[status(thm)],[64,121,113]) ).

tff(129,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(divide(b,b),divide(b,b)),b),
    inference(monotonicity,[status(thm)],[117,128]) ).

tff(130,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(b,b),b),
    inference(transitivity,[status(thm)],[129,59,43]) ).

tff(131,plain,
    divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(b,b),b)),
    inference(monotonicity,[status(thm)],[130]) ).

tff(132,plain,
    divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = b,
    inference(transitivity,[status(thm)],[131,127,124,122,121,113]) ).

tff(133,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))) = divide(b,b),
    inference(monotonicity,[status(thm)],[128,132]) ).

tff(134,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))) = divide(a,divide(b,divide(b,a))),
    inference(transitivity,[status(thm)],[133,53,50,66,57,55,17]) ).

tff(135,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),
    inference(monotonicity,[status(thm)],[134]) ).

tff(136,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(divide(b,divide(b,a)),divide(b,divide(b,a))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(137,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(divide(b,divide(b,a)),divide(b,divide(b,a))),
    inference(unit_resolution,[status(thm)],[136,7]) ).

tff(138,plain,
    divide(divide(b,divide(b,a)),divide(b,divide(b,a))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))),
    inference(symmetry,[status(thm)],[137]) ).

tff(139,plain,
    divide(divide(b,divide(b,a)),divide(b,divide(b,a))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
    inference(transitivity,[status(thm)],[138,135,77,74,66,57,98,97,88,96,15]) ).

tff(140,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a)))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))),
    inference(monotonicity,[status(thm)],[139]) ).

tff(141,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a)))) = divide(a,divide(divide(b,b),b)),
    inference(transitivity,[status(thm)],[140,111,13]) ).

tff(142,plain,
    divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a))))) = divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))),
    inference(monotonicity,[status(thm)],[141]) ).

tff(143,plain,
    divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a))))),
    inference(symmetry,[status(thm)],[142]) ).

tff(144,plain,
    divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))) = divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(b,divide(b,a)))))),
    inference(monotonicity,[status(thm)],[143]) ).

tff(145,plain,
    divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))) = divide(a,divide(divide(b,b),b)),
    inference(transitivity,[status(thm)],[144,11]) ).

tff(146,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
    inference(monotonicity,[status(thm)],[145]) ).

tff(147,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))))),
    inference(symmetry,[status(thm)],[146]) ).

tff(148,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(a,divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a)))))) = divide(a,divide(divide(b,b),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(149,plain,
    divide(a,divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a)))))) = divide(a,divide(divide(b,b),b)),
    inference(unit_resolution,[status(thm)],[148,7]) ).

tff(150,plain,
    divide(a,divide(b,divide(b,a))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
    inference(transitivity,[status(thm)],[84,83,98,97,88,96,15]) ).

tff(151,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a)))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))),
    inference(monotonicity,[status(thm)],[150]) ).

tff(152,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a)))) = divide(a,divide(divide(b,b),b)),
    inference(transitivity,[status(thm)],[151,111,13]) ).

tff(153,plain,
    divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a))))) = divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))),
    inference(monotonicity,[status(thm)],[152]) ).

tff(154,plain,
    divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a))))),
    inference(symmetry,[status(thm)],[153]) ).

tff(155,plain,
    divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))) = divide(a,divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(b,divide(b,a)))))),
    inference(monotonicity,[status(thm)],[154]) ).

tff(156,plain,
    divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))) = divide(a,divide(divide(b,b),b)),
    inference(transitivity,[status(thm)],[155,149]) ).

tff(157,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
    inference(monotonicity,[status(thm)],[156]) ).

tff(158,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b))))),
    inference(transitivity,[status(thm)],[157,147]) ).

tff(159,plain,
    divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))),
    inference(monotonicity,[status(thm)],[158]) ).

tff(160,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = a ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(161,plain,
    divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = a,
    inference(unit_resolution,[status(thm)],[160,7]) ).

tff(162,plain,
    a = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))),
    inference(symmetry,[status(thm)],[161]) ).

tff(163,plain,
    a = divide(b,divide(b,a)),
    inference(transitivity,[status(thm)],[162,159,9]) ).

tff(164,plain,
    multiply(b,a) = multiply(b,divide(b,divide(b,a))),
    inference(monotonicity,[status(thm)],[163]) ).

tff(165,plain,
    multiply(b,divide(b,divide(b,a))) = multiply(b,a),
    inference(symmetry,[status(thm)],[164]) ).

tff(166,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
    | ( multiply(b,divide(b,divide(b,a))) = divide(b,divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(167,plain,
    multiply(b,divide(b,divide(b,a))) = divide(b,divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a)))),
    inference(unit_resolution,[status(thm)],[166,24]) ).

tff(168,plain,
    divide(b,divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a)))) = multiply(b,divide(b,divide(b,a))),
    inference(symmetry,[status(thm)],[167]) ).

tff(169,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))) = divide(divide(b,b),divide(b,b)),
    inference(transitivity,[status(thm)],[77,74,66,57]) ).

tff(170,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(divide(b,b),divide(b,b)),b),
    inference(monotonicity,[status(thm)],[169,128]) ).

tff(171,plain,
    divide(divide(divide(b,b),divide(b,b)),b) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
    inference(symmetry,[status(thm)],[170]) ).

tff(172,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
    inference(transitivity,[status(thm)],[129,171]) ).

tff(173,plain,
    divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = divide(divide(b,divide(b,a)),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))),
    inference(monotonicity,[status(thm)],[172]) ).

tff(174,plain,
    divide(divide(b,divide(b,a)),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))),
    inference(symmetry,[status(thm)],[173]) ).

tff(175,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
    | ( multiply(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(b,divide(b,a)),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(176,plain,
    multiply(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(b,divide(b,a)),divide(divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))),
    inference(unit_resolution,[status(thm)],[175,24]) ).

tff(177,plain,
    divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))),
    inference(symmetry,[status(thm)],[159]) ).

tff(178,plain,
    divide(b,divide(b,a)) = divide(divide(b,divide(b,a)),divide(divide(a,divide(divide(b,b),b)),divide(divide(b,divide(b,a)),divide(divide(b,divide(b,a)),divide(a,divide(divide(b,b),b)))))),
    inference(symmetry,[status(thm)],[9]) ).

tff(179,plain,
    divide(b,divide(b,a)) = a,
    inference(transitivity,[status(thm)],[178,177,161]) ).

tff(180,plain,
    multiply(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = multiply(a,b),
    inference(monotonicity,[status(thm)],[179,128]) ).

tff(181,plain,
    multiply(a,b) = multiply(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
    inference(symmetry,[status(thm)],[180]) ).

tff(182,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) )
    | ( multiply(a,b) = divide(a,divide(divide(b,b),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(183,plain,
    multiply(a,b) = divide(a,divide(divide(b,b),b)),
    inference(unit_resolution,[status(thm)],[182,24]) ).

tff(184,plain,
    divide(a,divide(divide(b,b),b)) = multiply(a,b),
    inference(symmetry,[status(thm)],[183]) ).

tff(185,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(b,b),
    inference(monotonicity,[status(thm)],[128,128]) ).

tff(186,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b))),
    inference(transitivity,[status(thm)],[185,53,50,66,57,98,97,88,96,15]) ).

tff(187,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = divide(divide(a,divide(divide(b,b),b)),divide(divide(a,divide(divide(b,b),b)),divide(a,divide(divide(b,b),b)))),
    inference(monotonicity,[status(thm)],[186]) ).

tff(188,plain,
    divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))) = divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))),
    inference(transitivity,[status(thm)],[187,111,13,184,181,176,174]) ).

tff(189,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),
    inference(monotonicity,[status(thm)],[188]) ).

tff(190,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),
    inference(symmetry,[status(thm)],[189]) ).

tff(191,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(192,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),
    inference(unit_resolution,[status(thm)],[191,7]) ).

tff(193,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))))))) = divide(b,divide(b,a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(194,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))))))) = divide(b,divide(b,a)),
    inference(unit_resolution,[status(thm)],[193,7]) ).

tff(195,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))))) = divide(a,a) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(196,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))))) = divide(a,a),
    inference(unit_resolution,[status(thm)],[195,7]) ).

tff(197,plain,
    inverse(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = inverse(b),
    inference(monotonicity,[status(thm)],[128]) ).

tff(198,plain,
    ( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
    | ( inverse(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(a,a),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(199,plain,
    inverse(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = divide(divide(a,a),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
    inference(unit_resolution,[status(thm)],[198,39]) ).

tff(200,plain,
    divide(divide(a,a),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))) = inverse(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
    inference(symmetry,[status(thm)],[199]) ).

tff(201,plain,
    b = divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(b,divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))),
    inference(symmetry,[status(thm)],[113]) ).

tff(202,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a)))) = divide(b,divide(a,divide(b,divide(b,a)))),
    inference(monotonicity,[status(thm)],[128]) ).

tff(203,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a)))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
    inference(transitivity,[status(thm)],[202,46,201,120,49]) ).

tff(204,plain,
    divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))) = divide(divide(a,a),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))),
    inference(monotonicity,[status(thm)],[203]) ).

tff(205,plain,
    divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))) = divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a))))),
    inference(transitivity,[status(thm)],[204,200,197,43,58]) ).

tff(206,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(b,b),divide(b,divide(a,divide(b,divide(b,a)))))),
    inference(monotonicity,[status(thm)],[205]) ).

tff(207,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a)))))) = b,
    inference(transitivity,[status(thm)],[206,121,113]) ).

tff(208,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))))) = divide(b,b),
    inference(monotonicity,[status(thm)],[128,207]) ).

tff(209,plain,
    divide(b,b) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,a),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(a,divide(b,divide(b,a))))))),
    inference(symmetry,[status(thm)],[208]) ).

tff(210,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(b,divide(b,a)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(211,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(b,divide(b,a)),
    inference(unit_resolution,[status(thm)],[210,7]) ).

tff(212,plain,
    divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))))) = divide(divide(b,divide(b,a)),divide(b,divide(b,a))),
    inference(monotonicity,[status(thm)],[211]) ).

tff(213,plain,
    divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))))) = divide(a,a),
    inference(transitivity,[status(thm)],[212,138,135,77,74,80,52,209,196]) ).

tff(214,plain,
    divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))))) = divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(a,a)),
    inference(monotonicity,[status(thm)],[213]) ).

tff(215,plain,
    divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(a,a)) = divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))))),
    inference(symmetry,[status(thm)],[214]) ).

tff(216,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))) = divide(a,a),
    inference(transitivity,[status(thm)],[77,74,80,52,209,196]) ).

tff(217,plain,
    divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))) = divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(a,a)),
    inference(monotonicity,[status(thm)],[216]) ).

tff(218,plain,
    divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))) = divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))))),
    inference(transitivity,[status(thm)],[217,215]) ).

tff(219,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))))))),
    inference(monotonicity,[status(thm)],[218]) ).

tff(220,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a)))))) = divide(b,divide(b,a)),
    inference(transitivity,[status(thm)],[219,194]) ).

tff(221,plain,
    divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))) = divide(divide(divide(b,b),divide(b,b)),divide(b,divide(b,a))),
    inference(monotonicity,[status(thm)],[117,220]) ).

tff(222,plain,
    divide(divide(divide(b,b),divide(b,b)),divide(b,divide(b,a))) = divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(b,divide(b,a)),divide(divide(a,divide(b,divide(b,a))),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),divide(divide(a,divide(b,divide(b,a))),divide(a,divide(b,divide(b,a))))))),
    inference(symmetry,[status(thm)],[221]) ).

tff(223,plain,
    ( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
    | ( inverse(divide(b,divide(b,a))) = divide(divide(divide(b,b),divide(b,b)),divide(b,divide(b,a))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(224,plain,
    inverse(divide(b,divide(b,a))) = divide(divide(divide(b,b),divide(b,b)),divide(b,divide(b,a))),
    inference(unit_resolution,[status(thm)],[223,39]) ).

tff(225,plain,
    ( ~ ! [B: $i,A: $i] : ( inverse(A) = divide(divide(B,B),A) )
    | ( inverse(divide(b,divide(b,a))) = divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(226,plain,
    inverse(divide(b,divide(b,a))) = divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a))),
    inference(unit_resolution,[status(thm)],[225,39]) ).

tff(227,plain,
    divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a))) = inverse(divide(b,divide(b,a))),
    inference(symmetry,[status(thm)],[226]) ).

tff(228,plain,
    divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b))))),
    inference(transitivity,[status(thm)],[227,224,222,192,190]) ).

tff(229,plain,
    b = divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),
    inference(transitivity,[status(thm)],[201,120,49]) ).

tff(230,plain,
    divide(b,divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a)))) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))),
    inference(monotonicity,[status(thm)],[229,228]) ).

tff(231,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(b,divide(divide(divide(b,divide(b,a)),divide(b,divide(b,a))),divide(b,divide(b,a)))),
    inference(symmetry,[status(thm)],[230]) ).

tff(232,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( divide(A,divide(B,divide(C,divide(A,B)))) = C )
    | ( divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(a,divide(divide(b,b),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(233,plain,
    divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))) = divide(a,divide(divide(b,b),b)),
    inference(unit_resolution,[status(thm)],[232,7]) ).

tff(234,plain,
    divide(a,divide(divide(b,b),b)) = divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(divide(b,b),b)),divide(divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)),divide(divide(a,divide(b,divide(b,a))),divide(divide(divide(b,b),divide(b,b)),b)))))),
    inference(symmetry,[status(thm)],[233]) ).

tff(235,plain,
    multiply(a,b) = multiply(b,a),
    inference(transitivity,[status(thm)],[183,234,231,168,165]) ).

tff(236,plain,
    ( ( multiply(a,b) != multiply(b,a) )
  <=> ( multiply(a,b) != multiply(b,a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(237,axiom,
    multiply(a,b) != multiply(b,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).

tff(238,plain,
    multiply(a,b) != multiply(b,a),
    inference(modus_ponens,[status(thm)],[237,236]) ).

tff(239,plain,
    $false,
    inference(unit_resolution,[status(thm)],[238,235]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP524-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Aug 31 17:41:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.54/0.60  % SZS status Unsatisfiable
% 0.54/0.60  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------