Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : GRP491-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n007.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 : Sat Jun 21 05:07:55 AM UTC 2025

% Result   : Unsatisfiable 0.47s 0.65s
% Output   : Proof 0.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   37
% Syntax   : Number of formulae    :  164 ( 132 unt;   0 typ;   0 def)
%            Number of atoms       :  204 ( 199 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   63 (  27   ~;  23   |;   0   &)
%                                         (  13 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :   17 (   3 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   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   :  117 ( 110   !;   0   ?; 117   :)

% Comments : 
%------------------------------------------------------------------------------
tff(a2_type,type,
    a2: $i ).

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

tff(identity_type,type,
    identity: $i ).

tff(double_divide_type,type,
    double_divide: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

tff(8,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = a2 ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(9,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = a2,
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [A: $i] :
      refl(( ( identity = double_divide(A,inverse(A)) )
      <=> ( identity = double_divide(A,inverse(A)) ) )),
    inference(bind,[status(th)],[]) ).

tff(11,plain,
    ( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
  <=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
  <=> ! [A: $i] : ( identity = double_divide(A,inverse(A)) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(13,axiom,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).

tff(14,plain,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    inference(skolemize,[status(sab)],[14]) ).

tff(16,plain,
    ! [A: $i] : ( identity = double_divide(A,inverse(A)) ),
    inference(modus_ponens,[status(thm)],[15,11]) ).

tff(17,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(18,plain,
    identity = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(unit_resolution,[status(thm)],[17,16]) ).

tff(19,plain,
    double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))) = identity,
    inference(symmetry,[status(thm)],[18]) ).

tff(20,plain,
    double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(a2,identity),
    inference(monotonicity,[status(thm)],[19]) ).

tff(21,plain,
    double_divide(a2,identity) = double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(symmetry,[status(thm)],[20]) ).

tff(22,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))) = double_divide(a2,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(23,plain,
    double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))) = double_divide(a2,identity),
    inference(unit_resolution,[status(thm)],[22,7]) ).

tff(24,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))) = identity ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(25,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))) = identity,
    inference(unit_resolution,[status(thm)],[24,7]) ).

tff(26,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[19,19]) ).

tff(27,plain,
    double_divide(identity,identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(symmetry,[status(thm)],[26]) ).

tff(28,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[25]) ).

tff(29,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[28,27]) ).

tff(30,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[29,25]) ).

tff(31,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))),
    inference(symmetry,[status(thm)],[30]) ).

tff(32,plain,
    ^ [A: $i] :
      refl(( ( inverse(A) = double_divide(A,identity) )
      <=> ( inverse(A) = double_divide(A,identity) ) )),
    inference(bind,[status(th)],[]) ).

tff(33,plain,
    ( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
  <=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
    inference(quant_intro,[status(thm)],[32]) ).

tff(34,plain,
    ( ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
  <=> ! [A: $i] : ( inverse(A) = double_divide(A,identity) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(35,axiom,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).

tff(36,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(skolemize,[status(sab)],[36]) ).

tff(38,plain,
    ! [A: $i] : ( inverse(A) = double_divide(A,identity) ),
    inference(modus_ponens,[status(thm)],[37,33]) ).

tff(39,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(40,plain,
    inverse(double_divide(a2,identity)) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[39,38]) ).

tff(41,plain,
    double_divide(double_divide(a2,identity),identity) = inverse(double_divide(a2,identity)),
    inference(symmetry,[status(thm)],[40]) ).

tff(42,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(monotonicity,[status(thm)],[41]) ).

tff(43,plain,
    double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)) = identity,
    inference(transitivity,[status(thm)],[42,19]) ).

tff(44,plain,
    double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[43]) ).

tff(45,plain,
    double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[44,27]) ).

tff(46,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[45,43]) ).

tff(47,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))),
    inference(transitivity,[status(thm)],[46,31]) ).

tff(48,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))))),
    inference(monotonicity,[status(thm)],[47]) ).

tff(49,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)))),
    inference(symmetry,[status(thm)],[48]) ).

tff(50,plain,
    double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))) = double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity)),identity),double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),identity))))),
    inference(monotonicity,[status(thm)],[49]) ).

tff(51,plain,
    double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))) = double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[50,23,21]) ).

tff(52,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))) = double_divide(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(53,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))) = double_divide(identity,identity),
    inference(unit_resolution,[status(thm)],[52,7]) ).

tff(54,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[53,27]) ).

tff(55,plain,
    double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))),identity) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[54]) ).

tff(56,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))))))) = double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[55,51]) ).

tff(57,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))),
    inference(monotonicity,[status(thm)],[56]) ).

tff(58,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))))),
    inference(symmetry,[status(thm)],[57]) ).

tff(59,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(60,plain,
    identity = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(unit_resolution,[status(thm)],[59,16]) ).

tff(61,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))) = identity,
    inference(symmetry,[status(thm)],[60]) ).

tff(62,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(63,plain,
    inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(unit_resolution,[status(thm)],[62,38]) ).

tff(64,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(symmetry,[status(thm)],[63]) ).

tff(65,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[19]) ).

tff(66,plain,
    double_divide(identity,identity) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),identity),
    inference(symmetry,[status(thm)],[65]) ).

tff(67,plain,
    double_divide(identity,identity) = inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(transitivity,[status(thm)],[66,64]) ).

tff(68,plain,
    double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),inverse(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))),
    inference(monotonicity,[status(thm)],[18,67]) ).

tff(69,plain,
    double_divide(identity,double_divide(identity,identity)) = identity,
    inference(transitivity,[status(thm)],[68,61]) ).

tff(70,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,identity))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[69]) ).

tff(71,plain,
    double_divide(identity,identity) = double_divide(identity,double_divide(identity,double_divide(identity,identity))),
    inference(symmetry,[status(thm)],[70]) ).

tff(72,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[19]) ).

tff(73,plain,
    double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(identity,double_divide(identity,double_divide(identity,identity))),
    inference(transitivity,[status(thm)],[72,71]) ).

tff(74,plain,
    double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))))))))),
    inference(monotonicity,[status(thm)],[73,58]) ).

tff(75,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))))))))) = double_divide(double_divide(identity,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(a2,double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),
    inference(symmetry,[status(thm)],[74]) ).

tff(76,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))))))))) = double_divide(identity,double_divide(a2,identity)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(77,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))))))))) = double_divide(identity,double_divide(a2,identity)),
    inference(unit_resolution,[status(thm)],[76,7]) ).

tff(78,plain,
    double_divide(identity,double_divide(a2,identity)) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))))))))),
    inference(symmetry,[status(thm)],[77]) ).

tff(79,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(a2,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))) = double_divide(identity,double_divide(a2,identity)) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(80,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(a2,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))) = double_divide(identity,double_divide(a2,identity)),
    inference(unit_resolution,[status(thm)],[79,7]) ).

tff(81,plain,
    ( ~ ! [A: $i] : ( identity = double_divide(A,inverse(A)) )
    | ( identity = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(82,plain,
    identity = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))),
    inference(unit_resolution,[status(thm)],[81,16]) ).

tff(83,plain,
    double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))) = identity,
    inference(symmetry,[status(thm)],[82]) ).

tff(84,plain,
    ( ~ ! [A: $i] : ( inverse(A) = double_divide(A,identity) )
    | ( inverse(double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(85,plain,
    inverse(double_divide(double_divide(a2,identity),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
    inference(unit_resolution,[status(thm)],[84,38]) ).

tff(86,plain,
    double_divide(double_divide(double_divide(a2,identity),identity),identity) = inverse(double_divide(double_divide(a2,identity),identity)),
    inference(symmetry,[status(thm)],[85]) ).

tff(87,plain,
    double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)) = double_divide(double_divide(double_divide(a2,identity),identity),inverse(double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[86]) ).

tff(88,plain,
    double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)) = identity,
    inference(transitivity,[status(thm)],[87,83]) ).

tff(89,plain,
    double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[88]) ).

tff(90,plain,
    double_divide(identity,identity) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))),
    inference(symmetry,[status(thm)],[89]) ).

tff(91,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(92,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),
    inference(unit_resolution,[status(thm)],[91,7]) ).

tff(93,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),
    inference(monotonicity,[status(thm)],[92]) ).

tff(94,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[93,92]) ).

tff(95,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))))),
    inference(monotonicity,[status(thm)],[94]) ).

tff(96,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity)))))))) = double_divide(identity,identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(97,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity)))))))) = double_divide(identity,identity),
    inference(unit_resolution,[status(thm)],[96,7]) ).

tff(98,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(99,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity))))) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[98,7]) ).

tff(100,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity))))),identity) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
    inference(monotonicity,[status(thm)],[99]) ).

tff(101,plain,
    double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity)))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),
    inference(monotonicity,[status(thm)],[100,99]) ).

tff(102,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[101]) ).

tff(103,plain,
    double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity)))))))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[69,102]) ).

tff(104,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity)))))))),
    inference(symmetry,[status(thm)],[103]) ).

tff(105,plain,
    double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(identity,identity),
    inference(transitivity,[status(thm)],[104,97]) ).

tff(106,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))) = double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),
    inference(monotonicity,[status(thm)],[105,95]) ).

tff(107,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(108,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),
    inference(unit_resolution,[status(thm)],[107,7]) ).

tff(109,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))),
    inference(symmetry,[status(thm)],[108]) ).

tff(110,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(111,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),
    inference(unit_resolution,[status(thm)],[110,7]) ).

tff(112,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(113,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[112,7]) ).

tff(114,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity) = double_divide(double_divide(double_divide(a2,identity),identity),identity),
    inference(monotonicity,[status(thm)],[113]) ).

tff(115,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))) = double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),
    inference(monotonicity,[status(thm)],[114,113]) ).

tff(116,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),
    inference(monotonicity,[status(thm)],[115]) ).

tff(117,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))))),
    inference(symmetry,[status(thm)],[116]) ).

tff(118,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))),
    inference(symmetry,[status(thm)],[106]) ).

tff(119,plain,
    identity = double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),identity)))))),
    inference(symmetry,[status(thm)],[25]) ).

tff(120,plain,
    identity = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))))),
    inference(transitivity,[status(thm)],[119,118,108,117]) ).

tff(121,plain,
    double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity))))),identity),double_divide(double_divide(identity,identity),double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(a2,identity)))))))),
    inference(symmetry,[status(thm)],[97]) ).

tff(122,plain,
    double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),
    inference(transitivity,[status(thm)],[26,121,103]) ).

tff(123,plain,
    double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))),
    inference(monotonicity,[status(thm)],[122,120]) ).

tff(124,plain,
    ^ [B: $i,A: $i] :
      refl(( ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
      <=> ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) )),
    inference(bind,[status(th)],[]) ).

tff(125,plain,
    ( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
  <=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
    inference(quant_intro,[status(thm)],[124]) ).

tff(126,plain,
    ( ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
  <=> ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(127,axiom,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).

tff(128,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(modus_ponens,[status(thm)],[127,126]) ).

tff(129,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(skolemize,[status(sab)],[128]) ).

tff(130,plain,
    ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    inference(modus_ponens,[status(thm)],[129,125]) ).

tff(131,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(132,plain,
    multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(unit_resolution,[status(thm)],[131,130]) ).

tff(133,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))) = double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),
    inference(transitivity,[status(thm)],[109,106,25,18]) ).

tff(134,plain,
    multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))) = multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(monotonicity,[status(thm)],[133]) ).

tff(135,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(136,plain,
    multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(unit_resolution,[status(thm)],[135,130]) ).

tff(137,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = multiply(double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),
    inference(symmetry,[status(thm)],[136]) ).

tff(138,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity) = identity,
    inference(transitivity,[status(thm)],[137,134,132,123,111,109,106,25]) ).

tff(139,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)) = double_divide(identity,identity),
    inference(monotonicity,[status(thm)],[138]) ).

tff(140,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))) = identity,
    inference(transitivity,[status(thm)],[109,106,25]) ).

tff(141,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),identity),
    inference(monotonicity,[status(thm)],[19]) ).

tff(142,plain,
    double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),
    inference(symmetry,[status(thm)],[141]) ).

tff(143,plain,
    double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),
    inference(monotonicity,[status(thm)],[142,140]) ).

tff(144,plain,
    double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity)),
    inference(monotonicity,[status(thm)],[143]) ).

tff(145,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(146,plain,
    double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),
    inference(unit_resolution,[status(thm)],[145,7]) ).

tff(147,plain,
    double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),identity),
    inference(monotonicity,[status(thm)],[146]) ).

tff(148,plain,
    double_divide(double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity)))),
    inference(monotonicity,[status(thm)],[147,146]) ).

tff(149,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))))) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),identity),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))))),
    inference(monotonicity,[status(thm)],[148]) ).

tff(150,plain,
    double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))))) = double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity))),
    inference(transitivity,[status(thm)],[149,144,139,90]) ).

tff(151,plain,
    double_divide(identity,double_divide(a2,identity)) = a2,
    inference(transitivity,[status(thm)],[78,75,9]) ).

tff(152,plain,
    double_divide(identity,double_divide(identity,double_divide(a2,identity))) = double_divide(identity,a2),
    inference(monotonicity,[status(thm)],[151]) ).

tff(153,plain,
    double_divide(double_divide(identity,double_divide(identity,double_divide(a2,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))) = double_divide(double_divide(identity,a2),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)))),
    inference(monotonicity,[status(thm)],[152,150]) ).

tff(154,plain,
    double_divide(double_divide(identity,a2),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)))) = double_divide(double_divide(identity,double_divide(identity,double_divide(a2,identity))),double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity))))))),identity),double_divide(double_divide(identity,double_divide(a2,identity)),double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))),identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(a2,identity),identity),identity),double_divide(double_divide(a2,identity),identity))),double_divide(double_divide(a2,identity),inverse(double_divide(a2,identity)))))))))),
    inference(symmetry,[status(thm)],[153]) ).

tff(155,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C )
    | ( double_divide(double_divide(identity,a2),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)))) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(156,plain,
    double_divide(double_divide(identity,a2),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)))) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[155,7]) ).

tff(157,plain,
    double_divide(double_divide(a2,identity),identity) = double_divide(double_divide(identity,a2),double_divide(identity,double_divide(double_divide(double_divide(a2,identity),identity),double_divide(double_divide(double_divide(a2,identity),identity),identity)))),
    inference(symmetry,[status(thm)],[156]) ).

tff(158,plain,
    ( ~ ! [B: $i,A: $i] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) )
    | ( multiply(identity,a2) = double_divide(double_divide(a2,identity),identity) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(159,plain,
    multiply(identity,a2) = double_divide(double_divide(a2,identity),identity),
    inference(unit_resolution,[status(thm)],[158,130]) ).

tff(160,plain,
    multiply(identity,a2) = a2,
    inference(transitivity,[status(thm)],[159,157,154,80,78,75,9]) ).

tff(161,plain,
    ( ( multiply(identity,a2) != a2 )
  <=> ( multiply(identity,a2) != a2 ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(162,axiom,
    multiply(identity,a2) != a2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).

tff(163,plain,
    multiply(identity,a2) != a2,
    inference(modus_ponens,[status(thm)],[162,161]) ).

tff(164,plain,
    $false,
    inference(unit_resolution,[status(thm)],[163,160]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : GRP491-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.11  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n007.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Thu Jun 19 16:13:04 EDT 2025
% 0.11/0.32  % CPUTime    : 
% 0.47/0.65  % SZS status Unsatisfiable
% 0.47/0.65  % SZS output start Proof
% See solution above
% 0.50/0.70  % E exiting
%------------------------------------------------------------------------------