TSTP Solution File: ALG007-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n028.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 : Tue Sep  6 16:07:00 EDT 2022

% Result   : Unsatisfiable 9.30s 6.23s
% Output   : Proof 9.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :   57
% Syntax   : Number of formulae    :  251 ( 198 unt;   4 typ;   0 def)
%            Number of atoms       :  302 ( 298 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   98 (  46   ~;  42   |;   0   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of FOOLs       :    3 (   3 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  174 ( 167   !;   0   ?; 174   :)

% Comments : 
%------------------------------------------------------------------------------
tff(difference_type,type,
    difference: ( $i * $i ) > $i ).

tff(c_type,type,
    c: $i ).

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

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

tff(1,plain,
    ^ [Z: $i,Y: $i,X: $i] :
      refl(
        ( ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
      <=> ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
  <=> ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
  <=> ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_3_simplified) ).

tff(5,plain,
    ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(a,c),difference(b,c)) = difference(difference(a,difference(b,c)),c) ) ),
    inference(quant_inst,[status(thm)],]) ).

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

tff(10,plain,
    difference(difference(a,difference(b,c)),c) = difference(difference(a,c),difference(b,c)),
    inference(symmetry,[status(thm)],[9]) ).

tff(11,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ( difference(X,difference(Y,X)) = X )
      <=> ( difference(X,difference(Y,X)) = X ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
  <=> ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,plain,
    ( ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
  <=> ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,axiom,
    ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_1) ).

tff(15,plain,
    ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
    inference(modus_ponens,[status(thm)],[14,13]) ).

tff(16,plain,
    ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
    inference(skolemize,[status(sab)],[15]) ).

tff(17,plain,
    ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
    | ( difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,difference(b,c)),c))) = difference(difference(a,difference(b,c)),c) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(19,plain,
    difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,difference(b,c)),c))) = difference(difference(a,difference(b,c)),c),
    inference(unit_resolution,[status(thm)],[18,17]) ).

tff(20,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
    | ( difference(difference(difference(a,c),difference(difference(a,c),b)),difference(c,difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(a,c),difference(difference(a,c),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(21,plain,
    difference(difference(difference(a,c),difference(difference(a,c),b)),difference(c,difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(a,c),difference(difference(a,c),b)),
    inference(unit_resolution,[status(thm)],[20,17]) ).

tff(22,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(a,c),difference(difference(a,c),b)) = difference(difference(a,difference(difference(a,c),b)),c) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(23,plain,
    difference(difference(a,c),difference(difference(a,c),b)) = difference(difference(a,difference(difference(a,c),b)),c),
    inference(unit_resolution,[status(thm)],[22,7]) ).

tff(24,plain,
    difference(c,difference(difference(a,c),difference(difference(a,c),b))) = difference(c,difference(difference(a,difference(difference(a,c),b)),c)),
    inference(monotonicity,[status(thm)],[23]) ).

tff(25,plain,
    difference(c,difference(difference(a,difference(difference(a,c),b)),c)) = difference(c,difference(difference(a,c),difference(difference(a,c),b))),
    inference(symmetry,[status(thm)],[24]) ).

tff(26,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
    | ( difference(c,difference(difference(a,difference(difference(a,c),b)),c)) = c ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(27,plain,
    difference(c,difference(difference(a,difference(difference(a,c),b)),c)) = c,
    inference(unit_resolution,[status(thm)],[26,17]) ).

tff(28,plain,
    c = difference(c,difference(difference(a,difference(difference(a,c),b)),c)),
    inference(symmetry,[status(thm)],[27]) ).

tff(29,plain,
    c = difference(c,difference(difference(a,c),difference(difference(a,c),b))),
    inference(transitivity,[status(thm)],[28,25]) ).

tff(30,plain,
    difference(difference(difference(a,c),difference(difference(a,c),b)),c) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(c,difference(difference(a,c),difference(difference(a,c),b)))),
    inference(monotonicity,[status(thm)],[29]) ).

tff(31,plain,
    difference(difference(difference(a,c),difference(difference(a,c),b)),c) = difference(difference(a,c),difference(difference(a,c),b)),
    inference(transitivity,[status(thm)],[30,21]) ).

tff(32,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(monotonicity,[status(thm)],[31]) ).

tff(33,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(34,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(unit_resolution,[status(thm)],[33,7]) ).

tff(35,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
    | ( difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))) = difference(a,c) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(36,plain,
    difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))) = difference(a,c),
    inference(unit_resolution,[status(thm)],[35,17]) ).

tff(37,plain,
    difference(a,c) = difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),
    inference(symmetry,[status(thm)],[36]) ).

tff(38,plain,
    difference(difference(a,c),b) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),b),
    inference(monotonicity,[status(thm)],[37]) ).

tff(39,plain,
    difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),b) = difference(difference(a,c),b),
    inference(symmetry,[status(thm)],[38]) ).

tff(40,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(41,plain,
    difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),b),
    inference(unit_resolution,[status(thm)],[40,7]) ).

tff(42,plain,
    ^ [Y: $i,X: $i] :
      refl(
        ( ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
      <=> ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ) )),
    inference(bind,[status(th)],]) ).

tff(43,plain,
    ( ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
  <=> ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ) ),
    inference(quant_intro,[status(thm)],[42]) ).

tff(44,plain,
    ( ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
  <=> ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,axiom,
    ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_2) ).

tff(46,plain,
    ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
    inference(skolemize,[status(sab)],[46]) ).

tff(48,plain,
    ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ),
    inference(modus_ponens,[status(thm)],[47,43]) ).

tff(49,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
    | ( difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(50,plain,
    difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),
    inference(unit_resolution,[status(thm)],[49,48]) ).

tff(51,plain,
    difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
    inference(symmetry,[status(thm)],[50]) ).

tff(52,plain,
    difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(a,c),b),
    inference(transitivity,[status(thm)],[51,41,39]) ).

tff(53,plain,
    difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(a,c),difference(difference(a,c),b)),
    inference(monotonicity,[status(thm)],[52]) ).

tff(54,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(monotonicity,[status(thm)],[53]) ).

tff(55,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(56,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
    inference(unit_resolution,[status(thm)],[55,7]) ).

tff(57,plain,
    difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(symmetry,[status(thm)],[56]) ).

tff(58,plain,
    difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),b) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
    inference(symmetry,[status(thm)],[41]) ).

tff(59,plain,
    difference(difference(a,c),b) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),
    inference(transitivity,[status(thm)],[38,58,50]) ).

tff(60,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(a,c),b),difference(difference(a,c),b)) = difference(difference(difference(a,c),difference(difference(a,c),b)),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(61,plain,
    difference(difference(difference(a,c),b),difference(difference(a,c),b)) = difference(difference(difference(a,c),difference(difference(a,c),b)),b),
    inference(unit_resolution,[status(thm)],[60,7]) ).

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

tff(63,plain,
    difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
    inference(monotonicity,[status(thm)],[62,59]) ).

tff(64,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
    | ( difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(a,c),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(65,plain,
    difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(a,c),b),
    inference(unit_resolution,[status(thm)],[64,17]) ).

tff(66,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(67,plain,
    difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b),
    inference(unit_resolution,[status(thm)],[66,7]) ).

tff(68,plain,
    difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(symmetry,[status(thm)],[67]) ).

tff(69,plain,
    difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(symmetry,[status(thm)],[62]) ).

tff(70,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(71,plain,
    difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),
    inference(unit_resolution,[status(thm)],[70,7]) ).

tff(72,plain,
    difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(symmetry,[status(thm)],[71]) ).

tff(73,plain,
    difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(transitivity,[status(thm)],[72,69]) ).

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

tff(75,plain,
    difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),b) = difference(difference(a,c),b),
    inference(transitivity,[status(thm)],[74,68,65]) ).

tff(76,plain,
    difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)),
    inference(monotonicity,[status(thm)],[73,75]) ).

tff(77,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
    | ( difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),b)) = difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(78,plain,
    difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),b)) = difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),
    inference(unit_resolution,[status(thm)],[77,48]) ).

tff(79,plain,
    difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) = difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),b)),
    inference(symmetry,[status(thm)],[78]) ).

tff(80,plain,
    difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(transitivity,[status(thm)],[79,76,63,57,54]) ).

tff(81,plain,
    difference(difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),c) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),
    inference(monotonicity,[status(thm)],[80]) ).

tff(82,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),c) = difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(83,plain,
    difference(difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),c) = difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),
    inference(unit_resolution,[status(thm)],[82,7]) ).

tff(84,plain,
    difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) = difference(difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),c),
    inference(symmetry,[status(thm)],[83]) ).

tff(85,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
    | ( difference(difference(b,c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c))) = difference(b,c) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(86,plain,
    difference(difference(b,c),difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c))) = difference(b,c),
    inference(unit_resolution,[status(thm)],[85,17]) ).

tff(87,plain,
    difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
    inference(monotonicity,[status(thm)],[65]) ).

tff(88,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)) = difference(difference(difference(difference(a,c),b),difference(difference(a,c),b)),difference(difference(difference(a,c),b),difference(difference(a,c),b))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(89,plain,
    difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)) = difference(difference(difference(difference(a,c),b),difference(difference(a,c),b)),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(unit_resolution,[status(thm)],[88,7]) ).

tff(90,plain,
    difference(difference(difference(difference(a,c),b),difference(difference(a,c),b)),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(a,c),b)),
    inference(symmetry,[status(thm)],[89]) ).

tff(91,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(a,c),b),difference(a,c)) = difference(difference(difference(a,c),difference(a,c)),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(92,plain,
    difference(difference(difference(a,c),b),difference(a,c)) = difference(difference(difference(a,c),difference(a,c)),b),
    inference(unit_resolution,[status(thm)],[91,7]) ).

tff(93,plain,
    difference(difference(difference(a,c),difference(a,c)),b) = difference(difference(difference(a,c),b),difference(a,c)),
    inference(symmetry,[status(thm)],[92]) ).

tff(94,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
    inference(monotonicity,[status(thm)],[52,93]) ).

tff(95,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(a,c),b),
    inference(transitivity,[status(thm)],[94,41,39]) ).

tff(96,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
    inference(monotonicity,[status(thm)],[95,52]) ).

tff(97,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(a,c)),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(98,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(a,c)),b)),
    inference(unit_resolution,[status(thm)],[97,7]) ).

tff(99,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
    inference(symmetry,[status(thm)],[98]) ).

tff(100,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
    inference(monotonicity,[status(thm)],[52,52]) ).

tff(101,plain,
    difference(difference(difference(a,c),b),difference(difference(a,c),b)) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
    inference(symmetry,[status(thm)],[100]) ).

tff(102,plain,
    difference(difference(difference(a,c),difference(difference(a,c),b)),b) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
    inference(symmetry,[status(thm)],[61]) ).

tff(103,plain,
    difference(difference(difference(a,c),difference(difference(a,c),b)),b) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
    inference(transitivity,[status(thm)],[102,101]) ).

tff(104,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),difference(difference(difference(a,c),difference(a,c)),b)),
    inference(monotonicity,[status(thm)],[103]) ).

tff(105,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
    inference(transitivity,[status(thm)],[104,99,96]) ).

tff(106,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(a,c),difference(a,c)),b))) = difference(difference(difference(difference(a,c),b),difference(difference(a,c),b)),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(monotonicity,[status(thm)],[102,105]) ).

tff(107,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
    | ( difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(a,c),difference(a,c)),b))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(108,plain,
    difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(difference(a,c),difference(difference(a,c),b)),b),difference(difference(difference(a,c),difference(a,c)),b))),
    inference(unit_resolution,[status(thm)],[107,48]) ).

tff(109,plain,
    difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),b),difference(a,c)),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(monotonicity,[status(thm)],[93,102]) ).

tff(110,plain,
    difference(difference(difference(difference(a,c),b),difference(a,c)),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(symmetry,[status(thm)],[109]) ).

tff(111,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(a,c)) = difference(difference(difference(difference(a,c),b),difference(a,c)),difference(difference(difference(a,c),b),difference(difference(a,c),b))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(112,plain,
    difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(a,c)) = difference(difference(difference(difference(a,c),b),difference(a,c)),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(unit_resolution,[status(thm)],[111,7]) ).

tff(113,plain,
    difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(a,c)) = difference(difference(difference(a,c),b),difference(a,c)),
    inference(monotonicity,[status(thm)],[65]) ).

tff(114,plain,
    difference(difference(difference(a,c),b),difference(a,c)) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(a,c)),
    inference(symmetry,[status(thm)],[113]) ).

tff(115,plain,
    difference(difference(difference(a,c),difference(a,c)),b) = difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(transitivity,[status(thm)],[93,114,112,110]) ).

tff(116,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(a,c)) = difference(difference(difference(a,c),b),difference(a,c)),
    inference(monotonicity,[status(thm)],[52]) ).

tff(117,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(a,c)) = difference(difference(difference(a,c),difference(a,c)),b),
    inference(transitivity,[status(thm)],[116,92]) ).

tff(118,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(a,c)),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(difference(a,c),difference(a,c)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
    inference(monotonicity,[status(thm)],[117,115]) ).

tff(119,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(a,c)) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(a,c)),difference(difference(difference(a,c),difference(a,c)),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(120,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(a,c)) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(a,c)),difference(difference(difference(a,c),difference(a,c)),b)),
    inference(unit_resolution,[status(thm)],[119,7]) ).

tff(121,plain,
    difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),
    inference(symmetry,[status(thm)],[94]) ).

tff(122,plain,
    difference(difference(a,c),b) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),
    inference(transitivity,[status(thm)],[38,58,121]) ).

tff(123,plain,
    difference(difference(difference(a,c),b),difference(a,c)) = difference(difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(a,c)),b)),difference(a,c)),
    inference(monotonicity,[status(thm)],[122]) ).

tff(124,plain,
    difference(difference(difference(a,c),b),difference(a,c)) = difference(difference(difference(a,c),b),difference(difference(a,c),b)),
    inference(transitivity,[status(thm)],[123,120,118,108,106,90,87]) ).

tff(125,plain,
    difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(monotonicity,[status(thm)],[124]) ).

tff(126,plain,
    difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(a,c),difference(difference(difference(a,c),b),difference(a,c))),
    inference(symmetry,[status(thm)],[125]) ).

tff(127,plain,
    difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(a,c),
    inference(transitivity,[status(thm)],[72,69,126,36]) ).

tff(128,plain,
    difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)) = difference(difference(a,c),difference(b,c)),
    inference(monotonicity,[status(thm)],[127]) ).

tff(129,plain,
    difference(difference(a,c),difference(b,c)) = difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),
    inference(symmetry,[status(thm)],[128]) ).

tff(130,plain,
    difference(difference(a,difference(b,c)),c) = difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),
    inference(transitivity,[status(thm)],[10,129]) ).

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

tff(132,plain,
    difference(difference(b,c),difference(difference(a,difference(b,c)),c)) = difference(b,c),
    inference(transitivity,[status(thm)],[131,86]) ).

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

tff(134,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),difference(difference(a,difference(b,c)),c)) = difference(difference(difference(b,c),difference(difference(a,difference(b,c)),c)),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(135,plain,
    difference(difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),difference(difference(a,difference(b,c)),c)) = difference(difference(difference(b,c),difference(difference(a,difference(b,c)),c)),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),
    inference(unit_resolution,[status(thm)],[134,7]) ).

tff(136,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(b,difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),c),
    inference(symmetry,[status(thm)],[81]) ).

tff(137,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),
    inference(symmetry,[status(thm)],[34]) ).

tff(138,plain,
    difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),difference(difference(a,c),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(symmetry,[status(thm)],[32]) ).

tff(139,plain,
    difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(b,c),difference(b,difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c))),
    inference(transitivity,[status(thm)],[138,137,136,83]) ).

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

tff(141,plain,
    difference(difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,difference(b,c)),c)) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(transitivity,[status(thm)],[140,135,133,84,81,34,32]) ).

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

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

tff(144,plain,
    difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
    inference(monotonicity,[status(thm)],[130]) ).

tff(145,plain,
    difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(a,difference(b,c)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
    inference(symmetry,[status(thm)],[144]) ).

tff(146,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(147,plain,
    difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)),
    inference(unit_resolution,[status(thm)],[146,7]) ).

tff(148,plain,
    difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(b,c)),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
    inference(symmetry,[status(thm)],[147]) ).

tff(149,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) )
    | ( difference(b,difference(b,difference(a,c))) = difference(difference(a,c),difference(difference(a,c),b)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(150,plain,
    difference(b,difference(b,difference(a,c))) = difference(difference(a,c),difference(difference(a,c),b)),
    inference(unit_resolution,[status(thm)],[149,48]) ).

tff(151,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
    | ( difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = b ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(152,plain,
    difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = b,
    inference(unit_resolution,[status(thm)],[151,17]) ).

tff(153,plain,
    b = difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(symmetry,[status(thm)],[152]) ).

tff(154,plain,
    difference(b,difference(b,difference(a,c))) = difference(difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(b,difference(a,c))),
    inference(monotonicity,[status(thm)],[153]) ).

tff(155,plain,
    difference(difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(b,difference(a,c))) = difference(b,difference(b,difference(a,c))),
    inference(symmetry,[status(thm)],[154]) ).

tff(156,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(b,difference(b,difference(a,c))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(b,difference(a,c))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(157,plain,
    difference(difference(b,difference(b,difference(a,c))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(b,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(b,difference(a,c))),
    inference(unit_resolution,[status(thm)],[156,7]) ).

tff(158,plain,
    difference(difference(b,difference(b,difference(a,c))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(monotonicity,[status(thm)],[150]) ).

tff(159,plain,
    difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(b,difference(b,difference(a,c))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(symmetry,[status(thm)],[158]) ).

tff(160,plain,
    difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(a,c),difference(difference(a,c),b)),
    inference(transitivity,[status(thm)],[159,157,155,150]) ).

tff(161,plain,
    difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),c),
    inference(monotonicity,[status(thm)],[73]) ).

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

tff(163,plain,
    difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),c),
    inference(monotonicity,[status(thm)],[69]) ).

tff(164,plain,
    difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c) = difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),
    inference(transitivity,[status(thm)],[163,162]) ).

tff(165,plain,
    difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),difference(difference(a,c),difference(difference(a,c),b))),
    inference(monotonicity,[status(thm)],[164,160]) ).

tff(166,plain,
    difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
    inference(symmetry,[status(thm)],[165]) ).

tff(167,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))),c) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),difference(difference(a,c),difference(difference(a,c),b))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(168,plain,
    difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))),c) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),difference(difference(a,c),difference(difference(a,c),b))),
    inference(unit_resolution,[status(thm)],[167,7]) ).

tff(169,plain,
    difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
    inference(monotonicity,[status(thm)],[65]) ).

tff(170,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(171,plain,
    difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(unit_resolution,[status(thm)],[170,7]) ).

tff(172,plain,
    difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),b),difference(a,c))),
    inference(symmetry,[status(thm)],[171]) ).

tff(173,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(monotonicity,[status(thm)],[51,102]) ).

tff(174,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),b))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(175,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),b))),
    inference(unit_resolution,[status(thm)],[174,7]) ).

tff(176,plain,
    difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(symmetry,[status(thm)],[175]) ).

tff(177,plain,
    difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),b))),
    inference(monotonicity,[status(thm)],[72]) ).

tff(178,plain,
    difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(a,c),b),
    inference(transitivity,[status(thm)],[177,176,173,172,169,41,39]) ).

tff(179,plain,
    difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))),c) = difference(difference(difference(a,c),b),c),
    inference(monotonicity,[status(thm)],[178]) ).

tff(180,plain,
    difference(difference(difference(a,c),b),c) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))),c),
    inference(symmetry,[status(thm)],[179]) ).

tff(181,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(182,plain,
    difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c),
    inference(unit_resolution,[status(thm)],[181,7]) ).

tff(183,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(a,b),c) = difference(difference(a,c),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(184,plain,
    difference(difference(a,b),c) = difference(difference(a,c),b),
    inference(unit_resolution,[status(thm)],[183,7]) ).

tff(185,plain,
    difference(difference(difference(a,b),c),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
    inference(monotonicity,[status(thm)],[184]) ).

tff(186,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(a,b),c),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),c) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(187,plain,
    difference(difference(difference(a,b),c),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),c),
    inference(unit_resolution,[status(thm)],[186,7]) ).

tff(188,plain,
    difference(difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),c) = difference(difference(difference(a,b),c),difference(difference(difference(a,c),b),difference(a,c))),
    inference(symmetry,[status(thm)],[187]) ).

tff(189,plain,
    difference(difference(a,b),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),
    inference(monotonicity,[status(thm)],[93]) ).

tff(190,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(a,b),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(191,plain,
    difference(difference(a,b),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),
    inference(unit_resolution,[status(thm)],[190,7]) ).

tff(192,plain,
    difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b) = difference(difference(a,b),difference(difference(difference(a,c),difference(a,c)),b)),
    inference(symmetry,[status(thm)],[191]) ).

tff(193,plain,
    difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b) = difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),
    inference(transitivity,[status(thm)],[192,189]) ).

tff(194,plain,
    difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c) = difference(difference(difference(a,b),difference(difference(difference(a,c),b),difference(a,c))),c),
    inference(monotonicity,[status(thm)],[193]) ).

tff(195,plain,
    difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c) = difference(difference(a,c),b),
    inference(transitivity,[status(thm)],[194,188,185,41,39]) ).

tff(196,plain,
    difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c),difference(difference(difference(a,c),difference(a,c)),b)) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
    inference(monotonicity,[status(thm)],[195,93]) ).

tff(197,plain,
    difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),c),difference(difference(difference(a,c),difference(a,c)),b)),
    inference(symmetry,[status(thm)],[196]) ).

tff(198,plain,
    difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c),
    inference(transitivity,[status(thm)],[51,197,182]) ).

tff(199,plain,
    difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(c,difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c)),
    inference(monotonicity,[status(thm)],[198]) ).

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

tff(201,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
    | ( difference(c,difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c)) = c ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(202,plain,
    difference(c,difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c)) = c,
    inference(unit_resolution,[status(thm)],[201,17]) ).

tff(203,plain,
    c = difference(c,difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(a,c)),b)),b),difference(difference(difference(a,c),difference(a,c)),b)),c)),
    inference(symmetry,[status(thm)],[202]) ).

tff(204,plain,
    c = difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
    inference(transitivity,[status(thm)],[203,200]) ).

tff(205,plain,
    difference(difference(difference(a,c),b),c) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))),
    inference(monotonicity,[status(thm)],[59,204]) ).

tff(206,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(difference(a,c),b),c),
    inference(symmetry,[status(thm)],[205]) ).

tff(207,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
    | ( difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(208,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(c,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),
    inference(unit_resolution,[status(thm)],[207,17]) ).

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

tff(210,plain,
    difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(a,c),difference(difference(a,c),b))),
    inference(monotonicity,[status(thm)],[72,160]) ).

tff(211,plain,
    difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),
    inference(transitivity,[status(thm)],[210,176,173,172,169,50,209,206,180,168,166]) ).

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

tff(213,plain,
    difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)),
    inference(symmetry,[status(thm)],[212]) ).

tff(214,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),c) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(215,plain,
    difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),c),
    inference(unit_resolution,[status(thm)],[214,7]) ).

tff(216,plain,
    difference(difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),c) = difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
    inference(symmetry,[status(thm)],[215]) ).

tff(217,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
    | ( difference(b,difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b)) = b ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(218,plain,
    difference(b,difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b)) = b,
    inference(unit_resolution,[status(thm)],[217,17]) ).

tff(219,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(220,plain,
    difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),
    inference(unit_resolution,[status(thm)],[219,7]) ).

tff(221,plain,
    difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b) = difference(difference(a,c),b),
    inference(transitivity,[status(thm)],[68,65]) ).

tff(222,plain,
    difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(monotonicity,[status(thm)],[221,102]) ).

tff(223,plain,
    ( ~ ! [Z: $i,Y: $i,X: $i] : ( difference(difference(X,Y),Z) = difference(difference(X,Z),Y) )
    | ( difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(224,plain,
    difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),
    inference(unit_resolution,[status(thm)],[223,7]) ).

tff(225,plain,
    difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b) = difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(symmetry,[status(thm)],[224]) ).

tff(226,plain,
    difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b) = difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),
    inference(transitivity,[status(thm)],[225,222,65,38,58]) ).

tff(227,plain,
    difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))),
    inference(monotonicity,[status(thm)],[226,102]) ).

tff(228,plain,
    difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))),difference(difference(difference(a,c),b),difference(difference(a,c),b))) = difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),
    inference(symmetry,[status(thm)],[227]) ).

tff(229,plain,
    difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(a,c))) = difference(difference(difference(difference(a,c),b),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),b),difference(a,c))),
    inference(symmetry,[status(thm)],[169]) ).

tff(230,plain,
    difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b),
    inference(transitivity,[status(thm)],[51,229,171,228,220]) ).

tff(231,plain,
    difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = difference(b,difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),b),difference(difference(a,c),b))),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),b)),
    inference(monotonicity,[status(thm)],[230]) ).

tff(232,plain,
    difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))) = b,
    inference(transitivity,[status(thm)],[231,218]) ).

tff(233,plain,
    difference(difference(b,difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),c) = difference(b,c),
    inference(monotonicity,[status(thm)],[232]) ).

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

tff(235,plain,
    difference(b,c) = difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b)))),
    inference(transitivity,[status(thm)],[234,216]) ).

tff(236,plain,
    difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(difference(a,difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(a,c),difference(difference(a,c),b))),c),
    inference(symmetry,[status(thm)],[168]) ).

tff(237,plain,
    difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),
    inference(transitivity,[status(thm)],[165,236,179,205,208]) ).

tff(238,plain,
    difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))),
    inference(monotonicity,[status(thm)],[237,235]) ).

tff(239,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(difference(difference(difference(a,c),difference(difference(difference(a,c),difference(difference(a,c),b)),b)),c),difference(difference(difference(a,c),difference(difference(a,c),b)),difference(difference(difference(a,c),difference(difference(a,c),b)),b))),difference(b,c)),
    inference(symmetry,[status(thm)],[238]) ).

tff(240,plain,
    ( ~ ! [Y: $i,X: $i] : ( difference(X,difference(Y,X)) = X )
    | ( difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(241,plain,
    difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))) = difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),
    inference(unit_resolution,[status(thm)],[240,17]) ).

tff(242,plain,
    difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))) = difference(difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))),difference(difference(b,c),difference(difference(a,c),difference(difference(a,c),difference(difference(a,c),b))))),
    inference(symmetry,[status(thm)],[241]) ).

tff(243,plain,
    difference(difference(a,b),c) = difference(difference(a,c),difference(b,c)),
    inference(transitivity,[status(thm)],[184,38,58,50,242,239,213,148,145,143,19,10]) ).

tff(244,plain,
    ( ( difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)) )
  <=> ( difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(245,axiom,
    difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_difference_3) ).

tff(246,plain,
    difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
    inference(modus_ponens,[status(thm)],[245,244]) ).

tff(247,plain,
    $false,
    inference(unit_resolution,[status(thm)],[246,243]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Aug 29 13:08:47 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 9.30/6.23  % SZS status Unsatisfiable
% 9.30/6.23  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------