%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : REL001-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n011.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 20 02:59:49 EDT 2022

% Result   : Unsatisfiable 92.66s 60.09s
% Output   : Proof 92.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   62
% Syntax   : Number of formulae    :  247 ( 192 unt;   6 typ;   0 def)
%            Number of atoms       :  302 ( 295 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   95 (  40   ~;  36   |;   0   &)
%                                         (  19 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :   12 (   3 avg)
%            Number of FOOLs       :    6 (   6 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  176 ( 165   !;   0   ?; 176   :)

% Comments : 
%------------------------------------------------------------------------------
tff(sk1_type,type,
    sk1: $i ).

tff(join_type,type,
    join: ( $i * $i ) > $i ).

tff(zero_type,type,
    zero: $i ).

tff(complement_type,type,
    complement: $i > $i ).

tff(meet_type,type,
    meet: ( $i * $i ) > $i ).

tff(top_type,type,
    top: $i ).

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

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

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

tff(4,axiom,
    ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).

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

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

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

tff(8,plain,
    ( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
    | ( sk1 = join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    sk1 = join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))) = sk1,
    inference(symmetry,[status(thm)],[9]) ).

tff(11,plain,
    ( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
    | ( join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(12,plain,
    join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))),
    inference(unit_resolution,[status(thm)],[11,7]) ).

tff(13,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))) = join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),
    inference(symmetry,[status(thm)],[12]) ).

tff(14,plain,
    join(complement(sk1),sk1) = join(complement(sk1),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),
    inference(monotonicity,[status(thm)],[9]) ).

tff(15,plain,
    join(complement(sk1),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) = join(complement(sk1),sk1),
    inference(symmetry,[status(thm)],[14]) ).

tff(16,plain,
    ^ [B: $i,A: $i,C: $i] :
      refl(
        ( ( join(A,join(B,C)) = join(join(A,B),C) )
      <=> ( join(A,join(B,C)) = join(join(A,B),C) ) )),
    inference(bind,[status(th)],]) ).

tff(17,plain,
    ( ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
  <=> ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ) ),
    inference(quant_intro,[status(thm)],[16]) ).

tff(18,plain,
    ( ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
  <=> ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,axiom,
    ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).

tff(20,plain,
    ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
    inference(skolemize,[status(sab)],[20]) ).

tff(22,plain,
    ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
    inference(modus_ponens,[status(thm)],[21,17]) ).

tff(23,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(complement(sk1),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) = join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(24,plain,
    join(complement(sk1),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) = join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),
    inference(unit_resolution,[status(thm)],[23,22]) ).

tff(25,plain,
    join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))) = join(complement(sk1),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),
    inference(symmetry,[status(thm)],[24]) ).

tff(26,plain,
    ( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
    | ( join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(27,plain,
    join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),
    inference(unit_resolution,[status(thm)],[26,7]) ).

tff(28,plain,
    join(complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))) = join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),
    inference(symmetry,[status(thm)],[27]) ).

tff(29,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( join(A,B) = join(B,A) )
      <=> ( join(A,B) = join(B,A) ) )),
    inference(bind,[status(th)],]) ).

tff(30,plain,
    ( ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
  <=> ! [B: $i,A: $i] : ( join(A,B) = join(B,A) ) ),
    inference(quant_intro,[status(thm)],[29]) ).

tff(31,plain,
    ( ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
  <=> ! [B: $i,A: $i] : ( join(A,B) = join(B,A) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,axiom,
    ! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).

tff(33,plain,
    ! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
    inference(skolemize,[status(sab)],[33]) ).

tff(35,plain,
    ! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
    inference(modus_ponens,[status(thm)],[34,30]) ).

tff(36,plain,
    ( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
    | ( join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(sk1),sk1)),complement(join(complement(sk1),complement(sk1)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(37,plain,
    join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(sk1),sk1)),complement(join(complement(sk1),complement(sk1)))),
    inference(unit_resolution,[status(thm)],[36,35]) ).

tff(38,plain,
    join(complement(join(complement(sk1),sk1)),complement(join(complement(sk1),complement(sk1)))) = join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),
    inference(symmetry,[status(thm)],[37]) ).

tff(39,plain,
    ( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
    | ( join(complement(sk1),complement(sk1)) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(40,plain,
    join(complement(sk1),complement(sk1)) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),
    inference(unit_resolution,[status(thm)],[39,7]) ).

tff(41,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))) = join(complement(sk1),complement(sk1)),
    inference(symmetry,[status(thm)],[40]) ).

tff(42,plain,
    complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))) = complement(join(complement(sk1),complement(sk1))),
    inference(monotonicity,[status(thm)],[41]) ).

tff(43,plain,
    join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))) = join(complement(sk1),sk1),
    inference(transitivity,[status(thm)],[25,15]) ).

tff(44,plain,
    complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))) = complement(join(complement(sk1),sk1)),
    inference(monotonicity,[status(thm)],[43]) ).

tff(45,plain,
    join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))) = join(complement(join(complement(sk1),sk1)),complement(join(complement(sk1),complement(sk1)))),
    inference(monotonicity,[status(thm)],[44,42]) ).

tff(46,plain,
    join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))) = sk1,
    inference(transitivity,[status(thm)],[45,38,10]) ).

tff(47,plain,
    complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))) = complement(sk1),
    inference(monotonicity,[status(thm)],[46]) ).

tff(48,plain,
    complement(sk1) = complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),
    inference(symmetry,[status(thm)],[47]) ).

tff(49,plain,
    complement(sk1) = complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),
    inference(monotonicity,[status(thm)],[9]) ).

tff(50,plain,
    complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) = complement(sk1),
    inference(symmetry,[status(thm)],[49]) ).

tff(51,plain,
    complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) = complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),
    inference(transitivity,[status(thm)],[50,48]) ).

tff(52,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))) = join(complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),
    inference(monotonicity,[status(thm)],[51]) ).

tff(53,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))) = join(complement(sk1),sk1),
    inference(transitivity,[status(thm)],[52,28,25,15]) ).

tff(54,plain,
    complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))) = complement(join(complement(sk1),sk1)),
    inference(monotonicity,[status(thm)],[53]) ).

tff(55,plain,
    complement(join(complement(sk1),sk1)) = complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))),
    inference(symmetry,[status(thm)],[54]) ).

tff(56,plain,
    ^ [A: $i] :
      refl(
        ( ( top = join(A,complement(A)) )
      <=> ( top = join(A,complement(A)) ) )),
    inference(bind,[status(th)],]) ).

tff(57,plain,
    ( ! [A: $i] : ( top = join(A,complement(A)) )
  <=> ! [A: $i] : ( top = join(A,complement(A)) ) ),
    inference(quant_intro,[status(thm)],[56]) ).

tff(58,plain,
    ( ! [A: $i] : ( top = join(A,complement(A)) )
  <=> ! [A: $i] : ( top = join(A,complement(A)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(59,axiom,
    ! [A: $i] : ( top = join(A,complement(A)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',def_top_12) ).

tff(60,plain,
    ! [A: $i] : ( top = join(A,complement(A)) ),
    inference(modus_ponens,[status(thm)],[59,58]) ).

tff(61,plain,
    ! [A: $i] : ( top = join(A,complement(A)) ),
    inference(skolemize,[status(sab)],[60]) ).

tff(62,plain,
    ! [A: $i] : ( top = join(A,complement(A)) ),
    inference(modus_ponens,[status(thm)],[61,57]) ).

tff(63,plain,
    ( ~ ! [A: $i] : ( top = join(A,complement(A)) )
    | ( top = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(64,plain,
    top = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(unit_resolution,[status(thm)],[63,62]) ).

tff(65,plain,
    ( ~ ! [A: $i] : ( top = join(A,complement(A)) )
    | ( top = join(sk1,complement(sk1)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(66,plain,
    top = join(sk1,complement(sk1)),
    inference(unit_resolution,[status(thm)],[65,62]) ).

tff(67,plain,
    join(sk1,complement(sk1)) = top,
    inference(symmetry,[status(thm)],[66]) ).

tff(68,plain,
    join(sk1,complement(sk1)) = join(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),complement(sk1)),
    inference(monotonicity,[status(thm)],[9]) ).

tff(69,plain,
    join(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),complement(sk1)) = join(sk1,complement(sk1)),
    inference(symmetry,[status(thm)],[68]) ).

tff(70,plain,
    ( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
    | ( join(complement(sk1),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) = join(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),complement(sk1)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(71,plain,
    join(complement(sk1),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) = join(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),complement(sk1)),
    inference(unit_resolution,[status(thm)],[70,35]) ).

tff(72,plain,
    join(complement(sk1),sk1) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(transitivity,[status(thm)],[14,71,69,67,64]) ).

tff(73,plain,
    complement(join(complement(sk1),sk1)) = complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),
    inference(monotonicity,[status(thm)],[72]) ).

tff(74,plain,
    complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = complement(join(complement(sk1),sk1)),
    inference(symmetry,[status(thm)],[73]) ).

tff(75,plain,
    ^ [B: $i,A: $i] :
      refl(
        ( ( meet(A,B) = complement(join(complement(A),complement(B))) )
      <=> ( meet(A,B) = complement(join(complement(A),complement(B))) ) )),
    inference(bind,[status(th)],]) ).

tff(76,plain,
    ( ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) )
  <=> ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ) ),
    inference(quant_intro,[status(thm)],[75]) ).

tff(77,plain,
    ( ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) )
  <=> ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(78,axiom,
    ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).

tff(79,plain,
    ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
    inference(modus_ponens,[status(thm)],[78,77]) ).

tff(80,plain,
    ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
    inference(skolemize,[status(sab)],[79]) ).

tff(81,plain,
    ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
    inference(modus_ponens,[status(thm)],[80,76]) ).

tff(82,plain,
    ( ~ ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) )
    | ( meet(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(83,plain,
    meet(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),
    inference(unit_resolution,[status(thm)],[82,81]) ).

tff(84,plain,
    ^ [A: $i] :
      refl(
        ( ( zero = meet(A,complement(A)) )
      <=> ( zero = meet(A,complement(A)) ) )),
    inference(bind,[status(th)],]) ).

tff(85,plain,
    ( ! [A: $i] : ( zero = meet(A,complement(A)) )
  <=> ! [A: $i] : ( zero = meet(A,complement(A)) ) ),
    inference(quant_intro,[status(thm)],[84]) ).

tff(86,plain,
    ( ! [A: $i] : ( zero = meet(A,complement(A)) )
  <=> ! [A: $i] : ( zero = meet(A,complement(A)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(87,axiom,
    ! [A: $i] : ( zero = meet(A,complement(A)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',def_zero_13) ).

tff(88,plain,
    ! [A: $i] : ( zero = meet(A,complement(A)) ),
    inference(modus_ponens,[status(thm)],[87,86]) ).

tff(89,plain,
    ! [A: $i] : ( zero = meet(A,complement(A)) ),
    inference(skolemize,[status(sab)],[88]) ).

tff(90,plain,
    ! [A: $i] : ( zero = meet(A,complement(A)) ),
    inference(modus_ponens,[status(thm)],[89,85]) ).

tff(91,plain,
    ( ~ ! [A: $i] : ( zero = meet(A,complement(A)) )
    | ( zero = meet(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(92,plain,
    zero = meet(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),
    inference(unit_resolution,[status(thm)],[91,90]) ).

tff(93,plain,
    ( ~ ! [A: $i] : ( zero = meet(A,complement(A)) )
    | ( zero = meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(94,plain,
    zero = meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),
    inference(unit_resolution,[status(thm)],[93,90]) ).

tff(95,plain,
    meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))) = zero,
    inference(symmetry,[status(thm)],[94]) ).

tff(96,plain,
    meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))) = complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))),
    inference(transitivity,[status(thm)],[95,92,83,74,55]) ).

tff(97,plain,
    join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))),
    inference(monotonicity,[status(thm)],[96]) ).

tff(98,plain,
    ( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
    | ( join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(99,plain,
    join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),
    inference(unit_resolution,[status(thm)],[98,35]) ).

tff(100,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))) = join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))),
    inference(symmetry,[status(thm)],[99]) ).

tff(101,plain,
    ( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
    | ( meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))) = join(complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(102,plain,
    meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))) = join(complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))),
    inference(unit_resolution,[status(thm)],[101,7]) ).

tff(103,plain,
    join(complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))) = meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),
    inference(symmetry,[status(thm)],[102]) ).

tff(104,plain,
    join(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),complement(sk1)) = join(complement(sk1),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),
    inference(symmetry,[status(thm)],[71]) ).

tff(105,plain,
    ( ~ ! [A: $i] : ( top = join(A,complement(A)) )
    | ( top = join(complement(join(complement(sk1),sk1)),complement(complement(join(complement(sk1),sk1)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(106,plain,
    top = join(complement(join(complement(sk1),sk1)),complement(complement(join(complement(sk1),sk1)))),
    inference(unit_resolution,[status(thm)],[105,62]) ).

tff(107,plain,
    join(complement(join(complement(sk1),sk1)),complement(complement(join(complement(sk1),sk1)))) = top,
    inference(symmetry,[status(thm)],[106]) ).

tff(108,plain,
    ( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
    | ( join(complement(join(complement(sk1),sk1)),complement(complement(join(complement(sk1),sk1)))) = join(complement(complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(109,plain,
    join(complement(join(complement(sk1),sk1)),complement(complement(join(complement(sk1),sk1)))) = join(complement(complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1))),
    inference(unit_resolution,[status(thm)],[108,35]) ).

tff(110,plain,
    join(complement(complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(sk1),sk1)),complement(complement(join(complement(sk1),sk1)))),
    inference(symmetry,[status(thm)],[109]) ).

tff(111,plain,
    meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))) = complement(join(complement(sk1),sk1)),
    inference(transitivity,[status(thm)],[95,92,83,74]) ).

tff(112,plain,
    complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))) = complement(complement(join(complement(sk1),sk1))),
    inference(monotonicity,[status(thm)],[111]) ).

tff(113,plain,
    join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))))) = join(complement(complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1))),
    inference(monotonicity,[status(thm)],[112,44]) ).

tff(114,plain,
    join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))))) = join(complement(sk1),sk1),
    inference(transitivity,[status(thm)],[113,110,107,66,68,104,15]) ).

tff(115,plain,
    complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))) = complement(join(complement(sk1),sk1)),
    inference(monotonicity,[status(thm)],[114]) ).

tff(116,plain,
    complement(join(complement(sk1),sk1)) = complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))),
    inference(symmetry,[status(thm)],[115]) ).

tff(117,plain,
    meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))) = complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))),
    inference(transitivity,[status(thm)],[95,92,83,74,116]) ).

tff(118,plain,
    join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))) = join(complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))),
    inference(monotonicity,[status(thm)],[117]) ).

tff(119,plain,
    join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))) = meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),
    inference(transitivity,[status(thm)],[118,103]) ).

tff(120,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),
    inference(monotonicity,[status(thm)],[119]) ).

tff(121,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))))))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(122,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))))))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))),
    inference(unit_resolution,[status(thm)],[121,22]) ).

tff(123,plain,
    join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))))))),
    inference(symmetry,[status(thm)],[122]) ).

tff(124,plain,
    ( ~ ! [A: $i] : ( top = join(A,complement(A)) )
    | ( top = join(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(125,plain,
    top = join(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),
    inference(unit_resolution,[status(thm)],[124,62]) ).

tff(126,plain,
    join(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))) = top,
    inference(symmetry,[status(thm)],[125]) ).

tff(127,plain,
    ( ~ ! [A: $i] : ( top = join(A,complement(A)) )
    | ( top = join(join(complement(sk1),complement(sk1)),complement(join(complement(sk1),complement(sk1)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(128,plain,
    top = join(join(complement(sk1),complement(sk1)),complement(join(complement(sk1),complement(sk1)))),
    inference(unit_resolution,[status(thm)],[127,62]) ).

tff(129,plain,
    join(join(complement(sk1),complement(sk1)),complement(join(complement(sk1),complement(sk1)))) = top,
    inference(symmetry,[status(thm)],[128]) ).

tff(130,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = join(complement(sk1),complement(sk1)),
    inference(monotonicity,[status(thm)],[50,50]) ).

tff(131,plain,
    join(complement(sk1),complement(sk1)) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),
    inference(symmetry,[status(thm)],[130]) ).

tff(132,plain,
    complement(join(complement(sk1),complement(sk1))) = complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(monotonicity,[status(thm)],[131]) ).

tff(133,plain,
    complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = complement(join(complement(sk1),complement(sk1))),
    inference(symmetry,[status(thm)],[132]) ).

tff(134,plain,
    join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(join(complement(sk1),complement(sk1)),complement(join(complement(sk1),complement(sk1)))),
    inference(monotonicity,[status(thm)],[41,133]) ).

tff(135,plain,
    join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(complement(sk1),sk1),
    inference(transitivity,[status(thm)],[134,129,66,68,104,15]) ).

tff(136,plain,
    join(join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),complement(join(complement(sk1),sk1))) = join(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),
    inference(monotonicity,[status(thm)],[135]) ).

tff(137,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(sk1),sk1)))) = join(join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),complement(join(complement(sk1),sk1))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(138,plain,
    join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(sk1),sk1)))) = join(join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),complement(join(complement(sk1),sk1))),
    inference(unit_resolution,[status(thm)],[137,22]) ).

tff(139,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))),
    inference(monotonicity,[status(thm)],[133]) ).

tff(140,plain,
    join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(sk1),sk1))),
    inference(symmetry,[status(thm)],[139]) ).

tff(141,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),
    inference(transitivity,[status(thm)],[130,40]) ).

tff(142,plain,
    join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) = join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(sk1),sk1)))),
    inference(monotonicity,[status(thm)],[141,140]) ).

tff(143,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(144,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),
    inference(unit_resolution,[status(thm)],[143,22]) ).

tff(145,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) = join(complement(sk1),sk1),
    inference(monotonicity,[status(thm)],[50,10]) ).

tff(146,plain,
    join(complement(sk1),sk1) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),
    inference(symmetry,[status(thm)],[145]) ).

tff(147,plain,
    ( ~ ! [A: $i] : ( top = join(A,complement(A)) )
    | ( top = join(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(148,plain,
    top = join(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),
    inference(unit_resolution,[status(thm)],[147,62]) ).

tff(149,plain,
    join(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))) = top,
    inference(symmetry,[status(thm)],[148]) ).

tff(150,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))) = join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)),
    inference(monotonicity,[status(thm)],[133,43]) ).

tff(151,plain,
    ( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
    | ( join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))) = join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(152,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))) = join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),
    inference(unit_resolution,[status(thm)],[151,35]) ).

tff(153,plain,
    join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),
    inference(symmetry,[status(thm)],[152]) ).

tff(154,plain,
    join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)),
    inference(transitivity,[status(thm)],[153,150]) ).

tff(155,plain,
    join(join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))) = join(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),
    inference(monotonicity,[status(thm)],[154]) ).

tff(156,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))) = join(join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(157,plain,
    join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))) = join(join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),
    inference(unit_resolution,[status(thm)],[156,22]) ).

tff(158,plain,
    join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1))) = join(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),
    inference(monotonicity,[status(thm)],[43]) ).

tff(159,plain,
    join(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))) = join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1))),
    inference(symmetry,[status(thm)],[158]) ).

tff(160,plain,
    join(complement(sk1),sk1) = join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1))),
    inference(transitivity,[status(thm)],[14,71,69,67,125,159]) ).

tff(161,plain,
    join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1)))),
    inference(monotonicity,[status(thm)],[132,160]) ).

tff(162,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1)))) = join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)),
    inference(symmetry,[status(thm)],[161]) ).

tff(163,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1)))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(sk1),sk1))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(164,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1)))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(sk1),sk1))),
    inference(unit_resolution,[status(thm)],[163,22]) ).

tff(165,plain,
    join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1)))),
    inference(symmetry,[status(thm)],[164]) ).

tff(166,plain,
    join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(sk1),sk1))) = join(join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),complement(join(complement(sk1),sk1))),
    inference(monotonicity,[status(thm)],[152]) ).

tff(167,plain,
    join(join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),complement(join(complement(sk1),sk1))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),complement(join(complement(sk1),sk1))),
    inference(symmetry,[status(thm)],[166]) ).

tff(168,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(sk1),sk1)))) = join(join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),complement(join(complement(sk1),sk1))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(169,plain,
    join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(sk1),sk1)))) = join(join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),complement(join(complement(sk1),sk1))),
    inference(unit_resolution,[status(thm)],[168,22]) ).

tff(170,plain,
    join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(join(complement(sk1),complement(sk1)),complement(join(complement(sk1),complement(sk1)))),
    inference(monotonicity,[status(thm)],[130,133]) ).

tff(171,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))))) = join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(172,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))))) = join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),
    inference(unit_resolution,[status(thm)],[171,22]) ).

tff(173,plain,
    ( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
    | ( join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(174,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),
    inference(unit_resolution,[status(thm)],[173,35]) ).

tff(175,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),
    inference(symmetry,[status(thm)],[174]) ).

tff(176,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))))),
    inference(monotonicity,[status(thm)],[175]) ).

tff(177,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),
    inference(transitivity,[status(thm)],[176,172,170,129,66,68,104,24]) ).

tff(178,plain,
    join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) = join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(sk1),sk1)))),
    inference(monotonicity,[status(thm)],[177,140]) ).

tff(179,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(180,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),
    inference(unit_resolution,[status(thm)],[179,22]) ).

tff(181,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(182,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),
    inference(unit_resolution,[status(thm)],[181,22]) ).

tff(183,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)),
    inference(monotonicity,[status(thm)],[133,145]) ).

tff(184,plain,
    join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),
    inference(symmetry,[status(thm)],[183]) ).

tff(185,plain,
    join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),
    inference(transitivity,[status(thm)],[184,182]) ).

tff(186,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),
    inference(monotonicity,[status(thm)],[185]) ).

tff(187,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))) = join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)),
    inference(transitivity,[status(thm)],[186,180,178,169,167,165,162]) ).

tff(188,plain,
    complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))) = complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))),
    inference(monotonicity,[status(thm)],[187]) ).

tff(189,plain,
    complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))) = complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),
    inference(symmetry,[status(thm)],[188]) ).

tff(190,plain,
    complement(join(complement(sk1),complement(sk1))) = complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))),
    inference(symmetry,[status(thm)],[42]) ).

tff(191,plain,
    complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))),
    inference(transitivity,[status(thm)],[133,190]) ).

tff(192,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))),
    inference(monotonicity,[status(thm)],[191,189]) ).

tff(193,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),
    inference(symmetry,[status(thm)],[192]) ).

tff(194,plain,
    ( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
    | ( join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(195,plain,
    join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))),
    inference(unit_resolution,[status(thm)],[194,7]) ).

tff(196,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))),
    inference(transitivity,[status(thm)],[139,195,193]) ).

tff(197,plain,
    join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(sk1),sk1)))) = join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))),
    inference(monotonicity,[status(thm)],[196]) ).

tff(198,plain,
    join(join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),complement(join(complement(sk1),sk1))) = join(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(sk1),sk1)))),
    inference(symmetry,[status(thm)],[169]) ).

tff(199,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = join(complement(sk1),sk1),
    inference(transitivity,[status(thm)],[176,172,170,129,66,68,104,15]) ).

tff(200,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)),
    inference(monotonicity,[status(thm)],[133,199]) ).

tff(201,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(202,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(unit_resolution,[status(thm)],[201,22]) ).

tff(203,plain,
    join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),
    inference(symmetry,[status(thm)],[202]) ).

tff(204,plain,
    join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),
    inference(transitivity,[status(thm)],[203,200,161,164,166,198,197,157,155,149,66,68,104,15,146]) ).

tff(205,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),
    inference(monotonicity,[status(thm)],[204]) ).

tff(206,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(207,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(unit_resolution,[status(thm)],[206,22]) ).

tff(208,plain,
    join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),
    inference(symmetry,[status(thm)],[207]) ).

tff(209,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))))) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(symmetry,[status(thm)],[176]) ).

tff(210,plain,
    join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))))),
    inference(symmetry,[status(thm)],[172]) ).

tff(211,plain,
    join(join(complement(sk1),complement(sk1)),complement(join(complement(sk1),complement(sk1)))) = join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),
    inference(symmetry,[status(thm)],[170]) ).

tff(212,plain,
    join(complement(complement(join(complement(sk1),sk1))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))) = join(complement(complement(join(complement(sk1),sk1))),complement(join(complement(sk1),sk1))),
    inference(monotonicity,[status(thm)],[111]) ).

tff(213,plain,
    join(complement(complement(join(complement(sk1),sk1))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(transitivity,[status(thm)],[212,110,107,128,211,210,209]) ).

tff(214,plain,
    join(join(complement(complement(join(complement(sk1),sk1))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = join(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(monotonicity,[status(thm)],[213]) ).

tff(215,plain,
    ( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
    | ( join(complement(complement(join(complement(sk1),sk1))),join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(join(complement(complement(join(complement(sk1),sk1))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(216,plain,
    join(complement(complement(join(complement(sk1),sk1))),join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(join(complement(complement(join(complement(sk1),sk1))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(unit_resolution,[status(thm)],[215,22]) ).

tff(217,plain,
    join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = join(complement(join(complement(sk1),sk1)),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(monotonicity,[status(thm)],[111]) ).

tff(218,plain,
    join(complement(join(complement(sk1),sk1)),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(symmetry,[status(thm)],[217]) ).

tff(219,plain,
    join(complement(sk1),complement(join(complement(sk1),complement(sk1)))) = join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),
    inference(monotonicity,[status(thm)],[49,132]) ).

tff(220,plain,
    join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))) = join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),
    inference(symmetry,[status(thm)],[219]) ).

tff(221,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))) = join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),
    inference(transitivity,[status(thm)],[175,220]) ).

tff(222,plain,
    join(complement(join(complement(sk1),sk1)),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))) = join(complement(join(complement(sk1),sk1)),join(complement(sk1),complement(join(complement(sk1),complement(sk1))))),
    inference(monotonicity,[status(thm)],[221]) ).

tff(223,plain,
    join(complement(join(complement(sk1),sk1)),join(complement(sk1),complement(join(complement(sk1),complement(sk1))))) = join(complement(join(complement(sk1),sk1)),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(symmetry,[status(thm)],[222]) ).

tff(224,plain,
    ( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
    | ( join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(sk1),sk1)),join(complement(sk1),complement(join(complement(sk1),complement(sk1))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(225,plain,
    join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))) = join(complement(join(complement(sk1),sk1)),join(complement(sk1),complement(join(complement(sk1),complement(sk1))))),
    inference(unit_resolution,[status(thm)],[224,35]) ).

tff(226,plain,
    join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))) = join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),
    inference(transitivity,[status(thm)],[225,223,218]) ).

tff(227,plain,
    join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))) = join(complement(complement(join(complement(sk1),sk1))),join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))))),complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1))))))),
    inference(monotonicity,[status(thm)],[112,226]) ).

tff(228,plain,
    join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))) = join(complement(sk1),sk1),
    inference(transitivity,[status(thm)],[227,216,214,208,205,144,142,138,136,126,66,68,104,15]) ).

tff(229,plain,
    complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))))) = complement(join(complement(sk1),sk1)),
    inference(monotonicity,[status(thm)],[228]) ).

tff(230,plain,
    complement(join(complement(sk1),sk1)) = complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))))),
    inference(symmetry,[status(thm)],[229]) ).

tff(231,plain,
    zero = complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1))))),
    inference(transitivity,[status(thm)],[92,83,74,230]) ).

tff(232,plain,
    join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))) = join(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1))),complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1)))))))),
    inference(symmetry,[status(thm)],[97]) ).

tff(233,plain,
    sk1 = join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),
    inference(transitivity,[status(thm)],[9,12,232,99]) ).

tff(234,plain,
    join(sk1,zero) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),join(complement(join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))),join(complement(join(complement(join(complement(sk1),complement(sk1))),complement(join(complement(sk1),sk1)))),complement(join(complement(join(complement(sk1),complement(sk1))),join(complement(sk1),sk1))))))),meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),complement(join(complement(meet(join(complement(sk1),sk1),complement(join(complement(sk1),sk1)))),join(join(complement(sk1),complement(join(complement(sk1),complement(sk1)))),complement(join(complement(sk1),sk1)))))),
    inference(monotonicity,[status(thm)],[233,231]) ).

tff(235,plain,
    ( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
    | ( join(zero,sk1) = join(sk1,zero) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(236,plain,
    join(zero,sk1) = join(sk1,zero),
    inference(unit_resolution,[status(thm)],[235,35]) ).

tff(237,plain,
    join(zero,sk1) = sk1,
    inference(transitivity,[status(thm)],[236,234,123,120,100,97,13,10]) ).

tff(238,plain,
    ( ( join(zero,sk1) != sk1 )
  <=> ( join(zero,sk1) != sk1 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(239,axiom,
    join(zero,sk1) != sk1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).

tff(240,plain,
    join(zero,sk1) != sk1,
    inference(modus_ponens,[status(thm)],[239,238]) ).

tff(241,plain,
    $false,
    inference(unit_resolution,[status(thm)],[240,237]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : REL001-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34  % Computer : n011.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Fri Sep  2 19:18:58 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35  Usage: tptp [options] [-file:]file
% 0.14/0.35    -h, -?       prints this message.
% 0.14/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.35    -m, -model   generate model.
% 0.14/0.35    -p, -proof   generate proof.
% 0.14/0.35    -c, -core    generate unsat core of named formulas.
% 0.14/0.35    -st, -statistics display statistics.
% 0.14/0.35    -t:timeout   set timeout (in second).
% 0.14/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35    -<param>:<value> configuration parameter and value.
% 0.14/0.35    -o:<output-file> file to place output in.
% 92.66/60.09  % SZS status Unsatisfiable
% 92.66/60.09  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------