TSTP Solution File: REL002-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : REL002-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 02:59:50 EDT 2022
% Result : Unsatisfiable 1.81s 1.42s
% Output : Proof 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 69
% Syntax : Number of formulae : 312 ( 250 unt; 6 typ; 0 def)
% Number of atoms : 374 ( 367 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 109 ( 47 ~; 43 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 14 ( 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 : 187 ( 176 !; 0 ?; 187 :)
% Comments :
%------------------------------------------------------------------------------
tff(top_type,type,
top: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(zero_type,type,
zero: $i ).
tff(1,plain,
^ [A: $i] :
refl(
( ( top = join(A,complement(A)) )
<=> ( top = join(A,complement(A)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] : ( top = join(A,complement(A)) )
<=> ! [A: $i] : ( top = join(A,complement(A)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( top = join(A,complement(A)) )
<=> ! [A: $i] : ( top = join(A,complement(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i] : ( top = join(A,complement(A)) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_top_12) ).
tff(5,plain,
! [A: $i] : ( top = join(A,complement(A)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( top = join(A,complement(A)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( top = join(A,complement(A)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( top = join(A,complement(A)) )
| ( top = join(join(complement(join(complement(top),complement(top))),join(complement(top),top)),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
top = join(join(complement(join(complement(top),complement(top))),join(complement(top),top)),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
join(join(complement(join(complement(top),complement(top))),join(complement(top),top)),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))) = top,
inference(symmetry,[status(thm)],[9]) ).
tff(11,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(12,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)],[11]) ).
tff(13,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(14,axiom,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,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(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,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(21,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)],[20]) ).
tff(22,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(23,axiom,
! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).
tff(24,plain,
! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
| ( top = join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
top = join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
join(complement(top),top) = join(complement(top),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
join(complement(top),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(complement(top),top),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
^ [B: $i,A: $i] :
refl(
( ( join(A,B) = join(B,A) )
<=> ( join(A,B) = join(B,A) ) )),
inference(bind,[status(th)],]) ).
tff(32,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)],[31]) ).
tff(33,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(34,axiom,
! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
tff(35,plain,
! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(complement(top),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(top)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
join(complement(top),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(top)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(top)) = join(complement(top),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) = top,
inference(symmetry,[status(thm)],[28]) ).
tff(42,plain,
join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(top)) = join(top,complement(top)),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
join(top,complement(top)) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(top)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( ~ ! [A: $i] : ( top = join(A,complement(A)) )
| ( top = join(top,complement(top)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
top = join(top,complement(top)),
inference(unit_resolution,[status(thm)],[44,7]) ).
tff(46,plain,
join(top,complement(top)) = top,
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
join(complement(top),top) = top,
inference(transitivity,[status(thm)],[29,39,42,46]) ).
tff(48,plain,
complement(join(complement(top),top)) = complement(top),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
complement(top) = complement(join(complement(top),top)),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = complement(top),
inference(monotonicity,[status(thm)],[41]) ).
tff(51,plain,
complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = complement(join(complement(top),top)),
inference(transitivity,[status(thm)],[50,49]) ).
tff(52,plain,
complement(top) = complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(symmetry,[status(thm)],[50]) ).
tff(53,plain,
join(complement(top),complement(top)) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[52,52]) ).
tff(54,plain,
complement(join(complement(top),complement(top))) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = complement(join(complement(top),complement(top))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),
inference(monotonicity,[status(thm)],[55,51]) ).
tff(57,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(top),top),
inference(transitivity,[status(thm)],[56,41,45,43,40,30]) ).
tff(58,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = join(complement(join(complement(top),complement(top))),join(complement(top),top)),
inference(monotonicity,[status(thm)],[55,57]) ).
tff(59,plain,
join(complement(join(complement(top),complement(top))),join(complement(top),top)) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
join(complement(join(complement(top),complement(top))),join(complement(top),top)) = join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(transitivity,[status(thm)],[59,19]) ).
tff(61,plain,
join(join(complement(join(complement(top),complement(top))),join(complement(top),top)),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))) = join(join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
join(join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))) = join(join(complement(join(complement(top),complement(top))),join(complement(top),top)),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
| ( join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))) = join(join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))) = join(join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),
inference(unit_resolution,[status(thm)],[63,17]) ).
tff(65,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(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))) = join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))) = join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))),
inference(unit_resolution,[status(thm)],[65,17]) ).
tff(67,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
| ( join(complement(join(complement(top),complement(top))),join(complement(join(complement(top),top)),complement(top))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(top)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
join(complement(join(complement(top),complement(top))),join(complement(join(complement(top),top)),complement(top))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(top)),
inference(unit_resolution,[status(thm)],[67,17]) ).
tff(69,plain,
complement(join(complement(top),top)) = complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(transitivity,[status(thm)],[48,52]) ).
tff(70,plain,
join(complement(join(complement(top),top)),complement(top)) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[69,52]) ).
tff(71,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(top),top)),complement(top)),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
| ( join(complement(top),complement(top)) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
join(complement(top),complement(top)) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),
inference(unit_resolution,[status(thm)],[72,26]) ).
tff(74,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))) = join(complement(top),complement(top)),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))) = join(complement(join(complement(top),top)),complement(top)),
inference(transitivity,[status(thm)],[74,53,71]) ).
tff(76,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))) = join(complement(join(complement(top),complement(top))),join(complement(join(complement(top),top)),complement(top))),
inference(monotonicity,[status(thm)],[55,75]) ).
tff(77,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))) = join(complement(top),top),
inference(transitivity,[status(thm)],[76,68,40,30]) ).
tff(78,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))) = join(complement(join(complement(top),complement(top))),join(complement(top),top)),
inference(monotonicity,[status(thm)],[55,77]) ).
tff(79,plain,
join(complement(join(complement(top),complement(top))),join(complement(top),top)) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(complement(top),top),
inference(monotonicity,[status(thm)],[50,41]) ).
tff(81,plain,
join(complement(top),top) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
join(complement(join(complement(top),complement(top))),join(complement(top),top)) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[54,81]) ).
tff(83,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(top),complement(top))),join(complement(top),top)),
inference(symmetry,[status(thm)],[82]) ).
tff(84,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(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(unit_resolution,[status(thm)],[84,17]) ).
tff(86,plain,
join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,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(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
sk1 = join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(unit_resolution,[status(thm)],[87,26]) ).
tff(89,plain,
join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = sk1,
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)) = join(sk1,complement(sk1)),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
join(sk1,complement(sk1)) = join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [A: $i] : ( top = join(A,complement(A)) )
| ( top = join(sk1,complement(sk1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
top = join(sk1,complement(sk1)),
inference(unit_resolution,[status(thm)],[92,7]) ).
tff(94,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)),
inference(transitivity,[status(thm)],[56,41,93,91]) ).
tff(95,plain,
join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
| ( join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(unit_resolution,[status(thm)],[97,17]) ).
tff(99,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1)),
inference(unit_resolution,[status(thm)],[99,37]) ).
tff(101,plain,
( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
| ( join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[101,26]) ).
tff(103,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
| ( complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = join(complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = join(complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[104,26]) ).
tff(106,plain,
join(complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ~ ! [A: $i] : ( top = join(A,complement(A)) )
| ( top = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
top = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))),
inference(unit_resolution,[status(thm)],[107,7]) ).
tff(109,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))) = top,
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))) = join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))) = join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[110,37]) ).
tff(112,plain,
join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))) = complement(join(complement(top),complement(top))),
inference(monotonicity,[status(thm)],[74]) ).
tff(114,plain,
complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(transitivity,[status(thm)],[113,54]) ).
tff(115,plain,
join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))) = join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))) = top,
inference(transitivity,[status(thm)],[115,112,109]) ).
tff(117,plain,
complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = complement(top),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
complement(top) = complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
( ~ ! [A: $i] : ( top = join(A,complement(A)) )
| ( top = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
top = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(unit_resolution,[status(thm)],[119,7]) ).
tff(121,plain,
complement(top) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = complement(top),
inference(symmetry,[status(thm)],[121]) ).
tff(123,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(124,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)],[123]) ).
tff(125,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(126,axiom,
! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).
tff(127,plain,
! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
inference(skolemize,[status(sab)],[127]) ).
tff(129,plain,
! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
( ~ ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) )
| ( meet(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
meet(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[130,129]) ).
tff(132,plain,
^ [A: $i] :
refl(
( ( zero = meet(A,complement(A)) )
<=> ( zero = meet(A,complement(A)) ) )),
inference(bind,[status(th)],]) ).
tff(133,plain,
( ! [A: $i] : ( zero = meet(A,complement(A)) )
<=> ! [A: $i] : ( zero = meet(A,complement(A)) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,plain,
( ! [A: $i] : ( zero = meet(A,complement(A)) )
<=> ! [A: $i] : ( zero = meet(A,complement(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,axiom,
! [A: $i] : ( zero = meet(A,complement(A)) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
tff(136,plain,
! [A: $i] : ( zero = meet(A,complement(A)) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
! [A: $i] : ( zero = meet(A,complement(A)) ),
inference(skolemize,[status(sab)],[136]) ).
tff(138,plain,
! [A: $i] : ( zero = meet(A,complement(A)) ),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,plain,
( ~ ! [A: $i] : ( zero = meet(A,complement(A)) )
| ( zero = meet(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
zero = meet(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(unit_resolution,[status(thm)],[139,138]) ).
tff(141,plain,
( ~ ! [A: $i] : ( zero = meet(A,complement(A)) )
| ( zero = meet(join(complement(top),top),complement(join(complement(top),top))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(142,plain,
zero = meet(join(complement(top),top),complement(join(complement(top),top))),
inference(unit_resolution,[status(thm)],[141,138]) ).
tff(143,plain,
meet(join(complement(top),top),complement(join(complement(top),top))) = zero,
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
meet(join(complement(top),top),complement(join(complement(top),top))) = complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(transitivity,[status(thm)],[143,140,131,122,118]) ).
tff(145,plain,
join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),meet(join(complement(top),top),complement(join(complement(top),top)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),meet(join(complement(top),top),complement(join(complement(top),top)))),
inference(unit_resolution,[status(thm)],[146,37]) ).
tff(148,plain,
join(complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),meet(join(complement(top),top),complement(join(complement(top),top)))) = join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
join(complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),meet(join(complement(top),top),complement(join(complement(top),top)))) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(transitivity,[status(thm)],[148,145,106]) ).
tff(150,plain,
meet(join(complement(top),top),complement(join(complement(top),top))) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(transitivity,[status(thm)],[143,140,131]) ).
tff(151,plain,
join(meet(join(complement(top),top),complement(join(complement(top),top))),join(complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),meet(join(complement(top),top),complement(join(complement(top),top))))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[150,149]) ).
tff(152,plain,
join(meet(join(complement(top),top),complement(join(complement(top),top))),join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))))) = join(meet(join(complement(top),top),complement(join(complement(top),top))),join(complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),meet(join(complement(top),top),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[147]) ).
tff(153,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
| ( join(meet(join(complement(top),top),complement(join(complement(top),top))),join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))))) = join(join(meet(join(complement(top),top),complement(join(complement(top),top))),meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
join(meet(join(complement(top),top),complement(join(complement(top),top))),join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))))) = join(join(meet(join(complement(top),top),complement(join(complement(top),top))),meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[153,17]) ).
tff(155,plain,
join(join(meet(join(complement(top),top),complement(join(complement(top),top))),meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(meet(join(complement(top),top),complement(join(complement(top),top))),join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
meet(join(complement(top),top),complement(join(complement(top),top))) = complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(transitivity,[status(thm)],[143,140,131,122,52]) ).
tff(157,plain,
join(meet(join(complement(top),top),complement(join(complement(top),top))),meet(join(complement(top),top),complement(join(complement(top),top)))) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[156,156]) ).
tff(158,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(meet(join(complement(top),top),complement(join(complement(top),top))),meet(join(complement(top),top),complement(join(complement(top),top)))),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
| ( join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[159,26]) ).
tff(161,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) = join(complement(join(complement(top),top)),complement(join(complement(top),complement(top)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) = join(complement(join(complement(top),top)),complement(join(complement(top),complement(top)))),
inference(unit_resolution,[status(thm)],[162,37]) ).
tff(164,plain,
join(complement(join(complement(top),top)),complement(join(complement(top),complement(top)))) = join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
join(complement(top),complement(join(complement(top),complement(top)))) = join(complement(join(complement(top),top)),complement(join(complement(top),complement(top)))),
inference(monotonicity,[status(thm)],[49]) ).
tff(166,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))) = join(complement(top),complement(join(complement(top),complement(top)))),
inference(monotonicity,[status(thm)],[50,113]) ).
tff(167,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))) = top,
inference(transitivity,[status(thm)],[166,165,164,41]) ).
tff(168,plain,
complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = complement(top),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,plain,
complement(top) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(transitivity,[status(thm)],[50,169]) ).
tff(171,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),
inference(transitivity,[status(thm)],[171,161]) ).
tff(173,plain,
join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[56]) ).
tff(174,plain,
join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))))) = join(join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(monotonicity,[status(thm)],[173,172]) ).
tff(175,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
| ( join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))))) = join(join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,plain,
join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))))) = join(join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[175,17]) ).
tff(177,plain,
join(join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))))),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(top,complement(top)),
inference(monotonicity,[status(thm)],[41,50]) ).
tff(179,plain,
join(top,complement(top)) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = top,
inference(symmetry,[status(thm)],[120]) ).
tff(181,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(unit_resolution,[status(thm)],[181,37]) ).
tff(183,plain,
join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),meet(join(complement(top),top),complement(join(complement(top),top)))) = join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[156]) ).
tff(185,plain,
join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),meet(join(complement(top),top),complement(join(complement(top),top)))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(transitivity,[status(thm)],[184,183,180,45,179]) ).
tff(186,plain,
join(join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
| ( join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))))) = join(join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))))) = join(join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[187,17]) ).
tff(189,plain,
meet(join(complement(top),top),complement(join(complement(top),top))) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(transitivity,[status(thm)],[143,140,131,122,169]) ).
tff(190,plain,
join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) = join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(transitivity,[status(thm)],[160,191]) ).
tff(193,plain,
join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),join(meet(join(complement(top),top),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))))),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,plain,
complement(meet(join(complement(top),top),complement(join(complement(top),top)))) = complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[156]) ).
tff(195,plain,
join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = top,
inference(transitivity,[status(thm)],[195,193,188,186,177,174,86,83,79,66,64,62,10]) ).
tff(197,plain,
complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = complement(top),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
complement(top) = complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(transitivity,[status(thm)],[50,198]) ).
tff(200,plain,
join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[194]) ).
tff(201,plain,
join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = top,
inference(transitivity,[status(thm)],[200,183,180]) ).
tff(202,plain,
complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = complement(top),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
complement(top) = complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(transitivity,[status(thm)],[50,203]) ).
tff(205,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(monotonicity,[status(thm)],[204,199]) ).
tff(206,plain,
join(complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
| ( meet(join(complement(top),top),complement(join(complement(top),top))) = join(complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(208,plain,
meet(join(complement(top),top),complement(join(complement(top),top))) = join(complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(meet(join(complement(top),top),complement(join(complement(top),top)))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(unit_resolution,[status(thm)],[207,26]) ).
tff(209,plain,
meet(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = zero,
inference(symmetry,[status(thm)],[140]) ).
tff(210,plain,
complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = meet(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[131]) ).
tff(211,plain,
complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(meet(join(complement(top),top),complement(join(complement(top),top))),meet(join(complement(top),top),complement(join(complement(top),top)))),
inference(transitivity,[status(thm)],[117,121,210,209,142,208,206,158]) ).
tff(212,plain,
join(complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(join(meet(join(complement(top),top),complement(join(complement(top),top))),meet(join(complement(top),top),complement(join(complement(top),top)))),complement(join(complement(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(top),complement(top)),
inference(symmetry,[status(thm)],[53]) ).
tff(214,plain,
join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(transitivity,[status(thm)],[41,45,179]) ).
tff(215,plain,
join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(217,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[216,37]) ).
tff(218,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))) = join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(219,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))) = join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(unit_resolution,[status(thm)],[218,37]) ).
tff(220,plain,
join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = top,
inference(transitivity,[status(thm)],[222,217,215,177,174,86,83,79,66,64,62,10]) ).
tff(224,plain,
complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = complement(top),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(transitivity,[status(thm)],[224,52]) ).
tff(226,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(227,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(unit_resolution,[status(thm)],[226,37]) ).
tff(228,plain,
join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))))),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[221]) ).
tff(230,plain,
join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = top,
inference(transitivity,[status(thm)],[229,228,171,161,41]) ).
tff(231,plain,
complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = complement(top),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(transitivity,[status(thm)],[231,52]) ).
tff(233,plain,
join(complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[232,225]) ).
tff(234,plain,
( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
| ( join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(235,plain,
join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(unit_resolution,[status(thm)],[234,26]) ).
tff(236,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))) = join(complement(top),complement(top)),
inference(transitivity,[status(thm)],[219,235,233,213]) ).
tff(237,plain,
complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))) = complement(join(complement(top),complement(top))),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
join(complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[235]) ).
tff(239,plain,
join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(symmetry,[status(thm)],[233]) ).
tff(240,plain,
complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top))))),
inference(transitivity,[status(thm)],[50,121,210,209,142,208,206,239,238,220]) ).
tff(241,plain,
complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(join(complement(top),complement(top))),join(complement(top),top)))))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
complement(meet(join(complement(top),top),complement(join(complement(top),top)))) = join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),
inference(transitivity,[status(thm)],[194,241,237,54,105,212,155,152,151,103]) ).
tff(243,plain,
complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = complement(sk1),
inference(monotonicity,[status(thm)],[89]) ).
tff(244,plain,
join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))) = join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(monotonicity,[status(thm)],[243,242]) ).
tff(245,plain,
join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top)))))),
inference(monotonicity,[status(thm)],[245]) ).
tff(247,plain,
complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top)))))) = complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[246]) ).
tff(248,plain,
join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[243]) ).
tff(249,plain,
join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(monotonicity,[status(thm)],[249]) ).
tff(251,plain,
complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))))) = join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(monotonicity,[status(thm)],[251,247]) ).
tff(253,plain,
join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))))),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1))),
inference(monotonicity,[status(thm)],[253,100]) ).
tff(255,plain,
join(join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1))) = join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[254]) ).
tff(256,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(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top)))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1)))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(257,plain,
join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top)))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1)))) = join(join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1))),
inference(unit_resolution,[status(thm)],[256,17]) ).
tff(258,plain,
( ~ ! [A: $i] : ( top = join(A,complement(A)) )
| ( top = join(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(259,plain,
top = join(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(unit_resolution,[status(thm)],[258,7]) ).
tff(260,plain,
join(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))) = top,
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1)) = join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(symmetry,[status(thm)],[100]) ).
tff(262,plain,
join(join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1)),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))))) = join(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(monotonicity,[status(thm)],[261,247]) ).
tff(263,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1)),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top)))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(264,plain,
join(join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1)),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top)))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1))),
inference(unit_resolution,[status(thm)],[263,37]) ).
tff(265,plain,
join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top)))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1))) = join(join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1)),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top))))))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top)))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1))) = join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),
inference(transitivity,[status(thm)],[265,262,260,28]) ).
tff(267,plain,
join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top)))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1)))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(monotonicity,[status(thm)],[266]) ).
tff(268,plain,
join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(meet(join(complement(top),top),complement(join(complement(top),top)))))),join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(sk1)))),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(270,plain,
join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = join(complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),
inference(unit_resolution,[status(thm)],[269,37]) ).
tff(271,plain,
join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[251]) ).
tff(272,plain,
join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
join(complement(sk1),meet(join(complement(top),top),complement(join(complement(top),top)))) = join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[156]) ).
tff(274,plain,
join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(sk1),meet(join(complement(top),top),complement(join(complement(top),top)))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
| ( join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(276,plain,
join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))) = join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[275,26]) ).
tff(277,plain,
join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = join(complement(sk1),meet(join(complement(top),top),complement(join(complement(top),top)))),
inference(transitivity,[status(thm)],[277,274]) ).
tff(279,plain,
join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))) = join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),meet(join(complement(top),top),complement(join(complement(top),top))))),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),meet(join(complement(top),top),complement(join(complement(top),top))))) = join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
| ( join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),meet(join(complement(top),top),complement(join(complement(top),top))))) = join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)),meet(join(complement(top),top),complement(join(complement(top),top)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(282,plain,
join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),meet(join(complement(top),top),complement(join(complement(top),top))))) = join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)),meet(join(complement(top),top),complement(join(complement(top),top)))),
inference(unit_resolution,[status(thm)],[281,17]) ).
tff(283,plain,
join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)),meet(join(complement(top),top),complement(join(complement(top),top)))) = join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),meet(join(complement(top),top),complement(join(complement(top),top))))),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
join(sk1,complement(sk1)) = top,
inference(symmetry,[status(thm)],[93]) ).
tff(285,plain,
join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)) = join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),
inference(transitivity,[status(thm)],[90,284,120]) ).
tff(286,plain,
join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)),meet(join(complement(top),top),complement(join(complement(top),top)))) = join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))),
inference(monotonicity,[status(thm)],[285,150]) ).
tff(287,plain,
join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))) = join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(sk1)),meet(join(complement(top),top),complement(join(complement(top),top)))),
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
( ~ ! [A: $i] : ( top = join(A,complement(A)) )
| ( top = join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(289,plain,
top = join(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))),complement(complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))),
inference(unit_resolution,[status(thm)],[288,7]) ).
tff(290,plain,
join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))) = join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))),
inference(transitivity,[status(thm)],[41,289,287,283,280]) ).
tff(291,plain,
join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[290,250]) ).
tff(292,plain,
join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = join(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))),complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(symmetry,[status(thm)],[291]) ).
tff(293,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
| ( join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))) = join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(294,plain,
join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))) = join(join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[293,17]) ).
tff(295,plain,
( ~ ! [A: $i] : ( top = join(A,complement(A)) )
| ( top = join(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(296,plain,
top = join(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(unit_resolution,[status(thm)],[295,7]) ).
tff(297,plain,
join(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = top,
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
join(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = join(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))),complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),
inference(monotonicity,[status(thm)],[277,251]) ).
tff(299,plain,
join(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))) = top,
inference(transitivity,[status(thm)],[298,297]) ).
tff(300,plain,
join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))) = join(sk1,top),
inference(monotonicity,[status(thm)],[89,299]) ).
tff(301,plain,
join(sk1,top) = join(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(join(complement(sk1),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))),complement(join(complement(sk1),join(complement(join(complement(top),complement(top))),complement(join(complement(top),top))))))),complement(join(complement(join(complement(top),complement(top))),complement(join(complement(top),top)))))))),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
join(sk1,top) = top,
inference(transitivity,[status(thm)],[301,294,292,272,270,268,257,255,98,96,86,83,79,66,64,62,10]) ).
tff(303,plain,
( ( join(sk1,top) != top )
<=> ( join(sk1,top) != top ) ),
inference(rewrite,[status(thm)],]) ).
tff(304,axiom,
join(sk1,top) != top,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
tff(305,plain,
join(sk1,top) != top,
inference(modus_ponens,[status(thm)],[304,303]) ).
tff(306,plain,
$false,
inference(unit_resolution,[status(thm)],[305,302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL002-1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n019.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 19:24:50 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.
% 1.81/1.42 % SZS status Unsatisfiable
% 1.81/1.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------