%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL011-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 02:59:11 PM UTC 2026
% Result : Unsatisfiable 14.96s 15.24s
% Output : Proof 15.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 144
% Syntax : Number of formulae : 331 ( 96 unt; 0 typ; 0 def)
% Number of atoms : 1483 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 2243 (1100 ~;1083 |; 0 &)
% ( 60 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 554 ( 547 !; 0 ?; 554 :)
% Comments :
%------------------------------------------------------------------------------
tff(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
tff(equivalent_type,type,
equivalent: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(c_type,type,
c: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
<=> is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z)))) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
<=> ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z)))) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
<=> ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',yqj) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z)))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z)))),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z)))),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b)))),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [Y: $i,X: $i] :
refl(( ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
<=> ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
<=> ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
<=> ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X) )
<=> ( ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ) )),
( ( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) )
<=> ( ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y))
| is_a_theorem(Y) ) )),
rewrite(( ( ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y))
| is_a_theorem(Y) )
<=> ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ) )),
( ( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) )
<=> ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [Y: $i,X: $i] :
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) )
<=> ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [Y: $i,X: $i] :
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
tff(18,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(b,a),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))))),
inference(unit_resolution,[status(thm)],[24,21,11,9]) ).
tff(26,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))))),
inference(unit_resolution,[status(thm)],[26,7]) ).
tff(28,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))))) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))),
inference(unit_resolution,[status(thm)],[30,21,27,25]) ).
tff(32,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
is_a_theorem(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a)))),
inference(unit_resolution,[status(thm)],[34,7]) ).
tff(36,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c)))),
inference(unit_resolution,[status(thm)],[38,21,35,33]) ).
tff(40,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(a,c),equivalent(b,a)),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))),
inference(unit_resolution,[status(thm)],[42,21,39,31]) ).
tff(44,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))))),
inference(unit_resolution,[status(thm)],[44,7]) ).
tff(46,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))))) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))),equivalent(equivalent(a,c),equivalent(c,b)))) ),
inference(unit_resolution,[status(thm)],[48,21,45]) ).
tff(50,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))),
inference(unit_resolution,[status(thm)],[49,43]) ).
tff(51,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a))))),
inference(unit_resolution,[status(thm)],[51,7]) ).
tff(53,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
( is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(b,a),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(b,a)))),equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))) ),
inference(unit_resolution,[status(thm)],[55,21,52]) ).
tff(57,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))),
inference(unit_resolution,[status(thm)],[56,50]) ).
tff(58,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))))),
inference(unit_resolution,[status(thm)],[58,7]) ).
tff(60,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))))) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))) ),
inference(unit_resolution,[status(thm)],[62,21,59]) ).
tff(64,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))),
inference(unit_resolution,[status(thm)],[63,57]) ).
tff(65,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))),
inference(unit_resolution,[status(thm)],[65,7]) ).
tff(67,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c)))) ),
inference(unit_resolution,[status(thm)],[69,21,66]) ).
tff(71,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))))),
inference(unit_resolution,[status(thm)],[70,57]) ).
tff(72,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))))),
inference(unit_resolution,[status(thm)],[72,7]) ).
tff(74,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))))) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))))) ),
inference(unit_resolution,[status(thm)],[76,21,73]) ).
tff(78,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))),
inference(unit_resolution,[status(thm)],[77,71]) ).
tff(79,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b))))),
inference(unit_resolution,[status(thm)],[79,7]) ).
tff(81,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(equivalent(c,b),equivalent(c,b)),equivalent(equivalent(a,c),equivalent(c,b)))),equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))) ),
inference(unit_resolution,[status(thm)],[83,21,80]) ).
tff(85,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))),
inference(unit_resolution,[status(thm)],[84,78]) ).
tff(86,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))))),
inference(unit_resolution,[status(thm)],[86,7]) ).
tff(88,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))))) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))),equivalent(equivalent(c,b),equivalent(a,c)))) ),
inference(unit_resolution,[status(thm)],[90,21,87]) ).
tff(92,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))),
inference(unit_resolution,[status(thm)],[91,85]) ).
tff(93,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b))))),
inference(unit_resolution,[status(thm)],[93,7]) ).
tff(95,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
( is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(c,b)))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))) ),
inference(unit_resolution,[status(thm)],[97,21,94]) ).
tff(99,plain,
is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b)))),
inference(unit_resolution,[status(thm)],[98,92]) ).
tff(100,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
( is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(a,c),equivalent(c,b))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))) ),
inference(unit_resolution,[status(thm)],[102,21]) ).
tff(104,plain,
is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))),
inference(unit_resolution,[status(thm)],[103,99,64]) ).
tff(105,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))))),
inference(unit_resolution,[status(thm)],[105,7]) ).
tff(107,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))))) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
( is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(equivalent(c,b),equivalent(a,c)))) ),
inference(unit_resolution,[status(thm)],[109,21,106]) ).
tff(111,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))),
inference(unit_resolution,[status(thm)],[110,104]) ).
tff(112,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c)))),
inference(unit_resolution,[status(thm)],[112,7]) ).
tff(114,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
( is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))) ),
inference(unit_resolution,[status(thm)],[116,21,113]) ).
tff(118,plain,
is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))),
inference(unit_resolution,[status(thm)],[117,111]) ).
tff(119,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a))))),
inference(unit_resolution,[status(thm)],[119,7]) ).
tff(121,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a)),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a))))) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
( is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(b,a))) ),
inference(unit_resolution,[status(thm)],[123,21,120]) ).
tff(125,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a)))),
inference(unit_resolution,[status(thm)],[124,118]) ).
tff(126,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,a),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,a),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,a),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,a),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a)))) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
( is_a_theorem(equivalent(equivalent(b,a),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(b,a),equivalent(b,a)))) ),
inference(unit_resolution,[status(thm)],[128,21,113]) ).
tff(130,plain,
is_a_theorem(equivalent(equivalent(b,a),equivalent(b,a))),
inference(unit_resolution,[status(thm)],[129,125]) ).
tff(131,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,a)),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,a)),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))),
inference(unit_resolution,[status(thm)],[131,7]) ).
tff(133,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,a)),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,a)),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,a)),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,a)),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
( is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(b,a))) ),
inference(unit_resolution,[status(thm)],[135,21,132]) ).
tff(137,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b)))),
inference(unit_resolution,[status(thm)],[136,130]) ).
tff(138,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))))),
inference(unit_resolution,[status(thm)],[138,7]) ).
tff(140,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))))) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b)))) ),
inference(unit_resolution,[status(thm)],[142,21,139]) ).
tff(144,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))),
inference(unit_resolution,[status(thm)],[143,137]) ).
tff(145,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))))),
inference(unit_resolution,[status(thm)],[145,7]) ).
tff(147,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))))) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
( is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(b,a),equivalent(a,b)))) ),
inference(unit_resolution,[status(thm)],[149,21,146]) ).
tff(151,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))),
inference(unit_resolution,[status(thm)],[150,137]) ).
tff(152,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
is_a_theorem(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a)))),
inference(unit_resolution,[status(thm)],[152,7]) ).
tff(154,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))
| ~ is_a_theorem(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))
| ~ is_a_theorem(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))
| ~ is_a_theorem(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))
| ~ is_a_theorem(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
( is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))) ),
inference(unit_resolution,[status(thm)],[156,21,153]) ).
tff(158,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))),
inference(unit_resolution,[status(thm)],[157,151]) ).
tff(159,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a))))),
inference(unit_resolution,[status(thm)],[159,7]) ).
tff(161,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a))))) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
( is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(b,b))) ),
inference(unit_resolution,[status(thm)],[163,21,160]) ).
tff(165,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a)))),
inference(unit_resolution,[status(thm)],[164,158]) ).
tff(166,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b)))),
inference(unit_resolution,[status(thm)],[166,7]) ).
tff(168,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,b),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,b),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,b),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,b),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a)))) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
( is_a_theorem(equivalent(equivalent(b,b),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(b,b),equivalent(a,a)))) ),
inference(unit_resolution,[status(thm)],[170,21,167]) ).
tff(172,plain,
is_a_theorem(equivalent(equivalent(b,b),equivalent(a,a))),
inference(unit_resolution,[status(thm)],[171,165]) ).
tff(173,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(a,a)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(a,a)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))),
inference(unit_resolution,[status(thm)],[173,7]) ).
tff(175,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(b,b),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(a,a)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(b,b),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(a,a)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(b,b),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(a,a)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(b,b),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,b),equivalent(a,a)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))) ),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
( is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(b,b),equivalent(a,a))) ),
inference(unit_resolution,[status(thm)],[177,21,174]) ).
tff(179,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a)))),
inference(unit_resolution,[status(thm)],[178,172]) ).
tff(180,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))))),
inference(unit_resolution,[status(thm)],[180,7]) ).
tff(182,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(183,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))))) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
( is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(equivalent(a,a),equivalent(b,a)))) ),
inference(unit_resolution,[status(thm)],[184,21,181]) ).
tff(186,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))),
inference(unit_resolution,[status(thm)],[185,179]) ).
tff(187,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(188,plain,
is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b)))),
inference(unit_resolution,[status(thm)],[187,7]) ).
tff(189,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(190,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(191,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))) ),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
( is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))) ),
inference(unit_resolution,[status(thm)],[191,21,188]) ).
tff(193,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))),
inference(unit_resolution,[status(thm)],[192,186]) ).
tff(194,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(195,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b))))),
inference(unit_resolution,[status(thm)],[194,7]) ).
tff(196,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(198,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b)),equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b))))) ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
( is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(b,a)),equivalent(a,b))) ),
inference(unit_resolution,[status(thm)],[198,21,195]) ).
tff(200,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b)))),
inference(unit_resolution,[status(thm)],[199,193]) ).
tff(201,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a)))),
inference(unit_resolution,[status(thm)],[201,7]) ).
tff(203,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(204,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(205,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b)))) ),
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
( is_a_theorem(equivalent(equivalent(a,b),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(a,a),equivalent(b,a))),equivalent(equivalent(a,b),equivalent(a,b)))) ),
inference(unit_resolution,[status(thm)],[205,21,202]) ).
tff(207,plain,
is_a_theorem(equivalent(equivalent(a,b),equivalent(a,b))),
inference(unit_resolution,[status(thm)],[206,200]) ).
tff(208,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))),
inference(unit_resolution,[status(thm)],[208,7]) ).
tff(210,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(211,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(212,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))) ),
inference(modus_ponens,[status(thm)],[211,210]) ).
tff(213,plain,
( is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(a,b))) ),
inference(unit_resolution,[status(thm)],[212,21,209]) ).
tff(214,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a)))),
inference(unit_resolution,[status(thm)],[213,207]) ).
tff(215,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(216,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
( is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(a,b),equivalent(b,a))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))) ),
inference(unit_resolution,[status(thm)],[217,21]) ).
tff(219,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))),
inference(unit_resolution,[status(thm)],[218,214,144]) ).
tff(220,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(221,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))))),
inference(unit_resolution,[status(thm)],[220,7]) ).
tff(222,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(223,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(224,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))))) ),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
( is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(a,b)))) ),
inference(unit_resolution,[status(thm)],[224,21,221]) ).
tff(226,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))),
inference(unit_resolution,[status(thm)],[225,219]) ).
tff(227,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(229,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))) ),
inference(modus_ponens,[status(thm)],[228,227]) ).
tff(230,plain,
( is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))) ),
inference(unit_resolution,[status(thm)],[229,21,167]) ).
tff(231,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))),
inference(unit_resolution,[status(thm)],[230,226]) ).
tff(232,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(233,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a))))),
inference(unit_resolution,[status(thm)],[232,7]) ).
tff(234,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(235,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(236,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a))))) ),
inference(modus_ponens,[status(thm)],[235,234]) ).
tff(237,plain,
( is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(a,a))) ),
inference(unit_resolution,[status(thm)],[236,21,233]) ).
tff(238,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a)))),
inference(unit_resolution,[status(thm)],[237,231]) ).
tff(239,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(240,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a)))) ),
inference(modus_ponens,[status(thm)],[240,239]) ).
tff(242,plain,
( is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b))),equivalent(equivalent(a,a),equivalent(a,a)))) ),
inference(unit_resolution,[status(thm)],[241,21,167]) ).
tff(243,plain,
is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a))),
inference(unit_resolution,[status(thm)],[242,238]) ).
tff(244,plain,
( ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b))))
<=> ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(245,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_yqf) ).
tff(246,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(248,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(249,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b))))) ),
inference(modus_ponens,[status(thm)],[248,247]) ).
tff(250,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b))))) ),
inference(unit_resolution,[status(thm)],[249,21,246]) ).
tff(251,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b))))),
inference(unit_resolution,[status(thm)],[250,57]) ).
tff(252,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(253,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))))),
inference(unit_resolution,[status(thm)],[252,7]) ).
tff(254,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(255,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(256,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))))) ),
inference(modus_ponens,[status(thm)],[255,254]) ).
tff(257,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(c,b)),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))) ),
inference(unit_resolution,[status(thm)],[256,21,253]) ).
tff(258,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))),
inference(unit_resolution,[status(thm)],[257,251]) ).
tff(259,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(260,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))))),
inference(unit_resolution,[status(thm)],[259,7]) ).
tff(261,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(262,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(263,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(c,b),equivalent(a,c))),equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b))))) ),
inference(modus_ponens,[status(thm)],[262,261]) ).
tff(264,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))),
inference(unit_resolution,[status(thm)],[263,21,113,260]) ).
tff(265,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(266,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))) ),
inference(modus_ponens,[status(thm)],[266,265]) ).
tff(268,plain,
( is_a_theorem(equivalent(equivalent(equivalent(c,b),equivalent(a,c)),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))) ),
inference(unit_resolution,[status(thm)],[267,21,264]) ).
tff(269,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
inference(unit_resolution,[status(thm)],[268,258]) ).
tff(270,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(271,plain,
is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))),
inference(unit_resolution,[status(thm)],[270,7]) ).
tff(272,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(273,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(274,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))) ),
inference(modus_ponens,[status(thm)],[273,272]) ).
tff(275,plain,
( is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))) ),
inference(unit_resolution,[status(thm)],[274,21,271]) ).
tff(276,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))),
inference(unit_resolution,[status(thm)],[275,269]) ).
tff(277,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(278,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))))),
inference(unit_resolution,[status(thm)],[277,7]) ).
tff(279,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(280,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(281,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a))))) ),
inference(modus_ponens,[status(thm)],[280,279]) ).
tff(282,plain,
( is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a))))) ),
inference(unit_resolution,[status(thm)],[281,21,278]) ).
tff(283,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a))))),
inference(unit_resolution,[status(thm)],[282,276]) ).
tff(284,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(285,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))))),
inference(unit_resolution,[status(thm)],[284,7]) ).
tff(286,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(287,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(288,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))))) ),
inference(modus_ponens,[status(thm)],[287,286]) ).
tff(289,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(b,a)),equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b)))),equivalent(equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))),equivalent(equivalent(a,b),equivalent(b,a)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))))) ),
inference(unit_resolution,[status(thm)],[288,21,285]) ).
tff(290,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b))))),
inference(unit_resolution,[status(thm)],[289,283]) ).
tff(291,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)),equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(292,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)),equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))),
inference(unit_resolution,[status(thm)],[291,7]) ).
tff(293,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)),equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)),equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(294,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)),equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)),equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))) ),
inference(modus_ponens,[status(thm)],[294,293]) ).
tff(296,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,b),equivalent(a,b)),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(b,a),equivalent(equivalent(b,b),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))) ),
inference(unit_resolution,[status(thm)],[295,21,292]) ).
tff(297,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))),
inference(unit_resolution,[status(thm)],[296,290]) ).
tff(298,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(299,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))))),
inference(unit_resolution,[status(thm)],[298,7]) ).
tff(300,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(301,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(302,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))))
| ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),equivalent(b,b))),equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a))))) ),
inference(modus_ponens,[status(thm)],[301,300]) ).
tff(303,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))),
inference(unit_resolution,[status(thm)],[302,21,188,299]) ).
tff(304,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(305,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(306,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(a,b)),equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))) ),
inference(modus_ponens,[status(thm)],[305,304]) ).
tff(307,plain,
( is_a_theorem(equivalent(equivalent(equivalent(b,a),equivalent(b,b)),equivalent(b,a)))
| ~ is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b))) ),
inference(unit_resolution,[status(thm)],[306,21,303]) ).
tff(308,plain,
~ is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b))),
inference(unit_resolution,[status(thm)],[307,297]) ).
tff(309,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b)))
| ~ is_a_theorem(equivalent(a,a))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b)))
| ~ is_a_theorem(equivalent(a,a))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(310,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b)))
| ~ is_a_theorem(equivalent(a,a))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(311,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b)))
| ~ is_a_theorem(equivalent(a,a))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(b,a),equivalent(a,b)))) ),
inference(modus_ponens,[status(thm)],[310,309]) ).
tff(312,plain,
( is_a_theorem(equivalent(equivalent(b,a),equivalent(a,b)))
| ~ is_a_theorem(equivalent(a,a)) ),
inference(unit_resolution,[status(thm)],[311,21,167]) ).
tff(313,plain,
~ is_a_theorem(equivalent(a,a)),
inference(unit_resolution,[status(thm)],[312,308]) ).
tff(314,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(a,a))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(a,a))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(315,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(a,a))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(316,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(a,a))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))) ),
inference(modus_ponens,[status(thm)],[315,314]) ).
tff(317,plain,
( is_a_theorem(equivalent(a,a))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))) ),
inference(unit_resolution,[status(thm)],[316,21]) ).
tff(318,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))),
inference(unit_resolution,[status(thm)],[317,243,313]) ).
tff(319,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a))),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(320,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a))),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))))),
inference(unit_resolution,[status(thm)],[319,7]) ).
tff(321,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a)))),
inference(unit_resolution,[status(thm)],[321,7]) ).
tff(323,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a))),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a))),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(324,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a))),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(325,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(equivalent(a,a),equivalent(a,a))),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a))))) ),
inference(modus_ponens,[status(thm)],[324,323]) ).
tff(326,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a)))),
inference(unit_resolution,[status(thm)],[325,21,322,320]) ).
tff(327,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(328,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(329,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) )
| is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a)))) ),
inference(modus_ponens,[status(thm)],[328,327]) ).
tff(330,plain,
( is_a_theorem(equivalent(equivalent(equivalent(a,a),equivalent(a,a)),equivalent(a,a)))
| ~ is_a_theorem(equivalent(equivalent(a,a),equivalent(a,a))) ),
inference(unit_resolution,[status(thm)],[329,21,326]) ).
tff(331,plain,
$false,
inference(unit_resolution,[status(thm)],[330,318,243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 14:25:39 UTC 2026
% 0.09/0.35 % CPUTime :
% 14.96/15.24 % SZS status Unsatisfiable
% 14.96/15.24 % SZS output start Proof
% See solution above
% 0.14/15.57 % E exiting
%------------------------------------------------------------------------------