%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL126-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n018.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 02:59:21 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.49s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 30
% Syntax : Number of formulae : 65 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 314 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 457 ( 218 ~; 212 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 10 ( 10 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 : 156 ( 146 !; 0 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
tff(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
tff(equivalent_type,type,
equivalent: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y))))
<=> is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y))))
<=> ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y))))
<=> ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_3) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z))))
<=> is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z)))) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z))))
<=> ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z)))) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z))))
<=> ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_4) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z)))),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z)))),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z)))),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b)))))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,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(25,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)],[24]) ).
tff(26,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(27,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,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(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,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(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,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(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,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(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b)))))) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),
inference(unit_resolution,[status(thm)],[33,30,20,18]) ).
tff(35,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(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,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(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))) ) ),
inference(rewrite,[status(thm)],[]) ).
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,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))) ),
inference(quant_inst,[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,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b)))),
inference(unit_resolution,[status(thm)],[37,30,20,34]) ).
tff(39,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(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),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,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))) )
<=> ( ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))) ) ),
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(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),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,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))) ) ),
inference(monotonicity,[status(thm)],[40]) ).
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(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),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,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,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(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,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(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))))) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c)))),
inference(unit_resolution,[status(thm)],[44,30,38,9]) ).
tff(46,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y))))
| is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))),
inference(unit_resolution,[status(thm)],[46,7]) ).
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(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,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(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ( is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))) )
<=> ( ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,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(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,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(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,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(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,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(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,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(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))) ),
inference(quant_inst,[status(thm)],[]) ).
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(a,c),equivalent(equivalent(a,b),equivalent(c,b))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))))) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))),
inference(unit_resolution,[status(thm)],[53,30,20,47]) ).
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(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,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(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,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(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,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(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))))),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b))))),
inference(unit_resolution,[status(thm)],[57,30,18,54]) ).
tff(59,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c)))
<=> ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_q_2) ).
tff(61,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))),
inference(modus_ponens,[status(thm)],[60,59]) ).
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(a,b),equivalent(c,b)),equivalent(a,c)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),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,b),equivalent(c,b)),equivalent(a,c)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,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(c,b)),equivalent(a,c)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,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(c,b)),equivalent(a,c)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(equivalent(a,b),equivalent(c,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),equivalent(c,b)))),equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c)))) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,30,61,58,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL126-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n018.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 : Sat Sep 5 11:01:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.22/0.49 % SZS status Unsatisfiable
% 0.22/0.49 % SZS output start Proof
% See solution above
% 0.22/0.53 % E exiting
%------------------------------------------------------------------------------