%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL361-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n017.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 02:59:51 PM UTC 2026
% Result : Unsatisfiable 0.79s 1.05s
% Output : Proof 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 57 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 239 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 330 ( 158 ~; 150 |; 0 &)
% ( 22 <=>; 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; 2 con; 0-2 aty)
% Number of variables : 125 ( 116 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
tff(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(not_type,type,
not: $i > $i ).
tff(y_type,type,
y: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
<=> is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
<=> ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
<=> ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( is_a_theorem(implies(X,implies(not(X),Y)))
<=> is_a_theorem(implies(X,implies(not(X),Y))) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : is_a_theorem(implies(X,implies(not(X),Y)))
<=> ! [Y: $i,X: $i] : is_a_theorem(implies(X,implies(not(X),Y))) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : is_a_theorem(implies(X,implies(not(X),Y)))
<=> ! [Y: $i,X: $i] : is_a_theorem(implies(X,implies(not(X),Y))) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : is_a_theorem(implies(X,implies(not(X),Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
tff(14,plain,
! [Y: $i,X: $i] : is_a_theorem(implies(X,implies(not(X),Y))),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : is_a_theorem(implies(X,implies(not(X),Y))),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : is_a_theorem(implies(X,implies(not(X),Y))),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : is_a_theorem(implies(X,implies(not(X),Y)))
| is_a_theorem(implies(x,implies(not(x),y))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
is_a_theorem(implies(x,implies(not(x),y))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
refl(( ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
<=> ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
<=> ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
<=> ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
<=> ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) )),
( ( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) )
<=> ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ) )),
rewrite(( ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) )
<=> ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) )),
( ( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) )
<=> ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [Y: $i,X: $i] :
( ~ is_a_theorem(implies(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(implies(X,Y)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [Y: $i,X: $i] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
tff(25,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| ~ is_a_theorem(implies(x,implies(not(x),y)))
| is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))
| ~ is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| ~ is_a_theorem(implies(x,implies(not(x),y)))
| is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))
| ~ is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))
| ~ is_a_theorem(implies(x,implies(not(x),y)))
| ~ is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))) )
<=> ( ~ is_a_theorem(implies(x,implies(not(x),y)))
| is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))
| ~ is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))
| ~ is_a_theorem(implies(x,implies(not(x),y)))
| ~ is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| ~ is_a_theorem(implies(x,implies(not(x),y)))
| is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))
| ~ is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))
| ~ is_a_theorem(implies(x,implies(not(x),y)))
| ~ is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| ~ is_a_theorem(implies(x,implies(not(x),y)))
| is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))
| ~ is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))
| ~ is_a_theorem(implies(x,implies(not(x),y)))
| ~ is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| ~ is_a_theorem(implies(x,implies(not(x),y)))
| is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))
| ~ is_a_theorem(implies(implies(x,implies(not(x),y)),implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x)))))) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x))))),
inference(unit_resolution,[status(thm)],[34,28,18,9]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
is_a_theorem(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))),
inference(unit_resolution,[status(thm)],[36,7]) ).
tff(38,plain,
( ~ is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))
<=> ~ is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
~ is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_10) ).
tff(40,plain,
~ is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))
| ~ is_a_theorem(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))
| ~ is_a_theorem(implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))
| ~ is_a_theorem(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))
| ~ is_a_theorem(implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))
| ~ is_a_theorem(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))
| ~ is_a_theorem(implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))
| ~ is_a_theorem(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))
| ~ is_a_theorem(implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
~ is_a_theorem(implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x))))),
inference(unit_resolution,[status(thm)],[43,28,40,37]) ).
tff(45,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(x,implies(implies(y,x),implies(not(x),x))),implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
is_a_theorem(implies(implies(x,implies(implies(y,x),implies(not(x),x))),implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))))),
inference(unit_resolution,[status(thm)],[45,7]) ).
tff(47,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))))
| ~ is_a_theorem(implies(x,implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(x,implies(implies(y,x),implies(not(x),x))),implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))))
| ~ is_a_theorem(implies(x,implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(x,implies(implies(y,x),implies(not(x),x))),implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))))
| ~ is_a_theorem(implies(x,implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(x,implies(implies(y,x),implies(not(x),x))),implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))))
| ~ is_a_theorem(implies(x,implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(x,implies(implies(y,x),implies(not(x),x))),implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))))) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( is_a_theorem(implies(implies(implies(implies(y,x),implies(not(x),x)),implies(implies(implies(not(x),x),x),implies(implies(y,x),x))),implies(x,implies(implies(implies(not(x),x),x),implies(implies(y,x),x)))))
| ~ is_a_theorem(implies(x,implies(implies(y,x),implies(not(x),x)))) ),
inference(unit_resolution,[status(thm)],[49,28,46]) ).
tff(51,plain,
~ is_a_theorem(implies(x,implies(implies(y,x),implies(not(x),x)))),
inference(unit_resolution,[status(thm)],[50,44]) ).
tff(52,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
is_a_theorem(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x)))),
inference(unit_resolution,[status(thm)],[52,7]) ).
tff(54,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(x,implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(x,implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(x,implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(x,implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))))
| ~ is_a_theorem(implies(implies(implies(not(x),y),implies(implies(y,x),implies(not(x),x))),implies(x,implies(implies(y,x),implies(not(x),x))))) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
$false,
inference(unit_resolution,[status(thm)],[56,28,53,51,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL361-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 01:30:53 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.79/1.05 % SZS status Unsatisfiable
% 0.79/1.05 % SZS output start Proof
% See solution above
% 0.79/1.08 % E exiting
%------------------------------------------------------------------------------