%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL066-2 : TPTP v9.0.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:00:44 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 39 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 52 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 7 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 65 ( 60 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
tff(apply_type,type,
apply: ( $i * $i ) > $i ).
tff(z_type,type,
z: $i ).
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(q_type,type,
q: $i ).
tff(w_type,type,
w: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) )
<=> ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_definition) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) )
| ( apply(apply(apply(q,apply(x,y)),apply(x,y)),z) = apply(apply(x,y),apply(apply(x,y),z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
apply(apply(apply(q,apply(x,y)),apply(x,y)),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) )
| ( apply(apply(apply(q,x),apply(q,apply(x,y))),y) = apply(apply(q,apply(x,y)),apply(x,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
apply(apply(apply(q,x),apply(q,apply(x,y))),y) = apply(apply(q,apply(x,y)),apply(x,y)),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) )
| ( apply(apply(apply(q,q),apply(q,x)),apply(x,y)) = apply(apply(q,x),apply(q,apply(x,y))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
apply(apply(apply(q,q),apply(q,x)),apply(x,y)) = apply(apply(q,x),apply(q,apply(x,y))),
inference(unit_resolution,[status(thm)],[12,7]) ).
tff(14,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) )
| ( apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y) = apply(apply(apply(q,q),apply(q,x)),apply(x,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y) = apply(apply(apply(q,q),apply(q,x)),apply(x,y)),
inference(unit_resolution,[status(thm)],[14,7]) ).
tff(16,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) )
| ( apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)) = apply(apply(q,x),apply(apply(q,q),apply(q,x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)) = apply(apply(q,x),apply(apply(q,q),apply(q,x))),
inference(unit_resolution,[status(thm)],[16,7]) ).
tff(18,plain,
^ [Y: $i,X: $i] :
refl(( ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) )
<=> ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) )
<=> ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) )
<=> ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
tff(22,plain,
! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) )
| ( apply(apply(w,apply(q,apply(q,q))),apply(q,x)) = apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
apply(apply(w,apply(q,apply(q,q))),apply(q,x)) = apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) )
| ( apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) = apply(apply(w,apply(q,apply(q,q))),apply(q,x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) = apply(apply(w,apply(q,apply(q,q))),apply(q,x)),
inference(unit_resolution,[status(thm)],[27,7]) ).
tff(29,plain,
apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) = apply(apply(q,x),apply(apply(q,q),apply(q,x))),
inference(transitivity,[status(thm)],[28,26,17]) ).
tff(30,plain,
apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) = apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) = apply(apply(q,x),apply(q,apply(x,y))),
inference(transitivity,[status(thm)],[30,15,13]) ).
tff(32,plain,
apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) = apply(apply(apply(q,x),apply(q,apply(x,y))),y),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) = apply(apply(q,apply(x,y)),apply(x,y)),
inference(transitivity,[status(thm)],[32,11]) ).
tff(34,plain,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) = apply(apply(apply(q,apply(x,y)),apply(x,y)),z),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(transitivity,[status(thm)],[34,9]) ).
tff(36,plain,
( ( apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)) )
<=> ( apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p_combinator) ).
tff(38,plain,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL066-2 : TPTP v9.0.0. Bugfixed v1.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 12:11:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------