%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL064-9 : TPTP v9.0.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:00:43 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 54 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 70 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 14 ~; 10 |; 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 : 71 ( 66 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
tff(apply_type,type,
apply: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(z_type,type,
z: $i ).
tff(t_type,type,
t: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( apply(apply(t,X),Y) = apply(Y,X) )
<=> ( apply(apply(t,X),Y) = apply(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) )
<=> ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) )
<=> ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
tff(5,plain,
! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) )
| ( apply(apply(t,x),z) = apply(z,x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
apply(apply(t,x),z) = apply(z,x),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
apply(z,x) = apply(apply(t,x),z),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
apply(apply(z,x),y) = apply(apply(apply(t,x),z),y),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
apply(apply(apply(t,x),z),y) = apply(apply(z,x),y),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) )
| ( apply(apply(t,y),apply(apply(t,x),z)) = apply(apply(apply(t,x),z),y) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(14,plain,
apply(apply(t,y),apply(apply(t,x),z)) = apply(apply(apply(t,x),z),y),
inference(unit_resolution,[status(thm)],[13,7]) ).
tff(15,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
<=> ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
tff(19,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,apply(t,y)),apply(t,x)),z) = apply(apply(t,y),apply(apply(t,x),z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
apply(apply(apply(b,apply(t,y)),apply(t,x)),z) = apply(apply(t,y),apply(apply(t,x),z)),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,b),t),y) = apply(b,apply(t,y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
apply(apply(apply(b,b),t),y) = apply(b,apply(t,y)),
inference(unit_resolution,[status(thm)],[24,21]) ).
tff(26,plain,
apply(b,apply(t,y)) = apply(apply(apply(b,b),t),y),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
apply(apply(b,apply(t,y)),apply(t,x)) = apply(apply(apply(apply(b,b),t),y),apply(t,x)),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
apply(apply(apply(apply(b,b),t),y),apply(t,x)) = apply(apply(b,apply(t,y)),apply(t,x)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) )
| ( apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)) = apply(apply(apply(apply(b,b),t),y),apply(t,x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)) = apply(apply(apply(apply(b,b),t),y),apply(t,x)),
inference(unit_resolution,[status(thm)],[29,7]) ).
tff(31,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y) = apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y) = apply(apply(t,apply(t,x)),apply(apply(apply(b,b),t),y)),
inference(unit_resolution,[status(thm)],[31,21]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,apply(apply(b,b),t)),t),x) = apply(apply(apply(b,b),t),apply(t,x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
apply(apply(apply(b,apply(apply(b,b),t)),t),x) = apply(apply(apply(b,b),t),apply(t,x)),
inference(unit_resolution,[status(thm)],[33,21]) ).
tff(35,plain,
apply(apply(apply(b,b),t),apply(t,x)) = apply(apply(apply(b,apply(apply(b,b),t)),t),x),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,b),t),apply(t,x)) = apply(b,apply(t,apply(t,x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
apply(apply(apply(b,b),t),apply(t,x)) = apply(b,apply(t,apply(t,x))),
inference(unit_resolution,[status(thm)],[36,21]) ).
tff(38,plain,
apply(b,apply(t,apply(t,x))) = apply(apply(apply(b,b),t),apply(t,x)),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
apply(b,apply(t,apply(t,x))) = apply(apply(apply(b,apply(apply(b,b),t)),t),x),
inference(transitivity,[status(thm)],[38,35]) ).
tff(40,plain,
apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)) = apply(apply(apply(apply(b,apply(apply(b,b),t)),t),x),apply(apply(b,b),t)),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
apply(apply(apply(apply(b,apply(apply(b,b),t)),t),x),apply(apply(b,b),t)) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(t,X),Y) = apply(Y,X) )
| ( apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,apply(apply(b,b),t)),t),x)) = apply(apply(apply(apply(b,apply(apply(b,b),t)),t),x),apply(apply(b,b),t)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,apply(apply(b,b),t)),t),x)) = apply(apply(apply(apply(b,apply(apply(b,b),t)),t),x),apply(apply(b,b),t)),
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) )
| ( apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,apply(apply(b,b),t)),t)),x) = apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,apply(apply(b,b),t)),t),x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,apply(apply(b,b),t)),t)),x) = apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,apply(apply(b,b),t)),t),x)),
inference(unit_resolution,[status(thm)],[44,21]) ).
tff(46,plain,
apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,apply(apply(b,b),t)),t)),x) = apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),
inference(transitivity,[status(thm)],[45,43,41]) ).
tff(47,plain,
apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,apply(apply(b,b),t)),t)),x),y) = apply(apply(apply(b,apply(t,apply(t,x))),apply(apply(b,b),t)),y),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,apply(apply(b,b),t)),t)),x),y) = apply(apply(b,apply(t,y)),apply(t,x)),
inference(transitivity,[status(thm)],[47,32,30,28]) ).
tff(49,plain,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,apply(apply(b,b),t)),t)),x),y),z) = apply(apply(apply(b,apply(t,y)),apply(t,x)),z),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,apply(apply(b,b),t)),t)),x),y),z) = apply(apply(z,x),y),
inference(transitivity,[status(thm)],[49,23,14,12]) ).
tff(51,plain,
( ( apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,apply(apply(b,b),t)),t)),x),y),z) != apply(apply(z,x),y) )
<=> ( apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,apply(apply(b,b),t)),t)),x),y),z) != apply(apply(z,x),y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,apply(apply(b,b),t)),t)),x),y),z) != apply(apply(z,x),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_combinator) ).
tff(53,plain,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,apply(apply(b,b),t)),t)),x),y),z) != apply(apply(z,x),y),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
$false,
inference(unit_resolution,[status(thm)],[53,50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL064-9 : TPTP v9.0.0. Bugfixed v1.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 12:11:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43 % SZS output start Proof
% See solution above
% 0.21/0.44 % E exiting
%------------------------------------------------------------------------------