%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL012-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:00:35 AM UTC 2025
% Result : Unsatisfiable 0.50s 0.71s
% Output : Proof 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 22 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 2 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(apply_type,type,
apply: ( $i * $i ) > $i ).
tff(combinator_type,type,
combinator: $i ).
tff(u_type,type,
u: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) )
<=> ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) )
<=> ! [Y: $i,X: $i] : ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) )
<=> ! [Y: $i,X: $i] : ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_definition) ).
tff(5,plain,
! [Y: $i,X: $i] : ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( apply(apply(u,X),Y) = apply(Y,apply(apply(X,X),Y)) )
| ( apply(apply(u,u),combinator) = apply(combinator,apply(apply(u,u),combinator)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
apply(apply(u,u),combinator) = apply(combinator,apply(apply(u,u),combinator)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
apply(combinator,apply(apply(u,u),combinator)) = apply(apply(u,u),combinator),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
apply(combinator,apply(combinator,apply(apply(u,u),combinator))) = apply(combinator,apply(apply(u,u),combinator)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
apply(combinator,apply(apply(u,u),combinator)) = apply(combinator,apply(combinator,apply(apply(u,u),combinator))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
^ [Y: $i] :
refl(( ( Y != apply(combinator,Y) )
<=> ( Y != apply(combinator,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [Y: $i] : ( Y != apply(combinator,Y) )
<=> ! [Y: $i] : ( Y != apply(combinator,Y) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [Y: $i] : ( Y != apply(combinator,Y) )
<=> ! [Y: $i] : ( Y != apply(combinator,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
! [Y: $i] : ( Y != apply(combinator,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
tff(17,plain,
! [Y: $i] : ( Y != apply(combinator,Y) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [Y: $i] : ( Y != apply(combinator,Y) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Y: $i] : ( Y != apply(combinator,Y) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [Y: $i] : ( Y != apply(combinator,Y) )
| ( apply(combinator,apply(apply(u,u),combinator)) != apply(combinator,apply(combinator,apply(apply(u,u),combinator))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
apply(combinator,apply(apply(u,u),combinator)) != apply(combinator,apply(combinator,apply(apply(u,u),combinator))),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
$false,
inference(unit_resolution,[status(thm)],[21,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : COL012-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 12:02:55 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.50/0.71 % SZS status Unsatisfiable
% 0.50/0.71 % SZS output start Proof
% See solution above
% 0.50/0.71 % E exiting
%------------------------------------------------------------------------------