%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET054-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:25:00 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 16 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 4 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 22 ( 21 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(x_type,type,
x: $i ).
tff(1,plain,
( ~ subclass(x,x)
<=> ~ subclass(x,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ subclass(x,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_is_reflexive_1) ).
tff(3,plain,
~ subclass(x,x),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i] :
refl(( subclass(Y,Y)
<=> subclass(Y,Y) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i] : subclass(Y,Y)
<=> ! [Y: $i] : subclass(Y,Y) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i] : subclass(Y,Y)
<=> ! [Y: $i] : subclass(Y,Y) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
( ! [Y: $i,X: $i] : subclass(Y,Y)
<=> ! [Y: $i] : subclass(Y,Y) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(8,plain,
( ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(X,Y) )
<=> ! [Y: $i,X: $i] : subclass(Y,Y) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(9,plain,
( ! [Y: $i,X: $i] :
( ( X != Y )
| subclass(X,Y) )
<=> ! [Y: $i] : subclass(Y,Y) ),
inference(transitivity,[status(thm)],[8,7]) ).
tff(10,axiom,
! [Y: $i,X: $i] :
( ( X != Y )
| subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',equal_implies_subclass1) ).
tff(11,plain,
! [Y: $i] : subclass(Y,Y),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [Y: $i] : subclass(Y,Y),
inference(modus_ponens,[status(thm)],[11,6]) ).
tff(13,plain,
! [Y: $i] : subclass(Y,Y),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [Y: $i] : subclass(Y,Y),
inference(modus_ponens,[status(thm)],[13,5]) ).
tff(15,plain,
( ~ ! [Y: $i] : subclass(Y,Y)
| subclass(x,x) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
$false,
inference(unit_resolution,[status(thm)],[15,14,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET054-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 04:08:53 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39 % SZS output start Proof
% See solution above
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------