%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET082-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:25:09 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 35 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 140 ( 59 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 113 ( 17 ~; 79 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 47 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
tff(null_class_type,type,
null_class: $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(x_type,type,
x: $i ).
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(universal_class_type,type,
universal_class: $i ).
tff(1,plain,
( ~ member(x,universal_class)
<=> ~ member(x,universal_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_is_null_class_1) ).
tff(3,plain,
~ member(x,universal_class),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(( ( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) )
<=> ( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) )
<=> ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) )
<=> ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ( unordered_pair(X,Y) = null_class )
| member(X,universal_class) )
<=> ( member(X,universal_class)
| ( unordered_pair(X,Y) = null_class ) ) )),
( ( ( unordered_pair(X,Y) = null_class )
| member(X,universal_class)
| member(Y,universal_class) )
<=> ( member(X,universal_class)
| ( unordered_pair(X,Y) = null_class )
| member(Y,universal_class) ) )),
rewrite(( ( member(X,universal_class)
| ( unordered_pair(X,Y) = null_class )
| member(Y,universal_class) )
<=> ( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) ) )),
( ( ( unordered_pair(X,Y) = null_class )
| member(X,universal_class)
| member(Y,universal_class) )
<=> ( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Y: $i,X: $i] :
( ( unordered_pair(X,Y) = null_class )
| member(X,universal_class)
| member(Y,universal_class) )
<=> ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [Y: $i,X: $i] :
( ( unordered_pair(X,Y) = null_class )
| member(X,universal_class)
| member(Y,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_unordered_pair) ).
tff(10,plain,
! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) )
| member(x,universal_class)
| ( unordered_pair(x,x) = null_class ) )
<=> ( ~ ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) )
| member(x,universal_class)
| ( unordered_pair(x,x) = null_class ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ( member(x,universal_class)
| member(x,universal_class)
| ( unordered_pair(x,x) = null_class ) )
<=> ( member(x,universal_class)
| ( unordered_pair(x,x) = null_class ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ( ~ ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) )
| member(x,universal_class)
| member(x,universal_class)
| ( unordered_pair(x,x) = null_class ) )
<=> ( ~ ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) )
| member(x,universal_class)
| ( unordered_pair(x,x) = null_class ) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) )
| member(x,universal_class)
| member(x,universal_class)
| ( unordered_pair(x,x) = null_class ) )
<=> ( ~ ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) )
| member(x,universal_class)
| ( unordered_pair(x,x) = null_class ) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) )
| member(x,universal_class)
| member(x,universal_class)
| ( unordered_pair(x,x) = null_class ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [Y: $i,X: $i] :
( member(X,universal_class)
| member(Y,universal_class)
| ( unordered_pair(X,Y) = null_class ) )
| member(x,universal_class)
| ( unordered_pair(x,x) = null_class ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
unordered_pair(x,x) = null_class,
inference(unit_resolution,[status(thm)],[19,13,3]) ).
tff(21,plain,
^ [X: $i] :
refl(( ( unordered_pair(X,X) = singleton(X) )
<=> ( unordered_pair(X,X) = singleton(X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
<=> ! [X: $i] : ( unordered_pair(X,X) = singleton(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
<=> ! [X: $i] : ( unordered_pair(X,X) = singleton(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
tff(25,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
| ( unordered_pair(x,x) = singleton(x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
unordered_pair(x,x) = singleton(x),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
singleton(x) = unordered_pair(x,x),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
singleton(x) = null_class,
inference(transitivity,[status(thm)],[30,20]) ).
tff(32,plain,
( ( singleton(x) != null_class )
<=> ( singleton(x) != null_class ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
singleton(x) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_is_null_class_2) ).
tff(34,plain,
singleton(x) != null_class,
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
$false,
inference(unit_resolution,[status(thm)],[34,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET082-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Fri Jun 20 04:13:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% See solution above
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------