%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET103-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 05:25:14 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 31 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 40 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 45 ( 13 ~; 23 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 2 ( 2 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 30 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(x_type,type,
x: $i ).
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(null_class_type,type,
null_class: $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(universal_class_type,type,
universal_class: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
<=> ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
<=> ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
<=> ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
tff(5,plain,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
| ( unordered_pair(singleton(x),unordered_pair(x,singleton(y))) = ordered_pair(x,y) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
unordered_pair(singleton(x),unordered_pair(x,singleton(y))) = ordered_pair(x,y),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ member(y,universal_class)
<=> ~ member(y,universal_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ member(y,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_1_of_ordered_pair_2) ).
tff(12,plain,
~ member(y,universal_class),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X: $i] :
refl(( ( member(X,universal_class)
| ( singleton(X) = null_class ) )
<=> ( member(X,universal_class)
| ( singleton(X) = null_class ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) )
<=> ! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) )
<=> ! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
tff(17,plain,
! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ ! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) )
| member(y,universal_class)
| ( singleton(y) = null_class ) )
<=> ( ~ ! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) )
| member(y,universal_class)
| ( singleton(y) = null_class ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) )
| member(y,universal_class)
| ( singleton(y) = null_class ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [X: $i] :
( member(X,universal_class)
| ( singleton(X) = null_class ) )
| member(y,universal_class)
| ( singleton(y) = null_class ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
singleton(y) = null_class,
inference(unit_resolution,[status(thm)],[22,19,12]) ).
tff(24,plain,
unordered_pair(x,singleton(y)) = unordered_pair(x,null_class),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
unordered_pair(singleton(x),unordered_pair(x,singleton(y))) = unordered_pair(singleton(x),unordered_pair(x,null_class)),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
unordered_pair(singleton(x),unordered_pair(x,null_class)) = unordered_pair(singleton(x),unordered_pair(x,singleton(y))),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
unordered_pair(singleton(x),unordered_pair(x,null_class)) = ordered_pair(x,y),
inference(transitivity,[status(thm)],[26,9]) ).
tff(28,plain,
( ( unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y) )
<=> ( unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_1_of_ordered_pair_1) ).
tff(30,plain,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET103-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.13 % 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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 04:18:25 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% See solution above
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------