%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET025-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:24:53 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 27 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 9 ~; 2 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(little_set_type,type,
little_set: $i > $o ).
tff(non_ordered_pair_type,type,
non_ordered_pair: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(singleton_set_type,type,
singleton_set: $i > $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) )
<=> ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) )
<=> ! [Y: $i,X: $i] : ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) )
<=> ! [Y: $i,X: $i] : ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
tff(5,plain,
! [Y: $i,X: $i] : ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) )
| ( ordered_pair(a,b) = non_ordered_pair(singleton_set(a),non_ordered_pair(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ordered_pair(a,b) = non_ordered_pair(singleton_set(a),non_ordered_pair(a,b)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
non_ordered_pair(singleton_set(a),non_ordered_pair(a,b)) = ordered_pair(a,b),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( little_set(non_ordered_pair(singleton_set(a),non_ordered_pair(a,b)))
<=> little_set(ordered_pair(a,b)) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( little_set(ordered_pair(a,b))
<=> little_set(non_ordered_pair(singleton_set(a),non_ordered_pair(a,b))) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ little_set(ordered_pair(a,b))
<=> ~ little_set(non_ordered_pair(singleton_set(a),non_ordered_pair(a,b))) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ little_set(ordered_pair(a,b))
<=> ~ little_set(ordered_pair(a,b)) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
~ little_set(ordered_pair(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pairs_are_small) ).
tff(16,plain,
~ little_set(ordered_pair(a,b)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ little_set(non_ordered_pair(singleton_set(a),non_ordered_pair(a,b))),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
^ [Y: $i,X: $i] :
refl(( little_set(non_ordered_pair(X,Y))
<=> little_set(non_ordered_pair(X,Y)) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [Y: $i,X: $i] : little_set(non_ordered_pair(X,Y))
<=> ! [Y: $i,X: $i] : little_set(non_ordered_pair(X,Y)) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Y: $i,X: $i] : little_set(non_ordered_pair(X,Y))
<=> ! [Y: $i,X: $i] : little_set(non_ordered_pair(X,Y)) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [Y: $i,X: $i] : little_set(non_ordered_pair(X,Y)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair4) ).
tff(22,plain,
! [Y: $i,X: $i] : little_set(non_ordered_pair(X,Y)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [Y: $i,X: $i] : little_set(non_ordered_pair(X,Y)),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [Y: $i,X: $i] : little_set(non_ordered_pair(X,Y)),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] : little_set(non_ordered_pair(X,Y))
| little_set(non_ordered_pair(singleton_set(a),non_ordered_pair(a,b))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
little_set(non_ordered_pair(singleton_set(a),non_ordered_pair(a,b))),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
$false,
inference(unit_resolution,[status(thm)],[26,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET025-4 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 04:04:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------