%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET113-7 : TPTP v9.0.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:25:16 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 27 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 47 ( 12 ~; 27 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(x_type,type,
x: $i ).
tff(first_type,type,
first: $i > $i ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(universal_class_type,type,
universal_class: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(second_type,type,
second: $i > $i ).
tff(1,plain,
( ( first(x) != x )
<=> ( first(x) != x ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
first(x) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_in_pair_of_non_sets) ).
tff(3,plain,
first(x) != x,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class))
<=> ~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets1_1) ).
tff(6,plain,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [X: $i] :
refl(( ( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) )
<=> ( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) )
<=> ! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) )
<=> ! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( first(X) = X ) )
<=> ( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( first(X) = X ) )
<=> ! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X: $i] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| ( first(X) = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_2) ).
tff(13,plain,
! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) )
| ( first(x) = x )
| member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) )
<=> ( ~ ! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) )
| ( first(x) = x )
| member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) )
| ( first(x) = x )
| member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [X: $i] :
( ( first(X) = X )
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) )
| ( first(x) = x )
| member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET113-7 : TPTP v9.0.0. Bugfixed v7.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.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 04:19:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.40 % SZS status Unsatisfiable
% 0.11/0.40 % SZS output start Proof
% See solution above
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------