%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET924+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:26:40 AM UTC 2025
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 14 equ)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 37 ( 18 ~; 0 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 5 ( 5 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; 0-3 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 18 ( 16 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(singleton_type,type,
singleton: $i > $i ).
tff(set_difference_type,type,
set_difference: ( $i * $i ) > $i ).
tff(in_type,type,
in: ( $i * $i ) > $o ).
tff(1,plain,
^ [A: $i,B: $i] :
trans(rewrite(( ( ( set_difference(singleton(A),B) = singleton(A) )
<=> ~ in(A,B) )
<=> ~ ( in(A,B)
<=> ( set_difference(singleton(A),B) = singleton(A) ) ) )),
rewrite(( ~ ( in(A,B)
<=> ( set_difference(singleton(A),B) = singleton(A) ) )
<=> ~ ( in(A,B)
<=> ( set_difference(singleton(A),B) = singleton(A) ) ) )),
( ( ( set_difference(singleton(A),B) = singleton(A) )
<=> ~ in(A,B) )
<=> ~ ( in(A,B)
<=> ( set_difference(singleton(A),B) = singleton(A) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i,B: $i] :
( ( set_difference(singleton(A),B) = singleton(A) )
<=> ~ in(A,B) )
<=> ! [A: $i,B: $i] :
~ ( in(A,B)
<=> ( set_difference(singleton(A),B) = singleton(A) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,axiom,
! [A: $i,B: $i] :
( ( set_difference(singleton(A),B) = singleton(A) )
<=> ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
tff(4,plain,
! [A: $i,B: $i] :
~ ( in(A,B)
<=> ( set_difference(singleton(A),B) = singleton(A) ) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( ~ ! [A: $i,B: $i] :
( ( set_difference(singleton(A),B) = singleton(A) )
<=> ~ in(A,B) )
<=> ~ ! [A: $i,B: $i] :
~ ( in(A,B)
<=> ( set_difference(singleton(A),B) = singleton(A) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
~ ! [A: $i,B: $i] :
( ( set_difference(singleton(A),B) = singleton(A) )
<=> ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
tff(7,plain,
~ ! [A: $i,B: $i] :
~ ( in(A,B)
<=> ( set_difference(singleton(A),B) = singleton(A) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
$false,
inference(unit_resolution,[status(thm)],[7,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET924+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 05:52:41 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % SZS output start Proof
% See solution above
% 0.14/0.38 % E exiting
%------------------------------------------------------------------------------