%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET899+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:26:37 AM UTC 2025
% Result : Theorem 0.15s 0.40s
% Output : Proof 0.15s
% 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 ( 0 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 32 ( 9 ~; 15 |; 0 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 27 ( 24 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
tff(subset_type,type,
subset: ( $i * $i ) > $o ).
tff(in_type,type,
in: ( $i * $i ) > $o ).
tff(set_difference_type,type,
set_difference: ( $i * $i ) > $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(1,plain,
^ [A: $i,B: $i,C: $i] :
rewrite(( ( subset(A,B)
=> ( in(C,A)
| subset(A,set_difference(B,singleton(C))) ) )
<=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i,B: $i,C: $i] :
( subset(A,B)
=> ( in(C,A)
| subset(A,set_difference(B,singleton(C))) ) )
<=> ! [A: $i,B: $i,C: $i] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,axiom,
! [A: $i,B: $i,C: $i] :
( subset(A,B)
=> ( in(C,A)
| subset(A,set_difference(B,singleton(C))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
tff(4,plain,
! [A: $i,B: $i,C: $i] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( ~ ! [A: $i,B: $i,C: $i] :
( subset(A,B)
=> ( in(C,A)
| subset(A,set_difference(B,singleton(C))) ) )
<=> ~ ! [A: $i,B: $i,C: $i] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
~ ! [A: $i,B: $i,C: $i] :
( subset(A,B)
=> ( in(C,A)
| subset(A,set_difference(B,singleton(C))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).
tff(7,plain,
~ ! [A: $i,B: $i,C: $i] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
$false,
inference(unit_resolution,[status(thm)],[7,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SET899+1 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 05:49:10 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.15/0.40 % SZS status Theorem
% 0.15/0.40 % SZS output start Proof
% See solution above
% 0.15/0.40 % E exiting
%------------------------------------------------------------------------------