%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET927+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:26:41 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of formulae : 5 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 10 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 25 ( 9 ~; 5 |; 5 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 15 ( 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
tff(in_type,type,
in: ( $i * $i ) > $o ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(set_difference_type,type,
set_difference: ( $i * $i ) > $i ).
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A) )
<=> ( ~ in(A,C)
& ( in(B,C)
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
tff(2,plain,
( ~ ! [A: $i,B: $i,C: $i] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A) )
<=> ( ~ in(A,C)
& ( in(B,C)
| ( A = B ) ) ) )
<=> ~ ! [A: $i,B: $i,C: $i] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A) )
<=> ( ~ in(A,C)
& ( in(B,C)
| ( A = B ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ! [A: $i,B: $i,C: $i] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A) )
<=> ( ~ in(A,C)
& ( in(B,C)
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).
tff(4,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A) )
<=> ( ~ in(A,C)
& ( in(B,C)
| ( A = B ) ) ) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
$false,
inference(unit_resolution,[status(thm)],[4,1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET927+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.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 05:55:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------