%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET901+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.14s 0.39s
% 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 : 105 ( 80 equ)
% Maximal formula atoms : 10 ( 13 avg)
% Number of connectives : 190 ( 104 ~; 0 |; 60 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 27 ( 24 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
tff(subset_type,type,
subset: ( $i * $i ) > $o ).
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(empty_set_type,type,
empty_set: $i ).
tff(1,plain,
^ [A: $i,B: $i,C: $i] :
trans(trans(monotonicity(rewrite(( ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) )
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) )),
( ( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) )
<=> ( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ) )),
rewrite(( ( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) )
<=> ~ ( ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) )
<=> subset(A,unordered_pair(B,C)) ) )),
( ( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) )
<=> ~ ( ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) )
<=> subset(A,unordered_pair(B,C)) ) )),
rewrite(( ~ ( ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) )
<=> subset(A,unordered_pair(B,C)) )
<=> ~ ( ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) )
<=> subset(A,unordered_pair(B,C)) ) )),
( ( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) )
<=> ~ ( ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) )
<=> subset(A,unordered_pair(B,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) )
<=> ! [A: $i,B: $i,C: $i] :
~ ( ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) )
<=> subset(A,unordered_pair(B,C)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,axiom,
! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
tff(4,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) )
<=> subset(A,unordered_pair(B,C)) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( ~ ! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) )
<=> ~ ! [A: $i,B: $i,C: $i] :
~ ( ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) )
<=> subset(A,unordered_pair(B,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
~ ! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
tff(7,plain,
~ ! [A: $i,B: $i,C: $i] :
~ ( ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) )
<=> subset(A,unordered_pair(B,C)) ),
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 : SET901+1 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 05:50:25 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% See solution above
% 0.14/0.40 % E exiting
%------------------------------------------------------------------------------