%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU115+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 05:26:55 AM UTC 2025
% Result : Theorem 0.23s 0.40s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 39 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 121 ( 52 ~; 48 |; 0 &)
% ( 15 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 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; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 34 ( 30 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(singleton_type,type,
singleton: $i > $i ).
tff(empty_set_type,type,
empty_set: $i ).
tff(finite_subsets_type,type,
finite_subsets: $i > $i ).
tff(powerset_type,type,
powerset: $i > $i ).
tff(finite_type,type,
finite: $i > $o ).
tff(empty_type,type,
empty: $i > $o ).
tff(1,plain,
( ( powerset(empty_set) = singleton(empty_set) )
<=> ( powerset(empty_set) = singleton(empty_set) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
tff(3,plain,
powerset(empty_set) = singleton(empty_set),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( empty(empty_set)
<=> empty(empty_set) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
tff(6,plain,
empty(empty_set),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [A: $i] :
refl(( ( finite(A)
| ~ empty(A) )
<=> ( finite(A)
| ~ empty(A) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [A: $i] :
( finite(A)
| ~ empty(A) )
<=> ! [A: $i] :
( finite(A)
| ~ empty(A) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [A: $i] :
( finite(A)
| ~ empty(A) )
<=> ! [A: $i] :
( finite(A)
| ~ empty(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [A: $i] :
rewrite(( ( empty(A)
=> finite(A) )
<=> ( finite(A)
| ~ empty(A) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] :
( empty(A)
=> finite(A) )
<=> ! [A: $i] :
( finite(A)
| ~ empty(A) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [A: $i] :
( empty(A)
=> finite(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
tff(13,plain,
! [A: $i] :
( finite(A)
| ~ empty(A) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [A: $i] :
( finite(A)
| ~ empty(A) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [A: $i] :
( finite(A)
| ~ empty(A) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] :
( finite(A)
| ~ empty(A) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [A: $i] :
( finite(A)
| ~ empty(A) )
| finite(empty_set)
| ~ empty(empty_set) )
<=> ( ~ ! [A: $i] :
( finite(A)
| ~ empty(A) )
| finite(empty_set)
| ~ empty(empty_set) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [A: $i] :
( finite(A)
| ~ empty(A) )
| finite(empty_set)
| ~ empty(empty_set) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [A: $i] :
( finite(A)
| ~ empty(A) )
| finite(empty_set)
| ~ empty(empty_set) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
finite(empty_set),
inference(unit_resolution,[status(thm)],[19,16,6]) ).
tff(21,plain,
^ [A: $i] :
refl(( ( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) )
<=> ( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) )
<=> ! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) )
<=> ! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [A: $i] :
rewrite(( ( finite(A)
=> ( finite_subsets(A) = powerset(A) ) )
<=> ( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [A: $i] :
( finite(A)
=> ( finite_subsets(A) = powerset(A) ) )
<=> ! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [A: $i] :
( finite(A)
=> ( finite_subsets(A) = powerset(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finsub_1) ).
tff(27,plain,
! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) )
| ~ finite(empty_set)
| ( finite_subsets(empty_set) = powerset(empty_set) ) )
<=> ( ~ ! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) )
| ~ finite(empty_set)
| ( finite_subsets(empty_set) = powerset(empty_set) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) )
| ~ finite(empty_set)
| ( finite_subsets(empty_set) = powerset(empty_set) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [A: $i] :
( ~ finite(A)
| ( finite_subsets(A) = powerset(A) ) )
| ~ finite(empty_set)
| ( finite_subsets(empty_set) = powerset(empty_set) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
finite_subsets(empty_set) = powerset(empty_set),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
finite_subsets(empty_set) = singleton(empty_set),
inference(transitivity,[status(thm)],[34,3]) ).
tff(36,plain,
( ( finite_subsets(empty_set) != singleton(empty_set) )
<=> ( finite_subsets(empty_set) != singleton(empty_set) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
finite_subsets(empty_set) != singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finsub_1) ).
tff(38,plain,
finite_subsets(empty_set) != singleton(empty_set),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SEU115+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.14 % 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
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 06:04:40 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.23/0.40 % SZS status Theorem
% 0.23/0.40 % SZS output start Proof
% See solution above
% 0.23/0.41 % E exiting
%------------------------------------------------------------------------------