TSTP Solution File: SET044^23 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SET044^23 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 : Tue May 7 10:48:52 EDT 2024
% Result : Theorem 6.19s 2.24s
% Output : Refutation 6.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 38 ( 10 unt; 12 typ; 6 def)
% Number of atoms : 116 ( 21 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 268 ( 31 ~; 19 |; 3 &; 209 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 44 ( 23 ^ 18 !; 3 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mactual_type,type,
mactual: mworld ).
thf(mlocal_type,type,
mlocal: ( mworld > $o ) > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mnot_type,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
thf(mimplies_type,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mequiv_type,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(eiw_di_type,type,
eiw_di: $i > mworld > $o ).
thf(mforall_di_type,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] :
( ( eiw_di @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(mexists_di_type,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mexists_di_def,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
? [C: $i] :
( ( eiw_di @ C @ B )
& ( A @ C @ B ) ) ) ) ).
thf(element_type,type,
element: $i > $i > mworld > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(1,conjecture,
( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( element @ B @ A ) @ ( element @ B @ B ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [A: $i] :
( mexists_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( element @ C @ B ) @ ( mnot @ ( element @ C @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel40) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( element @ B @ A ) @ ( element @ B @ B ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [A: $i] :
( mexists_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( element @ C @ B ) @ ( mnot @ ( element @ C @ A ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ? [A: $i] :
( ( eiw_di @ A @ mactual )
& ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( element @ B @ A @ mactual )
= ( element @ B @ B @ mactual ) ) ) )
=> ~ ! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ? [B: $i] :
( ( eiw_di @ B @ mactual )
& ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( element @ C @ B @ mactual )
= ( ~ ( element @ C @ A @ mactual ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
eiw_di @ sk1 @ mactual,
inference(cnf,[status(esa)],[7]) ).
thf(8,plain,
! [A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ( eiw_di @ ( sk2 @ A ) @ mactual ) ),
inference(cnf,[status(esa)],[7]) ).
thf(12,plain,
! [A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ( eiw_di @ ( sk2 @ A ) @ mactual ) ),
inference(simp,[status(thm)],[8]) ).
thf(26,plain,
! [A: $i] :
( ( eiw_di @ ( sk2 @ A ) @ mactual )
| ( ( eiw_di @ sk1 @ mactual )
!= ( eiw_di @ A @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[11,12]) ).
thf(27,plain,
eiw_di @ ( sk2 @ sk1 ) @ mactual,
inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( sk1 ))]]) ).
thf(10,plain,
! [A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ( ( element @ A @ sk1 @ mactual )
= ( element @ A @ A @ mactual ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(15,plain,
! [A: $i] :
( ( ( element @ A @ sk1 @ mactual )
= ( element @ A @ A @ mactual ) )
| ~ ( eiw_di @ A @ mactual ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(293,plain,
! [A: $i] :
( ( ( element @ A @ sk1 @ mactual )
= ( element @ A @ A @ mactual ) )
| ( ( eiw_di @ ( sk2 @ sk1 ) @ mactual )
!= ( eiw_di @ A @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[27,15]) ).
thf(294,plain,
( ( element @ ( sk2 @ sk1 ) @ ( sk2 @ sk1 ) @ mactual )
= ( element @ ( sk2 @ sk1 ) @ sk1 @ mactual ) ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( sk2 @ sk1 ))]]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual )
| ( ( element @ B @ ( sk2 @ A ) @ mactual )
= ( ~ ( element @ B @ A @ mactual ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( ( element @ B @ ( sk2 @ A ) @ mactual )
= ( ~ ( element @ B @ A @ mactual ) ) )
| ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( ( element @ B @ ( sk2 @ A ) @ mactual )
= ( ~ ( element @ B @ A @ mactual ) ) )
| ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual ) ),
inference(simp,[status(thm)],[13]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( ( element @ ( sk2 @ sk1 ) @ sk1 @ mactual )
= ( ~ ( element @ B @ A @ mactual ) ) )
| ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual )
| ( ( element @ ( sk2 @ sk1 ) @ ( sk2 @ sk1 ) @ mactual )
!= ( element @ B @ ( sk2 @ A ) @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[294,14]) ).
thf(430,plain,
( ( ( ~ ( element @ ( sk2 @ sk1 ) @ sk1 @ mactual ) )
= ( element @ ( sk2 @ sk1 ) @ sk1 @ mactual ) )
| ~ ( eiw_di @ sk1 @ mactual )
| ~ ( eiw_di @ ( sk2 @ sk1 ) @ mactual ) ),
inference(pattern_uni,[status(thm)],[429:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ sk1 ))]]) ).
thf(462,plain,
( ~ ( eiw_di @ sk1 @ mactual )
| ~ ( eiw_di @ ( sk2 @ sk1 ) @ mactual ) ),
inference(simp,[status(thm)],[430]) ).
thf(466,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[462,11,27]) ).
thf(467,plain,
$false,
inference(simp,[status(thm)],[466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET044^23 : TPTP v8.1.2. Released v8.1.0.
% 0.08/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n019.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 6 20:39:39 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.86/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.01/0.89 % [INFO] Parsing done (114ms).
% 1.01/0.90 % [INFO] Running in sequential loop mode.
% 1.54/1.09 % [INFO] nitpick registered as external prover.
% 1.54/1.09 % [INFO] Scanning for conjecture ...
% 1.75/1.16 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.75/1.19 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.75/1.19 % [INFO] Problem is higher-order (TPTP THF).
% 1.75/1.19 % [INFO] Type checking passed.
% 1.75/1.20 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.19/2.23 % [INFO] Killing All external provers ...
% 6.19/2.23 % Time passed: 1747ms (effective reasoning time: 1331ms)
% 6.19/2.23 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.19/2.23 % Axioms used in derivation (0):
% 6.19/2.23 % No. of inferences in proof: 20
% 6.19/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1747 ms resp. 1331 ms w/o parsing
% 6.19/2.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.19/2.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------