TSTP Solution File: SET019^4 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET019^4 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 21 03:04:53 EDT 2024
% Result : Theorem 14.91s 4.38s
% Output : Refutation 15.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 35 ( 12 unt; 12 typ; 5 def)
% Number of atoms : 91 ( 15 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 200 ( 12 ~; 8 |; 10 &; 163 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 31 ( 18 ^ 13 !; 0 ?; 31 :)
% 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(mand_type,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
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(equal_set_type,type,
equal_set: $i > $i > mworld > $o ).
thf(subset_type,type,
subset: $i > $i > mworld > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) @ ( equal_set @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI02) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) @ ( equal_set @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(38,plain,
~ ! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( ( subset @ A @ B @ mactual )
& ( subset @ B @ A @ mactual ) )
=> ( equal_set @ A @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(43,plain,
eiw_di @ sk1 @ mactual,
inference(cnf,[status(esa)],[38]) ).
thf(41,plain,
eiw_di @ sk2 @ mactual,
inference(cnf,[status(esa)],[38]) ).
thf(8,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_0) ).
thf(56,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( equal_set @ A @ B @ mactual )
= ( ( subset @ A @ B @ mactual )
& ( subset @ B @ A @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual )
| ( ( equal_set @ A @ B @ mactual )
= ( ( subset @ A @ B @ mactual )
& ( subset @ B @ A @ mactual ) ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( ( equal_set @ A @ B @ mactual )
= ( ( subset @ A @ B @ mactual )
& ( subset @ B @ A @ mactual ) ) )
| ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(481,plain,
! [B: $i,A: $i] :
( ( ( equal_set @ A @ B @ mactual )
= ( ( subset @ A @ B @ mactual )
& ( subset @ B @ A @ mactual ) ) )
| ~ ( eiw_di @ A @ mactual )
| ( ( eiw_di @ sk2 @ mactual )
!= ( eiw_di @ B @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[41,58]) ).
thf(482,plain,
! [A: $i] :
( ( ( equal_set @ A @ sk2 @ mactual )
= ( ( subset @ A @ sk2 @ mactual )
& ( subset @ sk2 @ A @ mactual ) ) )
| ~ ( eiw_di @ A @ mactual ) ),
inference(pattern_uni,[status(thm)],[481:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(1241,plain,
! [A: $i] :
( ( ( equal_set @ A @ sk2 @ mactual )
= ( ( subset @ A @ sk2 @ mactual )
& ( subset @ sk2 @ A @ mactual ) ) )
| ( ( eiw_di @ sk1 @ mactual )
!= ( eiw_di @ A @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[43,482]) ).
thf(1242,plain,
( ( equal_set @ sk1 @ sk2 @ mactual )
= ( ( subset @ sk1 @ sk2 @ mactual )
& ( subset @ sk2 @ sk1 @ mactual ) ) ),
inference(pattern_uni,[status(thm)],[1241:[bind(A,$thf( sk1 ))]]) ).
thf(39,plain,
subset @ sk1 @ sk2 @ mactual,
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
subset @ sk2 @ sk1 @ mactual,
inference(cnf,[status(esa)],[38]) ).
thf(42,plain,
~ ( equal_set @ sk1 @ sk2 @ mactual ),
inference(cnf,[status(esa)],[38]) ).
thf(1349,plain,
~ ( $true
& $true ),
inference(rewrite,[status(thm)],[1242,39,40,42]) ).
thf(1350,plain,
$false,
inference(simp,[status(thm)],[1349]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET019^4 : TPTP v8.2.0. Released v8.1.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 11:23:24 EDT 2024
% 0.15/0.35 % CPUTime :
% 1.01/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.59/1.17 % [INFO] Parsing done (211ms).
% 1.59/1.18 % [INFO] Running in sequential loop mode.
% 2.08/1.44 % [INFO] nitpick registered as external prover.
% 2.08/1.45 % [INFO] Scanning for conjecture ...
% 2.33/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 35 axioms. Running axiom selection ...
% 2.52/1.68 % [INFO] Axiom selection finished. Selected 35 axioms (removed 0 axioms).
% 2.72/1.75 % [INFO] Problem is higher-order (TPTP THF).
% 2.72/1.76 % [INFO] Type checking passed.
% 2.72/1.76 % [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 ...
% 14.91/4.37 % [INFO] Killing All external provers ...
% 14.91/4.37 % Time passed: 3864ms (effective reasoning time: 3185ms)
% 14.91/4.37 % 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)>
% 14.91/4.37 % Axioms used in derivation (1): equal_set_0
% 14.91/4.37 % No. of inferences in proof: 18
% 14.91/4.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3864 ms resp. 3185 ms w/o parsing
% 15.07/4.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.07/4.44 % [INFO] Killing All external provers ...
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