TSTP Solution File: SET055^12 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET055^12 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 03:05:06 EDT 2024
% Result : Theorem 99.26s 17.15s
% Output : Refutation 99.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 47 ( 10 unt; 13 typ; 5 def)
% Number of atoms : 127 ( 14 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 347 ( 46 ~; 31 |; 6 &; 247 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 42 ( 19 ^ 23 !; 0 ?; 42 :)
% 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(qmltpeq_type,type,
qmltpeq: $i > $i > mworld > $o ).
thf(member_type,type,
member: $i > $i > mworld > $o ).
thf(subclass_type,type,
subclass: $i > $i > mworld > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk199_type,type,
sk199: $i ).
thf(57,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( subclass @ A @ B )
@ ( mforall_di
@ ^ [C: $i] : ( mimplies @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
thf(217,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( subclass @ A @ B @ mactual )
= ( ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual )
| ( ( subclass @ A @ B @ mactual )
= ( ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) ) ) ) ) ),
inference(cnf,[status(esa)],[217]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( ( subclass @ A @ B @ mactual )
= ( ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) ) ) ) )
| ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(9,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ A @ B ) @ ( mand @ ( subclass @ A @ B ) @ ( subclass @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
thf(103,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
= ( ( subclass @ A @ B @ mactual )
& ( subclass @ B @ A @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual )
| ( ( qmltpeq @ A @ B @ mactual )
= ( ( subclass @ A @ B @ mactual )
& ( subclass @ B @ A @ mactual ) ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( ( qmltpeq @ A @ B @ mactual )
= ( ( subclass @ A @ B @ mactual )
& ( subclass @ B @ A @ mactual ) ) )
| ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_0) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(87,plain,
~ ! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( qmltpeq @ A @ A @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(88,plain,
~ ( qmltpeq @ sk1 @ sk1 @ mactual ),
inference(cnf,[status(esa)],[87]) ).
thf(1373,plain,
! [B: $i,A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual )
| ~ ( ( subclass @ A @ B @ mactual )
& ( subclass @ B @ A @ mactual ) )
| ( ( qmltpeq @ A @ B @ mactual )
!= ( qmltpeq @ sk1 @ sk1 @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[105,88]) ).
thf(1374,plain,
( ~ ( eiw_di @ sk1 @ mactual )
| ~ ( eiw_di @ sk1 @ mactual )
| ~ ( ( subclass @ sk1 @ sk1 @ mactual )
& ( subclass @ sk1 @ sk1 @ mactual ) ) ),
inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1488,plain,
( ~ ( subclass @ sk1 @ sk1 @ mactual )
| ~ ( subclass @ sk1 @ sk1 @ mactual )
| ~ ( eiw_di @ sk1 @ mactual )
| ~ ( eiw_di @ sk1 @ mactual ) ),
inference(cnf,[status(esa)],[1374]) ).
thf(1489,plain,
( ~ ( subclass @ sk1 @ sk1 @ mactual )
| ~ ( eiw_di @ sk1 @ mactual ) ),
inference(simp,[status(thm)],[1488]) ).
thf(89,plain,
eiw_di @ sk1 @ mactual,
inference(cnf,[status(esa)],[87]) ).
thf(1528,plain,
( ~ ( subclass @ sk1 @ sk1 @ mactual )
| ~ $true ),
inference(rewrite,[status(thm)],[1489,89]) ).
thf(1529,plain,
~ ( subclass @ sk1 @ sk1 @ mactual ),
inference(simp,[status(thm)],[1528]) ).
thf(32201,plain,
! [B: $i,A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual )
| ~ ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) ) )
| ( ( subclass @ A @ B @ mactual )
!= ( subclass @ sk1 @ sk1 @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[219,1529]) ).
thf(32202,plain,
( ~ ( eiw_di @ sk1 @ mactual )
| ~ ( eiw_di @ sk1 @ mactual )
| ~ ! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( ( member @ A @ sk1 @ mactual )
=> ( member @ A @ sk1 @ mactual ) ) ) ),
inference(pattern_uni,[status(thm)],[32201:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(32614,plain,
( ( member @ sk199 @ sk1 @ mactual )
| ~ ( eiw_di @ sk1 @ mactual )
| ~ ( eiw_di @ sk1 @ mactual ) ),
inference(cnf,[status(esa)],[32202]) ).
thf(32617,plain,
( ( member @ sk199 @ sk1 @ mactual )
| ~ ( eiw_di @ sk1 @ mactual ) ),
inference(simp,[status(thm)],[32614]) ).
thf(32613,plain,
( ~ ( member @ sk199 @ sk1 @ mactual )
| ~ ( eiw_di @ sk1 @ mactual )
| ~ ( eiw_di @ sk1 @ mactual ) ),
inference(cnf,[status(esa)],[32202]) ).
thf(32616,plain,
( ~ ( member @ sk199 @ sk1 @ mactual )
| ~ ( eiw_di @ sk1 @ mactual ) ),
inference(simp,[status(thm)],[32613]) ).
thf(35081,plain,
( ~ ( member @ sk199 @ sk1 @ mactual )
| ~ $true ),
inference(rewrite,[status(thm)],[32616,89]) ).
thf(35082,plain,
~ ( member @ sk199 @ sk1 @ mactual ),
inference(simp,[status(thm)],[35081]) ).
thf(35880,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[32617,89,35082]) ).
thf(35881,plain,
$false,
inference(simp,[status(thm)],[35880]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET055^12 : TPTP v8.2.0. Released v8.1.0.
% 0.11/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 12:18:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.93/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.04 % [INFO] Parsing done (204ms).
% 1.40/1.05 % [INFO] Running in sequential loop mode.
% 2.03/1.24 % [INFO] nitpick registered as external prover.
% 2.03/1.25 % [INFO] Scanning for conjecture ...
% 2.19/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 85 axioms. Running axiom selection ...
% 2.60/1.40 % [INFO] Axiom selection finished. Selected 84 axioms (removed 1 axioms).
% 2.81/1.47 % [INFO] Problem is higher-order (TPTP THF).
% 2.81/1.48 % [INFO] Type checking passed.
% 2.81/1.48 % [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 ...
% 99.26/17.14 % [INFO] Killing All external provers ...
% 99.26/17.15 % Time passed: 16639ms (effective reasoning time: 16093ms)
% 99.26/17.15 % 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)>
% 99.26/17.15 % Axioms used in derivation (2): subclass_defn, extensionality
% 99.26/17.15 % No. of inferences in proof: 29
% 99.26/17.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 16639 ms resp. 16093 ms w/o parsing
% 99.26/17.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 99.26/17.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------