TSTP Solution File: SET047^1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SET047^1 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n017.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 : Mon Jun 24 14:43:42 EDT 2024
% Result : Theorem 4.78s 2.06s
% Output : Refutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 127 ( 41 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 243 ( 17 ~; 6 |; 0 &; 220 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 37 ( 15 ^ 22 !; 0 ?; 37 :)
% 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(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(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] : ( A @ C @ B ) ) ) ).
thf(set_equal_type,type,
set_equal: $i > $i > mworld > $o ).
thf(element_type,type,
element: $i > $i > mworld > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk13_type,type,
sk13: $i ).
thf(3,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( set_equal @ A @ B )
@ ( mforall_di
@ ^ [C: $i] : ( mequiv @ ( element @ C @ A ) @ ( element @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43_1) ).
thf(7,plain,
! [A: $i,B: $i] :
( ( set_equal @ A @ B @ mactual )
= ( ! [C: $i] :
( ( element @ C @ A @ mactual )
= ( element @ C @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ( set_equal @ A @ B @ mactual )
= ( ! [C: $i] :
( ( element @ C @ A @ mactual )
= ( element @ C @ B @ mactual ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( set_equal @ A @ B @ mactual )
= ( ! [C: $i] :
( ( element @ C @ A @ mactual )
= ( element @ C @ B @ mactual ) ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( set_equal @ A @ B ) @ ( set_equal @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( set_equal @ A @ B ) @ ( set_equal @ B @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i,B: $i] :
( ( set_equal @ A @ B @ mactual )
= ( set_equal @ B @ A @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( set_equal @ sk1 @ sk2 @ mactual )
!= ( set_equal @ sk2 @ sk1 @ mactual ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( set_equal @ sk2 @ sk1 @ mactual )
!= ( set_equal @ sk1 @ sk2 @ mactual ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( ! [C: $i] :
( ( element @ C @ A @ mactual )
= ( element @ C @ B @ mactual ) ) )
!= ( set_equal @ sk1 @ sk2 @ mactual ) )
| ( ( set_equal @ A @ B @ mactual )
!= ( set_equal @ sk2 @ sk1 @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[9,6]) ).
thf(17,plain,
( ( ! [A: $i] :
( ( element @ A @ sk2 @ mactual )
= ( element @ A @ sk1 @ mactual ) ) )
!= ( set_equal @ sk1 @ sk2 @ mactual ) ),
inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ( ! [C: $i] :
( ( element @ C @ A @ mactual )
= ( element @ C @ B @ mactual ) ) )
!= ( ! [C: $i] :
( ( element @ C @ sk2 @ mactual )
= ( element @ C @ sk1 @ mactual ) ) ) )
| ( ( set_equal @ A @ B @ mactual )
!= ( set_equal @ sk1 @ sk2 @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[9,17]) ).
thf(25,plain,
( ( ! [A: $i] :
( ( element @ A @ sk1 @ mactual )
= ( element @ A @ sk2 @ mactual ) ) )
!= ( ! [A: $i] :
( ( element @ A @ sk2 @ mactual )
= ( element @ A @ sk1 @ mactual ) ) ) ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(78,plain,
( ( ^ [A: $i] :
( ( element @ A @ sk1 @ mactual )
= ( element @ A @ sk2 @ mactual ) ) )
!= ( ^ [A: $i] :
( ( element @ A @ sk2 @ mactual )
= ( element @ A @ sk1 @ mactual ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(104,plain,
( ( ( element @ sk13 @ sk1 @ mactual )
= ( element @ sk13 @ sk2 @ mactual ) )
!= ( ( element @ sk13 @ sk2 @ mactual )
= ( element @ sk13 @ sk1 @ mactual ) ) ),
inference(func_ext,[status(esa)],[78]) ).
thf(210,plain,
( ( ( element @ sk13 @ sk1 @ mactual )
= ( element @ sk13 @ sk2 @ mactual ) )
| ( ( element @ sk13 @ sk2 @ mactual )
= ( element @ sk13 @ sk1 @ mactual ) ) ),
inference(bool_ext,[status(thm)],[104]) ).
thf(232,plain,
( ( ( element @ sk13 @ sk2 @ mactual )
= ( element @ sk13 @ sk1 @ mactual ) )
| ( ( element @ sk13 @ sk2 @ mactual )
= ( element @ sk13 @ sk1 @ mactual ) ) ),
inference(lifteq,[status(thm)],[210]) ).
thf(238,plain,
( ( element @ sk13 @ sk2 @ mactual )
= ( element @ sk13 @ sk1 @ mactual ) ),
inference(simp,[status(thm)],[232]) ).
thf(209,plain,
( ( ( element @ sk13 @ sk1 @ mactual )
!= ( element @ sk13 @ sk2 @ mactual ) )
| ( ( element @ sk13 @ sk2 @ mactual )
!= ( element @ sk13 @ sk1 @ mactual ) ) ),
inference(bool_ext,[status(thm)],[104]) ).
thf(231,plain,
( ( ( element @ sk13 @ sk2 @ mactual )
!= ( element @ sk13 @ sk1 @ mactual ) )
| ( ( element @ sk13 @ sk2 @ mactual )
!= ( element @ sk13 @ sk1 @ mactual ) ) ),
inference(lifteq,[status(thm)],[209]) ).
thf(237,plain,
( ( element @ sk13 @ sk2 @ mactual )
!= ( element @ sk13 @ sk1 @ mactual ) ),
inference(simp,[status(thm)],[231]) ).
thf(260,plain,
$false,
inference(simplifyReflect,[status(thm)],[238,237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET047^1 : TPTP v8.2.0. Released v8.1.0.
% 0.03/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.31 % Computer : n017.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Sun Jun 23 15:55:25 EDT 2024
% 0.17/0.31 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/0.97 % [INFO] Parsing done (116ms).
% 1.28/0.97 % [INFO] Running in sequential loop mode.
% 1.67/1.17 % [INFO] nitpick registered as external prover.
% 1.67/1.18 % [INFO] Scanning for conjecture ...
% 1.90/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.90/1.27 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.90/1.27 % [INFO] Problem is higher-order (TPTP THF).
% 1.90/1.27 % [INFO] Type checking passed.
% 1.90/1.27 % [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 ...
% 4.78/2.06 % [INFO] Killing All external provers ...
% 4.78/2.06 % Time passed: 1547ms (effective reasoning time: 1085ms)
% 4.78/2.06 % 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)>
% 4.78/2.06 % Axioms used in derivation (1): pel43_1
% 4.78/2.06 % No. of inferences in proof: 22
% 4.78/2.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1547 ms resp. 1085 ms w/o parsing
% 4.78/2.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.78/2.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------