TSTP Solution File: SEU519_8 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU519_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 : Fri May 19 11:59:30 EDT 2023
% Result : Theorem 3.05s 1.80s
% Output : Refutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 16 unt; 7 typ; 0 def)
% Number of atoms : 55 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 110 ( 9 ~; 4 |; 0 &; 79 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 35 ( 0 ^; 35 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(powersetI_type,type,
powersetI: $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(1,conjecture,
( emptysetE
=> ( powersetI
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( powersetI
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( emptysetE
=> ( powersetI
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ( in @ emptyset @ ( powerset @ sk1 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(3,axiom,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(9,plain,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(7,plain,
powersetI,
inference(cnf,[status(esa)],[5]) ).
thf(38,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ),
inference(rewrite,[status(thm)],[10,7]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( in @ ( sk2 @ B @ A ) @ B )
| ( in @ B @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(4,axiom,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(11,plain,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(8,plain,
emptysetE,
inference(cnf,[status(esa)],[5]) ).
thf(13,plain,
! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ),
inference(rewrite,[status(thm)],[12,8]) ).
thf(14,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| ( B
!= ( in @ emptyset @ ( powerset @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,6]) ).
thf(16,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( A )),bind(B,$thf( in @ emptyset @ ( powerset @ sk1 ) ))]]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk2 @ B @ A ) @ B )
!= ( in @ C @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[39,16]) ).
thf(51,plain,
! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( E )),bind(B,$thf( emptyset )),bind(C,$thf( sk2 @ emptyset @ E ))]]) ).
thf(58,plain,
! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ),
inference(simp,[status(thm)],[51]) ).
thf(62,plain,
~ $true,
inference(rewrite,[status(thm)],[6,58]) ).
thf(63,plain,
$false,
inference(simp,[status(thm)],[62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU519_8 : TPTP v8.1.2. Released v8.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n020.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 : Thu May 18 13:34:18 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.99/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.00 % [INFO] Parsing done (121ms).
% 1.31/1.01 % [INFO] Running in sequential loop mode.
% 1.66/1.23 % [INFO] eprover registered as external prover.
% 1.66/1.23 % [INFO] cvc4 registered as external prover.
% 1.66/1.23 % [INFO] Scanning for conjecture ...
% 1.66/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.66/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/1.30 % [INFO] Found a conjecture and 2 axioms. Running axiom selection ...
% 1.91/1.32 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.91/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.91/1.32 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.91/1.33 % [INFO] Type checking passed.
% 1.91/1.33 % [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 ...
% 3.05/1.79 % [INFO] Killing All external provers ...
% 3.05/1.79 % Time passed: 1277ms (effective reasoning time: 776ms)
% 3.05/1.79 % 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)>
% 3.05/1.80 % Axioms used in derivation (2): powersetI, emptysetE
% 3.05/1.80 % No. of inferences in proof: 23
% 3.05/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1277 ms resp. 776 ms w/o parsing
% 3.28/1.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.28/1.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------