TSTP Solution File: SEU623^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU623^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 03:43:02 EDT 2024
% Result : Theorem 4.05s 1.86s
% Output : Refutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 38 ( 13 unt; 13 typ; 4 def)
% Number of atoms : 81 ( 7 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 251 ( 17 ~; 10 |; 0 &; 192 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 62 ( 0 ^ 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(subsetE_type,type,
subsetE: $o ).
thf(subsetE_def,definition,
( subsetE
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) ) ) ) ).
thf(powersetsubset_type,type,
powersetsubset: $o ).
thf(powersetsubset_def,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(binunionLsub_type,type,
binunionLsub: $o ).
thf(binunionLsub_def,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
thf(singletoninpowerset_type,type,
singletoninpowerset: $o ).
thf(singletoninpowerset_def,definition,
( singletoninpowerset
= ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(2,negated_conjecture,
~ ( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(10,plain,
~ ( in @ ( setadjoin @ sk3 @ emptyset ) @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) )
!= ( in @ ( setadjoin @ sk3 @ emptyset ) @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(65,plain,
~ ( in @ sk3 @ ( binunion @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( binunion @ sk1 @ sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(9,plain,
! [B: $i,A: $i] : ( subset @ A @ ( binunion @ A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(11,plain,
! [B: $i,A: $i] : ( subset @ A @ ( binunion @ A @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(5,plain,
in @ sk3 @ sk1,
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( in @ C @ A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( in @ C @ B )
| ( ( in @ sk3 @ sk1 )
!= ( in @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5,6]) ).
thf(17,plain,
! [A: $i] :
( ~ ( subset @ sk1 @ A )
| ( in @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(23,plain,
! [A: $i] :
( ~ ( subset @ sk1 @ A )
| ( in @ sk3 @ A ) ),
inference(simp,[status(thm)],[17]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ sk3 @ C )
| ( ( subset @ A @ ( binunion @ A @ B ) )
!= ( subset @ sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11,23]) ).
thf(49,plain,
! [A: $i] : ( in @ sk3 @ ( binunion @ sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( sk1 )),bind(B,$thf( E )),bind(C,$thf( binunion @ sk1 @ E ))]]) ).
thf(50,plain,
! [A: $i] : ( in @ sk3 @ ( binunion @ sk1 @ A ) ),
inference(simp,[status(thm)],[49]) ).
thf(82,plain,
~ $true,
inference(rewrite,[status(thm)],[65,50]) ).
thf(83,plain,
$false,
inference(simp,[status(thm)],[82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU623^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n004.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 : Sun May 19 16:31:54 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (101ms).
% 1.19/0.96 % [INFO] Running in sequential loop mode.
% 1.54/1.16 % [INFO] nitpick registered as external prover.
% 1.54/1.16 % [INFO] Scanning for conjecture ...
% 1.65/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.88/1.25 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.88/1.25 % [INFO] Problem is higher-order (TPTP THF).
% 1.88/1.25 % [INFO] Type checking passed.
% 1.88/1.25 % [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 ...
% 4.05/1.86 % [INFO] Killing All external provers ...
% 4.05/1.86 % Time passed: 1336ms (effective reasoning time: 890ms)
% 4.05/1.86 % 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)>
% 4.05/1.86 % Axioms used in derivation (0):
% 4.05/1.86 % No. of inferences in proof: 21
% 4.05/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1336 ms resp. 890 ms w/o parsing
% 4.05/1.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.05/1.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------