TSTP Solution File: SEU740^2 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU740^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 03:43:35 EDT 2024
% Result : Theorem 4.29s 2.37s
% Output : Refutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 26 ( 8 unt; 10 typ; 2 def)
% Number of atoms : 54 ( 4 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 171 ( 10 ~; 5 |; 0 &; 131 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 0 ^ 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(binunionIL_type,type,
binunionIL: $o ).
thf(binunionIL_def,definition,
( binunionIL
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( in @ C @ ( binunion @ A @ B ) ) ) ) ) ).
thf(binintersect_type,type,
binintersect: $i > $i > $i ).
thf(binintersectEL_type,type,
binintersectEL: $o ).
thf(binintersectEL_def,definition,
( binintersectEL
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binintersect @ A @ B ) )
=> ( in @ C @ A ) ) ) ) ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(1,conjecture,
( binunionIL
=> ( binintersectEL
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binunion @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion) ).
thf(2,negated_conjecture,
~ ( binunionIL
=> ( binintersectEL
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binunion @ B @ D ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( in @ C @ ( binunion @ A @ B ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binintersect @ A @ B ) )
=> ( in @ C @ A ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binunion @ B @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
in @ sk5 @ ( binintersect @ sk2 @ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binintersect @ A @ B ) )
| ( in @ C @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binintersect @ A @ B ) )
| ( in @ C @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( ( in @ sk5 @ ( binintersect @ sk2 @ sk3 ) )
!= ( in @ C @ ( binintersect @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4,12]) ).
thf(83,plain,
in @ sk5 @ sk2,
inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk5 ))]]) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ ( binunion @ A @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
~ ( in @ sk5 @ ( binunion @ sk2 @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( ( in @ C @ ( binunion @ A @ B ) )
!= ( in @ sk5 @ ( binunion @ sk2 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(34,plain,
~ ( in @ sk5 @ sk2 ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 )),bind(C,$thf( sk5 ))]]) ).
thf(99,plain,
$false,
inference(rewrite,[status(thm)],[83,34]) ).
thf(100,plain,
$false,
inference(simp,[status(thm)],[99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU740^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n019.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun May 19 15:33:54 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.91/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.06 % [INFO] Parsing done (159ms).
% 1.20/1.07 % [INFO] Running in sequential loop mode.
% 1.72/1.41 % [INFO] nitpick registered as external prover.
% 1.72/1.42 % [INFO] Scanning for conjecture ...
% 1.96/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.04/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.56 % [INFO] Type checking passed.
% 2.04/1.56 % [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 ...
% 4.29/2.37 % [INFO] Killing All external provers ...
% 4.29/2.37 % Time passed: 1919ms (effective reasoning time: 1295ms)
% 4.29/2.37 % 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)>
% 4.29/2.37 % Axioms used in derivation (0):
% 4.29/2.37 % No. of inferences in proof: 14
% 4.29/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1919 ms resp. 1295 ms w/o parsing
% 4.32/2.41 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.32/2.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------