TSTP Solution File: SEU735^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU735^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% 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 : Tue May 21 03:43:34 EDT 2024
% Result : Theorem 5.58s 2.69s
% Output : Refutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 30 ( 9 unt; 10 typ; 2 def)
% Number of atoms : 59 ( 5 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 257 ( 14 ~; 11 |; 0 &; 214 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 35 ( 0 ^ 35 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(powersetI1_type,type,
powersetI1: $o ).
thf(powersetI1_def,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ) ).
thf(binintersect_type,type,
binintersect: $i > $i > $i ).
thf(setminus_type,type,
setminus: $i > $i > $i ).
thf(complementSubsetComplementIntersect_type,type,
complementSubsetComplementIntersect: $o ).
thf(complementSubsetComplementIntersect_def,definition,
( complementSubsetComplementIntersect
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( powersetI1
=> ( complementSubsetComplementIntersect
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ B ) @ ( powerset @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).
thf(2,negated_conjecture,
~ ( powersetI1
=> ( complementSubsetComplementIntersect
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ B ) @ ( powerset @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ B ) @ ( powerset @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
in @ sk2 @ ( powerset @ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
in @ sk3 @ ( powerset @ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ A ) )
| ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ A ) )
| ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) )
| ( ( in @ sk3 @ ( powerset @ sk1 ) )
!= ( in @ C @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,9]) ).
thf(19,plain,
! [A: $i] :
( ~ ( in @ A @ ( powerset @ sk1 ) )
| ( subset @ ( setminus @ sk1 @ A ) @ ( setminus @ sk1 @ ( binintersect @ A @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(27,plain,
! [A: $i] :
( ~ ( in @ A @ ( powerset @ sk1 ) )
| ( subset @ ( setminus @ sk1 @ A ) @ ( setminus @ sk1 @ ( binintersect @ A @ sk3 ) ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(82,plain,
! [A: $i] :
( ( subset @ ( setminus @ sk1 @ A ) @ ( setminus @ sk1 @ ( binintersect @ A @ sk3 ) ) )
| ( ( in @ sk2 @ ( powerset @ sk1 ) )
!= ( in @ A @ ( powerset @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,27]) ).
thf(83,plain,
subset @ ( setminus @ sk1 @ sk2 ) @ ( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( sk2 ))]]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ~ ( subset @ B @ A )
| ( in @ B @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( subset @ ( setminus @ sk1 @ sk2 ) @ ( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) ) )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[83,4]) ).
thf(90,plain,
in @ ( setminus @ sk1 @ sk2 ) @ ( powerset @ ( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) )),bind(B,$thf( setminus @ sk1 @ sk2 ))]]) ).
thf(5,plain,
~ ( in @ ( setminus @ sk1 @ sk2 ) @ ( powerset @ ( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(91,plain,
$false,
inference(rewrite,[status(thm)],[90,5]) ).
thf(92,plain,
$false,
inference(simp,[status(thm)],[91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEU735^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.12 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n017.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun May 19 16:30:09 EDT 2024
% 0.12/0.32 % CPUTime :
% 1.00/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/1.11 % [INFO] Parsing done (167ms).
% 1.32/1.13 % [INFO] Running in sequential loop mode.
% 1.89/1.49 % [INFO] nitpick registered as external prover.
% 1.89/1.49 % [INFO] Scanning for conjecture ...
% 2.06/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.16/1.63 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.16/1.63 % [INFO] Problem is higher-order (TPTP THF).
% 2.16/1.64 % [INFO] Type checking passed.
% 2.16/1.64 % [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 ...
% 5.58/2.68 % [INFO] Killing All external provers ...
% 5.58/2.69 % Time passed: 2211ms (effective reasoning time: 1552ms)
% 5.58/2.69 % 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)>
% 5.58/2.69 % Axioms used in derivation (0):
% 5.58/2.69 % No. of inferences in proof: 18
% 5.58/2.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2211 ms resp. 1552 ms w/o parsing
% 5.58/2.74 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.58/2.74 % [INFO] Killing All external provers ...
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