TSTP Solution File: SEU594^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU594^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 03:42:52 EDT 2024
% Result : Theorem 4.19s 2.77s
% Output : Refutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 37 ( 12 unt; 10 typ; 4 def)
% Number of atoms : 87 ( 19 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 209 ( 16 ~; 13 |; 0 &; 158 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 61 ( 11 ^ 50 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(in__Cong_def,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ) ) ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(subsetI1_type,type,
subsetI1: $o ).
thf(subsetI1_def,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf(binintersect_type,type,
binintersect: $i > $i > $i ).
thf(binintersect_def,definition,
( binintersect
= ( ^ [A: $i,B: $i] :
( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ B ) ) ) ) ).
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(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( in__Cong
=> ( subsetI1
=> ( binintersectEL
=> ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(2,negated_conjecture,
~ ( in__Cong
=> ( subsetI1
=> ( binintersectEL
=> ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C
@ ( dsetconstr @ A
@ ^ [D: $i] : ( in @ D @ B ) ) )
=> ( in @ C @ A ) )
=> ! [A: $i,B: $i] :
( ( ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ B ) )
= B )
=> ( subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(5,plain,
~ ( subset @ sk3 @ sk2 ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( ( subset @ A @ B )
!= ( subset @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[10,5]) ).
thf(17,plain,
in @ ( sk1 @ sk2 @ sk3 ) @ sk3,
inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(7,plain,
( ( dsetconstr @ sk2
@ ^ [A: $i] : ( in @ A @ sk3 ) )
= sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
( ( dsetconstr @ sk2
@ ^ [A: $i] : ( in @ A @ sk3 ) )
= sk3 ),
inference(lifteq,[status(thm)],[7]) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C
@ ( dsetconstr @ A
@ ^ [D: $i] : ( in @ D @ B ) ) )
| ( in @ C @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C
@ ( dsetconstr @ A
@ ^ [D: $i] : ( in @ D @ B ) ) )
| ( in @ C @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ sk3 )
| ( in @ C @ A )
| ( ( dsetconstr @ sk2
@ ^ [D: $i] : ( in @ D @ sk3 ) )
!= ( dsetconstr @ A
@ ^ [D: $i] : ( in @ D @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,14]) ).
thf(38,plain,
! [A: $i] :
( ~ ( in @ A @ sk3 )
| ( in @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(42,plain,
! [A: $i] :
( ~ ( in @ A @ sk3 )
| ( in @ A @ sk2 ) ),
inference(simp,[status(thm)],[38]) ).
thf(46,plain,
! [A: $i] :
( ( in @ A @ sk2 )
| ( ( in @ ( sk1 @ sk2 @ sk3 ) @ sk3 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[17,42]) ).
thf(47,plain,
in @ ( sk1 @ sk2 @ sk3 ) @ sk2,
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( sk1 @ sk2 @ sk3 ))]]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[4]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( ( subset @ A @ B )
!= ( subset @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[15,5]) ).
thf(19,plain,
~ ( in @ ( sk1 @ sk2 @ sk3 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(49,plain,
$false,
inference(rewrite,[status(thm)],[47,19]) ).
thf(50,plain,
$false,
inference(simp,[status(thm)],[49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU594^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun May 19 16:08:53 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.17/1.12 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.59/1.31 % [INFO] Parsing done (187ms).
% 1.59/1.33 % [INFO] Running in sequential loop mode.
% 2.30/1.78 % [INFO] nitpick registered as external prover.
% 2.30/1.79 % [INFO] Scanning for conjecture ...
% 2.58/1.92 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.58/1.96 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.58/1.96 % [INFO] Problem is higher-order (TPTP THF).
% 2.58/1.97 % [INFO] Type checking passed.
% 2.58/1.97 % [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 ...
% 4.19/2.76 % [INFO] Killing All external provers ...
% 4.19/2.77 % Time passed: 2254ms (effective reasoning time: 1431ms)
% 4.19/2.77 % 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)>
% 4.19/2.77 % Axioms used in derivation (0):
% 4.19/2.77 % No. of inferences in proof: 23
% 4.19/2.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2254 ms resp. 1431 ms w/o parsing
% 4.43/2.83 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.43/2.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------