TSTP Solution File: SEU819^2 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU819^2 : 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 03:43:57 EDT 2024
% Result : Theorem 4.07s 2.09s
% Output : Refutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 41 ( 9 unt; 12 typ; 3 def)
% Number of atoms : 107 ( 10 equ; 0 cnn)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 320 ( 34 ~; 29 |; 7 &; 222 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 44 ( 2 ^ 41 !; 1 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(transitiveset_type,type,
transitiveset: $i > $o ).
thf(transitiveset_def,definition,
( transitiveset
= ( ^ [A: $i] :
! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) ) ).
thf(setunionTransitive_type,type,
setunionTransitive: $o ).
thf(setunionTransitive_def,definition,
( setunionTransitive
= ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( transitiveset @ B ) )
=> ( transitiveset @ ( setunion @ A ) ) ) ) ) ).
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(ordinal_def,definition,
( ordinal
= ( ^ [A: $i] :
( ( transitiveset @ A )
& ( wellorderedByIn @ A ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(1,conjecture,
( setunionTransitive
=> ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ordinal @ B ) )
=> ( transitiveset @ ( setunion @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionOrdinalLem1) ).
thf(2,negated_conjecture,
~ ( setunionTransitive
=> ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ordinal @ B ) )
=> ( transitiveset @ ( setunion @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( subset @ C @ B ) ) )
=> ! [B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ( subset @ B @ ( setunion @ A ) ) ) )
=> ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( subset @ C @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ! [D: $i] :
( ( in @ D @ B )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( ( in @ C @ D )
& ( in @ D @ E ) )
=> ( in @ C @ E ) ) ) ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( ( C = D )
| ( in @ C @ D )
| ( in @ D @ C ) ) ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ~ ( in @ C @ C ) )
& ! [C: $i] :
( ( in @ C @ ( powerset @ B ) )
=> ( ( C != emptyset )
=> ? [D: $i] :
( ( in @ D @ C )
& ! [E: $i] :
( ( in @ E @ C )
=> ( ( D = E )
| ( in @ D @ E ) ) ) ) ) ) ) )
=> ! [B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ( subset @ B @ ( setunion @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( in @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ~ ( in @ B @ ( setunion @ A ) )
| ( subset @ B @ ( setunion @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
~ ( subset @ sk5 @ ( setunion @ sk3 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( in @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ~ ( in @ B @ ( setunion @ A ) )
| ( ( subset @ B @ ( setunion @ A ) )
!= ( subset @ sk5 @ ( setunion @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,10]) ).
thf(119,plain,
( ( in @ ( sk2 @ sk3 ) @ ( sk1 @ sk3 ) )
| ~ ( in @ sk5 @ ( setunion @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( sk3 )),bind(B,$thf( sk5 ))]]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ~ ( in @ B @ A )
| ( subset @ B @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ~ ( in @ B @ A )
| ( subset @ B @ A ) ),
inference(simp,[status(thm)],[12]) ).
thf(8,plain,
in @ sk5 @ ( setunion @ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ~ ( in @ B @ ( setunion @ A ) )
| ( subset @ B @ ( setunion @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( sk2 @ A ) @ ( sk1 @ A ) )
| ( subset @ B @ ( setunion @ A ) )
| ( ( in @ sk5 @ ( setunion @ sk3 ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,4]) ).
thf(60,plain,
( ~ ( subset @ ( sk2 @ sk3 ) @ ( sk1 @ sk3 ) )
| ( subset @ sk5 @ ( setunion @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( sk3 )),bind(B,$thf( sk5 ))]]) ).
thf(84,plain,
( ~ ( subset @ ( sk2 @ sk3 ) @ ( sk1 @ sk3 ) )
| $false ),
inference(rewrite,[status(thm)],[60,10]) ).
thf(85,plain,
~ ( subset @ ( sk2 @ sk3 ) @ ( sk1 @ sk3 ) ),
inference(simp,[status(thm)],[84]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ~ ( in @ B @ A )
| ( ( subset @ B @ A )
!= ( subset @ ( sk2 @ sk3 ) @ ( sk1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,85]) ).
thf(89,plain,
( ~ ( in @ ( sk1 @ sk3 ) @ sk3 )
| ~ ( in @ ( sk2 @ sk3 ) @ ( sk1 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( sk1 @ sk3 )),bind(B,$thf( sk2 @ sk3 ))]]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ A ) @ A )
| ~ ( in @ B @ ( setunion @ A ) )
| ( subset @ B @ ( setunion @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ A ) @ A )
| ~ ( in @ B @ ( setunion @ A ) )
| ( ( subset @ B @ ( setunion @ A ) )
!= ( subset @ sk5 @ ( setunion @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,10]) ).
thf(38,plain,
( ( in @ ( sk1 @ sk3 ) @ sk3 )
| ~ ( in @ sk5 @ ( setunion @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( sk3 )),bind(B,$thf( sk5 ))]]) ).
thf(41,plain,
( ( in @ ( sk1 @ sk3 ) @ sk3 )
| ~ $true ),
inference(rewrite,[status(thm)],[38,8]) ).
thf(42,plain,
in @ ( sk1 @ sk3 ) @ sk3,
inference(simp,[status(thm)],[41]) ).
thf(131,plain,
( ~ $true
| ~ ( in @ ( sk2 @ sk3 ) @ ( sk1 @ sk3 ) ) ),
inference(rewrite,[status(thm)],[89,42]) ).
thf(132,plain,
~ ( in @ ( sk2 @ sk3 ) @ ( sk1 @ sk3 ) ),
inference(simp,[status(thm)],[131]) ).
thf(137,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[119,132,8]) ).
thf(138,plain,
$false,
inference(simp,[status(thm)],[137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU819^2 : TPTP v8.2.0. Released v3.7.0.
% 0.16/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n004.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun May 19 16:23:54 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.00 % [INFO] Parsing done (125ms).
% 1.27/1.01 % [INFO] Running in sequential loop mode.
% 1.68/1.24 % [INFO] nitpick registered as external prover.
% 1.83/1.24 % [INFO] Scanning for conjecture ...
% 2.09/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.09/1.35 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.09/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.09/1.35 % [INFO] Type checking passed.
% 2.09/1.35 % [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 ...
% 4.07/2.08 % [INFO] Killing All external provers ...
% 4.07/2.09 % Time passed: 1549ms (effective reasoning time: 1071ms)
% 4.07/2.09 % 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)>
% 4.07/2.09 % Axioms used in derivation (0):
% 4.07/2.09 % No. of inferences in proof: 26
% 4.07/2.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1549 ms resp. 1071 ms w/o parsing
% 4.19/2.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.19/2.13 % [INFO] Killing All external provers ...
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