TSTP Solution File: SEU819^2 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---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 : n007.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 03:40:10 EDT 2024
% Result : Theorem 3.07s 1.91s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 15 ( 4 unt; 8 typ; 3 def)
% Number of atoms : 51 ( 6 equ; 0 cnn)
% Maximal formula atoms : 29 ( 7 avg)
% Number of connectives : 120 ( 4 ~; 3 |; 7 &; 78 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 2 ^ 23 !; 1 ?; 26 :)
% 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(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(24,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SEU819^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 16:23:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.96/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.04 % [INFO] Parsing done (139ms).
% 1.23/1.05 % [INFO] Running in sequential loop mode.
% 1.70/1.29 % [INFO] eprover registered as external prover.
% 1.70/1.29 % [INFO] cvc4 registered as external prover.
% 1.70/1.30 % [INFO] Scanning for conjecture ...
% 2.05/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.05/1.43 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.05/1.43 % [INFO] Problem is higher-order (TPTP THF).
% 2.05/1.43 % [INFO] Type checking passed.
% 2.05/1.43 % [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 ...
% 3.07/1.90 % External prover 'e' found a proof!
% 3.07/1.90 % [INFO] Killing All external provers ...
% 3.07/1.90 % Time passed: 1377ms (effective reasoning time: 851ms)
% 3.07/1.90 % 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)>
% 3.07/1.90 % Axioms used in derivation (0):
% 3.07/1.90 % No. of inferences in proof: 4
% 3.07/1.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1377 ms resp. 851 ms w/o parsing
% 3.38/1.95 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.38/1.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------