TSTP Solution File: SEU623^2 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU623^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 03:38:39 EDT 2024
% Result : Theorem 2.91s 1.67s
% Output : Refutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 18 ( 5 unt; 10 typ; 4 def)
% Number of atoms : 39 ( 4 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 98 ( 2 ~; 0 |; 0 &; 73 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 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 : 27 ( 0 ^ 27 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(subsetE_type,type,
subsetE: $o ).
thf(subsetE_def,definition,
( subsetE
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) ) ) ) ).
thf(powersetsubset_type,type,
powersetsubset: $o ).
thf(powersetsubset_def,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(binunionLsub_type,type,
binunionLsub: $o ).
thf(binunionLsub_def,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
thf(singletoninpowerset_type,type,
singletoninpowerset: $o ).
thf(singletoninpowerset_def,definition,
( singletoninpowerset
= ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
thf(1,conjecture,
( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(2,negated_conjecture,
~ ( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( in @ ( setadjoin @ C @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU623^2 : TPTP v8.2.0. Released v3.7.0.
% 0.16/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n002.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 16:12:39 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.99/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/0.98 % [INFO] Parsing done (115ms).
% 1.28/0.99 % [INFO] Running in sequential loop mode.
% 1.69/1.20 % [INFO] eprover registered as external prover.
% 1.69/1.21 % [INFO] cvc4 registered as external prover.
% 1.69/1.21 % [INFO] Scanning for conjecture ...
% 1.88/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.88/1.30 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.88/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.88/1.31 % [INFO] Type checking passed.
% 1.88/1.31 % [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 ...
% 2.91/1.67 % External prover 'e' found a proof!
% 2.91/1.67 % [INFO] Killing All external provers ...
% 2.91/1.67 % Time passed: 1141ms (effective reasoning time: 676ms)
% 2.91/1.67 % 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)>
% 2.91/1.67 % Axioms used in derivation (0):
% 2.91/1.67 % No. of inferences in proof: 4
% 2.91/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1141 ms resp. 676 ms w/o parsing
% 3.03/1.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.03/1.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------