TSTP Solution File: SET611+3 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SET611+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 7 08:07:36 EDT 2024
% Result : Theorem 7.78s 2.76s
% Output : Refutation 7.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 30 ( 7 unt; 6 typ; 0 def)
% Number of atoms : 78 ( 18 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 215 ( 10 ~; 0 |; 19 &; 151 @)
% ( 10 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 ^ 55 !; 0 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(11,axiom,
! [A: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(89,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( intersection @ A @ B ) )
<=> ( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
thf(33,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( intersection @ A @ B ) )
=> ( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( member @ C @ ( intersection @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( intersection @ A @ B )
= empty_set )
<=> ( ( difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th84) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( intersection @ A @ B )
= empty_set )
<=> ( ( difference @ A @ B )
= A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i] :
( ( ( ( intersection @ A @ B )
= empty_set )
=> ( ( difference @ A @ B )
= A ) )
& ( ( ( difference @ A @ B )
= A )
=> ( ( intersection @ A @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
thf(45,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( difference @ A @ B ) )
<=> ( ( member @ C @ A )
& ~ ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( difference @ A @ B ) )
=> ( ( member @ C @ A )
& ~ ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
& ~ ( member @ C @ B ) )
=> ( member @ C @ ( difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i] :
( ( empty @ A )
<=> ! [B: $i] :
~ ( member @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
thf(91,plain,
! [A: $i] :
( ( ( empty @ A )
=> ! [B: $i] :
~ ( member @ B @ A ) )
& ( ! [B: $i] :
~ ( member @ B @ A )
=> ( empty @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( member @ C @ A )
<=> ( member @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
thf(23,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( member @ C @ A )
=> ( member @ C @ B ) )
& ( ( member @ C @ B )
=> ( member @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ! [C: $i] :
( ( member @ C @ A )
<=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ! [C: $i] :
( ( ( member @ C @ A )
=> ( member @ C @ B ) )
& ( ( member @ C @ B )
=> ( member @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( ( member @ C @ A )
=> ( member @ C @ B ) )
& ( ( member @ C @ B )
=> ( member @ C @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(955,plain,
$false,
inference(e,[status(thm)],[89,33,13,45,59,39,91,48,23,82,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET611+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 6 13:18:54 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.93/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.98 % [INFO] Parsing done (126ms).
% 1.21/0.98 % [INFO] Running in sequential loop mode.
% 1.63/1.20 % [INFO] eprover registered as external prover.
% 1.63/1.21 % [INFO] cvc4 registered as external prover.
% 1.63/1.21 % [INFO] Scanning for conjecture ...
% 1.78/1.27 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.78/1.29 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.78/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 1.98/1.31 % [INFO] Type checking passed.
% 1.98/1.32 % [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 ...
% 7.78/2.75 % External prover 'e' found a proof!
% 7.78/2.76 % [INFO] Killing All external provers ...
% 7.78/2.76 % Time passed: 2239ms (effective reasoning time: 1769ms)
% 7.78/2.76 % 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)>
% 7.78/2.76 % Axioms used in derivation (10): reflexivity_of_subset, equal_member_defn, empty_set_defn, equal_defn, subset_defn, intersection_defn, member_equal, empty_defn, commutativity_of_intersection, difference_defn
% 7.78/2.76 % No. of inferences in proof: 24
% 7.78/2.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2239 ms resp. 1769 ms w/o parsing
% 7.78/2.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.78/2.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------