TSTP Solution File: SET063+3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET063+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 : Fri May 19 11:52:18 EDT 2023
% Result : Theorem 2.55s 1.62s
% Output : Refutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 20 ( 7 unt; 4 typ; 0 def)
% Number of atoms : 37 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 85 ( 7 ~; 0 |; 6 &; 57 @)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 25 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(25,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)],[6]) ).
thf(8,axiom,
! [A: $i] :
( ( empty @ A )
<=> ! [B: $i] :
~ ( member @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
thf(38,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)],[8]) ).
thf(1,conjecture,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_of_empty_set_is_empty_set) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_subset) ).
thf(13,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(18,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)],[5]) ).
thf(7,axiom,
! [A: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(36,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
thf(15,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,plain,
$false,
inference(e,[status(thm)],[25,38,9,13,18,36,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET063+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 19:41:50 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.82/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.06/0.99 % [INFO] Parsing done (124ms).
% 1.06/1.00 % [INFO] Running in sequential loop mode.
% 1.63/1.20 % [INFO] eprover registered as external prover.
% 1.63/1.20 % [INFO] cvc4 registered as external prover.
% 1.69/1.20 % [INFO] Scanning for conjecture ...
% 1.78/1.25 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.78/1.27 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.78/1.29 % [INFO] Problem is first-order (TPTP FOF).
% 1.78/1.29 % [INFO] Type checking passed.
% 1.78/1.29 % [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 ...
% 2.55/1.61 % External prover 'e' found a proof!
% 2.55/1.61 % [INFO] Killing All external provers ...
% 2.55/1.61 % Time passed: 1098ms (effective reasoning time: 612ms)
% 2.55/1.61 % 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)>
% 2.55/1.62 % Axioms used in derivation (6): reflexivity_of_subset, empty_set_defn, empty_defn, empty_set_subset, equal_defn, subset_defn
% 2.55/1.62 % No. of inferences in proof: 16
% 2.55/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1098 ms resp. 612 ms w/o parsing
% 2.91/1.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.91/1.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------