TSTP Solution File: SET619+3 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET619+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 11:53:49 EDT 2023
% Result : Theorem 3.46s 1.82s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 36 ( 20 unt; 6 typ; 0 def)
% Number of atoms : 69 ( 23 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 243 ( 2 ~; 3 |; 13 &; 202 @)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 68 ( 0 ^; 68 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_type,type,
union: $i > $i > $i ).
thf(symmetric_difference_type,type,
symmetric_difference: $i > $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $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(5,axiom,
! [A: $i,B: $i] :
( ( union @ A @ ( intersection @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( union @ A @ ( intersection @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,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(84,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)],[14]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ! [C: $i] :
( ( member @ C @ A )
<=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(64,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)],[13]) ).
thf(15,axiom,
! [A: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(91,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection_difference) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( intersection @ A @ B ) )
<=> ( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
thf(38,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)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( union @ ( union @ A @ B ) @ C )
= ( union @ A @ ( union @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_union) ).
thf(22,plain,
! [A: $i,B: $i,C: $i] :
( ( union @ ( union @ A @ B ) @ C )
= ( union @ A @ ( union @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(44,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)],[9]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ ( symmetric_difference @ A @ B ) @ ( intersection @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th95) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ ( symmetric_difference @ A @ B ) @ ( intersection @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ ( symmetric_difference @ A @ B ) @ ( intersection @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
<=> ( ( member @ C @ A )
| ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( union @ A @ B ) )
=> ( ( member @ C @ A )
| ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
| ( member @ C @ B ) )
=> ( member @ C @ ( union @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(93,plain,
$false,
inference(e,[status(thm)],[25,84,61,64,91,55,58,19,28,38,22,44,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET619+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n014.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 : Thu May 18 19:07:13 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/0.96 % [INFO] Parsing done (116ms).
% 1.27/0.97 % [INFO] Running in sequential loop mode.
% 1.52/1.15 % [INFO] eprover registered as external prover.
% 1.52/1.15 % [INFO] cvc4 registered as external prover.
% 1.52/1.16 % [INFO] Scanning for conjecture ...
% 1.79/1.21 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.89/1.24 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.89/1.26 % [INFO] Problem is first-order (TPTP FOF).
% 1.89/1.27 % [INFO] Type checking passed.
% 1.89/1.27 % [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 ...
% 3.46/1.82 % External prover 'e' found a proof!
% 3.46/1.82 % [INFO] Killing All external provers ...
% 3.46/1.82 % Time passed: 1300ms (effective reasoning time: 851ms)
% 3.46/1.82 % 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)>
% 3.46/1.82 % Axioms used in derivation (13): reflexivity_of_subset, equal_defn, commutativity_of_symmetric_difference, intersection_defn, associativity_of_union, equal_member_defn, union_intersection, union_intersection_difference, symmetric_difference_defn, commutativity_of_intersection, commutativity_of_union, union_defn, subset_defn
% 3.46/1.82 % No. of inferences in proof: 30
% 3.46/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1300 ms resp. 851 ms w/o parsing
% 3.46/1.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.46/1.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------