TSTP Solution File: SET637+3 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 11:53:55 EDT 2023
% Result : Theorem 3.16s 1.84s
% Output : Refutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 26 ( 5 unt; 6 typ; 0 def)
% Number of atoms : 60 ( 8 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 171 ( 10 ~; 0 |; 14 &; 121 @)
% ( 8 <=>; 18 =>; 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 : 45 ( 0 ^; 42 !; 3 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersect_type,type,
intersect: $i > $i > $o ).
thf(not_equal_type,type,
not_equal: $i > $i > $o ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( not_equal @ A @ B )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( ( not_equal @ A @ B )
=> ( A != B ) )
& ( ( A != B )
=> ( not_equal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
thf(29,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i] :
( ( empty @ A )
<=> ! [B: $i] :
~ ( member @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
thf(65,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)],[10]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( intersect @ A @ B )
=> ( intersect @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( intersect @ A @ B )
=> ( intersect @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( intersect @ A @ B )
<=> ( not_equal @ ( intersection @ A @ B ) @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th119) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( intersect @ A @ B )
<=> ( not_equal @ ( intersection @ A @ B ) @ empty_set ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i] :
( ( ( intersect @ A @ B )
=> ( not_equal @ ( intersection @ A @ B ) @ empty_set ) )
& ( ( not_equal @ ( intersection @ A @ B ) @ empty_set )
=> ( intersect @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( intersect @ A @ B )
<=> ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( ( intersect @ A @ B )
=> ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ( ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( intersect @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,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(32,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)],[6]) ).
thf(3,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(17,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)],[3]) ).
thf(70,plain,
$false,
inference(e,[status(thm)],[52,29,60,65,63,11,23,32,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n012.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
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 19:09:47 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.94/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.02 % [INFO] Parsing done (129ms).
% 1.19/1.03 % [INFO] Running in sequential loop mode.
% 1.63/1.25 % [INFO] eprover registered as external prover.
% 1.63/1.25 % [INFO] cvc4 registered as external prover.
% 1.63/1.26 % [INFO] Scanning for conjecture ...
% 1.63/1.31 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.84/1.34 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.84/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 1.84/1.36 % [INFO] Type checking passed.
% 1.84/1.36 % [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 ...
% 3.12/1.83 % External prover 'e' found a proof!
% 3.12/1.83 % [INFO] Killing All external provers ...
% 3.12/1.83 % Time passed: 1316ms (effective reasoning time: 801ms)
% 3.12/1.83 % 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)>
% 3.12/1.84 % Axioms used in derivation (8): equal_member_defn, empty_defn, commutativity_of_intersection, not_equal_defn, symmetry_of_intersect, intersection_defn, empty_set_defn, intersect_defn
% 3.12/1.84 % No. of inferences in proof: 20
% 3.16/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1316 ms resp. 801 ms w/o parsing
% 3.29/1.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.29/1.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------