TSTP Solution File: SET630+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET630+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:53:53 EDT 2023
% Result : Theorem 3.03s 1.67s
% Output : Refutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 33 ( 14 unt; 7 typ; 0 def)
% Number of atoms : 64 ( 11 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 219 ( 5 ~; 3 |; 13 &; 176 @)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 57 !; 3 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(symmetric_difference_type,type,
symmetric_difference: $i > $i > $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(intersect_type,type,
intersect: $i > $i > $o ).
thf(member_type,type,
member: $i > $i > $o ).
thf(13,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(56,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(1,conjecture,
! [A: $i,B: $i] : ( disjoint @ ( intersection @ A @ B ) @ ( symmetric_difference @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_and_symmetric_difference_disjoint) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] : ( disjoint @ ( intersection @ A @ B ) @ ( symmetric_difference @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i] : ( disjoint @ ( intersection @ A @ B ) @ ( symmetric_difference @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,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(28,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)],[6]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( intersect @ A @ B )
=> ( intersect @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( intersect @ A @ B )
=> ( intersect @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
thf(16,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(7,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(34,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)],[7]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(45,plain,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ~ ( intersect @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( ( disjoint @ A @ B )
=> ~ ( intersect @ A @ B ) )
& ( ~ ( intersect @ A @ B )
=> ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i,B: $i] : ( disjoint @ ( intersection @ A @ B ) @ ( difference @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_and_union_disjoint) ).
thf(26,plain,
! [A: $i,B: $i] : ( disjoint @ ( intersection @ A @ B ) @ ( difference @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( intersect @ A @ ( union @ B @ C ) )
<=> ( ( intersect @ A @ B )
| ( intersect @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_with_union) ).
thf(19,plain,
! [A: $i,B: $i,C: $i] :
( ( ( intersect @ A @ ( union @ B @ C ) )
=> ( ( intersect @ A @ B )
| ( intersect @ A @ C ) ) )
& ( ( ( intersect @ A @ B )
| ( intersect @ A @ C ) )
=> ( intersect @ A @ ( union @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(76,plain,
$false,
inference(e,[status(thm)],[56,14,28,54,48,16,34,45,40,26,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET630+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n013.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 19:04:07 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.93/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.95 % [INFO] Parsing done (111ms).
% 1.22/0.96 % [INFO] Running in sequential loop mode.
% 1.64/1.15 % [INFO] eprover registered as external prover.
% 1.64/1.15 % [INFO] cvc4 registered as external prover.
% 1.64/1.15 % [INFO] Scanning for conjecture ...
% 1.73/1.20 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.73/1.22 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.91/1.24 % [INFO] Problem is first-order (TPTP FOF).
% 1.91/1.24 % [INFO] Type checking passed.
% 1.91/1.24 % [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 ...
% 2.75/1.62 % External prover 'e' found a proof!
% 2.75/1.62 % [INFO] Killing All external provers ...
% 2.75/1.62 % Time passed: 1104ms (effective reasoning time: 658ms)
% 2.75/1.62 % 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)>
% 2.75/1.62 % Axioms used in derivation (11): intersection_and_union_disjoint, equal_member_defn, intersect_defn, symmetric_difference_defn, disjoint_defn, intersect_with_union, commutativity_of_symmetric_difference, symmetry_of_intersect, intersection_defn, commutativity_of_intersection, commutativity_of_union
% 2.75/1.62 % No. of inferences in proof: 26
% 3.03/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1104 ms resp. 658 ms w/o parsing
% 3.20/1.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.20/1.73 % [INFO] Killing All external provers ...
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