TSTP Solution File: SET013-1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET013-1 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 21 03:00:46 EDT 2024
% Result : Unsatisfiable 3.93s 2.36s
% Output : Refutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 49 ( 7 unt; 10 typ; 0 def)
% Number of atoms : 81 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 288 ( 42 ~; 42 |; 0 &; 204 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 0 ^ 84 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(equal_sets_type,type,
equal_sets: $i > $i > $o ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(as_type,type,
as: $i ).
thf(bs_type,type,
bs: $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(member_of_1_not_of_2_type,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(union_type,type,
union: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( subset @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ( member @ A @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ( member @ A @ ( intersection @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [A: $i] : ( equal_sets @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_set_equal) ).
thf(50,plain,
! [A: $i] : ( equal_sets @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ~ ( equal_sets @ B @ C )
| ( equal_sets @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_set_equal) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ~ ( equal_sets @ B @ C )
| ( equal_sets @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( subset @ B @ C )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( subset @ B @ C )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
~ ( equal_sets @ ( intersection @ as @ bs ) @ ( intersection @ bs @ as ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
thf(20,plain,
~ ( equal_sets @ ( intersection @ as @ bs ) @ ( intersection @ bs @ as ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_sets @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_sets @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( union @ B @ C ) )
| ( member @ A @ B )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( union @ B @ C ) )
| ( member @ A @ B )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( union @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set2_is_member_of_union) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( union @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ ( complement @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_member_of_set_and_complement) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ ( complement @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ ( member_of_1_not_of_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ ( member_of_1_not_of_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ A @ B ) @ B )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ A @ B ) @ B )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( union @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( union @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( equal_sets @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_for_set_equal) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( equal_sets @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( member @ A @ B )
| ( member @ A @ ( complement @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set_or_complement) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( member @ A @ B )
| ( member @ A @ ( complement @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(30,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(60,plain,
$false,
inference(cvc4,[status(thm)],[53,48,50,42,24,20,46,28,38,32,34,22,44,40,26,55,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET013-1 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.09/0.13 % Command : run_Leo-III %s %d
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon May 20 12:08:09 EDT 2024
% 0.13/0.33 % CPUTime :
% 1.01/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.14 % [INFO] Parsing done (172ms).
% 1.30/1.15 % [INFO] Running in sequential loop mode.
% 1.95/1.52 % [INFO] eprover registered as external prover.
% 1.95/1.52 % [INFO] cvc4 registered as external prover.
% 2.01/1.53 % [INFO] Scanning for conjecture ...
% 2.17/1.62 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 2.17/1.67 % [INFO] Axiom selection finished. Selected 18 axioms (removed 3 axioms).
% 2.35/1.70 % [INFO] Problem is propositional (TPTP CNF).
% 2.35/1.70 % [INFO] Type checking passed.
% 2.35/1.71 % [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 ...
% 3.93/2.36 % External prover 'cvc4' found a proof!
% 3.93/2.36 % [INFO] Killing All external provers ...
% 3.93/2.36 % Time passed: 1874ms (effective reasoning time: 1201ms)
% 3.93/2.36 % Axioms used in derivation (18): member_of_intersection_is_member_of_set2, reflexivity_for_set_equal, set_equal_sets_are_subsets2, subsets_are_set_equal_sets, member_of_intersection_is_member_of_set1, set_equal_sets_are_subsets1, transitivity_for_set_equal, member_of_set_or_complement, symmetry_for_set_equal, member_of_set1_is_member_of_union, member_of_union_is_member_of_one_set, not_member_of_set_and_complement, subsets_axiom2, empty_set, member_of_set2_is_member_of_union, member_of_both_is_member_of_intersection, membership_in_subsets, subsets_axiom1
% 3.93/2.36 % No. of inferences in proof: 39
% 3.93/2.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1874 ms resp. 1201 ms w/o parsing
% 3.99/2.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.99/2.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------