TSTP Solution File: SET014-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET014-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 11:51:53 EDT 2023
% Result : Unsatisfiable 3.12s 1.73s
% Output : Refutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 54 ( 11 unt; 11 typ; 0 def)
% Number of atoms : 85 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 292 ( 42 ~; 42 |; 0 &; 208 @)
% ( 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 : 12 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 84 ( 0 ^; 84 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf(union_type,type,
union: $i > $i > $i ).
thf(as_type,type,
as: $i ).
thf(bs_type,type,
bs: $i ).
thf(cs_type,type,
cs: $i ).
thf(equal_sets_type,type,
equal_sets: $i > $i > $o ).
thf(member_type,type,
member: $i > $i > $o ).
thf(complement_type,type,
complement: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(member_of_1_not_of_2_type,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(19,axiom,
subset @ bs @ cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_subset_of_c) ).
thf(56,plain,
subset @ bs @ cs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_sets @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_sets @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ ( complement @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_member_of_set_and_complement) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ ( complement @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
subset @ as @ cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_subset_of_c) ).
thf(41,plain,
subset @ as @ cs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ ( member_of_1_not_of_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom1) ).
thf(54,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)],[18]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( equal_sets @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_for_set_equal) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( equal_sets @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ( member @ A @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
thf(35,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)],[8]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( union @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( union @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).
thf(42,plain,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,axiom,
! [A: $i] : ( equal_sets @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_set_equal) ).
thf(24,plain,
! [A: $i] : ( equal_sets @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( member @ A @ B )
| ( member @ A @ ( complement @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set_or_complement) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( member @ A @ B )
| ( member @ A @ ( complement @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( subset @ B @ C )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( subset @ B @ C )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( union @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set2_is_member_of_union) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( member @ A @ ( union @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ~ ( equal_sets @ B @ C )
| ( equal_sets @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_set_equal) ).
thf(29,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)],[5]) ).
thf(1,negated_conjecture,
~ ( subset @ ( union @ as @ bs ) @ cs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_union_b_subset_of_c) ).
thf(22,plain,
~ ( subset @ ( union @ as @ bs ) @ cs ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ A @ B ) @ B )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom2) ).
thf(44,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)],[13]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( subset @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(27,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( union @ B @ C ) )
| ( member @ A @ B )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).
thf(50,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)],[16]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(67,plain,
$false,
inference(cvc4,[status(thm)],[56,52,33,41,54,39,35,48,42,24,37,25,46,57,29,22,44,59,27,50,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET014-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n020.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % 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 19:21:33 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.94/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.04 % [INFO] Parsing done (136ms).
% 1.22/1.05 % [INFO] Running in sequential loop mode.
% 1.75/1.24 % [INFO] eprover registered as external prover.
% 1.75/1.25 % [INFO] cvc4 registered as external prover.
% 1.75/1.25 % [INFO] Scanning for conjecture ...
% 1.88/1.30 % [INFO] Found a conjecture and 23 axioms. Running axiom selection ...
% 1.88/1.34 % [INFO] Axiom selection finished. Selected 20 axioms (removed 3 axioms).
% 2.08/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 2.08/1.36 % [INFO] Type checking passed.
% 2.08/1.36 % [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 ...
% 3.12/1.72 % External prover 'cvc4' found a proof!
% 3.12/1.72 % [INFO] Killing All external provers ...
% 3.12/1.72 % Time passed: 1195ms (effective reasoning time: 674ms)
% 3.12/1.72 % 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)>
% 3.12/1.73 % Axioms used in derivation (20): 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, a_subset_of_c, 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, b_subset_of_c, empty_set, member_of_set2_is_member_of_union, member_of_both_is_member_of_intersection, membership_in_subsets, subsets_axiom1
% 3.12/1.73 % No. of inferences in proof: 43
% 3.12/1.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1195 ms resp. 674 ms w/o parsing
% 3.29/1.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.29/1.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------