TSTP Solution File: SET001-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET001-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 11:51:48 EDT 2023
% Result : Unsatisfiable 2.69s 1.54s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 26 ( 7 unt; 7 typ; 0 def)
% Number of atoms : 35 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 108 ( 16 ~; 16 |; 0 &; 76 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_type,type,
member: $i > $i > $o ).
thf(element_of_b_type,type,
element_of_b: $i ).
thf(bb_type,type,
bb: $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(member_of_1_not_of_2_type,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(equal_sets_type,type,
equal_sets: $i > $i > $o ).
thf(b_type,type,
b: $i ).
thf(1,negated_conjecture,
~ ( member @ element_of_b @ bb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_element_of_bb) ).
thf(10,plain,
~ ( member @ element_of_b @ bb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,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(14,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)],[3]) ).
thf(6,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(20,plain,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( subset @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,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(22,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_sets @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,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(12,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( subset @ B @ C )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,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(18,plain,
! [B: $i,A: $i] :
( ~ ( equal_sets @ A @ B )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,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(16,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)],[4]) ).
thf(8,axiom,
equal_sets @ b @ bb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_equals_bb) ).
thf(24,plain,
equal_sets @ b @ bb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
member @ element_of_b @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_of_b) ).
thf(25,plain,
member @ element_of_b @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,plain,
$false,
inference(e,[status(thm)],[10,14,20,22,12,18,16,24,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET001-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 19:11:10 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.14/0.97 % [INFO] Parsing done (117ms).
% 1.14/0.98 % [INFO] Running in sequential loop mode.
% 1.64/1.18 % [INFO] eprover registered as external prover.
% 1.64/1.18 % [INFO] cvc4 registered as external prover.
% 1.64/1.18 % [INFO] Scanning for conjecture ...
% 1.64/1.23 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.82/1.25 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.82/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 1.82/1.26 % [INFO] Type checking passed.
% 1.82/1.26 % [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 ...
% 2.69/1.54 % External prover 'e' found a proof!
% 2.69/1.54 % [INFO] Killing All external provers ...
% 2.69/1.54 % Time passed: 1011ms (effective reasoning time: 561ms)
% 2.69/1.54 % 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)>
% 2.69/1.54 % Axioms used in derivation (8): set_equal_sets_are_subsets2, subsets_are_set_equal_sets, subsets_axiom2, b_equals_bb, set_equal_sets_are_subsets1, element_of_b, membership_in_subsets, subsets_axiom1
% 2.69/1.54 % No. of inferences in proof: 19
% 2.69/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1011 ms resp. 561 ms w/o parsing
% 2.76/1.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.76/1.59 % [INFO] Killing All external provers ...
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