TSTP Solution File: SET626+3 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 7 08:07:41 EDT 2024
% Result : Theorem 3.06s 1.71s
% Output : Refutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 17 ( 3 unt; 3 typ; 0 def)
% Number of atoms : 44 ( 5 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 128 ( 2 ~; 0 |; 11 &; 96 @)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 37 ( 0 ^ 34 !; 3 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersect_type,type,
intersect: $i > $i > $o ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,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(29,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)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( intersect @ A @ B )
=> ( intersect @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( intersect @ A @ B )
=> ( intersect @ B @ A ) ),
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(12,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(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(18,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(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( intersect @ A @ ( intersection @ B @ C ) )
=> ( intersect @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th102) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( intersect @ A @ ( intersection @ B @ C ) )
=> ( intersect @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( intersect @ A @ ( intersection @ B @ C ) )
=> ( intersect @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(52,plain,
$false,
inference(e,[status(thm)],[24,29,27,12,18,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n021.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 13:25:09 EDT 2024
% 0.17/0.37 % CPUTime :
% 1.00/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.98 % [INFO] Parsing done (108ms).
% 1.16/0.99 % [INFO] Running in sequential loop mode.
% 1.66/1.20 % [INFO] eprover registered as external prover.
% 1.66/1.20 % [INFO] cvc4 registered as external prover.
% 1.66/1.21 % [INFO] Scanning for conjecture ...
% 1.79/1.26 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.79/1.28 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.79/1.29 % [INFO] Problem is first-order (TPTP FOF).
% 1.79/1.29 % [INFO] Type checking passed.
% 1.79/1.30 % [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 ...
% 3.06/1.70 % External prover 'e' found a proof!
% 3.06/1.71 % [INFO] Killing All external provers ...
% 3.06/1.71 % Time passed: 1164ms (effective reasoning time: 712ms)
% 3.06/1.71 % 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)>
% 3.06/1.71 % Axioms used in derivation (5): equal_member_defn, intersect_defn, commutativity_of_intersection, symmetry_of_intersect, intersection_defn
% 3.06/1.71 % No. of inferences in proof: 14
% 3.06/1.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1164 ms resp. 712 ms w/o parsing
% 3.06/1.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.06/1.76 % [INFO] Killing All external provers ...
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