TSTP Solution File: SET649^3 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET649^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 03:03:25 EDT 2024
% Result : Theorem 3.61s 2.14s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 14 ( 6 unt; 5 typ; 5 def)
% Number of atoms : 23 ( 5 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 57 ( 2 ~; 0 |; 5 &; 42 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-4 aty)
% Number of variables : 32 ( 12 ^ 16 !; 4 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(subset_def,definition,
( subset
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: $i] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(cartesian_product_type,type,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(cartesian_product_def,definition,
( cartesian_product
= ( ^ [A: $i > $o,B: $i > $o,C: $i,D: $i] :
( ( A @ C )
& ( B @ D ) ) ) ) ).
thf(sub_rel_type,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(sub_rel_def,definition,
( sub_rel
= ( ^ [A: $i > $i > $o,B: $i > $i > $o] :
! [C: $i,D: $i] :
( ( A @ C @ D )
=> ( B @ C @ D ) ) ) ) ).
thf(rel_codomain_type,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(rel_codomain_def,definition,
( rel_codomain
= ( ^ [A: $i > $i > $o,B: $i] :
? [C: $i] : ( A @ C @ B ) ) ) ).
thf(rel_domain_type,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(rel_domain_def,definition,
( rel_domain
= ( ^ [A: $i > $i > $o,B: $i] :
? [C: $i] : ( A @ B @ C ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
( ( ( subset @ ( rel_domain @ A ) @ B )
& ( subset @ ( rel_codomain @ A ) @ C ) )
=> ( sub_rel @ A @ ( cartesian_product @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
( ( ( subset @ ( rel_domain @ A ) @ B )
& ( subset @ ( rel_codomain @ A ) @ C ) )
=> ( sub_rel @ A @ ( cartesian_product @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
( ( ! [D: $i] :
( ? [E: $i] : ( A @ D @ E )
=> ( B @ D ) )
& ! [D: $i] :
( ? [E: $i] : ( A @ E @ D )
=> ( C @ D ) ) )
=> ! [D: $i,E: $i] :
( ( A @ D @ E )
=> ( ( B @ D )
& ( C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET649^3 : TPTP v8.2.0. Released v3.6.0.
% 0.09/0.11 % Command : run_Leo-III %s %d
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 20 11:35:24 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.94/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/1.15 % [INFO] Parsing done (241ms).
% 1.34/1.16 % [INFO] Running in sequential loop mode.
% 2.06/1.50 % [INFO] eprover registered as external prover.
% 2.06/1.50 % [INFO] cvc4 registered as external prover.
% 2.06/1.51 % [INFO] Scanning for conjecture ...
% 2.40/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.57/1.69 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.57/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 2.57/1.70 % [INFO] Type checking passed.
% 2.57/1.70 % [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 ...
% 3.61/2.14 % External prover 'e' found a proof!
% 3.61/2.14 % [INFO] Killing All external provers ...
% 3.61/2.14 % Time passed: 1692ms (effective reasoning time: 975ms)
% 3.61/2.14 % 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)>
% 3.61/2.14 % Axioms used in derivation (0):
% 3.61/2.14 % No. of inferences in proof: 4
% 3.61/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1692 ms resp. 975 ms w/o parsing
% 3.61/2.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.61/2.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------