TSTP Solution File: SET647^3 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SET647^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 08:07:45 EDT 2024
% Result : Theorem 3.04s 1.72s
% Output : Refutation 3.38s
% 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 : 21 ( 5 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 2 ~; 0 |; 2 &; 36 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-4 aty)
% Number of variables : 28 ( 12 ^ 12 !; 4 ?; 28 :)
% 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] :
( ( subset @ ( rel_domain @ A ) @ B )
=> ( sub_rel @ A @ ( cartesian_product @ B @ ( rel_codomain @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o,B: $i > $o] :
( ( subset @ ( rel_domain @ A ) @ B )
=> ( sub_rel @ A @ ( cartesian_product @ B @ ( rel_codomain @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i > $o] :
( ! [C: $i] :
( ? [D: $i] : ( A @ C @ D )
=> ( B @ C ) )
=> ! [C: $i,D: $i] :
( ( A @ C @ D )
=> ( ( B @ C )
& ? [E: $i] : ( A @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
$false,
inference(cvc4,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET647^3 : TPTP v8.1.2. Released v3.6.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n019.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 13:19:09 EDT 2024
% 0.17/0.37 % CPUTime :
% 1.05/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.55/1.06 % [INFO] Parsing done (157ms).
% 1.55/1.07 % [INFO] Running in sequential loop mode.
% 1.98/1.29 % [INFO] eprover registered as external prover.
% 1.98/1.29 % [INFO] cvc4 registered as external prover.
% 1.98/1.30 % [INFO] Scanning for conjecture ...
% 2.34/1.41 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 2.34/1.42 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.34/1.43 % [INFO] Problem is higher-order (TPTP THF).
% 2.34/1.43 % [INFO] Type checking passed.
% 2.34/1.43 % [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 ...
% 3.04/1.71 % External prover 'cvc4' found a proof!
% 3.04/1.71 % [INFO] Killing All external provers ...
% 3.04/1.71 % Time passed: 1178ms (effective reasoning time: 640ms)
% 3.04/1.71 % 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)>
% 3.04/1.72 % Axioms used in derivation (0):
% 3.04/1.72 % No. of inferences in proof: 4
% 3.04/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1178 ms resp. 640 ms w/o parsing
% 3.38/1.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.38/1.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------