TSTP Solution File: SET647^3 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SET647^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n024.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 : Mon Jun 24 14:45:29 EDT 2024
% Result : Theorem 3.05s 1.92s
% Output : Refutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 5 def)
% Number of atoms : 39 ( 7 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 84 ( 11 ~; 5 |; 2 &; 59 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 35 ( 12 ^ 19 !; 4 ?; 35 :)
% 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(sk1_type,type,
sk1: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i > $o ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
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/sandbox/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(5,plain,
sk1 @ sk3 @ sk4,
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ( sk2 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( sk2 @ A )
| ( ( sk1 @ sk3 @ sk4 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5,6]) ).
thf(11,plain,
sk2 @ sk3,
inference(pattern_uni,[status(thm)],[10:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(4,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 )
| ~ ( sk1 @ A @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 )
| ~ ( sk1 @ A @ sk4 ) ),
inference(simp,[status(thm)],[4]) ).
thf(8,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 )
| ( ( sk1 @ sk3 @ sk4 )
!= ( sk1 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[5,7]) ).
thf(9,plain,
~ ( sk2 @ sk3 ),
inference(pattern_uni,[status(thm)],[8:[bind(A,$thf( sk3 ))]]) ).
thf(12,plain,
$false,
inference(rewrite,[status(thm)],[11,9]) ).
thf(13,plain,
$false,
inference(simp,[status(thm)],[12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET647^3 : TPTP v8.2.0. Released v3.6.0.
% 0.02/0.11 % Command : run_Leo-III %s %d SAT
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Jun 23 14:47:40 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.07 % [INFO] Parsing done (192ms).
% 1.28/1.08 % [INFO] Running in sequential loop mode.
% 1.93/1.37 % [INFO] nitpick registered as external prover.
% 1.93/1.38 % [INFO] Scanning for conjecture ...
% 2.24/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.31/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.31/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.31/1.54 % [INFO] Type checking passed.
% 2.31/1.54 % [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 ...
% 3.05/1.91 % [INFO] Killing All external provers ...
% 3.05/1.92 % Time passed: 1466ms (effective reasoning time: 827ms)
% 3.05/1.92 % 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)>
% 3.05/1.92 % Axioms used in derivation (0):
% 3.05/1.92 % No. of inferences in proof: 13
% 3.05/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1466 ms resp. 827 ms w/o parsing
% 3.05/1.97 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.05/1.97 % [INFO] Killing All external provers ...
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