TSTP Solution File: SET673^3 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SET673^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 10:50:19 EDT 2024
% Result : Theorem 3.45s 1.86s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 32 ( 14 unt; 8 typ; 3 def)
% Number of atoms : 55 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 127 ( 13 ~; 7 |; 15 &; 82 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 49 ( 17 ^ 30 !; 2 ?; 49 :)
% 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(is_rel_on_type,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(is_rel_on_def,definition,
( is_rel_on
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
! [D: $i,E: $i] :
( ( A @ D @ E )
=> ( ( B @ D )
& ( C @ E ) ) ) ) ) ).
thf(restrict_rel_codomain_type,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(restrict_rel_codomain_def,definition,
( restrict_rel_codomain
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i,D: $i] :
( ( B @ D )
& ( A @ C @ D ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $o ).
thf(sk2_type,type,
sk2: $i > $i > $o ).
thf(sk4_type,type,
sk4: $i > $o ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ( ( is_rel_on @ B @ C @ D )
& ( subset @ D @ A ) )
=> ( ( restrict_rel_codomain @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ( ( is_rel_on @ B @ C @ D )
& ( subset @ D @ A ) )
=> ( ( restrict_rel_codomain @ B @ A )
= B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ( ! [E: $i,F: $i] :
( ( B @ E @ F )
=> ( ( C @ E )
& ( D @ F ) ) )
& ! [E: $i] :
( ( D @ E )
=> ( A @ E ) ) )
=> ( ( ^ [E: $i,F: $i] :
( ( A @ F )
& ( B @ E @ F ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: $i > $o,B: $i > $i > $o] :
( ? [C: $i > $o,D: $i > $o] :
( ! [E: $i,F: $i] :
( ( B @ E @ F )
=> ( ( C @ E )
& ( D @ F ) ) )
& ! [E: $i] :
( ( D @ E )
=> ( A @ E ) ) )
=> ( ( ^ [C: $i,D: $i] :
( ( A @ D )
& ( B @ C @ D ) ) )
= B ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
( ( ^ [A: $i,B: $i] :
( ( sk1 @ B )
& ( sk2 @ A @ B ) ) )
!= sk2 ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
( ( ^ [A: $i,B: $i] :
( ( sk1 @ B )
& ( sk2 @ A @ B ) ) )
!= sk2 ),
inference(lifteq,[status(thm)],[5]) ).
thf(11,plain,
( ( ( sk1 @ sk6 )
& ( sk2 @ sk5 @ sk6 ) )
!= ( sk2 @ sk5 @ sk6 ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(13,plain,
( ( ( sk1 @ sk6 )
& ( sk2 @ sk5 @ sk6 ) )
| ( sk2 @ sk5 @ sk6 ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(16,plain,
( ( sk2 @ sk5 @ sk6 )
| ( sk2 @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[13]) ).
thf(18,plain,
sk2 @ sk5 @ sk6,
inference(simp,[status(thm)],[16]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ~ ( sk2 @ A @ B )
| ( sk4 @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( sk4 @ B )
| ( ( sk2 @ sk5 @ sk6 )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18,8]) ).
thf(28,plain,
sk4 @ sk6,
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(6,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ( sk1 @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(10,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ( sk1 @ A ) ),
inference(simp,[status(thm)],[6]) ).
thf(29,plain,
! [A: $i] :
( ( sk1 @ A )
| ( ( sk4 @ sk6 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28,10]) ).
thf(30,plain,
sk1 @ sk6,
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( sk6 ))]]) ).
thf(19,plain,
~ ( ( sk1 @ sk6 )
& $true ),
inference(rewrite,[status(thm)],[11,18]) ).
thf(20,plain,
~ ( sk1 @ sk6 ),
inference(simp,[status(thm)],[19]) ).
thf(31,plain,
$false,
inference(rewrite,[status(thm)],[30,20]) ).
thf(32,plain,
$false,
inference(simp,[status(thm)],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET673^3 : TPTP v8.1.2. Released v3.6.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n014.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 20:37:09 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.92/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.54/1.08 % [INFO] Parsing done (202ms).
% 1.54/1.09 % [INFO] Running in sequential loop mode.
% 1.87/1.31 % [INFO] nitpick registered as external prover.
% 1.87/1.31 % [INFO] Scanning for conjecture ...
% 2.18/1.42 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 2.37/1.44 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.37/1.44 % [INFO] Problem is higher-order (TPTP THF).
% 2.37/1.45 % [INFO] Type checking passed.
% 2.37/1.45 % [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 ...
% 3.45/1.86 % [INFO] Killing All external provers ...
% 3.45/1.86 % Time passed: 1310ms (effective reasoning time: 764ms)
% 3.45/1.86 % 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)>
% 3.45/1.86 % Axioms used in derivation (0):
% 3.45/1.86 % No. of inferences in proof: 21
% 3.45/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1310 ms resp. 764 ms w/o parsing
% 3.45/1.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.45/1.89 % [INFO] Killing All external provers ...
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