TSTP Solution File: SEV481^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV481^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n029.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 15:59:08 EDT 2024
% Result : Theorem 14.48s 9.05s
% Output : Refutation 14.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 94 ( 1 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 295 ( 12 ~; 6 |; 14 &; 256 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 12 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 65 ( 9 ^ 38 !; 18 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/sets/SETSPEC\'_type',type,
'\'const/sets/SETSPEC\'':
!>[TA: $tType] : ( TA > $o > TA > $o ) ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('\'const/sets/GSPEC\'_type',type,
'\'const/sets/GSPEC\'':
!>[TA: $tType] : ( ( TA > $o ) > TA > $o ) ).
thf('\'const/sets/FINITE\'_type',type,
'\'const/sets/FINITE\'':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('\'const/pair/,\'_type',type,
'\'const/pair/,\'':
!>[TA: $tType,TB: $tType] : ( TB > TA > ( '\'type/pair/prod\'' @ TB @ TA ) ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(sk1_type,type,
sk1: skt1 > $o ).
thf(sk2_type,type,
sk2: skt2 > $o ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA > TC,B: TB > $o,C: TB > TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TB @ B )
& ! [D: TB] :
( ( '\'const/sets/IN\'' @ TB @ D @ B )
=> ( '\'const/sets/FINITE\'' @ TA @ ( C @ D ) ) ) )
=> ( '\'const/sets/FINITE\'' @ TC
@ ( '\'const/sets/GSPEC\'' @ TC
@ ^ [D: TC] :
? [E: TB,F: TA] :
( '\'const/sets/SETSPEC\'' @ TC @ D
@ ( ( '\'const/sets/IN\'' @ TB @ E @ B )
& ( '\'const/sets/IN\'' @ TA @ F @ ( C @ E ) ) )
@ ( A @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_PRODUCT_DEPENDENT_') ).
thf(8,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA > TC,B: TB > $o,C: TB > TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TB @ B )
& ! [D: TB] :
( ( '\'const/sets/IN\'' @ TB @ D @ B )
=> ( '\'const/sets/FINITE\'' @ TA @ ( C @ D ) ) ) )
=> ( '\'const/sets/FINITE\'' @ TC
@ ( '\'const/sets/GSPEC\'' @ TC
@ ^ [D: TC] :
? [E: TB,F: TA] :
( '\'const/sets/SETSPEC\'' @ TC @ D
@ ( ( '\'const/sets/IN\'' @ TB @ E @ B )
& ( '\'const/sets/IN\'' @ TA @ F @ ( C @ E ) ) )
@ ( A @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TB > TC > $o,B: TB > $o,A: TB > TC > TA] :
( ~ ( '\'const/sets/FINITE\'' @ TB @ B )
| ~ ( '\'const/sets/FINITE\'' @ TC @ ( C @ ( sk3 @ TC @ TB @ TA @ C @ B @ A ) ) )
| ( '\'const/sets/FINITE\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [D: TA] :
? [E: TB,F: TC] :
( '\'const/sets/SETSPEC\'' @ TA @ D
@ ( ( '\'const/sets/IN\'' @ TB @ E @ B )
& ( '\'const/sets/IN\'' @ TC @ F @ ( C @ E ) ) )
@ ( A @ E @ F ) ) ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TB @ A )
& ( '\'const/sets/FINITE\'' @ TA @ B ) )
=> ( '\'const/sets/FINITE\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
@ ( '\'const/sets/GSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
@ ^ [C: '\'type/pair/prod\'' @ TB @ TA] :
? [D: TB,E: TA] :
( '\'const/sets/SETSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA ) @ C
@ ( ( '\'const/sets/IN\'' @ TB @ D @ A )
& ( '\'const/sets/IN\'' @ TA @ E @ B ) )
@ ( '\'const/pair/,\'' @ TB @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_PRODUCT_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TB @ A )
& ( '\'const/sets/FINITE\'' @ TA @ B ) )
=> ( '\'const/sets/FINITE\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
@ ( '\'const/sets/GSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
@ ^ [C: '\'type/pair/prod\'' @ TB @ TA] :
? [D: TB,E: TA] :
( '\'const/sets/SETSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA ) @ C
@ ( ( '\'const/sets/IN\'' @ TB @ D @ A )
& ( '\'const/sets/IN\'' @ TA @ E @ B ) )
@ ( '\'const/pair/,\'' @ TB @ TA @ D @ E ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TB @ A )
& ( '\'const/sets/FINITE\'' @ TA @ B ) )
=> ( '\'const/sets/FINITE\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
@ ( '\'const/sets/GSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA )
@ ^ [C: '\'type/pair/prod\'' @ TB @ TA] :
? [D: TB,E: TA] :
( '\'const/sets/SETSPEC\'' @ ( '\'type/pair/prod\'' @ TB @ TA ) @ C
@ ( ( '\'const/sets/IN\'' @ TB @ D @ A )
& ( '\'const/sets/IN\'' @ TA @ E @ B ) )
@ ( '\'const/pair/,\'' @ TB @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
~ ( '\'const/sets/FINITE\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 )
@ ( '\'const/sets/GSPEC\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 )
@ ^ [A: '\'type/pair/prod\'' @ skt1 @ skt2] :
? [B: skt1,C: skt2] :
( '\'const/sets/SETSPEC\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ A
@ ( ( '\'const/sets/IN\'' @ skt1 @ B @ sk1 )
& ( '\'const/sets/IN\'' @ skt2 @ C @ sk2 ) )
@ ( '\'const/pair/,\'' @ skt1 @ skt2 @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(13,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TB > TC > $o,B: TB > $o,A: TB > TC > TA] :
( ~ ( '\'const/sets/FINITE\'' @ TB @ B )
| ~ ( '\'const/sets/FINITE\'' @ TC @ ( C @ ( sk3 @ TC @ TB @ TA @ C @ B @ A ) ) )
| ( ( '\'const/sets/FINITE\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [D: TA] :
? [E: TB,F: TC] :
( '\'const/sets/SETSPEC\'' @ TA @ D
@ ( ( '\'const/sets/IN\'' @ TB @ E @ B )
& ( '\'const/sets/IN\'' @ TC @ F @ ( C @ E ) ) )
@ ( A @ E @ F ) ) ) )
!= ( '\'const/sets/FINITE\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 )
@ ( '\'const/sets/GSPEC\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 )
@ ^ [D: '\'type/pair/prod\'' @ skt1 @ skt2] :
? [E: skt1,F: skt2] :
( '\'const/sets/SETSPEC\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ D
@ ( ( '\'const/sets/IN\'' @ skt1 @ E @ sk1 )
& ( '\'const/sets/IN\'' @ skt2 @ F @ sk2 ) )
@ ( '\'const/pair/,\'' @ skt1 @ skt2 @ E @ F ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,5]) ).
thf(14,plain,
( ~ ( '\'const/sets/FINITE\'' @ skt1 @ sk1 )
| ~ ( '\'const/sets/FINITE\'' @ skt2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( '\'const/pair/,\'' @ skt1 @ skt2 )),bind(B,$thf( sk1 )),bind(C,$thf( ^ [D: skt1] : sk2 )),bind_type(TA,$thf( '\'type/pair/prod\'' @ skt1 @ skt2 )),bind_type(TB,$thf( skt1 )),bind_type(TC,$thf( skt2 ))]]) ).
thf(6,plain,
'\'const/sets/FINITE\'' @ skt2 @ sk2,
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
'\'const/sets/FINITE\'' @ skt1 @ sk1,
inference(cnf,[status(esa)],[4]) ).
thf(32,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[14,6,7]) ).
thf(33,plain,
$false,
inference(simp,[status(thm)],[32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV481^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n029.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 21 19:09:55 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.91/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.97 % [INFO] Parsing done (116ms).
% 1.21/0.98 % [INFO] Running in sequential loop mode.
% 1.66/1.18 % [INFO] eprover registered as external prover.
% 1.66/1.19 % [INFO] Scanning for conjecture ...
% 1.85/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.92/1.28 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.92/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.92/1.29 % [INFO] Type checking passed.
% 1.92/1.29 % [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 ...
% 14.27/9.05 % [INFO] Killing All external provers ...
% 14.27/9.05 % Time passed: 8532ms (effective reasoning time: 8069ms)
% 14.27/9.05 % 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)>
% 14.27/9.05 % Axioms used in derivation (1): thm/sets/FINITE_PRODUCT_DEPENDENT_
% 14.27/9.05 % No. of inferences in proof: 13
% 14.48/9.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8532 ms resp. 8069 ms w/o parsing
% 14.48/9.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.48/9.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------