TSTP Solution File: SEV513^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV513^1 : 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 15:59:13 EDT 2024
% Result : Theorem 22.06s 13.42s
% Output : Refutation 22.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 7 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 254 ( 7 ~; 0 |; 10 &; 230 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 1 con; 0-5 aty)
% Number of variables : 56 ( 15 ^ 31 !; 10 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
'\'type/realax/real\'': $tType ).
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/realax/real_add\'_type',type,
'\'const/realax/real_add\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/iterate/sum\'_type',type,
'\'const/iterate/sum\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > '\'type/realax/real\'' ) > '\'type/realax/real\'' ) ).
thf('\'const/iterate/monoidal\'_type',type,
'\'const/iterate/monoidal\'':
!>[TA: $tType] : ( ( TA > TA > TA ) > $o ) ).
thf('\'const/iterate/iterate\'_type',type,
'\'const/iterate/iterate\'':
!>[TA: $tType,TB: $tType] : ( ( TA > TA > TA ) > ( TB > $o ) > ( TB > TA ) > TA ) ).
thf('\'const/class/COND\'_type',type,
'\'const/class/COND\'':
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 > $o ).
thf(3,axiom,
! [TA: $tType] :
( ( '\'const/iterate/sum\'' @ TA )
= ( '\'const/iterate/iterate\'' @ TA @ '\'type/realax/real\'' @ '\'const/realax/real_add\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/sum_') ).
thf(10,plain,
! [TA: $tType] :
( ( '\'const/iterate/sum\'' @ TA )
= ( '\'const/iterate/iterate\'' @ TA @ '\'type/realax/real\'' @ '\'const/realax/real_add\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > '\'type/realax/real\'',D: TA > '\'type/realax/real\''] :
( ( '\'const/sets/FINITE\'' @ TA @ A )
=> ( ( '\'const/iterate/sum\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/class/COND\'' @ '\'type/realax/real\'' @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
= ( '\'const/realax/real_add\''
@ ( '\'const/iterate/sum\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [E: TA] :
? [F: TA] :
( '\'const/sets/SETSPEC\'' @ TA @ E
@ ( ( '\'const/sets/IN\'' @ TA @ F @ A )
& ( B @ F ) )
@ F ) )
@ C )
@ ( '\'const/iterate/sum\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [E: TA] :
? [F: TA] :
( '\'const/sets/SETSPEC\'' @ TA @ E
@ ( ( '\'const/sets/IN\'' @ TA @ F @ A )
& ~ ( B @ F ) )
@ F ) )
@ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_CASES_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > '\'type/realax/real\'',D: TA > '\'type/realax/real\''] :
( ( '\'const/sets/FINITE\'' @ TA @ A )
=> ( ( '\'const/iterate/sum\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/class/COND\'' @ '\'type/realax/real\'' @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
= ( '\'const/realax/real_add\''
@ ( '\'const/iterate/sum\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [E: TA] :
? [F: TA] :
( '\'const/sets/SETSPEC\'' @ TA @ E
@ ( ( '\'const/sets/IN\'' @ TA @ F @ A )
& ( B @ F ) )
@ F ) )
@ C )
@ ( '\'const/iterate/sum\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [E: TA] :
? [F: TA] :
( '\'const/sets/SETSPEC\'' @ TA @ E
@ ( ( '\'const/sets/IN\'' @ TA @ F @ A )
& ~ ( B @ F ) )
@ F ) )
@ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > '\'type/realax/real\'',D: TA > '\'type/realax/real\''] :
( ( '\'const/sets/FINITE\'' @ TA @ A )
=> ( ( '\'const/iterate/sum\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/class/COND\'' @ '\'type/realax/real\'' @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) )
= ( '\'const/realax/real_add\''
@ ( '\'const/iterate/sum\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [E: TA] :
? [F: TA] :
( '\'const/sets/SETSPEC\'' @ TA @ E
@ ( ( '\'const/sets/IN\'' @ TA @ F @ A )
& ( B @ F ) )
@ F ) )
@ C )
@ ( '\'const/iterate/sum\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [E: TA] :
? [F: TA] :
( '\'const/sets/SETSPEC\'' @ TA @ E
@ ( ( '\'const/sets/IN\'' @ TA @ F @ A )
& ~ ( B @ F ) )
@ F ) )
@ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > TA] :
( ( '\'const/iterate/monoidal\'' @ TA @ A )
=> ! [B: TB > $o,C: TB > $o,D: TB > TA,E: TB > TA] :
( ( '\'const/sets/FINITE\'' @ TB @ B )
=> ( ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ B
@ ^ [F: TB] : ( '\'const/class/COND\'' @ TA @ ( C @ F ) @ ( D @ F ) @ ( E @ F ) ) )
= ( A
@ ( '\'const/iterate/iterate\'' @ TB @ TA @ A
@ ( '\'const/sets/GSPEC\'' @ TB
@ ^ [F: TB] :
? [G: TB] :
( '\'const/sets/SETSPEC\'' @ TB @ F
@ ( ( '\'const/sets/IN\'' @ TB @ G @ B )
& ( C @ G ) )
@ G ) )
@ D )
@ ( '\'const/iterate/iterate\'' @ TB @ TA @ A
@ ( '\'const/sets/GSPEC\'' @ TB
@ ^ [F: TB] :
? [G: TB] :
( '\'const/sets/SETSPEC\'' @ TB @ F
@ ( ( '\'const/sets/IN\'' @ TB @ G @ B )
& ~ ( C @ G ) )
@ G ) )
@ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CASES_') ).
thf(13,plain,
! [TA: $tType,TB: $tType,A: TA > TA > TA] :
( ( '\'const/iterate/monoidal\'' @ TA @ A )
=> ! [B: TB > $o,C: TB > $o,D: TB > TA,E: TB > TA] :
( ( '\'const/sets/FINITE\'' @ TB @ B )
=> ( ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ B
@ ^ [F: TB] : ( '\'const/class/COND\'' @ TA @ ( C @ F ) @ ( D @ F ) @ ( E @ F ) ) )
= ( A
@ ( '\'const/iterate/iterate\'' @ TB @ TA @ A
@ ( '\'const/sets/GSPEC\'' @ TB
@ ^ [F: TB] :
? [G: TB] :
( '\'const/sets/SETSPEC\'' @ TB @ F
@ ( ( '\'const/sets/IN\'' @ TB @ G @ B )
& ( C @ G ) )
@ G ) )
@ D )
@ ( '\'const/iterate/iterate\'' @ TB @ TA @ A
@ ( '\'const/sets/GSPEC\'' @ TB
@ ^ [F: TB] :
? [G: TB] :
( '\'const/sets/SETSPEC\'' @ TB @ F
@ ( ( '\'const/sets/IN\'' @ TB @ G @ B )
& ~ ( C @ G ) )
@ G ) )
@ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
'\'const/iterate/monoidal\'' @ '\'type/realax/real\'' @ '\'const/realax/real_add\'',
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(16,plain,
'\'const/iterate/monoidal\'' @ '\'type/realax/real\'' @ '\'const/realax/real_add\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,plain,
'\'const/sets/FINITE\'' @ skt1 @ sk1,
inference(cnf,[status(esa)],[6]) ).
thf(122,plain,
$false,
inference(e,[status(thm)],[10,6,13,16,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEV513^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:00:25 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.02/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.05 % [INFO] Parsing done (132ms).
% 1.27/1.05 % [INFO] Running in sequential loop mode.
% 1.75/1.25 % [INFO] eprover registered as external prover.
% 1.75/1.26 % [INFO] Scanning for conjecture ...
% 1.75/1.30 % [INFO] No direction of definition thm/iterate/sum_ detected. Treating as axiom ...
% 2.01/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.01/1.35 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.01/1.35 % [INFO] No direction of definition thm/iterate/sum_ detected. Treating as axiom ...
% 2.01/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.01/1.37 % [INFO] Type checking passed.
% 2.01/1.37 % [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 ...
% 22.06/13.42 % External prover 'e' found a proof!
% 22.06/13.42 % [INFO] Killing All external provers ...
% 22.06/13.42 % Time passed: 12885ms (effective reasoning time: 12359ms)
% 22.06/13.42 % 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)>
% 22.06/13.42 % Axioms used in derivation (3): thm/iterate/sum_, thm/iterate/ITERATE_CASES_, thm/iterate/MONOIDAL_REAL_ADD_
% 22.06/13.42 % No. of inferences in proof: 11
% 22.06/13.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12885 ms resp. 12359 ms w/o parsing
% 22.06/13.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.06/13.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------