TSTP Solution File: ANA106^1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : ANA106^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 May 20 18:39:46 EDT 2024
% Result : Theorem 3.68s 1.83s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 7 unt; 10 typ; 0 def)
% Number of atoms : 49 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 269 ( 13 ~; 5 |; 0 &; 249 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 53 ( 13 ^ 38 !; 0 ?; 53 :)
% ( 2 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
'\'type/realax/real\'': $tType ).
thf('\'type/nums/num\'_type',type,
'\'type/nums/num\'': $tType ).
thf('\'const/sets/FINITE\'_type',type,
'\'const/sets/FINITE\'':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('\'const/realax/real_sub\'_type',type,
'\'const/realax/real_sub\'': '\'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/..\'_type',type,
'\'const/iterate/..\'': '\'type/nums/num\'' > '\'type/nums/num\'' > '\'type/nums/num\'' > $o ).
thf(sk1_type,type,
sk1: '\'type/nums/num\'' > '\'type/realax/real\'' ).
thf(sk2_type,type,
sk2: '\'type/nums/num\'' > '\'type/realax/real\'' ).
thf(sk3_type,type,
sk3: '\'type/nums/num\'' ).
thf(sk4_type,type,
sk4: '\'type/nums/num\'' ).
thf(3,axiom,
! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > '\'type/realax/real\'',C: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ C )
=> ( ( '\'const/iterate/sum\'' @ TA @ C
@ ^ [D: TA] : ( '\'const/realax/real_sub\'' @ ( A @ D ) @ ( B @ D ) ) )
= ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_SUB_') ).
thf(8,plain,
! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > '\'type/realax/real\'',C: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ C )
=> ( ( '\'const/iterate/sum\'' @ TA @ C
@ ^ [D: TA] : ( '\'const/realax/real_sub\'' @ ( A @ D ) @ ( B @ D ) ) )
= ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
( ~ ( '\'const/sets/FINITE\'' @ TA @ C )
| ( ( '\'const/iterate/sum\'' @ TA @ C
@ ^ [D: TA] : ( '\'const/realax/real_sub\'' @ ( A @ D ) @ ( B @ D ) ) )
= ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
( ( ( '\'const/iterate/sum\'' @ TA @ C
@ ^ [D: TA] : ( '\'const/realax/real_sub\'' @ ( A @ D ) @ ( B @ D ) ) )
= ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) )
| ~ ( '\'const/sets/FINITE\'' @ TA @ C ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'' > '\'type/realax/real\'',C: '\'type/nums/num\'',D: '\'type/nums/num\''] :
( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ C @ D )
@ ^ [E: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( A @ E ) @ ( B @ E ) ) )
= ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ C @ D ) @ A ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_SUB_NUMSEG_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'' > '\'type/realax/real\'',C: '\'type/nums/num\'',D: '\'type/nums/num\''] :
( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ C @ D )
@ ^ [E: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( A @ E ) @ ( B @ E ) ) )
= ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ C @ D ) @ A ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ C @ D ) @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'' > '\'type/realax/real\'',C: '\'type/nums/num\'',D: '\'type/nums/num\''] :
( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ C @ D )
@ ^ [E: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( A @ E ) @ ( B @ E ) ) )
= ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ C @ D ) @ A ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 )
@ ^ [A: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk1 ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk2 ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 )
@ ^ [A: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk1 ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk2 ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(17,plain,
! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
( ~ ( '\'const/sets/FINITE\'' @ TA @ C )
| ( ( '\'const/iterate/sum\'' @ TA @ C
@ ^ [D: TA] : ( '\'const/realax/real_sub\'' @ ( A @ D ) @ ( B @ D ) ) )
!= ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 )
@ ^ [D: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( sk1 @ D ) @ ( sk2 @ D ) ) ) )
| ( ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) )
!= ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk1 ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(18,plain,
( ~ ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) )
| ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 )
@ ^ [A: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 )
@ ^ [A: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( '\'const/iterate/..\'' @ sk3 @ sk4 )),bind_type(TA,$thf( '\'type/nums/num\'' ))]]) ).
thf(25,plain,
~ ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[18]) ).
thf(4,axiom,
! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] : ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/FINITE_NUMSEG_') ).
thf(11,plain,
! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] : ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] : ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ A @ B ) ),
inference(cnf,[status(esa)],[11]) ).
thf(29,plain,
~ $true,
inference(rewrite,[status(thm)],[25,12]) ).
thf(30,plain,
$false,
inference(simp,[status(thm)],[29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA106^1 : TPTP v8.2.0. Released v7.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n018.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 20 07:41:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.97/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.97 % [INFO] Parsing done (114ms).
% 1.16/0.98 % [INFO] Running in sequential loop mode.
% 1.63/1.19 % [INFO] nitpick registered as external prover.
% 1.63/1.19 % [INFO] Scanning for conjecture ...
% 1.82/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.91/1.27 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.91/1.28 % [INFO] Problem is higher-order (TPTP THF).
% 1.91/1.29 % [INFO] Type checking passed.
% 1.91/1.29 % [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 ...
% 3.68/1.83 % [INFO] Killing All external provers ...
% 3.68/1.83 % Time passed: 1309ms (effective reasoning time: 849ms)
% 3.68/1.83 % 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)>
% 3.68/1.83 % Axioms used in derivation (2): thm/iterate/SUM_SUB_, thm/iterate/FINITE_NUMSEG_
% 3.68/1.83 % No. of inferences in proof: 17
% 3.68/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1309 ms resp. 849 ms w/o parsing
% 3.68/1.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.68/1.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------