TSTP Solution File: ANA108^1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : ANA108^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 5.97s 2.80s
% Output : Refutation 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 45 ( 13 unt; 13 typ; 0 def)
% Number of atoms : 88 ( 22 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 283 ( 25 ~; 14 |; 4 &; 231 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 61 ( 0 ^ 60 !; 0 ?; 61 :)
% ( 1 !>; 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/realax/real_of_num\'_type',type,
'\'const/realax/real_of_num\'': '\'type/nums/num\'' > '\'type/realax/real\'' ).
thf('\'const/nums/NUMERAL\'_type',type,
'\'const/nums/NUMERAL\'': '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/nums/_0\'_type',type,
'\'const/nums/_0\'': '\'type/nums/num\'' ).
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('\'const/arith/<=\'_type',type,
'\'const/arith/<=\'': '\'type/nums/num\'' > '\'type/nums/num\'' > $o ).
thf('\'const/arith/<\'_type',type,
'\'const/arith/<\'': '\'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\'' ).
thf(sk3_type,type,
sk3: '\'type/nums/num\'' ).
thf(sk4_type,type,
sk4: '\'type/nums/num\'' > '\'type/nums/num\'' > ( '\'type/nums/num\'' > '\'type/realax/real\'' ) > '\'type/nums/num\'' ).
thf(6,axiom,
! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( ! [D: '\'type/nums/num\''] :
( ( ( '\'const/arith/<=\'' @ B @ D )
& ( '\'const/arith/<=\'' @ D @ C ) )
=> ( ( A @ D )
= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) )
=> ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A )
= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_EQ_0_NUMSEG_') ).
thf(19,plain,
! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( ! [D: '\'type/nums/num\''] :
( ( ( '\'const/arith/<=\'' @ B @ D )
& ( '\'const/arith/<=\'' @ D @ C ) )
=> ( ( A @ D )
= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) )
=> ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A )
= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
! [C: '\'type/nums/num\'',B: '\'type/nums/num\'',A: '\'type/nums/num\'' > '\'type/realax/real\''] :
( ( '\'const/arith/<=\'' @ ( sk4 @ C @ B @ A ) @ C )
| ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A )
= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(24,plain,
! [C: '\'type/nums/num\'',B: '\'type/nums/num\'',A: '\'type/nums/num\'' > '\'type/realax/real\''] :
( ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A )
= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) )
| ( '\'const/arith/<=\'' @ ( sk4 @ C @ B @ A ) @ C ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(1,conjecture,
! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( ( '\'const/arith/<\'' @ C @ B )
=> ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A )
= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_TRIV_NUMSEG_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( ( '\'const/arith/<\'' @ C @ B )
=> ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A )
= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( ( '\'const/arith/<\'' @ C @ B )
=> ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A )
= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 ) @ sk1 )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(10,plain,
( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 ) @ sk1 )
!= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(167,plain,
! [C: '\'type/nums/num\'',B: '\'type/nums/num\'',A: '\'type/nums/num\'' > '\'type/realax/real\''] :
( ( '\'const/arith/<=\'' @ ( sk4 @ C @ B @ A ) @ C )
| ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A )
!= ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,10]) ).
thf(168,plain,
'\'const/arith/<=\'' @ ( sk4 @ sk3 @ sk2 @ sk1 ) @ sk3,
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(20,plain,
! [C: '\'type/nums/num\'',B: '\'type/nums/num\'',A: '\'type/nums/num\'' > '\'type/realax/real\''] :
( ( '\'const/arith/<=\'' @ B @ ( sk4 @ C @ B @ A ) )
| ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A )
= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(23,plain,
! [C: '\'type/nums/num\'',B: '\'type/nums/num\'',A: '\'type/nums/num\'' > '\'type/realax/real\''] :
( ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A )
= ( '\'const/realax/real_of_num\'' @ ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) )
| ( '\'const/arith/<=\'' @ B @ ( sk4 @ C @ B @ A ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(79,plain,
! [C: '\'type/nums/num\'',B: '\'type/nums/num\'',A: '\'type/nums/num\'' > '\'type/realax/real\''] :
( ( '\'const/arith/<=\'' @ B @ ( sk4 @ C @ B @ A ) )
| ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A )
!= ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[23,10]) ).
thf(80,plain,
'\'const/arith/<=\'' @ sk2 @ ( sk4 @ sk3 @ sk2 @ sk1 ),
inference(pattern_uni,[status(thm)],[79:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(5,axiom,
! [A: '\'type/nums/num\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( ( ( '\'const/arith/<=\'' @ A @ B )
& ( '\'const/arith/<=\'' @ B @ C ) )
=> ( '\'const/arith/<=\'' @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/LE_TRANS_') ).
thf(17,plain,
! [A: '\'type/nums/num\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( ( ( '\'const/arith/<=\'' @ A @ B )
& ( '\'const/arith/<=\'' @ B @ C ) )
=> ( '\'const/arith/<=\'' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
! [C: '\'type/nums/num\'',B: '\'type/nums/num\'',A: '\'type/nums/num\''] :
( ~ ( '\'const/arith/<=\'' @ A @ B )
| ~ ( '\'const/arith/<=\'' @ B @ C )
| ( '\'const/arith/<=\'' @ A @ C ) ),
inference(cnf,[status(esa)],[17]) ).
thf(9,plain,
'\'const/arith/<\'' @ sk3 @ sk2,
inference(cnf,[status(esa)],[7]) ).
thf(4,axiom,
! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] :
( ( ~ ( '\'const/arith/<\'' @ A @ B ) )
= ( '\'const/arith/<=\'' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/NOT_LT_') ).
thf(14,plain,
! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] :
( ( ~ ( '\'const/arith/<\'' @ A @ B ) )
= ( '\'const/arith/<=\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] :
( ( ~ ( '\'const/arith/<\'' @ A @ B ) )
= ( '\'const/arith/<=\'' @ B @ A ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] :
( ( ~ ( '\'const/arith/<\'' @ A @ B ) )
= ( '\'const/arith/<=\'' @ B @ A ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(28,plain,
! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] :
( ~ ( '\'const/arith/<=\'' @ B @ A )
| ( ( '\'const/arith/<\'' @ sk3 @ sk2 )
!= ( '\'const/arith/<\'' @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9,16]) ).
thf(29,plain,
~ ( '\'const/arith/<=\'' @ sk2 @ sk3 ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(42,plain,
! [C: '\'type/nums/num\'',B: '\'type/nums/num\'',A: '\'type/nums/num\''] :
( ~ ( '\'const/arith/<=\'' @ A @ B )
| ~ ( '\'const/arith/<=\'' @ B @ C )
| ( ( '\'const/arith/<=\'' @ A @ C )
!= ( '\'const/arith/<=\'' @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[18,29]) ).
thf(43,plain,
! [A: '\'type/nums/num\''] :
( ~ ( '\'const/arith/<=\'' @ sk2 @ A )
| ~ ( '\'const/arith/<=\'' @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(62,plain,
! [A: '\'type/nums/num\''] :
( ~ ( '\'const/arith/<=\'' @ sk2 @ A )
| ~ ( '\'const/arith/<=\'' @ A @ sk3 ) ),
inference(simp,[status(thm)],[43]) ).
thf(112,plain,
! [A: '\'type/nums/num\''] :
( ~ ( '\'const/arith/<=\'' @ A @ sk3 )
| ( ( '\'const/arith/<=\'' @ sk2 @ ( sk4 @ sk3 @ sk2 @ sk1 ) )
!= ( '\'const/arith/<=\'' @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[80,62]) ).
thf(113,plain,
~ ( '\'const/arith/<=\'' @ ( sk4 @ sk3 @ sk2 @ sk1 ) @ sk3 ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( sk4 @ sk3 @ sk2 @ sk1 ))]]) ).
thf(208,plain,
$false,
inference(rewrite,[status(thm)],[168,113]) ).
thf(209,plain,
$false,
inference(simp,[status(thm)],[208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ANA108^1 : TPTP v8.2.0. Released v7.0.0.
% 0.05/0.13 % Command : run_Leo-III %s %d
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon May 20 07:59:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.97/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.11 % [INFO] Parsing done (173ms).
% 1.27/1.12 % [INFO] Running in sequential loop mode.
% 1.90/1.48 % [INFO] nitpick registered as external prover.
% 1.90/1.49 % [INFO] Scanning for conjecture ...
% 2.12/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.12/1.61 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.12/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.12/1.64 % [INFO] Type checking passed.
% 2.12/1.65 % [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 ...
% 5.97/2.78 % [INFO] Killing All external provers ...
% 5.97/2.80 % Time passed: 2318ms (effective reasoning time: 1669ms)
% 5.97/2.80 % 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)>
% 5.97/2.80 % Axioms used in derivation (3): thm/iterate/SUM_EQ_0_NUMSEG_, thm/arith/LE_TRANS_, thm/arith/NOT_LT_
% 5.97/2.80 % No. of inferences in proof: 32
% 5.97/2.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2318 ms resp. 1669 ms w/o parsing
% 5.97/2.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.97/2.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------