TSTP Solution File: ANA107^1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : ANA107^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 3.47s 2.20s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 24 ( 2 unt; 10 typ; 0 def)
% Number of atoms : 34 ( 1 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 155 ( 8 ~; 2 |; 0 &; 143 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 38 ( 9 ^ 27 !; 0 ?; 38 :)
% ( 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_le\'_type',type,
'\'const/realax/real_le\'': '\'type/realax/real\'' > '\'type/realax/real\'' > $o ).
thf('\'const/realax/real_abs\'_type',type,
'\'const/realax/real_abs\'': '\'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\'' ).
thf(sk3_type,type,
sk3: '\'type/nums/num\'' ).
thf(3,axiom,
! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ B )
=> ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) )
@ ( '\'const/iterate/sum\'' @ TA @ B
@ ^ [C: TA] : ( '\'const/realax/real_abs\'' @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_ABS_') ).
thf(7,plain,
! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ B )
=> ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) )
@ ( '\'const/iterate/sum\'' @ TA @ B
@ ^ [C: TA] : ( '\'const/realax/real_abs\'' @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType,B: TA > $o,A: TA > '\'type/realax/real\''] :
( ~ ( '\'const/sets/FINITE\'' @ TA @ B )
| ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) )
@ ( '\'const/iterate/sum\'' @ TA @ B
@ ^ [C: TA] : ( '\'const/realax/real_abs\'' @ ( A @ C ) ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(1,conjecture,
! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A ) )
@ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C )
@ ^ [D: '\'type/nums/num\''] : ( '\'const/realax/real_abs\'' @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_ABS_NUMSEG_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A ) )
@ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C )
@ ^ [D: '\'type/nums/num\''] : ( '\'const/realax/real_abs\'' @ ( A @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C ) @ A ) )
@ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ B @ C )
@ ^ [D: '\'type/nums/num\''] : ( '\'const/realax/real_abs\'' @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 ) @ sk1 ) )
@ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 )
@ ^ [A: '\'type/nums/num\''] : ( '\'const/realax/real_abs\'' @ ( sk1 @ A ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(11,plain,
! [TA: $tType,B: TA > $o,A: TA > '\'type/realax/real\''] :
( ~ ( '\'const/sets/FINITE\'' @ TA @ B )
| ( ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) )
@ ( '\'const/iterate/sum\'' @ TA @ B
@ ^ [C: TA] : ( '\'const/realax/real_abs\'' @ ( A @ C ) ) ) )
!= ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 ) @ sk1 ) )
@ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 )
@ ^ [C: '\'type/nums/num\''] : ( '\'const/realax/real_abs\'' @ ( sk1 @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,6]) ).
thf(12,plain,
~ ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( sk1 )),bind(B,$thf( '\'const/iterate/..\'' @ sk2 @ sk3 )),bind_type(TA,$thf( '\'type/nums/num\'' ))]]) ).
thf(4,axiom,
! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] : ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/FINITE_NUMSEG_') ).
thf(9,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(10,plain,
! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] : ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ A @ B ) ),
inference(cnf,[status(esa)],[9]) ).
thf(15,plain,
~ $true,
inference(rewrite,[status(thm)],[12,10]) ).
thf(16,plain,
$false,
inference(simp,[status(thm)],[15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ANA107^1 : TPTP v8.2.0. Released v7.0.0.
% 0.05/0.12 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 20 07:51:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 1.00/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.12 % [INFO] Parsing done (164ms).
% 1.31/1.13 % [INFO] Running in sequential loop mode.
% 1.89/1.49 % [INFO] nitpick registered as external prover.
% 1.89/1.50 % [INFO] Scanning for conjecture ...
% 2.06/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.06/1.62 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.06/1.63 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.64 % [INFO] Type checking passed.
% 2.25/1.64 % [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 ...
% 3.47/2.20 % [INFO] Killing All external provers ...
% 3.47/2.20 % Time passed: 1723ms (effective reasoning time: 1064ms)
% 3.47/2.20 % 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)>
% 3.47/2.20 % Axioms used in derivation (2): thm/iterate/SUM_ABS_, thm/iterate/FINITE_NUMSEG_
% 3.47/2.20 % No. of inferences in proof: 14
% 3.47/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1723 ms resp. 1064 ms w/o parsing
% 3.49/2.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.49/2.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------