TSTP Solution File: ANA115^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ANA115^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 : Tue May 7 07:27:54 EDT 2024
% Result : Theorem 3.01s 1.67s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 15 ( 4 unt; 7 typ; 0 def)
% Number of atoms : 18 ( 5 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 73 ( 2 ~; 0 |; 0 &; 69 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 27 ( 5 ^ 19 !; 0 ?; 27 :)
% ( 3 !>; 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_of_num\'_type',type,
'\'const/realax/real_of_num\'': '\'type/nums/num\'' > '\'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/nsum\'_type',type,
'\'const/iterate/nsum\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > '\'type/nums/num\'' ) > '\'type/nums/num\'' ) ).
thf('\'const/iterate/..\'_type',type,
'\'const/iterate/..\'': '\'type/nums/num\'' > '\'type/nums/num\'' > '\'type/nums/num\'' > $o ).
thf(1,conjecture,
! [A: '\'type/nums/num\'' > '\'type/nums/num\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( ( '\'const/realax/real_of_num\'' @ ( '\'const/iterate/nsum\'' @ '\'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_of_num\'' @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/REAL_OF_NUM_SUM_NUMSEG_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/nums/num\'' > '\'type/nums/num\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( ( '\'const/realax/real_of_num\'' @ ( '\'const/iterate/nsum\'' @ '\'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_of_num\'' @ ( A @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: '\'type/nums/num\'' > '\'type/nums/num\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
( ( '\'const/realax/real_of_num\'' @ ( '\'const/iterate/nsum\'' @ '\'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_of_num\'' @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [TA: $tType,A: TA > '\'type/nums/num\'',B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ B )
=> ( ( '\'const/realax/real_of_num\'' @ ( '\'const/iterate/nsum\'' @ TA @ B @ A ) )
= ( '\'const/iterate/sum\'' @ TA @ B
@ ^ [C: TA] : ( '\'const/realax/real_of_num\'' @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/REAL_OF_NUM_SUM_') ).
thf(8,plain,
! [TA: $tType,A: TA > '\'type/nums/num\'',B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ B )
=> ( ( '\'const/realax/real_of_num\'' @ ( '\'const/iterate/nsum\'' @ TA @ B @ A ) )
= ( '\'const/iterate/sum\'' @ TA @ B
@ ^ [C: TA] : ( '\'const/realax/real_of_num\'' @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(13,plain,
$false,
inference(e,[status(thm)],[5,8,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ANA115^1 : TPTP v8.1.2. Released v7.0.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 6 12:45:09 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.99 % [INFO] Parsing done (117ms).
% 1.32/1.00 % [INFO] Running in sequential loop mode.
% 1.66/1.21 % [INFO] eprover registered as external prover.
% 1.66/1.22 % [INFO] cvc4 registered as external prover.
% 1.66/1.22 % [INFO] Scanning for conjecture ...
% 1.94/1.28 % [INFO] Found a conjecture and 2 axioms. Running axiom selection ...
% 1.94/1.30 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.94/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.94/1.31 % [INFO] Type checking passed.
% 1.94/1.32 % [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 ...
% 3.01/1.67 % External prover 'e' found a proof!
% 3.01/1.67 % [INFO] Killing All external provers ...
% 3.01/1.67 % Time passed: 1130ms (effective reasoning time: 669ms)
% 3.01/1.67 % 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)>
% 3.01/1.67 % Axioms used in derivation (2): thm/iterate/REAL_OF_NUM_SUM_, thm/iterate/FINITE_NUMSEG_
% 3.01/1.67 % No. of inferences in proof: 8
% 3.01/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1130 ms resp. 669 ms w/o parsing
% 3.36/1.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.36/1.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------