TSTP Solution File: ANA106^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---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 : n020.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 18:39:18 EDT 2024
% Result : Theorem 3.29s 2.16s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 14 ( 4 unt; 6 typ; 0 def)
% Number of atoms : 21 ( 5 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 109 ( 2 ~; 0 |; 0 &; 105 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-3 aty)
% Number of variables : 31 ( 5 ^ 24 !; 0 ?; 31 :)
% ( 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(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(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(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
% 0.00/0.09 % Problem : ANA106^1 : TPTP v8.2.0. Released v7.0.0.
% 0.09/0.11 % Command : run_Leo-III %s %d
% 0.11/0.30 % Computer : n020.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Mon May 20 07:41:53 EDT 2024
% 0.11/0.30 % CPUTime :
% 0.99/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.09 % [INFO] Parsing done (163ms).
% 1.30/1.11 % [INFO] Running in sequential loop mode.
% 1.85/1.46 % [INFO] eprover registered as external prover.
% 1.85/1.46 % [INFO] cvc4 registered as external prover.
% 1.85/1.47 % [INFO] Scanning for conjecture ...
% 2.02/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.11/1.60 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.11/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.11/1.61 % [INFO] Type checking passed.
% 2.11/1.62 % [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 ...
% 3.29/2.15 % External prover 'e' found a proof!
% 3.29/2.15 % [INFO] Killing All external provers ...
% 3.29/2.15 % Time passed: 1710ms (effective reasoning time: 1042ms)
% 3.29/2.16 % 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)>
% 3.29/2.16 % Axioms used in derivation (2): thm/iterate/SUM_SUB_, thm/iterate/FINITE_NUMSEG_
% 3.29/2.16 % No. of inferences in proof: 8
% 3.29/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1710 ms resp. 1042 ms w/o parsing
% 3.54/2.26 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.54/2.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------