TSTP Solution File: ANA108^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---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 : n028.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 18:39:19 EDT 2024
% Result : Theorem 3.13s 1.76s
% Output : Refutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 22 ( 5 unt; 10 typ; 0 def)
% Number of atoms : 34 ( 11 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 96 ( 4 ~; 0 |; 4 &; 79 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 33 ( 0 ^ 31 !; 0 ?; 33 :)
% ( 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/trivia/I\'_type',type,
'\'const/trivia/I\'':
!>[TA: $tType] : ( TA > TA ) ).
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(4,axiom,
! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] :
( ( ~ ( '\'const/arith/<\'' @ A @ B ) )
= ( '\'const/arith/<=\'' @ B @ A ) ),
file('/export/starexec/sandbox/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(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/sandbox/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(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/sandbox/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(3,axiom,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/trivia/I_THM_') ).
thf(11,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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/sandbox/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(32,plain,
$false,
inference(e,[status(thm)],[14,17,7,11,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA108^1 : TPTP v8.2.0. Released v7.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n028.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 20 07:59:23 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.97/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.02 % [INFO] Parsing done (128ms).
% 1.30/1.03 % [INFO] Running in sequential loop mode.
% 1.74/1.24 % [INFO] eprover registered as external prover.
% 1.74/1.24 % [INFO] cvc4 registered as external prover.
% 1.74/1.25 % [INFO] Scanning for conjecture ...
% 1.74/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.97/1.33 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.97/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 1.97/1.34 % [INFO] Type checking passed.
% 1.97/1.34 % [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 ...
% 3.13/1.75 % External prover 'e' found a proof!
% 3.13/1.75 % [INFO] Killing All external provers ...
% 3.13/1.76 % Time passed: 1249ms (effective reasoning time: 719ms)
% 3.13/1.76 % 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)>
% 3.13/1.76 % Axioms used in derivation (4): thm/arith/NOT_LT_, thm/arith/LE_TRANS_, thm/trivia/I_THM_, thm/iterate/SUM_EQ_0_NUMSEG_
% 3.13/1.76 % No. of inferences in proof: 12
% 3.13/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1249 ms resp. 719 ms w/o parsing
% 3.13/1.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.13/1.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------