TSTP Solution File: ANA108^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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 ... 
%------------------------------------------------------------------------------