TSTP Solution File: ANA106^1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : n018.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 3.68s 1.83s
% Output   : Refutation 3.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   27 (   7 unt;  10 typ;   0 def)
%            Number of atoms       :   49 (  12 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  269 (  13   ~;   5   |;   0   &; 249   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   34 (  34   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :   53 (  13   ^  38   !;   0   ?;  53   :)
%                                         (   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(sk1_type,type,
    sk1: '\'type/nums/num\'' > '\'type/realax/real\'' ).

thf(sk2_type,type,
    sk2: '\'type/nums/num\'' > '\'type/realax/real\'' ).

thf(sk3_type,type,
    sk3: '\'type/nums/num\'' ).

thf(sk4_type,type,
    sk4: '\'type/nums/num\'' ).

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(9,plain,
    ! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
      ( ~ ( '\'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(cnf,[status(esa)],[8]) ).

thf(10,plain,
    ! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
      ( ( ( '\'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 ) ) )
      | ~ ( '\'const/sets/FINITE\'' @ TA @ C ) ),
    inference(lifteq,[status(thm)],[9]) ).

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(6,plain,
    ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 )
      @ ^ [A: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
   != ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk1 ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk2 ) ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(7,plain,
    ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 )
      @ ^ [A: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
   != ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk1 ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk2 ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(17,plain,
    ! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/FINITE\'' @ TA @ C )
      | ( ( '\'const/iterate/sum\'' @ TA @ C
          @ ^ [D: TA] : ( '\'const/realax/real_sub\'' @ ( A @ D ) @ ( B @ D ) ) )
       != ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 )
          @ ^ [D: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( sk1 @ D ) @ ( sk2 @ D ) ) ) )
      | ( ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) )
       != ( '\'const/realax/real_sub\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk1 ) @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10,7]) ).

thf(18,plain,
    ( ~ ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) )
    | ( ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 )
        @ ^ [A: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
     != ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 )
        @ ^ [A: '\'type/nums/num\''] : ( '\'const/realax/real_sub\'' @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( '\'const/iterate/..\'' @ sk3 @ sk4 )),bind_type(TA,$thf( '\'type/nums/num\'' ))]]) ).

thf(25,plain,
    ~ ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk3 @ sk4 ) ),
    inference(simp,[status(thm)],[18]) ).

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(12,plain,
    ! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] : ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ A @ B ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(29,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[25,12]) ).

thf(30,plain,
    $false,
    inference(simp,[status(thm)],[29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : ANA106^1 : TPTP v8.2.0. Released v7.0.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n018.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 07:41:54 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.97/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.16/0.97  % [INFO] 	 Parsing done (114ms). 
% 1.16/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.63/1.19  % [INFO] 	 nitpick registered as external prover. 
% 1.63/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.82/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 1.91/1.27  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.91/1.28  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.91/1.29  % [INFO] 	 Type checking passed. 
% 1.91/1.29  % [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 ... 
% 3.68/1.83  % [INFO] 	 Killing All external provers ... 
% 3.68/1.83  % Time passed: 1309ms (effective reasoning time: 849ms)
% 3.68/1.83  % 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)>
% 3.68/1.83  % Axioms used in derivation (2): thm/iterate/SUM_SUB_, thm/iterate/FINITE_NUMSEG_
% 3.68/1.83  % No. of inferences in proof: 17
% 3.68/1.83  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1309 ms resp. 849 ms w/o parsing
% 3.68/1.89  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.68/1.89  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------