TSTP Solution File: ANA107^1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : ANA107^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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 3.47s 2.20s
% Output   : Refutation 3.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   24 (   2 unt;  10 typ;   0 def)
%            Number of atoms       :   34 (   1 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  155 (   8   ~;   2   |;   0   &; 143   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   8 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :   38 (   9   ^  27   !;   0   ?;  38   :)
%                                         (   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_le\'_type',type,
    '\'const/realax/real_le\'': '\'type/realax/real\'' > '\'type/realax/real\'' > $o ).

thf('\'const/realax/real_abs\'_type',type,
    '\'const/realax/real_abs\'': '\'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\'' ).

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

thf(3,axiom,
    ! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > $o] :
      ( ( '\'const/sets/FINITE\'' @ TA @ B )
     => ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) )
        @ ( '\'const/iterate/sum\'' @ TA @ B
          @ ^ [C: TA] : ( '\'const/realax/real_abs\'' @ ( A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_ABS_') ).

thf(7,plain,
    ! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > $o] :
      ( ( '\'const/sets/FINITE\'' @ TA @ B )
     => ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) )
        @ ( '\'const/iterate/sum\'' @ TA @ B
          @ ^ [C: TA] : ( '\'const/realax/real_abs\'' @ ( A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,plain,
    ! [TA: $tType,B: TA > $o,A: TA > '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/FINITE\'' @ TA @ B )
      | ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) )
        @ ( '\'const/iterate/sum\'' @ TA @ B
          @ ^ [C: TA] : ( '\'const/realax/real_abs\'' @ ( A @ C ) ) ) ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(1,conjecture,
    ! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
      ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ '\'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_abs\'' @ ( A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_ABS_NUMSEG_') ).

thf(2,negated_conjecture,
    ~ ! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
        ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ '\'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_abs\'' @ ( A @ D ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ! [A: '\'type/nums/num\'' > '\'type/realax/real\'',B: '\'type/nums/num\'',C: '\'type/nums/num\''] :
        ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ '\'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_abs\'' @ ( A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    ~ ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 ) @ sk1 ) )
      @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 )
        @ ^ [A: '\'type/nums/num\''] : ( '\'const/realax/real_abs\'' @ ( sk1 @ A ) ) ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(11,plain,
    ! [TA: $tType,B: TA > $o,A: TA > '\'type/realax/real\''] :
      ( ~ ( '\'const/sets/FINITE\'' @ TA @ B )
      | ( ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ TA @ B @ A ) )
          @ ( '\'const/iterate/sum\'' @ TA @ B
            @ ^ [C: TA] : ( '\'const/realax/real_abs\'' @ ( A @ C ) ) ) )
       != ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 ) @ sk1 ) )
          @ ( '\'const/iterate/sum\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 )
            @ ^ [C: '\'type/nums/num\''] : ( '\'const/realax/real_abs\'' @ ( sk1 @ C ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,6]) ).

thf(12,plain,
    ~ ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( sk1 )),bind(B,$thf( '\'const/iterate/..\'' @ sk2 @ sk3 )),bind_type(TA,$thf( '\'type/nums/num\'' ))]]) ).

thf(4,axiom,
    ! [A: '\'type/nums/num\'',B: '\'type/nums/num\''] : ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/FINITE_NUMSEG_') ).

thf(9,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(10,plain,
    ! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] : ( '\'const/sets/FINITE\'' @ '\'type/nums/num\'' @ ( '\'const/iterate/..\'' @ A @ B ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(15,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[12,10]) ).

thf(16,plain,
    $false,
    inference(simp,[status(thm)],[15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : ANA107^1 : TPTP v8.2.0. Released v7.0.0.
% 0.05/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n024.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Mon May 20 07:51:24 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 1.00/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.31/1.12  % [INFO] 	 Parsing done (164ms). 
% 1.31/1.13  % [INFO] 	 Running in sequential loop mode. 
% 1.89/1.49  % [INFO] 	 nitpick registered as external prover. 
% 1.89/1.50  % [INFO] 	 Scanning for conjecture ... 
% 2.06/1.59  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 2.06/1.62  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 2.06/1.63  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.06/1.64  % [INFO] 	 Type checking passed. 
% 2.25/1.64  % [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 ... 
% 3.47/2.20  % [INFO] 	 Killing All external provers ... 
% 3.47/2.20  % Time passed: 1723ms (effective reasoning time: 1064ms)
% 3.47/2.20  % 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)>
% 3.47/2.20  % Axioms used in derivation (2): thm/iterate/SUM_ABS_, thm/iterate/FINITE_NUMSEG_
% 3.47/2.20  % No. of inferences in proof: 14
% 3.47/2.20  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1723 ms resp. 1064 ms w/o parsing
% 3.49/2.28  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.49/2.28  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------