TSTP Solution File: COM003_1 by Leo-III---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : COM003_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n017.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 Jun 24 04:56:17 EDT 2024

% Result   : Theorem 2.87s 1.51s
% Output   : Refutation 2.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   24 (   4 unt;  12 typ;   0 def)
%            Number of atoms       :   68 (   0 equ;   0 cnn)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  260 (  17   ~;   0   |;  28   &; 187   @)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   9 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   47 (   0   ^  32   !;  15   ?;  47   :)

% Comments : 
%------------------------------------------------------------------------------
thf(program_type,type,
    program: $tType ).

thf(algorithm_type,type,
    algorithm: $tType ).

thf(input_type,type,
    input: $tType ).

thf(output_type,type,
    output: $tType ).

thf(bad_type,type,
    bad: output ).

thf(good_type,type,
    good: output ).

thf(decides_type,type,
    decides: algorithm > program > input > $o ).

thf(halts2_type,type,
    halts2: program > input > $o ).

thf(halts3_type,type,
    halts3: program > program > input > $o ).

thf(outputs_type,type,
    outputs: program > output > $o ).

thf(algorithm_of_type,type,
    algorithm_of: program > algorithm ).

thf(as_input_type,type,
    as_input: program > input ).

thf(3,axiom,
    ( ? [A: algorithm] :
      ! [B: program,C: input] : ( decides @ A @ B @ C )
   => ? [A: program] :
      ! [B: program,C: input] : ( decides @ ( algorithm_of @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

thf(10,plain,
    ( ? [A: algorithm] :
      ! [B: program,C: input] : ( decides @ A @ B @ C )
   => ? [A: program] :
      ! [B: program,C: input] : ( decides @ ( algorithm_of @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ( ? [A: program] :
      ! [B: program] :
        ( ( ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts3 @ A @ B @ ( as_input @ B ) )
            & ( outputs @ A @ good ) ) )
        & ( ~ ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts3 @ A @ B @ ( as_input @ B ) )
            & ( outputs @ A @ bad ) ) ) )
   => ? [A: program] :
      ! [B: program] :
        ( ( ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts2 @ A @ ( as_input @ B ) )
            & ( outputs @ A @ good ) ) )
        & ( ~ ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts2 @ A @ ( as_input @ B ) )
            & ( outputs @ A @ bad ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

thf(20,plain,
    ( ? [A: program] :
      ! [B: program] :
        ( ( ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts3 @ A @ B @ ( as_input @ B ) )
            & ( outputs @ A @ good ) ) )
        & ( ~ ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts3 @ A @ B @ ( as_input @ B ) )
            & ( outputs @ A @ bad ) ) ) )
   => ? [A: program] :
      ! [B: program] :
        ( ( ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts2 @ A @ ( as_input @ B ) )
            & ( outputs @ A @ good ) ) )
        & ( ~ ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts2 @ A @ ( as_input @ B ) )
            & ( outputs @ A @ bad ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(6,axiom,
    ( ? [A: program] :
      ! [B: program] :
        ( ( ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts2 @ A @ ( as_input @ B ) )
            & ( outputs @ A @ good ) ) )
        & ( ~ ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts2 @ A @ ( as_input @ B ) )
            & ( outputs @ A @ bad ) ) ) )
   => ? [A: program] :
      ! [B: program] :
        ( ( ( halts2 @ B @ ( as_input @ B ) )
         => ~ ( halts2 @ A @ ( as_input @ B ) ) )
        & ( ~ ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts2 @ A @ ( as_input @ B ) )
            & ( outputs @ A @ bad ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).

thf(34,plain,
    ( ? [A: program] :
      ! [B: program] :
        ( ( ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts2 @ A @ ( as_input @ B ) )
            & ( outputs @ A @ good ) ) )
        & ( ~ ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts2 @ A @ ( as_input @ B ) )
            & ( outputs @ A @ bad ) ) ) )
   => ? [A: program] :
      ! [B: program] :
        ( ( ( halts2 @ B @ ( as_input @ B ) )
         => ~ ( halts2 @ A @ ( as_input @ B ) ) )
        & ( ~ ( halts2 @ B @ ( as_input @ B ) )
         => ( ( halts2 @ A @ ( as_input @ B ) )
            & ( outputs @ A @ bad ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [A: program,B: program,C: input] :
      ( ( decides @ ( algorithm_of @ A ) @ B @ C )
     => ! [D: program,E: input] :
          ( ( ( halts2 @ D @ E )
           => ( ( halts3 @ A @ D @ E )
              & ( outputs @ A @ good ) ) )
          & ( ~ ( halts2 @ D @ E )
           => ( ( halts3 @ A @ D @ E )
              & ( outputs @ A @ bad ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

thf(12,plain,
    ! [A: program,B: program,C: input] :
      ( ( decides @ ( algorithm_of @ A ) @ B @ C )
     => ! [D: program,E: input] :
          ( ( ( halts2 @ D @ E )
           => ( ( halts3 @ A @ D @ E )
              & ( outputs @ A @ good ) ) )
          & ( ~ ( halts2 @ D @ E )
           => ( ( halts3 @ A @ D @ E )
              & ( outputs @ A @ bad ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1,conjecture,
    ~ ? [A: algorithm] :
      ! [B: program,C: input] : ( decides @ A @ B @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

thf(2,negated_conjecture,
    ~ ~ ? [A: algorithm] :
        ! [B: program,C: input] : ( decides @ A @ B @ C ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ~ ? [A: algorithm] :
        ! [B: program,C: input] : ( decides @ A @ B @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(49,plain,
    $false,
    inference(e,[status(thm)],[10,20,34,12,7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : COM003_1 : TPTP v8.2.0. Released v5.0.0.
% 0.00/0.09  % Command  : run_Leo-III %s %d THM
% 0.09/0.27  % Computer : n017.cluster.edu
% 0.09/0.27  % Model    : x86_64 x86_64
% 0.09/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27  % Memory   : 8042.1875MB
% 0.09/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27  % CPULimit : 300
% 0.09/0.27  % WCLimit  : 300
% 0.09/0.27  % DateTime : Fri Jun 21 00:14:40 EDT 2024
% 0.09/0.27  % CPUTime  : 
% 0.81/0.72  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.01/0.83  % [INFO] 	 Parsing done (113ms). 
% 1.01/0.84  % [INFO] 	 Running in sequential loop mode. 
% 1.47/1.04  % [INFO] 	 eprover registered as external prover. 
% 1.47/1.04  % [INFO] 	 Scanning for conjecture ... 
% 1.65/1.10  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 1.65/1.12  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.65/1.14  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 1.65/1.15  % [INFO] 	 Type checking passed. 
% 1.65/1.15  % [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 ... 
% 2.87/1.51  % External prover 'e' found a proof!
% 2.87/1.51  % [INFO] 	 Killing All external provers ... 
% 2.87/1.51  % Time passed: 1071ms (effective reasoning time: 667ms)
% 2.87/1.51  % 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)>
% 2.87/1.51  % Axioms used in derivation (4): p1, p3, p4, p2
% 2.87/1.51  % No. of inferences in proof: 12
% 2.87/1.51  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1071 ms resp. 667 ms w/o parsing
% 2.97/1.54  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.97/1.54  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------