TSTP Solution File: SYN078+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYN078+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.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 : Tue May 21 08:17:26 EDT 2024

% Result   : Theorem 2.93s 1.98s
% Output   : Refutation 3.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   34 (   6 unt;   6 typ;   0 def)
%            Number of atoms       :   79 (  13 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  139 (  28   ~;  28   |;   5   &;  66   @)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   6 con; 0-2 aty)
%            Number of variables   :   21 (   0   ^  17   !;   4   ?;  21   :)

% Comments : 
%------------------------------------------------------------------------------
thf(big_p_type,type,
    big_p: $i > $o ).

thf(f_type,type,
    f: $i > $i ).

thf(sk1_type,type,
    sk1: $o ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(1,conjecture,
    ( ! [A: $i] :
        ( ? [B: $i] :
            ( ( big_p @ B )
            & ( A
              = ( f @ B ) ) )
       => ( big_p @ A ) )
  <=> ! [A: $i] :
        ( ( big_p @ A )
       => ( big_p @ ( f @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel56) ).

thf(2,negated_conjecture,
    ~ ( ! [A: $i] :
          ( ? [B: $i] :
              ( ( big_p @ B )
              & ( A
                = ( f @ B ) ) )
         => ( big_p @ A ) )
    <=> ! [A: $i] :
          ( ( big_p @ A )
         => ( big_p @ ( f @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ! [A: $i] :
            ( ? [B: $i] :
                ( ( big_p @ B )
                & ( A
                  = ( f @ B ) ) )
           => ( big_p @ A ) )
       => ! [A: $i] :
            ( ( big_p @ A )
           => ( big_p @ ( f @ A ) ) ) )
      & ( ! [A: $i] :
            ( ( big_p @ A )
           => ( big_p @ ( f @ A ) ) )
       => ! [A: $i] :
            ( ? [B: $i] :
                ( ( big_p @ B )
                & ( A
                  = ( f @ B ) ) )
           => ( big_p @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    ( sk1
    | ~ ( big_p @ sk3 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ( ( big_p @ sk2 )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_p @ B )
      | ( A
       != ( f @ B ) )
      | ( big_p @ A )
      | ~ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( f @ B ) )
      | ~ ( big_p @ B )
      | ( big_p @ A )
      | ~ sk1 ),
    inference(lifteq,[status(thm)],[9]) ).

thf(12,plain,
    ! [A: $i] :
      ( ~ ( big_p @ A )
      | ( big_p @ ( f @ A ) )
      | ~ sk1 ),
    inference(simp,[status(thm)],[11]) ).

thf(5,plain,
    ( ~ ( big_p @ ( f @ sk2 ) )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(23,plain,
    ! [A: $i] :
      ( ~ ( big_p @ A )
      | ~ sk1
      | ( ( big_p @ ( f @ A ) )
       != ( big_p @ ( f @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,5]) ).

thf(24,plain,
    ( ~ ( big_p @ sk2 )
    | ~ sk1 ),
    inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk2 ))]]) ).

thf(35,plain,
    ( ~ sk1
    | ( ( big_p @ sk2 )
     != ( big_p @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[10,24]) ).

thf(36,plain,
    ~ sk1,
    inference(pattern_uni,[status(thm)],[35:[]]) ).

thf(64,plain,
    ( $false
    | ~ ( big_p @ sk3 ) ),
    inference(rewrite,[status(thm)],[7,36]) ).

thf(65,plain,
    ~ ( big_p @ sk3 ),
    inference(simp,[status(thm)],[64]) ).

thf(6,plain,
    ( sk1
    | ( big_p @ sk4 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [A: $i] :
      ( sk1
      | ~ ( big_p @ A )
      | ( big_p @ ( f @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(13,plain,
    ! [A: $i] :
      ( sk1
      | ~ ( big_p @ A )
      | ( big_p @ ( f @ A ) ) ),
    inference(simp,[status(thm)],[8]) ).

thf(47,plain,
    ! [A: $i] :
      ( sk1
      | ( big_p @ ( f @ A ) )
      | ( ( big_p @ sk4 )
       != ( big_p @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[6,13]) ).

thf(48,plain,
    ( sk1
    | ( big_p @ ( f @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( sk4 ))]]) ).

thf(4,plain,
    ( sk1
    | ( sk3
      = ( f @ sk4 ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ( ( ( f @ sk4 )
      = sk3 )
    | sk1 ),
    inference(lifteq,[status(thm)],[4]) ).

thf(58,plain,
    ( ( ( f @ sk4 )
      = sk3 )
    | $false ),
    inference(rewrite,[status(thm)],[14,36]) ).

thf(59,plain,
    ( ( f @ sk4 )
    = sk3 ),
    inference(simp,[status(thm)],[58]) ).

thf(72,plain,
    ( $false
    | ( big_p @ sk3 ) ),
    inference(rewrite,[status(thm)],[48,36,59]) ).

thf(73,plain,
    big_p @ sk3,
    inference(simp,[status(thm)],[72]) ).

thf(74,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[65,73]) ).

thf(75,plain,
    $false,
    inference(simp,[status(thm)],[74]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SYN078+1 : TPTP v8.2.0. Released v2.0.0.
% 0.05/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.33  % Computer : n014.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Mon May 20 13:44:09 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.76/0.77  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.00/0.88  % [INFO] 	 Parsing done (114ms). 
% 1.00/0.89  % [INFO] 	 Running in sequential loop mode. 
% 1.53/1.24  % [INFO] 	 nitpick registered as external prover. 
% 1.53/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.58/1.31  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.76/1.33  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.76/1.33  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.76/1.34  % [INFO] 	 Type checking passed. 
% 1.76/1.34  % [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 ... 
% 2.93/1.98  % [INFO] 	 Killing All external provers ... 
% 2.93/1.98  % Time passed: 1548ms (effective reasoning time: 1083ms)
% 2.93/1.98  % 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)>
% 2.93/1.98  % Axioms used in derivation (0): 
% 2.93/1.98  % No. of inferences in proof: 28
% 2.93/1.98  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1548 ms resp. 1083 ms w/o parsing
% 3.07/2.02  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.07/2.02  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------