TSTP Solution File: SYN051+1 by LEO-II---1.7.0

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%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN051+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% 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  : 600s
% DateTime : Thu Jul 21 08:22:59 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   36 (  19 unt;   4 typ;   0 def)
%            Number of atoms       :  146 (  38 equ;   0 cnn)
%            Maximal formula atoms :    2 (   4 avg)
%            Number of connectives :  103 (  31   ~;  28   |;   2   &;  34   @)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   5 con; 0-2 aty)
%            Number of variables   :   26 (   0   ^  18   !;   8   ?;  26   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_big_f,type,
    big_f: $i > $o ).

thf(tp_p,type,
    p: $o ).

thf(tp_sK1_X,type,
    sK1_X: $i ).

thf(tp_sK2_X,type,
    sK2_X: $i ).

thf(1,axiom,
    ? [X: $i] :
      ( ( big_f @ X )
     => p ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel21_2) ).

thf(2,axiom,
    ? [X: $i] :
      ( p
     => ( big_f @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel21_1) ).

thf(3,conjecture,
    ? [X: $i] :
      ( p
    <=> ( big_f @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel21) ).

thf(4,negated_conjecture,
    ( ( ? [X: $i] :
          ( p
        <=> ( big_f @ X ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[3]) ).

thf(5,plain,
    ( ( ? [X: $i] :
          ( p
        <=> ( big_f @ X ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ? [X: $i] :
          ( ( big_f @ X )
         => p ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(7,plain,
    ( ( ? [X: $i] :
          ( p
         => ( big_f @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(8,plain,
    ( ( ~ ? [X: $i] :
            ( p
          <=> ( big_f @ X ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(9,plain,
    ( ( ( ! [X: $i] :
            ~ ( big_f @ X )
        | ~ p )
      & ( ! [X: $i] : ( big_f @ X )
        | p ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    ( ( ~ ( big_f @ sK1_X )
      | p )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(11,plain,
    ( ( ~ p
      | ( big_f @ sK2_X ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(12,plain,
    ( ( ~ p
      | ( big_f @ sK2_X ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(13,plain,
    ( ( ~ ( big_f @ sK1_X )
      | p )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(14,plain,
    ( ( ( ! [X: $i] :
            ~ ( big_f @ X )
        | ~ p )
      & ( ! [X: $i] : ( big_f @ X )
        | p ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(15,plain,
    ( ( ~ ( ~ ( ! [SX0: $i] :
                  ~ ( big_f @ SX0 )
              | ~ p )
          | ~ ( ! [SX0: $i] : ( big_f @ SX0 )
              | p ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ( ~ p )
      = $true )
    | ( ( big_f @ sK2_X )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12]) ).

thf(17,plain,
    ( ( ( ~ ( big_f @ sK1_X ) )
      = $true )
    | ( p = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13]) ).

thf(18,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( big_f @ SX0 )
          | ~ p )
      | ~ ( ! [SX0: $i] : ( big_f @ SX0 )
          | p ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(19,plain,
    ( ( p = $false )
    | ( ( big_f @ sK2_X )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ( big_f @ sK1_X )
      = $false )
    | ( p = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( big_f @ SX0 )
          | ~ p ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ~ ( ! [SX0: $i] : ( big_f @ SX0 )
          | p ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[18]) ).

thf(23,plain,
    ( ( ! [SX0: $i] :
          ~ ( big_f @ SX0 )
      | ~ p )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[21]) ).

thf(24,plain,
    ( ( ! [SX0: $i] : ( big_f @ SX0 )
      | p )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[22]) ).

thf(25,plain,
    ( ( ( ! [SX0: $i] :
            ~ ( big_f @ SX0 ) )
      = $true )
    | ( ( ~ p )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(26,plain,
    ( ( ( ! [SX0: $i] : ( big_f @ SX0 ) )
      = $true )
    | ( p = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[24]) ).

thf(27,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( big_f @ SV1 ) )
        = $true )
      | ( ( ~ p )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(28,plain,
    ! [SV2: $i] :
      ( ( ( big_f @ SV2 )
        = $true )
      | ( p = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(29,plain,
    ! [SV1: $i] :
      ( ( ( big_f @ SV1 )
        = $false )
      | ( ( ~ p )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(30,plain,
    ! [SV1: $i] :
      ( ( p = $false )
      | ( ( big_f @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(31,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[19,30,28,20]) ).

thf(32,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SYN051+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n018.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue Jul 12 03:12:59 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 2
% 0.13/0.36  
% 0.13/0.36   Length.of.Defs: 0
% 0.13/0.36  
% 0.13/0.36   Contains.Choice.Funs: false
% 0.13/0.36  (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:4,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.13/0.38  
% 0.13/0.38  ********************************
% 0.13/0.38  *   All subproblems solved!    *
% 0.13/0.38  ********************************
% 0.13/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.38  
% 0.13/0.38  %**** Beginning of derivation protocol ****
% 0.13/0.38  % SZS output start CNFRefutation
% See solution above
% 0.13/0.38  
% 0.13/0.38  %**** End of derivation protocol ****
% 0.13/0.38  %**** no. of clauses in derivation: 32 ****
% 0.13/0.38  %**** clause counter: 31 ****
% 0.13/0.38  
% 0.13/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------