TSTP Solution File: SYN343+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN343+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 : n007.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 08:25:22 EDT 2022

% Result   : Theorem 0.11s 0.35s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   30 (  20 unt;   2 typ;   0 def)
%            Number of atoms       :  162 (  33 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :  350 (  68   ~;  48   |;   8   &; 214   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2 usr;   2 con; 0-2 aty)
%            Number of variables   :   72 (   0   ^  60   !;  12   ?;  72   :)

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

thf(tp_sK1_Z,type,
    sK1_Z: $i > $i > $i ).

thf(1,conjecture,
    ? [X: $i,Y1: $i,Y2: $i] :
    ! [Z: $i] :
      ( ( ( ( big_f @ X @ Y1 )
         => ( big_f @ Z @ X ) )
       => ( big_f @ X @ X ) )
     => ( ( big_f @ X @ X )
        & ( big_f @ Y1 @ Y2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_16_2) ).

thf(2,negated_conjecture,
    ( ( ? [X: $i,Y1: $i,Y2: $i] :
        ! [Z: $i] :
          ( ( ( ( big_f @ X @ Y1 )
             => ( big_f @ Z @ X ) )
           => ( big_f @ X @ X ) )
         => ( ( big_f @ X @ X )
            & ( big_f @ Y1 @ Y2 ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ? [X: $i,Y1: $i,Y2: $i] :
        ! [Z: $i] :
          ( ( ( ( big_f @ X @ Y1 )
             => ( big_f @ Z @ X ) )
           => ( big_f @ X @ X ) )
         => ( ( big_f @ X @ X )
            & ( big_f @ Y1 @ Y2 ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ~ ? [X: $i,Y1: $i,Y2: $i] :
          ! [Z: $i] :
            ( ( ( ( big_f @ X @ Y1 )
               => ( big_f @ Z @ X ) )
             => ( big_f @ X @ X ) )
           => ( ( big_f @ X @ X )
              & ( big_f @ Y1 @ Y2 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [X: $i,Y1: $i] :
          ( ( ( big_f @ X @ Y1 )
            | ( big_f @ X @ X ) )
          & ( ~ ( big_f @ ( sK1_Z @ Y1 @ X ) @ X )
            | ( big_f @ X @ X ) )
          & ( ~ ( big_f @ X @ X )
            | ! [Y2: $i] :
                ~ ( big_f @ Y1 @ Y2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [X: $i,Y1: $i] :
          ( ( ( big_f @ X @ Y1 )
            | ( big_f @ X @ X ) )
          & ( ~ ( big_f @ ( sK1_Z @ Y1 @ X ) @ X )
            | ( big_f @ X @ X ) )
          & ( ~ ( big_f @ X @ X )
            | ! [Y2: $i] :
                ~ ( big_f @ Y1 @ Y2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ~ ( ~ ( ( big_f @ SX0 @ SX1 )
                      | ( big_f @ SX0 @ SX0 ) )
                  | ~ ( ~ ( big_f @ ( sK1_Z @ SX1 @ SX0 ) @ SX0 )
                      | ( big_f @ SX0 @ SX0 ) ) )
            | ~ ( ~ ( big_f @ SX0 @ SX0 )
                | ! [SX2: $i] :
                    ~ ( big_f @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(8,plain,
    ! [SV1: $i] :
      ( ( ! [SY4: $i] :
            ~ ( ~ ~ ( ~ ( ( big_f @ SV1 @ SY4 )
                        | ( big_f @ SV1 @ SV1 ) )
                    | ~ ( ~ ( big_f @ ( sK1_Z @ SY4 @ SV1 ) @ SV1 )
                        | ( big_f @ SV1 @ SV1 ) ) )
              | ~ ( ~ ( big_f @ SV1 @ SV1 )
                  | ! [SX2: $i] :
                      ~ ( big_f @ SY4 @ SX2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7]) ).

thf(9,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( ~ ~ ( ~ ( ( big_f @ SV1 @ SV2 )
                      | ( big_f @ SV1 @ SV1 ) )
                  | ~ ( ~ ( big_f @ ( sK1_Z @ SV2 @ SV1 ) @ SV1 )
                      | ( big_f @ SV1 @ SV1 ) ) )
            | ~ ( ~ ( big_f @ SV1 @ SV1 )
                | ! [SY6: $i] :
                    ~ ( big_f @ SV2 @ SY6 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8]) ).

thf(10,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ~ ( ~ ( ( big_f @ SV1 @ SV2 )
                  | ( big_f @ SV1 @ SV1 ) )
              | ~ ( ~ ( big_f @ ( sK1_Z @ SV2 @ SV1 ) @ SV1 )
                  | ( big_f @ SV1 @ SV1 ) ) )
        | ~ ( ~ ( big_f @ SV1 @ SV1 )
            | ! [SY6: $i] :
                ~ ( big_f @ SV2 @ SY6 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[9]) ).

thf(11,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ~ ( ~ ( ( big_f @ SV1 @ SV2 )
                  | ( big_f @ SV1 @ SV1 ) )
              | ~ ( ~ ( big_f @ ( sK1_Z @ SV2 @ SV1 ) @ SV1 )
                  | ( big_f @ SV1 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[10]) ).

thf(12,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( ~ ( big_f @ SV1 @ SV1 )
            | ! [SY6: $i] :
                ~ ( big_f @ SV2 @ SY6 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[10]) ).

thf(13,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( ~ ( ( big_f @ SV1 @ SV2 )
                | ( big_f @ SV1 @ SV1 ) )
            | ~ ( ~ ( big_f @ ( sK1_Z @ SV2 @ SV1 ) @ SV1 )
                | ( big_f @ SV1 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[11]) ).

thf(14,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( big_f @ SV1 @ SV1 )
        | ! [SY6: $i] :
            ~ ( big_f @ SV2 @ SY6 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( ( big_f @ SV1 @ SV2 )
            | ( big_f @ SV1 @ SV1 ) )
        | ~ ( ~ ( big_f @ ( sK1_Z @ SV2 @ SV1 ) @ SV1 )
            | ( big_f @ SV1 @ SV1 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(16,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( ~ ( big_f @ SV1 @ SV1 ) )
        = $true )
      | ( ( ! [SY6: $i] :
              ~ ( big_f @ SV2 @ SY6 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14]) ).

thf(17,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( ( big_f @ SV1 @ SV2 )
            | ( big_f @ SV1 @ SV1 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(18,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ~ ( big_f @ ( sK1_Z @ SV2 @ SV1 ) @ SV1 )
            | ( big_f @ SV1 @ SV1 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( big_f @ SV1 @ SV1 )
        = $false )
      | ( ( ! [SY6: $i] :
              ~ ( big_f @ SV2 @ SY6 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(20,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( big_f @ SV1 @ SV2 )
        | ( big_f @ SV1 @ SV1 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( big_f @ ( sK1_Z @ SV2 @ SV1 ) @ SV1 )
        | ( big_f @ SV1 @ SV1 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV1: $i,SV3: $i,SV2: $i] :
      ( ( ( ~ ( big_f @ SV2 @ SV3 ) )
        = $true )
      | ( ( big_f @ SV1 @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( big_f @ SV1 @ SV2 )
        = $true )
      | ( ( big_f @ SV1 @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( big_f @ ( sK1_Z @ SV2 @ SV1 ) @ SV1 ) )
        = $true )
      | ( ( big_f @ SV1 @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[21]) ).

thf(25,plain,
    ! [SV1: $i,SV3: $i,SV2: $i] :
      ( ( ( big_f @ SV2 @ SV3 )
        = $false )
      | ( ( big_f @ SV1 @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( big_f @ ( sK1_Z @ SV2 @ SV1 ) @ SV1 )
        = $false )
      | ( ( big_f @ SV1 @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(27,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[23,26,25]) ).

thf(28,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SYN343+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.31  % Computer : n007.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 600
% 0.11/0.31  % DateTime : Mon Jul 11 20:25:48 EDT 2022
% 0.11/0.31  % CPUTime  : 
% 0.11/0.32  
% 0.11/0.32   No.of.Axioms: 0
% 0.11/0.32  
% 0.11/0.32   Length.of.Defs: 0
% 0.11/0.32  
% 0.11/0.32   Contains.Choice.Funs: false
% 0.11/0.32  (rf:0,axioms:0,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:2,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.11/0.35  
% 0.11/0.35  ********************************
% 0.11/0.35  *   All subproblems solved!    *
% 0.11/0.35  ********************************
% 0.11/0.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.35  
% 0.11/0.35  %**** Beginning of derivation protocol ****
% 0.11/0.35  % SZS output start CNFRefutation
% See solution above
% 0.11/0.35  
% 0.11/0.35  %**** End of derivation protocol ****
% 0.11/0.35  %**** no. of clauses in derivation: 28 ****
% 0.11/0.35  %**** clause counter: 27 ****
% 0.11/0.35  
% 0.11/0.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------