TSTP Solution File: SYN980+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN980+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% 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  : 600s
% DateTime : Thu Jul 21 08:30:58 EDT 2022

% Result   : Theorem 0.12s 0.37s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   44 (  27 unt;   5 typ;   0 def)
%            Number of atoms       :  207 (  48 equ;   0 cnn)
%            Maximal formula atoms :    6 (   5 avg)
%            Number of connectives :  352 (  51   ~;  42   |;  10   &; 229   @)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   79 (   0   ^  67   !;  12   ?;  79   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_f,type,
    f: $i > $i ).

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

thf(tp_q,type,
    q: $i > $i > $o ).

thf(tp_r,type,
    r: $i > $o ).

thf(tp_sK1_B,type,
    sK1_B: $i ).

thf(1,conjecture,
    ! [B: $i] :
      ( ! [Y: $i] :
          ( ( ( r @ B )
           => ( r @ Y ) )
         => ( p @ ( f @ Y ) @ Y ) )
     => ? [X: $i,Y: $i] :
          ( ( p @ X @ Y )
          & ( ( q @ ( f @ B ) @ B )
           => ( q @ X @ Y ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

thf(2,negated_conjecture,
    ( ( ! [B: $i] :
          ( ! [Y: $i] :
              ( ( ( r @ B )
               => ( r @ Y ) )
             => ( p @ ( f @ Y ) @ Y ) )
         => ? [X: $i,Y: $i] :
              ( ( p @ X @ Y )
              & ( ( q @ ( f @ B ) @ B )
               => ( q @ X @ Y ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [B: $i] :
          ( ! [Y: $i] :
              ( ( ( r @ B )
               => ( r @ Y ) )
             => ( p @ ( f @ Y ) @ Y ) )
         => ? [X: $i,Y: $i] :
              ( ( p @ X @ Y )
              & ( ( q @ ( f @ B ) @ B )
               => ( q @ X @ Y ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY4: $i] :
          ( ( ( r @ sK1_B )
           => ( r @ SY4 ) )
         => ( p @ ( f @ SY4 ) @ SY4 ) )
     => ? [SY5: $i,SY6: $i] :
          ( ( p @ SY5 @ SY6 )
          & ( ( q @ ( f @ sK1_B ) @ sK1_B )
           => ( q @ SY5 @ SY6 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY4: $i] :
          ( ( ( r @ sK1_B )
           => ( r @ SY4 ) )
         => ( p @ ( f @ SY4 ) @ SY4 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ? [SY5: $i,SY6: $i] :
          ( ( p @ SY5 @ SY6 )
          & ( ( q @ ( f @ sK1_B ) @ sK1_B )
           => ( q @ SY5 @ SY6 ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ~ ? [SY5: $i,SY6: $i] :
            ( ( p @ SY5 @ SY6 )
            & ( ( q @ ( f @ sK1_B ) @ sK1_B )
             => ( q @ SY5 @ SY6 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ( ( q @ ( f @ sK1_B ) @ sK1_B )
        | ! [SY5: $i,SY6: $i] :
            ~ ( p @ SY5 @ SY6 ) )
      & ! [SY5: $i,SY6: $i] :
          ( ~ ( q @ SY5 @ SY6 )
          | ~ ( p @ SY5 @ SY6 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(9,plain,
    ( ( ( ( r @ sK1_B )
        | ! [SY4: $i] : ( p @ ( f @ SY4 ) @ SY4 ) )
      & ! [SY4: $i] :
          ( ~ ( r @ SY4 )
          | ( p @ ( f @ SY4 ) @ SY4 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(10,plain,
    ( ( ( ( r @ sK1_B )
        | ! [SY4: $i] : ( p @ ( f @ SY4 ) @ SY4 ) )
      & ! [SY4: $i] :
          ( ~ ( r @ SY4 )
          | ( p @ ( f @ SY4 ) @ SY4 ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ( ( q @ ( f @ sK1_B ) @ sK1_B )
        | ! [SY5: $i,SY6: $i] :
            ~ ( p @ SY5 @ SY6 ) )
      & ! [SY5: $i,SY6: $i] :
          ( ~ ( q @ SY5 @ SY6 )
          | ~ ( p @ SY5 @ SY6 ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(12,plain,
    ( ( ~ ( ~ ( ( q @ ( f @ sK1_B ) @ sK1_B )
              | ! [SX0: $i,SX1: $i] :
                  ~ ( p @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( q @ SX0 @ SX1 )
                | ~ ( p @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(13,plain,
    ( ( ~ ( ~ ( ( r @ sK1_B )
              | ! [SX0: $i] : ( p @ ( f @ SX0 ) @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( r @ SX0 )
                | ( p @ ( f @ SX0 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(14,plain,
    ( ( ~ ( ( q @ ( f @ sK1_B ) @ sK1_B )
          | ! [SX0: $i,SX1: $i] :
              ~ ( p @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( q @ SX0 @ SX1 )
            | ~ ( p @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ( ( ~ ( ( r @ sK1_B )
          | ! [SX0: $i] : ( p @ ( f @ SX0 ) @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( r @ SX0 )
            | ( p @ ( f @ SX0 ) @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ( ( q @ ( f @ sK1_B ) @ sK1_B )
          | ! [SX0: $i,SX1: $i] :
              ~ ( p @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( q @ SX0 @ SX1 )
            | ~ ( p @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ~ ( ( r @ sK1_B )
          | ! [SX0: $i] : ( p @ ( f @ SX0 ) @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( r @ SX0 )
            | ( p @ ( f @ SX0 ) @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(20,plain,
    ( ( ( q @ ( f @ sK1_B ) @ sK1_B )
      | ! [SX0: $i,SX1: $i] :
          ~ ( p @ SX0 @ SX1 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(21,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( q @ SX0 @ SX1 )
          | ~ ( p @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(22,plain,
    ( ( ( r @ sK1_B )
      | ! [SX0: $i] : ( p @ ( f @ SX0 ) @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(23,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( r @ SX0 )
          | ( p @ ( f @ SX0 ) @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(24,plain,
    ( ( ( q @ ( f @ sK1_B ) @ sK1_B )
      = $true )
    | ( ( ! [SX0: $i,SX1: $i] :
            ~ ( p @ SX0 @ SX1 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[20]) ).

thf(25,plain,
    ! [SV1: $i] :
      ( ( ! [SY7: $i] :
            ( ~ ( q @ SV1 @ SY7 )
            | ~ ( p @ SV1 @ SY7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(26,plain,
    ( ( ( r @ sK1_B )
      = $true )
    | ( ( ! [SX0: $i] : ( p @ ( f @ SX0 ) @ SX0 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV2: $i] :
      ( ( ~ ( r @ SV2 )
        | ( p @ ( f @ SV2 ) @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV3: $i] :
      ( ( ( ! [SY8: $i] :
              ~ ( p @ SV3 @ SY8 ) )
        = $true )
      | ( ( q @ ( f @ sK1_B ) @ sK1_B )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(29,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ~ ( q @ SV1 @ SV4 )
        | ~ ( p @ SV1 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV5: $i] :
      ( ( ( p @ ( f @ SV5 ) @ SV5 )
        = $true )
      | ( ( r @ sK1_B )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( r @ SV2 ) )
        = $true )
      | ( ( p @ ( f @ SV2 ) @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV6: $i,SV3: $i] :
      ( ( ( ~ ( p @ SV3 @ SV6 ) )
        = $true )
      | ( ( q @ ( f @ sK1_B ) @ sK1_B )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ~ ( q @ SV1 @ SV4 ) )
        = $true )
      | ( ( ~ ( p @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV2: $i] :
      ( ( ( r @ SV2 )
        = $false )
      | ( ( p @ ( f @ SV2 ) @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(35,plain,
    ! [SV6: $i,SV3: $i] :
      ( ( ( p @ SV3 @ SV6 )
        = $false )
      | ( ( q @ ( f @ sK1_B ) @ sK1_B )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(36,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( q @ SV1 @ SV4 )
        = $false )
      | ( ( ~ ( p @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(37,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( p @ SV1 @ SV4 )
        = $false )
      | ( ( q @ SV1 @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(38,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[30,37,35,34]) ).

thf(39,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN980+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jul 11 13:55:19 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 0
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (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)..
% 0.12/0.37  
% 0.12/0.37  ********************************
% 0.12/0.37  *   All subproblems solved!    *
% 0.12/0.37  ********************************
% 0.12/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:38,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.37  
% 0.12/0.37  %**** Beginning of derivation protocol ****
% 0.12/0.37  % SZS output start CNFRefutation
% See solution above
% 0.12/0.37  
% 0.12/0.37  %**** End of derivation protocol ****
% 0.12/0.37  %**** no. of clauses in derivation: 39 ****
% 0.12/0.37  %**** clause counter: 38 ****
% 0.12/0.37  
% 0.12/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:38,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------