TSTP Solution File: SYN944+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN944+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 : n012.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 08:30:43 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   43 (  27 unt;   7 typ;   0 def)
%            Number of atoms       :  190 (  42 equ;   0 cnn)
%            Maximal formula atoms :    9 (   5 avg)
%            Number of connectives :  243 (  20   ~;  18   |;  32   &; 153   @)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   80 (   0   ^  64   !;  16   ?;  80   :)

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

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

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

thf(tp_s,type,
    s: $i > $o ).

thf(tp_sK1_A,type,
    sK1_A: $i ).

thf(tp_sK2_SY8,type,
    sK2_SY8: $i ).

thf(tp_sK3_SY15,type,
    sK3_SY15: $i ).

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

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

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

thf(4,plain,
    ( ( ! [SY8: $i,SY9: $i] :
          ( ( ( s @ sK1_A )
            & ( s @ SY8 )
            & ( r @ SY8 @ SY9 )
            & ! [X: $i] :
                ( ( s @ X )
               => ( p @ X ) )
            & ! [X: $i,Y: $i] :
                ( ( r @ X @ Y )
               => ( q @ X @ Y ) ) )
         => ? [X: $i,Y: $i] :
              ( ( p @ X )
              & ( q @ X @ Y ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY15: $i] :
          ( ( ( s @ sK1_A )
            & ( s @ sK2_SY8 )
            & ( r @ sK2_SY8 @ SY15 )
            & ! [X: $i] :
                ( ( s @ X )
               => ( p @ X ) )
            & ! [X: $i,Y: $i] :
                ( ( r @ X @ Y )
               => ( q @ X @ Y ) ) )
         => ? [X: $i,Y: $i] :
              ( ( p @ X )
              & ( q @ X @ Y ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ( ( s @ sK1_A )
        & ( s @ sK2_SY8 )
        & ( r @ sK2_SY8 @ sK3_SY15 )
        & ! [X: $i] :
            ( ( s @ X )
           => ( p @ X ) )
        & ! [X: $i,Y: $i] :
            ( ( r @ X @ Y )
           => ( q @ X @ Y ) ) )
     => ? [X: $i,Y: $i] :
          ( ( p @ X )
          & ( q @ X @ Y ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[5]) ).

thf(7,plain,
    ( ( s @ sK1_A )
    = $true ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(8,plain,
    ( ( s @ sK2_SY8 )
    = $true ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(9,plain,
    ( ( r @ sK2_SY8 @ sK3_SY15 )
    = $true ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(10,plain,
    ( ( ! [X: $i] :
          ( ( s @ X )
         => ( p @ X ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(11,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( r @ X @ Y )
         => ( q @ X @ Y ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(12,plain,
    ( ( ? [X: $i,Y: $i] :
          ( ( p @ X )
          & ( q @ X @ Y ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[6]) ).

thf(13,plain,
    ( ( ~ ? [X: $i,Y: $i] :
            ( ( p @ X )
            & ( q @ X @ Y ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ! [X: $i] :
          ( ~ ( p @ X )
          | ! [Y: $i] :
              ~ ( q @ X @ Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(15,plain,
    ( ( ! [X: $i] :
          ( ~ ( s @ X )
          | ( p @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(16,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( r @ X @ Y )
          | ( q @ X @ Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( r @ X @ Y )
          | ( q @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(18,plain,
    ( ( ! [X: $i] :
          ( ~ ( s @ X )
          | ( p @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(19,plain,
    ( ( r @ sK2_SY8 @ sK3_SY15 )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(20,plain,
    ( ( s @ sK2_SY8 )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(21,plain,
    ( ( s @ sK1_A )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(22,plain,
    ( ( ! [X: $i] :
          ( ~ ( p @ X )
          | ! [Y: $i] :
              ~ ( q @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(23,plain,
    ! [SV1: $i] :
      ( ( ! [SY26: $i] :
            ( ~ ( r @ SV1 @ SY26 )
            | ( q @ SV1 @ SY26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(24,plain,
    ! [SV2: $i] :
      ( ( ~ ( s @ SV2 )
        | ( p @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(25,plain,
    ! [SV3: $i] :
      ( ( ~ ( p @ SV3 )
        | ! [SY27: $i] :
            ~ ( q @ SV3 @ SY27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ~ ( r @ SV1 @ SV4 )
        | ( q @ SV1 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(27,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( s @ SV2 ) )
        = $true )
      | ( ( p @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[24]) ).

thf(28,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( p @ SV3 ) )
        = $true )
      | ( ( ! [SY27: $i] :
              ~ ( q @ SV3 @ SY27 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(29,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ~ ( r @ SV1 @ SV4 ) )
        = $true )
      | ( ( q @ SV1 @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(30,plain,
    ! [SV2: $i] :
      ( ( ( s @ SV2 )
        = $false )
      | ( ( p @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV3: $i] :
      ( ( ( p @ SV3 )
        = $false )
      | ( ( ! [SY27: $i] :
              ~ ( q @ SV3 @ SY27 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( r @ SV1 @ SV4 )
        = $false )
      | ( ( q @ SV1 @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(33,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ( ~ ( q @ SV3 @ SV5 ) )
        = $true )
      | ( ( p @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(34,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ( q @ SV3 @ SV5 )
        = $false )
      | ( ( p @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(35,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[19,34,32,30,21,20]) ).

thf(36,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN944+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jul 12 08:44:42 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 0
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 0
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.35  (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).
% 0.13/0.37  
% 0.13/0.37  ********************************
% 0.13/0.37  *   All subproblems solved!    *
% 0.13/0.37  ********************************
% 0.13/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:35,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: 36 ****
% 0.13/0.38  %**** clause counter: 35 ****
% 0.13/0.38  
% 0.13/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------