TSTP Solution File: SYN361^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN361^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n023.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 08:25:36 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   33 (  22 unt;   5 typ;   0 def)
%            Number of atoms       :  119 (  31 equ;   0 cnn)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :  152 (  25   ~;  12   |;   6   &;  98   @)
%                                         (   0 <=>;  11  =>;   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   :   54 (   0   ^  41   !;  13   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_cP,type,
    cP: $i > $i > $o ).

thf(tp_cQ,type,
    cQ: $i > $i > $o ).

thf(tp_cS,type,
    cS: $i > $o ).

thf(tp_sK1_Xv,type,
    sK1_Xv: $i ).

thf(tp_sK2_Xy,type,
    sK2_Xy: $i > $i ).

thf(1,conjecture,
    ( ( ? [Xv: $i] :
        ! [Xx: $i] : ( cP @ Xx @ Xv )
      & ! [Xx: $i] :
          ( ( cS @ Xx )
         => ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
      & ! [Xx: $i,Xy: $i] :
          ( ( cP @ Xx @ Xy )
         => ~ ( cQ @ Xx @ Xy ) ) )
   => ? [Xu: $i] :
        ~ ( cS @ Xu ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX2112) ).

thf(2,negated_conjecture,
    ( ( ( ? [Xv: $i] :
          ! [Xx: $i] : ( cP @ Xx @ Xv )
        & ! [Xx: $i] :
            ( ( cS @ Xx )
           => ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
        & ! [Xx: $i,Xy: $i] :
            ( ( cP @ Xx @ Xy )
           => ~ ( cQ @ Xx @ Xy ) ) )
     => ? [Xu: $i] :
          ~ ( cS @ Xu ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( ? [Xv: $i] :
          ! [Xx: $i] : ( cP @ Xx @ Xv )
        & ! [Xx: $i] :
            ( ( cS @ Xx )
           => ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
        & ! [Xx: $i,Xy: $i] :
            ( ( cP @ Xx @ Xy )
           => ~ ( cQ @ Xx @ Xy ) ) )
     => ? [Xu: $i] :
          ~ ( cS @ Xu ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ? [Xv: $i] :
        ! [Xx: $i] : ( cP @ Xx @ Xv ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xx: $i] :
          ( ( cS @ Xx )
         => ? [Xy: $i] : ( cQ @ Xy @ Xx ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( cP @ Xx @ Xy )
         => ~ ( cQ @ Xx @ Xy ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ? [Xu: $i] :
          ~ ( cS @ Xu ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(8,plain,
    ( ( ~ ? [Xu: $i] :
            ~ ( cS @ Xu ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [Xu: $i] : ( cS @ Xu ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    ( ( ! [SY7: $i] : ( cP @ SY7 @ sK1_Xv ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(11,plain,
    ( ( ! [Xx: $i] :
          ( ~ ( cS @ Xx )
          | ( cQ @ ( sK2_Xy @ Xx ) @ Xx ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(12,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ~ ( cP @ Xx @ Xy )
          | ~ ( cQ @ Xx @ Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(13,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ~ ( cP @ Xx @ Xy )
          | ~ ( cQ @ Xx @ Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ! [Xx: $i] :
          ( ~ ( cS @ Xx )
          | ( cQ @ ( sK2_Xy @ Xx ) @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(15,plain,
    ( ( ! [SY7: $i] : ( cP @ SY7 @ sK1_Xv ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(16,plain,
    ( ( ! [Xu: $i] : ( cS @ Xu ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(17,plain,
    ! [SV1: $i] :
      ( ( ! [SY8: $i] :
            ( ~ ( cP @ SV1 @ SY8 )
            | ~ ( cQ @ SV1 @ SY8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(18,plain,
    ! [SV2: $i] :
      ( ( ~ ( cS @ SV2 )
        | ( cQ @ ( sK2_Xy @ SV2 ) @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(19,plain,
    ! [SV3: $i] :
      ( ( cP @ SV3 @ sK1_Xv )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(20,plain,
    ! [SV4: $i] :
      ( ( cS @ SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(21,plain,
    ! [SV5: $i,SV1: $i] :
      ( ( ~ ( cP @ SV1 @ SV5 )
        | ~ ( cQ @ SV1 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(22,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( cS @ SV2 ) )
        = $true )
      | ( ( cQ @ ( sK2_Xy @ SV2 ) @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(23,plain,
    ! [SV5: $i,SV1: $i] :
      ( ( ( ~ ( cP @ SV1 @ SV5 ) )
        = $true )
      | ( ( ~ ( cQ @ SV1 @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[21]) ).

thf(24,plain,
    ! [SV2: $i] :
      ( ( ( cS @ SV2 )
        = $false )
      | ( ( cQ @ ( sK2_Xy @ SV2 ) @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(25,plain,
    ! [SV5: $i,SV1: $i] :
      ( ( ( cP @ SV1 @ SV5 )
        = $false )
      | ( ( ~ ( cQ @ SV1 @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(26,plain,
    ! [SV5: $i,SV1: $i] :
      ( ( ( cQ @ SV1 @ SV5 )
        = $false )
      | ( ( cP @ SV1 @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(27,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[19,26,24,20]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SYN361^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n023.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 13:07:39 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  
% 0.12/0.33   No.of.Axioms: 0
% 0.12/0.33  
% 0.12/0.33   Length.of.Defs: 0
% 0.12/0.33  
% 0.12/0.33   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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.12/0.36  
% 0.12/0.36  ********************************
% 0.12/0.36  *   All subproblems solved!    *
% 0.12/0.36  ********************************
% 0.12/0.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:27,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.36  
% 0.12/0.36  %**** Beginning of derivation protocol ****
% 0.12/0.36  % SZS output start CNFRefutation
% See solution above
% 0.12/0.36  
% 0.12/0.36  %**** End of derivation protocol ****
% 0.12/0.36  %**** no. of clauses in derivation: 28 ****
% 0.12/0.36  %**** clause counter: 27 ****
% 0.12/0.36  
% 0.12/0.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:27,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------