TSTP Solution File: SEV311^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV311^5 : 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 : n008.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 : Tue Jul 19 17:36:08 EDT 2022

% Result   : Theorem 0.19s 0.39s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   48 (  27 unt;   5 typ;   0 def)
%            Number of atoms       :  239 (  60 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :  514 (  93   ~;  68   |;   6   &; 303   @)
%                                         (   0 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   68 (  68   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  130 (  11   ^ 119   !;   0   ?; 130   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $tType ).

thf(tp_cF,type,
    cF: ( a > $o ) > a > $o ).

thf(tp_sK1_Xx,type,
    sK1_Xx: a ).

thf(tp_sK2_SY13,type,
    sK2_SY13: a > $o ).

thf(tp_sK3_Xx,type,
    sK3_Xx: ( a > $o ) > ( a > $o ) > a ).

thf(1,conjecture,
    ( ! [X: a > $o,Y: a > $o] :
        ( ! [Xx: a] :
            ( ( X @ Xx )
           => ( Y @ Xx ) )
       => ! [Xx: a] :
            ( ( cF @ X @ Xx )
           => ( cF @ Y @ Xx ) ) )
   => ! [Xx: a] :
        ( ( cF
          @ ^ [Xx0: a] :
            ! [S: a > $o] :
              ( ! [Xx1: a] :
                  ( ( cF @ S @ Xx1 )
                 => ( S @ Xx1 ) )
             => ( S @ Xx0 ) )
          @ Xx )
       => ! [S: a > $o] :
            ( ! [Xx0: a] :
                ( ( cF @ S @ Xx0 )
               => ( S @ Xx0 ) )
           => ( S @ Xx ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM521_pme) ).

thf(2,negated_conjecture,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ! [Xx: a] :
              ( ( X @ Xx )
             => ( Y @ Xx ) )
         => ! [Xx: a] :
              ( ( cF @ X @ Xx )
             => ( cF @ Y @ Xx ) ) )
     => ! [Xx: a] :
          ( ( cF
            @ ^ [Xx0: a] :
              ! [S: a > $o] :
                ( ! [Xx1: a] :
                    ( ( cF @ S @ Xx1 )
                   => ( S @ Xx1 ) )
               => ( S @ Xx0 ) )
            @ Xx )
         => ! [S: a > $o] :
              ( ! [Xx0: a] :
                  ( ( cF @ S @ Xx0 )
                 => ( S @ Xx0 ) )
             => ( S @ Xx ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ! [Xx: a] :
              ( ( X @ Xx )
             => ( Y @ Xx ) )
         => ! [Xx: a] :
              ( ( cF @ X @ Xx )
             => ( cF @ Y @ Xx ) ) )
     => ! [Xx: a] :
          ( ( cF
            @ ^ [Xx0: a] :
              ! [S: a > $o] :
                ( ! [Xx1: a] :
                    ( ( cF @ S @ Xx1 )
                   => ( S @ Xx1 ) )
               => ( S @ Xx0 ) )
            @ Xx )
         => ! [S: a > $o] :
              ( ! [Xx0: a] :
                  ( ( cF @ S @ Xx0 )
                 => ( S @ Xx0 ) )
             => ( S @ Xx ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ! [Xx: a] :
              ( ( X @ Xx )
             => ( Y @ Xx ) )
         => ! [Xx: a] :
              ( ( cF @ X @ Xx )
             => ( cF @ Y @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xx: a] :
          ( ( cF
            @ ^ [Xx0: a] :
              ! [S: a > $o] :
                ( ! [Xx1: a] :
                    ( ( cF @ S @ Xx1 )
                   => ( S @ Xx1 ) )
               => ( S @ Xx0 ) )
            @ Xx )
         => ! [S: a > $o] :
              ( ! [Xx0: a] :
                  ( ( cF @ S @ Xx0 )
                 => ( S @ Xx0 ) )
             => ( S @ Xx ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ~ ! [Xx: a] :
            ( ( cF
              @ ^ [Xx0: a] :
                ! [S: a > $o] :
                  ( ! [Xx1: a] :
                      ( ( cF @ S @ Xx1 )
                     => ( S @ Xx1 ) )
                 => ( S @ Xx0 ) )
              @ Xx )
           => ! [S: a > $o] :
                ( ! [Xx0: a] :
                    ( ( cF @ S @ Xx0 )
                   => ( S @ Xx0 ) )
               => ( S @ Xx ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ( cF
        @ ^ [Xx0: a] :
          ! [S: a > $o] :
            ( ! [Xx1: a] :
                ( ( cF @ S @ Xx1 )
               => ( S @ Xx1 ) )
           => ( S @ Xx0 ) )
        @ sK1_Xx )
      & ! [SY15: a] :
          ( ~ ( cF @ sK2_SY13 @ SY15 )
          | ( sK2_SY13 @ SY15 ) )
      & ~ ( sK2_SY13 @ sK1_Xx ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ( ( X @ ( sK3_Xx @ Y @ X ) )
            & ~ ( Y @ ( sK3_Xx @ Y @ X ) ) )
          | ! [Xx: a] :
              ( ~ ( cF @ X @ Xx )
              | ( cF @ Y @ Xx ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ( ( X @ ( sK3_Xx @ Y @ X ) )
            & ~ ( Y @ ( sK3_Xx @ Y @ X ) ) )
          | ! [Xx: a] :
              ( ~ ( cF @ X @ Xx )
              | ( cF @ Y @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ( cF
        @ ^ [Xx0: a] :
          ! [S: a > $o] :
            ( ! [Xx1: a] :
                ( ( cF @ S @ Xx1 )
               => ( S @ Xx1 ) )
           => ( S @ Xx0 ) )
        @ sK1_Xx )
      & ! [SY15: a] :
          ( ~ ( cF @ sK2_SY13 @ SY15 )
          | ( sK2_SY13 @ SY15 ) )
      & ~ ( sK2_SY13 @ sK1_Xx ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ! [SX0: a > $o,SX1: a > $o] :
          ( ~ ( ~ ( SX0 @ ( sK3_Xx @ SX1 @ SX0 ) )
              | ~ ~ ( SX1 @ ( sK3_Xx @ SX1 @ SX0 ) ) )
          | ! [SX2: a] :
              ( ~ ( cF @ SX0 @ SX2 )
              | ( cF @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ~ ( ~ ( cF
              @ ^ [SX0: a] :
                ! [SX1: a > $o] :
                  ( ~ ! [SX2: a] :
                        ( ~ ( cF @ SX1 @ SX2 )
                        | ( SX1 @ SX2 ) )
                  | ( SX1 @ SX0 ) )
              @ sK1_Xx )
          | ~ ~ ( ~ ! [SX0: a] :
                      ( ~ ( cF @ sK2_SY13 @ SX0 )
                      | ( sK2_SY13 @ SX0 ) )
                | ~ ~ ( sK2_SY13 @ sK1_Xx ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(13,plain,
    ! [SV1: a > $o] :
      ( ( ! [SY16: a > $o] :
            ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SY16 @ SV1 ) )
                | ~ ~ ( SY16 @ ( sK3_Xx @ SY16 @ SV1 ) ) )
            | ! [SY17: a] :
                ( ~ ( cF @ SV1 @ SY17 )
                | ( cF @ SY16 @ SY17 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ( cF
          @ ^ [SX0: a] :
            ! [SX1: a > $o] :
              ( ~ ! [SX2: a] :
                    ( ~ ( cF @ SX1 @ SX2 )
                    | ( SX1 @ SX2 ) )
              | ( SX1 @ SX0 ) )
          @ sK1_Xx )
      | ~ ~ ( ~ ! [SX0: a] :
                  ( ~ ( cF @ sK2_SY13 @ SX0 )
                  | ( sK2_SY13 @ SX0 ) )
            | ~ ~ ( sK2_SY13 @ sK1_Xx ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
            | ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
        | ! [SY18: a] :
            ( ~ ( cF @ SV1 @ SY18 )
            | ( cF @ SV2 @ SY18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ( cF
          @ ^ [SX0: a] :
            ! [SX1: a > $o] :
              ( ~ ! [SX2: a] :
                    ( ~ ( cF @ SX1 @ SX2 )
                    | ( SX1 @ SX2 ) )
              | ( SX1 @ SX0 ) )
          @ sK1_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ~ ( ~ ! [SX0: a] :
                  ( ~ ( cF @ sK2_SY13 @ SX0 )
                  | ( sK2_SY13 @ SX0 ) )
            | ~ ~ ( sK2_SY13 @ sK1_Xx ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
              | ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) ) )
        = $true )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV1 @ SY18 )
              | ( cF @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[15]) ).

thf(19,plain,
    ( ( cF
      @ ^ [SX0: a] :
        ! [SX1: a > $o] :
          ( ~ ! [SX2: a] :
                ( ~ ( cF @ SX1 @ SX2 )
                | ( SX1 @ SX2 ) )
          | ( SX1 @ SX0 ) )
      @ sK1_Xx )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ~ ( ~ ! [SX0: a] :
                ( ~ ( cF @ sK2_SY13 @ SX0 )
                | ( sK2_SY13 @ SX0 ) )
          | ~ ~ ( sK2_SY13 @ sK1_Xx ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
          | ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV1 @ SY18 )
              | ( cF @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ~ ! [SX0: a] :
            ( ~ ( cF @ sK2_SY13 @ SX0 )
            | ( sK2_SY13 @ SX0 ) )
      | ~ ~ ( sK2_SY13 @ sK1_Xx ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(23,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV1 @ SY18 )
              | ( cF @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(24,plain,
    ! [SV1: a > $o,SV2: a > $o] :
      ( ( ( ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV1 @ SY18 )
              | ( cF @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ~ ! [SX0: a] :
            ( ~ ( cF @ sK2_SY13 @ SX0 )
            | ( sK2_SY13 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(26,plain,
    ( ( ~ ~ ( sK2_SY13 @ sK1_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV2: a > $o,SV1: a > $o] :
      ( ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $true )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV1 @ SY18 )
              | ( cF @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV1: a > $o,SV2: a > $o] :
      ( ( ( ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV1 @ SY18 )
              | ( cF @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ! [SX0: a] :
          ( ~ ( cF @ sK2_SY13 @ SX0 )
          | ( sK2_SY13 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(30,plain,
    ( ( ~ ( sK2_SY13 @ sK1_Xx ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV2: a > $o,SV3: a,SV1: a > $o] :
      ( ( ( ~ ( cF @ SV1 @ SV3 )
          | ( cF @ SV2 @ SV3 ) )
        = $true )
      | ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV1: a > $o,SV2: a > $o] :
      ( ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $false )
      | ( ( ! [SY18: a] :
              ( ~ ( cF @ SV1 @ SY18 )
              | ( cF @ SV2 @ SY18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV4: a] :
      ( ( ~ ( cF @ sK2_SY13 @ SV4 )
        | ( sK2_SY13 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(34,plain,
    ( ( sK2_SY13 @ sK1_Xx )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV2: a > $o,SV3: a,SV1: a > $o] :
      ( ( ( ~ ( cF @ SV1 @ SV3 ) )
        = $true )
      | ( ( cF @ SV2 @ SV3 )
        = $true )
      | ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV2: a > $o,SV5: a,SV1: a > $o] :
      ( ( ( ~ ( cF @ SV1 @ SV5 )
          | ( cF @ SV2 @ SV5 ) )
        = $true )
      | ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV4: a] :
      ( ( ( ~ ( cF @ sK2_SY13 @ SV4 ) )
        = $true )
      | ( ( sK2_SY13 @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[33]) ).

thf(38,plain,
    ! [SV2: a > $o,SV3: a,SV1: a > $o] :
      ( ( ( cF @ SV1 @ SV3 )
        = $false )
      | ( ( cF @ SV2 @ SV3 )
        = $true )
      | ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(39,plain,
    ! [SV2: a > $o,SV5: a,SV1: a > $o] :
      ( ( ( ~ ( cF @ SV1 @ SV5 ) )
        = $true )
      | ( ( cF @ SV2 @ SV5 )
        = $true )
      | ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[36]) ).

thf(40,plain,
    ! [SV4: a] :
      ( ( ( cF @ sK2_SY13 @ SV4 )
        = $false )
      | ( ( sK2_SY13 @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(41,plain,
    ! [SV2: a > $o,SV5: a,SV1: a > $o] :
      ( ( ( cF @ SV1 @ SV5 )
        = $false )
      | ( ( cF @ SV2 @ SV5 )
        = $true )
      | ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(42,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[19,41,40,38,34]) ).

thf(43,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV311^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.33  % Computer : n008.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Tue Jun 28 06:13:08 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 0.19/0.34  
% 0.19/0.34   No.of.Axioms: 0
% 0.19/0.34  
% 0.19/0.34   Length.of.Defs: 0
% 0.19/0.34  
% 0.19/0.34   Contains.Choice.Funs: false
% 0.19/0.34  (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)...
% 0.19/0.39  
% 0.19/0.39  ********************************
% 0.19/0.39  *   All subproblems solved!    *
% 0.19/0.39  ********************************
% 0.19/0.39  % SZS status Theorem for /export/starexec/sandbox/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:42,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.39  
% 0.19/0.39  %**** Beginning of derivation protocol ****
% 0.19/0.39  % SZS output start CNFRefutation
% See solution above
% 0.19/0.39  
% 0.19/0.39  %**** End of derivation protocol ****
% 0.19/0.39  %**** no. of clauses in derivation: 43 ****
% 0.19/0.39  %**** clause counter: 42 ****
% 0.19/0.39  
% 0.19/0.39  % SZS status Theorem for /export/starexec/sandbox/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:42,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------