TSTP Solution File: SEV015^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV015^5 : 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 : n013.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 17:34:22 EDT 2022

% Result   : Theorem 0.19s 0.38s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   41 (  31 unt;   4 typ;   0 def)
%            Number of atoms       :  169 (  49 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  273 (  34   ~;  26   |;  15   &; 178   @)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   4 con; 0-2 aty)
%            Number of variables   :   79 (   0   ^  79   !;   0   ?;  79   :)

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

thf(tp_sK1_Xp,type,
    sK1_Xp: a > a > $o ).

thf(tp_sK2_SY13,type,
    sK2_SY13: a ).

thf(tp_sK3_SY15,type,
    sK3_SY15: a ).

thf(1,conjecture,
    ! [Xp: a > a > $o] :
      ( ( ! [Xx: a,Xy: a] :
            ( ( Xp @ Xx @ Xy )
           => ( Xp @ Xy @ Xx ) )
        & ! [Xx: a,Xy: a,Xz: a] :
            ( ( ( Xp @ Xx @ Xy )
              & ( Xp @ Xy @ Xz ) )
           => ( Xp @ Xx @ Xz ) )
        & ( Xp = Xp ) )
     => ! [Xx: a,Xy: a] :
          ( ( Xp @ Xx @ Xy )
         => ( Xp @ Xx @ Xx ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM520_pme) ).

thf(2,negated_conjecture,
    ( ( ! [Xp: a > a > $o] :
          ( ( ! [Xx: a,Xy: a] :
                ( ( Xp @ Xx @ Xy )
               => ( Xp @ Xy @ Xx ) )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( ( Xp @ Xx @ Xy )
                  & ( Xp @ Xy @ Xz ) )
               => ( Xp @ Xx @ Xz ) )
            & ( Xp = Xp ) )
         => ! [Xx: a,Xy: a] :
              ( ( Xp @ Xx @ Xy )
             => ( Xp @ Xx @ Xx ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xp: a > a > $o] :
          ( ( ! [Xx: a,Xy: a] :
                ( ( Xp @ Xx @ Xy )
               => ( Xp @ Xy @ Xx ) )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( ( Xp @ Xx @ Xy )
                  & ( Xp @ Xy @ Xz ) )
               => ( Xp @ Xx @ Xz ) )
            & ( Xp = Xp ) )
         => ! [Xx: a,Xy: a] :
              ( ( Xp @ Xx @ Xy )
             => ( Xp @ Xx @ Xx ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ( ! [SY8: a,SY9: a] :
            ( ( sK1_Xp @ SY8 @ SY9 )
           => ( sK1_Xp @ SY9 @ SY8 ) )
        & ! [SY10: a,SY11: a,SY12: a] :
            ( ( ( sK1_Xp @ SY10 @ SY11 )
              & ( sK1_Xp @ SY11 @ SY12 ) )
           => ( sK1_Xp @ SY10 @ SY12 ) )
        & ( sK1_Xp = sK1_Xp ) )
     => ! [SY13: a,SY14: a] :
          ( ( sK1_Xp @ SY13 @ SY14 )
         => ( sK1_Xp @ SY13 @ SY13 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY8: a,SY9: a] :
          ( ( sK1_Xp @ SY8 @ SY9 )
         => ( sK1_Xp @ SY9 @ SY8 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ! [SY10: a,SY11: a,SY12: a] :
          ( ( ( sK1_Xp @ SY10 @ SY11 )
            & ( sK1_Xp @ SY11 @ SY12 ) )
         => ( sK1_Xp @ SY10 @ SY12 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(7,plain,
    ( ( sK1_Xp = sK1_Xp )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(8,plain,
    ( ( ! [SY13: a,SY14: a] :
          ( ( sK1_Xp @ SY13 @ SY14 )
         => ( sK1_Xp @ SY13 @ SY13 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(9,plain,
    ( ( ~ ! [SY13: a,SY14: a] :
            ( ( sK1_Xp @ SY13 @ SY14 )
           => ( sK1_Xp @ SY13 @ SY13 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ( sK1_Xp @ sK2_SY13 @ sK3_SY15 )
      & ~ ( sK1_Xp @ sK2_SY13 @ sK2_SY13 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(11,plain,
    ( ( ! [SY8: a,SY9: a] :
          ( ~ ( sK1_Xp @ SY8 @ SY9 )
          | ( sK1_Xp @ SY9 @ SY8 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(12,plain,
    ( ( ! [SY10: a,SY11: a,SY12: a] :
          ( ~ ( sK1_Xp @ SY10 @ SY11 )
          | ~ ( sK1_Xp @ SY11 @ SY12 )
          | ( sK1_Xp @ SY10 @ SY12 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(13,plain,
    $true = $true,
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(14,plain,
    $true = $true,
    inference(copy,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ! [SY10: a,SY11: a,SY12: a] :
          ( ~ ( sK1_Xp @ SY10 @ SY11 )
          | ~ ( sK1_Xp @ SY11 @ SY12 )
          | ( sK1_Xp @ SY10 @ SY12 ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(16,plain,
    ( ( ! [SY8: a,SY9: a] :
          ( ~ ( sK1_Xp @ SY8 @ SY9 )
          | ( sK1_Xp @ SY9 @ SY8 ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(17,plain,
    ( ( ( sK1_Xp @ sK2_SY13 @ sK3_SY15 )
      & ~ ( sK1_Xp @ sK2_SY13 @ sK2_SY13 ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(18,plain,
    ( ( ~ ( ~ ( sK1_Xp @ sK2_SY13 @ sK3_SY15 )
          | ~ ~ ( sK1_Xp @ sK2_SY13 @ sK2_SY13 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(19,plain,
    ! [SV1: a] :
      ( ( ! [SY16: a,SY17: a] :
            ( ~ ( sK1_Xp @ SV1 @ SY16 )
            | ~ ( sK1_Xp @ SY16 @ SY17 )
            | ( sK1_Xp @ SV1 @ SY17 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(20,plain,
    ! [SV2: a] :
      ( ( ! [SY18: a] :
            ( ~ ( sK1_Xp @ SV2 @ SY18 )
            | ( sK1_Xp @ SY18 @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(21,plain,
    ( ( ~ ( sK1_Xp @ sK2_SY13 @ sK3_SY15 )
      | ~ ~ ( sK1_Xp @ sK2_SY13 @ sK2_SY13 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV3: a,SV1: a] :
      ( ( ! [SY19: a] :
            ( ~ ( sK1_Xp @ SV1 @ SV3 )
            | ~ ( sK1_Xp @ SV3 @ SY19 )
            | ( sK1_Xp @ SV1 @ SY19 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV4: a,SV2: a] :
      ( ( ~ ( sK1_Xp @ SV2 @ SV4 )
        | ( sK1_Xp @ SV4 @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ( sK1_Xp @ sK2_SY13 @ sK3_SY15 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ~ ~ ( sK1_Xp @ sK2_SY13 @ sK2_SY13 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV5: a,SV3: a,SV1: a] :
      ( ( ~ ( sK1_Xp @ SV1 @ SV3 )
        | ~ ( sK1_Xp @ SV3 @ SV5 )
        | ( sK1_Xp @ SV1 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV4: a,SV2: a] :
      ( ( ( ~ ( sK1_Xp @ SV2 @ SV4 ) )
        = $true )
      | ( ( sK1_Xp @ SV4 @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(28,plain,
    ( ( sK1_Xp @ sK2_SY13 @ sK3_SY15 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ~ ( sK1_Xp @ sK2_SY13 @ sK2_SY13 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV5: a,SV3: a,SV1: a] :
      ( ( ( ~ ( sK1_Xp @ SV1 @ SV3 )
          | ~ ( sK1_Xp @ SV3 @ SV5 ) )
        = $true )
      | ( ( sK1_Xp @ SV1 @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV4: a,SV2: a] :
      ( ( ( sK1_Xp @ SV2 @ SV4 )
        = $false )
      | ( ( sK1_Xp @ SV4 @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(32,plain,
    ( ( sK1_Xp @ sK2_SY13 @ sK2_SY13 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(33,plain,
    ! [SV5: a,SV3: a,SV1: a] :
      ( ( ( ~ ( sK1_Xp @ SV1 @ SV3 ) )
        = $true )
      | ( ( ~ ( sK1_Xp @ SV3 @ SV5 ) )
        = $true )
      | ( ( sK1_Xp @ SV1 @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(34,plain,
    ! [SV5: a,SV3: a,SV1: a] :
      ( ( ( sK1_Xp @ SV1 @ SV3 )
        = $false )
      | ( ( ~ ( sK1_Xp @ SV3 @ SV5 ) )
        = $true )
      | ( ( sK1_Xp @ SV1 @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(35,plain,
    ! [SV1: a,SV5: a,SV3: a] :
      ( ( ( sK1_Xp @ SV3 @ SV5 )
        = $false )
      | ( ( sK1_Xp @ SV1 @ SV3 )
        = $false )
      | ( ( sK1_Xp @ SV1 @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(36,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[14,35,32,31,28]) ).

thf(37,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV015^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n013.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun 28 15:58:44 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 0
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.35  (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: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).
% 0.19/0.38  
% 0.19/0.38  ********************************
% 0.19/0.38  *   All subproblems solved!    *
% 0.19/0.38  ********************************
% 0.19/0.38  % SZS status Theorem for /export/starexec/sandbox2/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:36,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.38  
% 0.19/0.38  %**** Beginning of derivation protocol ****
% 0.19/0.38  % SZS output start CNFRefutation
% See solution above
% 0.19/0.38  
% 0.19/0.38  %**** End of derivation protocol ****
% 0.19/0.38  %**** no. of clauses in derivation: 37 ****
% 0.19/0.38  %**** clause counter: 36 ****
% 0.19/0.38  
% 0.19/0.38  % SZS status Theorem for /export/starexec/sandbox2/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:36,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------