TSTP Solution File: SEU932^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU932^5 : 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 12:15:48 EDT 2022

% Result   : Theorem 0.18s 0.37s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   35 (  29 unt;   3 typ;   0 def)
%            Number of atoms       :  138 ( 104 equ;   0 cnn)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :  177 (  38   ~;  19   |;  14   &;  97   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   3 con; 0-2 aty)
%            Number of variables   :   66 (  24   ^  26   !;  16   ?;  66   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_sK1_Xf,type,
    sK1_Xf: $i > $i ).

thf(tp_sK2_SY7,type,
    sK2_SY7: $i > $i ).

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

thf(1,conjecture,
    ! [Xf: $i > $i] :
      ( ? [Xg: $i > $i] :
          ( ( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
            = ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) )
          & ? [Xx: $i] :
              ( ( ( Xg @ Xx )
                = Xx )
              & ! [Xz: $i] :
                  ( ( ( Xg @ Xz )
                    = Xz )
                 => ( Xz = Xx ) ) ) )
     => ? [Xy: $i] :
          ( ( Xf @ Xy )
          = Xy ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM141_pme) ).

thf(2,negated_conjecture,
    ( ( ! [Xf: $i > $i] :
          ( ? [Xg: $i > $i] :
              ( ( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
                = ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) )
              & ? [Xx: $i] :
                  ( ( ( Xg @ Xx )
                    = Xx )
                  & ! [Xz: $i] :
                      ( ( ( Xg @ Xz )
                        = Xz )
                     => ( Xz = Xx ) ) ) )
         => ? [Xy: $i] :
              ( ( Xf @ Xy )
              = Xy ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xf: $i > $i] :
          ( ? [Xg: $i > $i] :
              ( ( ( ^ [Xx: $i] : ( Xf @ ( Xg @ Xx ) ) )
                = ( ^ [Xx: $i] : ( Xg @ ( Xf @ Xx ) ) ) )
              & ? [Xx: $i] :
                  ( ( ( Xg @ Xx )
                    = Xx )
                  & ! [Xz: $i] :
                      ( ( ( Xg @ Xz )
                        = Xz )
                     => ( Xz = Xx ) ) ) )
         => ? [Xy: $i] :
              ( ( Xf @ Xy )
              = Xy ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ? [SY7: $i > $i] :
          ( ( ( ^ [SY8: $i] : ( sK1_Xf @ ( SY7 @ SY8 ) ) )
            = ( ^ [SY9: $i] : ( SY7 @ ( sK1_Xf @ SY9 ) ) ) )
          & ? [Xx: $i] :
              ( ( ( SY7 @ Xx )
                = Xx )
              & ! [Xz: $i] :
                  ( ( ( SY7 @ Xz )
                    = Xz )
                 => ( Xz = Xx ) ) ) )
     => ? [SY12: $i] :
          ( ( sK1_Xf @ SY12 )
          = SY12 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ? [SY7: $i > $i] :
          ( ( ( ^ [SY8: $i] : ( sK1_Xf @ ( SY7 @ SY8 ) ) )
            = ( ^ [SY9: $i] : ( SY7 @ ( sK1_Xf @ SY9 ) ) ) )
          & ? [Xx: $i] :
              ( ( ( SY7 @ Xx )
                = Xx )
              & ! [Xz: $i] :
                  ( ( ( SY7 @ Xz )
                    = Xz )
                 => ( Xz = Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ? [SY12: $i] :
          ( ( sK1_Xf @ SY12 )
          = SY12 ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ~ ? [SY12: $i] :
            ( ( sK1_Xf @ SY12 )
            = SY12 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [SY12: $i] :
          ( ( sK1_Xf @ SY12 )
         != SY12 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(9,plain,
    ( ( ( ( ^ [SY13: $i] : ( sK1_Xf @ ( sK2_SY7 @ SY13 ) ) )
        = ( ^ [SY14: $i] : ( sK2_SY7 @ ( sK1_Xf @ SY14 ) ) ) )
      & ! [SY17: $i] :
          ( ( ( sK2_SY7 @ SY17 )
           != SY17 )
          | ( SY17 = sK3_SY15 ) )
      & ( ( sK2_SY7 @ sK3_SY15 )
        = sK3_SY15 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(10,plain,
    ( ( ( ( ^ [SY13: $i] : ( sK1_Xf @ ( sK2_SY7 @ SY13 ) ) )
        = ( ^ [SY14: $i] : ( sK2_SY7 @ ( sK1_Xf @ SY14 ) ) ) )
      & ! [SY17: $i] :
          ( ( ( sK2_SY7 @ SY17 )
           != SY17 )
          | ( SY17 = sK3_SY15 ) )
      & ( ( sK2_SY7 @ sK3_SY15 )
        = sK3_SY15 ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ! [SY12: $i] :
          ( ( sK1_Xf @ SY12 )
         != SY12 ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(12,plain,
    ( ( ~ ( ( ( ^ [SX0: $i] : ( sK1_Xf @ ( sK2_SY7 @ SX0 ) ) )
           != ( ^ [SX0: $i] : ( sK2_SY7 @ ( sK1_Xf @ SX0 ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ( ( sK2_SY7 @ SX0 )
                       != SX0 )
                      | ( SX0 = sK3_SY15 ) )
                | ( ( sK2_SY7 @ sK3_SY15 )
                 != sK3_SY15 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(13,plain,
    ! [SV1: $i] :
      ( ( ( ( sK1_Xf @ SV1 )
         != SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ( ( ^ [SX0: $i] : ( sK1_Xf @ ( sK2_SY7 @ SX0 ) ) )
       != ( ^ [SX0: $i] : ( sK2_SY7 @ ( sK1_Xf @ SX0 ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ( ( sK2_SY7 @ SX0 )
                   != SX0 )
                  | ( SX0 = sK3_SY15 ) )
            | ( ( sK2_SY7 @ sK3_SY15 )
             != sK3_SY15 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV1: $i] :
      ( ( ( sK1_Xf @ SV1 )
        = SV1 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ( ( ^ [SX0: $i] : ( sK1_Xf @ ( sK2_SY7 @ SX0 ) ) )
       != ( ^ [SX0: $i] : ( sK2_SY7 @ ( sK1_Xf @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ( ( sK2_SY7 @ SX0 )
                   != SX0 )
                  | ( SX0 = sK3_SY15 ) )
            | ( ( sK2_SY7 @ sK3_SY15 )
             != sK3_SY15 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ( ^ [SX0: $i] : ( sK1_Xf @ ( sK2_SY7 @ SX0 ) ) )
      = ( ^ [SX0: $i] : ( sK2_SY7 @ ( sK1_Xf @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( ( sK2_SY7 @ SX0 )
                 != SX0 )
                | ( SX0 = sK3_SY15 ) )
          | ( ( sK2_SY7 @ sK3_SY15 )
           != sK3_SY15 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ! [SV2: $i] :
          ( ( sK1_Xf @ ( sK2_SY7 @ SV2 ) )
          = ( sK2_SY7 @ ( sK1_Xf @ SV2 ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ( ^ [SX0: $i] : ( sK1_Xf @ ( sK2_SY7 @ SX0 ) ) )
      = ( ^ [SX0: $i] : ( sK2_SY7 @ ( sK1_Xf @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( sK2_SY7 @ SX0 )
             != SX0 )
            | ( SX0 = sK3_SY15 ) )
      | ( ( sK2_SY7 @ sK3_SY15 )
       != sK3_SY15 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV3: $i] :
      ( ( ( sK1_Xf @ ( sK2_SY7 @ SV3 ) )
        = ( sK2_SY7 @ ( sK1_Xf @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( sK2_SY7 @ SX0 )
             != SX0 )
            | ( SX0 = sK3_SY15 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(25,plain,
    ( ( ( ( sK2_SY7 @ sK3_SY15 )
       != sK3_SY15 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(26,plain,
    ( ( ! [SX0: $i] :
          ( ( ( sK2_SY7 @ SX0 )
           != SX0 )
          | ( SX0 = sK3_SY15 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(27,plain,
    ( ( ( sK2_SY7 @ sK3_SY15 )
      = sK3_SY15 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(28,plain,
    ! [SV4: $i] :
      ( ( ( ( sK2_SY7 @ SV4 )
         != SV4 )
        | ( SV4 = sK3_SY15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(29,plain,
    ! [SV4: $i] :
      ( ( ( ( ( sK2_SY7 @ SV4 )
           != SV4 ) )
        = $true )
      | ( ( SV4 = sK3_SY15 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[28]) ).

thf(30,plain,
    ! [SV4: $i] :
      ( ( ( ( sK2_SY7 @ SV4 )
          = SV4 )
        = $false )
      | ( ( SV4 = sK3_SY15 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(31,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[15,30,27,23,21]) ).

thf(32,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU932^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n008.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 : Sun Jun 19 21:31:22 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.34  
% 0.18/0.34   No.of.Axioms: 0
% 0.18/0.34  
% 0.18/0.34   Length.of.Defs: 0
% 0.18/0.34  
% 0.18/0.34   Contains.Choice.Funs: false
% 0.18/0.34  (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).
% 0.18/0.37  
% 0.18/0.37  ********************************
% 0.18/0.37  *   All subproblems solved!    *
% 0.18/0.37  ********************************
% 0.18/0.37  % 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:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.37  
% 0.18/0.37  %**** Beginning of derivation protocol ****
% 0.18/0.37  % SZS output start CNFRefutation
% See solution above
% 0.18/0.37  
% 0.18/0.37  %**** End of derivation protocol ****
% 0.18/0.37  %**** no. of clauses in derivation: 32 ****
% 0.18/0.37  %**** clause counter: 31 ****
% 0.18/0.37  
% 0.18/0.37  % 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:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------