TSTP Solution File: SEV164^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV164^5 : 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 17:35:27 EDT 2022

% Result   : Theorem 0.11s 0.38s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   39 (  33 unt;   5 typ;   0 def)
%            Number of atoms       :  110 (  33 equ;   0 cnn)
%            Maximal formula atoms :    1 (   3 avg)
%            Number of connectives :  191 (  31   ~;   4   |;   4   &; 144   @)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   65 (  65   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :  151 (  96   ^  31   !;  24   ?; 151   :)

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

thf(tp_sK1_Xr,type,
    sK1_Xr: a > a > $o ).

thf(tp_sK2_SY8,type,
    sK2_SY8: a ).

thf(tp_sK3_SY15,type,
    sK3_SY15: a ).

thf(tp_sK4_SY10,type,
    sK4_SY10: ( a > a > a ) > a ).

thf(1,conjecture,
    ! [Xr: a > a > $o] :
      ( ? [Xx: a,Xy: a] : ( Xr @ Xx @ Xy )
    <=> ? [Xp: ( a > a > a ) > a] :
          ( Xr
          @ ( Xp
            @ ^ [Xx: a,Xy: a] : Xx )
          @ ( Xp
            @ ^ [Xx: a,Xy: a] : Xy ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM185_pme) ).

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

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

thf(4,plain,
    ( ( ? [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 )
    <=> ? [SY10: ( a > a > a ) > a] :
          ( sK1_Xr
          @ ( SY10
            @ ^ [Xx: a,Xy: a] : Xx )
          @ ( SY10
            @ ^ [Xx: a,Xy: a] : Xy ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ? [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 )
     => ? [SY10: ( a > a > a ) > a] :
          ( sK1_Xr
          @ ( SY10
            @ ^ [Xx: a,Xy: a] : Xx )
          @ ( SY10
            @ ^ [Xx: a,Xy: a] : Xy ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[4]) ).

thf(6,plain,
    ( ( ? [SY10: ( a > a > a ) > a] :
          ( sK1_Xr
          @ ( SY10
            @ ^ [Xx: a,Xy: a] : Xx )
          @ ( SY10
            @ ^ [Xx: a,Xy: a] : Xy ) )
     => ? [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[4]) ).

thf(7,plain,
    ( ( ~ ( ? [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 )
         => ? [SY10: ( a > a > a ) > a] :
              ( sK1_Xr
              @ ( SY10
                @ ^ [Xx: a,Xy: a] : Xx )
              @ ( SY10
                @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ~ ( ? [SY10: ( a > a > a ) > a] :
              ( sK1_Xr
              @ ( SY10
                @ ^ [Xx: a,Xy: a] : Xx )
              @ ( SY10
                @ ^ [Xx: a,Xy: a] : Xy ) )
         => ? [SY8: a,SY9: a] : ( sK1_Xr @ SY8 @ SY9 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ( sK1_Xr @ sK2_SY8 @ sK3_SY15 )
      & ! [SY10: ( a > a > a ) > a] :
          ~ ( sK1_Xr
            @ ( SY10
              @ ^ [Xx: a,Xy: a] : Xx )
            @ ( SY10
              @ ^ [Xx: a,Xy: a] : Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(10,plain,
    ( ( ( sK1_Xr
        @ ( sK4_SY10
          @ ^ [Xx: a,Xy: a] : Xx )
        @ ( sK4_SY10
          @ ^ [Xx: a,Xy: a] : Xy ) )
      & ! [SY8: a,SY9: a] :
          ~ ( sK1_Xr @ SY8 @ SY9 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(11,plain,
    ( ( ( sK1_Xr @ sK2_SY8 @ sK3_SY15 )
      & ! [SY10: ( a > a > a ) > a] :
          ~ ( sK1_Xr
            @ ( SY10
              @ ^ [Xx: a,Xy: a] : Xx )
            @ ( SY10
              @ ^ [Xx: a,Xy: a] : Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ~ ( ~ ( sK1_Xr @ sK2_SY8 @ sK3_SY15 )
          | ~ ! [SX0: ( a > a > a ) > a] :
                ~ ( sK1_Xr
                  @ ( SX0
                    @ ^ [SX1: a,SX2: a] : SX1 )
                  @ ( SX0
                    @ ^ [SX1: a,SX2: a] : SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(13,plain,
    ( ( ~ ( sK1_Xr @ sK2_SY8 @ sK3_SY15 )
      | ~ ! [SX0: ( a > a > a ) > a] :
            ~ ( sK1_Xr
              @ ( SX0
                @ ^ [SX1: a,SX2: a] : SX1 )
              @ ( SX0
                @ ^ [SX1: a,SX2: a] : SX2 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ~ ( sK1_Xr @ sK2_SY8 @ sK3_SY15 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ~ ! [SX0: ( a > a > a ) > a] :
            ~ ( sK1_Xr
              @ ( SX0
                @ ^ [SX1: a,SX2: a] : SX1 )
              @ ( SX0
                @ ^ [SX1: a,SX2: a] : SX2 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(16,plain,
    ( ( sK1_Xr @ sK2_SY8 @ sK3_SY15 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ! [SX0: ( a > a > a ) > a] :
          ~ ( sK1_Xr
            @ ( SX0
              @ ^ [SX1: a,SX2: a] : SX1 )
            @ ( SX0
              @ ^ [SX1: a,SX2: a] : SX2 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[15]) ).

thf(18,plain,
    ! [SV1: ( a > a > a ) > a] :
      ( ( ~ ( sK1_Xr
            @ ( SV1
              @ ^ [SX1: a,SX2: a] : SX1 )
            @ ( SV1
              @ ^ [SX1: a,SX2: a] : SX2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(19,plain,
    ! [SV1: ( a > a > a ) > a] :
      ( ( sK1_Xr
        @ ( SV1
          @ ^ [SX1: a,SX2: a] : SX1 )
        @ ( SV1
          @ ^ [SX1: a,SX2: a] : SX2 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(20,plain,
    ! [SV2: ( a > a > a ) > a] :
      ( ( sK1_Xr
        @ ( SV2
          @ ^ [SX0: a,SX1: a] : SX0 )
        @ ( SV2
          @ ^ [SX0: a,SX1: a] : SX1 ) )
      = $false ),
    inference(rename,[status(thm)],[19]) ).

thf(21,plain,
    ! [SV2: ( a > a > a ) > a] :
      ( ( ( sK1_Xr
          @ ( SV2
            @ ^ [SX0: a,SX1: a] : SX0 )
          @ ( SV2
            @ ^ [SX0: a,SX1: a] : SX1 ) )
        = ( sK1_Xr @ sK2_SY8 @ sK3_SY15 ) )
      = $false ),
    inference(res,[status(thm)],[20,16]) ).

thf(22,plain,
    $false = $true,
    inference(extuni,[status(esa)],[21:[bind(SV2,$thf( ^ [SX0: a > a > a] : ( SX0 @ ( SX0 @ ( SX0 @ sK2_SY8 @ ( SV29 @ SX0 ) ) @ ( SV9 @ SX0 ) ) @ sK3_SY15 ) ))]]) ).

thf(23,plain,
    ( ( ( sK1_Xr
        @ ( sK4_SY10
          @ ^ [Xx: a,Xy: a] : Xx )
        @ ( sK4_SY10
          @ ^ [Xx: a,Xy: a] : Xy ) )
      & ! [SY8: a,SY9: a] :
          ~ ( sK1_Xr @ SY8 @ SY9 ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(24,plain,
    ( ( ~ ( ~ ( sK1_Xr
              @ ( sK4_SY10
                @ ^ [SX0: a,SX1: a] : SX0 )
              @ ( sK4_SY10
                @ ^ [SX0: a,SX1: a] : SX1 ) )
          | ~ ! [SX0: a,SX1: a] :
                ~ ( sK1_Xr @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(25,plain,
    ( ( ~ ( sK1_Xr
          @ ( sK4_SY10
            @ ^ [SX0: a,SX1: a] : SX0 )
          @ ( sK4_SY10
            @ ^ [SX0: a,SX1: a] : SX1 ) )
      | ~ ! [SX0: a,SX1: a] :
            ~ ( sK1_Xr @ SX0 @ SX1 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(26,plain,
    ( ( ~ ( sK1_Xr
          @ ( sK4_SY10
            @ ^ [SX0: a,SX1: a] : SX0 )
          @ ( sK4_SY10
            @ ^ [SX0: a,SX1: a] : SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(27,plain,
    ( ( ~ ! [SX0: a,SX1: a] :
            ~ ( sK1_Xr @ SX0 @ SX1 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(28,plain,
    ( ( sK1_Xr
      @ ( sK4_SY10
        @ ^ [SX0: a,SX1: a] : SX0 )
      @ ( sK4_SY10
        @ ^ [SX0: a,SX1: a] : SX1 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(29,plain,
    ( ( ! [SX0: a,SX1: a] :
          ~ ( sK1_Xr @ SX0 @ SX1 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(30,plain,
    ! [SV67: a] :
      ( ( ! [SY40: a] :
            ~ ( sK1_Xr @ SV67 @ SY40 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(31,plain,
    ! [SV68: a,SV67: a] :
      ( ( ~ ( sK1_Xr @ SV67 @ SV68 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(32,plain,
    ! [SV68: a,SV67: a] :
      ( ( sK1_Xr @ SV67 @ SV68 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(33,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[28,32]) ).

thf(34,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[33,22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07  % Problem  : SEV164^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.08  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.06/0.26  % Computer : n008.cluster.edu
% 0.06/0.26  % Model    : x86_64 x86_64
% 0.06/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26  % Memory   : 8042.1875MB
% 0.06/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26  % CPULimit : 300
% 0.06/0.26  % WCLimit  : 600
% 0.06/0.26  % DateTime : Tue Jun 28 17:25:38 EDT 2022
% 0.06/0.26  % CPUTime  : 
% 0.06/0.27  
% 0.06/0.27   No.of.Axioms: 0
% 0.06/0.27  
% 0.06/0.27   Length.of.Defs: 0
% 0.06/0.27  
% 0.06/0.27   Contains.Choice.Funs: false
% 0.06/0.27  (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).
% 0.11/0.38  
% 0.11/0.38  ********************************
% 0.11/0.38  *   All subproblems solved!    *
% 0.11/0.38  ********************************
% 0.11/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:33,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.38  
% 0.11/0.38  %**** Beginning of derivation protocol ****
% 0.11/0.38  % SZS output start CNFRefutation
% See solution above
% 0.11/0.38  
% 0.11/0.38  %**** End of derivation protocol ****
% 0.11/0.38  %**** no. of clauses in derivation: 34 ****
% 0.11/0.38  %**** clause counter: 33 ****
% 0.11/0.38  
% 0.11/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:33,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------