TSTP Solution File: ALG279^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : ALG279^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 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 14 17:25:41 EDT 2022

% Result   : Theorem 0.14s 0.39s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   33 (  25 unt;   7 typ;   2 def)
%            Number of atoms       :   89 (  59 equ;   0 cnn)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :  159 (   3   ~;   0   |;  10   &; 141   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   68 (   4   ^  59   !;   5   ?;  68   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_g,type,
    g: $tType ).

thf(tp_cGRP_RIGHT_INVERSE,type,
    cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).

thf(tp_cGRP_RIGHT_UNIT,type,
    cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).

thf(tp_sK1_SY0,type,
    sK1_SY0: g > g > g ).

thf(tp_sK2_SY23,type,
    sK2_SY23: g ).

thf(tp_sK3_SY37,type,
    sK3_SY37: g ).

thf(tp_sK4_SY36,type,
    sK4_SY36: g > g ).

thf(cGRP_RIGHT_INVERSE,definition,
    ( cGRP_RIGHT_INVERSE
    = ( ^ [Xf: g > g > g,Xe: g] :
        ! [Xa: g] :
        ? [Xb: g] :
          ( ( Xf @ Xa @ Xb )
          = Xe ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE) ).

thf(cGRP_RIGHT_UNIT,definition,
    ( cGRP_RIGHT_UNIT
    = ( ^ [Xf: g > g > g,Xe: g] :
        ! [Xa: g] :
          ( ( Xf @ Xa @ Xe )
          = Xa ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT) ).

thf(1,conjecture,
    ! [Xf: g > g > g,Xe: g] :
      ( ( ! [Xb: g,Xc: g,Xa: g] :
            ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
            = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) )
        & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
        & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) )
     => ! [Xa: g] :
          ( ( Xf @ Xe @ Xa )
          = Xa ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE13A2A) ).

thf(2,negated_conjecture,
    ( ( ! [Xf: g > g > g,Xe: g] :
          ( ( ! [Xb: g,Xc: g,Xa: g] :
                ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
                = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) )
            & ( cGRP_RIGHT_UNIT @ Xf @ Xe )
            & ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) )
         => ! [Xa: g] :
              ( ( Xf @ Xe @ Xa )
              = Xa ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [SY0: g > g > g,SY1: g] :
          ( ( ! [Xb: g,Xc: g,Xa: g] :
                ( ( SY0 @ ( SY0 @ Xa @ Xb ) @ Xc )
                = ( SY0 @ Xa @ ( SY0 @ Xb @ Xc ) ) )
            & ! [SY7: g] :
                ( ( SY0 @ SY7 @ SY1 )
                = SY7 )
            & ! [SY11: g] :
              ? [SY12: g] :
                ( ( SY0 @ SY11 @ SY12 )
                = SY1 ) )
         => ! [Xa: g] :
              ( ( SY0 @ SY1 @ Xa )
              = Xa ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,cGRP_RIGHT_INVERSE,cGRP_RIGHT_UNIT]) ).

thf(4,plain,
    ( ( ! [SY23: g] :
          ( ( ! [SY24: g,SY25: g,SY26: g] :
                ( ( sK1_SY0 @ ( sK1_SY0 @ SY26 @ SY24 ) @ SY25 )
                = ( sK1_SY0 @ SY26 @ ( sK1_SY0 @ SY24 @ SY25 ) ) )
            & ! [SY27: g] :
                ( ( sK1_SY0 @ SY27 @ SY23 )
                = SY27 )
            & ! [SY28: g] :
              ? [SY29: g] :
                ( ( sK1_SY0 @ SY28 @ SY29 )
                = SY23 ) )
         => ! [SY30: g] :
              ( ( sK1_SY0 @ SY23 @ SY30 )
              = SY30 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ( ! [SY24: g,SY25: g,SY26: g] :
            ( ( sK1_SY0 @ ( sK1_SY0 @ SY26 @ SY24 ) @ SY25 )
            = ( sK1_SY0 @ SY26 @ ( sK1_SY0 @ SY24 @ SY25 ) ) )
        & ! [SY34: g] :
            ( ( sK1_SY0 @ SY34 @ sK2_SY23 )
            = SY34 )
        & ! [SY35: g] :
          ? [SY36: g] :
            ( ( sK1_SY0 @ SY35 @ SY36 )
            = sK2_SY23 ) )
     => ! [SY37: g] :
          ( ( sK1_SY0 @ sK2_SY23 @ SY37 )
          = SY37 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [SY24: g,SY25: g,SY26: g] :
          ( ( sK1_SY0 @ ( sK1_SY0 @ SY26 @ SY24 ) @ SY25 )
          = ( sK1_SY0 @ SY26 @ ( sK1_SY0 @ SY24 @ SY25 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SY34: g] :
          ( ( sK1_SY0 @ SY34 @ sK2_SY23 )
          = SY34 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ! [SY35: g] :
        ? [SY36: g] :
          ( ( sK1_SY0 @ SY35 @ SY36 )
          = sK2_SY23 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(9,plain,
    ( ( ! [SY37: g] :
          ( ( sK1_SY0 @ sK2_SY23 @ SY37 )
          = SY37 ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(10,plain,
    ( ( ~ ! [SY37: g] :
            ( ( sK1_SY0 @ sK2_SY23 @ SY37 )
            = SY37 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ( ( sK1_SY0 @ sK2_SY23 @ sK3_SY37 )
       != sK3_SY37 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(12,plain,
    ( ( ! [SY35: g] :
          ( ( sK1_SY0 @ SY35 @ ( sK4_SY36 @ SY35 ) )
          = sK2_SY23 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(13,plain,
    ( ( ! [SY35: g] :
          ( ( sK1_SY0 @ SY35 @ ( sK4_SY36 @ SY35 ) )
          = sK2_SY23 ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ! [SY34: g] :
          ( ( sK1_SY0 @ SY34 @ sK2_SY23 )
          = SY34 ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(15,plain,
    ( ( ! [SY24: g,SY25: g,SY26: g] :
          ( ( sK1_SY0 @ ( sK1_SY0 @ SY26 @ SY24 ) @ SY25 )
          = ( sK1_SY0 @ SY26 @ ( sK1_SY0 @ SY24 @ SY25 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(16,plain,
    ( ( ( ( sK1_SY0 @ sK2_SY23 @ sK3_SY37 )
       != sK3_SY37 ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(17,plain,
    ! [SV1: g] :
      ( ( ( sK1_SY0 @ SV1 @ ( sK4_SY36 @ SV1 ) )
        = sK2_SY23 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(18,plain,
    ! [SV2: g] :
      ( ( ( sK1_SY0 @ SV2 @ sK2_SY23 )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(19,plain,
    ! [SV3: g] :
      ( ( ! [SY38: g,SY39: g] :
            ( ( sK1_SY0 @ ( sK1_SY0 @ SY39 @ SV3 ) @ SY38 )
            = ( sK1_SY0 @ SY39 @ ( sK1_SY0 @ SV3 @ SY38 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(20,plain,
    ( ( ( sK1_SY0 @ sK2_SY23 @ sK3_SY37 )
      = sK3_SY37 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(21,plain,
    ! [SV4: g,SV3: g] :
      ( ( ! [SY40: g] :
            ( ( sK1_SY0 @ ( sK1_SY0 @ SY40 @ SV3 ) @ SV4 )
            = ( sK1_SY0 @ SY40 @ ( sK1_SY0 @ SV3 @ SV4 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(22,plain,
    ! [SV4: g,SV3: g,SV5: g] :
      ( ( ( sK1_SY0 @ ( sK1_SY0 @ SV5 @ SV3 ) @ SV4 )
        = ( sK1_SY0 @ SV5 @ ( sK1_SY0 @ SV3 @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(23,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[17,22,20,18]) ).

thf(24,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ALG279^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n023.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Wed Jun  8 17:08:08 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  
% 0.14/0.35   No.of.Axioms: 0
% 0.14/0.35  
% 0.14/0.35   Length.of.Defs: 386
% 0.14/0.35  
% 0.14/0.35   Contains.Choice.Funs: false
% 0.14/0.35  (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).
% 0.14/0.39  
% 0.14/0.39  ********************************
% 0.14/0.39  *   All subproblems solved!    *
% 0.14/0.39  ********************************
% 0.14/0.39  % 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:23,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.14/0.39  
% 0.14/0.39  %**** Beginning of derivation protocol ****
% 0.14/0.39  % SZS output start CNFRefutation
% See solution above
% 0.14/0.39  
% 0.14/0.39  %**** End of derivation protocol ****
% 0.14/0.39  %**** no. of clauses in derivation: 24 ****
% 0.14/0.39  %**** clause counter: 23 ****
% 0.14/0.39  
% 0.14/0.39  % 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:23,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------