TSTP Solution File: ALG282^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : ALG282^5 : 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 : n021.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 0.12s 0.37s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   28 (  21 unt;   6 typ;   0 def)
%            Number of atoms       :   71 (  49 equ;   0 cnn)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :  125 (   4   ~;   0   |;   6   &; 112   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :   55 (   0   ^  50   !;   5   ?;  55   :)

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

thf(tp_cE,type,
    cE: a ).

thf(tp_cJ,type,
    cJ: a > a ).

thf(tp_cP,type,
    cP: a > a > a ).

thf(tp_sK1_X,type,
    sK1_X: a ).

thf(tp_sK2_SY8,type,
    sK2_SY8: a ).

thf(1,conjecture,
    ( ( ! [Xx: a,Xy: a,Xz: a] :
          ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
          = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
      & ! [Xx: a] :
          ( ( cP @ cE @ Xx )
          = Xx )
      & ! [Xy: a] :
          ( ( cP @ ( cJ @ Xy ) @ Xy )
          = cE ) )
   => ! [X: a,Y: a] :
      ? [W: a] :
        ( ( cP @ W @ X )
        = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM21_pme) ).

thf(2,negated_conjecture,
    ( ( ( ! [Xx: a,Xy: a,Xz: a] :
            ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
            = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
        & ! [Xx: a] :
            ( ( cP @ cE @ Xx )
            = Xx )
        & ! [Xy: a] :
            ( ( cP @ ( cJ @ Xy ) @ Xy )
            = cE ) )
     => ! [X: a,Y: a] :
        ? [W: a] :
          ( ( cP @ W @ X )
          = Y ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( ! [Xx: a,Xy: a,Xz: a] :
            ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
            = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
        & ! [Xx: a] :
            ( ( cP @ cE @ Xx )
            = Xx )
        & ! [Xy: a] :
            ( ( cP @ ( cJ @ Xy ) @ Xy )
            = cE ) )
     => ! [X: a,Y: a] :
        ? [W: a] :
          ( ( cP @ W @ X )
          = Y ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [Xx: a,Xy: a,Xz: a] :
          ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
          = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xx: a] :
          ( ( cP @ cE @ Xx )
          = Xx ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ! [Xy: a] :
          ( ( cP @ ( cJ @ Xy ) @ Xy )
          = cE ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ! [X: a,Y: a] :
        ? [W: a] :
          ( ( cP @ W @ X )
          = Y ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(8,plain,
    ( ( ~ ! [X: a,Y: a] :
          ? [W: a] :
            ( ( cP @ W @ X )
            = Y ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [SY10: a] :
          ( ( cP @ SY10 @ sK1_X )
         != sK2_SY8 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    ( ( ! [Xy: a] :
          ( ( cP @ ( cJ @ Xy ) @ Xy )
          = cE ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(11,plain,
    ( ( ! [Xx: a] :
          ( ( cP @ cE @ Xx )
          = Xx ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(12,plain,
    ( ( ! [Xx: a,Xy: a,Xz: a] :
          ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
          = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[4]) ).

thf(13,plain,
    ( ( ! [SY10: a] :
          ( ( cP @ SY10 @ sK1_X )
         != sK2_SY8 ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(14,plain,
    ! [SV1: a] :
      ( ( ( cP @ ( cJ @ SV1 ) @ SV1 )
        = cE )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10]) ).

thf(15,plain,
    ! [SV2: a] :
      ( ( ( cP @ cE @ SV2 )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(16,plain,
    ! [SV3: a] :
      ( ( ! [SY11: a,SY12: a] :
            ( ( cP @ ( cP @ SV3 @ SY11 ) @ SY12 )
            = ( cP @ SV3 @ ( cP @ SY11 @ SY12 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(17,plain,
    ! [SV4: a] :
      ( ( ( ( cP @ SV4 @ sK1_X )
         != sK2_SY8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(18,plain,
    ! [SV5: a,SV3: a] :
      ( ( ! [SY13: a] :
            ( ( cP @ ( cP @ SV3 @ SV5 ) @ SY13 )
            = ( cP @ SV3 @ ( cP @ SV5 @ SY13 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(19,plain,
    ! [SV4: a] :
      ( ( ( cP @ SV4 @ sK1_X )
        = sK2_SY8 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(20,plain,
    ! [SV6: a,SV5: a,SV3: a] :
      ( ( ( cP @ ( cP @ SV3 @ SV5 ) @ SV6 )
        = ( cP @ SV3 @ ( cP @ SV5 @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(21,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[14,20,19,15]) ).

thf(22,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ALG282^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n021.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 : Wed Jun  8 10:37:37 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).
% 0.12/0.37  
% 0.12/0.37  ********************************
% 0.12/0.37  *   All subproblems solved!    *
% 0.12/0.37  ********************************
% 0.12/0.37  % 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:21,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.38  
% 0.12/0.38  %**** Beginning of derivation protocol ****
% 0.12/0.38  % SZS output start CNFRefutation
% See solution above
% 0.12/0.38  
% 0.12/0.38  %**** End of derivation protocol ****
% 0.12/0.38  %**** no. of clauses in derivation: 22 ****
% 0.12/0.38  %**** clause counter: 21 ****
% 0.12/0.38  
% 0.12/0.38  % 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:21,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------