TSTP Solution File: SYO038^1.003.003 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO038^1.003.003 : TPTP v8.1.0. Released v5.3.0.
% 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 : Thu Jul 21 17:31:31 EDT 2022

% Result   : Theorem 0.19s 0.39s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   35 (  28 unt;   4 typ;   0 def)
%            Number of atoms       :   90 (  39 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :  164 (   6   ~;   5   |;   0   &; 151   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   25 (   0   ^  25   !;   0   ?;  25   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_d,type,
    d: $i > $o ).

thf(tp_f,type,
    f: $i > $i > $i ).

thf(tp_one,type,
    one: $i ).

thf(tp_s,type,
    s: $i > $i ).

thf(1,axiom,
    ! [X: $i] :
      ( ( d @ X )
     => ( d @ ( s @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

thf(2,axiom,
    d @ one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

thf(3,axiom,
    ! [N: $i,X: $i] :
      ( ( f @ ( s @ N ) @ ( s @ X ) )
      = ( f @ N @ ( f @ ( s @ N ) @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

thf(4,axiom,
    ! [X: $i] :
      ( ( f @ one @ ( s @ X ) )
      = ( s @ ( s @ ( f @ one @ X ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

thf(5,axiom,
    ! [N: $i] :
      ( ( f @ N @ one )
      = ( s @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

thf(6,conjecture,
    d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(7,negated_conjecture,
    ( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[6]) ).

thf(8,plain,
    ( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [X: $i] :
          ( ( d @ X )
         => ( d @ ( s @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(10,plain,
    ( ( d @ one )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(11,plain,
    ( ( ! [N: $i,X: $i] :
          ( ( f @ ( s @ N ) @ ( s @ X ) )
          = ( f @ N @ ( f @ ( s @ N ) @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(12,plain,
    ( ( ! [X: $i] :
          ( ( f @ one @ ( s @ X ) )
          = ( s @ ( s @ ( f @ one @ X ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(13,plain,
    ( ( ! [N: $i] :
          ( ( f @ N @ one )
          = ( s @ one ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(14,plain,
    ( ( ~ ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(15,plain,
    ( ( ! [X: $i] :
          ( ~ ( d @ X )
          | ( d @ ( s @ X ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(16,plain,
    ( ( ! [N: $i] :
          ( ( f @ N @ one )
          = ( s @ one ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ! [X: $i] :
          ( ( f @ one @ ( s @ X ) )
          = ( s @ ( s @ ( f @ one @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(18,plain,
    ( ( ! [N: $i,X: $i] :
          ( ( f @ ( s @ N ) @ ( s @ X ) )
          = ( f @ N @ ( f @ ( s @ N ) @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(19,plain,
    ( ( d @ one )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(20,plain,
    ( ( ! [X: $i] :
          ( ~ ( d @ X )
          | ( d @ ( s @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(21,plain,
    ( ( ~ ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(22,plain,
    ! [SV1: $i] :
      ( ( ( f @ SV1 @ one )
        = ( s @ one ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(23,plain,
    ! [SV2: $i] :
      ( ( ( f @ one @ ( s @ SV2 ) )
        = ( s @ ( s @ ( f @ one @ SV2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(24,plain,
    ! [SV3: $i] :
      ( ( ! [SY5: $i] :
            ( ( f @ ( s @ SV3 ) @ ( s @ SY5 ) )
            = ( f @ SV3 @ ( f @ ( s @ SV3 ) @ SY5 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(25,plain,
    ! [SV4: $i] :
      ( ( ~ ( d @ SV4 )
        | ( d @ ( s @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(26,plain,
    ( ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(27,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ( f @ ( s @ SV3 ) @ ( s @ SV5 ) )
        = ( f @ SV3 @ ( f @ ( s @ SV3 ) @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(28,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( d @ SV4 ) )
        = $true )
      | ( ( d @ ( s @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(29,plain,
    ! [SV4: $i] :
      ( ( ( d @ SV4 )
        = $false )
      | ( ( d @ ( s @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(30,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[19,29,27,26,23,22]) ).

thf(31,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO038^1.003.003 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n008.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sat Jul  9 06:19:23 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 5
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 0
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.34  (rf:0,axioms:5,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:7,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.19/0.39  
% 0.19/0.39  ********************************
% 0.19/0.39  *   All subproblems solved!    *
% 0.19/0.39  ********************************
% 0.19/0.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:30,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.39  
% 0.19/0.39  %**** Beginning of derivation protocol ****
% 0.19/0.39  % SZS output start CNFRefutation
% See solution above
% 0.19/0.39  
% 0.19/0.39  %**** End of derivation protocol ****
% 0.19/0.39  %**** no. of clauses in derivation: 31 ****
% 0.19/0.39  %**** clause counter: 30 ****
% 0.19/0.39  
% 0.19/0.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:30,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------