TSTP Solution File: ROB013-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : ROB013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n019.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 : Mon Jul 18 20:54:06 EDT 2022

% Result   : Unsatisfiable 0.13s 0.39s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   37 (  32 unt;   5 typ;   0 def)
%            Number of atoms       :   82 (  49 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  168 (   6   ~;   0   |;   0   &; 162   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :   38 (   0   ^  38   !;   0   ?;  38   :)

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

thf(tp_add,type,
    add: $i > $i > $i ).

thf(tp_b,type,
    b: $i ).

thf(tp_c,type,
    c: $i ).

thf(tp_negate,type,
    negate: $i > $i ).

thf(1,axiom,
    ! [X: $i,Y: $i] :
      ( ( negate @ ( add @ ( negate @ ( add @ X @ Y ) ) @ ( negate @ ( add @ X @ ( negate @ Y ) ) ) ) )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',robbins_axiom) ).

thf(2,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( add @ ( add @ X @ Y ) @ Z )
      = ( add @ X @ ( add @ Y @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).

thf(3,axiom,
    ! [X: $i,Y: $i] :
      ( ( add @ X @ Y )
      = ( add @ Y @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).

thf(4,axiom,
    ( ( negate @ ( add @ a @ b ) )
    = c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).

thf(5,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(6,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[5]) ).

thf(7,negated_conjecture,
    ( negate @ ( add @ c @ ( negate @ ( add @ ( negate @ b ) @ a ) ) ) )
 != a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_result) ).

thf(8,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( negate @ ( add @ ( negate @ ( add @ X @ Y ) ) @ ( negate @ ( add @ X @ ( negate @ Y ) ) ) ) )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(10,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( add @ ( add @ X @ Y ) @ Z )
          = ( add @ X @ ( add @ Y @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

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

thf(12,plain,
    ( ( ( negate @ ( add @ a @ b ) )
      = c )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(13,plain,
    ( ( ( ( negate @ ( add @ c @ ( negate @ ( add @ ( negate @ b ) @ a ) ) ) )
       != a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(14,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(15,plain,
    ( ( ( ( negate @ ( add @ c @ ( negate @ ( add @ ( negate @ b ) @ a ) ) ) )
       != a ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(16,plain,
    ( ( ( ( negate @ ( add @ c @ ( negate @ ( add @ ( negate @ b ) @ a ) ) ) )
       != a ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(17,plain,
    ( ( ( negate @ ( add @ a @ b ) )
      = c )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

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

thf(19,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( add @ ( add @ X @ Y ) @ Z )
          = ( add @ X @ ( add @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(20,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( negate @ ( add @ ( negate @ ( add @ X @ Y ) ) @ ( negate @ ( add @ X @ ( negate @ Y ) ) ) ) )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(21,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(22,plain,
    ( ( ( negate @ ( add @ c @ ( negate @ ( add @ ( negate @ b ) @ a ) ) ) )
      = a )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(23,plain,
    ! [SV1: $i] :
      ( ( ! [SY7: $i] :
            ( ( add @ SV1 @ SY7 )
            = ( add @ SY7 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(24,plain,
    ! [SV2: $i] :
      ( ( ! [SY8: $i,SY9: $i] :
            ( ( add @ ( add @ SV2 @ SY8 ) @ SY9 )
            = ( add @ SV2 @ ( add @ SY8 @ SY9 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(25,plain,
    ! [SV3: $i] :
      ( ( ! [SY10: $i] :
            ( ( negate @ ( add @ ( negate @ ( add @ SV3 @ SY10 ) ) @ ( negate @ ( add @ SV3 @ ( negate @ SY10 ) ) ) ) )
            = SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(26,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(27,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( add @ SV1 @ SV4 )
        = ( add @ SV4 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ! [SY11: $i] :
            ( ( add @ ( add @ SV2 @ SV5 ) @ SY11 )
            = ( add @ SV2 @ ( add @ SV5 @ SY11 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(29,plain,
    ! [SV6: $i,SV3: $i] :
      ( ( ( negate @ ( add @ ( negate @ ( add @ SV3 @ SV6 ) ) @ ( negate @ ( add @ SV3 @ ( negate @ SV6 ) ) ) ) )
        = SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV7: $i,SV5: $i,SV2: $i] :
      ( ( ( add @ ( add @ SV2 @ SV5 ) @ SV7 )
        = ( add @ SV2 @ ( add @ SV5 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(31,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[17,30,29,27,26,22]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ROB013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun  9 13:42:10 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 5
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:7,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.13/0.39  
% 0.13/0.39  ********************************
% 0.13/0.39  *   All subproblems solved!    *
% 0.13/0.39  ********************************
% 0.13/0.39  % SZS status Unsatisfiable 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.39  
% 0.13/0.39  %**** Beginning of derivation protocol ****
% 0.13/0.39  % SZS output start CNFRefutation
% See solution above
% 0.13/0.39  
% 0.13/0.39  %**** End of derivation protocol ****
% 0.13/0.39  %**** no. of clauses in derivation: 32 ****
% 0.13/0.39  %**** clause counter: 31 ****
% 0.13/0.39  
% 0.13/0.39  % SZS status Unsatisfiable 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------