TSTP Solution File: LCL146-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LCL146-1 : 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 : n020.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 : Sun Jul 17 12:20:58 EDT 2022

% Result   : Unsatisfiable 0.38s 0.57s
% Output   : CNFRefutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   66 (  52 unt;   8 typ;   0 def)
%            Number of atoms       :  175 ( 101 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  342 (  19   ~;  15   |;   0   &; 308   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   92 (   0   ^  92   !;   0   ?;  92   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_big_V,type,
    big_V: $i > $i > $i ).

thf(tp_big_hat,type,
    big_hat: $i > $i > $i ).

thf(tp_implies,type,
    implies: $i > $i > $i ).

thf(tp_not,type,
    not: $i > $i ).

thf(tp_ordered,type,
    ordered: $i > $i > $o ).

thf(tp_truth,type,
    truth: $i ).

thf(tp_x,type,
    x: $i ).

thf(tp_y,type,
    y: $i ).

thf(1,axiom,
    ! [X: $i,Y: $i] :
      ( ( ( implies @ X @ Y )
       != truth )
      | ( ordered @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition2) ).

thf(2,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( ordered @ X @ Y )
      | ( ( implies @ X @ Y )
        = truth ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition1) ).

thf(3,axiom,
    ! [X: $i,Y: $i] :
      ( ( big_hat @ X @ Y )
      = ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_hat_definition) ).

thf(4,axiom,
    ! [X: $i,Y: $i] :
      ( ( big_V @ X @ Y )
      = ( implies @ ( implies @ X @ Y ) @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_V_definition) ).

thf(5,axiom,
    ! [X: $i,Y: $i] :
      ( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
      = truth ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).

thf(6,axiom,
    ! [X: $i,Y: $i] :
      ( ( implies @ ( implies @ X @ Y ) @ Y )
      = ( implies @ ( implies @ Y @ X ) @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).

thf(7,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
      = truth ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).

thf(8,axiom,
    ! [X: $i] :
      ( ( implies @ truth @ X )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).

thf(9,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(10,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[9]) ).

thf(11,negated_conjecture,
    ( not @ ( big_hat @ x @ y ) )
 != ( big_V @ ( not @ x ) @ ( not @ y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).

thf(12,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( implies @ X @ Y )
           != truth )
          | ( ordered @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(14,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( ordered @ X @ Y )
          | ( ( implies @ X @ Y )
            = truth ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(15,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( big_hat @ X @ Y )
          = ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(16,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( big_V @ X @ Y )
          = ( implies @ ( implies @ X @ Y ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
          = truth ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(18,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( implies @ ( implies @ X @ Y ) @ Y )
          = ( implies @ ( implies @ Y @ X ) @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(19,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
          = truth ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(20,plain,
    ( ( ! [X: $i] :
          ( ( implies @ truth @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(21,plain,
    ( ( ( ( not @ ( big_hat @ x @ y ) )
       != ( big_V @ ( not @ x ) @ ( not @ y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(22,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[12]) ).

thf(23,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( implies @ X @ Y )
           != truth )
          | ( ordered @ X @ Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(24,plain,
    ( ( ( ( not @ ( big_hat @ x @ y ) )
       != ( big_V @ ( not @ x ) @ ( not @ y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[21]) ).

thf(25,plain,
    ( ( ( ( not @ ( big_hat @ x @ y ) )
       != ( big_V @ ( not @ x ) @ ( not @ y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(26,plain,
    ( ( ! [X: $i] :
          ( ( implies @ truth @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(27,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
          = truth ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(28,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( implies @ ( implies @ X @ Y ) @ Y )
          = ( implies @ ( implies @ Y @ X ) @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(29,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
          = truth ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(30,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( big_V @ X @ Y )
          = ( implies @ ( implies @ X @ Y ) @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(31,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( big_hat @ X @ Y )
          = ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(32,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( ordered @ X @ Y )
          | ( ( implies @ X @ Y )
            = truth ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(33,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( implies @ X @ Y )
           != truth )
          | ( ordered @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(34,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(35,plain,
    ( ( ( not @ ( big_hat @ x @ y ) )
      = ( big_V @ ( not @ x ) @ ( not @ y ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(36,plain,
    ! [SV1: $i] :
      ( ( ( implies @ truth @ SV1 )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(37,plain,
    ! [SV2: $i] :
      ( ( ! [SY16: $i,SY17: $i] :
            ( ( implies @ ( implies @ SV2 @ SY16 ) @ ( implies @ ( implies @ SY16 @ SY17 ) @ ( implies @ SV2 @ SY17 ) ) )
            = truth ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(38,plain,
    ! [SV3: $i] :
      ( ( ! [SY18: $i] :
            ( ( implies @ ( implies @ SV3 @ SY18 ) @ SY18 )
            = ( implies @ ( implies @ SY18 @ SV3 ) @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(39,plain,
    ! [SV4: $i] :
      ( ( ! [SY19: $i] :
            ( ( implies @ ( implies @ ( not @ SV4 ) @ ( not @ SY19 ) ) @ ( implies @ SY19 @ SV4 ) )
            = truth ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(40,plain,
    ! [SV5: $i] :
      ( ( ! [SY20: $i] :
            ( ( big_V @ SV5 @ SY20 )
            = ( implies @ ( implies @ SV5 @ SY20 ) @ SY20 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(41,plain,
    ! [SV6: $i] :
      ( ( ! [SY21: $i] :
            ( ( big_hat @ SV6 @ SY21 )
            = ( not @ ( big_V @ ( not @ SV6 ) @ ( not @ SY21 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(42,plain,
    ! [SV7: $i] :
      ( ( ! [SY22: $i] :
            ( ~ ( ordered @ SV7 @ SY22 )
            | ( ( implies @ SV7 @ SY22 )
              = truth ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(43,plain,
    ! [SV8: $i] :
      ( ( ! [SY23: $i] :
            ( ( ( implies @ SV8 @ SY23 )
             != truth )
            | ( ordered @ SV8 @ SY23 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(44,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(45,plain,
    ! [SV9: $i,SV2: $i] :
      ( ( ! [SY24: $i] :
            ( ( implies @ ( implies @ SV2 @ SV9 ) @ ( implies @ ( implies @ SV9 @ SY24 ) @ ( implies @ SV2 @ SY24 ) ) )
            = truth ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(46,plain,
    ! [SV10: $i,SV3: $i] :
      ( ( ( implies @ ( implies @ SV3 @ SV10 ) @ SV10 )
        = ( implies @ ( implies @ SV10 @ SV3 ) @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(47,plain,
    ! [SV11: $i,SV4: $i] :
      ( ( ( implies @ ( implies @ ( not @ SV4 ) @ ( not @ SV11 ) ) @ ( implies @ SV11 @ SV4 ) )
        = truth )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(48,plain,
    ! [SV12: $i,SV5: $i] :
      ( ( ( big_V @ SV5 @ SV12 )
        = ( implies @ ( implies @ SV5 @ SV12 ) @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(49,plain,
    ! [SV13: $i,SV6: $i] :
      ( ( ( big_hat @ SV6 @ SV13 )
        = ( not @ ( big_V @ ( not @ SV6 ) @ ( not @ SV13 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(50,plain,
    ! [SV14: $i,SV7: $i] :
      ( ( ~ ( ordered @ SV7 @ SV14 )
        | ( ( implies @ SV7 @ SV14 )
          = truth ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(51,plain,
    ! [SV15: $i,SV8: $i] :
      ( ( ( ( implies @ SV8 @ SV15 )
         != truth )
        | ( ordered @ SV8 @ SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(52,plain,
    ! [SV16: $i,SV9: $i,SV2: $i] :
      ( ( ( implies @ ( implies @ SV2 @ SV9 ) @ ( implies @ ( implies @ SV9 @ SV16 ) @ ( implies @ SV2 @ SV16 ) ) )
        = truth )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(53,plain,
    ! [SV14: $i,SV7: $i] :
      ( ( ( ~ ( ordered @ SV7 @ SV14 ) )
        = $true )
      | ( ( ( implies @ SV7 @ SV14 )
          = truth )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[50]) ).

thf(54,plain,
    ! [SV15: $i,SV8: $i] :
      ( ( ( ( ( implies @ SV8 @ SV15 )
           != truth ) )
        = $true )
      | ( ( ordered @ SV8 @ SV15 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(55,plain,
    ! [SV14: $i,SV7: $i] :
      ( ( ( ordered @ SV7 @ SV14 )
        = $false )
      | ( ( ( implies @ SV7 @ SV14 )
          = truth )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(56,plain,
    ! [SV15: $i,SV8: $i] :
      ( ( ( ( implies @ SV8 @ SV15 )
          = truth )
        = $false )
      | ( ( ordered @ SV8 @ SV15 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(57,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[35,56,55,52,49,48,47,46,44,36]) ).

thf(58,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[57]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n020.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 : Sun Jul  3 18:35:00 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 9
% 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:9,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:11,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.38/0.57  
% 0.38/0.57  ********************************
% 0.38/0.57  *   All subproblems solved!    *
% 0.38/0.57  ********************************
% 0.38/0.57  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.38/0.57  
% 0.38/0.57  %**** Beginning of derivation protocol ****
% 0.38/0.57  % SZS output start CNFRefutation
% See solution above
% 0.38/0.57  
% 0.38/0.57  %**** End of derivation protocol ****
% 0.38/0.57  %**** no. of clauses in derivation: 58 ****
% 0.38/0.57  %**** clause counter: 57 ****
% 0.38/0.57  
% 0.38/0.57  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------