TSTP Solution File: LAT026-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LAT026-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n013.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 05:44:04 EDT 2022

% Result   : Unsatisfiable 26.63s 26.80s
% Output   : CNFRefutation 26.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   54 (  49 unt;   5 typ;   0 def)
%            Number of atoms       :  127 (  80 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  234 (   6   ~;   0   |;   0   &; 228   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :   82 (   0   ^  82   !;   0   ?;  82   :)

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

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

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

thf(tp_join,type,
    join: $i > $i > $i ).

thf(tp_meet,type,
    meet: $i > $i > $i ).

thf(1,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( join @ ( join @ ( meet @ X @ Y ) @ ( meet @ Z @ Y ) ) @ Y )
      = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wal_2) ).

thf(2,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( meet @ ( meet @ ( join @ X @ Y ) @ ( join @ Z @ Y ) ) @ Y )
      = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wal_1) ).

thf(3,axiom,
    ! [X: $i,Y: $i] :
      ( ( join @ X @ Y )
      = ( join @ Y @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).

thf(4,axiom,
    ! [X: $i,Y: $i] :
      ( ( meet @ X @ Y )
      = ( meet @ Y @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).

thf(5,axiom,
    ! [X: $i] :
      ( ( join @ X @ X )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).

thf(6,axiom,
    ! [X: $i] :
      ( ( meet @ X @ X )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).

thf(7,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( meet @ X @ ( join @ Y @ ( join @ X @ Z ) ) )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorbtion) ).

thf(8,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(9,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[8]) ).

thf(10,negated_conjecture,
    ( meet @ ( meet @ a @ b ) @ c )
 != ( meet @ a @ ( meet @ b @ c ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_meet) ).

thf(11,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( join @ ( join @ ( meet @ X @ Y ) @ ( meet @ Z @ Y ) ) @ Y )
          = Y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(13,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( meet @ ( meet @ ( join @ X @ Y ) @ ( join @ Z @ Y ) ) @ Y )
          = Y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(14,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( join @ X @ Y )
          = ( join @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(15,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( meet @ X @ Y )
          = ( meet @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(16,plain,
    ( ( ! [X: $i] :
          ( ( join @ X @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(17,plain,
    ( ( ! [X: $i] :
          ( ( meet @ X @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(18,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( meet @ X @ ( join @ Y @ ( join @ X @ Z ) ) )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(19,plain,
    ( ( ( ( meet @ ( meet @ a @ b ) @ c )
       != ( meet @ a @ ( meet @ b @ c ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(20,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[11]) ).

thf(21,plain,
    ( ( ( ( meet @ ( meet @ a @ b ) @ c )
       != ( meet @ a @ ( meet @ b @ c ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(22,plain,
    ( ( ( ( meet @ ( meet @ a @ b ) @ c )
       != ( meet @ a @ ( meet @ b @ c ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(23,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( meet @ X @ ( join @ Y @ ( join @ X @ Z ) ) )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(24,plain,
    ( ( ! [X: $i] :
          ( ( meet @ X @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(25,plain,
    ( ( ! [X: $i] :
          ( ( join @ X @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(26,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( meet @ X @ Y )
          = ( meet @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(27,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( join @ X @ Y )
          = ( join @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(28,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( meet @ ( meet @ ( join @ X @ Y ) @ ( join @ Z @ Y ) ) @ Y )
          = Y ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(29,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( join @ ( join @ ( meet @ X @ Y ) @ ( meet @ Z @ Y ) ) @ Y )
          = Y ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(30,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(31,plain,
    ( ( ( meet @ ( meet @ a @ b ) @ c )
      = ( meet @ a @ ( meet @ b @ c ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(32,plain,
    ! [SV1: $i] :
      ( ( ! [SY15: $i,SY16: $i] :
            ( ( meet @ SV1 @ ( join @ SY15 @ ( join @ SV1 @ SY16 ) ) )
            = SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(33,plain,
    ! [SV2: $i] :
      ( ( ( meet @ SV2 @ SV2 )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(34,plain,
    ! [SV3: $i] :
      ( ( ( join @ SV3 @ SV3 )
        = SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(35,plain,
    ! [SV4: $i] :
      ( ( ! [SY17: $i] :
            ( ( meet @ SV4 @ SY17 )
            = ( meet @ SY17 @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(36,plain,
    ! [SV5: $i] :
      ( ( ! [SY18: $i] :
            ( ( join @ SV5 @ SY18 )
            = ( join @ SY18 @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(37,plain,
    ! [SV6: $i] :
      ( ( ! [SY19: $i,SY20: $i] :
            ( ( meet @ ( meet @ ( join @ SV6 @ SY19 ) @ ( join @ SY20 @ SY19 ) ) @ SY19 )
            = SY19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(38,plain,
    ! [SV7: $i] :
      ( ( ! [SY21: $i,SY22: $i] :
            ( ( join @ ( join @ ( meet @ SV7 @ SY21 ) @ ( meet @ SY22 @ SY21 ) ) @ SY21 )
            = SY21 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(39,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(40,plain,
    ! [SV8: $i,SV1: $i] :
      ( ( ! [SY23: $i] :
            ( ( meet @ SV1 @ ( join @ SV8 @ ( join @ SV1 @ SY23 ) ) )
            = SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(41,plain,
    ! [SV9: $i,SV4: $i] :
      ( ( ( meet @ SV4 @ SV9 )
        = ( meet @ SV9 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(42,plain,
    ! [SV10: $i,SV5: $i] :
      ( ( ( join @ SV5 @ SV10 )
        = ( join @ SV10 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(43,plain,
    ! [SV11: $i,SV6: $i] :
      ( ( ! [SY24: $i] :
            ( ( meet @ ( meet @ ( join @ SV6 @ SV11 ) @ ( join @ SY24 @ SV11 ) ) @ SV11 )
            = SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(44,plain,
    ! [SV12: $i,SV7: $i] :
      ( ( ! [SY25: $i] :
            ( ( join @ ( join @ ( meet @ SV7 @ SV12 ) @ ( meet @ SY25 @ SV12 ) ) @ SV12 )
            = SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(45,plain,
    ! [SV13: $i,SV8: $i,SV1: $i] :
      ( ( ( meet @ SV1 @ ( join @ SV8 @ ( join @ SV1 @ SV13 ) ) )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(46,plain,
    ! [SV14: $i,SV11: $i,SV6: $i] :
      ( ( ( meet @ ( meet @ ( join @ SV6 @ SV11 ) @ ( join @ SV14 @ SV11 ) ) @ SV11 )
        = SV11 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(47,plain,
    ! [SV15: $i,SV12: $i,SV7: $i] :
      ( ( ( join @ ( join @ ( meet @ SV7 @ SV12 ) @ ( meet @ SV15 @ SV12 ) ) @ SV12 )
        = SV12 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(48,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[31,47,46,45,42,41,39,34,33]) ).

thf(49,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : LAT026-1 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun 29 16:56:44 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 8
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (rf:0,axioms:8,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:10,loop_count:0,foatp_calls:0,translation:fof_full)..
% 26.63/26.80  
% 26.63/26.80  ********************************
% 26.63/26.80  *   All subproblems solved!    *
% 26.63/26.80  ********************************
% 26.63/26.80  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:48,loop_count:0,foatp_calls:1,translation:fof_full)
% 26.63/26.80  
% 26.63/26.80  %**** Beginning of derivation protocol ****
% 26.63/26.80  % SZS output start CNFRefutation
% See solution above
% 26.63/26.80  
% 26.63/26.80  %**** End of derivation protocol ****
% 26.63/26.80  %**** no. of clauses in derivation: 49 ****
% 26.63/26.80  %**** clause counter: 48 ****
% 26.63/26.80  
% 26.63/26.80  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,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:48,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------