TSTP Solution File: HWV052-1.002.001 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : HWV052-1.002.001 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n025.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 : Sat Jul 16 18:18:43 EDT 2022

% Result   : Unsatisfiable 0.91s 1.09s
% Output   : CNFRefutation 0.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   65 (  57 unt;   6 typ;   0 def)
%            Number of atoms       :  160 ( 104 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :  248 (   7   ~;   5   |;   0   &; 236   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :   91 (   0   ^  91   !;   0   ?;  91   :)

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

thf(tp_inv,type,
    inv: $i > $i ).

thf(tp_o,type,
    o: $i ).

thf(tp_pack1,type,
    pack1: $i > $i > $i ).

thf(tp_unpack1,type,
    unpack1: $i > $i > $i > $i ).

thf(tp_unpack2,type,
    unpack2: $i > $i > $i > $i ).

thf(1,axiom,
    ! [X1: $i,X2: $i] :
      ( ( unpack2 @ X1 @ X2 @ ( inv @ ( pack1 @ X1 @ X2 ) ) )
      = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack2_06) ).

thf(2,axiom,
    ! [X1: $i,X2: $i] :
      ( ( unpack2 @ X1 @ ( inv @ X2 ) @ ( pack1 @ X1 @ X2 ) )
      = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack2_05) ).

thf(3,axiom,
    ! [X1: $i,X2: $i] :
      ( ( unpack2 @ ( inv @ X1 ) @ X2 @ ( pack1 @ X1 @ X2 ) )
      = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack2_04) ).

thf(4,axiom,
    ! [X1: $i,X2: $i] :
      ( ( unpack2 @ X1 @ X2 @ ( pack1 @ X1 @ X2 ) )
      = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack2) ).

thf(5,axiom,
    ! [X1: $i,X2: $i] :
      ( ( unpack1 @ X1 @ X2 @ ( inv @ ( pack1 @ X1 @ X2 ) ) )
      = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack1_03) ).

thf(6,axiom,
    ! [X1: $i,X2: $i] :
      ( ( unpack1 @ X1 @ ( inv @ X2 ) @ ( pack1 @ X1 @ X2 ) )
      = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack1_02) ).

thf(7,axiom,
    ! [X1: $i,X2: $i] :
      ( ( unpack1 @ ( inv @ X1 ) @ X2 @ ( pack1 @ X1 @ X2 ) )
      = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack1_01) ).

thf(8,axiom,
    ! [X1: $i,X2: $i] :
      ( ( unpack1 @ X1 @ X2 @ ( pack1 @ X1 @ X2 ) )
      = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack1) ).

thf(9,axiom,
    ! [X: $i] :
      ( ( inv @ X )
     != X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bit_inverse) ).

thf(10,axiom,
    ! [X: $i] :
      ( ( X = o )
      | ( X = i ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bit_domain) ).

thf(11,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(12,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[11]) ).

thf(13,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack2 @ X1 @ X2 @ ( inv @ ( pack1 @ X1 @ X2 ) ) )
          = X2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(15,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack2 @ X1 @ ( inv @ X2 ) @ ( pack1 @ X1 @ X2 ) )
          = X2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(16,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack2 @ ( inv @ X1 ) @ X2 @ ( pack1 @ X1 @ X2 ) )
          = X2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(17,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack2 @ X1 @ X2 @ ( pack1 @ X1 @ X2 ) )
          = X2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(18,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack1 @ X1 @ X2 @ ( inv @ ( pack1 @ X1 @ X2 ) ) )
          = X1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(19,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack1 @ X1 @ ( inv @ X2 ) @ ( pack1 @ X1 @ X2 ) )
          = X1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(20,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack1 @ ( inv @ X1 ) @ X2 @ ( pack1 @ X1 @ X2 ) )
          = X1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(21,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack1 @ X1 @ X2 @ ( pack1 @ X1 @ X2 ) )
          = X1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(22,plain,
    ( ( ! [X: $i] :
          ( ( inv @ X )
         != X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(23,plain,
    ( ( ! [X: $i] :
          ( ( X = o )
          | ( X = i ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(24,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[13]) ).

thf(25,plain,
    ( ( ! [X: $i] :
          ( ( inv @ X )
         != X ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[22]) ).

thf(26,plain,
    ( ( ! [X: $i] :
          ( ( X = o )
          | ( X = i ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(27,plain,
    ( ( ! [X: $i] :
          ( ( inv @ X )
         != X ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(28,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack1 @ X1 @ X2 @ ( pack1 @ X1 @ X2 ) )
          = X1 ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(29,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack1 @ ( inv @ X1 ) @ X2 @ ( pack1 @ X1 @ X2 ) )
          = X1 ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(30,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack1 @ X1 @ ( inv @ X2 ) @ ( pack1 @ X1 @ X2 ) )
          = X1 ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(31,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack1 @ X1 @ X2 @ ( inv @ ( pack1 @ X1 @ X2 ) ) )
          = X1 ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(32,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack2 @ X1 @ X2 @ ( pack1 @ X1 @ X2 ) )
          = X2 ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(33,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack2 @ ( inv @ X1 ) @ X2 @ ( pack1 @ X1 @ X2 ) )
          = X2 ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(34,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack2 @ X1 @ ( inv @ X2 ) @ ( pack1 @ X1 @ X2 ) )
          = X2 ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(35,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ( unpack2 @ X1 @ X2 @ ( inv @ ( pack1 @ X1 @ X2 ) ) )
          = X2 ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(36,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(37,plain,
    ! [SV1: $i] :
      ( ( ( SV1 = o )
        | ( SV1 = i ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(38,plain,
    ! [SV2: $i] :
      ( ( ( ( inv @ SV2 )
         != SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(39,plain,
    ! [SV3: $i] :
      ( ( ! [SY18: $i] :
            ( ( unpack1 @ SV3 @ SY18 @ ( pack1 @ SV3 @ SY18 ) )
            = SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(40,plain,
    ! [SV4: $i] :
      ( ( ! [SY19: $i] :
            ( ( unpack1 @ ( inv @ SV4 ) @ SY19 @ ( pack1 @ SV4 @ SY19 ) )
            = SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(41,plain,
    ! [SV5: $i] :
      ( ( ! [SY20: $i] :
            ( ( unpack1 @ SV5 @ ( inv @ SY20 ) @ ( pack1 @ SV5 @ SY20 ) )
            = SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(42,plain,
    ! [SV6: $i] :
      ( ( ! [SY21: $i] :
            ( ( unpack1 @ SV6 @ SY21 @ ( inv @ ( pack1 @ SV6 @ SY21 ) ) )
            = SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(43,plain,
    ! [SV7: $i] :
      ( ( ! [SY22: $i] :
            ( ( unpack2 @ SV7 @ SY22 @ ( pack1 @ SV7 @ SY22 ) )
            = SY22 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(44,plain,
    ! [SV8: $i] :
      ( ( ! [SY23: $i] :
            ( ( unpack2 @ ( inv @ SV8 ) @ SY23 @ ( pack1 @ SV8 @ SY23 ) )
            = SY23 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(45,plain,
    ! [SV9: $i] :
      ( ( ! [SY24: $i] :
            ( ( unpack2 @ SV9 @ ( inv @ SY24 ) @ ( pack1 @ SV9 @ SY24 ) )
            = SY24 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(46,plain,
    ! [SV10: $i] :
      ( ( ! [SY25: $i] :
            ( ( unpack2 @ SV10 @ SY25 @ ( inv @ ( pack1 @ SV10 @ SY25 ) ) )
            = SY25 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(47,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(48,plain,
    ! [SV1: $i] :
      ( ( ( SV1 = o )
        = $true )
      | ( ( SV1 = i )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(49,plain,
    ! [SV2: $i] :
      ( ( ( inv @ SV2 )
        = SV2 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(50,plain,
    ! [SV11: $i,SV3: $i] :
      ( ( ( unpack1 @ SV3 @ SV11 @ ( pack1 @ SV3 @ SV11 ) )
        = SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(51,plain,
    ! [SV12: $i,SV4: $i] :
      ( ( ( unpack1 @ ( inv @ SV4 ) @ SV12 @ ( pack1 @ SV4 @ SV12 ) )
        = SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(52,plain,
    ! [SV13: $i,SV5: $i] :
      ( ( ( unpack1 @ SV5 @ ( inv @ SV13 ) @ ( pack1 @ SV5 @ SV13 ) )
        = SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(53,plain,
    ! [SV14: $i,SV6: $i] :
      ( ( ( unpack1 @ SV6 @ SV14 @ ( inv @ ( pack1 @ SV6 @ SV14 ) ) )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(54,plain,
    ! [SV15: $i,SV7: $i] :
      ( ( ( unpack2 @ SV7 @ SV15 @ ( pack1 @ SV7 @ SV15 ) )
        = SV15 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(55,plain,
    ! [SV16: $i,SV8: $i] :
      ( ( ( unpack2 @ ( inv @ SV8 ) @ SV16 @ ( pack1 @ SV8 @ SV16 ) )
        = SV16 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(56,plain,
    ! [SV17: $i,SV9: $i] :
      ( ( ( unpack2 @ SV9 @ ( inv @ SV17 ) @ ( pack1 @ SV9 @ SV17 ) )
        = SV17 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(57,plain,
    ! [SV18: $i,SV10: $i] :
      ( ( ( unpack2 @ SV10 @ SV18 @ ( inv @ ( pack1 @ SV10 @ SV18 ) ) )
        = SV18 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(58,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[47,57,56,55,54,53,52,51,50,49,48]) ).

thf(59,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[58]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : HWV052-1.002.001 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n025.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 : Fri Jun 17 06:21:42 EDT 2022
% 0.18/0.33  % CPUTime  : 
% 0.18/0.34  
% 0.18/0.34   No.of.Axioms: 10
% 0.18/0.34  
% 0.18/0.34   Length.of.Defs: 0
% 0.18/0.34  
% 0.18/0.34   Contains.Choice.Funs: false
% 0.18/0.34  (rf:0,axioms:10,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:12,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.91/1.09  
% 0.91/1.09  ********************************
% 0.91/1.09  *   All subproblems solved!    *
% 0.91/1.09  ********************************
% 0.91/1.09  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:58,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.91/1.09  
% 0.91/1.09  %**** Beginning of derivation protocol ****
% 0.91/1.09  % SZS output start CNFRefutation
% See solution above
% 0.91/1.09  
% 0.91/1.09  %**** End of derivation protocol ****
% 0.91/1.09  %**** no. of clauses in derivation: 59 ****
% 0.91/1.09  %**** clause counter: 58 ****
% 0.91/1.09  
% 0.91/1.09  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:58,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------