TSTP Solution File: LCL046-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LCL046-1 : 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 : n028.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 12:20:12 EDT 2022

% Result   : Unsatisfiable 0.18s 0.37s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   40 (  31 unt;   4 typ;   0 def)
%            Number of atoms       :  124 (  35 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  214 (  19   ~;  18   |;   0   &; 177   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 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   :   50 (   0   ^  50   !;   0   ?;  50   :)

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

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

thf(tp_is_a_theorem,type,
    is_a_theorem: $i > $o ).

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

thf(1,axiom,
    ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ ( not @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).

thf(2,axiom,
    ! [X: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ X ) @ X ) @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_2) ).

thf(3,axiom,
    ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_1) ).

thf(4,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( is_a_theorem @ ( implies @ X @ Y ) )
      | ~ ( is_a_theorem @ X )
      | ( is_a_theorem @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).

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,
    ~ ( is_a_theorem @ ( implies @ a @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_16) ).

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

thf(9,plain,
    ( ( ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ ( not @ X ) @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(10,plain,
    ( ( ! [X: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ X ) @ X ) @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

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

thf(12,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( is_a_theorem @ ( implies @ X @ Y ) )
          | ~ ( is_a_theorem @ X )
          | ( is_a_theorem @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(13,plain,
    ( ( ~ ( is_a_theorem @ ( implies @ a @ a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

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

thf(15,plain,
    ( ( ~ ( is_a_theorem @ ( implies @ a @ a ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( is_a_theorem @ ( implies @ X @ Y ) )
          | ~ ( is_a_theorem @ X )
          | ( is_a_theorem @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(18,plain,
    ( ( ! [X: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ X ) @ X ) @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(19,plain,
    ( ( ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ ( not @ X ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(20,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(21,plain,
    ( ( is_a_theorem @ ( implies @ a @ a ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(22,plain,
    ! [SV1: $i] :
      ( ( ! [SY8: $i] :
            ( ~ ( is_a_theorem @ ( implies @ SV1 @ SY8 ) )
            | ~ ( is_a_theorem @ SV1 )
            | ( is_a_theorem @ SY8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(23,plain,
    ! [SV2: $i] :
      ( ( ! [SY9: $i,SY10: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV2 @ SY9 ) @ ( implies @ ( implies @ SY9 @ SY10 ) @ ( implies @ SV2 @ SY10 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(24,plain,
    ! [SV3: $i] :
      ( ( is_a_theorem @ ( implies @ ( implies @ ( not @ SV3 ) @ SV3 ) @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(25,plain,
    ! [SV4: $i] :
      ( ( ! [SY11: $i] : ( is_a_theorem @ ( implies @ SV4 @ ( implies @ ( not @ SV4 ) @ SY11 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(26,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(27,plain,
    ! [SV5: $i,SV1: $i] :
      ( ( ~ ( is_a_theorem @ ( implies @ SV1 @ SV5 ) )
        | ~ ( is_a_theorem @ SV1 )
        | ( is_a_theorem @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(28,plain,
    ! [SV6: $i,SV2: $i] :
      ( ( ! [SY12: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV2 @ SV6 ) @ ( implies @ ( implies @ SV6 @ SY12 ) @ ( implies @ SV2 @ SY12 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(29,plain,
    ! [SV7: $i,SV4: $i] :
      ( ( is_a_theorem @ ( implies @ SV4 @ ( implies @ ( not @ SV4 ) @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV5: $i,SV1: $i] :
      ( ( ( ~ ( is_a_theorem @ ( implies @ SV1 @ SV5 ) ) )
        = $true )
      | ( ( ~ ( is_a_theorem @ SV1 )
          | ( is_a_theorem @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV8: $i,SV6: $i,SV2: $i] :
      ( ( is_a_theorem @ ( implies @ ( implies @ SV2 @ SV6 ) @ ( implies @ ( implies @ SV6 @ SV8 ) @ ( implies @ SV2 @ SV8 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV5: $i,SV1: $i] :
      ( ( ( is_a_theorem @ ( implies @ SV1 @ SV5 ) )
        = $false )
      | ( ( ~ ( is_a_theorem @ SV1 )
          | ( is_a_theorem @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(33,plain,
    ! [SV5: $i,SV1: $i] :
      ( ( ( ~ ( is_a_theorem @ SV1 ) )
        = $true )
      | ( ( is_a_theorem @ SV5 )
        = $true )
      | ( ( is_a_theorem @ ( implies @ SV1 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[32]) ).

thf(34,plain,
    ! [SV5: $i,SV1: $i] :
      ( ( ( is_a_theorem @ SV1 )
        = $false )
      | ( ( is_a_theorem @ SV5 )
        = $true )
      | ( ( is_a_theorem @ ( implies @ SV1 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(35,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[21,34,31,29,26,24]) ).

thf(36,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : LCL046-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n028.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 : Mon Jul  4 14:21:49 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 5
% 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: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).
% 0.18/0.37  
% 0.18/0.37  ********************************
% 0.18/0.37  *   All subproblems solved!    *
% 0.18/0.37  ********************************
% 0.18/0.37  % 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:35,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.37  
% 0.18/0.37  %**** Beginning of derivation protocol ****
% 0.18/0.37  % SZS output start CNFRefutation
% See solution above
% 0.18/0.37  
% 0.18/0.37  %**** End of derivation protocol ****
% 0.18/0.37  %**** no. of clauses in derivation: 36 ****
% 0.18/0.37  %**** clause counter: 35 ****
% 0.18/0.37  
% 0.18/0.37  % 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:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------