TSTP Solution File: SEU843^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU843^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n029.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 : Tue Jul 19 12:15:20 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   53 (  25 unt;   4 typ;   0 def)
%            Number of atoms       :  290 (  85 equ;   0 cnn)
%            Maximal formula atoms :    3 (   5 avg)
%            Number of connectives :  275 (  49   ~;  74   |;   2   &; 138   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   3 con; 0-2 aty)
%            Number of variables   :   50 (   8   ^  42   !;   0   ?;  50   :)

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

thf(tp_sK1_S,type,
    sK1_S: a > $o ).

thf(tp_sK2_SY4,type,
    sK2_SY4: a > $o ).

thf(tp_sK3_SY8,type,
    sK3_SY8: a ).

thf(1,conjecture,
    ! [S: a > $o,T: a > $o] :
      ( ( ( ^ [Xz: a] :
              ( ( S @ Xz )
              | ( T @ Xz ) ) )
        = S )
     => ! [Xx: a] :
          ( ( T @ Xx )
         => ( S @ Xx ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM23_pme) ).

thf(2,negated_conjecture,
    ( ( ! [S: a > $o,T: a > $o] :
          ( ( ( ^ [Xz: a] :
                  ( ( S @ Xz )
                  | ( T @ Xz ) ) )
            = S )
         => ! [Xx: a] :
              ( ( T @ Xx )
             => ( S @ Xx ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [S: a > $o,T: a > $o] :
          ( ( ( ^ [Xz: a] :
                  ( ( S @ Xz )
                  | ( T @ Xz ) ) )
            = S )
         => ! [Xx: a] :
              ( ( T @ Xx )
             => ( S @ Xx ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY4: a > $o] :
          ( ( ( ^ [SY5: a] :
                  ( ( sK1_S @ SY5 )
                  | ( SY4 @ SY5 ) ) )
            = sK1_S )
         => ! [SY6: a] :
              ( ( SY4 @ SY6 )
             => ( sK1_S @ SY6 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ( ( ^ [SY7: a] :
              ( ( sK1_S @ SY7 )
              | ( sK2_SY4 @ SY7 ) ) )
        = sK1_S )
     => ! [SY8: a] :
          ( ( sK2_SY4 @ SY8 )
         => ( sK1_S @ SY8 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ( ^ [SY7: a] :
            ( ( sK1_S @ SY7 )
            | ( sK2_SY4 @ SY7 ) ) )
      = sK1_S )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SY8: a] :
          ( ( sK2_SY4 @ SY8 )
         => ( sK1_S @ SY8 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ~ ! [SY8: a] :
            ( ( sK2_SY4 @ SY8 )
           => ( sK1_S @ SY8 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ( sK2_SY4 @ sK3_SY8 )
      & ~ ( sK1_S @ sK3_SY8 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    ( ( ( ^ [SY7: a] :
            ( ( sK1_S @ SY7 )
            | ( sK2_SY4 @ SY7 ) ) )
      = sK1_S )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(11,plain,
    ( ( ( sK2_SY4 @ sK3_SY8 )
      & ~ ( sK1_S @ sK3_SY8 ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ~ ( ~ ( sK2_SY4 @ sK3_SY8 )
          | ~ ~ ( sK1_S @ sK3_SY8 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(13,plain,
    ( ( ! [SV1: a] :
          ( ( ( sK1_S @ SV1 )
            | ( sK2_SY4 @ SV1 ) )
          = ( sK1_S @ SV1 ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10]) ).

thf(14,plain,
    ( ( ( ^ [SY7: a] :
            ( ( sK1_S @ SY7 )
            | ( sK2_SY4 @ SY7 ) ) )
      = sK1_S )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10]) ).

thf(15,plain,
    ( ( ~ ( sK2_SY4 @ sK3_SY8 )
      | ~ ~ ( sK1_S @ sK3_SY8 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(16,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_S @ SV2 )
          | ( sK2_SY4 @ SV2 ) )
        = ( sK1_S @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ~ ( sK2_SY4 @ sK3_SY8 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(18,plain,
    ( ( ~ ~ ( sK1_S @ sK3_SY8 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV2: a] :
      ( ( ~ ( ( sK1_S @ SV2 )
            | ( sK2_SY4 @ SV2 )
            | ( sK1_S @ SV2 ) )
        | ~ ( ~ ( ( sK1_S @ SV2 )
                | ( sK2_SY4 @ SV2 ) )
            | ~ ( sK1_S @ SV2 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[16]) ).

thf(20,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_S @ SV2 )
          | ( sK2_SY4 @ SV2 ) )
        = ( sK1_S @ SV2 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[16]) ).

thf(21,plain,
    ( ( sK2_SY4 @ sK3_SY8 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(22,plain,
    ( ( ~ ( sK1_S @ sK3_SY8 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(23,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_S @ SV2 )
              | ( sK2_SY4 @ SV2 )
              | ( sK1_S @ SV2 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ( sK1_S @ SV2 )
                  | ( sK2_SY4 @ SV2 ) )
              | ~ ( sK1_S @ SV2 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[19]) ).

thf(24,plain,
    ( ( sK1_S @ sK3_SY8 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(25,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_S @ SV2 )
          | ( sK2_SY4 @ SV2 )
          | ( sK1_S @ SV2 ) )
        = $false )
      | ( ( ~ ( ~ ( ( sK1_S @ SV2 )
                  | ( sK2_SY4 @ SV2 ) )
              | ~ ( sK1_S @ SV2 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(26,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_S @ SV2 )
          | ( sK2_SY4 @ SV2 ) )
        = $false )
      | ( ( ~ ( ~ ( ( sK1_S @ SV2 )
                  | ( sK2_SY4 @ SV2 ) )
              | ~ ( sK1_S @ SV2 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(27,plain,
    ! [SV2: a] :
      ( ( ( sK1_S @ SV2 )
        = $false )
      | ( ( ~ ( ~ ( ( sK1_S @ SV2 )
                  | ( sK2_SY4 @ SV2 ) )
              | ~ ( sK1_S @ SV2 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(28,plain,
    ! [SV2: a] :
      ( ( ( sK1_S @ SV2 )
        = $false )
      | ( ( ~ ( ~ ( ( sK1_S @ SV2 )
                  | ( sK2_SY4 @ SV2 ) )
              | ~ ( sK1_S @ SV2 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[26]) ).

thf(29,plain,
    ! [SV2: a] :
      ( ( ( sK2_SY4 @ SV2 )
        = $false )
      | ( ( ~ ( ~ ( ( sK1_S @ SV2 )
                  | ( sK2_SY4 @ SV2 ) )
              | ~ ( sK1_S @ SV2 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[26]) ).

thf(30,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_S @ SV2 )
              | ( sK2_SY4 @ SV2 ) )
          | ~ ( sK1_S @ SV2 ) )
        = $false )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_S @ SV2 )
              | ( sK2_SY4 @ SV2 ) )
          | ~ ( sK1_S @ SV2 ) )
        = $false )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_S @ SV2 )
              | ( sK2_SY4 @ SV2 ) )
          | ~ ( sK1_S @ SV2 ) )
        = $false )
      | ( ( sK2_SY4 @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(33,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_S @ SV2 )
              | ( sK2_SY4 @ SV2 ) ) )
        = $false )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(34,plain,
    ! [SV2: a] :
      ( ( ( ~ ( sK1_S @ SV2 ) )
        = $false )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_S @ SV2 )
              | ( sK2_SY4 @ SV2 ) ) )
        = $false )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV2: a] :
      ( ( ( ~ ( sK1_S @ SV2 ) )
        = $false )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(37,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_S @ SV2 )
              | ( sK2_SY4 @ SV2 ) ) )
        = $false )
      | ( ( sK2_SY4 @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(38,plain,
    ! [SV2: a] :
      ( ( ( ~ ( sK1_S @ SV2 ) )
        = $false )
      | ( ( sK2_SY4 @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(39,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_S @ SV2 )
          | ( sK2_SY4 @ SV2 ) )
        = $true )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(40,plain,
    ! [SV2: a] :
      ( ( ( sK1_S @ SV2 )
        = $true )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_S @ SV2 )
          | ( sK2_SY4 @ SV2 ) )
        = $true )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(42,plain,
    ! [SV2: a] :
      ( ( ( sK1_S @ SV2 )
        = $true )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[36]) ).

thf(43,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_S @ SV2 )
          | ( sK2_SY4 @ SV2 ) )
        = $true )
      | ( ( sK2_SY4 @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[37]) ).

thf(44,plain,
    ! [SV2: a] :
      ( ( ( sK1_S @ SV2 )
        = $true )
      | ( ( sK2_SY4 @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(45,plain,
    ! [SV2: a] :
      ( ( ( sK1_S @ SV2 )
        = $true )
      | ( ( sK2_SY4 @ SV2 )
        = $true )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(46,plain,
    ! [SV2: a] :
      ( ( ( sK1_S @ SV2 )
        = $true )
      | ( ( sK2_SY4 @ SV2 )
        = $true )
      | ( ( sK1_S @ SV2 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[41]) ).

thf(47,plain,
    ! [SV2: a] :
      ( ( ( sK1_S @ SV2 )
        = $true )
      | ( ( sK2_SY4 @ SV2 )
        = $true )
      | ( ( sK2_SY4 @ SV2 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[43]) ).

thf(48,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[14,47,46,45,44,42,40,24,21,20]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SEU843^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n029.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 : Sun Jun 19 09:40:44 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 0
% 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:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)
% 0.12/0.36  ********************************
% 0.12/0.36  *   All subproblems solved!    *
% 0.12/0.36  ********************************
% 0.12/0.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:48,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.36  
% 0.12/0.36  %**** Beginning of derivation protocol ****
% 0.12/0.36  % SZS output start CNFRefutation
% See solution above
% 0.12/0.36  
% 0.12/0.36  %**** End of derivation protocol ****
% 0.12/0.36  %**** no. of clauses in derivation: 49 ****
% 0.12/0.36  %**** clause counter: 48 ****
% 0.12/0.36  
% 0.12/0.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:48,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------