TSTP Solution File: SEU758^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU758^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n027.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 12:14:30 EDT 2022

% Result   : Theorem 0.13s 0.39s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   55 (  38 unt;   9 typ;   2 def)
%            Number of atoms       :  228 (  53 equ;   0 cnn)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :  479 (  80   ~;  40   |;   6   &; 323   @)
%                                         (   0 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :   86 (   0   ^  86   !;   0   ?;  86   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_binintersect,type,
    binintersect: $i > $i > $i ).

thf(tp_binintersectEL,type,
    binintersectEL: $o ).

thf(tp_in,type,
    in: $i > $i > $o ).

thf(tp_powerset,type,
    powerset: $i > $i ).

thf(tp_powersetE,type,
    powersetE: $o ).

thf(tp_sK1_A,type,
    sK1_A: $i ).

thf(tp_sK2_SY14,type,
    sK2_SY14: $i ).

thf(tp_sK3_SY17,type,
    sK3_SY17: $i ).

thf(tp_sK4_SY19,type,
    sK4_SY19: $i ).

thf(binintersectEL,definition,
    ( binintersectEL
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( binintersect @ A @ B ) )
         => ( in @ Xx @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).

thf(powersetE,definition,
    ( powersetE
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).

thf(1,conjecture,
    ( powersetE
   => ( binintersectEL
     => ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                 => ( in @ Xx @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule0) ).

thf(2,negated_conjecture,
    ( ( powersetE
     => ( binintersectEL
       => ! [A: $i,X: $i] :
            ( ( in @ X @ ( powerset @ A ) )
           => ! [Y: $i] :
                ( ( in @ Y @ ( powerset @ A ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                   => ( in @ Xx @ A ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ A ) ) )
     => ( ! [A: $i,B: $i,Xx: $i] :
            ( ( in @ Xx @ ( binintersect @ A @ B ) )
           => ( in @ Xx @ A ) )
       => ! [A: $i,X: $i] :
            ( ( in @ X @ ( powerset @ A ) )
           => ! [Y: $i] :
                ( ( in @ Y @ ( powerset @ A ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                   => ( in @ Xx @ A ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,binintersectEL,powersetE]) ).

thf(4,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( binintersect @ A @ B ) )
         => ( in @ Xx @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                 => ( in @ Xx @ A ) ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ~ ! [A: $i,X: $i] :
            ( ( in @ X @ ( powerset @ A ) )
           => ! [Y: $i] :
                ( ( in @ Y @ ( powerset @ A ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                   => ( in @ Xx @ A ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ( in @ sK2_SY14 @ ( powerset @ sK1_A ) )
      & ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
      & ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) )
      & ~ ( in @ sK4_SY19 @ sK1_A ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(9,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ B @ ( powerset @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ B )
              | ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(10,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
          | ( in @ Xx @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(11,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
          | ( in @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ B @ ( powerset @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ B )
              | ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(13,plain,
    ( ( ( in @ sK2_SY14 @ ( powerset @ sK1_A ) )
      & ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
      & ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) )
      & ~ ( in @ sK4_SY19 @ sK1_A ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(14,plain,
    ( ( ~ ( ~ ( in @ sK2_SY14 @ ( powerset @ sK1_A ) )
          | ~ ~ ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
                | ~ ~ ( ~ ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) )
                      | ~ ~ ( in @ sK4_SY19 @ sK1_A ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13,binintersectEL,powersetE]) ).

thf(15,plain,
    ! [SV1: $i] :
      ( ( ! [SY20: $i,SY21: $i] :
            ( ~ ( in @ SY21 @ ( binintersect @ SV1 @ SY20 ) )
            | ( in @ SY21 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(16,plain,
    ! [SV2: $i] :
      ( ( ! [SY22: $i] :
            ( ~ ( in @ SY22 @ ( powerset @ SV2 ) )
            | ! [SY23: $i] :
                ( ~ ( in @ SY23 @ SY22 )
                | ( in @ SY23 @ SV2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(17,plain,
    ( ( ~ ( in @ sK2_SY14 @ ( powerset @ sK1_A ) )
      | ~ ~ ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
            | ~ ~ ( ~ ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) )
                  | ~ ~ ( in @ sK4_SY19 @ sK1_A ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[14]) ).

thf(18,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ! [SY24: $i] :
            ( ~ ( in @ SY24 @ ( binintersect @ SV1 @ SV3 ) )
            | ( in @ SY24 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV2: $i,SV4: $i] :
      ( ( ~ ( in @ SV4 @ ( powerset @ SV2 ) )
        | ! [SY25: $i] :
            ( ~ ( in @ SY25 @ SV4 )
            | ( in @ SY25 @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ~ ( in @ sK2_SY14 @ ( powerset @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ~ ~ ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
            | ~ ~ ( ~ ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) )
                  | ~ ~ ( in @ sK4_SY19 @ sK1_A ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(22,plain,
    ! [SV3: $i,SV1: $i,SV5: $i] :
      ( ( ~ ( in @ SV5 @ ( binintersect @ SV1 @ SV3 ) )
        | ( in @ SV5 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(23,plain,
    ! [SV2: $i,SV4: $i] :
      ( ( ( ~ ( in @ SV4 @ ( powerset @ SV2 ) ) )
        = $true )
      | ( ( ! [SY25: $i] :
              ( ~ ( in @ SY25 @ SV4 )
              | ( in @ SY25 @ SV2 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[19]) ).

thf(24,plain,
    ( ( in @ sK2_SY14 @ ( powerset @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[20]) ).

thf(25,plain,
    ( ( ~ ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
          | ~ ~ ( ~ ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) )
                | ~ ~ ( in @ sK4_SY19 @ sK1_A ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV3: $i,SV1: $i,SV5: $i] :
      ( ( ( ~ ( in @ SV5 @ ( binintersect @ SV1 @ SV3 ) ) )
        = $true )
      | ( ( in @ SV5 @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV2: $i,SV4: $i] :
      ( ( ( in @ SV4 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( ! [SY25: $i] :
              ( ~ ( in @ SY25 @ SV4 )
              | ( in @ SY25 @ SV2 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
      | ~ ~ ( ~ ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) )
            | ~ ~ ( in @ sK4_SY19 @ sK1_A ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(29,plain,
    ! [SV3: $i,SV1: $i,SV5: $i] :
      ( ( ( in @ SV5 @ ( binintersect @ SV1 @ SV3 ) )
        = $false )
      | ( ( in @ SV5 @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(30,plain,
    ! [SV2: $i,SV4: $i,SV6: $i] :
      ( ( ( ~ ( in @ SV6 @ SV4 )
          | ( in @ SV6 @ SV2 ) )
        = $true )
      | ( ( in @ SV4 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(31,plain,
    ( ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[28]) ).

thf(32,plain,
    ( ( ~ ~ ( ~ ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) )
            | ~ ~ ( in @ sK4_SY19 @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV2: $i,SV4: $i,SV6: $i] :
      ( ( ( ~ ( in @ SV6 @ SV4 ) )
        = $true )
      | ( ( in @ SV6 @ SV2 )
        = $true )
      | ( ( in @ SV4 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(34,plain,
    ( ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[31]) ).

thf(35,plain,
    ( ( ~ ( ~ ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) )
          | ~ ~ ( in @ sK4_SY19 @ sK1_A ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[32]) ).

thf(36,plain,
    ! [SV2: $i,SV4: $i,SV6: $i] :
      ( ( ( in @ SV6 @ SV4 )
        = $false )
      | ( ( in @ SV6 @ SV2 )
        = $true )
      | ( ( in @ SV4 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(37,plain,
    ( ( ~ ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) )
      | ~ ~ ( in @ sK4_SY19 @ sK1_A ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(38,plain,
    ( ( ~ ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(39,plain,
    ( ( ~ ~ ( in @ sK4_SY19 @ sK1_A ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(40,plain,
    ( ( in @ sK4_SY19 @ ( binintersect @ sK2_SY14 @ sK3_SY17 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(41,plain,
    ( ( ~ ( in @ sK4_SY19 @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(42,plain,
    ( ( in @ sK4_SY19 @ sK1_A )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(43,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[24,42,40,36,34,29]) ).

thf(44,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU758^2 : TPTP v8.1.0. Released v3.7.0.
% 0.10/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n027.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 : Mon Jun 20 04:13:09 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 0
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 385
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (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)..
% 0.13/0.39  
% 0.13/0.39  ********************************
% 0.13/0.39  *   All subproblems solved!    *
% 0.13/0.39  ********************************
% 0.13/0.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:43,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.39  
% 0.13/0.39  %**** Beginning of derivation protocol ****
% 0.13/0.39  % SZS output start CNFRefutation
% See solution above
% 0.13/0.39  
% 0.13/0.39  %**** End of derivation protocol ****
% 0.13/0.39  %**** no. of clauses in derivation: 44 ****
% 0.13/0.39  %**** clause counter: 43 ****
% 0.13/0.39  
% 0.13/0.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:43,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------