TSTP Solution File: SYO375^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO375^5 : 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 : n024.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 : Thu Jul 21 17:33:40 EDT 2022

% Result   : Theorem 0.19s 0.38s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   63 (  50 unt;   4 typ;   0 def)
%            Number of atoms       :  245 (  65 equ;   0 cnn)
%            Maximal formula atoms :    2 (   4 avg)
%            Number of connectives :  268 (  72   ~;  42   |;   7   &; 126   @)
%                                         (  12 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :   57 (   0   ^  57   !;   0   ?;  57   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_sK1_X,type,
    sK1_X: $i > $o ).

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

thf(tp_sK3_SY8,type,
    sK3_SY8: $i ).

thf(tp_sK4_SY8,type,
    sK4_SY8: $i ).

thf(1,conjecture,
    ! [X: $i > $o,Y: $i > $o] :
      ( ! [W: $i] :
          ( ( X @ W )
        <=> ( Y @ W ) )
     => ! [Xx: $i] :
          ( ( X @ Xx )
        <=> ( Y @ Xx ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT_SET1) ).

thf(2,negated_conjecture,
    ( ( ! [X: $i > $o,Y: $i > $o] :
          ( ! [W: $i] :
              ( ( X @ W )
            <=> ( Y @ W ) )
         => ! [Xx: $i] :
              ( ( X @ Xx )
            <=> ( Y @ Xx ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [X: $i > $o,Y: $i > $o] :
          ( ! [W: $i] :
              ( ( X @ W )
            <=> ( Y @ W ) )
         => ! [Xx: $i] :
              ( ( X @ Xx )
            <=> ( Y @ Xx ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY4: $i > $o] :
          ( ! [SY5: $i] :
              ( ( sK1_X @ SY5 )
            <=> ( SY4 @ SY5 ) )
         => ! [SY6: $i] :
              ( ( sK1_X @ SY6 )
            <=> ( SY4 @ SY6 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY7: $i] :
          ( ( sK1_X @ SY7 )
        <=> ( sK2_SY4 @ SY7 ) )
     => ! [SY8: $i] :
          ( ( sK1_X @ SY8 )
        <=> ( sK2_SY4 @ SY8 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [SY7: $i] :
          ( ( sK1_X @ SY7 )
        <=> ( sK2_SY4 @ SY7 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SY8: $i] :
          ( ( sK1_X @ SY8 )
        <=> ( sK2_SY4 @ SY8 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ! [SY8: $i] :
          ( ( sK1_X @ SY8 )
         => ( sK2_SY4 @ SY8 ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[7]) ).

thf(9,plain,
    ( ( ! [SY8: $i] :
          ( ( sK2_SY4 @ SY8 )
         => ( sK1_X @ SY8 ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[7]) ).

thf(10,plain,
    ( ( ~ ! [SY8: $i] :
            ( ( sK1_X @ SY8 )
           => ( sK2_SY4 @ SY8 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ~ ! [SY8: $i] :
            ( ( sK2_SY4 @ SY8 )
           => ( sK1_X @ SY8 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ( sK1_X @ sK3_SY8 )
      & ~ ( sK2_SY4 @ sK3_SY8 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(13,plain,
    ( ( ( sK2_SY4 @ sK4_SY8 )
      & ~ ( sK1_X @ sK4_SY8 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(14,plain,
    ( ( ! [SY7: $i] :
          ( ~ ( sK1_X @ SY7 )
          | ( sK2_SY4 @ SY7 ) )
      & ! [SY7: $i] :
          ( ~ ( sK2_SY4 @ SY7 )
          | ( sK1_X @ SY7 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(15,plain,
    ( ( ! [SY7: $i] :
          ( ~ ( sK1_X @ SY7 )
          | ( sK2_SY4 @ SY7 ) )
      & ! [SY7: $i] :
          ( ~ ( sK2_SY4 @ SY7 )
          | ( sK1_X @ SY7 ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ( sK1_X @ sK3_SY8 )
      & ~ ( sK2_SY4 @ sK3_SY8 ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(17,plain,
    ( ( ~ ( ~ ( sK1_X @ sK3_SY8 )
          | ~ ~ ( sK2_SY4 @ sK3_SY8 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(18,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( sK1_X @ SX0 )
                | ( sK2_SY4 @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( sK2_SY4 @ SX0 )
                | ( sK1_X @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ~ ( sK1_X @ sK3_SY8 )
      | ~ ~ ( sK2_SY4 @ sK3_SY8 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK1_X @ SX0 )
            | ( sK2_SY4 @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( sK2_SY4 @ SX0 )
            | ( sK1_X @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ~ ( sK1_X @ sK3_SY8 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[19]) ).

thf(22,plain,
    ( ( ~ ~ ( sK2_SY4 @ sK3_SY8 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[19]) ).

thf(23,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK1_X @ SX0 )
            | ( sK2_SY4 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK2_SY4 @ SX0 )
            | ( sK1_X @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(25,plain,
    ( ( sK1_X @ sK3_SY8 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[21]) ).

thf(26,plain,
    ( ( ~ ( sK2_SY4 @ sK3_SY8 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( sK1_X @ SX0 )
          | ( sK2_SY4 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( sK2_SY4 @ SX0 )
          | ( sK1_X @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(29,plain,
    ( ( sK2_SY4 @ sK3_SY8 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(30,plain,
    ! [SV1: $i] :
      ( ( ~ ( sK1_X @ SV1 )
        | ( sK2_SY4 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV2: $i] :
      ( ( ~ ( sK2_SY4 @ SV2 )
        | ( sK1_X @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( sK1_X @ SV1 ) )
        = $true )
      | ( ( sK2_SY4 @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(33,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( sK2_SY4 @ SV2 ) )
        = $true )
      | ( ( sK1_X @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(34,plain,
    ! [SV1: $i] :
      ( ( ( sK1_X @ SV1 )
        = $false )
      | ( ( sK2_SY4 @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(35,plain,
    ! [SV2: $i] :
      ( ( ( sK2_SY4 @ SV2 )
        = $false )
      | ( ( sK1_X @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(36,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[25,35,34,29]) ).

thf(37,plain,
    ( ( ! [SY7: $i] :
          ( ~ ( sK1_X @ SY7 )
          | ( sK2_SY4 @ SY7 ) )
      & ! [SY7: $i] :
          ( ~ ( sK2_SY4 @ SY7 )
          | ( sK1_X @ SY7 ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(38,plain,
    ( ( ( sK2_SY4 @ sK4_SY8 )
      & ~ ( sK1_X @ sK4_SY8 ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(39,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( sK1_X @ SX0 )
                | ( sK2_SY4 @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( sK2_SY4 @ SX0 )
                | ( sK1_X @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(40,plain,
    ( ( ~ ( ~ ( sK2_SY4 @ sK4_SY8 )
          | ~ ~ ( sK1_X @ sK4_SY8 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[38]) ).

thf(41,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK1_X @ SX0 )
            | ( sK2_SY4 @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( sK2_SY4 @ SX0 )
            | ( sK1_X @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(42,plain,
    ( ( ~ ( sK2_SY4 @ sK4_SY8 )
      | ~ ~ ( sK1_X @ sK4_SY8 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(43,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK1_X @ SX0 )
            | ( sK2_SY4 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[41]) ).

thf(44,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK2_SY4 @ SX0 )
            | ( sK1_X @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[41]) ).

thf(45,plain,
    ( ( ~ ( sK2_SY4 @ sK4_SY8 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[42]) ).

thf(46,plain,
    ( ( ~ ~ ( sK1_X @ sK4_SY8 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[42]) ).

thf(47,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( sK1_X @ SX0 )
          | ( sK2_SY4 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(48,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( sK2_SY4 @ SX0 )
          | ( sK1_X @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(49,plain,
    ( ( sK2_SY4 @ sK4_SY8 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[45]) ).

thf(50,plain,
    ( ( ~ ( sK1_X @ sK4_SY8 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[46]) ).

thf(51,plain,
    ! [SV3: $i] :
      ( ( ~ ( sK1_X @ SV3 )
        | ( sK2_SY4 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(52,plain,
    ! [SV4: $i] :
      ( ( ~ ( sK2_SY4 @ SV4 )
        | ( sK1_X @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(53,plain,
    ( ( sK1_X @ sK4_SY8 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(54,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( sK1_X @ SV3 ) )
        = $true )
      | ( ( sK2_SY4 @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(55,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( sK2_SY4 @ SV4 ) )
        = $true )
      | ( ( sK1_X @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(56,plain,
    ! [SV3: $i] :
      ( ( ( sK1_X @ SV3 )
        = $false )
      | ( ( sK2_SY4 @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(57,plain,
    ! [SV4: $i] :
      ( ( ( sK2_SY4 @ SV4 )
        = $false )
      | ( ( sK1_X @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(58,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[49,57,56,53]) ).

thf(59,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[58,36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYO375^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n024.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 : Sat Jul  9 07:46:28 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).
% 0.19/0.38  
% 0.19/0.38  ********************************
% 0.19/0.38  *   All subproblems solved!    *
% 0.19/0.38  ********************************
% 0.19/0.38  % SZS status Theorem for /export/starexec/sandbox2/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:58,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.38  
% 0.19/0.38  %**** Beginning of derivation protocol ****
% 0.19/0.38  % SZS output start CNFRefutation
% See solution above
% 0.19/0.38  
% 0.19/0.38  %**** End of derivation protocol ****
% 0.19/0.38  %**** no. of clauses in derivation: 59 ****
% 0.19/0.38  %**** clause counter: 58 ****
% 0.19/0.38  
% 0.19/0.38  % SZS status Theorem for /export/starexec/sandbox2/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:58,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------