TSTP Solution File: SEU828^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU828^1 : 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 : n010.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 12:15:17 EDT 2022

% Result   : Theorem 0.19s 0.39s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   73 (  47 unt;   7 typ;   4 def)
%            Number of atoms       :  344 ( 111 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  193 (  67   ~;  40   |;   4   &;  68   @)
%                                         (   3 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   28 (  28   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   64 (  30   ^  34   !;   0   ?;  64   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
    emptyset: $i > $o ).

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

thf(tp_sK1_SY8,type,
    sK1_SY8: $i > $o ).

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

thf(tp_sK3_SV2,type,
    sK3_SV2: $i ).

thf(tp_seteq,type,
    seteq: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).

thf(tp_subseteq,type,
    subseteq: ( $i > $o ) > ( $i > $o ) > $o ).

thf(emptyset,definition,
    ( emptyset
    = ( ^ [X: $i] : $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset) ).

thf(powerset,definition,
    ( powerset
    = ( ^ [X: $i > $o,Y: $i > $o] : ( subseteq @ Y @ X ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset) ).

thf(seteq,definition,
    ( seteq
    = ( ^ [X: ( $i > $o ) > $o,Y: ( $i > $o ) > $o] :
        ! [U: $i > $o] :
          ( ( X @ U )
        <=> ( Y @ U ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',seteq) ).

thf(subseteq,definition,
    ( subseteq
    = ( ^ [X: $i > $o,Y: $i > $o] :
        ! [U: $i] :
          ( ( X @ U )
         => ( Y @ U ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subseteq) ).

thf(1,conjecture,
    ( seteq @ ( powerset @ emptyset )
    @ ^ [X: $i > $o] : ( X = emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ( ( seteq @ ( powerset @ emptyset )
      @ ^ [X: $i > $o] : ( X = emptyset ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [SY8: $i > $o] :
          ( ! [SY6: $i] :
              ( ( SY8 @ SY6 )
             => $false )
        <=> ( SY8
            = ( ^ [X: $i] : $false ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,emptyset,powerset,seteq,subseteq]) ).

thf(4,plain,
    ( ( ! [SY14: $i] :
          ( ( sK1_SY8 @ SY14 )
         => $false )
    <=> ( sK1_SY8
        = ( ^ [X: $i] : $false ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY14: $i] :
          ( ( sK1_SY8 @ SY14 )
         => $false )
     => ( sK1_SY8
        = ( ^ [X: $i] : $false ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[4]) ).

thf(6,plain,
    ( ( ( sK1_SY8
        = ( ^ [X: $i] : $false ) )
     => ! [SY14: $i] :
          ( ( sK1_SY8 @ SY14 )
         => $false ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[4]) ).

thf(7,plain,
    ( ( ~ ( ! [SY14: $i] :
              ( ( sK1_SY8 @ SY14 )
             => $false )
         => ( sK1_SY8
            = ( ^ [X: $i] : $false ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ~ ( ( sK1_SY8
            = ( ^ [X: $i] : $false ) )
         => ! [SY14: $i] :
              ( ( sK1_SY8 @ SY14 )
             => $false ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ! [SY14: $i] :
          ~ ( sK1_SY8 @ SY14 )
      & ( sK1_SY8
       != ( ^ [X: $i] : $false ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(10,plain,
    ( ( ( sK1_SY8
        = ( ^ [X: $i] : $false ) )
      & ( sK1_SY8 @ sK2_SY14 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(11,plain,
    ( ( ! [SY14: $i] :
          ~ ( sK1_SY8 @ SY14 )
      & ( sK1_SY8
       != ( ^ [X: $i] : $false ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ~ ( sK1_SY8 @ SX0 )
          | ~ ( ( sK1_SY8
               != ( ^ [SX0: $i] : $false ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11,emptyset,powerset,seteq,subseteq]) ).

thf(13,plain,
    ( ( ~ ! [SX0: $i] :
            ~ ( sK1_SY8 @ SX0 )
      | ~ ( ( sK1_SY8
           != ( ^ [SX0: $i] : $false ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ~ ! [SX0: $i] :
            ~ ( sK1_SY8 @ SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ~ ( ( sK1_SY8
           != ( ^ [SX0: $i] : $false ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ! [SX0: $i] :
          ~ ( sK1_SY8 @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ( sK1_SY8
       != ( ^ [SX0: $i] : $false ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[15]) ).

thf(18,plain,
    ! [SV1: $i] :
      ( ( ~ ( sK1_SY8 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(19,plain,
    ( ( sK1_SY8
      = ( ^ [SX0: $i] : $false ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(20,plain,
    ! [SV1: $i] :
      ( ( sK1_SY8 @ SV1 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ! [SV2: $i] :
          ( ( sK1_SY8 @ SV2 )
          = $false ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[19]) ).

thf(22,plain,
    ( ( sK1_SY8
      = ( ^ [SX0: $i] : $false ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[19]) ).

thf(23,plain,
    ( ( ( sK1_SY8 @ sK3_SV2 )
      = $false )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[21]) ).

thf(24,plain,
    ( ( ~ ( ( sK1_SY8 @ sK3_SV2 )
          | $false )
      | ~ ( ~ ( sK1_SY8 @ sK3_SV2 )
          | ~ $false ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[23]) ).

thf(25,plain,
    ( ( ( sK1_SY8 @ sK3_SV2 )
      = $false )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[23]) ).

thf(26,plain,
    ( ( ~ ( ( sK1_SY8 @ sK3_SV2 )
          | $false ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(27,plain,
    ( ( ~ ( ~ ( sK1_SY8 @ sK3_SV2 )
          | ~ $false ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(28,plain,
    ( ( ( sK1_SY8 @ sK3_SV2 )
      | $false )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(29,plain,
    ( ( ~ ( sK1_SY8 @ sK3_SV2 )
      | ~ $false )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(30,plain,
    ( ( ( sK1_SY8 @ sK3_SV2 )
      = $true )
    | ( $false = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[28]) ).

thf(31,plain,
    ( ( ( ~ ( sK1_SY8 @ sK3_SV2 ) )
      = $true )
    | ( ( ~ $false )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[29]) ).

thf(32,plain,
    ( ( ( sK1_SY8 @ sK3_SV2 )
      = $false )
    | ( ( ~ $false )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(33,plain,
    ( ( $false = $false )
    | ( ( sK1_SY8 @ sK3_SV2 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(34,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[20,33,30,25,22]) ).

thf(35,plain,
    ( ( ( sK1_SY8
        = ( ^ [X: $i] : $false ) )
      & ( sK1_SY8 @ sK2_SY14 ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(36,plain,
    ( ( ~ ( ( sK1_SY8
           != ( ^ [SX0: $i] : $false ) )
          | ~ ( sK1_SY8 @ sK2_SY14 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35,emptyset,powerset,seteq,subseteq]) ).

thf(37,plain,
    ( ( ( sK1_SY8
       != ( ^ [SX0: $i] : $false ) )
      | ~ ( sK1_SY8 @ sK2_SY14 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(38,plain,
    ( ( ( sK1_SY8
       != ( ^ [SX0: $i] : $false ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(39,plain,
    ( ( ~ ( sK1_SY8 @ sK2_SY14 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(40,plain,
    ( ( sK1_SY8
      = ( ^ [SX0: $i] : $false ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(41,plain,
    ( ( sK1_SY8 @ sK2_SY14 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(42,plain,
    ( ( ! [SV3: $i] :
          ( ( sK1_SY8 @ SV3 )
          = $false ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[40]) ).

thf(43,plain,
    ( ( sK1_SY8
      = ( ^ [SX0: $i] : $false ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[40]) ).

thf(44,plain,
    ! [SV4: $i] :
      ( ( ( sK1_SY8 @ SV4 )
        = $false )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(45,plain,
    ! [SV4: $i] :
      ( ( ~ ( ( sK1_SY8 @ SV4 )
            | $false )
        | ~ ( ~ ( sK1_SY8 @ SV4 )
            | ~ $false ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[44]) ).

thf(46,plain,
    ! [SV4: $i] :
      ( ( ( sK1_SY8 @ SV4 )
        = $false )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[44]) ).

thf(47,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ( sK1_SY8 @ SV4 )
              | $false ) )
        = $true )
      | ( ( ~ ( ~ ( sK1_SY8 @ SV4 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(48,plain,
    ! [SV4: $i] :
      ( ( ( ( sK1_SY8 @ SV4 )
          | $false )
        = $false )
      | ( ( ~ ( ~ ( sK1_SY8 @ SV4 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(49,plain,
    ! [SV4: $i] :
      ( ( ( sK1_SY8 @ SV4 )
        = $false )
      | ( ( ~ ( ~ ( sK1_SY8 @ SV4 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[48]) ).

thf(50,plain,
    ! [SV4: $i] :
      ( ( $false = $false )
      | ( ( ~ ( ~ ( sK1_SY8 @ SV4 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[48]) ).

thf(51,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( sK1_SY8 @ SV4 )
          | ~ $false )
        = $false )
      | ( ( sK1_SY8 @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(52,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( sK1_SY8 @ SV4 )
          | ~ $false )
        = $false )
      | ( $false = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(53,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( sK1_SY8 @ SV4 ) )
        = $false )
      | ( ( sK1_SY8 @ SV4 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[51]) ).

thf(54,plain,
    ! [SV4: $i] :
      ( ( ( ~ $false )
        = $false )
      | ( ( sK1_SY8 @ SV4 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[51]) ).

thf(55,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( sK1_SY8 @ SV4 ) )
        = $false )
      | ( $false = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[52]) ).

thf(56,plain,
    ( ( ( ~ $false )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[52]) ).

thf(57,plain,
    ! [SV4: $i] :
      ( ( ( sK1_SY8 @ SV4 )
        = $true )
      | ( ( sK1_SY8 @ SV4 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[53]) ).

thf(58,plain,
    ! [SV4: $i] :
      ( ( $false = $true )
      | ( ( sK1_SY8 @ SV4 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[54]) ).

thf(59,plain,
    ! [SV4: $i] :
      ( ( ( sK1_SY8 @ SV4 )
        = $true )
      | ( $false = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(60,plain,
    ( ( $false = $true )
    | ( $false = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[56]) ).

thf(61,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[41,60,59,58,57,46,43]) ).

thf(62,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[61,34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEU828^1 : TPTP v8.1.0. Released v3.7.0.
% 0.04/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sat Jun 18 20:04:38 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 0
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 608
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.34  (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).
% 0.19/0.39  
% 0.19/0.39  ********************************
% 0.19/0.39  *   All subproblems solved!    *
% 0.19/0.39  ********************************
% 0.19/0.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:61,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.39  
% 0.19/0.39  %**** Beginning of derivation protocol ****
% 0.19/0.39  % SZS output start CNFRefutation
% See solution above
% 0.19/0.39  
% 0.19/0.39  %**** End of derivation protocol ****
% 0.19/0.39  %**** no. of clauses in derivation: 62 ****
% 0.19/0.39  %**** clause counter: 61 ****
% 0.19/0.39  
% 0.19/0.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------