TSTP Solution File: SEU891^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU891^5 : 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 : n022.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 12:15:38 EDT 2022

% Result   : Theorem 0.19s 0.36s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   55 (  26 unt;   9 typ;   0 def)
%            Number of atoms       :  273 ( 120 equ;   0 cnn)
%            Maximal formula atoms :    7 (   5 avg)
%            Number of connectives :  316 (  95   ~;  71   |;  24   &; 120   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   39 (   0   ^  23   !;  16   ?;  39   :)

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

thf(tp_b,type,
    b: $tType ).

thf(tp_cF,type,
    cF: b > a ).

thf(tp_cR,type,
    cR: b > $o ).

thf(tp_cS,type,
    cS: b > $o ).

thf(tp_sK1_Xx,type,
    sK1_Xx: a ).

thf(tp_sK2_SY5,type,
    sK2_SY5: b ).

thf(tp_sK3_SY4,type,
    sK3_SY4: b ).

thf(tp_sK4_REN,type,
    sK4_REN: $o ).

thf(1,conjecture,
    ! [Xx: a] :
      ( ( ? [Xt: b] :
            ( ( cR @ Xt )
            & ( Xx
              = ( cF @ Xt ) ) )
        | ? [Xt: b] :
            ( ( cS @ Xt )
            & ( Xx
              = ( cF @ Xt ) ) ) )
     => ? [Xt: b] :
          ( ( ( cR @ Xt )
            | ( cS @ Xt ) )
          & ( Xx
            = ( cF @ Xt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM34B_pme) ).

thf(2,negated_conjecture,
    ( ( ! [Xx: a] :
          ( ( ? [Xt: b] :
                ( ( cR @ Xt )
                & ( Xx
                  = ( cF @ Xt ) ) )
            | ? [Xt: b] :
                ( ( cS @ Xt )
                & ( Xx
                  = ( cF @ Xt ) ) ) )
         => ? [Xt: b] :
              ( ( ( cR @ Xt )
                | ( cS @ Xt ) )
              & ( Xx
                = ( cF @ Xt ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xx: a] :
          ( ( ? [Xt: b] :
                ( ( cR @ Xt )
                & ( Xx
                  = ( cF @ Xt ) ) )
            | ? [Xt: b] :
                ( ( cS @ Xt )
                & ( Xx
                  = ( cF @ Xt ) ) ) )
         => ? [Xt: b] :
              ( ( ( cR @ Xt )
                | ( cS @ Xt ) )
              & ( Xx
                = ( cF @ Xt ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ( ? [SY4: b] :
            ( ( cR @ SY4 )
            & ( sK1_Xx
              = ( cF @ SY4 ) ) )
        | ? [SY5: b] :
            ( ( cS @ SY5 )
            & ( sK1_Xx
              = ( cF @ SY5 ) ) ) )
     => ? [SY6: b] :
          ( ( ( cR @ SY6 )
            | ( cS @ SY6 ) )
          & ( sK1_Xx
            = ( cF @ SY6 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ? [SY4: b] :
          ( ( cR @ SY4 )
          & ( sK1_Xx
            = ( cF @ SY4 ) ) )
      | ? [SY5: b] :
          ( ( cS @ SY5 )
          & ( sK1_Xx
            = ( cF @ SY5 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ? [SY6: b] :
          ( ( ( cR @ SY6 )
            | ( cS @ SY6 ) )
          & ( sK1_Xx
            = ( cF @ SY6 ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ~ ? [SY6: b] :
            ( ( ( cR @ SY6 )
              | ( cS @ SY6 ) )
            & ( sK1_Xx
              = ( cF @ SY6 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [SY6: b] :
          ( ( sK1_Xx
           != ( cF @ SY6 ) )
          | ~ ( cR @ SY6 ) )
      & ! [SY6: b] :
          ( ( sK1_Xx
           != ( cF @ SY6 ) )
          | ~ ( cS @ SY6 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(9,plain,
    ( ( ( sK4_REN
        | ( ( sK1_Xx
            = ( cF @ sK2_SY5 ) )
          & ( cS @ sK2_SY5 ) ) )
      & ( sK4_REN
       => ( ( sK1_Xx
            = ( cF @ sK3_SY4 ) )
          & ( cR @ sK3_SY4 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(10,plain,
    ( ( ( sK4_REN
        | ( ( sK1_Xx
            = ( cF @ sK2_SY5 ) )
          & ( cS @ sK2_SY5 ) ) )
      & ( sK4_REN
       => ( ( sK1_Xx
            = ( cF @ sK3_SY4 ) )
          & ( cR @ sK3_SY4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ! [SY6: b] :
          ( ( sK1_Xx
           != ( cF @ SY6 ) )
          | ~ ( cR @ SY6 ) )
      & ! [SY6: b] :
          ( ( sK1_Xx
           != ( cF @ SY6 ) )
          | ~ ( cS @ SY6 ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(12,plain,
    ( ( ~ ( ~ ! [SX0: b] :
                ( ( sK1_Xx
                 != ( cF @ SX0 ) )
                | ~ ( cR @ SX0 ) )
          | ~ ! [SX0: b] :
                ( ( sK1_Xx
                 != ( cF @ SX0 ) )
                | ~ ( cS @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(13,plain,
    ( ( ~ ( ~ ( sK4_REN
              | ~ ( ( sK1_Xx
                   != ( cF @ sK2_SY5 ) )
                  | ~ ( cS @ sK2_SY5 ) ) )
          | ~ ( ~ sK4_REN
              | ~ ( ( sK1_Xx
                   != ( cF @ sK3_SY4 ) )
                  | ~ ( cR @ sK3_SY4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(14,plain,
    ( ( ~ ! [SX0: b] :
            ( ( sK1_Xx
             != ( cF @ SX0 ) )
            | ~ ( cR @ SX0 ) )
      | ~ ! [SX0: b] :
            ( ( sK1_Xx
             != ( cF @ SX0 ) )
            | ~ ( cS @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ( ( ~ ( sK4_REN
          | ~ ( ( sK1_Xx
               != ( cF @ sK2_SY5 ) )
              | ~ ( cS @ sK2_SY5 ) ) )
      | ~ ( ~ sK4_REN
          | ~ ( ( sK1_Xx
               != ( cF @ sK3_SY4 ) )
              | ~ ( cR @ sK3_SY4 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ! [SX0: b] :
            ( ( sK1_Xx
             != ( cF @ SX0 ) )
            | ~ ( cR @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ! [SX0: b] :
            ( ( sK1_Xx
             != ( cF @ SX0 ) )
            | ~ ( cS @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ~ ( sK4_REN
          | ~ ( ( sK1_Xx
               != ( cF @ sK2_SY5 ) )
              | ~ ( cS @ sK2_SY5 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ~ ( ~ sK4_REN
          | ~ ( ( sK1_Xx
               != ( cF @ sK3_SY4 ) )
              | ~ ( cR @ sK3_SY4 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(20,plain,
    ( ( ! [SX0: b] :
          ( ( sK1_Xx
           != ( cF @ SX0 ) )
          | ~ ( cR @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(21,plain,
    ( ( ! [SX0: b] :
          ( ( sK1_Xx
           != ( cF @ SX0 ) )
          | ~ ( cS @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(22,plain,
    ( ( sK4_REN
      | ~ ( ( sK1_Xx
           != ( cF @ sK2_SY5 ) )
          | ~ ( cS @ sK2_SY5 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(23,plain,
    ( ( ~ sK4_REN
      | ~ ( ( sK1_Xx
           != ( cF @ sK3_SY4 ) )
          | ~ ( cR @ sK3_SY4 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(24,plain,
    ! [SV1: b] :
      ( ( ( sK1_Xx
         != ( cF @ SV1 ) )
        | ~ ( cR @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(25,plain,
    ! [SV2: b] :
      ( ( ( sK1_Xx
         != ( cF @ SV2 ) )
        | ~ ( cS @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(26,plain,
    ( ( sK4_REN = $true )
    | ( ( ~ ( ( sK1_Xx
             != ( cF @ sK2_SY5 ) )
            | ~ ( cS @ sK2_SY5 ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ( ~ sK4_REN )
      = $true )
    | ( ( ~ ( ( sK1_Xx
             != ( cF @ sK3_SY4 ) )
            | ~ ( cR @ sK3_SY4 ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV1: b] :
      ( ( ( ( sK1_Xx
           != ( cF @ SV1 ) ) )
        = $true )
      | ( ( ~ ( cR @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[24]) ).

thf(29,plain,
    ! [SV2: b] :
      ( ( ( ( sK1_Xx
           != ( cF @ SV2 ) ) )
        = $true )
      | ( ( ~ ( cS @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(30,plain,
    ( ( ( ( sK1_Xx
         != ( cF @ sK2_SY5 ) )
        | ~ ( cS @ sK2_SY5 ) )
      = $false )
    | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(31,plain,
    ( ( sK4_REN = $false )
    | ( ( ~ ( ( sK1_Xx
             != ( cF @ sK3_SY4 ) )
            | ~ ( cR @ sK3_SY4 ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV1: b] :
      ( ( ( sK1_Xx
          = ( cF @ SV1 ) )
        = $false )
      | ( ( ~ ( cR @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV2: b] :
      ( ( ( sK1_Xx
          = ( cF @ SV2 ) )
        = $false )
      | ( ( ~ ( cS @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(34,plain,
    ( ( ( ( sK1_Xx
         != ( cF @ sK2_SY5 ) ) )
      = $false )
    | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(35,plain,
    ( ( ( ~ ( cS @ sK2_SY5 ) )
      = $false )
    | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(36,plain,
    ( ( ( ( sK1_Xx
         != ( cF @ sK3_SY4 ) )
        | ~ ( cR @ sK3_SY4 ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(37,plain,
    ! [SV1: b] :
      ( ( ( cR @ SV1 )
        = $false )
      | ( ( sK1_Xx
          = ( cF @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(38,plain,
    ! [SV2: b] :
      ( ( ( cS @ SV2 )
        = $false )
      | ( ( sK1_Xx
          = ( cF @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(39,plain,
    ( ( ( sK1_Xx
        = ( cF @ sK2_SY5 ) )
      = $true )
    | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(40,plain,
    ( ( ( cS @ sK2_SY5 )
      = $true )
    | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(41,plain,
    ( ( ( ( sK1_Xx
         != ( cF @ sK3_SY4 ) ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(42,plain,
    ( ( ( ~ ( cR @ sK3_SY4 ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(43,plain,
    ( ( ( sK1_Xx
        = ( cF @ sK3_SY4 ) )
      = $true )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(44,plain,
    ( ( ( cR @ sK3_SY4 )
      = $true )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(45,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[37,44,43,40,39,38]) ).

thf(46,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU891^5 : 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 : n022.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jun 20 05:38:31 EDT 2022
% 0.12/0.34  % 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).
% 0.19/0.36  
% 0.19/0.36  ********************************
% 0.19/0.36  *   All subproblems solved!    *
% 0.19/0.36  ********************************
% 0.19/0.36  % 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:45,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.36  
% 0.19/0.36  %**** Beginning of derivation protocol ****
% 0.19/0.36  % SZS output start CNFRefutation
% See solution above
% 0.19/0.36  
% 0.19/0.36  %**** End of derivation protocol ****
% 0.19/0.36  %**** no. of clauses in derivation: 46 ****
% 0.19/0.36  %**** clause counter: 45 ****
% 0.19/0.36  
% 0.19/0.36  % 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:45,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------