TSTP Solution File: SYN058^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN058^5 : 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 : n011.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 08:23:07 EDT 2022

% Result   : Theorem 0.14s 0.39s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   71 (  35 unt;  10 typ;   0 def)
%            Number of atoms       :  357 (  86 equ;   0 cnn)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  400 ( 120   ~;  73   |;  25   &; 156   @)
%                                         (   0 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   57 (   0   ^  49   !;   8   ?;  57   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_cF,type,
    cF: $i > $o ).

thf(tp_cG,type,
    cG: $i > $o ).

thf(tp_cP,type,
    cP: $i > $o ).

thf(tp_cQ,type,
    cQ: $i > $o ).

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

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

thf(tp_sK1_Xx,type,
    sK1_Xx: $i ).

thf(tp_sK2_Xx,type,
    sK2_Xx: $i ).

thf(tp_sK3_Xx,type,
    sK3_Xx: $i ).

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

thf(1,conjecture,
    ( ( ! [Xx: $i] :
          ( ( cP @ Xx )
         => ! [Xx0: $i] : ( cQ @ Xx0 ) )
      & ( ! [Xx: $i] :
            ( ( cQ @ Xx )
            | ( cR @ Xx ) )
       => ? [Xx: $i] :
            ( ( cQ @ Xx )
            & ( cS @ Xx ) ) )
      & ( ? [Xx: $i] : ( cS @ Xx )
       => ! [Xx: $i] :
            ( ( cF @ Xx )
           => ( cG @ Xx ) ) ) )
   => ! [Xx: $i] :
        ( ( ( cP @ Xx )
          & ( cF @ Xx ) )
       => ( cG @ Xx ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPELL28) ).

thf(2,negated_conjecture,
    ( ( ( ! [Xx: $i] :
            ( ( cP @ Xx )
           => ! [Xx0: $i] : ( cQ @ Xx0 ) )
        & ( ! [Xx: $i] :
              ( ( cQ @ Xx )
              | ( cR @ Xx ) )
         => ? [Xx: $i] :
              ( ( cQ @ Xx )
              & ( cS @ Xx ) ) )
        & ( ? [Xx: $i] : ( cS @ Xx )
         => ! [Xx: $i] :
              ( ( cF @ Xx )
             => ( cG @ Xx ) ) ) )
     => ! [Xx: $i] :
          ( ( ( cP @ Xx )
            & ( cF @ Xx ) )
         => ( cG @ Xx ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( ! [Xx: $i] :
            ( ( cP @ Xx )
           => ! [Xx0: $i] : ( cQ @ Xx0 ) )
        & ( ! [Xx: $i] :
              ( ( cQ @ Xx )
              | ( cR @ Xx ) )
         => ? [Xx: $i] :
              ( ( cQ @ Xx )
              & ( cS @ Xx ) ) )
        & ( ? [Xx: $i] : ( cS @ Xx )
         => ! [Xx: $i] :
              ( ( cF @ Xx )
             => ( cG @ Xx ) ) ) )
     => ! [Xx: $i] :
          ( ( ( cP @ Xx )
            & ( cF @ Xx ) )
         => ( cG @ Xx ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [Xx: $i] :
          ( ( cP @ Xx )
         => ! [Xx0: $i] : ( cQ @ Xx0 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xx: $i] :
          ( ( cQ @ Xx )
          | ( cR @ Xx ) )
     => ? [Xx: $i] :
          ( ( cQ @ Xx )
          & ( cS @ Xx ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ? [Xx: $i] : ( cS @ Xx )
     => ! [Xx: $i] :
          ( ( cF @ Xx )
         => ( cG @ Xx ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ! [Xx: $i] :
          ( ( ( cP @ Xx )
            & ( cF @ Xx ) )
         => ( cG @ Xx ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(8,plain,
    ( ( ~ ! [Xx: $i] :
            ( ( ( cP @ Xx )
              & ( cF @ Xx ) )
           => ( cG @ Xx ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ( cF @ sK1_Xx )
      & ( cP @ sK1_Xx )
      & ~ ( cG @ sK1_Xx ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    ( ( ! [Xx: $i] :
          ~ ( cP @ Xx )
      | ! [Xx0: $i] : ( cQ @ Xx0 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(11,plain,
    ( ( ( sK4_REN
        | ( ( cQ @ sK2_Xx )
          & ( cS @ sK2_Xx ) ) )
      & ( sK4_REN
       => ( ~ ( cQ @ sK3_Xx )
          & ~ ( cR @ sK3_Xx ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(12,plain,
    ( ( ! [Xx: $i] :
          ~ ( cS @ Xx )
      | ! [Xx: $i] :
          ( ~ ( cF @ Xx )
          | ( cG @ Xx ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(13,plain,
    ( ( ! [Xx: $i] :
          ~ ( cS @ Xx )
      | ! [Xx: $i] :
          ( ~ ( cF @ Xx )
          | ( cG @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ( sK4_REN
        | ( ( cQ @ sK2_Xx )
          & ( cS @ sK2_Xx ) ) )
      & ( sK4_REN
       => ( ~ ( cQ @ sK3_Xx )
          & ~ ( cR @ sK3_Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(15,plain,
    ( ( ! [Xx: $i] :
          ~ ( cP @ Xx )
      | ! [Xx0: $i] : ( cQ @ Xx0 ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(16,plain,
    ( ( ( cF @ sK1_Xx )
      & ( cP @ sK1_Xx )
      & ~ ( cG @ sK1_Xx ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(17,plain,
    ( ( ~ ( ~ ( sK4_REN
              | ~ ( ~ ( cQ @ sK2_Xx )
                  | ~ ( cS @ sK2_Xx ) ) )
          | ~ ( ~ sK4_REN
              | ~ ( ~ ~ ( cQ @ sK3_Xx )
                  | ~ ~ ( cR @ sK3_Xx ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ~ ( ~ ~ ( ~ ( cF @ sK1_Xx )
                | ~ ( cP @ sK1_Xx ) )
          | ~ ~ ( cG @ sK1_Xx ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ( ! [Xx: $i] :
            ~ ( cS @ Xx ) )
      = $true )
    | ( ( ! [Xx: $i] :
            ( ~ ( cF @ Xx )
            | ( cG @ Xx ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13]) ).

thf(20,plain,
    ( ( ( ! [Xx: $i] :
            ~ ( cP @ Xx ) )
      = $true )
    | ( ( ! [Xx0: $i] : ( cQ @ Xx0 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[15]) ).

thf(21,plain,
    ( ( ~ ( sK4_REN
          | ~ ( ~ ( cQ @ sK2_Xx )
              | ~ ( cS @ sK2_Xx ) ) )
      | ~ ( ~ sK4_REN
          | ~ ( ~ ~ ( cQ @ sK3_Xx )
              | ~ ~ ( cR @ sK3_Xx ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(22,plain,
    ( ( ~ ~ ( ~ ( cF @ sK1_Xx )
            | ~ ( cP @ sK1_Xx ) )
      | ~ ~ ( cG @ sK1_Xx ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(23,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( cS @ SV1 ) )
        = $true )
      | ( ( ! [Xx: $i] :
              ( ~ ( cF @ Xx )
              | ( cG @ Xx ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(24,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( cP @ SV2 ) )
        = $true )
      | ( ( ! [Xx0: $i] : ( cQ @ Xx0 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(25,plain,
    ( ( ~ ( sK4_REN
          | ~ ( ~ ( cQ @ sK2_Xx )
              | ~ ( cS @ sK2_Xx ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(26,plain,
    ( ( ~ ( ~ sK4_REN
          | ~ ( ~ ~ ( cQ @ sK3_Xx )
              | ~ ~ ( cR @ sK3_Xx ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(27,plain,
    ( ( ~ ~ ( ~ ( cF @ sK1_Xx )
            | ~ ( cP @ sK1_Xx ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(28,plain,
    ( ( ~ ~ ( cG @ sK1_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(29,plain,
    ! [SV1: $i] :
      ( ( ( cS @ SV1 )
        = $false )
      | ( ( ! [Xx: $i] :
              ( ~ ( cF @ Xx )
              | ( cG @ Xx ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(30,plain,
    ! [SV2: $i] :
      ( ( ( cP @ SV2 )
        = $false )
      | ( ( ! [Xx0: $i] : ( cQ @ Xx0 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(31,plain,
    ( ( sK4_REN
      | ~ ( ~ ( cQ @ sK2_Xx )
          | ~ ( cS @ sK2_Xx ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(32,plain,
    ( ( ~ sK4_REN
      | ~ ( ~ ~ ( cQ @ sK3_Xx )
          | ~ ~ ( cR @ sK3_Xx ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(33,plain,
    ( ( ~ ( ~ ( cF @ sK1_Xx )
          | ~ ( cP @ sK1_Xx ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(34,plain,
    ( ( ~ ( cG @ sK1_Xx ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[28]) ).

thf(35,plain,
    ! [SV1: $i,SV3: $i] :
      ( ( ( ~ ( cF @ SV3 )
          | ( cG @ SV3 ) )
        = $true )
      | ( ( cS @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(36,plain,
    ! [SV2: $i,SV4: $i] :
      ( ( ( cQ @ SV4 )
        = $true )
      | ( ( cP @ SV2 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(37,plain,
    ( ( sK4_REN = $true )
    | ( ( ~ ( ~ ( cQ @ sK2_Xx )
            | ~ ( cS @ sK2_Xx ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(38,plain,
    ( ( ( ~ sK4_REN )
      = $true )
    | ( ( ~ ( ~ ~ ( cQ @ sK3_Xx )
            | ~ ~ ( cR @ sK3_Xx ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[32]) ).

thf(39,plain,
    ( ( ~ ( cF @ sK1_Xx )
      | ~ ( cP @ sK1_Xx ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(40,plain,
    ( ( cG @ sK1_Xx )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV1: $i,SV3: $i] :
      ( ( ( ~ ( cF @ SV3 ) )
        = $true )
      | ( ( cG @ SV3 )
        = $true )
      | ( ( cS @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[35]) ).

thf(42,plain,
    ( ( ( ~ ( cQ @ sK2_Xx )
        | ~ ( cS @ sK2_Xx ) )
      = $false )
    | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(43,plain,
    ( ( sK4_REN = $false )
    | ( ( ~ ( ~ ~ ( cQ @ sK3_Xx )
            | ~ ~ ( cR @ sK3_Xx ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(44,plain,
    ( ( ~ ( cF @ sK1_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(45,plain,
    ( ( ~ ( cP @ sK1_Xx ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(46,plain,
    ! [SV1: $i,SV3: $i] :
      ( ( ( cF @ SV3 )
        = $false )
      | ( ( cG @ SV3 )
        = $true )
      | ( ( cS @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(47,plain,
    ( ( ( ~ ( cQ @ sK2_Xx ) )
      = $false )
    | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[42]) ).

thf(48,plain,
    ( ( ( ~ ( cS @ sK2_Xx ) )
      = $false )
    | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[42]) ).

thf(49,plain,
    ( ( ( ~ ~ ( cQ @ sK3_Xx )
        | ~ ~ ( cR @ sK3_Xx ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(50,plain,
    ( ( cF @ sK1_Xx )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(51,plain,
    ( ( cP @ sK1_Xx )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[45]) ).

thf(52,plain,
    ( ( ( cQ @ sK2_Xx )
      = $true )
    | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[47]) ).

thf(53,plain,
    ( ( ( cS @ sK2_Xx )
      = $true )
    | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[48]) ).

thf(54,plain,
    ( ( ( ~ ~ ( cQ @ sK3_Xx ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(55,plain,
    ( ( ( ~ ~ ( cR @ sK3_Xx ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(56,plain,
    ( ( ( ~ ( cQ @ sK3_Xx ) )
      = $true )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[54]) ).

thf(57,plain,
    ( ( ( ~ ( cR @ sK3_Xx ) )
      = $true )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(58,plain,
    ( ( ( cQ @ sK3_Xx )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(59,plain,
    ( ( ( cR @ sK3_Xx )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(60,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[36,59,58,53,52,51,50,46,40]) ).

thf(61,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : SYN058^5 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue Jul 12 07:54:43 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  
% 0.14/0.36   No.of.Axioms: 0
% 0.14/0.36  
% 0.14/0.36   Length.of.Defs: 0
% 0.14/0.36  
% 0.14/0.36   Contains.Choice.Funs: false
% 0.14/0.36  (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)..
% 0.14/0.39  
% 0.14/0.39  ********************************
% 0.14/0.39  *   All subproblems solved!    *
% 0.14/0.39  ********************************
% 0.14/0.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:60,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.14/0.40  
% 0.14/0.40  %**** Beginning of derivation protocol ****
% 0.14/0.40  % SZS output start CNFRefutation
% See solution above
% 0.14/0.40  
% 0.14/0.40  %**** End of derivation protocol ****
% 0.14/0.40  %**** no. of clauses in derivation: 61 ****
% 0.14/0.40  %**** clause counter: 60 ****
% 0.14/0.40  
% 0.14/0.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:60,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------