TSTP Solution File: SEV060^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV060^5 : 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 : n019.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 17:34:37 EDT 2022

% Result   : Theorem 0.18s 0.36s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   50 (  35 unt;   8 typ;   0 def)
%            Number of atoms       :  209 (  86 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  349 (  48   ~;  56   |;  19   &; 202   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   26 (  26   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   6 con; 0-2 aty)
%            Number of variables   :   96 (   0   ^  96   !;   0   ?;  96   :)

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

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

thf(tp_sK1_Xx,type,
    sK1_Xx: b ).

thf(tp_sK2_SY8,type,
    sK2_SY8: a ).

thf(tp_sK3_SY15,type,
    sK3_SY15: b > a > $o ).

thf(tp_sK4_SY21,type,
    sK4_SY21: b > a > $o ).

thf(tp_sK5_SY28,type,
    sK5_SY28: b ).

thf(tp_sK6_SY30,type,
    sK6_SY30: a ).

thf(1,conjecture,
    ! [Xx: b,Xy: a,Xs: b > a > $o,Xk: b > a > $o] :
      ( ( ! [Xx_0: b,Xy_9: a] :
            ( ( Xk @ Xx_0 @ Xy_9 )
           => ( ( Xs @ Xx_0 @ Xy_9 )
              | ( ( Xx_0 = Xx )
                & ( Xy_9 = Xy ) ) ) )
        & ~ ( Xk @ Xx @ Xy ) )
     => ! [Xx0: b,Xy0: a] :
          ( ( Xk @ Xx0 @ Xy0 )
         => ( Xs @ Xx0 @ Xy0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM173_pme) ).

thf(2,negated_conjecture,
    ( ( ! [Xx: b,Xy: a,Xs: b > a > $o,Xk: b > a > $o] :
          ( ( ! [Xx_0: b,Xy_9: a] :
                ( ( Xk @ Xx_0 @ Xy_9 )
               => ( ( Xs @ Xx_0 @ Xy_9 )
                  | ( ( Xx_0 = Xx )
                    & ( Xy_9 = Xy ) ) ) )
            & ~ ( Xk @ Xx @ Xy ) )
         => ! [Xx0: b,Xy0: a] :
              ( ( Xk @ Xx0 @ Xy0 )
             => ( Xs @ Xx0 @ Xy0 ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xx: b,Xy: a,Xs: b > a > $o,Xk: b > a > $o] :
          ( ( ! [Xx_0: b,Xy_9: a] :
                ( ( Xk @ Xx_0 @ Xy_9 )
               => ( ( Xs @ Xx_0 @ Xy_9 )
                  | ( ( Xx_0 = Xx )
                    & ( Xy_9 = Xy ) ) ) )
            & ~ ( Xk @ Xx @ Xy ) )
         => ! [Xx0: b,Xy0: a] :
              ( ( Xk @ Xx0 @ Xy0 )
             => ( Xs @ Xx0 @ Xy0 ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY8: a,SY9: b > a > $o,SY10: b > a > $o] :
          ( ( ! [SY11: b,SY12: a] :
                ( ( SY10 @ SY11 @ SY12 )
               => ( ( SY9 @ SY11 @ SY12 )
                  | ( ( SY11 = sK1_Xx )
                    & ( SY12 = SY8 ) ) ) )
            & ~ ( SY10 @ sK1_Xx @ SY8 ) )
         => ! [Xx0: b,Xy0: a] :
              ( ( SY10 @ Xx0 @ Xy0 )
             => ( SY9 @ Xx0 @ Xy0 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY15: b > a > $o,SY16: b > a > $o] :
          ( ( ! [SY17: b,SY18: a] :
                ( ( SY16 @ SY17 @ SY18 )
               => ( ( SY15 @ SY17 @ SY18 )
                  | ( ( SY17 = sK1_Xx )
                    & ( SY18 = sK2_SY8 ) ) ) )
            & ~ ( SY16 @ sK1_Xx @ sK2_SY8 ) )
         => ! [Xx0: b,Xy0: a] :
              ( ( SY16 @ Xx0 @ Xy0 )
             => ( SY15 @ Xx0 @ Xy0 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [SY21: b > a > $o] :
          ( ( ! [SY22: b,SY23: a] :
                ( ( SY21 @ SY22 @ SY23 )
               => ( ( sK3_SY15 @ SY22 @ SY23 )
                  | ( ( SY22 = sK1_Xx )
                    & ( SY23 = sK2_SY8 ) ) ) )
            & ~ ( SY21 @ sK1_Xx @ sK2_SY8 ) )
         => ! [SY24: b,SY25: a] :
              ( ( SY21 @ SY24 @ SY25 )
             => ( sK3_SY15 @ SY24 @ SY25 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[5]) ).

thf(7,plain,
    ( ( ( ! [SY26: b,SY27: a] :
            ( ( sK4_SY21 @ SY26 @ SY27 )
           => ( ( sK3_SY15 @ SY26 @ SY27 )
              | ( ( SY26 = sK1_Xx )
                & ( SY27 = sK2_SY8 ) ) ) )
        & ~ ( sK4_SY21 @ sK1_Xx @ sK2_SY8 ) )
     => ! [SY28: b,SY29: a] :
          ( ( sK4_SY21 @ SY28 @ SY29 )
         => ( sK3_SY15 @ SY28 @ SY29 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [SY26: b,SY27: a] :
          ( ( sK4_SY21 @ SY26 @ SY27 )
         => ( ( sK3_SY15 @ SY26 @ SY27 )
            | ( ( SY26 = sK1_Xx )
              & ( SY27 = sK2_SY8 ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ~ ( sK4_SY21 @ sK1_Xx @ sK2_SY8 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ! [SY28: b,SY29: a] :
          ( ( sK4_SY21 @ SY28 @ SY29 )
         => ( sK3_SY15 @ SY28 @ SY29 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ~ ! [SY28: b,SY29: a] :
            ( ( sK4_SY21 @ SY28 @ SY29 )
           => ( sK3_SY15 @ SY28 @ SY29 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ( sK4_SY21 @ sK5_SY28 @ sK6_SY30 )
      & ~ ( sK3_SY15 @ sK5_SY28 @ sK6_SY30 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(13,plain,
    ( ( ! [SY26: b,SY27: a] :
          ( ~ ( sK4_SY21 @ SY26 @ SY27 )
          | ( SY26 = sK1_Xx )
          | ( sK3_SY15 @ SY26 @ SY27 ) )
      & ! [SY26: b,SY27: a] :
          ( ~ ( sK4_SY21 @ SY26 @ SY27 )
          | ( SY27 = sK2_SY8 )
          | ( sK3_SY15 @ SY26 @ SY27 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(14,plain,
    ( ( ~ ( sK4_SY21 @ sK1_Xx @ sK2_SY8 ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(15,plain,
    ( ( ! [SY26: b,SY27: a] :
          ( ~ ( sK4_SY21 @ SY26 @ SY27 )
          | ( SY26 = sK1_Xx )
          | ( sK3_SY15 @ SY26 @ SY27 ) )
      & ! [SY26: b,SY27: a] :
          ( ~ ( sK4_SY21 @ SY26 @ SY27 )
          | ( SY27 = sK2_SY8 )
          | ( sK3_SY15 @ SY26 @ SY27 ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ( sK4_SY21 @ sK5_SY28 @ sK6_SY30 )
      & ~ ( sK3_SY15 @ sK5_SY28 @ sK6_SY30 ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(17,plain,
    ( ( ~ ( ~ ( sK4_SY21 @ sK5_SY28 @ sK6_SY30 )
          | ~ ~ ( sK3_SY15 @ sK5_SY28 @ sK6_SY30 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(18,plain,
    ( ( ~ ( ~ ! [SX0: b,SX1: a] :
                ( ~ ( sK4_SY21 @ SX0 @ SX1 )
                | ( SX0 = sK1_Xx )
                | ( sK3_SY15 @ SX0 @ SX1 ) )
          | ~ ! [SX0: b,SX1: a] :
                ( ~ ( sK4_SY21 @ SX0 @ SX1 )
                | ( SX1 = sK2_SY8 )
                | ( sK3_SY15 @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(19,plain,
    ( ( sK4_SY21 @ sK1_Xx @ sK2_SY8 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[14]) ).

thf(20,plain,
    ( ( ~ ( sK4_SY21 @ sK5_SY28 @ sK6_SY30 )
      | ~ ~ ( sK3_SY15 @ sK5_SY28 @ sK6_SY30 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ~ ! [SX0: b,SX1: a] :
            ( ~ ( sK4_SY21 @ SX0 @ SX1 )
            | ( SX0 = sK1_Xx )
            | ( sK3_SY15 @ SX0 @ SX1 ) )
      | ~ ! [SX0: b,SX1: a] :
            ( ~ ( sK4_SY21 @ SX0 @ SX1 )
            | ( SX1 = sK2_SY8 )
            | ( sK3_SY15 @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ~ ( sK4_SY21 @ sK5_SY28 @ sK6_SY30 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(23,plain,
    ( ( ~ ~ ( sK3_SY15 @ sK5_SY28 @ sK6_SY30 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ! [SX0: b,SX1: a] :
            ( ~ ( sK4_SY21 @ SX0 @ SX1 )
            | ( SX0 = sK1_Xx )
            | ( sK3_SY15 @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ~ ! [SX0: b,SX1: a] :
            ( ~ ( sK4_SY21 @ SX0 @ SX1 )
            | ( SX1 = sK2_SY8 )
            | ( sK3_SY15 @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(26,plain,
    ( ( sK4_SY21 @ sK5_SY28 @ sK6_SY30 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ~ ( sK3_SY15 @ sK5_SY28 @ sK6_SY30 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ! [SX0: b,SX1: a] :
          ( ~ ( sK4_SY21 @ SX0 @ SX1 )
          | ( SX0 = sK1_Xx )
          | ( sK3_SY15 @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ! [SX0: b,SX1: a] :
          ( ~ ( sK4_SY21 @ SX0 @ SX1 )
          | ( SX1 = sK2_SY8 )
          | ( sK3_SY15 @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(30,plain,
    ( ( sK3_SY15 @ sK5_SY28 @ sK6_SY30 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV1: b] :
      ( ( ! [SY31: a] :
            ( ~ ( sK4_SY21 @ SV1 @ SY31 )
            | ( SV1 = sK1_Xx )
            | ( sK3_SY15 @ SV1 @ SY31 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV2: b] :
      ( ( ! [SY32: a] :
            ( ~ ( sK4_SY21 @ SV2 @ SY32 )
            | ( SY32 = sK2_SY8 )
            | ( sK3_SY15 @ SV2 @ SY32 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(33,plain,
    ! [SV3: a,SV1: b] :
      ( ( ~ ( sK4_SY21 @ SV1 @ SV3 )
        | ( SV1 = sK1_Xx )
        | ( sK3_SY15 @ SV1 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(34,plain,
    ! [SV4: a,SV2: b] :
      ( ( ~ ( sK4_SY21 @ SV2 @ SV4 )
        | ( SV4 = sK2_SY8 )
        | ( sK3_SY15 @ SV2 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(35,plain,
    ! [SV3: a,SV1: b] :
      ( ( ( ~ ( sK4_SY21 @ SV1 @ SV3 ) )
        = $true )
      | ( ( ( SV1 = sK1_Xx )
          | ( sK3_SY15 @ SV1 @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[33]) ).

thf(36,plain,
    ! [SV4: a,SV2: b] :
      ( ( ( ~ ( sK4_SY21 @ SV2 @ SV4 ) )
        = $true )
      | ( ( ( SV4 = sK2_SY8 )
          | ( sK3_SY15 @ SV2 @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[34]) ).

thf(37,plain,
    ! [SV3: a,SV1: b] :
      ( ( ( sK4_SY21 @ SV1 @ SV3 )
        = $false )
      | ( ( ( SV1 = sK1_Xx )
          | ( sK3_SY15 @ SV1 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(38,plain,
    ! [SV4: a,SV2: b] :
      ( ( ( sK4_SY21 @ SV2 @ SV4 )
        = $false )
      | ( ( ( SV4 = sK2_SY8 )
          | ( sK3_SY15 @ SV2 @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(39,plain,
    ! [SV3: a,SV1: b] :
      ( ( ( SV1 = sK1_Xx )
        = $true )
      | ( ( sK3_SY15 @ SV1 @ SV3 )
        = $true )
      | ( ( sK4_SY21 @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(40,plain,
    ! [SV2: b,SV4: a] :
      ( ( ( SV4 = sK2_SY8 )
        = $true )
      | ( ( sK3_SY15 @ SV2 @ SV4 )
        = $true )
      | ( ( sK4_SY21 @ SV2 @ SV4 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(41,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[19,40,39,30,26]) ).

thf(42,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEV060^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.32  % Computer : n019.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 600
% 0.13/0.32  % DateTime : Tue Jun 28 17:24:24 EDT 2022
% 0.13/0.32  % CPUTime  : 
% 0.13/0.33  
% 0.13/0.33   No.of.Axioms: 0
% 0.13/0.33  
% 0.13/0.33   Length.of.Defs: 0
% 0.13/0.33  
% 0.13/0.33   Contains.Choice.Funs: false
% 0.13/0.33  (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)..
% 0.18/0.36  
% 0.18/0.36  ********************************
% 0.18/0.36  *   All subproblems solved!    *
% 0.18/0.36  ********************************
% 0.18/0.36  % SZS status Theorem for /export/starexec/sandbox/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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.36  
% 0.18/0.36  %**** Beginning of derivation protocol ****
% 0.18/0.36  % SZS output start CNFRefutation
% See solution above
% 0.18/0.36  
% 0.18/0.36  %**** End of derivation protocol ****
% 0.18/0.36  %**** no. of clauses in derivation: 42 ****
% 0.18/0.36  %**** clause counter: 41 ****
% 0.18/0.36  
% 0.18/0.36  % SZS status Theorem for /export/starexec/sandbox/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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------