TSTP Solution File: SYO267^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO267^5 : 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 : n003.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 17:33:05 EDT 2022

% Result   : Theorem 6.57s 6.74s
% Output   : CNFRefutation 6.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   34 (  17 unt;  16 typ;   0 def)
%            Number of atoms       :   49 (  16 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  221 (  47   ~;  17   |;  16   &; 131   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  190 ( 190   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   2 con; 0-4 aty)
%            Number of variables   :   43 (  10   ^  28   !;   5   ?;  43   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_sK10_E,type,
    sK10_E: ( ( $i > $i ) > ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK11_E,type,
    sK11_E: ( ( $i > $i ) > ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK12_E,type,
    sK12_E: ( ( $i > $i ) > ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK13_E,type,
    sK13_E: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK14_E,type,
    sK14_E: ( ( $i > $i ) > ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > ( $i > $i ) > $o ) > ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK15_E,type,
    sK15_E: ( ( $i > $i ) > ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK16_E,type,
    sK16_E: ( ( $i > $i ) > ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK1_P,type,
    sK1_P: $i > $o ).

thf(tp_sK2_SY7,type,
    sK2_SY7: ( ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK3_SY11,type,
    sK3_SY11: ( ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK4_SY12,type,
    sK4_SY12: ( ( $i > $i ) > $o ) > $i ).

thf(tp_sK5_E,type,
    sK5_E: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK6_E,type,
    sK6_E: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK7_E,type,
    sK7_E: ( ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > $i ) > $i > $i ).

thf(tp_sK8_E,type,
    sK8_E: ( ( $i > $i ) > ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).

thf(tp_sK9_E,type,
    sK9_E: ( ( $i > $i ) > ( $i > $i ) > $i ) > ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).

thf(1,conjecture,
    ! [P: $i > $o] :
    ? [M: ( $i > $i ) > $o] :
    ! [G: $i > $i,H: $i > $i] :
      ( ( ( M @ G )
        & ( M @ H ) )
     => ( ( M
          @ ^ [Z: $i] : ( G @ ( H @ Z ) ) )
        & ! [Y: $i] :
            ( ( P @ Y )
           => ( P @ ( G @ Y ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM111) ).

thf(2,negated_conjecture,
    ( ( ! [P: $i > $o] :
        ? [M: ( $i > $i ) > $o] :
        ! [G: $i > $i,H: $i > $i] :
          ( ( ( M @ G )
            & ( M @ H ) )
         => ( ( M
              @ ^ [Z: $i] : ( G @ ( H @ Z ) ) )
            & ! [Y: $i] :
                ( ( P @ Y )
               => ( P @ ( G @ Y ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [P: $i > $o] :
        ? [M: ( $i > $i ) > $o] :
        ! [G: $i > $i,H: $i > $i] :
          ( ( ( M @ G )
            & ( M @ H ) )
         => ( ( M
              @ ^ [Z: $i] : ( G @ ( H @ Z ) ) )
            & ! [Y: $i] :
                ( ( P @ Y )
               => ( P @ ( G @ Y ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ? [SY6: ( $i > $i ) > $o] :
        ! [SY7: $i > $i,SY8: $i > $i] :
          ( ( ( SY6 @ SY7 )
            & ( SY6 @ SY8 ) )
         => ( ( SY6
              @ ^ [Z: $i] : ( SY7 @ ( SY8 @ Z ) ) )
            & ! [SY10: $i] :
                ( ( sK1_P @ SY10 )
               => ( sK1_P @ ( SY7 @ SY10 ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ~ ? [SY6: ( $i > $i ) > $o] :
          ! [SY7: $i > $i,SY8: $i > $i] :
            ( ( ( SY6 @ SY7 )
              & ( SY6 @ SY8 ) )
           => ( ( SY6
                @ ^ [Z: $i] : ( SY7 @ ( SY8 @ Z ) ) )
              & ! [SY10: $i] :
                  ( ( sK1_P @ SY10 )
                 => ( sK1_P @ ( SY7 @ SY10 ) ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ! [SY6: ( $i > $i ) > $o] :
          ( ( SY6 @ ( sK2_SY7 @ SY6 ) )
          & ( SY6 @ ( sK3_SY11 @ SY6 ) )
          & ( ( ( sK1_P @ ( sK4_SY12 @ SY6 ) )
              & ~ ( sK1_P @ ( sK2_SY7 @ SY6 @ ( sK4_SY12 @ SY6 ) ) ) )
            | ~ ( SY6
                @ ^ [SY15: $i] : ( sK2_SY7 @ SY6 @ ( sK3_SY11 @ SY6 @ SY15 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(7,plain,
    ( ( ! [SY6: ( $i > $i ) > $o] :
          ( ( SY6 @ ( sK2_SY7 @ SY6 ) )
          & ( SY6 @ ( sK3_SY11 @ SY6 ) )
          & ( ( ( sK1_P @ ( sK4_SY12 @ SY6 ) )
              & ~ ( sK1_P @ ( sK2_SY7 @ SY6 @ ( sK4_SY12 @ SY6 ) ) ) )
            | ~ ( SY6
                @ ^ [SY15: $i] : ( sK2_SY7 @ SY6 @ ( sK3_SY11 @ SY6 @ SY15 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [SX0: ( $i > $i ) > $o] :
          ~ ( ~ ~ ( ~ ( SX0 @ ( sK2_SY7 @ SX0 ) )
                  | ~ ( SX0 @ ( sK3_SY11 @ SX0 ) ) )
            | ~ ( ~ ( ~ ( sK1_P @ ( sK4_SY12 @ SX0 ) )
                    | ~ ~ ( sK1_P @ ( sK2_SY7 @ SX0 @ ( sK4_SY12 @ SX0 ) ) ) )
                | ~ ( SX0
                    @ ^ [SX1: $i] : ( sK2_SY7 @ SX0 @ ( sK3_SY11 @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(9,plain,
    ! [SV1: ( $i > $i ) > $o] :
      ( ( ~ ( ~ ~ ( ~ ( SV1 @ ( sK2_SY7 @ SV1 ) )
                  | ~ ( SV1 @ ( sK3_SY11 @ SV1 ) ) )
            | ~ ( ~ ( ~ ( sK1_P @ ( sK4_SY12 @ SV1 ) )
                    | ~ ~ ( sK1_P @ ( sK2_SY7 @ SV1 @ ( sK4_SY12 @ SV1 ) ) ) )
                | ~ ( SV1
                    @ ^ [SY16: $i] : ( sK2_SY7 @ SV1 @ ( sK3_SY11 @ SV1 @ SY16 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8]) ).

thf(10,plain,
    ! [SV1: ( $i > $i ) > $o] :
      ( ( ~ ~ ( ~ ( SV1 @ ( sK2_SY7 @ SV1 ) )
              | ~ ( SV1 @ ( sK3_SY11 @ SV1 ) ) )
        | ~ ( ~ ( ~ ( sK1_P @ ( sK4_SY12 @ SV1 ) )
                | ~ ~ ( sK1_P @ ( sK2_SY7 @ SV1 @ ( sK4_SY12 @ SV1 ) ) ) )
            | ~ ( SV1
                @ ^ [SY16: $i] : ( sK2_SY7 @ SV1 @ ( sK3_SY11 @ SV1 @ SY16 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[9]) ).

thf(11,plain,
    ! [SV1: ( $i > $i ) > $o] :
      ( ( ~ ~ ( ~ ( SV1 @ ( sK2_SY7 @ SV1 ) )
              | ~ ( SV1 @ ( sK3_SY11 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[10]) ).

thf(13,plain,
    ! [SV1: ( $i > $i ) > $o] :
      ( ( ~ ( ~ ( SV1 @ ( sK2_SY7 @ SV1 ) )
            | ~ ( SV1 @ ( sK3_SY11 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[11]) ).

thf(15,plain,
    ! [SV1: ( $i > $i ) > $o] :
      ( ( ~ ( SV1 @ ( sK2_SY7 @ SV1 ) )
        | ~ ( SV1 @ ( sK3_SY11 @ SV1 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(17,plain,
    ! [SV1: ( $i > $i ) > $o] :
      ( ( ~ ( SV1 @ ( sK2_SY7 @ SV1 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(20,plain,
    ! [SV1: ( $i > $i ) > $o] :
      ( ( SV1 @ ( sK2_SY7 @ SV1 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(30,plain,
    $false = $true,
    inference(prim_subst,[status(thm)],[20:[bind(SV1,$thf( ^ [SV4: $i > $i] : $false ))]]) ).

thf(127,plain,
    $false = $true,
    inference(sim,[status(thm)],[30]) ).

thf(128,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[127]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYO267^5 : 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 : n003.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 13:07:28 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)....
% 6.57/6.74  
% 6.57/6.74  ********************************
% 6.57/6.74  *   All subproblems solved!    *
% 6.57/6.74  ********************************
% 6.57/6.74  % 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:127,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.57/6.74  
% 6.57/6.74  %**** Beginning of derivation protocol ****
% 6.57/6.74  % SZS output start CNFRefutation
% See solution above
% 6.57/6.74  
% 6.57/6.74  %**** End of derivation protocol ****
% 6.57/6.74  %**** no. of clauses in derivation: 18 ****
% 6.57/6.74  %**** clause counter: 127 ****
% 6.57/6.74  
% 6.57/6.74  % 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:127,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------