TSTP Solution File: SEV049^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV049^5 : 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 : n018.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 17:34:31 EDT 2022

% Result   : Theorem 0.46s 0.70s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   48
% Syntax   : Number of formulae    :   65 (   9 unt;  47 typ;   0 def)
%            Number of atoms       :  134 (  24 equ;   0 cnn)
%            Maximal formula atoms :    2 (   7 avg)
%            Number of connectives :  241 (  44   ~;  23   |;  12   &; 158   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  103 ( 103   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   50 (  47 usr;  33 con; 0-2 aty)
%            Number of variables   :   57 (  30   ^  23   !;   4   ?;  57   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_sK10_SV66,type,
    sK10_SV66: $i ).

thf(tp_sK11_SV67,type,
    sK11_SV67: $i > $i ).

thf(tp_sK12_SV68,type,
    sK12_SV68: $i ).

thf(tp_sK13_SV69,type,
    sK13_SV69: $i ).

thf(tp_sK14_SV70,type,
    sK14_SV70: $i ).

thf(tp_sK15_SV71,type,
    sK15_SV71: $i ).

thf(tp_sK16_SV72,type,
    sK16_SV72: $i ).

thf(tp_sK17_SV73,type,
    sK17_SV73: $i ).

thf(tp_sK18_SV74,type,
    sK18_SV74: $i > $i ).

thf(tp_sK19_SV75,type,
    sK19_SV75: $i > $i ).

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

thf(tp_sK20_SV76,type,
    sK20_SV76: $i > $i ).

thf(tp_sK21_SV77,type,
    sK21_SV77: $i > $i ).

thf(tp_sK22_E,type,
    sK22_E: $i > $i ).

thf(tp_sK23_E,type,
    sK23_E: $i > $i ).

thf(tp_sK24_E,type,
    sK24_E: $i > $i ).

thf(tp_sK25_E,type,
    sK25_E: $i > $i ).

thf(tp_sK26_E,type,
    sK26_E: $i > $i ).

thf(tp_sK27_E,type,
    sK27_E: $i > $i ).

thf(tp_sK28_E,type,
    sK28_E: $i > $i ).

thf(tp_sK29_E,type,
    sK29_E: $i > $i ).

thf(tp_sK2_SY6,type,
    sK2_SY6: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(tp_sK30_E,type,
    sK30_E: $i ).

thf(tp_sK31_E,type,
    sK31_E: $i ).

thf(tp_sK32_E,type,
    sK32_E: $i ).

thf(tp_sK33_E,type,
    sK33_E: $i ).

thf(tp_sK34_E,type,
    sK34_E: $i ).

thf(tp_sK35_E,type,
    sK35_E: $i ).

thf(tp_sK36_E,type,
    sK36_E: $i ).

thf(tp_sK37_E,type,
    sK37_E: $i ).

thf(tp_sK38_E,type,
    sK38_E: $i ).

thf(tp_sK39_E,type,
    sK39_E: $i ).

thf(tp_sK3_SY8,type,
    sK3_SY8: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(tp_sK40_E,type,
    sK40_E: $i ).

thf(tp_sK41_E,type,
    sK41_E: $i ).

thf(tp_sK42_E,type,
    sK42_E: $i ).

thf(tp_sK43_E,type,
    sK43_E: $i ).

thf(tp_sK44_E,type,
    sK44_E: $i ).

thf(tp_sK45_E,type,
    sK45_E: $i ).

thf(tp_sK46_E,type,
    sK46_E: $i ).

thf(tp_sK47_E,type,
    sK47_E: $i ).

thf(tp_sK4_SV58,type,
    sK4_SV58: $i ).

thf(tp_sK5_SV59,type,
    sK5_SV59: $i ).

thf(tp_sK6_SV61,type,
    sK6_SV61: $i ).

thf(tp_sK7_SV62,type,
    sK7_SV62: $i ).

thf(tp_sK8_SV64,type,
    sK8_SV64: $i ).

thf(tp_sK9_SV65,type,
    sK9_SV65: $i ).

thf(1,conjecture,
    ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ~ ( R
          @ ^ [Xx: $i] : $true
          @ ^ [Xx: $i] : $false )
      & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
          ( ( ( R @ Xx @ Xy )
            & ( R @ Xy @ Xz ) )
         => ( R @ Xx @ Xz ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120A_pme) ).

thf(2,negated_conjecture,
    ( ( ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
          ( ~ ( R
              @ ^ [Xx: $i] : $true
              @ ^ [Xx: $i] : $false )
          & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
              ( ( ( R @ Xx @ Xy )
                & ( R @ Xy @ Xz ) )
             => ( R @ Xx @ Xz ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
          ( ~ ( R
              @ ^ [Xx: $i] : $true
              @ ^ [Xx: $i] : $false )
          & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
              ( ( ( R @ Xx @ Xy )
                & ( R @ Xy @ Xz ) )
             => ( R @ Xx @ Xz ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ~ ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
            ( ~ ( R
                @ ^ [Xx: $i] : $true
                @ ^ [Xx: $i] : $false )
            & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
                ( ( ( R @ Xx @ Xy )
                  & ( R @ Xy @ Xz ) )
               => ( R @ Xx @ Xz ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [R: ( $i > $o ) > ( $i > $o ) > $o] :
          ( ( R
            @ ^ [Xx: $i] : $true
            @ ^ [Xx: $i] : $false )
          | ( ( R @ ( sK1_Xx @ R ) @ ( sK2_SY6 @ R ) )
            & ( R @ ( sK2_SY6 @ R ) @ ( sK3_SY8 @ R ) )
            & ~ ( R @ ( sK1_Xx @ R ) @ ( sK3_SY8 @ R ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [R: ( $i > $o ) > ( $i > $o ) > $o] :
          ( ( R
            @ ^ [Xx: $i] : $true
            @ ^ [Xx: $i] : $false )
          | ( ( R @ ( sK1_Xx @ R ) @ ( sK2_SY6 @ R ) )
            & ( R @ ( sK2_SY6 @ R ) @ ( sK3_SY8 @ R ) )
            & ~ ( R @ ( sK1_Xx @ R ) @ ( sK3_SY8 @ R ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SX0: ( $i > $o ) > ( $i > $o ) > $o] :
          ( ( SX0
            @ ^ [SX1: $i] : $true
            @ ^ [SX1: $i] : $false )
          | ~ ( ~ ~ ( ~ ( SX0 @ ( sK1_Xx @ SX0 ) @ ( sK2_SY6 @ SX0 ) )
                    | ~ ( SX0 @ ( sK2_SY6 @ SX0 ) @ ( sK3_SY8 @ SX0 ) ) )
              | ~ ~ ( SX0 @ ( sK1_Xx @ SX0 ) @ ( sK3_SY8 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(8,plain,
    ! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( SV1
          @ ^ [SX1: $i] : $true
          @ ^ [SX1: $i] : $false )
        | ~ ( ~ ~ ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK2_SY6 @ SV1 ) )
                  | ~ ( SV1 @ ( sK2_SY6 @ SV1 ) @ ( sK3_SY8 @ SV1 ) ) )
            | ~ ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK3_SY8 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7]) ).

thf(9,plain,
    ! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( SV1
          @ ^ [SX1: $i] : $true
          @ ^ [SX1: $i] : $false )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK2_SY6 @ SV1 ) )
                    | ~ ( SV1 @ ( sK2_SY6 @ SV1 ) @ ( sK3_SY8 @ SV1 ) ) )
              | ~ ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK3_SY8 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8]) ).

thf(10,plain,
    ! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( ~ ~ ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK2_SY6 @ SV1 ) )
                | ~ ( SV1 @ ( sK2_SY6 @ SV1 ) @ ( sK3_SY8 @ SV1 ) ) )
          | ~ ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK3_SY8 @ SV1 ) ) )
        = $false )
      | ( ( SV1
          @ ^ [SX1: $i] : $true
          @ ^ [SX1: $i] : $false )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[9]) ).

thf(11,plain,
    ! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( ~ ~ ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK2_SY6 @ SV1 ) )
                | ~ ( SV1 @ ( sK2_SY6 @ SV1 ) @ ( sK3_SY8 @ SV1 ) ) ) )
        = $false )
      | ( ( SV1
          @ ^ [SX1: $i] : $true
          @ ^ [SX1: $i] : $false )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[10]) ).

thf(13,plain,
    ! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( ~ ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK2_SY6 @ SV1 ) )
              | ~ ( SV1 @ ( sK2_SY6 @ SV1 ) @ ( sK3_SY8 @ SV1 ) ) ) )
        = $true )
      | ( ( SV1
          @ ^ [SX1: $i] : $true
          @ ^ [SX1: $i] : $false )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[11]) ).

thf(15,plain,
    ! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK2_SY6 @ SV1 ) )
          | ~ ( SV1 @ ( sK2_SY6 @ SV1 ) @ ( sK3_SY8 @ SV1 ) ) )
        = $false )
      | ( ( SV1
          @ ^ [SX1: $i] : $true
          @ ^ [SX1: $i] : $false )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(17,plain,
    ! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( ~ ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK2_SY6 @ SV1 ) ) )
        = $false )
      | ( ( SV1
          @ ^ [SX1: $i] : $true
          @ ^ [SX1: $i] : $false )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV1: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( SV1 @ ( sK1_Xx @ SV1 ) @ ( sK2_SY6 @ SV1 ) )
        = $true )
      | ( ( SV1
          @ ^ [SX1: $i] : $true
          @ ^ [SX1: $i] : $false )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(27,plain,
    ( ( $false = $true )
    | ( $false = $true ) ),
    inference(prim_subst,[status(thm)],[19:[bind(SV1,$thf( ^ [SV5: $i > $o] : ^ [SV6: $i > $o] : $false ))]]) ).

thf(587,plain,
    $false = $true,
    inference(sim,[status(thm)],[27]) ).

thf(588,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[587]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV049^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 27 19:26:28 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: 0
% 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)........
% 0.46/0.70  
% 0.46/0.70  ********************************
% 0.46/0.70  *   All subproblems solved!    *
% 0.46/0.70  ********************************
% 0.46/0.70  % SZS status Theorem for /export/starexec/sandbox/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:587,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.46/0.70  
% 0.46/0.70  %**** Beginning of derivation protocol ****
% 0.46/0.70  % SZS output start CNFRefutation
% See solution above
% 0.46/0.70  
% 0.46/0.70  %**** End of derivation protocol ****
% 0.46/0.70  %**** no. of clauses in derivation: 18 ****
% 0.46/0.70  %**** clause counter: 587 ****
% 0.46/0.70  
% 0.46/0.70  % SZS status Theorem for /export/starexec/sandbox/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:587,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------