TSTP Solution File: SEU648^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU648^2 : TPTP v8.1.0. Released v3.7.0.
% 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 12:13:38 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   35 (  23 unt;   8 typ;   2 def)
%            Number of atoms       :  104 (  73 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  462 (  21   ~;  10   |;   2   &; 418   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   8 con; 0-2 aty)
%            Number of variables   :   66 (   2   ^  64   !;   0   ?;  66   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
    emptyset: $i ).

thf(tp_kpair,type,
    kpair: $i > $i > $i ).

thf(tp_sK1_SY0,type,
    sK1_SY0: $i ).

thf(tp_sK2_SY14,type,
    sK2_SY14: $i ).

thf(tp_sK3_SY17,type,
    sK3_SY17: $i ).

thf(tp_sK4_SY19,type,
    sK4_SY19: $i ).

thf(tp_setadjoin,type,
    setadjoin: $i > $i > $i ).

thf(tp_setukpairinjL2,type,
    setukpairinjL2: $o ).

thf(kpair,definition,
    ( kpair
    = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).

thf(setukpairinjL2,definition,
    ( setukpairinjL2
    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( Xx = Xz ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).

thf(1,conjecture,
    ( setukpairinjL2
   => ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
        ( ( ( kpair @ Xx @ Xy )
          = ( kpair @ Xz @ Xu ) )
       => ( Xx = Xz ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).

thf(2,negated_conjecture,
    ( ( setukpairinjL2
     => ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
            = ( kpair @ Xz @ Xu ) )
         => ( Xx = Xz ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( Xx = Xz ) )
     => ! [SY0: $i,SY1: $i,SY2: $i,SY3: $i] :
          ( ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) )
         => ( SY0 = SY2 ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,kpair,setukpairinjL2]) ).

thf(4,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( Xx = Xz ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [SY0: $i,SY1: $i,SY2: $i,SY3: $i] :
          ( ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) )
         => ( SY0 = SY2 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ~ ! [SY0: $i,SY1: $i,SY2: $i,SY3: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
              = ( setadjoin @ ( setadjoin @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) )
           => ( SY0 = SY2 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
      & ( sK1_SY0 != sK3_SY17 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ! [Xu: $i] :
              ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
          | ( Xx = Xz ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ! [Xu: $i] :
              ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
          | ( Xx = Xz ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
      & ( sK1_SY0 != sK3_SY17 ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ~ ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
           != ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
          | ~ ( ( sK1_SY0 != sK3_SY17 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10,kpair,setukpairinjL2]) ).

thf(12,plain,
    ! [SV1: $i] :
      ( ( ! [SY20: $i,SY21: $i] :
            ( ! [SY22: $i] :
                ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY20 @ emptyset ) ) @ emptyset ) )
               != ( setadjoin @ ( setadjoin @ SY21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY21 @ ( setadjoin @ SY22 @ emptyset ) ) @ emptyset ) ) )
            | ( SV1 = SY21 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[9]) ).

thf(13,plain,
    ( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
      | ~ ( ( sK1_SY0 != sK3_SY17 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11]) ).

thf(14,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ! [SY23: $i] :
            ( ! [SY24: $i] :
                ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
               != ( setadjoin @ ( setadjoin @ SY23 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY23 @ ( setadjoin @ SY24 @ emptyset ) ) @ emptyset ) ) )
            | ( SV1 = SY23 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(15,plain,
    ( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
       != ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ( ( sK1_SY0 != sK3_SY17 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(17,plain,
    ! [SV3: $i,SV2: $i,SV1: $i] :
      ( ( ! [SY25: $i] :
            ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
           != ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SY25 @ emptyset ) ) @ emptyset ) ) )
        | ( SV1 = SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
      = ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ( sK1_SY0 != sK3_SY17 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(20,plain,
    ! [SV3: $i,SV2: $i,SV1: $i] :
      ( ( ( ! [SY25: $i] :
              ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SY25 @ emptyset ) ) @ emptyset ) ) ) )
        = $true )
      | ( ( SV1 = SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[17]) ).

thf(21,plain,
    ( ( sK1_SY0 = sK3_SY17 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(22,plain,
    ! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
      ( ( ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
           != ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) ) )
        = $true )
      | ( ( SV1 = SV3 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(23,plain,
    ! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( SV1 = SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(24,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[18,23,21]) ).

thf(25,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU648^2 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n022.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sat Jun 18 23:04:31 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 0
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 608
% 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)..
% 0.13/0.38  
% 0.13/0.38  ********************************
% 0.13/0.38  *   All subproblems solved!    *
% 0.13/0.38  ********************************
% 0.13/0.38  % 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:24,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.38  
% 0.13/0.38  %**** Beginning of derivation protocol ****
% 0.13/0.38  % SZS output start CNFRefutation
% See solution above
% 0.13/0.39  
% 0.13/0.39  %**** End of derivation protocol ****
% 0.13/0.39  %**** no. of clauses in derivation: 25 ****
% 0.13/0.39  %**** clause counter: 24 ****
% 0.13/0.39  
% 0.13/0.39  % 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:24,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------