TSTP Solution File: SEV169^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV169^5 : 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 : n008.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 17:35:28 EDT 2022

% Result   : Theorem 0.19s 0.38s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   32 (  27 unt;   4 typ;   0 def)
%            Number of atoms       :  100 (  72 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  138 (   2   ~;   0   |;  15   &; 116   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   1 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :   71 (  71   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :  164 ( 152   ^  12   !;   0   ?; 164   :)

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

thf(tp_sK1_Xp,type,
    sK1_Xp: ( a > a > a ) > a ).

thf(tp_sK2_SY20,type,
    sK2_SY20: ( a > a > a ) > a ).

thf(tp_sK3_SV5,type,
    sK3_SV5: a > a > a ).

thf(1,conjecture,
    ! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
      ( ( ( Xp
          = ( ^ [Xg: a > a > a] :
                ( Xg
                @ ( Xp
                  @ ^ [Xx: a,Xy: a] : Xx )
                @ ( Xp
                  @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
        & ( Xq
          = ( ^ [Xg: a > a > a] :
                ( Xg
                @ ( Xq
                  @ ^ [Xx: a,Xy: a] : Xx )
                @ ( Xq
                  @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
        & ( ( Xp
            @ ^ [Xx: a,Xy: a] : Xx )
          = ( Xq
            @ ^ [Xx: a,Xy: a] : Xx ) )
        & ( ( Xp
            @ ^ [Xx: a,Xy: a] : Xy )
          = ( Xq
            @ ^ [Xx: a,Xy: a] : Xy ) ) )
     => ( Xp = Xq ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM188_pme) ).

thf(2,negated_conjecture,
    ( ( ! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
          ( ( ( Xp
              = ( ^ [Xg: a > a > a] :
                    ( Xg
                    @ ( Xp
                      @ ^ [Xx: a,Xy: a] : Xx )
                    @ ( Xp
                      @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
            & ( Xq
              = ( ^ [Xg: a > a > a] :
                    ( Xg
                    @ ( Xq
                      @ ^ [Xx: a,Xy: a] : Xx )
                    @ ( Xq
                      @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
            & ( ( Xp
                @ ^ [Xx: a,Xy: a] : Xx )
              = ( Xq
                @ ^ [Xx: a,Xy: a] : Xx ) )
            & ( ( Xp
                @ ^ [Xx: a,Xy: a] : Xy )
              = ( Xq
                @ ^ [Xx: a,Xy: a] : Xy ) ) )
         => ( Xp = Xq ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
          ( ( ( Xp
              = ( ^ [Xg: a > a > a] :
                    ( Xg
                    @ ( Xp
                      @ ^ [Xx: a,Xy: a] : Xx )
                    @ ( Xp
                      @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
            & ( Xq
              = ( ^ [Xg: a > a > a] :
                    ( Xg
                    @ ( Xq
                      @ ^ [Xx: a,Xy: a] : Xx )
                    @ ( Xq
                      @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
            & ( ( Xp
                @ ^ [Xx: a,Xy: a] : Xx )
              = ( Xq
                @ ^ [Xx: a,Xy: a] : Xx ) )
            & ( ( Xp
                @ ^ [Xx: a,Xy: a] : Xy )
              = ( Xq
                @ ^ [Xx: a,Xy: a] : Xy ) ) )
         => ( Xp = Xq ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY20: ( a > a > a ) > a] :
          ( ( ( sK1_Xp
              = ( ^ [SY21: a > a > a] :
                    ( SY21
                    @ ( sK1_Xp
                      @ ^ [Xx: a,Xy: a] : Xx )
                    @ ( sK1_Xp
                      @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
            & ( SY20
              = ( ^ [Xg: a > a > a] :
                    ( Xg
                    @ ( SY20
                      @ ^ [Xx: a,Xy: a] : Xx )
                    @ ( SY20
                      @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
            & ( ( sK1_Xp
                @ ^ [Xx: a,Xy: a] : Xx )
              = ( SY20
                @ ^ [Xx: a,Xy: a] : Xx ) )
            & ( ( sK1_Xp
                @ ^ [Xx: a,Xy: a] : Xy )
              = ( SY20
                @ ^ [Xx: a,Xy: a] : Xy ) ) )
         => ( sK1_Xp = SY20 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ( ( sK1_Xp
          = ( ^ [SY21: a > a > a] :
                ( SY21
                @ ( sK1_Xp
                  @ ^ [Xx: a,Xy: a] : Xx )
                @ ( sK1_Xp
                  @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
        & ( sK2_SY20
          = ( ^ [SY44: a > a > a] :
                ( SY44
                @ ( sK2_SY20
                  @ ^ [Xx: a,Xy: a] : Xx )
                @ ( sK2_SY20
                  @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
        & ( ( sK1_Xp
            @ ^ [Xx: a,Xy: a] : Xx )
          = ( sK2_SY20
            @ ^ [Xx: a,Xy: a] : Xx ) )
        & ( ( sK1_Xp
            @ ^ [Xx: a,Xy: a] : Xy )
          = ( sK2_SY20
            @ ^ [Xx: a,Xy: a] : Xy ) ) )
     => ( sK1_Xp = sK2_SY20 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( sK1_Xp
      = ( ^ [SY21: a > a > a] :
            ( SY21
            @ ( sK1_Xp
              @ ^ [Xx: a,Xy: a] : Xx )
            @ ( sK1_Xp
              @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(7,plain,
    ( ( sK2_SY20
      = ( ^ [SY44: a > a > a] :
            ( SY44
            @ ( sK2_SY20
              @ ^ [Xx: a,Xy: a] : Xx )
            @ ( sK2_SY20
              @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ( sK1_Xp
        @ ^ [Xx: a,Xy: a] : Xx )
      = ( sK2_SY20
        @ ^ [Xx: a,Xy: a] : Xx ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(9,plain,
    ( ( ( sK1_Xp
        @ ^ [Xx: a,Xy: a] : Xy )
      = ( sK2_SY20
        @ ^ [Xx: a,Xy: a] : Xy ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(10,plain,
    ( ( sK1_Xp = sK2_SY20 )
    = $false ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(11,plain,
    ( ( ( sK1_Xp != sK2_SY20 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ( sK1_Xp
        @ ^ [Xx: a,Xy: a] : Xy )
      = ( sK2_SY20
        @ ^ [Xx: a,Xy: a] : Xy ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(13,plain,
    ( ( ( sK1_Xp
        @ ^ [Xx: a,Xy: a] : Xx )
      = ( sK2_SY20
        @ ^ [Xx: a,Xy: a] : Xx ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(14,plain,
    ( ( sK2_SY20
      = ( ^ [SY44: a > a > a] :
            ( SY44
            @ ( sK2_SY20
              @ ^ [Xx: a,Xy: a] : Xx )
            @ ( sK2_SY20
              @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(15,plain,
    ( ( sK1_Xp
      = ( ^ [SY21: a > a > a] :
            ( SY21
            @ ( sK1_Xp
              @ ^ [Xx: a,Xy: a] : Xx )
            @ ( sK1_Xp
              @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(16,plain,
    ( ( ( sK1_Xp != sK2_SY20 ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(17,plain,
    ( ( ! [SV1: a > a > a] :
          ( ( sK2_SY20 @ SV1 )
          = ( SV1
            @ ( sK2_SY20
              @ ^ [Xx: a,Xy: a] : Xx )
            @ ( sK2_SY20
              @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[14]) ).

thf(18,plain,
    ( ( sK2_SY20
      = ( ^ [SY44: a > a > a] :
            ( SY44
            @ ( sK2_SY20
              @ ^ [Xx: a,Xy: a] : Xx )
            @ ( sK2_SY20
              @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[14]) ).

thf(19,plain,
    ( ( ! [SV2: a > a > a] :
          ( ( sK1_Xp @ SV2 )
          = ( SV2
            @ ( sK1_Xp
              @ ^ [Xx: a,Xy: a] : Xx )
            @ ( sK1_Xp
              @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[15]) ).

thf(20,plain,
    ( ( sK1_Xp
      = ( ^ [SY21: a > a > a] :
            ( SY21
            @ ( sK1_Xp
              @ ^ [Xx: a,Xy: a] : Xx )
            @ ( sK1_Xp
              @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[15]) ).

thf(21,plain,
    ( ( sK1_Xp = sK2_SY20 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(22,plain,
    ! [SV3: a > a > a] :
      ( ( ( sK2_SY20 @ SV3 )
        = ( SV3
          @ ( sK2_SY20
            @ ^ [Xx: a,Xy: a] : Xx )
          @ ( sK2_SY20
            @ ^ [Xx: a,Xy: a] : Xy ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(23,plain,
    ! [SV4: a > a > a] :
      ( ( ( sK1_Xp @ SV4 )
        = ( SV4
          @ ( sK1_Xp
            @ ^ [Xx: a,Xy: a] : Xx )
          @ ( sK1_Xp
            @ ^ [Xx: a,Xy: a] : Xy ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(24,plain,
    ( ( ! [SV5: a > a > a] :
          ( ( sK1_Xp @ SV5 )
          = ( sK2_SY20 @ SV5 ) ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[21]) ).

thf(25,plain,
    ( ( sK1_Xp = sK2_SY20 )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[21]) ).

thf(26,plain,
    ( ( ( sK1_Xp @ sK3_SV5 )
      = ( sK2_SY20 @ sK3_SV5 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[24]) ).

thf(27,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[12,26,25,23,22,20,18,13]) ).

thf(28,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEV169^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n008.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 20:03:53 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
% 0.13/0.35  (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)
% 0.19/0.38  ********************************
% 0.19/0.38  *   All subproblems solved!    *
% 0.19/0.38  ********************************
% 0.19/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.38  
% 0.19/0.38  %**** Beginning of derivation protocol ****
% 0.19/0.38  % SZS output start CNFRefutation
% See solution above
% 0.19/0.38  
% 0.19/0.38  %**** End of derivation protocol ****
% 0.19/0.38  %**** no. of clauses in derivation: 28 ****
% 0.19/0.38  %**** clause counter: 27 ****
% 0.19/0.38  
% 0.19/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------