TSTP Solution File: SEU936^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU936^5 : 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 12:15:49 EDT 2022

% Result   : Theorem 0.14s 0.38s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   32 (  22 unt;   7 typ;   0 def)
%            Number of atoms       :  103 (  76 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  121 (  19   ~;   8   |;   2   &;  74   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    3 (   3 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :   45 (   0   ^  45   !;   0   ?;  45   :)

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

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

thf(tp_c,type,
    c: $tType ).

thf(tp_sK1_F,type,
    sK1_F: a > b ).

thf(tp_sK2_SY6,type,
    sK2_SY6: b > c ).

thf(tp_sK3_SY9,type,
    sK3_SY9: a ).

thf(tp_sK4_SY15,type,
    sK4_SY15: a ).

thf(1,conjecture,
    ! [F: a > b,G: b > c] :
      ( ! [Xx: a,Xy: a] :
          ( ( ( G @ ( F @ Xx ) )
            = ( G @ ( F @ Xy ) ) )
         => ( Xx = Xy ) )
     => ! [Xx: a,Xy: a] :
          ( ( ( F @ Xx )
            = ( F @ Xy ) )
         => ( Xx = Xy ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cFN_THM_3_pme) ).

thf(2,negated_conjecture,
    ( ( ! [F: a > b,G: b > c] :
          ( ! [Xx: a,Xy: a] :
              ( ( ( G @ ( F @ Xx ) )
                = ( G @ ( F @ Xy ) ) )
             => ( Xx = Xy ) )
         => ! [Xx: a,Xy: a] :
              ( ( ( F @ Xx )
                = ( F @ Xy ) )
             => ( Xx = Xy ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [F: a > b,G: b > c] :
          ( ! [Xx: a,Xy: a] :
              ( ( ( G @ ( F @ Xx ) )
                = ( G @ ( F @ Xy ) ) )
             => ( Xx = Xy ) )
         => ! [Xx: a,Xy: a] :
              ( ( ( F @ Xx )
                = ( F @ Xy ) )
             => ( Xx = Xy ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY6: b > c] :
          ( ! [SY7: a,SY8: a] :
              ( ( ( SY6 @ ( sK1_F @ SY7 ) )
                = ( SY6 @ ( sK1_F @ SY8 ) ) )
             => ( SY7 = SY8 ) )
         => ! [SY9: a,SY10: a] :
              ( ( ( sK1_F @ SY9 )
                = ( sK1_F @ SY10 ) )
             => ( SY9 = SY10 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY11: a,SY12: a] :
          ( ( ( sK2_SY6 @ ( sK1_F @ SY11 ) )
            = ( sK2_SY6 @ ( sK1_F @ SY12 ) ) )
         => ( SY11 = SY12 ) )
     => ! [SY9: a,SY10: a] :
          ( ( ( sK1_F @ SY9 )
            = ( sK1_F @ SY10 ) )
         => ( SY9 = SY10 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [SY11: a,SY12: a] :
          ( ( ( sK2_SY6 @ ( sK1_F @ SY11 ) )
            = ( sK2_SY6 @ ( sK1_F @ SY12 ) ) )
         => ( SY11 = SY12 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SY9: a,SY10: a] :
          ( ( ( sK1_F @ SY9 )
            = ( sK1_F @ SY10 ) )
         => ( SY9 = SY10 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ~ ! [SY9: a,SY10: a] :
            ( ( ( sK1_F @ SY9 )
              = ( sK1_F @ SY10 ) )
           => ( SY9 = SY10 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ( ( sK1_F @ sK3_SY9 )
        = ( sK1_F @ sK4_SY15 ) )
      & ( sK3_SY9 != sK4_SY15 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    ( ( ! [SY11: a,SY12: a] :
          ( ( ( sK2_SY6 @ ( sK1_F @ SY11 ) )
           != ( sK2_SY6 @ ( sK1_F @ SY12 ) ) )
          | ( SY11 = SY12 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(11,plain,
    ( ( ! [SY11: a,SY12: a] :
          ( ( ( sK2_SY6 @ ( sK1_F @ SY11 ) )
           != ( sK2_SY6 @ ( sK1_F @ SY12 ) ) )
          | ( SY11 = SY12 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ( ( sK1_F @ sK3_SY9 )
        = ( sK1_F @ sK4_SY15 ) )
      & ( sK3_SY9 != sK4_SY15 ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(13,plain,
    ( ( ~ ( ( ( sK1_F @ sK3_SY9 )
           != ( sK1_F @ sK4_SY15 ) )
          | ~ ( ( sK3_SY9 != sK4_SY15 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(14,plain,
    ! [SV1: a] :
      ( ( ! [SY16: a] :
            ( ( ( sK2_SY6 @ ( sK1_F @ SV1 ) )
             != ( sK2_SY6 @ ( sK1_F @ SY16 ) ) )
            | ( SV1 = SY16 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(15,plain,
    ( ( ( ( sK1_F @ sK3_SY9 )
       != ( sK1_F @ sK4_SY15 ) )
      | ~ ( ( sK3_SY9 != sK4_SY15 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(16,plain,
    ! [SV2: a,SV1: a] :
      ( ( ( ( sK2_SY6 @ ( sK1_F @ SV1 ) )
         != ( sK2_SY6 @ ( sK1_F @ SV2 ) ) )
        | ( SV1 = SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ( ( sK1_F @ sK3_SY9 )
       != ( sK1_F @ sK4_SY15 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(18,plain,
    ( ( ~ ( ( sK3_SY9 != sK4_SY15 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV2: a,SV1: a] :
      ( ( ( ( ( sK2_SY6 @ ( sK1_F @ SV1 ) )
           != ( sK2_SY6 @ ( sK1_F @ SV2 ) ) ) )
        = $true )
      | ( ( SV1 = SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ( sK1_F @ sK3_SY9 )
      = ( sK1_F @ sK4_SY15 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ( sK3_SY9 != sK4_SY15 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV2: a,SV1: a] :
      ( ( ( ( sK2_SY6 @ ( sK1_F @ SV1 ) )
          = ( sK2_SY6 @ ( sK1_F @ SV2 ) ) )
        = $false )
      | ( ( SV1 = SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(23,plain,
    ( ( sK3_SY9 = sK4_SY15 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(24,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[20,23,22]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU936^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n018.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sun Jun 19 05:58:19 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  
% 0.14/0.35   No.of.Axioms: 0
% 0.14/0.35  
% 0.14/0.35   Length.of.Defs: 0
% 0.14/0.35  
% 0.14/0.35   Contains.Choice.Funs: false
% 0.14/0.35  (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).
% 0.14/0.38  
% 0.14/0.38  ********************************
% 0.14/0.38  *   All subproblems solved!    *
% 0.14/0.38  ********************************
% 0.14/0.38  % 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)
% 0.14/0.38  
% 0.14/0.38  %**** Beginning of derivation protocol ****
% 0.14/0.38  % SZS output start CNFRefutation
% See solution above
% 0.14/0.38  
% 0.14/0.38  %**** End of derivation protocol ****
% 0.14/0.38  %**** no. of clauses in derivation: 25 ****
% 0.14/0.38  %**** clause counter: 24 ****
% 0.14/0.38  
% 0.14/0.38  % 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)
%------------------------------------------------------------------------------