TSTP Solution File: SEU303+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU303+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n019.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 12:09:51 EDT 2022

% Result   : Theorem 0.21s 0.39s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   74 (  47 unt;   8 typ;   0 def)
%            Number of atoms       :  337 (  94 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  391 (  59   ~;  67   |;  14   &; 235   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   60 (   0   ^  58   !;   2   ?;  60   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_finite,type,
    finite: $i > $o ).

thf(tp_function,type,
    function: $i > $o ).

thf(tp_relation,type,
    relation: $i > $o ).

thf(tp_relation_dom,type,
    relation_dom: $i > $i ).

thf(tp_relation_image,type,
    relation_image: $i > $i > $i ).

thf(tp_relation_rng,type,
    relation_rng: $i > $i ).

thf(tp_sK1_A,type,
    sK1_A: $i ).

thf(tp_sK2_A,type,
    sK2_A: $i ).

thf(1,axiom,
    ! [A: $i,B: $i] :
      ( ( ( relation @ B )
        & ( function @ B ) )
     => ( ( finite @ A )
       => ( finite @ ( relation_image @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).

thf(2,axiom,
    ! [A: $i] :
      ( ( relation @ A )
     => ( ( relation_image @ A @ ( relation_dom @ A ) )
        = ( relation_rng @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).

thf(3,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( function @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( ( relation @ A )
        & ( function @ A )
        & ( finite @ B ) )
     => ( finite @ ( relation_image @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).

thf(5,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relat_1) ).

thf(6,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).

thf(7,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).

thf(8,conjecture,
    ! [A: $i] :
      ( ( ( relation @ A )
        & ( function @ A ) )
     => ( ( finite @ ( relation_dom @ A ) )
       => ( finite @ ( relation_rng @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).

thf(9,negated_conjecture,
    ( ( ! [A: $i] :
          ( ( ( relation @ A )
            & ( function @ A ) )
         => ( ( finite @ ( relation_dom @ A ) )
           => ( finite @ ( relation_rng @ A ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[8]) ).

thf(10,plain,
    ( ( ! [A: $i] :
          ( ( ( relation @ A )
            & ( function @ A ) )
         => ( ( finite @ ( relation_dom @ A ) )
           => ( finite @ ( relation_rng @ A ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( relation @ B )
            & ( function @ B ) )
         => ( ( finite @ A )
           => ( finite @ ( relation_image @ B @ A ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(12,plain,
    ( ( ! [A: $i] :
          ( ( relation @ A )
         => ( ( relation_image @ A @ ( relation_dom @ A ) )
            = ( relation_rng @ A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(13,plain,
    ( ( ? [A: $i] :
          ( ( relation @ A )
          & ( function @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(14,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( relation @ A )
            & ( function @ A )
            & ( finite @ B ) )
         => ( finite @ ( relation_image @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(15,plain,
    $true = $true,
    inference(unfold_def,[status(thm)],[5]) ).

thf(16,plain,
    $true = $true,
    inference(unfold_def,[status(thm)],[6]) ).

thf(17,plain,
    $true = $true,
    inference(unfold_def,[status(thm)],[7]) ).

thf(18,plain,
    ( ( ( ( relation @ sK1_A )
        & ( function @ sK1_A ) )
     => ( ( finite @ ( relation_dom @ sK1_A ) )
       => ( finite @ ( relation_rng @ sK1_A ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[10]) ).

thf(19,plain,
    ( ( relation @ sK1_A )
    = $true ),
    inference(standard_cnf,[status(thm)],[18]) ).

thf(20,plain,
    ( ( function @ sK1_A )
    = $true ),
    inference(standard_cnf,[status(thm)],[18]) ).

thf(21,plain,
    ( ( finite @ ( relation_dom @ sK1_A ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[18]) ).

thf(22,plain,
    ( ( finite @ ( relation_rng @ sK1_A ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[18]) ).

thf(23,plain,
    ( ( ~ ( finite @ ( relation_rng @ sK1_A ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[22]) ).

thf(24,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( function @ B )
          | ~ ( relation @ B )
          | ~ ( finite @ A )
          | ( finite @ ( relation_image @ B @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(25,plain,
    ( ( ! [A: $i] :
          ( ~ ( relation @ A )
          | ( ( relation_image @ A @ ( relation_dom @ A ) )
            = ( relation_rng @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(26,plain,
    ( ( ( function @ sK2_A )
      & ( relation @ sK2_A ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(27,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( function @ A )
          | ~ ( relation @ A )
          | ~ ( finite @ B )
          | ( finite @ ( relation_image @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[14]) ).

thf(28,plain,
    $true = $true,
    inference(copy,[status(thm)],[17]) ).

thf(29,plain,
    $true = $true,
    inference(copy,[status(thm)],[16]) ).

thf(30,plain,
    $true = $true,
    inference(copy,[status(thm)],[15]) ).

thf(31,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( function @ A )
          | ~ ( relation @ A )
          | ~ ( finite @ B )
          | ( finite @ ( relation_image @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(32,plain,
    ( ( ( function @ sK2_A )
      & ( relation @ sK2_A ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(33,plain,
    ( ( ! [A: $i] :
          ( ~ ( relation @ A )
          | ( ( relation_image @ A @ ( relation_dom @ A ) )
            = ( relation_rng @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(34,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( function @ B )
          | ~ ( relation @ B )
          | ~ ( finite @ A )
          | ( finite @ ( relation_image @ B @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(35,plain,
    ( ( finite @ ( relation_dom @ sK1_A ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(36,plain,
    ( ( function @ sK1_A )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(37,plain,
    ( ( relation @ sK1_A )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(38,plain,
    ( ( ~ ( finite @ ( relation_rng @ sK1_A ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(39,plain,
    ( ( ~ ( ~ ( function @ sK2_A )
          | ~ ( relation @ sK2_A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(40,plain,
    ! [SV1: $i] :
      ( ( ! [SY7: $i] :
            ( ~ ( function @ SV1 )
            | ~ ( relation @ SV1 )
            | ~ ( finite @ SY7 )
            | ( finite @ ( relation_image @ SV1 @ SY7 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(41,plain,
    ! [SV2: $i] :
      ( ( ~ ( relation @ SV2 )
        | ( ( relation_image @ SV2 @ ( relation_dom @ SV2 ) )
          = ( relation_rng @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(42,plain,
    ! [SV3: $i] :
      ( ( ! [SY8: $i] :
            ( ~ ( function @ SY8 )
            | ~ ( relation @ SY8 )
            | ~ ( finite @ SV3 )
            | ( finite @ ( relation_image @ SY8 @ SV3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(43,plain,
    ( ( finite @ ( relation_rng @ sK1_A ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(44,plain,
    ( ( ~ ( function @ sK2_A )
      | ~ ( relation @ sK2_A ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(45,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ~ ( function @ SV1 )
        | ~ ( relation @ SV1 )
        | ~ ( finite @ SV4 )
        | ( finite @ ( relation_image @ SV1 @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(46,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( relation @ SV2 ) )
        = $true )
      | ( ( ( relation_image @ SV2 @ ( relation_dom @ SV2 ) )
          = ( relation_rng @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[41]) ).

thf(47,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ~ ( function @ SV5 )
        | ~ ( relation @ SV5 )
        | ~ ( finite @ SV3 )
        | ( finite @ ( relation_image @ SV5 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(48,plain,
    ( ( ~ ( function @ sK2_A ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[44]) ).

thf(49,plain,
    ( ( ~ ( relation @ sK2_A ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[44]) ).

thf(50,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ~ ( function @ SV1 )
          | ~ ( relation @ SV1 )
          | ~ ( finite @ SV4 ) )
        = $true )
      | ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV2: $i] :
      ( ( ( relation @ SV2 )
        = $false )
      | ( ( ( relation_image @ SV2 @ ( relation_dom @ SV2 ) )
          = ( relation_rng @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( ~ ( function @ SV5 )
          | ~ ( relation @ SV5 ) )
        = $true )
      | ( ( ~ ( finite @ SV3 )
          | ( finite @ ( relation_image @ SV5 @ SV3 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[47]) ).

thf(53,plain,
    ( ( function @ sK2_A )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[48]) ).

thf(54,plain,
    ( ( relation @ sK2_A )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[49]) ).

thf(55,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ~ ( function @ SV1 )
          | ~ ( relation @ SV1 ) )
        = $true )
      | ( ( ~ ( finite @ SV4 ) )
        = $true )
      | ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[50]) ).

thf(56,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( ~ ( function @ SV5 ) )
        = $true )
      | ( ( ~ ( relation @ SV5 ) )
        = $true )
      | ( ( ~ ( finite @ SV3 )
          | ( finite @ ( relation_image @ SV5 @ SV3 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(57,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ~ ( function @ SV1 ) )
        = $true )
      | ( ( ~ ( relation @ SV1 ) )
        = $true )
      | ( ( ~ ( finite @ SV4 ) )
        = $true )
      | ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[55]) ).

thf(58,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( function @ SV5 )
        = $false )
      | ( ( ~ ( relation @ SV5 ) )
        = $true )
      | ( ( ~ ( finite @ SV3 )
          | ( finite @ ( relation_image @ SV5 @ SV3 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(59,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( function @ SV1 )
        = $false )
      | ( ( ~ ( relation @ SV1 ) )
        = $true )
      | ( ( ~ ( finite @ SV4 ) )
        = $true )
      | ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(60,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( relation @ SV5 )
        = $false )
      | ( ( function @ SV5 )
        = $false )
      | ( ( ~ ( finite @ SV3 )
          | ( finite @ ( relation_image @ SV5 @ SV3 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[58]) ).

thf(61,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( relation @ SV1 )
        = $false )
      | ( ( function @ SV1 )
        = $false )
      | ( ( ~ ( finite @ SV4 ) )
        = $true )
      | ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(62,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ( ~ ( finite @ SV3 ) )
        = $true )
      | ( ( finite @ ( relation_image @ SV5 @ SV3 ) )
        = $true )
      | ( ( function @ SV5 )
        = $false )
      | ( ( relation @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[60]) ).

thf(63,plain,
    ! [SV1: $i,SV4: $i] :
      ( ( ( finite @ SV4 )
        = $false )
      | ( ( function @ SV1 )
        = $false )
      | ( ( relation @ SV1 )
        = $false )
      | ( ( finite @ ( relation_image @ SV1 @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(64,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ( finite @ SV3 )
        = $false )
      | ( ( finite @ ( relation_image @ SV5 @ SV3 ) )
        = $true )
      | ( ( function @ SV5 )
        = $false )
      | ( ( relation @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(65,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[28,64,63,54,53,51,43,37,36,35,30,29]) ).

thf(66,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[65]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU303+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n019.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 : Sat Jun 18 19:26:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 7
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (rf:0,axioms:7,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:9,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.21/0.39  
% 0.21/0.39  ********************************
% 0.21/0.39  *   All subproblems solved!    *
% 0.21/0.39  ********************************
% 0.21/0.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:65,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.39  
% 0.21/0.39  %**** Beginning of derivation protocol ****
% 0.21/0.39  % SZS output start CNFRefutation
% See solution above
% 0.21/0.39  
% 0.21/0.39  %**** End of derivation protocol ****
% 0.21/0.39  %**** no. of clauses in derivation: 66 ****
% 0.21/0.39  %**** clause counter: 65 ****
% 0.21/0.39  
% 0.21/0.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:65,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------