TSTP Solution File: SET915+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SET915+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n024.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 03:06:12 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   55 (  37 unt;   8 typ;   0 def)
%            Number of atoms       :  168 (  46 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  217 (  33   ~;  18   |;   0   &; 155   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   59 (   0   ^  55   !;   4   ?;  59   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_disjoint,type,
    disjoint: $i > $i > $o ).

thf(tp_empty,type,
    empty: $i > $o ).

thf(tp_in,type,
    in: $i > $i > $o ).

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

thf(tp_sK2_SY10,type,
    sK2_SY10: $i ).

thf(tp_sK3_A,type,
    sK3_A: $i ).

thf(tp_sK4_A,type,
    sK4_A: $i ).

thf(tp_singleton,type,
    singleton: $i > $i ).

thf(1,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( in @ A @ B )
     => ( disjoint @ ( singleton @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).

thf(2,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(3,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( disjoint @ A @ B )
     => ( disjoint @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

thf(6,conjecture,
    ! [A: $i,B: $i] :
      ( ~ ( in @ A @ B )
     => ( disjoint @ ( singleton @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_zfmisc_1) ).

thf(7,negated_conjecture,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
         => ( disjoint @ ( singleton @ A ) @ B ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[6]) ).

thf(8,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
         => ( disjoint @ ( singleton @ A ) @ B ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
         => ( disjoint @ ( singleton @ A ) @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(10,plain,
    ( ( ? [A: $i] :
          ~ ( empty @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(11,plain,
    ( ( ? [A: $i] : ( empty @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(12,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ A @ B )
         => ~ ( in @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(13,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( disjoint @ A @ B )
         => ( disjoint @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(14,plain,
    ( ( ! [SY10: $i] :
          ( ~ ( in @ sK1_A @ SY10 )
         => ( disjoint @ ( singleton @ sK1_A ) @ SY10 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[8]) ).

thf(15,plain,
    ( ( ~ ( in @ sK1_A @ sK2_SY10 )
     => ( disjoint @ ( singleton @ sK1_A ) @ sK2_SY10 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[14]) ).

thf(16,plain,
    ( ( ~ ( in @ sK1_A @ sK2_SY10 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[15]) ).

thf(17,plain,
    ( ( disjoint @ ( singleton @ sK1_A ) @ sK2_SY10 )
    = $false ),
    inference(standard_cnf,[status(thm)],[15]) ).

thf(18,plain,
    ( ( ~ ( disjoint @ ( singleton @ sK1_A ) @ sK2_SY10 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[17]) ).

thf(19,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ A @ B )
          | ( disjoint @ ( singleton @ A ) @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(20,plain,
    ( ( ~ ( empty @ sK3_A ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(21,plain,
    ( ( empty @ sK4_A )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(22,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ~ ( in @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(23,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( disjoint @ A @ B )
          | ( disjoint @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(24,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( disjoint @ A @ B )
          | ( disjoint @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(25,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ~ ( in @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(26,plain,
    ( ( empty @ sK4_A )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(27,plain,
    ( ( ~ ( empty @ sK3_A ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(28,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ A @ B )
          | ( disjoint @ ( singleton @ A ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(29,plain,
    ( ( ~ ( in @ sK1_A @ sK2_SY10 ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(30,plain,
    ( ( ~ ( disjoint @ ( singleton @ sK1_A ) @ sK2_SY10 ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(31,plain,
    ! [SV1: $i] :
      ( ( ! [SY11: $i] :
            ( ~ ( disjoint @ SV1 @ SY11 )
            | ( disjoint @ SY11 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(32,plain,
    ! [SV2: $i] :
      ( ( ! [SY12: $i] :
            ( ~ ( in @ SV2 @ SY12 )
            | ~ ( in @ SY12 @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(33,plain,
    ( ( empty @ sK3_A )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(34,plain,
    ! [SV3: $i] :
      ( ( ! [SY13: $i] :
            ( ( in @ SV3 @ SY13 )
            | ( disjoint @ ( singleton @ SV3 ) @ SY13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(35,plain,
    ( ( in @ sK1_A @ sK2_SY10 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(36,plain,
    ( ( disjoint @ ( singleton @ sK1_A ) @ sK2_SY10 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(37,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ~ ( disjoint @ SV1 @ SV4 )
        | ( disjoint @ SV4 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(38,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ( in @ SV2 @ SV5 )
        | ~ ( in @ SV5 @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(39,plain,
    ! [SV6: $i,SV3: $i] :
      ( ( ( in @ SV3 @ SV6 )
        | ( disjoint @ ( singleton @ SV3 ) @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(40,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ~ ( disjoint @ SV1 @ SV4 ) )
        = $true )
      | ( ( disjoint @ SV4 @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(41,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ( ~ ( in @ SV2 @ SV5 ) )
        = $true )
      | ( ( ~ ( in @ SV5 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(42,plain,
    ! [SV6: $i,SV3: $i] :
      ( ( ( in @ SV3 @ SV6 )
        = $true )
      | ( ( disjoint @ ( singleton @ SV3 ) @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(43,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( disjoint @ SV1 @ SV4 )
        = $false )
      | ( ( disjoint @ SV4 @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(44,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ( in @ SV2 @ SV5 )
        = $false )
      | ( ( ~ ( in @ SV5 @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(45,plain,
    ! [SV2: $i,SV5: $i] :
      ( ( ( in @ SV5 @ SV2 )
        = $false )
      | ( ( in @ SV2 @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(46,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[26,45,43,42,36,35,33]) ).

thf(47,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[46]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET915+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n024.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 Jul  9 23:22:28 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 5
% 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:5,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:7,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:6,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:46,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
% 0.13/0.38  
% 0.13/0.38  %**** End of derivation protocol ****
% 0.13/0.38  %**** no. of clauses in derivation: 47 ****
% 0.13/0.38  %**** clause counter: 46 ****
% 0.13/0.38  
% 0.13/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:46,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------