TSTP Solution File: SET015-4 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SET015-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n011.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 02:57:54 EDT 2022

% Result   : Unsatisfiable 0.91s 1.17s
% Output   : CNFRefutation 0.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  122 (  73 unt;  12 typ;   0 def)
%            Number of atoms       :  482 ( 168 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  730 (  88   ~; 116   |;   0   &; 526   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :  198 (   0   ^ 198   !;   0   ?; 198   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_as,type,
    as: $i ).

thf(tp_bs,type,
    bs: $i ).

thf(tp_complement,type,
    complement: $i > $i ).

thf(tp_cs,type,
    cs: $i ).

thf(tp_ds,type,
    ds: $i ).

thf(tp_empty_set,type,
    empty_set: $i ).

thf(tp_f1,type,
    f1: $i > $i > $i ).

thf(tp_intersection,type,
    intersection: $i > $i > $i ).

thf(tp_little_set,type,
    little_set: $i > $o ).

thf(tp_member,type,
    member: $i > $i > $o ).

thf(tp_union,type,
    union: $i > $i > $i ).

thf(tp_universal_set,type,
    universal_set: $i ).

thf(1,axiom,
    ! [Z: $i] :
      ( ( member @ Z @ universal_set )
      | ~ ( little_set @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',universal_set) ).

thf(2,axiom,
    ! [Z: $i] :
      ~ ( member @ Z @ empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).

thf(3,axiom,
    ! [X: $i,Y: $i] :
      ( ( union @ X @ Y )
      = ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).

thf(4,axiom,
    ! [Z: $i,X: $i] :
      ( ( member @ Z @ ( complement @ X ) )
      | ~ ( little_set @ Z )
      | ( member @ Z @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).

thf(5,axiom,
    ! [Z: $i,X: $i] :
      ( ~ ( member @ Z @ ( complement @ X ) )
      | ~ ( member @ Z @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).

thf(6,axiom,
    ! [Z: $i,X: $i,Y: $i] :
      ( ( member @ Z @ ( intersection @ X @ Y ) )
      | ~ ( member @ Z @ X )
      | ~ ( member @ Z @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).

thf(7,axiom,
    ! [Z: $i,X: $i,Y: $i] :
      ( ~ ( member @ Z @ ( intersection @ X @ Y ) )
      | ( member @ Z @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).

thf(8,axiom,
    ! [Z: $i,X: $i,Y: $i] :
      ( ~ ( member @ Z @ ( intersection @ X @ Y ) )
      | ( member @ Z @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).

thf(9,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( member @ ( f1 @ X @ Y ) @ X )
      | ~ ( member @ ( f1 @ X @ Y ) @ Y )
      | ( X = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).

thf(10,axiom,
    ! [X: $i,Y: $i] :
      ( ( member @ ( f1 @ X @ Y ) @ X )
      | ( member @ ( f1 @ X @ Y ) @ Y )
      | ( X = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).

thf(11,axiom,
    ! [X: $i,Y: $i] :
      ( ( little_set @ ( f1 @ X @ Y ) )
      | ( X = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).

thf(12,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( member @ X @ Y )
      | ( little_set @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).

thf(13,axiom,
    ( ( union @ bs @ as )
    = ds ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_union_a_is_d) ).

thf(14,axiom,
    ( ( union @ as @ bs )
    = cs ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_union_b_is_c) ).

thf(15,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(16,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[15]) ).

thf(17,negated_conjecture,
    cs != ds,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).

thf(18,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ! [Z: $i] :
          ( ( member @ Z @ universal_set )
          | ~ ( little_set @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(20,plain,
    ( ( ! [Z: $i] :
          ~ ( member @ Z @ empty_set ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(21,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( union @ X @ Y )
          = ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(22,plain,
    ( ( ! [Z: $i,X: $i] :
          ( ( member @ Z @ ( complement @ X ) )
          | ~ ( little_set @ Z )
          | ( member @ Z @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(23,plain,
    ( ( ! [Z: $i,X: $i] :
          ( ~ ( member @ Z @ ( complement @ X ) )
          | ~ ( member @ Z @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(24,plain,
    ( ( ! [Z: $i,X: $i,Y: $i] :
          ( ( member @ Z @ ( intersection @ X @ Y ) )
          | ~ ( member @ Z @ X )
          | ~ ( member @ Z @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(25,plain,
    ( ( ! [Z: $i,X: $i,Y: $i] :
          ( ~ ( member @ Z @ ( intersection @ X @ Y ) )
          | ( member @ Z @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(26,plain,
    ( ( ! [Z: $i,X: $i,Y: $i] :
          ( ~ ( member @ Z @ ( intersection @ X @ Y ) )
          | ( member @ Z @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(27,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( member @ ( f1 @ X @ Y ) @ X )
          | ~ ( member @ ( f1 @ X @ Y ) @ Y )
          | ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(28,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( member @ ( f1 @ X @ Y ) @ X )
          | ( member @ ( f1 @ X @ Y ) @ Y )
          | ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(29,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( little_set @ ( f1 @ X @ Y ) )
          | ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(30,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( member @ X @ Y )
          | ( little_set @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(31,plain,
    ( ( ( union @ bs @ as )
      = ds )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(32,plain,
    ( ( ( union @ as @ bs )
      = cs )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(33,plain,
    ( ( ( cs != ds ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(34,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[18]) ).

thf(35,plain,
    ( ( ! [Z: $i,X: $i] :
          ( ! [Y: $i] :
              ~ ( member @ Z @ ( intersection @ X @ Y ) )
          | ( member @ Z @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[26]) ).

thf(36,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( member @ ( f1 @ X @ Y ) @ X )
          | ( X = Y )
          | ( member @ ( f1 @ X @ Y ) @ Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[28]) ).

thf(37,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X = Y )
          | ( little_set @ ( f1 @ X @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[29]) ).

thf(38,plain,
    ( ( ! [X: $i] :
          ( ! [Y: $i] :
              ~ ( member @ X @ Y )
          | ( little_set @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[30]) ).

thf(39,plain,
    ( ( ( cs != ds ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[33]) ).

thf(40,plain,
    ( ( ( cs != ds ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(41,plain,
    ( ( ( union @ as @ bs )
      = cs )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(42,plain,
    ( ( ( union @ bs @ as )
      = ds )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(43,plain,
    ( ( ! [X: $i] :
          ( ! [Y: $i] :
              ~ ( member @ X @ Y )
          | ( little_set @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(44,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X = Y )
          | ( little_set @ ( f1 @ X @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(45,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( member @ ( f1 @ X @ Y ) @ X )
          | ( X = Y )
          | ( member @ ( f1 @ X @ Y ) @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(46,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( member @ ( f1 @ X @ Y ) @ X )
          | ~ ( member @ ( f1 @ X @ Y ) @ Y )
          | ( X = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(47,plain,
    ( ( ! [Z: $i,X: $i] :
          ( ! [Y: $i] :
              ~ ( member @ Z @ ( intersection @ X @ Y ) )
          | ( member @ Z @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(48,plain,
    ( ( ! [Z: $i,X: $i,Y: $i] :
          ( ~ ( member @ Z @ ( intersection @ X @ Y ) )
          | ( member @ Z @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(49,plain,
    ( ( ! [Z: $i,X: $i,Y: $i] :
          ( ( member @ Z @ ( intersection @ X @ Y ) )
          | ~ ( member @ Z @ X )
          | ~ ( member @ Z @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(50,plain,
    ( ( ! [Z: $i,X: $i] :
          ( ~ ( member @ Z @ ( complement @ X ) )
          | ~ ( member @ Z @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(51,plain,
    ( ( ! [Z: $i,X: $i] :
          ( ( member @ Z @ ( complement @ X ) )
          | ~ ( little_set @ Z )
          | ( member @ Z @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(52,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( union @ X @ Y )
          = ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(53,plain,
    ( ( ! [Z: $i] :
          ~ ( member @ Z @ empty_set ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(54,plain,
    ( ( ! [Z: $i] :
          ( ( member @ Z @ universal_set )
          | ~ ( little_set @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(55,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(56,plain,
    ( ( cs = ds )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(57,plain,
    ! [SV1: $i] :
      ( ( ! [SY25: $i] :
            ~ ( member @ SV1 @ SY25 )
        | ( little_set @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(58,plain,
    ! [SV2: $i] :
      ( ( ! [SY26: $i] :
            ( ( SV2 = SY26 )
            | ( little_set @ ( f1 @ SV2 @ SY26 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(59,plain,
    ! [SV3: $i] :
      ( ( ! [SY27: $i] :
            ( ( member @ ( f1 @ SV3 @ SY27 ) @ SV3 )
            | ( SV3 = SY27 )
            | ( member @ ( f1 @ SV3 @ SY27 ) @ SY27 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(60,plain,
    ! [SV4: $i] :
      ( ( ! [SY28: $i] :
            ( ~ ( member @ ( f1 @ SV4 @ SY28 ) @ SV4 )
            | ~ ( member @ ( f1 @ SV4 @ SY28 ) @ SY28 )
            | ( SV4 = SY28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(61,plain,
    ! [SV5: $i] :
      ( ( ! [SY29: $i] :
            ( ! [SY30: $i] :
                ~ ( member @ SV5 @ ( intersection @ SY29 @ SY30 ) )
            | ( member @ SV5 @ SY29 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(62,plain,
    ! [SV6: $i] :
      ( ( ! [SY31: $i,SY32: $i] :
            ( ~ ( member @ SV6 @ ( intersection @ SY31 @ SY32 ) )
            | ( member @ SV6 @ SY32 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(63,plain,
    ! [SV7: $i] :
      ( ( ! [SY33: $i,SY34: $i] :
            ( ( member @ SV7 @ ( intersection @ SY33 @ SY34 ) )
            | ~ ( member @ SV7 @ SY33 )
            | ~ ( member @ SV7 @ SY34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(64,plain,
    ! [SV8: $i] :
      ( ( ! [SY35: $i] :
            ( ~ ( member @ SV8 @ ( complement @ SY35 ) )
            | ~ ( member @ SV8 @ SY35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(65,plain,
    ! [SV9: $i] :
      ( ( ! [SY36: $i] :
            ( ( member @ SV9 @ ( complement @ SY36 ) )
            | ~ ( little_set @ SV9 )
            | ( member @ SV9 @ SY36 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(66,plain,
    ! [SV10: $i] :
      ( ( ! [SY37: $i] :
            ( ( union @ SV10 @ SY37 )
            = ( complement @ ( intersection @ ( complement @ SV10 ) @ ( complement @ SY37 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(67,plain,
    ! [SV11: $i] :
      ( ( ~ ( member @ SV11 @ empty_set ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(68,plain,
    ! [SV12: $i] :
      ( ( ( member @ SV12 @ universal_set )
        | ~ ( little_set @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(69,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(70,plain,
    ! [SV1: $i] :
      ( ( ( ! [SY25: $i] :
              ~ ( member @ SV1 @ SY25 ) )
        = $true )
      | ( ( little_set @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[57]) ).

thf(71,plain,
    ! [SV13: $i,SV2: $i] :
      ( ( ( SV2 = SV13 )
        | ( little_set @ ( f1 @ SV2 @ SV13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(72,plain,
    ! [SV14: $i,SV3: $i] :
      ( ( ( member @ ( f1 @ SV3 @ SV14 ) @ SV3 )
        | ( SV3 = SV14 )
        | ( member @ ( f1 @ SV3 @ SV14 ) @ SV14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(73,plain,
    ! [SV15: $i,SV4: $i] :
      ( ( ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV4 )
        | ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV15 )
        | ( SV4 = SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(74,plain,
    ! [SV16: $i,SV5: $i] :
      ( ( ! [SY38: $i] :
            ~ ( member @ SV5 @ ( intersection @ SV16 @ SY38 ) )
        | ( member @ SV5 @ SV16 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(75,plain,
    ! [SV17: $i,SV6: $i] :
      ( ( ! [SY39: $i] :
            ( ~ ( member @ SV6 @ ( intersection @ SV17 @ SY39 ) )
            | ( member @ SV6 @ SY39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(76,plain,
    ! [SV18: $i,SV7: $i] :
      ( ( ! [SY40: $i] :
            ( ( member @ SV7 @ ( intersection @ SV18 @ SY40 ) )
            | ~ ( member @ SV7 @ SV18 )
            | ~ ( member @ SV7 @ SY40 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(77,plain,
    ! [SV19: $i,SV8: $i] :
      ( ( ~ ( member @ SV8 @ ( complement @ SV19 ) )
        | ~ ( member @ SV8 @ SV19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(78,plain,
    ! [SV20: $i,SV9: $i] :
      ( ( ( member @ SV9 @ ( complement @ SV20 ) )
        | ~ ( little_set @ SV9 )
        | ( member @ SV9 @ SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(79,plain,
    ! [SV21: $i,SV10: $i] :
      ( ( ( union @ SV10 @ SV21 )
        = ( complement @ ( intersection @ ( complement @ SV10 ) @ ( complement @ SV21 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(80,plain,
    ! [SV11: $i] :
      ( ( member @ SV11 @ empty_set )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(81,plain,
    ! [SV12: $i] :
      ( ( ( member @ SV12 @ universal_set )
        = $true )
      | ( ( ~ ( little_set @ SV12 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[68]) ).

thf(82,plain,
    ! [SV22: $i,SV1: $i] :
      ( ( ( ~ ( member @ SV1 @ SV22 ) )
        = $true )
      | ( ( little_set @ SV1 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(83,plain,
    ! [SV13: $i,SV2: $i] :
      ( ( ( SV2 = SV13 )
        = $true )
      | ( ( little_set @ ( f1 @ SV2 @ SV13 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[71]) ).

thf(84,plain,
    ! [SV14: $i,SV3: $i] :
      ( ( ( member @ ( f1 @ SV3 @ SV14 ) @ SV3 )
        = $true )
      | ( ( ( SV3 = SV14 )
          | ( member @ ( f1 @ SV3 @ SV14 ) @ SV14 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[72]) ).

thf(85,plain,
    ! [SV15: $i,SV4: $i] :
      ( ( ( ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV4 ) )
        = $true )
      | ( ( ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV15 )
          | ( SV4 = SV15 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[73]) ).

thf(86,plain,
    ! [SV16: $i,SV5: $i] :
      ( ( ( ! [SY38: $i] :
              ~ ( member @ SV5 @ ( intersection @ SV16 @ SY38 ) ) )
        = $true )
      | ( ( member @ SV5 @ SV16 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[74]) ).

thf(87,plain,
    ! [SV23: $i,SV17: $i,SV6: $i] :
      ( ( ~ ( member @ SV6 @ ( intersection @ SV17 @ SV23 ) )
        | ( member @ SV6 @ SV23 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(88,plain,
    ! [SV24: $i,SV18: $i,SV7: $i] :
      ( ( ( member @ SV7 @ ( intersection @ SV18 @ SV24 ) )
        | ~ ( member @ SV7 @ SV18 )
        | ~ ( member @ SV7 @ SV24 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(89,plain,
    ! [SV19: $i,SV8: $i] :
      ( ( ( ~ ( member @ SV8 @ ( complement @ SV19 ) ) )
        = $true )
      | ( ( ~ ( member @ SV8 @ SV19 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[77]) ).

thf(90,plain,
    ! [SV20: $i,SV9: $i] :
      ( ( ( member @ SV9 @ ( complement @ SV20 ) )
        = $true )
      | ( ( ~ ( little_set @ SV9 )
          | ( member @ SV9 @ SV20 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[78]) ).

thf(91,plain,
    ! [SV12: $i] :
      ( ( ( little_set @ SV12 )
        = $false )
      | ( ( member @ SV12 @ universal_set )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[81]) ).

thf(92,plain,
    ! [SV22: $i,SV1: $i] :
      ( ( ( member @ SV1 @ SV22 )
        = $false )
      | ( ( little_set @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[82]) ).

thf(93,plain,
    ! [SV14: $i,SV3: $i] :
      ( ( ( SV3 = SV14 )
        = $true )
      | ( ( member @ ( f1 @ SV3 @ SV14 ) @ SV14 )
        = $true )
      | ( ( member @ ( f1 @ SV3 @ SV14 ) @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[84]) ).

thf(94,plain,
    ! [SV15: $i,SV4: $i] :
      ( ( ( member @ ( f1 @ SV4 @ SV15 ) @ SV4 )
        = $false )
      | ( ( ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV15 )
          | ( SV4 = SV15 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(95,plain,
    ! [SV25: $i,SV16: $i,SV5: $i] :
      ( ( ( ~ ( member @ SV5 @ ( intersection @ SV16 @ SV25 ) ) )
        = $true )
      | ( ( member @ SV5 @ SV16 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(96,plain,
    ! [SV23: $i,SV17: $i,SV6: $i] :
      ( ( ( ~ ( member @ SV6 @ ( intersection @ SV17 @ SV23 ) ) )
        = $true )
      | ( ( member @ SV6 @ SV23 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[87]) ).

thf(97,plain,
    ! [SV24: $i,SV18: $i,SV7: $i] :
      ( ( ( member @ SV7 @ ( intersection @ SV18 @ SV24 ) )
        = $true )
      | ( ( ~ ( member @ SV7 @ SV18 )
          | ~ ( member @ SV7 @ SV24 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(98,plain,
    ! [SV19: $i,SV8: $i] :
      ( ( ( member @ SV8 @ ( complement @ SV19 ) )
        = $false )
      | ( ( ~ ( member @ SV8 @ SV19 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[89]) ).

thf(99,plain,
    ! [SV20: $i,SV9: $i] :
      ( ( ( ~ ( little_set @ SV9 ) )
        = $true )
      | ( ( member @ SV9 @ SV20 )
        = $true )
      | ( ( member @ SV9 @ ( complement @ SV20 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[90]) ).

thf(100,plain,
    ! [SV15: $i,SV4: $i] :
      ( ( ( ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV15 ) )
        = $true )
      | ( ( SV4 = SV15 )
        = $true )
      | ( ( member @ ( f1 @ SV4 @ SV15 ) @ SV4 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[94]) ).

thf(101,plain,
    ! [SV25: $i,SV16: $i,SV5: $i] :
      ( ( ( member @ SV5 @ ( intersection @ SV16 @ SV25 ) )
        = $false )
      | ( ( member @ SV5 @ SV16 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[95]) ).

thf(102,plain,
    ! [SV23: $i,SV17: $i,SV6: $i] :
      ( ( ( member @ SV6 @ ( intersection @ SV17 @ SV23 ) )
        = $false )
      | ( ( member @ SV6 @ SV23 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(103,plain,
    ! [SV24: $i,SV18: $i,SV7: $i] :
      ( ( ( ~ ( member @ SV7 @ SV18 ) )
        = $true )
      | ( ( ~ ( member @ SV7 @ SV24 ) )
        = $true )
      | ( ( member @ SV7 @ ( intersection @ SV18 @ SV24 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[97]) ).

thf(104,plain,
    ! [SV19: $i,SV8: $i] :
      ( ( ( member @ SV8 @ SV19 )
        = $false )
      | ( ( member @ SV8 @ ( complement @ SV19 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[98]) ).

thf(105,plain,
    ! [SV20: $i,SV9: $i] :
      ( ( ( little_set @ SV9 )
        = $false )
      | ( ( member @ SV9 @ SV20 )
        = $true )
      | ( ( member @ SV9 @ ( complement @ SV20 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(106,plain,
    ! [SV15: $i,SV4: $i] :
      ( ( ( member @ ( f1 @ SV4 @ SV15 ) @ SV15 )
        = $false )
      | ( ( SV4 = SV15 )
        = $true )
      | ( ( member @ ( f1 @ SV4 @ SV15 ) @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(107,plain,
    ! [SV24: $i,SV18: $i,SV7: $i] :
      ( ( ( member @ SV7 @ SV18 )
        = $false )
      | ( ( ~ ( member @ SV7 @ SV24 ) )
        = $true )
      | ( ( member @ SV7 @ ( intersection @ SV18 @ SV24 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[103]) ).

thf(108,plain,
    ! [SV18: $i,SV24: $i,SV7: $i] :
      ( ( ( member @ SV7 @ SV24 )
        = $false )
      | ( ( member @ SV7 @ SV18 )
        = $false )
      | ( ( member @ SV7 @ ( intersection @ SV18 @ SV24 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[107]) ).

thf(109,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[41,108,106,105,104,102,101,93,92,91,83,80,79,69,56,42]) ).

thf(110,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[109]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET015-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n011.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 : Sun Jul 10 22:47:41 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 15
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.36  (rf:0,axioms:15,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:17,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.91/1.17  
% 0.91/1.17  ********************************
% 0.91/1.17  *   All subproblems solved!    *
% 0.91/1.17  ********************************
% 0.91/1.17  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:109,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.99/1.17  
% 0.99/1.17  %**** Beginning of derivation protocol ****
% 0.99/1.17  % SZS output start CNFRefutation
% See solution above
% 0.99/1.17  
% 0.99/1.17  %**** End of derivation protocol ****
% 0.99/1.17  %**** no. of clauses in derivation: 110 ****
% 0.99/1.17  %**** clause counter: 109 ****
% 0.99/1.17  
% 0.99/1.17  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:109,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------