TSTP Solution File: SET821-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SET821-2 : 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 : n017.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 03:05:16 EDT 2022

% Result   : Unsatisfiable 0.18s 0.40s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   86 (  53 unt;  10 typ;   0 def)
%            Number of atoms       :  315 (  95 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  614 (  54   ~;  71   |;   0   &; 489   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :  175 (   0   ^ 175   !;   0   ?; 175   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c_in,type,
    c_in: $i > $i > $i > $o ).

thf(tp_c_insert,type,
    c_insert: $i > $i > $i > $i ).

thf(tp_c_less,type,
    c_less: $i > $i > $i > $o ).

thf(tp_c_uminus,type,
    c_uminus: $i > $i > $i ).

thf(tp_class_Orderings_Oorder,type,
    class_Orderings_Oorder: $i > $o ).

thf(tp_tc_IntDef_Oint,type,
    tc_IntDef_Oint: $i ).

thf(tp_tc_set,type,
    tc_set: $i > $i ).

thf(tp_v_a,type,
    v_a: $i ).

thf(tp_v_b,type,
    v_b: $i ).

thf(tp_v_c,type,
    v_c: $i ).

thf(1,axiom,
    class_Orderings_Oorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

thf(2,axiom,
    ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
      ( ~ ( c_in @ V_a @ ( c_insert @ V_b @ V_A @ T_a ) @ T_a )
      | ( c_in @ V_a @ V_A @ T_a )
      | ( V_a = V_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(3,axiom,
    ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

thf(4,axiom,
    ! [V_a: $i,V_B: $i,T_a: $i,V_b: $i] :
      ( ~ ( c_in @ V_a @ V_B @ T_a )
      | ( c_in @ V_a @ ( c_insert @ V_b @ V_B @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).

thf(5,axiom,
    ! [V_c: $i,V_A: $i,T_a: $i] :
      ( ( c_in @ V_c @ V_A @ T_a )
      | ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).

thf(6,axiom,
    ! [V_c: $i,V_A: $i,T_a: $i] :
      ( ~ ( c_in @ V_c @ V_A @ T_a )
      | ~ ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).

thf(7,axiom,
    ! [T_a: $i,V_x: $i] :
      ( ~ ( class_Orderings_Oorder @ T_a )
      | ~ ( c_less @ V_x @ V_x @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).

thf(8,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(9,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[8]) ).

thf(10,negated_conjecture,
    ! [V_U: $i] :
      ( ( c_in @ v_c @ V_U @ tc_IntDef_Oint )
      | ~ ( c_in @ v_b @ V_U @ tc_IntDef_Oint )
      | ( c_in @ v_a @ V_U @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(11,negated_conjecture,
    c_less @ v_b @ v_c @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(12,negated_conjecture,
    c_less @ v_a @ v_b @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(13,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[9]) ).

thf(14,plain,
    ( ( class_Orderings_Oorder @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(15,plain,
    ( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ ( c_insert @ V_b @ V_A @ T_a ) @ T_a )
          | ( c_in @ V_a @ V_A @ T_a )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(16,plain,
    ( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(17,plain,
    ( ( ! [V_a: $i,V_B: $i,T_a: $i,V_b: $i] :
          ( ~ ( c_in @ V_a @ V_B @ T_a )
          | ( c_in @ V_a @ ( c_insert @ V_b @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(18,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ( c_in @ V_c @ V_A @ T_a )
          | ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(19,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ~ ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(20,plain,
    ( ( ! [T_a: $i,V_x: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ~ ( c_less @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(21,plain,
    ( ( ! [V_U: $i] :
          ( ( c_in @ v_c @ V_U @ tc_IntDef_Oint )
          | ~ ( c_in @ v_b @ V_U @ tc_IntDef_Oint )
          | ( c_in @ v_a @ V_U @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(22,plain,
    ( ( c_less @ v_b @ v_c @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(23,plain,
    ( ( c_less @ v_a @ v_b @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(24,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[13]) ).

thf(25,plain,
    ( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ ( c_insert @ V_b @ V_A @ T_a ) @ T_a )
          | ( V_a = V_b )
          | ( c_in @ V_a @ V_A @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(26,plain,
    ( ( ! [V_a: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ V_B @ T_a )
          | ! [V_b: $i] : ( c_in @ V_a @ ( c_insert @ V_b @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[17]) ).

thf(27,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i] :
              ~ ( c_less @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[20]) ).

thf(28,plain,
    ( ( c_less @ v_a @ v_b @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(29,plain,
    ( ( c_less @ v_b @ v_c @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(30,plain,
    ( ( ! [V_U: $i] :
          ( ( c_in @ v_c @ V_U @ tc_IntDef_Oint )
          | ~ ( c_in @ v_b @ V_U @ tc_IntDef_Oint )
          | ( c_in @ v_a @ V_U @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(31,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i] :
              ~ ( c_less @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(32,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ~ ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(33,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ( c_in @ V_c @ V_A @ T_a )
          | ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(34,plain,
    ( ( ! [V_a: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ V_B @ T_a )
          | ! [V_b: $i] : ( c_in @ V_a @ ( c_insert @ V_b @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(35,plain,
    ( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(36,plain,
    ( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ ( c_insert @ V_b @ V_A @ T_a ) @ T_a )
          | ( V_a = V_b )
          | ( c_in @ V_a @ V_A @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(37,plain,
    ( ( class_Orderings_Oorder @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(38,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(39,plain,
    ! [SV1: $i] :
      ( ( ( c_in @ v_c @ SV1 @ tc_IntDef_Oint )
        | ~ ( c_in @ v_b @ SV1 @ tc_IntDef_Oint )
        | ( c_in @ v_a @ SV1 @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(40,plain,
    ! [SV2: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV2 )
        | ! [SY20: $i] :
            ~ ( c_less @ SY20 @ SY20 @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(41,plain,
    ! [SV3: $i] :
      ( ( ! [SY21: $i,SY22: $i] :
            ( ~ ( c_in @ SV3 @ SY21 @ SY22 )
            | ~ ( c_in @ SV3 @ ( c_uminus @ SY21 @ ( tc_set @ SY22 ) ) @ SY22 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(42,plain,
    ! [SV4: $i] :
      ( ( ! [SY23: $i,SY24: $i] :
            ( ( c_in @ SV4 @ SY23 @ SY24 )
            | ( c_in @ SV4 @ ( c_uminus @ SY23 @ ( tc_set @ SY24 ) ) @ SY24 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(43,plain,
    ! [SV5: $i] :
      ( ( ! [SY25: $i,SY26: $i] :
            ( ~ ( c_in @ SV5 @ SY25 @ SY26 )
            | ! [SY27: $i] : ( c_in @ SV5 @ ( c_insert @ SY27 @ SY25 @ SY26 ) @ SY26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(44,plain,
    ! [SV6: $i] :
      ( ( ! [SY28: $i,SY29: $i] : ( c_in @ SV6 @ ( c_insert @ SV6 @ SY28 @ SY29 ) @ SY29 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(45,plain,
    ! [SV7: $i] :
      ( ( ! [SY30: $i,SY31: $i,SY32: $i] :
            ( ~ ( c_in @ SV7 @ ( c_insert @ SY30 @ SY31 @ SY32 ) @ SY32 )
            | ( SV7 = SY30 )
            | ( c_in @ SV7 @ SY31 @ SY32 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(46,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(47,plain,
    ! [SV1: $i] :
      ( ( ( c_in @ v_c @ SV1 @ tc_IntDef_Oint )
        = $true )
      | ( ( ~ ( c_in @ v_b @ SV1 @ tc_IntDef_Oint )
          | ( c_in @ v_a @ SV1 @ tc_IntDef_Oint ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(48,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV2 ) )
        = $true )
      | ( ( ! [SY20: $i] :
              ~ ( c_less @ SY20 @ SY20 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(49,plain,
    ! [SV8: $i,SV3: $i] :
      ( ( ! [SY33: $i] :
            ( ~ ( c_in @ SV3 @ SV8 @ SY33 )
            | ~ ( c_in @ SV3 @ ( c_uminus @ SV8 @ ( tc_set @ SY33 ) ) @ SY33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(50,plain,
    ! [SV9: $i,SV4: $i] :
      ( ( ! [SY34: $i] :
            ( ( c_in @ SV4 @ SV9 @ SY34 )
            | ( c_in @ SV4 @ ( c_uminus @ SV9 @ ( tc_set @ SY34 ) ) @ SY34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(51,plain,
    ! [SV10: $i,SV5: $i] :
      ( ( ! [SY35: $i] :
            ( ~ ( c_in @ SV5 @ SV10 @ SY35 )
            | ! [SY36: $i] : ( c_in @ SV5 @ ( c_insert @ SY36 @ SV10 @ SY35 ) @ SY35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(52,plain,
    ! [SV11: $i,SV6: $i] :
      ( ( ! [SY37: $i] : ( c_in @ SV6 @ ( c_insert @ SV6 @ SV11 @ SY37 ) @ SY37 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(53,plain,
    ! [SV12: $i,SV7: $i] :
      ( ( ! [SY38: $i,SY39: $i] :
            ( ~ ( c_in @ SV7 @ ( c_insert @ SV12 @ SY38 @ SY39 ) @ SY39 )
            | ( SV7 = SV12 )
            | ( c_in @ SV7 @ SY38 @ SY39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(54,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( c_in @ v_b @ SV1 @ tc_IntDef_Oint ) )
        = $true )
      | ( ( c_in @ v_a @ SV1 @ tc_IntDef_Oint )
        = $true )
      | ( ( c_in @ v_c @ SV1 @ tc_IntDef_Oint )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[47]) ).

thf(55,plain,
    ! [SV2: $i] :
      ( ( ( class_Orderings_Oorder @ SV2 )
        = $false )
      | ( ( ! [SY20: $i] :
              ~ ( c_less @ SY20 @ SY20 @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(56,plain,
    ! [SV13: $i,SV8: $i,SV3: $i] :
      ( ( ~ ( c_in @ SV3 @ SV8 @ SV13 )
        | ~ ( c_in @ SV3 @ ( c_uminus @ SV8 @ ( tc_set @ SV13 ) ) @ SV13 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(57,plain,
    ! [SV14: $i,SV9: $i,SV4: $i] :
      ( ( ( c_in @ SV4 @ SV9 @ SV14 )
        | ( c_in @ SV4 @ ( c_uminus @ SV9 @ ( tc_set @ SV14 ) ) @ SV14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(58,plain,
    ! [SV15: $i,SV10: $i,SV5: $i] :
      ( ( ~ ( c_in @ SV5 @ SV10 @ SV15 )
        | ! [SY40: $i] : ( c_in @ SV5 @ ( c_insert @ SY40 @ SV10 @ SV15 ) @ SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(59,plain,
    ! [SV16: $i,SV11: $i,SV6: $i] :
      ( ( c_in @ SV6 @ ( c_insert @ SV6 @ SV11 @ SV16 ) @ SV16 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(60,plain,
    ! [SV17: $i,SV12: $i,SV7: $i] :
      ( ( ! [SY41: $i] :
            ( ~ ( c_in @ SV7 @ ( c_insert @ SV12 @ SV17 @ SY41 ) @ SY41 )
            | ( SV7 = SV12 )
            | ( c_in @ SV7 @ SV17 @ SY41 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(61,plain,
    ! [SV1: $i] :
      ( ( ( c_in @ v_b @ SV1 @ tc_IntDef_Oint )
        = $false )
      | ( ( c_in @ v_a @ SV1 @ tc_IntDef_Oint )
        = $true )
      | ( ( c_in @ v_c @ SV1 @ tc_IntDef_Oint )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(62,plain,
    ! [SV2: $i,SV18: $i] :
      ( ( ( ~ ( c_less @ SV18 @ SV18 @ SV2 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV2 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(63,plain,
    ! [SV13: $i,SV8: $i,SV3: $i] :
      ( ( ( ~ ( c_in @ SV3 @ SV8 @ SV13 ) )
        = $true )
      | ( ( ~ ( c_in @ SV3 @ ( c_uminus @ SV8 @ ( tc_set @ SV13 ) ) @ SV13 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[56]) ).

thf(64,plain,
    ! [SV14: $i,SV9: $i,SV4: $i] :
      ( ( ( c_in @ SV4 @ SV9 @ SV14 )
        = $true )
      | ( ( c_in @ SV4 @ ( c_uminus @ SV9 @ ( tc_set @ SV14 ) ) @ SV14 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[57]) ).

thf(65,plain,
    ! [SV15: $i,SV10: $i,SV5: $i] :
      ( ( ( ~ ( c_in @ SV5 @ SV10 @ SV15 ) )
        = $true )
      | ( ( ! [SY40: $i] : ( c_in @ SV5 @ ( c_insert @ SY40 @ SV10 @ SV15 ) @ SV15 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[58]) ).

thf(66,plain,
    ! [SV19: $i,SV17: $i,SV12: $i,SV7: $i] :
      ( ( ~ ( c_in @ SV7 @ ( c_insert @ SV12 @ SV17 @ SV19 ) @ SV19 )
        | ( SV7 = SV12 )
        | ( c_in @ SV7 @ SV17 @ SV19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(67,plain,
    ! [SV2: $i,SV18: $i] :
      ( ( ( c_less @ SV18 @ SV18 @ SV2 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(68,plain,
    ! [SV13: $i,SV8: $i,SV3: $i] :
      ( ( ( c_in @ SV3 @ SV8 @ SV13 )
        = $false )
      | ( ( ~ ( c_in @ SV3 @ ( c_uminus @ SV8 @ ( tc_set @ SV13 ) ) @ SV13 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(69,plain,
    ! [SV15: $i,SV10: $i,SV5: $i] :
      ( ( ( c_in @ SV5 @ SV10 @ SV15 )
        = $false )
      | ( ( ! [SY40: $i] : ( c_in @ SV5 @ ( c_insert @ SY40 @ SV10 @ SV15 ) @ SV15 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(70,plain,
    ! [SV19: $i,SV17: $i,SV12: $i,SV7: $i] :
      ( ( ( ~ ( c_in @ SV7 @ ( c_insert @ SV12 @ SV17 @ SV19 ) @ SV19 ) )
        = $true )
      | ( ( ( SV7 = SV12 )
          | ( c_in @ SV7 @ SV17 @ SV19 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(71,plain,
    ! [SV13: $i,SV8: $i,SV3: $i] :
      ( ( ( c_in @ SV3 @ ( c_uminus @ SV8 @ ( tc_set @ SV13 ) ) @ SV13 )
        = $false )
      | ( ( c_in @ SV3 @ SV8 @ SV13 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(72,plain,
    ! [SV15: $i,SV10: $i,SV20: $i,SV5: $i] :
      ( ( ( c_in @ SV5 @ ( c_insert @ SV20 @ SV10 @ SV15 ) @ SV15 )
        = $true )
      | ( ( c_in @ SV5 @ SV10 @ SV15 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(73,plain,
    ! [SV19: $i,SV17: $i,SV12: $i,SV7: $i] :
      ( ( ( c_in @ SV7 @ ( c_insert @ SV12 @ SV17 @ SV19 ) @ SV19 )
        = $false )
      | ( ( ( SV7 = SV12 )
          | ( c_in @ SV7 @ SV17 @ SV19 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(74,plain,
    ! [SV19: $i,SV17: $i,SV12: $i,SV7: $i] :
      ( ( ( SV7 = SV12 )
        = $true )
      | ( ( c_in @ SV7 @ SV17 @ SV19 )
        = $true )
      | ( ( c_in @ SV7 @ ( c_insert @ SV12 @ SV17 @ SV19 ) @ SV19 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[73]) ).

thf(75,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[28,74,72,71,67,64,61,59,46,37,29]) ).

thf(76,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[75]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET821-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.33  % Computer : n017.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Mon Jul 11 01:44:33 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.11/0.34  
% 0.11/0.34   No.of.Axioms: 10
% 0.11/0.34  
% 0.11/0.34   Length.of.Defs: 0
% 0.11/0.34  
% 0.11/0.34   Contains.Choice.Funs: false
% 0.11/0.35  (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:12,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.18/0.40  
% 0.18/0.40  ********************************
% 0.18/0.40  *   All subproblems solved!    *
% 0.18/0.40  ********************************
% 0.18/0.40  % SZS status Unsatisfiable 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:75,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.41  
% 0.18/0.41  %**** Beginning of derivation protocol ****
% 0.18/0.41  % SZS output start CNFRefutation
% See solution above
% 0.18/0.41  
% 0.18/0.41  %**** End of derivation protocol ****
% 0.18/0.41  %**** no. of clauses in derivation: 76 ****
% 0.18/0.41  %**** clause counter: 75 ****
% 0.18/0.41  
% 0.18/0.41  % SZS status Unsatisfiable 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:75,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------