TSTP Solution File: LCL109-5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n025.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 : Sun Jul 17 12:20:43 EDT 2022

% Result   : Unsatisfiable 0.18s 0.47s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  122 (  94 unt;   8 typ;   0 def)
%            Number of atoms       :  381 ( 181 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  861 (  47   ~;  49   |;   0   &; 765   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  250 (   0   ^ 250   !;   0   ?; 250   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_big_V,type,
    big_V: $i > $i > $i ).

thf(tp_big_hat,type,
    big_hat: $i > $i > $i ).

thf(tp_implies,type,
    implies: $i > $i > $i ).

thf(tp_not,type,
    not: $i > $i ).

thf(tp_ordered,type,
    ordered: $i > $i > $o ).

thf(tp_truth,type,
    truth: $i ).

thf(tp_x,type,
    x: $i ).

thf(tp_y,type,
    y: $i ).

thf(1,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( implies @ X @ ( big_hat @ Y @ Z ) )
      = ( big_hat @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_7) ).

thf(2,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( implies @ ( big_V @ X @ Y ) @ Z )
      = ( big_hat @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_6) ).

thf(3,axiom,
    ! [X: $i,Y: $i] :
      ( ( not @ ( big_hat @ X @ Y ) )
      = ( big_V @ ( not @ X ) @ ( not @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_5) ).

thf(4,axiom,
    ! [X: $i,Y: $i] :
      ( ( not @ ( big_V @ X @ Y ) )
      = ( big_hat @ ( not @ X ) @ ( not @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_4) ).

thf(5,axiom,
    ! [Y: $i,X: $i,Z: $i] :
      ( ~ ( ordered @ Y @ ( implies @ X @ Z ) )
      | ( ordered @ X @ ( implies @ Y @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_2) ).

thf(6,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( ordered @ X @ ( implies @ Y @ Z ) )
      | ( ordered @ Y @ ( implies @ X @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_1) ).

thf(7,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( ordered @ X @ Y )
      | ( ordered @ ( implies @ Z @ X ) @ ( implies @ Z @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_2) ).

thf(8,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( ordered @ X @ Y )
      | ( ordered @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).

thf(9,axiom,
    ! [X: $i,Y: $i] :
      ( ( ( implies @ X @ Y )
       != truth )
      | ( ordered @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition2) ).

thf(10,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( ordered @ X @ Y )
      | ( ( implies @ X @ Y )
        = truth ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition1) ).

thf(11,axiom,
    ! [X: $i,Y: $i] :
      ( ( big_hat @ X @ Y )
      = ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_hat_definition) ).

thf(12,axiom,
    ! [X: $i,Y: $i] :
      ( ( big_V @ X @ Y )
      = ( implies @ ( implies @ X @ Y ) @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_V_definition) ).

thf(13,axiom,
    ! [X: $i,Y: $i] :
      ( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
      = truth ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).

thf(14,axiom,
    ! [X: $i,Y: $i] :
      ( ( implies @ ( implies @ X @ Y ) @ Y )
      = ( implies @ ( implies @ Y @ X ) @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).

thf(15,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
      = truth ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).

thf(16,axiom,
    ! [X: $i] :
      ( ( implies @ truth @ X )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).

thf(17,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(18,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[17]) ).

thf(19,negated_conjecture,
    ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
 != truth,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_mv_4) ).

thf(20,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( implies @ X @ ( big_hat @ Y @ Z ) )
          = ( big_hat @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(22,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( implies @ ( big_V @ X @ Y ) @ Z )
          = ( big_hat @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(23,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( not @ ( big_hat @ X @ Y ) )
          = ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(24,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( not @ ( big_V @ X @ Y ) )
          = ( big_hat @ ( not @ X ) @ ( not @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(25,plain,
    ( ( ! [Y: $i,X: $i,Z: $i] :
          ( ~ ( ordered @ Y @ ( implies @ X @ Z ) )
          | ( ordered @ X @ ( implies @ Y @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(26,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( ordered @ X @ ( implies @ Y @ Z ) )
          | ( ordered @ Y @ ( implies @ X @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(27,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( ordered @ X @ Y )
          | ( ordered @ ( implies @ Z @ X ) @ ( implies @ Z @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(28,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( ordered @ X @ Y )
          | ( ordered @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(29,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( implies @ X @ Y )
           != truth )
          | ( ordered @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(30,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( ordered @ X @ Y )
          | ( ( implies @ X @ Y )
            = truth ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(31,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( big_hat @ X @ Y )
          = ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(32,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( big_V @ X @ Y )
          = ( implies @ ( implies @ X @ Y ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(33,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
          = truth ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(34,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( implies @ ( implies @ X @ Y ) @ Y )
          = ( implies @ ( implies @ Y @ X ) @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(35,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
          = truth ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(36,plain,
    ( ( ! [X: $i] :
          ( ( implies @ truth @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(37,plain,
    ( ( ( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
       != truth ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(38,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[20]) ).

thf(39,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( ordered @ X @ Y )
          | ! [Z: $i] : ( ordered @ ( implies @ Z @ X ) @ ( implies @ Z @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[27]) ).

thf(40,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( ordered @ X @ Y )
          | ! [Z: $i] : ( ordered @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[28]) ).

thf(41,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( implies @ X @ Y )
           != truth )
          | ( ordered @ X @ Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[29]) ).

thf(42,plain,
    ( ( ( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
       != truth ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[37]) ).

thf(43,plain,
    ( ( ( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
       != truth ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(44,plain,
    ( ( ! [X: $i] :
          ( ( implies @ truth @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(45,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) )
          = truth ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(46,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( implies @ ( implies @ X @ Y ) @ Y )
          = ( implies @ ( implies @ Y @ X ) @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(47,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( implies @ ( implies @ ( not @ X ) @ ( not @ Y ) ) @ ( implies @ Y @ X ) )
          = truth ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(48,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( big_V @ X @ Y )
          = ( implies @ ( implies @ X @ Y ) @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(49,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( big_hat @ X @ Y )
          = ( not @ ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(50,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( ordered @ X @ Y )
          | ( ( implies @ X @ Y )
            = truth ) ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(51,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( implies @ X @ Y )
           != truth )
          | ( ordered @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(52,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( ordered @ X @ Y )
          | ! [Z: $i] : ( ordered @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(53,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( ordered @ X @ Y )
          | ! [Z: $i] : ( ordered @ ( implies @ Z @ X ) @ ( implies @ Z @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(54,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( ordered @ X @ ( implies @ Y @ Z ) )
          | ( ordered @ Y @ ( implies @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(55,plain,
    ( ( ! [Y: $i,X: $i,Z: $i] :
          ( ~ ( ordered @ Y @ ( implies @ X @ Z ) )
          | ( ordered @ X @ ( implies @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(56,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( not @ ( big_V @ X @ Y ) )
          = ( big_hat @ ( not @ X ) @ ( not @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(57,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( not @ ( big_hat @ X @ Y ) )
          = ( big_V @ ( not @ X ) @ ( not @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(58,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( implies @ ( big_V @ X @ Y ) @ Z )
          = ( big_hat @ ( implies @ X @ Z ) @ ( implies @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(59,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( implies @ X @ ( big_hat @ Y @ Z ) )
          = ( big_hat @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(60,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(61,plain,
    ( ( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
      = truth )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(62,plain,
    ! [SV1: $i] :
      ( ( ( implies @ truth @ SV1 )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(63,plain,
    ! [SV2: $i] :
      ( ( ! [SY38: $i,SY39: $i] :
            ( ( implies @ ( implies @ SV2 @ SY38 ) @ ( implies @ ( implies @ SY38 @ SY39 ) @ ( implies @ SV2 @ SY39 ) ) )
            = truth ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(64,plain,
    ! [SV3: $i] :
      ( ( ! [SY40: $i] :
            ( ( implies @ ( implies @ SV3 @ SY40 ) @ SY40 )
            = ( implies @ ( implies @ SY40 @ SV3 ) @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(65,plain,
    ! [SV4: $i] :
      ( ( ! [SY41: $i] :
            ( ( implies @ ( implies @ ( not @ SV4 ) @ ( not @ SY41 ) ) @ ( implies @ SY41 @ SV4 ) )
            = truth ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(66,plain,
    ! [SV5: $i] :
      ( ( ! [SY42: $i] :
            ( ( big_V @ SV5 @ SY42 )
            = ( implies @ ( implies @ SV5 @ SY42 ) @ SY42 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(67,plain,
    ! [SV6: $i] :
      ( ( ! [SY43: $i] :
            ( ( big_hat @ SV6 @ SY43 )
            = ( not @ ( big_V @ ( not @ SV6 ) @ ( not @ SY43 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(68,plain,
    ! [SV7: $i] :
      ( ( ! [SY44: $i] :
            ( ~ ( ordered @ SV7 @ SY44 )
            | ( ( implies @ SV7 @ SY44 )
              = truth ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(69,plain,
    ! [SV8: $i] :
      ( ( ! [SY45: $i] :
            ( ( ( implies @ SV8 @ SY45 )
             != truth )
            | ( ordered @ SV8 @ SY45 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(70,plain,
    ! [SV9: $i] :
      ( ( ! [SY46: $i] :
            ( ~ ( ordered @ SV9 @ SY46 )
            | ! [SY47: $i] : ( ordered @ ( implies @ SV9 @ SY47 ) @ ( implies @ SY46 @ SY47 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(71,plain,
    ! [SV10: $i] :
      ( ( ! [SY48: $i] :
            ( ~ ( ordered @ SV10 @ SY48 )
            | ! [SY49: $i] : ( ordered @ ( implies @ SY49 @ SV10 ) @ ( implies @ SY49 @ SY48 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(72,plain,
    ! [SV11: $i] :
      ( ( ! [SY50: $i,SY51: $i] :
            ( ~ ( ordered @ SV11 @ ( implies @ SY50 @ SY51 ) )
            | ( ordered @ SY50 @ ( implies @ SV11 @ SY51 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(73,plain,
    ! [SV12: $i] :
      ( ( ! [SY52: $i,SY53: $i] :
            ( ~ ( ordered @ SV12 @ ( implies @ SY52 @ SY53 ) )
            | ( ordered @ SY52 @ ( implies @ SV12 @ SY53 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(74,plain,
    ! [SV13: $i] :
      ( ( ! [SY54: $i] :
            ( ( not @ ( big_V @ SV13 @ SY54 ) )
            = ( big_hat @ ( not @ SV13 ) @ ( not @ SY54 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(75,plain,
    ! [SV14: $i] :
      ( ( ! [SY55: $i] :
            ( ( not @ ( big_hat @ SV14 @ SY55 ) )
            = ( big_V @ ( not @ SV14 ) @ ( not @ SY55 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(76,plain,
    ! [SV15: $i] :
      ( ( ! [SY56: $i,SY57: $i] :
            ( ( implies @ ( big_V @ SV15 @ SY56 ) @ SY57 )
            = ( big_hat @ ( implies @ SV15 @ SY57 ) @ ( implies @ SY56 @ SY57 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(77,plain,
    ! [SV16: $i] :
      ( ( ! [SY58: $i,SY59: $i] :
            ( ( implies @ SV16 @ ( big_hat @ SY58 @ SY59 ) )
            = ( big_hat @ ( implies @ SV16 @ SY58 ) @ ( implies @ SV16 @ SY59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(78,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(79,plain,
    ! [SV17: $i,SV2: $i] :
      ( ( ! [SY60: $i] :
            ( ( implies @ ( implies @ SV2 @ SV17 ) @ ( implies @ ( implies @ SV17 @ SY60 ) @ ( implies @ SV2 @ SY60 ) ) )
            = truth ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(80,plain,
    ! [SV18: $i,SV3: $i] :
      ( ( ( implies @ ( implies @ SV3 @ SV18 ) @ SV18 )
        = ( implies @ ( implies @ SV18 @ SV3 ) @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(81,plain,
    ! [SV19: $i,SV4: $i] :
      ( ( ( implies @ ( implies @ ( not @ SV4 ) @ ( not @ SV19 ) ) @ ( implies @ SV19 @ SV4 ) )
        = truth )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(82,plain,
    ! [SV20: $i,SV5: $i] :
      ( ( ( big_V @ SV5 @ SV20 )
        = ( implies @ ( implies @ SV5 @ SV20 ) @ SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(83,plain,
    ! [SV21: $i,SV6: $i] :
      ( ( ( big_hat @ SV6 @ SV21 )
        = ( not @ ( big_V @ ( not @ SV6 ) @ ( not @ SV21 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(84,plain,
    ! [SV22: $i,SV7: $i] :
      ( ( ~ ( ordered @ SV7 @ SV22 )
        | ( ( implies @ SV7 @ SV22 )
          = truth ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(85,plain,
    ! [SV23: $i,SV8: $i] :
      ( ( ( ( implies @ SV8 @ SV23 )
         != truth )
        | ( ordered @ SV8 @ SV23 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(86,plain,
    ! [SV24: $i,SV9: $i] :
      ( ( ~ ( ordered @ SV9 @ SV24 )
        | ! [SY61: $i] : ( ordered @ ( implies @ SV9 @ SY61 ) @ ( implies @ SV24 @ SY61 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(87,plain,
    ! [SV25: $i,SV10: $i] :
      ( ( ~ ( ordered @ SV10 @ SV25 )
        | ! [SY62: $i] : ( ordered @ ( implies @ SY62 @ SV10 ) @ ( implies @ SY62 @ SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(88,plain,
    ! [SV26: $i,SV11: $i] :
      ( ( ! [SY63: $i] :
            ( ~ ( ordered @ SV11 @ ( implies @ SV26 @ SY63 ) )
            | ( ordered @ SV26 @ ( implies @ SV11 @ SY63 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(89,plain,
    ! [SV27: $i,SV12: $i] :
      ( ( ! [SY64: $i] :
            ( ~ ( ordered @ SV12 @ ( implies @ SV27 @ SY64 ) )
            | ( ordered @ SV27 @ ( implies @ SV12 @ SY64 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(90,plain,
    ! [SV28: $i,SV13: $i] :
      ( ( ( not @ ( big_V @ SV13 @ SV28 ) )
        = ( big_hat @ ( not @ SV13 ) @ ( not @ SV28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(91,plain,
    ! [SV29: $i,SV14: $i] :
      ( ( ( not @ ( big_hat @ SV14 @ SV29 ) )
        = ( big_V @ ( not @ SV14 ) @ ( not @ SV29 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(92,plain,
    ! [SV30: $i,SV15: $i] :
      ( ( ! [SY65: $i] :
            ( ( implies @ ( big_V @ SV15 @ SV30 ) @ SY65 )
            = ( big_hat @ ( implies @ SV15 @ SY65 ) @ ( implies @ SV30 @ SY65 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(93,plain,
    ! [SV31: $i,SV16: $i] :
      ( ( ! [SY66: $i] :
            ( ( implies @ SV16 @ ( big_hat @ SV31 @ SY66 ) )
            = ( big_hat @ ( implies @ SV16 @ SV31 ) @ ( implies @ SV16 @ SY66 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(94,plain,
    ! [SV32: $i,SV17: $i,SV2: $i] :
      ( ( ( implies @ ( implies @ SV2 @ SV17 ) @ ( implies @ ( implies @ SV17 @ SV32 ) @ ( implies @ SV2 @ SV32 ) ) )
        = truth )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(95,plain,
    ! [SV22: $i,SV7: $i] :
      ( ( ( ~ ( ordered @ SV7 @ SV22 ) )
        = $true )
      | ( ( ( implies @ SV7 @ SV22 )
          = truth )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[84]) ).

thf(96,plain,
    ! [SV23: $i,SV8: $i] :
      ( ( ( ( ( implies @ SV8 @ SV23 )
           != truth ) )
        = $true )
      | ( ( ordered @ SV8 @ SV23 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[85]) ).

thf(97,plain,
    ! [SV24: $i,SV9: $i] :
      ( ( ( ~ ( ordered @ SV9 @ SV24 ) )
        = $true )
      | ( ( ! [SY61: $i] : ( ordered @ ( implies @ SV9 @ SY61 ) @ ( implies @ SV24 @ SY61 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[86]) ).

thf(98,plain,
    ! [SV25: $i,SV10: $i] :
      ( ( ( ~ ( ordered @ SV10 @ SV25 ) )
        = $true )
      | ( ( ! [SY62: $i] : ( ordered @ ( implies @ SY62 @ SV10 ) @ ( implies @ SY62 @ SV25 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[87]) ).

thf(99,plain,
    ! [SV33: $i,SV26: $i,SV11: $i] :
      ( ( ~ ( ordered @ SV11 @ ( implies @ SV26 @ SV33 ) )
        | ( ordered @ SV26 @ ( implies @ SV11 @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(100,plain,
    ! [SV34: $i,SV27: $i,SV12: $i] :
      ( ( ~ ( ordered @ SV12 @ ( implies @ SV27 @ SV34 ) )
        | ( ordered @ SV27 @ ( implies @ SV12 @ SV34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(101,plain,
    ! [SV35: $i,SV30: $i,SV15: $i] :
      ( ( ( implies @ ( big_V @ SV15 @ SV30 ) @ SV35 )
        = ( big_hat @ ( implies @ SV15 @ SV35 ) @ ( implies @ SV30 @ SV35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(102,plain,
    ! [SV36: $i,SV31: $i,SV16: $i] :
      ( ( ( implies @ SV16 @ ( big_hat @ SV31 @ SV36 ) )
        = ( big_hat @ ( implies @ SV16 @ SV31 ) @ ( implies @ SV16 @ SV36 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(103,plain,
    ! [SV22: $i,SV7: $i] :
      ( ( ( ordered @ SV7 @ SV22 )
        = $false )
      | ( ( ( implies @ SV7 @ SV22 )
          = truth )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[95]) ).

thf(104,plain,
    ! [SV23: $i,SV8: $i] :
      ( ( ( ( implies @ SV8 @ SV23 )
          = truth )
        = $false )
      | ( ( ordered @ SV8 @ SV23 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(105,plain,
    ! [SV24: $i,SV9: $i] :
      ( ( ( ordered @ SV9 @ SV24 )
        = $false )
      | ( ( ! [SY61: $i] : ( ordered @ ( implies @ SV9 @ SY61 ) @ ( implies @ SV24 @ SY61 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[97]) ).

thf(106,plain,
    ! [SV25: $i,SV10: $i] :
      ( ( ( ordered @ SV10 @ SV25 )
        = $false )
      | ( ( ! [SY62: $i] : ( ordered @ ( implies @ SY62 @ SV10 ) @ ( implies @ SY62 @ SV25 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[98]) ).

thf(107,plain,
    ! [SV33: $i,SV26: $i,SV11: $i] :
      ( ( ( ~ ( ordered @ SV11 @ ( implies @ SV26 @ SV33 ) ) )
        = $true )
      | ( ( ordered @ SV26 @ ( implies @ SV11 @ SV33 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[99]) ).

thf(108,plain,
    ! [SV34: $i,SV27: $i,SV12: $i] :
      ( ( ( ~ ( ordered @ SV12 @ ( implies @ SV27 @ SV34 ) ) )
        = $true )
      | ( ( ordered @ SV27 @ ( implies @ SV12 @ SV34 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[100]) ).

thf(109,plain,
    ! [SV24: $i,SV37: $i,SV9: $i] :
      ( ( ( ordered @ ( implies @ SV9 @ SV37 ) @ ( implies @ SV24 @ SV37 ) )
        = $true )
      | ( ( ordered @ SV9 @ SV24 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[105]) ).

thf(110,plain,
    ! [SV25: $i,SV10: $i,SV38: $i] :
      ( ( ( ordered @ ( implies @ SV38 @ SV10 ) @ ( implies @ SV38 @ SV25 ) )
        = $true )
      | ( ( ordered @ SV10 @ SV25 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[106]) ).

thf(111,plain,
    ! [SV33: $i,SV26: $i,SV11: $i] :
      ( ( ( ordered @ SV11 @ ( implies @ SV26 @ SV33 ) )
        = $false )
      | ( ( ordered @ SV26 @ ( implies @ SV11 @ SV33 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[107]) ).

thf(112,plain,
    ! [SV34: $i,SV27: $i,SV12: $i] :
      ( ( ( ordered @ SV12 @ ( implies @ SV27 @ SV34 ) )
        = $false )
      | ( ( ordered @ SV27 @ ( implies @ SV12 @ SV34 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[108]) ).

thf(113,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[61,112,111,110,109,104,103,102,101,94,91,90,83,82,81,80,78,62]) ).

thf(114,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[113]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jul  2 09:55:39 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 17
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.36  (rf:0,axioms:17,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:19,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.18/0.47  
% 0.18/0.47  ********************************
% 0.18/0.47  *   All subproblems solved!    *
% 0.18/0.47  ********************************
% 0.18/0.47  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,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:113,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.47  
% 0.18/0.47  %**** Beginning of derivation protocol ****
% 0.18/0.47  % SZS output start CNFRefutation
% See solution above
% 0.18/0.47  
% 0.18/0.47  %**** End of derivation protocol ****
% 0.18/0.47  %**** no. of clauses in derivation: 114 ****
% 0.18/0.47  %**** clause counter: 113 ****
% 0.18/0.47  
% 0.18/0.47  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,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:113,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------