TSTP Solution File: SYN069-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN069-1 : 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 : n027.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 : Thu Jul 21 08:23:17 EDT 2022

% Result   : Unsatisfiable 0.21s 0.40s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   93 (  38 unt;   9 typ;   0 def)
%            Number of atoms       :  585 ( 150 equ;   0 cnn)
%            Maximal formula atoms :    5 (   6 avg)
%            Number of connectives :  759 ( 134   ~; 201   |;   0   &; 424   @)
%                                         (   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     :   12 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :  113 (   0   ^ 113   !;   0   ?; 113   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $i ).

thf(tp_big_f,type,
    big_f: $i > $o ).

thf(tp_big_g,type,
    big_g: $i > $o ).

thf(tp_big_h,type,
    big_h: $i > $i > $o ).

thf(tp_big_j,type,
    big_j: $i > $i > $o ).

thf(tp_big_k,type,
    big_k: $i > $o ).

thf(tp_big_l,type,
    big_l: $i > $o ).

thf(tp_f,type,
    f: $i > $i ).

thf(tp_g,type,
    g: $i > $i ).

thf(1,axiom,
    ! [X: $i] :
      ( ~ ( big_g @ X )
      | ~ ( big_h @ a @ X )
      | ( big_j @ a @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).

thf(2,axiom,
    ! [X: $i] :
      ( ~ ( big_h @ a @ X )
      | ( big_l @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).

thf(3,axiom,
    big_f @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).

thf(4,axiom,
    ! [X: $i] :
      ( ~ ( big_l @ X )
      | ~ ( big_k @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).

thf(5,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( big_f @ X )
      | ~ ( big_j @ X @ ( f @ X ) )
      | ~ ( big_g @ Y )
      | ~ ( big_h @ X @ Y )
      | ( big_k @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).

thf(6,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( big_f @ X )
      | ( big_h @ X @ ( f @ X ) )
      | ~ ( big_g @ Y )
      | ~ ( big_h @ X @ Y )
      | ( big_k @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).

thf(7,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( big_f @ X )
      | ( big_g @ ( f @ X ) )
      | ~ ( big_g @ Y )
      | ~ ( big_h @ X @ Y )
      | ( big_k @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).

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,
    ! [X: $i] :
      ( ~ ( big_f @ X )
      | ( big_h @ X @ ( g @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).

thf(11,negated_conjecture,
    ! [X: $i] :
      ( ~ ( big_f @ X )
      | ( big_g @ ( g @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).

thf(12,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[9]) ).

thf(13,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_g @ X )
          | ~ ( big_h @ a @ X )
          | ( big_j @ a @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(14,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_h @ a @ X )
          | ( big_l @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(15,plain,
    ( ( big_f @ a )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(16,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_l @ X )
          | ~ ( big_k @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( big_f @ X )
          | ~ ( big_j @ X @ ( f @ X ) )
          | ~ ( big_g @ Y )
          | ~ ( big_h @ X @ Y )
          | ( big_k @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(18,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( big_f @ X )
          | ( big_h @ X @ ( f @ X ) )
          | ~ ( big_g @ Y )
          | ~ ( big_h @ X @ Y )
          | ( big_k @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(19,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( big_f @ X )
          | ( big_g @ ( f @ X ) )
          | ~ ( big_g @ Y )
          | ~ ( big_h @ X @ Y )
          | ( big_k @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(20,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_f @ X )
          | ( big_h @ X @ ( g @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(21,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_f @ X )
          | ( big_g @ ( g @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(22,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[12]) ).

thf(23,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_f @ X )
          | ~ ( big_j @ X @ ( f @ X ) )
          | ! [Y: $i] :
              ( ~ ( big_g @ Y )
              | ~ ( big_h @ X @ Y )
              | ( big_k @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[17]) ).

thf(24,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_f @ X )
          | ( big_h @ X @ ( f @ X ) )
          | ! [Y: $i] :
              ( ~ ( big_g @ Y )
              | ~ ( big_h @ X @ Y )
              | ( big_k @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[18]) ).

thf(25,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_f @ X )
          | ( big_g @ ( f @ X ) )
          | ! [Y: $i] :
              ( ~ ( big_g @ Y )
              | ~ ( big_h @ X @ Y )
              | ( big_k @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(26,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_f @ X )
          | ( big_g @ ( g @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(27,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_f @ X )
          | ( big_h @ X @ ( g @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(28,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_f @ X )
          | ( big_g @ ( f @ X ) )
          | ! [Y: $i] :
              ( ~ ( big_g @ Y )
              | ~ ( big_h @ X @ Y )
              | ( big_k @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(29,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_f @ X )
          | ( big_h @ X @ ( f @ X ) )
          | ! [Y: $i] :
              ( ~ ( big_g @ Y )
              | ~ ( big_h @ X @ Y )
              | ( big_k @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(30,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_f @ X )
          | ~ ( big_j @ X @ ( f @ X ) )
          | ! [Y: $i] :
              ( ~ ( big_g @ Y )
              | ~ ( big_h @ X @ Y )
              | ( big_k @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(31,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_l @ X )
          | ~ ( big_k @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(32,plain,
    ( ( big_f @ a )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(33,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_h @ a @ X )
          | ( big_l @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(34,plain,
    ( ( ! [X: $i] :
          ( ~ ( big_g @ X )
          | ~ ( big_h @ a @ X )
          | ( big_j @ a @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(35,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(36,plain,
    ! [SV1: $i] :
      ( ( ~ ( big_f @ SV1 )
        | ( big_g @ ( g @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(37,plain,
    ! [SV2: $i] :
      ( ( ~ ( big_f @ SV2 )
        | ( big_h @ SV2 @ ( g @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(38,plain,
    ! [SV3: $i] :
      ( ( ~ ( big_f @ SV3 )
        | ( big_g @ ( f @ SV3 ) )
        | ! [SY11: $i] :
            ( ~ ( big_g @ SY11 )
            | ~ ( big_h @ SV3 @ SY11 )
            | ( big_k @ SY11 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(39,plain,
    ! [SV4: $i] :
      ( ( ~ ( big_f @ SV4 )
        | ( big_h @ SV4 @ ( f @ SV4 ) )
        | ! [SY12: $i] :
            ( ~ ( big_g @ SY12 )
            | ~ ( big_h @ SV4 @ SY12 )
            | ( big_k @ SY12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(40,plain,
    ! [SV5: $i] :
      ( ( ~ ( big_f @ SV5 )
        | ~ ( big_j @ SV5 @ ( f @ SV5 ) )
        | ! [SY13: $i] :
            ( ~ ( big_g @ SY13 )
            | ~ ( big_h @ SV5 @ SY13 )
            | ( big_k @ SY13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(41,plain,
    ! [SV6: $i] :
      ( ( ~ ( big_l @ SV6 )
        | ~ ( big_k @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(42,plain,
    ! [SV7: $i] :
      ( ( ~ ( big_h @ a @ SV7 )
        | ( big_l @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(43,plain,
    ! [SV8: $i] :
      ( ( ~ ( big_g @ SV8 )
        | ~ ( big_h @ a @ SV8 )
        | ( big_j @ a @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(44,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(45,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( big_f @ SV1 ) )
        = $true )
      | ( ( big_g @ ( g @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[36]) ).

thf(46,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( big_f @ SV2 ) )
        = $true )
      | ( ( big_h @ SV2 @ ( g @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(47,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( big_f @ SV3 ) )
        = $true )
      | ( ( ( big_g @ ( f @ SV3 ) )
          | ! [SY11: $i] :
              ( ~ ( big_g @ SY11 )
              | ~ ( big_h @ SV3 @ SY11 )
              | ( big_k @ SY11 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(48,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( big_f @ SV4 ) )
        = $true )
      | ( ( ( big_h @ SV4 @ ( f @ SV4 ) )
          | ! [SY12: $i] :
              ( ~ ( big_g @ SY12 )
              | ~ ( big_h @ SV4 @ SY12 )
              | ( big_k @ SY12 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(49,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( big_f @ SV5 ) )
        = $true )
      | ( ( ~ ( big_j @ SV5 @ ( f @ SV5 ) )
          | ! [SY13: $i] :
              ( ~ ( big_g @ SY13 )
              | ~ ( big_h @ SV5 @ SY13 )
              | ( big_k @ SY13 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(50,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( big_l @ SV6 ) )
        = $true )
      | ( ( ~ ( big_k @ SV6 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[41]) ).

thf(51,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( big_h @ a @ SV7 ) )
        = $true )
      | ( ( big_l @ SV7 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[42]) ).

thf(52,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( big_g @ SV8 ) )
        = $true )
      | ( ( ~ ( big_h @ a @ SV8 )
          | ( big_j @ a @ SV8 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[43]) ).

thf(53,plain,
    ! [SV1: $i] :
      ( ( ( big_f @ SV1 )
        = $false )
      | ( ( big_g @ ( g @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(54,plain,
    ! [SV2: $i] :
      ( ( ( big_f @ SV2 )
        = $false )
      | ( ( big_h @ SV2 @ ( g @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(55,plain,
    ! [SV3: $i] :
      ( ( ( big_f @ SV3 )
        = $false )
      | ( ( ( big_g @ ( f @ SV3 ) )
          | ! [SY11: $i] :
              ( ~ ( big_g @ SY11 )
              | ~ ( big_h @ SV3 @ SY11 )
              | ( big_k @ SY11 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(56,plain,
    ! [SV4: $i] :
      ( ( ( big_f @ SV4 )
        = $false )
      | ( ( ( big_h @ SV4 @ ( f @ SV4 ) )
          | ! [SY12: $i] :
              ( ~ ( big_g @ SY12 )
              | ~ ( big_h @ SV4 @ SY12 )
              | ( big_k @ SY12 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(57,plain,
    ! [SV5: $i] :
      ( ( ( big_f @ SV5 )
        = $false )
      | ( ( ~ ( big_j @ SV5 @ ( f @ SV5 ) )
          | ! [SY13: $i] :
              ( ~ ( big_g @ SY13 )
              | ~ ( big_h @ SV5 @ SY13 )
              | ( big_k @ SY13 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(58,plain,
    ! [SV6: $i] :
      ( ( ( big_l @ SV6 )
        = $false )
      | ( ( ~ ( big_k @ SV6 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(59,plain,
    ! [SV7: $i] :
      ( ( ( big_h @ a @ SV7 )
        = $false )
      | ( ( big_l @ SV7 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(60,plain,
    ! [SV8: $i] :
      ( ( ( big_g @ SV8 )
        = $false )
      | ( ( ~ ( big_h @ a @ SV8 )
          | ( big_j @ a @ SV8 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(61,plain,
    ! [SV3: $i] :
      ( ( ( big_g @ ( f @ SV3 ) )
        = $true )
      | ( ( ! [SY11: $i] :
              ( ~ ( big_g @ SY11 )
              | ~ ( big_h @ SV3 @ SY11 )
              | ( big_k @ SY11 ) ) )
        = $true )
      | ( ( big_f @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[55]) ).

thf(62,plain,
    ! [SV4: $i] :
      ( ( ( big_h @ SV4 @ ( f @ SV4 ) )
        = $true )
      | ( ( ! [SY12: $i] :
              ( ~ ( big_g @ SY12 )
              | ~ ( big_h @ SV4 @ SY12 )
              | ( big_k @ SY12 ) ) )
        = $true )
      | ( ( big_f @ SV4 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[56]) ).

thf(63,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( big_j @ SV5 @ ( f @ SV5 ) ) )
        = $true )
      | ( ( ! [SY13: $i] :
              ( ~ ( big_g @ SY13 )
              | ~ ( big_h @ SV5 @ SY13 )
              | ( big_k @ SY13 ) ) )
        = $true )
      | ( ( big_f @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[57]) ).

thf(64,plain,
    ! [SV6: $i] :
      ( ( ( big_k @ SV6 )
        = $false )
      | ( ( big_l @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[58]) ).

thf(65,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( big_h @ a @ SV8 ) )
        = $true )
      | ( ( big_j @ a @ SV8 )
        = $true )
      | ( ( big_g @ SV8 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[60]) ).

thf(66,plain,
    ! [SV3: $i,SV9: $i] :
      ( ( ( ~ ( big_g @ SV9 )
          | ~ ( big_h @ SV3 @ SV9 )
          | ( big_k @ SV9 ) )
        = $true )
      | ( ( big_g @ ( f @ SV3 ) )
        = $true )
      | ( ( big_f @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(67,plain,
    ! [SV4: $i,SV10: $i] :
      ( ( ( ~ ( big_g @ SV10 )
          | ~ ( big_h @ SV4 @ SV10 )
          | ( big_k @ SV10 ) )
        = $true )
      | ( ( big_h @ SV4 @ ( f @ SV4 ) )
        = $true )
      | ( ( big_f @ SV4 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(68,plain,
    ! [SV5: $i] :
      ( ( ( big_j @ SV5 @ ( f @ SV5 ) )
        = $false )
      | ( ( ! [SY13: $i] :
              ( ~ ( big_g @ SY13 )
              | ~ ( big_h @ SV5 @ SY13 )
              | ( big_k @ SY13 ) ) )
        = $true )
      | ( ( big_f @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(69,plain,
    ! [SV8: $i] :
      ( ( ( big_h @ a @ SV8 )
        = $false )
      | ( ( big_j @ a @ SV8 )
        = $true )
      | ( ( big_g @ SV8 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(70,plain,
    ! [SV3: $i,SV9: $i] :
      ( ( ( ~ ( big_g @ SV9 ) )
        = $true )
      | ( ( ~ ( big_h @ SV3 @ SV9 )
          | ( big_k @ SV9 ) )
        = $true )
      | ( ( big_g @ ( f @ SV3 ) )
        = $true )
      | ( ( big_f @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(71,plain,
    ! [SV4: $i,SV10: $i] :
      ( ( ( ~ ( big_g @ SV10 ) )
        = $true )
      | ( ( ~ ( big_h @ SV4 @ SV10 )
          | ( big_k @ SV10 ) )
        = $true )
      | ( ( big_h @ SV4 @ ( f @ SV4 ) )
        = $true )
      | ( ( big_f @ SV4 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[67]) ).

thf(72,plain,
    ! [SV5: $i,SV11: $i] :
      ( ( ( ~ ( big_g @ SV11 )
          | ~ ( big_h @ SV5 @ SV11 )
          | ( big_k @ SV11 ) )
        = $true )
      | ( ( big_j @ SV5 @ ( f @ SV5 ) )
        = $false )
      | ( ( big_f @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(73,plain,
    ! [SV3: $i,SV9: $i] :
      ( ( ( big_g @ SV9 )
        = $false )
      | ( ( ~ ( big_h @ SV3 @ SV9 )
          | ( big_k @ SV9 ) )
        = $true )
      | ( ( big_g @ ( f @ SV3 ) )
        = $true )
      | ( ( big_f @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(74,plain,
    ! [SV4: $i,SV10: $i] :
      ( ( ( big_g @ SV10 )
        = $false )
      | ( ( ~ ( big_h @ SV4 @ SV10 )
          | ( big_k @ SV10 ) )
        = $true )
      | ( ( big_h @ SV4 @ ( f @ SV4 ) )
        = $true )
      | ( ( big_f @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(75,plain,
    ! [SV5: $i,SV11: $i] :
      ( ( ( ~ ( big_g @ SV11 ) )
        = $true )
      | ( ( ~ ( big_h @ SV5 @ SV11 )
          | ( big_k @ SV11 ) )
        = $true )
      | ( ( big_j @ SV5 @ ( f @ SV5 ) )
        = $false )
      | ( ( big_f @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[72]) ).

thf(76,plain,
    ! [SV9: $i,SV3: $i] :
      ( ( ( ~ ( big_h @ SV3 @ SV9 ) )
        = $true )
      | ( ( big_k @ SV9 )
        = $true )
      | ( ( big_g @ SV9 )
        = $false )
      | ( ( big_g @ ( f @ SV3 ) )
        = $true )
      | ( ( big_f @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[73]) ).

thf(77,plain,
    ! [SV10: $i,SV4: $i] :
      ( ( ( ~ ( big_h @ SV4 @ SV10 ) )
        = $true )
      | ( ( big_k @ SV10 )
        = $true )
      | ( ( big_g @ SV10 )
        = $false )
      | ( ( big_h @ SV4 @ ( f @ SV4 ) )
        = $true )
      | ( ( big_f @ SV4 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[74]) ).

thf(78,plain,
    ! [SV5: $i,SV11: $i] :
      ( ( ( big_g @ SV11 )
        = $false )
      | ( ( ~ ( big_h @ SV5 @ SV11 )
          | ( big_k @ SV11 ) )
        = $true )
      | ( ( big_j @ SV5 @ ( f @ SV5 ) )
        = $false )
      | ( ( big_f @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[75]) ).

thf(79,plain,
    ! [SV9: $i,SV3: $i] :
      ( ( ( big_h @ SV3 @ SV9 )
        = $false )
      | ( ( big_k @ SV9 )
        = $true )
      | ( ( big_g @ SV9 )
        = $false )
      | ( ( big_g @ ( f @ SV3 ) )
        = $true )
      | ( ( big_f @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(80,plain,
    ! [SV10: $i,SV4: $i] :
      ( ( ( big_h @ SV4 @ SV10 )
        = $false )
      | ( ( big_k @ SV10 )
        = $true )
      | ( ( big_g @ SV10 )
        = $false )
      | ( ( big_h @ SV4 @ ( f @ SV4 ) )
        = $true )
      | ( ( big_f @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[77]) ).

thf(81,plain,
    ! [SV11: $i,SV5: $i] :
      ( ( ( ~ ( big_h @ SV5 @ SV11 ) )
        = $true )
      | ( ( big_k @ SV11 )
        = $true )
      | ( ( big_g @ SV11 )
        = $false )
      | ( ( big_j @ SV5 @ ( f @ SV5 ) )
        = $false )
      | ( ( big_f @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[78]) ).

thf(82,plain,
    ! [SV11: $i,SV5: $i] :
      ( ( ( big_h @ SV5 @ SV11 )
        = $false )
      | ( ( big_k @ SV11 )
        = $true )
      | ( ( big_g @ SV11 )
        = $false )
      | ( ( big_j @ SV5 @ ( f @ SV5 ) )
        = $false )
      | ( ( big_f @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[81]) ).

thf(83,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[32,82,80,79,69,64,59,54,53,44]) ).

thf(84,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN069-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 20:24:19 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  
% 0.14/0.35   No.of.Axioms: 9
% 0.14/0.35  
% 0.14/0.35   Length.of.Defs: 0
% 0.14/0.35  
% 0.14/0.35   Contains.Choice.Funs: false
% 0.21/0.35  (rf:0,axioms:9,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:11,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.21/0.40  
% 0.21/0.40  ********************************
% 0.21/0.40  *   All subproblems solved!    *
% 0.21/0.40  ********************************
% 0.21/0.40  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,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:83,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.40  
% 0.21/0.40  %**** Beginning of derivation protocol ****
% 0.21/0.40  % SZS output start CNFRefutation
% See solution above
% 0.21/0.40  
% 0.21/0.40  %**** End of derivation protocol ****
% 0.21/0.40  %**** no. of clauses in derivation: 84 ****
% 0.21/0.40  %**** clause counter: 83 ****
% 0.21/0.40  
% 0.21/0.40  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,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:83,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------