TSTP Solution File: KLE089+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : KLE089+1 : TPTP v6.4.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n083.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.75MB
% OS       : Linux 3.10.0-327.36.3.el7.x86_64
% CPULimit : 300s
% DateTime : Tue Jan 17 18:03:38 EST 2017

% Result   : Theorem 0.06s
% Output   : CNFRefutation 0.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   32
% Syntax   : Number of formulae    :  133 ( 116 unt;  11 typ;   0 def)
%            Number of atoms       :  366 ( 238 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :  784 (  39   ~;  24   |;   4   &; 709   @)
%                                         (   2 <=>;   0  =>;   6  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg; 709 nst)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :  201 (   0   ^ 201   !;   0   ?; 201   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_addition,type,
    addition: $i > $i > $i ).

thf(tp_antidomain,type,
    antidomain: $i > $i ).

thf(tp_coantidomain,type,
    coantidomain: $i > $i ).

thf(tp_codomain,type,
    codomain: $i > $i ).

thf(tp_domain,type,
    domain: $i > $i ).

thf(tp_leq,type,
    leq: $i > $i > $o ).

thf(tp_multiplication,type,
    multiplication: $i > $i > $i ).

thf(tp_one,type,
    one: $i ).

thf(tp_sK1_X0,type,
    sK1_X0: $i ).

thf(tp_sK2_SY34,type,
    sK2_SY34: $i ).

thf(tp_zero,type,
    zero: $i ).

thf(1,axiom,
    ! [X0: $i] :
      ( ( codomain @ X0 )
      = ( coantidomain @ ( coantidomain @ X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).

thf(2,axiom,
    ! [X0: $i] :
      ( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
      = one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).

thf(3,axiom,
    ! [X0: $i,X1: $i] :
      ( ( addition @ ( coantidomain @ ( multiplication @ X0 @ X1 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) )
      = ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain2) ).

thf(4,axiom,
    ! [X0: $i] :
      ( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).

thf(5,axiom,
    ! [X0: $i] :
      ( ( domain @ X0 )
      = ( antidomain @ ( antidomain @ X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).

thf(6,axiom,
    ! [X0: $i] :
      ( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
      = one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).

thf(7,axiom,
    ! [X0: $i,X1: $i] :
      ( ( addition @ ( antidomain @ ( multiplication @ X0 @ X1 ) ) @ ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) )
      = ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).

thf(8,axiom,
    ! [X0: $i] :
      ( ( multiplication @ ( antidomain @ X0 ) @ X0 )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( leq @ A @ B )
    <=> ( ( addition @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( multiplication @ zero @ A )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( multiplication @ A @ zero )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( multiplication @ ( addition @ A @ B ) @ C )
      = ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( multiplication @ A @ ( addition @ B @ C ) )
      = ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( multiplication @ one @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( multiplication @ A @ one )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).

thf(16,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( multiplication @ A @ ( multiplication @ B @ C ) )
      = ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( addition @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( addition @ A @ zero )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( addition @ A @ ( addition @ B @ C ) )
      = ( addition @ ( addition @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( addition @ A @ B )
      = ( addition @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).

thf(21,conjecture,
    ! [X0: $i,X1: $i] :
      ( ( ( multiplication @ ( domain @ X0 ) @ X1 )
        = zero )
     <= ( ( addition @ ( domain @ X0 ) @ ( antidomain @ X1 ) )
        = ( antidomain @ X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

thf(22,negated_conjecture,
    ( ( ! [X0: $i,X1: $i] :
          ( ( ( multiplication @ ( domain @ X0 ) @ X1 )
            = zero )
         <= ( ( addition @ ( domain @ X0 ) @ ( antidomain @ X1 ) )
            = ( antidomain @ X1 ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[21]) ).

thf(23,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( ( multiplication @ ( domain @ X0 ) @ X1 )
            = zero )
         <= ( ( addition @ ( domain @ X0 ) @ ( antidomain @ X1 ) )
            = ( antidomain @ X1 ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(24,plain,
    ( ( ! [X0: $i] :
          ( ( codomain @ X0 )
          = ( coantidomain @ ( coantidomain @ X0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(25,plain,
    ( ( ! [X0: $i] :
          ( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
          = one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(26,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( addition @ ( coantidomain @ ( multiplication @ X0 @ X1 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) )
          = ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(27,plain,
    ( ( ! [X0: $i] :
          ( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(28,plain,
    ( ( ! [X0: $i] :
          ( ( domain @ X0 )
          = ( antidomain @ ( antidomain @ X0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(29,plain,
    ( ( ! [X0: $i] :
          ( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
          = one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(30,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( addition @ ( antidomain @ ( multiplication @ X0 @ X1 ) ) @ ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) )
          = ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(31,plain,
    ( ( ! [X0: $i] :
          ( ( multiplication @ ( antidomain @ X0 ) @ X0 )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(32,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( leq @ A @ B )
        <=> ( ( addition @ A @ B )
            = B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(33,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ zero @ A )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(34,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ A @ zero )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(35,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ ( addition @ A @ B ) @ C )
          = ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(36,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( addition @ B @ C ) )
          = ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(37,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ one @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(38,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ A @ one )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(39,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( multiplication @ B @ C ) )
          = ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(40,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(41,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ zero )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(42,plain,
    ( ( ! [C: $i,B: $i,A: $i] :
          ( ( addition @ A @ ( addition @ B @ C ) )
          = ( addition @ ( addition @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(43,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( addition @ A @ B )
          = ( addition @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(44,plain,
    ( ( ! [SY34: $i] :
          ( ( ( multiplication @ ( domain @ sK1_X0 ) @ SY34 )
            = zero )
         <= ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ SY34 ) )
            = ( antidomain @ SY34 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[23]) ).

thf(45,plain,
    ( ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
        = zero )
     <= ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
        = ( antidomain @ sK2_SY34 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[44]) ).

thf(46,plain,
    ( ( ~ ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
            = zero )
         <= ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
            = ( antidomain @ sK2_SY34 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[45]) ).

thf(47,plain,
    ( ( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
        = ( antidomain @ sK2_SY34 ) )
      & ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
       != zero ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[46]) ).

thf(48,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( addition @ A @ B )
           != B )
          | ( leq @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ~ ( leq @ A @ B )
          | ( ( addition @ A @ B )
            = B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[32]) ).

thf(49,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( addition @ A @ B )
          = ( addition @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(50,plain,
    ( ( ! [C: $i,B: $i,A: $i] :
          ( ( addition @ A @ ( addition @ B @ C ) )
          = ( addition @ ( addition @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(51,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ zero )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(52,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(53,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( multiplication @ B @ C ) )
          = ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(54,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ A @ one )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(55,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ one @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(56,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( addition @ B @ C ) )
          = ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(57,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ ( addition @ A @ B ) @ C )
          = ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(58,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ A @ zero )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(59,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ zero @ A )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(60,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( addition @ A @ B )
           != B )
          | ( leq @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ~ ( leq @ A @ B )
          | ( ( addition @ A @ B )
            = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[48]) ).

thf(61,plain,
    ( ( ! [X0: $i] :
          ( ( multiplication @ ( antidomain @ X0 ) @ X0 )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(62,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( addition @ ( antidomain @ ( multiplication @ X0 @ X1 ) ) @ ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) )
          = ( antidomain @ ( multiplication @ X0 @ ( antidomain @ ( antidomain @ X1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(63,plain,
    ( ( ! [X0: $i] :
          ( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
          = one ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(64,plain,
    ( ( ! [X0: $i] :
          ( ( domain @ X0 )
          = ( antidomain @ ( antidomain @ X0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(65,plain,
    ( ( ! [X0: $i] :
          ( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(66,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( addition @ ( coantidomain @ ( multiplication @ X0 @ X1 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) )
          = ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ X0 ) ) @ X1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(67,plain,
    ( ( ! [X0: $i] :
          ( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
          = one ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(68,plain,
    ( ( ! [X0: $i] :
          ( ( codomain @ X0 )
          = ( coantidomain @ ( coantidomain @ X0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(69,plain,
    ( ( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
        = ( antidomain @ sK2_SY34 ) )
      & ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
       != zero ) )
    = $true ),
    inference(copy,[status(thm)],[47]) ).

thf(70,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( addition @ SX0 @ SX1 )
                 != SX1 )
                | ( leq @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( leq @ SX0 @ SX1 )
                | ( ( addition @ SX0 @ SX1 )
                  = SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[60]) ).

thf(71,plain,
    ( ( ~ ( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
           != ( antidomain @ sK2_SY34 ) )
          | ~ ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
               != zero ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[69]) ).

thf(72,plain,
    ! [SV1: $i] :
      ( ( ! [SY35: $i] :
            ( ( addition @ SV1 @ SY35 )
            = ( addition @ SY35 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(73,plain,
    ! [SV2: $i] :
      ( ( ! [SY36: $i,SY37: $i] :
            ( ( addition @ SY37 @ ( addition @ SY36 @ SV2 ) )
            = ( addition @ ( addition @ SY37 @ SY36 ) @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(74,plain,
    ! [SV3: $i] :
      ( ( ( addition @ SV3 @ zero )
        = SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(75,plain,
    ! [SV4: $i] :
      ( ( ( addition @ SV4 @ SV4 )
        = SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(76,plain,
    ! [SV5: $i] :
      ( ( ! [SY38: $i,SY39: $i] :
            ( ( multiplication @ SV5 @ ( multiplication @ SY38 @ SY39 ) )
            = ( multiplication @ ( multiplication @ SV5 @ SY38 ) @ SY39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(77,plain,
    ! [SV6: $i] :
      ( ( ( multiplication @ SV6 @ one )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(78,plain,
    ! [SV7: $i] :
      ( ( ( multiplication @ one @ SV7 )
        = SV7 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(79,plain,
    ! [SV8: $i] :
      ( ( ! [SY40: $i,SY41: $i] :
            ( ( multiplication @ SV8 @ ( addition @ SY40 @ SY41 ) )
            = ( addition @ ( multiplication @ SV8 @ SY40 ) @ ( multiplication @ SV8 @ SY41 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(80,plain,
    ! [SV9: $i] :
      ( ( ! [SY42: $i,SY43: $i] :
            ( ( multiplication @ ( addition @ SV9 @ SY42 ) @ SY43 )
            = ( addition @ ( multiplication @ SV9 @ SY43 ) @ ( multiplication @ SY42 @ SY43 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(81,plain,
    ! [SV10: $i] :
      ( ( ( multiplication @ SV10 @ zero )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(82,plain,
    ! [SV11: $i] :
      ( ( ( multiplication @ zero @ SV11 )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(83,plain,
    ! [SV12: $i] :
      ( ( ( multiplication @ ( antidomain @ SV12 ) @ SV12 )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(84,plain,
    ! [SV13: $i] :
      ( ( ! [SY44: $i] :
            ( ( addition @ ( antidomain @ ( multiplication @ SV13 @ SY44 ) ) @ ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SY44 ) ) ) ) )
            = ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SY44 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(85,plain,
    ! [SV14: $i] :
      ( ( ( addition @ ( antidomain @ ( antidomain @ SV14 ) ) @ ( antidomain @ SV14 ) )
        = one )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(86,plain,
    ! [SV15: $i] :
      ( ( ( domain @ SV15 )
        = ( antidomain @ ( antidomain @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(87,plain,
    ! [SV16: $i] :
      ( ( ( multiplication @ SV16 @ ( coantidomain @ SV16 ) )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(88,plain,
    ! [SV17: $i] :
      ( ( ! [SY45: $i] :
            ( ( addition @ ( coantidomain @ ( multiplication @ SV17 @ SY45 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SY45 ) ) )
            = ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SY45 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(89,plain,
    ! [SV18: $i] :
      ( ( ( addition @ ( coantidomain @ ( coantidomain @ SV18 ) ) @ ( coantidomain @ SV18 ) )
        = one )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(90,plain,
    ! [SV19: $i] :
      ( ( ( codomain @ SV19 )
        = ( coantidomain @ ( coantidomain @ SV19 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(91,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( addition @ SX0 @ SX1 )
             != SX1 )
            | ( leq @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( leq @ SX0 @ SX1 )
            | ( ( addition @ SX0 @ SX1 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(92,plain,
    ( ( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
       != ( antidomain @ sK2_SY34 ) )
      | ~ ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
           != zero ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(93,plain,
    ! [SV20: $i,SV1: $i] :
      ( ( ( addition @ SV1 @ SV20 )
        = ( addition @ SV20 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(94,plain,
    ! [SV2: $i,SV21: $i] :
      ( ( ! [SY46: $i] :
            ( ( addition @ SY46 @ ( addition @ SV21 @ SV2 ) )
            = ( addition @ ( addition @ SY46 @ SV21 ) @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(95,plain,
    ! [SV22: $i,SV5: $i] :
      ( ( ! [SY47: $i] :
            ( ( multiplication @ SV5 @ ( multiplication @ SV22 @ SY47 ) )
            = ( multiplication @ ( multiplication @ SV5 @ SV22 ) @ SY47 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(96,plain,
    ! [SV23: $i,SV8: $i] :
      ( ( ! [SY48: $i] :
            ( ( multiplication @ SV8 @ ( addition @ SV23 @ SY48 ) )
            = ( addition @ ( multiplication @ SV8 @ SV23 ) @ ( multiplication @ SV8 @ SY48 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(97,plain,
    ! [SV24: $i,SV9: $i] :
      ( ( ! [SY49: $i] :
            ( ( multiplication @ ( addition @ SV9 @ SV24 ) @ SY49 )
            = ( addition @ ( multiplication @ SV9 @ SY49 ) @ ( multiplication @ SV24 @ SY49 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(98,plain,
    ! [SV25: $i,SV13: $i] :
      ( ( ( addition @ ( antidomain @ ( multiplication @ SV13 @ SV25 ) ) @ ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SV25 ) ) ) ) )
        = ( antidomain @ ( multiplication @ SV13 @ ( antidomain @ ( antidomain @ SV25 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(99,plain,
    ! [SV26: $i,SV17: $i] :
      ( ( ( addition @ ( coantidomain @ ( multiplication @ SV17 @ SV26 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SV26 ) ) )
        = ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV17 ) ) @ SV26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(100,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( addition @ SX0 @ SX1 )
             != SX1 )
            | ( leq @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[91]) ).

thf(101,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( leq @ SX0 @ SX1 )
            | ( ( addition @ SX0 @ SX1 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[91]) ).

thf(102,plain,
    ( ( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
       != ( antidomain @ sK2_SY34 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[92]) ).

thf(103,plain,
    ( ( ~ ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
           != zero ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[92]) ).

thf(104,plain,
    ! [SV2: $i,SV21: $i,SV27: $i] :
      ( ( ( addition @ SV27 @ ( addition @ SV21 @ SV2 ) )
        = ( addition @ ( addition @ SV27 @ SV21 ) @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(105,plain,
    ! [SV28: $i,SV22: $i,SV5: $i] :
      ( ( ( multiplication @ SV5 @ ( multiplication @ SV22 @ SV28 ) )
        = ( multiplication @ ( multiplication @ SV5 @ SV22 ) @ SV28 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[95]) ).

thf(106,plain,
    ! [SV29: $i,SV23: $i,SV8: $i] :
      ( ( ( multiplication @ SV8 @ ( addition @ SV23 @ SV29 ) )
        = ( addition @ ( multiplication @ SV8 @ SV23 ) @ ( multiplication @ SV8 @ SV29 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(107,plain,
    ! [SV30: $i,SV24: $i,SV9: $i] :
      ( ( ( multiplication @ ( addition @ SV9 @ SV24 ) @ SV30 )
        = ( addition @ ( multiplication @ SV9 @ SV30 ) @ ( multiplication @ SV24 @ SV30 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(108,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( addition @ SX0 @ SX1 )
           != SX1 )
          | ( leq @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[100]) ).

thf(109,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( leq @ SX0 @ SX1 )
          | ( ( addition @ SX0 @ SX1 )
            = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[101]) ).

thf(110,plain,
    ( ( ( addition @ ( domain @ sK1_X0 ) @ ( antidomain @ sK2_SY34 ) )
      = ( antidomain @ sK2_SY34 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[102]) ).

thf(111,plain,
    ( ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
       != zero ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[103]) ).

thf(112,plain,
    ! [SV31: $i] :
      ( ( ! [SY50: $i] :
            ( ( ( addition @ SV31 @ SY50 )
             != SY50 )
            | ( leq @ SV31 @ SY50 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(113,plain,
    ! [SV32: $i] :
      ( ( ! [SY51: $i] :
            ( ~ ( leq @ SV32 @ SY51 )
            | ( ( addition @ SV32 @ SY51 )
              = SY51 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(114,plain,
    ( ( ( multiplication @ ( domain @ sK1_X0 ) @ sK2_SY34 )
      = zero )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(115,plain,
    ! [SV33: $i,SV31: $i] :
      ( ( ( ( addition @ SV31 @ SV33 )
         != SV33 )
        | ( leq @ SV31 @ SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(116,plain,
    ! [SV34: $i,SV32: $i] :
      ( ( ~ ( leq @ SV32 @ SV34 )
        | ( ( addition @ SV32 @ SV34 )
          = SV34 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(117,plain,
    ! [SV33: $i,SV31: $i] :
      ( ( ( ( ( addition @ SV31 @ SV33 )
           != SV33 ) )
        = $true )
      | ( ( leq @ SV31 @ SV33 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[115]) ).

thf(118,plain,
    ! [SV34: $i,SV32: $i] :
      ( ( ( ~ ( leq @ SV32 @ SV34 ) )
        = $true )
      | ( ( ( addition @ SV32 @ SV34 )
          = SV34 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[116]) ).

thf(119,plain,
    ! [SV33: $i,SV31: $i] :
      ( ( ( ( addition @ SV31 @ SV33 )
          = SV33 )
        = $false )
      | ( ( leq @ SV31 @ SV33 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[117]) ).

thf(120,plain,
    ! [SV34: $i,SV32: $i] :
      ( ( ( leq @ SV32 @ SV34 )
        = $false )
      | ( ( ( addition @ SV32 @ SV34 )
          = SV34 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[118]) ).

thf(121,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[74,120,119,114,110,107,106,105,104,99,98,93,90,89,87,86,85,83,82,81,78,77,75]) ).

thf(122,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[121]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KLE089+1 : TPTP v6.4.0. Released v4.0.0.
% 0.00/0.04  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.03/0.23  % Computer : n083.star.cs.uiowa.edu
% 0.03/0.23  % Model    : x86_64 x86_64
% 0.03/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23  % Memory   : 32218.75MB
% 0.03/0.23  % OS       : Linux 3.10.0-327.36.3.el7.x86_64
% 0.03/0.23  % CPULimit : 300
% 0.03/0.23  % DateTime : Sat Jan 14 16:34:33 CST 2017
% 0.03/0.23  % CPUTime  : 
% 0.03/0.24  
% 0.03/0.24   No.of.Axioms: 20
% 0.03/0.24  
% 0.03/0.24   Length.of.Defs: 0
% 0.03/0.24  
% 0.03/0.24   Contains.Choice.Funs: false
% 0.03/0.25  .
% 0.03/0.25  (rf:0,axioms:20,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:22,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.06/0.65  
% 0.06/0.65  ********************************
% 0.06/0.65  *   All subproblems solved!    *
% 0.06/0.65  ********************************
% 0.06/0.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:121,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.65  
% 0.06/0.65  %**** Beginning of derivation protocol ****
% 0.06/0.65  % SZS output start CNFRefutation
% See solution above
% 0.06/0.65  % SZS output end CNFRefutation
% 0.06/0.65  
% 0.06/0.65  %**** End of derivation protocol ****
% 0.06/0.65  %**** no. of clauses in derivation: 122 ****
% 0.06/0.65  %**** clause counter: 121 ****
% 0.06/0.65  
% 0.06/0.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:121,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------