TSTP Solution File: KLE090-10 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n021.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 02:11:18 EDT 2022

% Result   : Unsatisfiable 26.03s 26.29s
% Output   : CNFRefutation 26.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   40
% Syntax   : Number of formulae    :  139 ( 125 unt;  14 typ;   0 def)
%            Number of atoms       :  321 ( 215 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  687 (   6   ~;   0   |;   0   &; 681   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   7 con; 0-4 aty)
%            Number of variables   :  206 (   0   ^ 206   !;   0   ?; 206   :)

% 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_ifeq,type,
    ifeq: $i > $i > $i > $i > $i ).

thf(tp_ifeq2,type,
    ifeq2: $i > $i > $i > $i > $i ).

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

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

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

thf(tp_sK1_goals_X1,type,
    sK1_goals_X1: $i ).

thf(tp_sK2_goals_X0,type,
    sK2_goals_X0: $i ).

thf(tp_true,type,
    true: $i ).

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

thf(1,axiom,
    ! [X0: $i] :
      ( ( codomain @ X0 )
      = ( coantidomain @ ( coantidomain @ X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain4) ).

thf(2,axiom,
    ! [X0: $i] :
      ( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
      = one ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',codomain2) ).

thf(4,axiom,
    ! [X0: $i] :
      ( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
      = zero ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain1) ).

thf(5,axiom,
    ! [X0: $i] :
      ( ( domain @ X0 )
      = ( antidomain @ ( antidomain @ X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).

thf(6,axiom,
    ! [X0: $i] :
      ( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
      = one ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',domain2) ).

thf(8,axiom,
    ! [X0: $i] :
      ( ( multiplication @ ( antidomain @ X0 ) @ X0 )
      = zero ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( ifeq2 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
      = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( ifeq @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order_1) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( multiplication @ zero @ A )
      = zero ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( multiplication @ A @ zero )
      = zero ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( multiplication @ ( addition @ A @ B ) @ C )
      = ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( multiplication @ A @ ( addition @ B @ C ) )
      = ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( multiplication @ one @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( multiplication @ A @ one )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( multiplication @ A @ ( multiplication @ B @ C ) )
      = ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( addition @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( addition @ A @ zero )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( addition @ A @ ( addition @ B @ C ) )
      = ( addition @ ( addition @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( addition @ A @ B )
      = ( addition @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ifeq @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ifeq2 @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).

thf(24,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(25,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[24]) ).

thf(26,negated_conjecture,
    ( addition @ ( antidomain @ sK1_goals_X1 ) @ ( antidomain @ sK2_goals_X0 ) )
 != ( antidomain @ sK2_goals_X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_1) ).

thf(27,negated_conjecture,
    ( ( addition @ sK2_goals_X0 @ sK1_goals_X1 )
    = sK1_goals_X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

thf(28,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[25]) ).

thf(29,plain,
    ( ( ! [X0: $i] :
          ( ( codomain @ X0 )
          = ( coantidomain @ ( coantidomain @ X0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(30,plain,
    ( ( ! [X0: $i] :
          ( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
          = one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(31,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(32,plain,
    ( ( ! [X0: $i] :
          ( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(33,plain,
    ( ( ! [X0: $i] :
          ( ( domain @ X0 )
          = ( antidomain @ ( antidomain @ X0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(34,plain,
    ( ( ! [X0: $i] :
          ( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
          = one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(35,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(36,plain,
    ( ( ! [X0: $i] :
          ( ( multiplication @ ( antidomain @ X0 ) @ X0 )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(37,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ifeq2 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(38,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ifeq @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
          = B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(39,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ zero @ A )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(40,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ A @ zero )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(41,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)],[13]) ).

thf(42,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)],[14]) ).

thf(43,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ one @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(44,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ A @ one )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(45,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( multiplication @ B @ C ) )
          = ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(46,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(47,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ zero )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(48,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( addition @ A @ ( addition @ B @ C ) )
          = ( addition @ ( addition @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(49,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( addition @ A @ B )
          = ( addition @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(50,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ifeq @ A @ A @ B @ C )
          = B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(51,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ifeq2 @ A @ A @ B @ C )
          = B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(52,plain,
    ( ( ( ( addition @ ( antidomain @ sK1_goals_X1 ) @ ( antidomain @ sK2_goals_X0 ) )
       != ( antidomain @ sK2_goals_X0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(53,plain,
    ( ( ( addition @ sK2_goals_X0 @ sK1_goals_X1 )
      = sK1_goals_X1 )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(54,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[28]) ).

thf(55,plain,
    ( ( ( ( addition @ ( antidomain @ sK1_goals_X1 ) @ ( antidomain @ sK2_goals_X0 ) )
       != ( antidomain @ sK2_goals_X0 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[52]) ).

thf(56,plain,
    ( ( ( addition @ sK2_goals_X0 @ sK1_goals_X1 )
      = sK1_goals_X1 )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(57,plain,
    ( ( ( ( addition @ ( antidomain @ sK1_goals_X1 ) @ ( antidomain @ sK2_goals_X0 ) )
       != ( antidomain @ sK2_goals_X0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(58,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ifeq2 @ A @ A @ B @ C )
          = B ) )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(59,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ifeq @ A @ A @ B @ C )
          = B ) )
    = $true ),
    inference(copy,[status(thm)],[50]) ).

thf(60,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( addition @ A @ B )
          = ( addition @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[49]) ).

thf(61,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( addition @ A @ ( addition @ B @ C ) )
          = ( addition @ ( addition @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[48]) ).

thf(62,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ zero )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[47]) ).

thf(63,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(64,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( multiplication @ B @ C ) )
          = ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(65,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ A @ one )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(66,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ one @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(67,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( addition @ B @ C ) )
          = ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(68,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ ( addition @ A @ B ) @ C )
          = ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(69,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ A @ zero )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(70,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ zero @ A )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(71,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ifeq @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
          = B ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(72,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ifeq2 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(73,plain,
    ( ( ! [X0: $i] :
          ( ( multiplication @ ( antidomain @ X0 ) @ X0 )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(74,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)],[35]) ).

thf(75,plain,
    ( ( ! [X0: $i] :
          ( ( addition @ ( antidomain @ ( antidomain @ X0 ) ) @ ( antidomain @ X0 ) )
          = one ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(76,plain,
    ( ( ! [X0: $i] :
          ( ( domain @ X0 )
          = ( antidomain @ ( antidomain @ X0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(77,plain,
    ( ( ! [X0: $i] :
          ( ( multiplication @ X0 @ ( coantidomain @ X0 ) )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(78,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)],[31]) ).

thf(79,plain,
    ( ( ! [X0: $i] :
          ( ( addition @ ( coantidomain @ ( coantidomain @ X0 ) ) @ ( coantidomain @ X0 ) )
          = one ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(80,plain,
    ( ( ! [X0: $i] :
          ( ( codomain @ X0 )
          = ( coantidomain @ ( coantidomain @ X0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(81,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(82,plain,
    ( ( ( addition @ ( antidomain @ sK1_goals_X1 ) @ ( antidomain @ sK2_goals_X0 ) )
      = ( antidomain @ sK2_goals_X0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(83,plain,
    ! [SV1: $i] :
      ( ( ! [SY40: $i,SY41: $i] :
            ( ( ifeq2 @ SV1 @ SV1 @ SY40 @ SY41 )
            = SY40 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(84,plain,
    ! [SV2: $i] :
      ( ( ! [SY42: $i,SY43: $i] :
            ( ( ifeq @ SV2 @ SV2 @ SY42 @ SY43 )
            = SY42 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(85,plain,
    ! [SV3: $i] :
      ( ( ! [SY44: $i] :
            ( ( addition @ SV3 @ SY44 )
            = ( addition @ SY44 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(86,plain,
    ! [SV4: $i] :
      ( ( ! [SY45: $i,SY46: $i] :
            ( ( addition @ SV4 @ ( addition @ SY45 @ SY46 ) )
            = ( addition @ ( addition @ SV4 @ SY45 ) @ SY46 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(87,plain,
    ! [SV5: $i] :
      ( ( ( addition @ SV5 @ zero )
        = SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(88,plain,
    ! [SV6: $i] :
      ( ( ( addition @ SV6 @ SV6 )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(89,plain,
    ! [SV7: $i] :
      ( ( ! [SY47: $i,SY48: $i] :
            ( ( multiplication @ SV7 @ ( multiplication @ SY47 @ SY48 ) )
            = ( multiplication @ ( multiplication @ SV7 @ SY47 ) @ SY48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(90,plain,
    ! [SV8: $i] :
      ( ( ( multiplication @ SV8 @ one )
        = SV8 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(91,plain,
    ! [SV9: $i] :
      ( ( ( multiplication @ one @ SV9 )
        = SV9 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(92,plain,
    ! [SV10: $i] :
      ( ( ! [SY49: $i,SY50: $i] :
            ( ( multiplication @ SV10 @ ( addition @ SY49 @ SY50 ) )
            = ( addition @ ( multiplication @ SV10 @ SY49 ) @ ( multiplication @ SV10 @ SY50 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(93,plain,
    ! [SV11: $i] :
      ( ( ! [SY51: $i,SY52: $i] :
            ( ( multiplication @ ( addition @ SV11 @ SY51 ) @ SY52 )
            = ( addition @ ( multiplication @ SV11 @ SY52 ) @ ( multiplication @ SY51 @ SY52 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(94,plain,
    ! [SV12: $i] :
      ( ( ( multiplication @ SV12 @ zero )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(95,plain,
    ! [SV13: $i] :
      ( ( ( multiplication @ zero @ SV13 )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(96,plain,
    ! [SV14: $i] :
      ( ( ! [SY53: $i] :
            ( ( ifeq @ ( leq @ SV14 @ SY53 ) @ true @ ( addition @ SV14 @ SY53 ) @ SY53 )
            = SY53 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(97,plain,
    ! [SV15: $i] :
      ( ( ! [SY54: $i] :
            ( ( ifeq2 @ ( addition @ SV15 @ SY54 ) @ SY54 @ ( leq @ SV15 @ SY54 ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(98,plain,
    ! [SV16: $i] :
      ( ( ( multiplication @ ( antidomain @ SV16 ) @ SV16 )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(99,plain,
    ! [SV17: $i] :
      ( ( ! [SY55: $i] :
            ( ( addition @ ( antidomain @ ( multiplication @ SV17 @ SY55 ) ) @ ( antidomain @ ( multiplication @ SV17 @ ( antidomain @ ( antidomain @ SY55 ) ) ) ) )
            = ( antidomain @ ( multiplication @ SV17 @ ( antidomain @ ( antidomain @ SY55 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(100,plain,
    ! [SV18: $i] :
      ( ( ( addition @ ( antidomain @ ( antidomain @ SV18 ) ) @ ( antidomain @ SV18 ) )
        = one )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(101,plain,
    ! [SV19: $i] :
      ( ( ( domain @ SV19 )
        = ( antidomain @ ( antidomain @ SV19 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(102,plain,
    ! [SV20: $i] :
      ( ( ( multiplication @ SV20 @ ( coantidomain @ SV20 ) )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(103,plain,
    ! [SV21: $i] :
      ( ( ! [SY56: $i] :
            ( ( addition @ ( coantidomain @ ( multiplication @ SV21 @ SY56 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV21 ) ) @ SY56 ) ) )
            = ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV21 ) ) @ SY56 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(104,plain,
    ! [SV22: $i] :
      ( ( ( addition @ ( coantidomain @ ( coantidomain @ SV22 ) ) @ ( coantidomain @ SV22 ) )
        = one )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(105,plain,
    ! [SV23: $i] :
      ( ( ( codomain @ SV23 )
        = ( coantidomain @ ( coantidomain @ SV23 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(106,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[81]) ).

thf(107,plain,
    ! [SV24: $i,SV1: $i] :
      ( ( ! [SY57: $i] :
            ( ( ifeq2 @ SV1 @ SV1 @ SV24 @ SY57 )
            = SV24 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(108,plain,
    ! [SV25: $i,SV2: $i] :
      ( ( ! [SY58: $i] :
            ( ( ifeq @ SV2 @ SV2 @ SV25 @ SY58 )
            = SV25 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(109,plain,
    ! [SV26: $i,SV3: $i] :
      ( ( ( addition @ SV3 @ SV26 )
        = ( addition @ SV26 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(110,plain,
    ! [SV27: $i,SV4: $i] :
      ( ( ! [SY59: $i] :
            ( ( addition @ SV4 @ ( addition @ SV27 @ SY59 ) )
            = ( addition @ ( addition @ SV4 @ SV27 ) @ SY59 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(111,plain,
    ! [SV28: $i,SV7: $i] :
      ( ( ! [SY60: $i] :
            ( ( multiplication @ SV7 @ ( multiplication @ SV28 @ SY60 ) )
            = ( multiplication @ ( multiplication @ SV7 @ SV28 ) @ SY60 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(112,plain,
    ! [SV29: $i,SV10: $i] :
      ( ( ! [SY61: $i] :
            ( ( multiplication @ SV10 @ ( addition @ SV29 @ SY61 ) )
            = ( addition @ ( multiplication @ SV10 @ SV29 ) @ ( multiplication @ SV10 @ SY61 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(113,plain,
    ! [SV30: $i,SV11: $i] :
      ( ( ! [SY62: $i] :
            ( ( multiplication @ ( addition @ SV11 @ SV30 ) @ SY62 )
            = ( addition @ ( multiplication @ SV11 @ SY62 ) @ ( multiplication @ SV30 @ SY62 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(114,plain,
    ! [SV31: $i,SV14: $i] :
      ( ( ( ifeq @ ( leq @ SV14 @ SV31 ) @ true @ ( addition @ SV14 @ SV31 ) @ SV31 )
        = SV31 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(115,plain,
    ! [SV32: $i,SV15: $i] :
      ( ( ( ifeq2 @ ( addition @ SV15 @ SV32 ) @ SV32 @ ( leq @ SV15 @ SV32 ) @ true )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(116,plain,
    ! [SV33: $i,SV17: $i] :
      ( ( ( addition @ ( antidomain @ ( multiplication @ SV17 @ SV33 ) ) @ ( antidomain @ ( multiplication @ SV17 @ ( antidomain @ ( antidomain @ SV33 ) ) ) ) )
        = ( antidomain @ ( multiplication @ SV17 @ ( antidomain @ ( antidomain @ SV33 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[99]) ).

thf(117,plain,
    ! [SV34: $i,SV21: $i] :
      ( ( ( addition @ ( coantidomain @ ( multiplication @ SV21 @ SV34 ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV21 ) ) @ SV34 ) ) )
        = ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ SV21 ) ) @ SV34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[103]) ).

thf(118,plain,
    ! [SV35: $i,SV24: $i,SV1: $i] :
      ( ( ( ifeq2 @ SV1 @ SV1 @ SV24 @ SV35 )
        = SV24 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[107]) ).

thf(119,plain,
    ! [SV36: $i,SV25: $i,SV2: $i] :
      ( ( ( ifeq @ SV2 @ SV2 @ SV25 @ SV36 )
        = SV25 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(120,plain,
    ! [SV37: $i,SV27: $i,SV4: $i] :
      ( ( ( addition @ SV4 @ ( addition @ SV27 @ SV37 ) )
        = ( addition @ ( addition @ SV4 @ SV27 ) @ SV37 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[110]) ).

thf(121,plain,
    ! [SV38: $i,SV28: $i,SV7: $i] :
      ( ( ( multiplication @ SV7 @ ( multiplication @ SV28 @ SV38 ) )
        = ( multiplication @ ( multiplication @ SV7 @ SV28 ) @ SV38 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[111]) ).

thf(122,plain,
    ! [SV39: $i,SV29: $i,SV10: $i] :
      ( ( ( multiplication @ SV10 @ ( addition @ SV29 @ SV39 ) )
        = ( addition @ ( multiplication @ SV10 @ SV29 ) @ ( multiplication @ SV10 @ SV39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(123,plain,
    ! [SV40: $i,SV30: $i,SV11: $i] :
      ( ( ( multiplication @ ( addition @ SV11 @ SV30 ) @ SV40 )
        = ( addition @ ( multiplication @ SV11 @ SV40 ) @ ( multiplication @ SV30 @ SV40 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(124,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[56,123,122,121,120,119,118,117,116,115,114,109,106,105,104,102,101,100,98,95,94,91,90,88,87,82]) ).

thf(125,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[124]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Thu Jun 16 13:56:00 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.37  
% 0.13/0.37   No.of.Axioms: 25
% 0.13/0.37  
% 0.13/0.37   Length.of.Defs: 0
% 0.13/0.37  
% 0.13/0.37   Contains.Choice.Funs: false
% 0.13/0.37  .
% 0.13/0.38  (rf:0,axioms:25,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:27,loop_count:0,foatp_calls:0,translation:fof_full)......
% 26.03/26.29  
% 26.03/26.29  ********************************
% 26.03/26.29  *   All subproblems solved!    *
% 26.03/26.29  ********************************
% 26.03/26.29  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:124,loop_count:0,foatp_calls:1,translation:fof_full)
% 26.03/26.29  
% 26.03/26.29  %**** Beginning of derivation protocol ****
% 26.03/26.29  % SZS output start CNFRefutation
% See solution above
% 26.03/26.29  
% 26.03/26.29  %**** End of derivation protocol ****
% 26.03/26.29  %**** no. of clauses in derivation: 125 ****
% 26.03/26.29  %**** clause counter: 124 ****
% 26.03/26.29  
% 26.03/26.29  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:124,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------