TSTP Solution File: KLE137+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : KLE137+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n032.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 02:11:30 EDT 2022

% Result   : Theorem 21.71s 21.93s
% Output   : CNFRefutation 21.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  127 ( 105 unt;   8 typ;   0 def)
%            Number of atoms       :  390 ( 196 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  880 (  45   ~;  43   |;   2   &; 782   @)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  246 (   0   ^ 246   !;   0   ?; 246   :)

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

thf(tp_strong_iteration,type,
    strong_iteration: $i > $i ).

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

thf(1,axiom,
    ! [A: $i,B: $i] :
      ( ( leq @ A @ B )
    <=> ( ( addition @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

thf(2,axiom,
    ! [A: $i] :
      ( ( strong_iteration @ A )
      = ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',isolation) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
     => ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( strong_iteration @ A )
      = ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
     => ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction2) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
     => ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction1) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
      = ( star @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold2) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
      = ( star @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( multiplication @ zero @ A )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).

thf(10,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',distributivity2) ).

thf(11,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',distributivity1) ).

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

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

thf(14,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(15,axiom,
    ! [A: $i] :
      ( ( addition @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( addition @ A @ zero )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).

thf(17,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(18,axiom,
    ! [A: $i,B: $i] :
      ( ( addition @ A @ B )
      = ( addition @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).

thf(19,conjecture,
    ! [X0: $i] : ( leq @ X0 @ ( strong_iteration @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

thf(20,negated_conjecture,
    ( ( ! [X0: $i] : ( leq @ X0 @ ( strong_iteration @ one ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[19]) ).

thf(21,plain,
    ( ( ! [X0: $i] : ( leq @ X0 @ ( strong_iteration @ one ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(22,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( leq @ A @ B )
        <=> ( ( addition @ A @ B )
            = B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(23,plain,
    ( ( ! [A: $i] :
          ( ( strong_iteration @ A )
          = ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(24,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
         => ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(25,plain,
    ( ( ! [A: $i] :
          ( ( strong_iteration @ A )
          = ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(26,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
         => ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(27,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
         => ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(28,plain,
    ( ( ! [A: $i] :
          ( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
          = ( star @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(29,plain,
    ( ( ! [A: $i] :
          ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
          = ( star @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(30,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ zero @ A )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(31,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)],[10]) ).

thf(32,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)],[11]) ).

thf(33,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ one @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(34,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ A @ one )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(35,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( multiplication @ B @ C ) )
          = ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(36,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(37,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ zero )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(38,plain,
    ( ( ! [C: $i,B: $i,A: $i] :
          ( ( addition @ A @ ( addition @ B @ C ) )
          = ( addition @ ( addition @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(39,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( addition @ A @ B )
          = ( addition @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(40,plain,
    ( ( leq @ sK1_X0 @ ( strong_iteration @ one ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[21]) ).

thf(41,plain,
    ( ( ~ ( leq @ sK1_X0 @ ( strong_iteration @ one ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[40]) ).

thf(42,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)],[22]) ).

thf(43,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
          | ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[24]) ).

thf(44,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
          | ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[26]) ).

thf(45,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
          | ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[27]) ).

thf(46,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( addition @ A @ B )
          = ( addition @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(47,plain,
    ( ( ! [C: $i,B: $i,A: $i] :
          ( ( addition @ A @ ( addition @ B @ C ) )
          = ( addition @ ( addition @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(48,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ zero )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(49,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(50,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( multiplication @ B @ C ) )
          = ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(51,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ A @ one )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(52,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ one @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(53,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( addition @ B @ C ) )
          = ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(54,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ ( addition @ A @ B ) @ C )
          = ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(55,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ zero @ A )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(56,plain,
    ( ( ! [A: $i] :
          ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
          = ( star @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(57,plain,
    ( ( ! [A: $i] :
          ( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
          = ( star @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(58,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
          | ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(59,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
          | ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(60,plain,
    ( ( ! [A: $i] :
          ( ( strong_iteration @ A )
          = ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(61,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
          | ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(62,plain,
    ( ( ! [A: $i] :
          ( ( strong_iteration @ A )
          = ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(63,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)],[42]) ).

thf(64,plain,
    ( ( ~ ( leq @ sK1_X0 @ ( strong_iteration @ one ) ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(65,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)],[63]) ).

thf(66,plain,
    ! [SV1: $i] :
      ( ( ! [SY35: $i] :
            ( ( addition @ SV1 @ SY35 )
            = ( addition @ SY35 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(67,plain,
    ! [SV2: $i] :
      ( ( ! [SY36: $i,SY37: $i] :
            ( ( addition @ SY37 @ ( addition @ SY36 @ SV2 ) )
            = ( addition @ ( addition @ SY37 @ SY36 ) @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(68,plain,
    ! [SV3: $i] :
      ( ( ( addition @ SV3 @ zero )
        = SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(69,plain,
    ! [SV4: $i] :
      ( ( ( addition @ SV4 @ SV4 )
        = SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(70,plain,
    ! [SV5: $i] :
      ( ( ! [SY38: $i,SY39: $i] :
            ( ( multiplication @ SV5 @ ( multiplication @ SY38 @ SY39 ) )
            = ( multiplication @ ( multiplication @ SV5 @ SY38 ) @ SY39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(71,plain,
    ! [SV6: $i] :
      ( ( ( multiplication @ SV6 @ one )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(72,plain,
    ! [SV7: $i] :
      ( ( ( multiplication @ one @ SV7 )
        = SV7 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(73,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)],[53]) ).

thf(74,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)],[54]) ).

thf(75,plain,
    ! [SV10: $i] :
      ( ( ( multiplication @ zero @ SV10 )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(76,plain,
    ! [SV11: $i] :
      ( ( ( addition @ one @ ( multiplication @ SV11 @ ( star @ SV11 ) ) )
        = ( star @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(77,plain,
    ! [SV12: $i] :
      ( ( ( addition @ one @ ( multiplication @ ( star @ SV12 ) @ SV12 ) )
        = ( star @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(78,plain,
    ! [SV13: $i] :
      ( ( ! [SY44: $i,SY45: $i] :
            ( ~ ( leq @ ( addition @ ( multiplication @ SV13 @ SY45 ) @ SY44 ) @ SY45 )
            | ( leq @ ( multiplication @ ( star @ SV13 ) @ SY44 ) @ SY45 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(79,plain,
    ! [SV14: $i] :
      ( ( ! [SY46: $i,SY47: $i] :
            ( ~ ( leq @ ( addition @ ( multiplication @ SY47 @ SV14 ) @ SY46 ) @ SY47 )
            | ( leq @ ( multiplication @ SY46 @ ( star @ SV14 ) ) @ SY47 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(80,plain,
    ! [SV15: $i] :
      ( ( ( strong_iteration @ SV15 )
        = ( addition @ ( multiplication @ SV15 @ ( strong_iteration @ SV15 ) ) @ one ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(81,plain,
    ! [SV16: $i] :
      ( ( ! [SY48: $i,SY49: $i] :
            ( ~ ( leq @ SY49 @ ( addition @ ( multiplication @ SV16 @ SY49 ) @ SY48 ) )
            | ( leq @ SY49 @ ( multiplication @ ( strong_iteration @ SV16 ) @ SY48 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(82,plain,
    ! [SV17: $i] :
      ( ( ( strong_iteration @ SV17 )
        = ( addition @ ( star @ SV17 ) @ ( multiplication @ ( strong_iteration @ SV17 ) @ zero ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(83,plain,
    ( ( leq @ sK1_X0 @ ( strong_iteration @ one ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[64]) ).

thf(84,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)],[65]) ).

thf(85,plain,
    ! [SV18: $i,SV1: $i] :
      ( ( ( addition @ SV1 @ SV18 )
        = ( addition @ SV18 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(86,plain,
    ! [SV2: $i,SV19: $i] :
      ( ( ! [SY50: $i] :
            ( ( addition @ SY50 @ ( addition @ SV19 @ SV2 ) )
            = ( addition @ ( addition @ SY50 @ SV19 ) @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(87,plain,
    ! [SV20: $i,SV5: $i] :
      ( ( ! [SY51: $i] :
            ( ( multiplication @ SV5 @ ( multiplication @ SV20 @ SY51 ) )
            = ( multiplication @ ( multiplication @ SV5 @ SV20 ) @ SY51 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(88,plain,
    ! [SV21: $i,SV8: $i] :
      ( ( ! [SY52: $i] :
            ( ( multiplication @ SV8 @ ( addition @ SV21 @ SY52 ) )
            = ( addition @ ( multiplication @ SV8 @ SV21 ) @ ( multiplication @ SV8 @ SY52 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(89,plain,
    ! [SV22: $i,SV9: $i] :
      ( ( ! [SY53: $i] :
            ( ( multiplication @ ( addition @ SV9 @ SV22 ) @ SY53 )
            = ( addition @ ( multiplication @ SV9 @ SY53 ) @ ( multiplication @ SV22 @ SY53 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(90,plain,
    ! [SV23: $i,SV13: $i] :
      ( ( ! [SY54: $i] :
            ( ~ ( leq @ ( addition @ ( multiplication @ SV13 @ SY54 ) @ SV23 ) @ SY54 )
            | ( leq @ ( multiplication @ ( star @ SV13 ) @ SV23 ) @ SY54 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(91,plain,
    ! [SV24: $i,SV14: $i] :
      ( ( ! [SY55: $i] :
            ( ~ ( leq @ ( addition @ ( multiplication @ SY55 @ SV14 ) @ SV24 ) @ SY55 )
            | ( leq @ ( multiplication @ SV24 @ ( star @ SV14 ) ) @ SY55 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(92,plain,
    ! [SV25: $i,SV16: $i] :
      ( ( ! [SY56: $i] :
            ( ~ ( leq @ SY56 @ ( addition @ ( multiplication @ SV16 @ SY56 ) @ SV25 ) )
            | ( leq @ SY56 @ ( multiplication @ ( strong_iteration @ SV16 ) @ SV25 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(93,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( addition @ SX0 @ SX1 )
             != SX1 )
            | ( leq @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[84]) ).

thf(94,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( leq @ SX0 @ SX1 )
            | ( ( addition @ SX0 @ SX1 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[84]) ).

thf(95,plain,
    ! [SV2: $i,SV19: $i,SV26: $i] :
      ( ( ( addition @ SV26 @ ( addition @ SV19 @ SV2 ) )
        = ( addition @ ( addition @ SV26 @ SV19 ) @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(96,plain,
    ! [SV27: $i,SV20: $i,SV5: $i] :
      ( ( ( multiplication @ SV5 @ ( multiplication @ SV20 @ SV27 ) )
        = ( multiplication @ ( multiplication @ SV5 @ SV20 ) @ SV27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(97,plain,
    ! [SV28: $i,SV21: $i,SV8: $i] :
      ( ( ( multiplication @ SV8 @ ( addition @ SV21 @ SV28 ) )
        = ( addition @ ( multiplication @ SV8 @ SV21 ) @ ( multiplication @ SV8 @ SV28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(98,plain,
    ! [SV29: $i,SV22: $i,SV9: $i] :
      ( ( ( multiplication @ ( addition @ SV9 @ SV22 ) @ SV29 )
        = ( addition @ ( multiplication @ SV9 @ SV29 ) @ ( multiplication @ SV22 @ SV29 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(99,plain,
    ! [SV23: $i,SV30: $i,SV13: $i] :
      ( ( ~ ( leq @ ( addition @ ( multiplication @ SV13 @ SV30 ) @ SV23 ) @ SV30 )
        | ( leq @ ( multiplication @ ( star @ SV13 ) @ SV23 ) @ SV30 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(100,plain,
    ! [SV24: $i,SV14: $i,SV31: $i] :
      ( ( ~ ( leq @ ( addition @ ( multiplication @ SV31 @ SV14 ) @ SV24 ) @ SV31 )
        | ( leq @ ( multiplication @ SV24 @ ( star @ SV14 ) ) @ SV31 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(101,plain,
    ! [SV25: $i,SV16: $i,SV32: $i] :
      ( ( ~ ( leq @ SV32 @ ( addition @ ( multiplication @ SV16 @ SV32 ) @ SV25 ) )
        | ( leq @ SV32 @ ( multiplication @ ( strong_iteration @ SV16 ) @ SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(102,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( addition @ SX0 @ SX1 )
           != SX1 )
          | ( leq @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[93]) ).

thf(103,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( leq @ SX0 @ SX1 )
          | ( ( addition @ SX0 @ SX1 )
            = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[94]) ).

thf(104,plain,
    ! [SV23: $i,SV30: $i,SV13: $i] :
      ( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV13 @ SV30 ) @ SV23 ) @ SV30 ) )
        = $true )
      | ( ( leq @ ( multiplication @ ( star @ SV13 ) @ SV23 ) @ SV30 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[99]) ).

thf(105,plain,
    ! [SV24: $i,SV14: $i,SV31: $i] :
      ( ( ( ~ ( leq @ ( addition @ ( multiplication @ SV31 @ SV14 ) @ SV24 ) @ SV31 ) )
        = $true )
      | ( ( leq @ ( multiplication @ SV24 @ ( star @ SV14 ) ) @ SV31 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[100]) ).

thf(106,plain,
    ! [SV25: $i,SV16: $i,SV32: $i] :
      ( ( ( ~ ( leq @ SV32 @ ( addition @ ( multiplication @ SV16 @ SV32 ) @ SV25 ) ) )
        = $true )
      | ( ( leq @ SV32 @ ( multiplication @ ( strong_iteration @ SV16 ) @ SV25 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[101]) ).

thf(107,plain,
    ! [SV33: $i] :
      ( ( ! [SY57: $i] :
            ( ( ( addition @ SV33 @ SY57 )
             != SY57 )
            | ( leq @ SV33 @ SY57 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[102]) ).

thf(108,plain,
    ! [SV34: $i] :
      ( ( ! [SY58: $i] :
            ( ~ ( leq @ SV34 @ SY58 )
            | ( ( addition @ SV34 @ SY58 )
              = SY58 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[103]) ).

thf(109,plain,
    ! [SV23: $i,SV30: $i,SV13: $i] :
      ( ( ( leq @ ( addition @ ( multiplication @ SV13 @ SV30 ) @ SV23 ) @ SV30 )
        = $false )
      | ( ( leq @ ( multiplication @ ( star @ SV13 ) @ SV23 ) @ SV30 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[104]) ).

thf(110,plain,
    ! [SV24: $i,SV14: $i,SV31: $i] :
      ( ( ( leq @ ( addition @ ( multiplication @ SV31 @ SV14 ) @ SV24 ) @ SV31 )
        = $false )
      | ( ( leq @ ( multiplication @ SV24 @ ( star @ SV14 ) ) @ SV31 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[105]) ).

thf(111,plain,
    ! [SV25: $i,SV16: $i,SV32: $i] :
      ( ( ( leq @ SV32 @ ( addition @ ( multiplication @ SV16 @ SV32 ) @ SV25 ) )
        = $false )
      | ( ( leq @ SV32 @ ( multiplication @ ( strong_iteration @ SV16 ) @ SV25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[106]) ).

thf(112,plain,
    ! [SV35: $i,SV33: $i] :
      ( ( ( ( addition @ SV33 @ SV35 )
         != SV35 )
        | ( leq @ SV33 @ SV35 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[107]) ).

thf(113,plain,
    ! [SV36: $i,SV34: $i] :
      ( ( ~ ( leq @ SV34 @ SV36 )
        | ( ( addition @ SV34 @ SV36 )
          = SV36 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(114,plain,
    ! [SV35: $i,SV33: $i] :
      ( ( ( ( ( addition @ SV33 @ SV35 )
           != SV35 ) )
        = $true )
      | ( ( leq @ SV33 @ SV35 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[112]) ).

thf(115,plain,
    ! [SV36: $i,SV34: $i] :
      ( ( ( ~ ( leq @ SV34 @ SV36 ) )
        = $true )
      | ( ( ( addition @ SV34 @ SV36 )
          = SV36 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[113]) ).

thf(116,plain,
    ! [SV35: $i,SV33: $i] :
      ( ( ( ( addition @ SV33 @ SV35 )
          = SV35 )
        = $false )
      | ( ( leq @ SV33 @ SV35 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[114]) ).

thf(117,plain,
    ! [SV36: $i,SV34: $i] :
      ( ( ( leq @ SV34 @ SV36 )
        = $false )
      | ( ( ( addition @ SV34 @ SV36 )
          = SV36 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[115]) ).

thf(118,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[68,117,116,111,110,109,98,97,96,95,85,83,82,80,77,76,75,72,71,69]) ).

thf(119,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[118]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : KLE137+1 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.09  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 600
% 0.08/0.28  % DateTime : Thu Jun 16 08:38:29 EDT 2022
% 0.08/0.28  % CPUTime  : 
% 0.08/0.29  
% 0.08/0.29   No.of.Axioms: 18
% 0.08/0.29  
% 0.08/0.29   Length.of.Defs: 0
% 0.08/0.29  
% 0.08/0.29   Contains.Choice.Funs: false
% 0.08/0.30  (rf:0,axioms:18,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:20,loop_count:0,foatp_calls:0,translation:fof_full).......
% 21.71/21.93  
% 21.71/21.93  ********************************
% 21.71/21.93  *   All subproblems solved!    *
% 21.71/21.93  ********************************
% 21.71/21.93  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,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:118,loop_count:0,foatp_calls:1,translation:fof_full)
% 21.71/21.94  
% 21.71/21.94  %**** Beginning of derivation protocol ****
% 21.71/21.94  % SZS output start CNFRefutation
% See solution above
% 21.71/21.94  
% 21.71/21.94  %**** End of derivation protocol ****
% 21.71/21.94  %**** no. of clauses in derivation: 119 ****
% 21.71/21.94  %**** clause counter: 118 ****
% 21.71/21.94  
% 21.71/21.94  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,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:118,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------