TSTP Solution File: KLE142+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : KLE142+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 02:11:32 EDT 2022

% Result   : Theorem 261.68s 262.11s
% Output   : CNFRefutation 261.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  105 (  89 unt;   8 typ;   0 def)
%            Number of atoms       :  304 ( 176 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  624 (  33   ~;  29   |;   2   &; 556   @)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   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   :  188 (   0   ^ 188   !;   0   ?; 188   :)

% 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(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(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] :
      ( ( strong_iteration @ ( strong_iteration @ X0 ) )
      = ( strong_iteration @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

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

thf(21,plain,
    ( ( ! [X0: $i] :
          ( ( strong_iteration @ ( strong_iteration @ 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,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(24,plain,
    ( ( ! [A: $i] :
          ( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
          = ( star @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(25,plain,
    ( ( ! [A: $i] :
          ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
          = ( star @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(26,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ zero @ A )
          = zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(27,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(28,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(29,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(30,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(31,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ zero )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(32,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(33,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( addition @ A @ B )
          = ( addition @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(34,plain,
    ( ( ! [A: $i] :
          ( ( strong_iteration @ A )
          = ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

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

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

thf(37,plain,
    ( ( ( strong_iteration @ ( strong_iteration @ sK1_X0 ) )
      = ( strong_iteration @ one ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[21]) ).

thf(38,plain,
    ( ( ( ( strong_iteration @ ( strong_iteration @ sK1_X0 ) )
       != ( strong_iteration @ one ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[37]) ).

thf(39,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(40,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)],[23]) ).

thf(41,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ A @ one )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(42,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ one @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(43,plain,
    ( ( ! [A: $i] :
          ( ( strong_iteration @ A )
          = ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(44,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( addition @ A @ B )
          = ( addition @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(45,plain,
    ( ( ! [C: $i,B: $i,A: $i] :
          ( ( addition @ A @ ( addition @ B @ C ) )
          = ( addition @ ( addition @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(46,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ zero )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(47,plain,
    ( ( ! [A: $i] :
          ( ( addition @ A @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(48,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( multiplication @ B @ C ) )
          = ( multiplication @ ( multiplication @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(49,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ A @ ( addition @ B @ C ) )
          = ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(50,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( multiplication @ ( addition @ A @ B ) @ C )
          = ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(51,plain,
    ( ( ! [A: $i] :
          ( ( multiplication @ zero @ A )
          = zero ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(52,plain,
    ( ( ! [A: $i] :
          ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
          = ( star @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(53,plain,
    ( ( ! [A: $i] :
          ( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
          = ( star @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(54,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)],[40]) ).

thf(55,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)],[39]) ).

thf(56,plain,
    ( ( ( ( strong_iteration @ ( strong_iteration @ sK1_X0 ) )
       != ( strong_iteration @ one ) ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(57,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)],[55]) ).

thf(58,plain,
    ! [SV1: $i] :
      ( ( ( multiplication @ SV1 @ one )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(59,plain,
    ! [SV2: $i] :
      ( ( ( multiplication @ one @ SV2 )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(60,plain,
    ! [SV3: $i] :
      ( ( ( strong_iteration @ SV3 )
        = ( addition @ ( multiplication @ SV3 @ ( strong_iteration @ SV3 ) ) @ one ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(61,plain,
    ! [SV4: $i] :
      ( ( ! [SY170: $i] :
            ( ( addition @ SV4 @ SY170 )
            = ( addition @ SY170 @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(62,plain,
    ! [SV5: $i] :
      ( ( ! [SY171: $i,SY172: $i] :
            ( ( addition @ SY172 @ ( addition @ SY171 @ SV5 ) )
            = ( addition @ ( addition @ SY172 @ SY171 ) @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(63,plain,
    ! [SV6: $i] :
      ( ( ( addition @ SV6 @ zero )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(64,plain,
    ! [SV7: $i] :
      ( ( ( addition @ SV7 @ SV7 )
        = SV7 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(65,plain,
    ! [SV8: $i] :
      ( ( ! [SY173: $i,SY174: $i] :
            ( ( multiplication @ SV8 @ ( multiplication @ SY173 @ SY174 ) )
            = ( multiplication @ ( multiplication @ SV8 @ SY173 ) @ SY174 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(66,plain,
    ! [SV9: $i] :
      ( ( ! [SY175: $i,SY176: $i] :
            ( ( multiplication @ SV9 @ ( addition @ SY175 @ SY176 ) )
            = ( addition @ ( multiplication @ SV9 @ SY175 ) @ ( multiplication @ SV9 @ SY176 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(67,plain,
    ! [SV10: $i] :
      ( ( ! [SY177: $i,SY178: $i] :
            ( ( multiplication @ ( addition @ SV10 @ SY177 ) @ SY178 )
            = ( addition @ ( multiplication @ SV10 @ SY178 ) @ ( multiplication @ SY177 @ SY178 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(68,plain,
    ! [SV11: $i] :
      ( ( ( multiplication @ zero @ SV11 )
        = zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(69,plain,
    ! [SV12: $i] :
      ( ( ( addition @ one @ ( multiplication @ SV12 @ ( star @ SV12 ) ) )
        = ( star @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(70,plain,
    ! [SV13: $i] :
      ( ( ( addition @ one @ ( multiplication @ ( star @ SV13 ) @ SV13 ) )
        = ( star @ SV13 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(71,plain,
    ! [SV14: $i] :
      ( ( ! [SY179: $i,SY180: $i] :
            ( ~ ( leq @ SY180 @ ( addition @ ( multiplication @ SV14 @ SY180 ) @ SY179 ) )
            | ( leq @ SY180 @ ( multiplication @ ( strong_iteration @ SV14 ) @ SY179 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(72,plain,
    ( ( ( strong_iteration @ ( strong_iteration @ sK1_X0 ) )
      = ( strong_iteration @ one ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(73,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)],[57]) ).

thf(74,plain,
    ! [SV15: $i,SV4: $i] :
      ( ( ( addition @ SV4 @ SV15 )
        = ( addition @ SV15 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(75,plain,
    ! [SV5: $i,SV16: $i] :
      ( ( ! [SY181: $i] :
            ( ( addition @ SY181 @ ( addition @ SV16 @ SV5 ) )
            = ( addition @ ( addition @ SY181 @ SV16 ) @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(76,plain,
    ! [SV17: $i,SV8: $i] :
      ( ( ! [SY182: $i] :
            ( ( multiplication @ SV8 @ ( multiplication @ SV17 @ SY182 ) )
            = ( multiplication @ ( multiplication @ SV8 @ SV17 ) @ SY182 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(77,plain,
    ! [SV18: $i,SV9: $i] :
      ( ( ! [SY183: $i] :
            ( ( multiplication @ SV9 @ ( addition @ SV18 @ SY183 ) )
            = ( addition @ ( multiplication @ SV9 @ SV18 ) @ ( multiplication @ SV9 @ SY183 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(78,plain,
    ! [SV19: $i,SV10: $i] :
      ( ( ! [SY184: $i] :
            ( ( multiplication @ ( addition @ SV10 @ SV19 ) @ SY184 )
            = ( addition @ ( multiplication @ SV10 @ SY184 ) @ ( multiplication @ SV19 @ SY184 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(79,plain,
    ! [SV20: $i,SV14: $i] :
      ( ( ! [SY185: $i] :
            ( ~ ( leq @ SY185 @ ( addition @ ( multiplication @ SV14 @ SY185 ) @ SV20 ) )
            | ( leq @ SY185 @ ( multiplication @ ( strong_iteration @ SV14 ) @ SV20 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(80,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( addition @ SX0 @ SX1 )
             != SX1 )
            | ( leq @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[73]) ).

thf(81,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( leq @ SX0 @ SX1 )
            | ( ( addition @ SX0 @ SX1 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[73]) ).

thf(82,plain,
    ! [SV5: $i,SV16: $i,SV21: $i] :
      ( ( ( addition @ SV21 @ ( addition @ SV16 @ SV5 ) )
        = ( addition @ ( addition @ SV21 @ SV16 ) @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(83,plain,
    ! [SV22: $i,SV17: $i,SV8: $i] :
      ( ( ( multiplication @ SV8 @ ( multiplication @ SV17 @ SV22 ) )
        = ( multiplication @ ( multiplication @ SV8 @ SV17 ) @ SV22 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(84,plain,
    ! [SV23: $i,SV18: $i,SV9: $i] :
      ( ( ( multiplication @ SV9 @ ( addition @ SV18 @ SV23 ) )
        = ( addition @ ( multiplication @ SV9 @ SV18 ) @ ( multiplication @ SV9 @ SV23 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(85,plain,
    ! [SV24: $i,SV19: $i,SV10: $i] :
      ( ( ( multiplication @ ( addition @ SV10 @ SV19 ) @ SV24 )
        = ( addition @ ( multiplication @ SV10 @ SV24 ) @ ( multiplication @ SV19 @ SV24 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(86,plain,
    ! [SV20: $i,SV14: $i,SV25: $i] :
      ( ( ~ ( leq @ SV25 @ ( addition @ ( multiplication @ SV14 @ SV25 ) @ SV20 ) )
        | ( leq @ SV25 @ ( multiplication @ ( strong_iteration @ SV14 ) @ SV20 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(87,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( addition @ SX0 @ SX1 )
           != SX1 )
          | ( leq @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[80]) ).

thf(88,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( leq @ SX0 @ SX1 )
          | ( ( addition @ SX0 @ SX1 )
            = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[81]) ).

thf(89,plain,
    ! [SV20: $i,SV14: $i,SV25: $i] :
      ( ( ( ~ ( leq @ SV25 @ ( addition @ ( multiplication @ SV14 @ SV25 ) @ SV20 ) ) )
        = $true )
      | ( ( leq @ SV25 @ ( multiplication @ ( strong_iteration @ SV14 ) @ SV20 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[86]) ).

thf(90,plain,
    ! [SV26: $i] :
      ( ( ! [SY186: $i] :
            ( ( ( addition @ SV26 @ SY186 )
             != SY186 )
            | ( leq @ SV26 @ SY186 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(91,plain,
    ! [SV27: $i] :
      ( ( ! [SY187: $i] :
            ( ~ ( leq @ SV27 @ SY187 )
            | ( ( addition @ SV27 @ SY187 )
              = SY187 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(92,plain,
    ! [SV20: $i,SV14: $i,SV25: $i] :
      ( ( ( leq @ SV25 @ ( addition @ ( multiplication @ SV14 @ SV25 ) @ SV20 ) )
        = $false )
      | ( ( leq @ SV25 @ ( multiplication @ ( strong_iteration @ SV14 ) @ SV20 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[89]) ).

thf(93,plain,
    ! [SV28: $i,SV26: $i] :
      ( ( ( ( addition @ SV26 @ SV28 )
         != SV28 )
        | ( leq @ SV26 @ SV28 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(94,plain,
    ! [SV29: $i,SV27: $i] :
      ( ( ~ ( leq @ SV27 @ SV29 )
        | ( ( addition @ SV27 @ SV29 )
          = SV29 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(95,plain,
    ! [SV28: $i,SV26: $i] :
      ( ( ( ( ( addition @ SV26 @ SV28 )
           != SV28 ) )
        = $true )
      | ( ( leq @ SV26 @ SV28 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[93]) ).

thf(96,plain,
    ! [SV29: $i,SV27: $i] :
      ( ( ( ~ ( leq @ SV27 @ SV29 ) )
        = $true )
      | ( ( ( addition @ SV27 @ SV29 )
          = SV29 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[94]) ).

thf(97,plain,
    ! [SV28: $i,SV26: $i] :
      ( ( ( ( addition @ SV26 @ SV28 )
          = SV28 )
        = $false )
      | ( ( leq @ SV26 @ SV28 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[95]) ).

thf(98,plain,
    ! [SV29: $i,SV27: $i] :
      ( ( ( leq @ SV27 @ SV29 )
        = $false )
      | ( ( ( addition @ SV27 @ SV29 )
          = SV29 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(99,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[58,98,97,92,85,84,83,82,74,72,70,69,68,64,63,60,59]) ).

thf(100,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[99]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : KLE142+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.10  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 600
% 0.10/0.30  % DateTime : Thu Jun 16 15:27:30 EDT 2022
% 0.10/0.30  % CPUTime  : 
% 0.10/0.31  
% 0.10/0.31   No.of.Axioms: 18
% 0.10/0.31  
% 0.10/0.31   Length.of.Defs: 0
% 0.10/0.31  
% 0.10/0.31   Contains.Choice.Funs: false
% 0.16/0.32  (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).......eprover: CPU time limit exceeded, terminating
% 148.24/148.48  eprover: CPU time limit exceeded, terminating
% 148.29/148.56  .
% 148.29/148.57  (rf:0,axioms:18,ps:2,u:1,ude:false,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).....eprover: CPU time limit exceeded, terminating
% 186.36/186.65  .eprover: CPU time limit exceeded, terminating
% 224.47/224.73  .
% 224.47/224.73  (rf:0,axioms:18,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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)......eprover: CPU time limit exceeded, terminating
% 261.56/261.82  ..
% 261.62/261.88  (rf:2,axioms:15,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,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).....
% 261.68/262.11  
% 261.68/262.11  ********************************
% 261.68/262.11  *   All subproblems solved!    *
% 261.68/262.11  ********************************
% 261.68/262.11  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:15,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:149,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:99,loop_count:0,foatp_calls:1,translation:fof_full)
% 261.68/262.12  
% 261.68/262.12  %**** Beginning of derivation protocol ****
% 261.68/262.12  % SZS output start CNFRefutation
% See solution above
% 261.68/262.12  
% 261.68/262.12  %**** End of derivation protocol ****
% 261.68/262.12  %**** no. of clauses in derivation: 97 ****
% 261.68/262.12  %**** clause counter: 99 ****
% 261.68/262.12  
% 261.68/262.12  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:15,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:149,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:99,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------