TSTP Solution File: NUM802^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM802^5 : 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 : n012.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 : Mon Jul 18 11:55:41 EDT 2022

% Result   : Theorem 0.19s 0.48s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   92 (  18 unt;   5 typ;   0 def)
%            Number of atoms       :  454 ( 222 equ;   0 cnn)
%            Maximal formula atoms :    3 (   5 avg)
%            Number of connectives :  879 ( 303   ~; 126   |;   5   &; 435   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   68 (  68   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :  152 (  45   ^ 102   !;   5   ?; 152   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_absval,type,
    absval: $i > $i ).

thf(tp_c0,type,
    c0: $i ).

thf(tp_c_2,type,
    c_2: $i ).

thf(tp_c_less_,type,
    c_less_: $i > $i > $o ).

thf(tp_sK1_Xy,type,
    sK1_Xy: ( $i > $o ) > $i ).

thf(1,conjecture,
    ( ( c_less_ @ c_2 @ c0 )
   => ( ! [Xu: $i,Xv: $i] :
          ( ( c_less_ @ Xu @ c0 )
         => ( Xu
           != ( absval @ Xv ) ) )
     => ? [A: $i > $o] :
          ( ! [Xy: $i] :
              ~ ( A @ ( absval @ Xy ) )
          & ( A @ c_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE_FENG_8) ).

thf(2,negated_conjecture,
    ( ( ( c_less_ @ c_2 @ c0 )
     => ( ! [Xu: $i,Xv: $i] :
            ( ( c_less_ @ Xu @ c0 )
           => ( Xu
             != ( absval @ Xv ) ) )
       => ? [A: $i > $o] :
            ( ! [Xy: $i] :
                ~ ( A @ ( absval @ Xy ) )
            & ( A @ c_2 ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( c_less_ @ c_2 @ c0 )
     => ( ! [Xu: $i,Xv: $i] :
            ( ( c_less_ @ Xu @ c0 )
           => ( Xu
             != ( absval @ Xv ) ) )
       => ? [A: $i > $o] :
            ( ! [Xy: $i] :
                ~ ( A @ ( absval @ Xy ) )
            & ( A @ c_2 ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( c_less_ @ c_2 @ c0 )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xu: $i,Xv: $i] :
          ( ( c_less_ @ Xu @ c0 )
         => ( Xu
           != ( absval @ Xv ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ? [A: $i > $o] :
          ( ! [Xy: $i] :
              ~ ( A @ ( absval @ Xy ) )
          & ( A @ c_2 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ~ ? [A: $i > $o] :
            ( ! [Xy: $i] :
                ~ ( A @ ( absval @ Xy ) )
            & ( A @ c_2 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [A: $i > $o] :
          ( ( A @ ( absval @ ( sK1_Xy @ A ) ) )
          | ~ ( A @ c_2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(9,plain,
    ( ( ! [Xu: $i] :
          ( ~ ( c_less_ @ Xu @ c0 )
          | ! [Xv: $i] :
              ( Xu
             != ( absval @ Xv ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(10,plain,
    ( ( ! [Xu: $i] :
          ( ~ ( c_less_ @ Xu @ c0 )
          | ! [Xv: $i] :
              ( Xu
             != ( absval @ Xv ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(11,plain,
    ( ( c_less_ @ c_2 @ c0 )
    = $true ),
    inference(copy,[status(thm)],[4]) ).

thf(12,plain,
    ( ( ! [A: $i > $o] :
          ( ( A @ ( absval @ ( sK1_Xy @ A ) ) )
          | ~ ( A @ c_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(13,plain,
    ! [SV1: $i] :
      ( ( ~ ( c_less_ @ SV1 @ c0 )
        | ! [SY4: $i] :
            ( SV1
           != ( absval @ SY4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10]) ).

thf(14,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) )
        | ~ ( SV2 @ c_2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( c_less_ @ SV1 @ c0 ) )
        = $true )
      | ( ( ! [SY4: $i] :
              ( SV1
             != ( absval @ SY4 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13]) ).

thf(16,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) )
        = $true )
      | ( ( ~ ( SV2 @ c_2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14]) ).

thf(17,plain,
    ! [SV1: $i] :
      ( ( ( c_less_ @ SV1 @ c0 )
        = $false )
      | ( ( ! [SY4: $i] :
              ( SV1
             != ( absval @ SY4 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(18,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ c_2 )
        = $false )
      | ( ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(19,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ( SV1
           != ( absval @ SV3 ) ) )
        = $true )
      | ( ( c_less_ @ SV1 @ c0 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(20,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( SV1
          = ( absval @ SV3 ) )
        = $false )
      | ( ( c_less_ @ SV1 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV5: $i > $o] :
      ( ( ( ~ ( SV5 @ c_2 ) )
        = $false )
      | ( ( ~ ( SV5
              @ ( absval
                @ ( sK1_Xy
                  @ ^ [SX0: $i] :
                      ~ ( SV5 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[18:[bind(SV2,$thf( ^ [SV4: $i] : ~ ( SV5 @ SV4 ) ))]]) ).

thf(24,plain,
    ( ( ( c_2 = c_2 )
      = $false )
    | ( ( ( absval
          @ ( sK1_Xy
            @ ^ [SX0: $i] : ( SX0 = c_2 ) ) )
        = c_2 )
      = $true ) ),
    inference(prim_subst,[status(thm)],[18:[bind(SV2,$thf( ^ [SV8: $i] : ( SV8 = c_2 ) ))]]) ).

thf(26,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ c_2 )
        = $false )
      | ( ( ( SV2 @ c_2 )
          = ( ~ ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) ) ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[18]) ).

thf(27,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( c_less_ @ SV1 @ c0 )
        = $false )
      | ( ( ( SV1
            = ( absval @ SV3 ) )
          = ( c_less_ @ SV1 @ c0 ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[20]) ).

thf(28,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ( ( SV2 @ c_2 )
              | ~ ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) ) )
          | ~ ( ~ ( SV2 @ c_2 )
              | ~ ~ ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) ) ) )
        = $false )
      | ( ( SV2 @ c_2 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[26]) ).

thf(29,plain,
    ! [SV2: $i > $o] :
      ( ( ( ( SV2 @ c_2 )
          = ( ~ ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) ) ) )
        = $false )
      | ( ( SV2 @ c_2 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[26]) ).

thf(30,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ( ( SV1
                = ( absval @ SV3 ) )
              | ( c_less_ @ SV1 @ c0 ) )
          | ~ ( ( SV1
               != ( absval @ SV3 ) )
              | ~ ( c_less_ @ SV1 @ c0 ) ) )
        = $false )
      | ( ( c_less_ @ SV1 @ c0 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[27]) ).

thf(33,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ( ~ ( SV2 @ c_2 )
              | ~ ~ ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) ) ) )
        = $false )
      | ( ( SV2 @ c_2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[28]) ).

thf(35,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ( ( SV1
               != ( absval @ SV3 ) )
              | ~ ( c_less_ @ SV1 @ c0 ) ) )
        = $false )
      | ( ( c_less_ @ SV1 @ c0 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(37,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ c_2 )
          | ~ ~ ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) ) )
        = $true )
      | ( ( SV2 @ c_2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(39,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ( SV1
           != ( absval @ SV3 ) )
          | ~ ( c_less_ @ SV1 @ c0 ) )
        = $true )
      | ( ( c_less_ @ SV1 @ c0 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(41,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ c_2 ) )
        = $true )
      | ( ( ~ ~ ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) ) )
        = $true )
      | ( ( SV2 @ c_2 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(43,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ( SV1
           != ( absval @ SV3 ) ) )
        = $true )
      | ( ( ~ ( c_less_ @ SV1 @ c0 ) )
        = $true )
      | ( ( c_less_ @ SV1 @ c0 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(45,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ c_2 )
        = $false )
      | ( ( ~ ~ ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) ) )
        = $true )
      | ( ( SV2 @ c_2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(46,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( SV1
          = ( absval @ SV3 ) )
        = $false )
      | ( ( ~ ( c_less_ @ SV1 @ c0 ) )
        = $true )
      | ( ( c_less_ @ SV1 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(47,plain,
    ! [SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) ) )
        = $false )
      | ( ( SV2 @ c_2 )
        = $false )
      | ( ( SV2 @ c_2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(48,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( c_less_ @ SV1 @ c0 )
        = $false )
      | ( ( SV1
          = ( absval @ SV3 ) )
        = $false )
      | ( ( c_less_ @ SV1 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(49,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) )
        = $true )
      | ( ( SV2 @ c_2 )
        = $false )
      | ( ( SV2 @ c_2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV24: $i > $o] :
      ( ( ( ~ ~ ~ ~ ~ ( SV24 @ c_2 ) )
        = $false )
      | ( ( ~ ( SV24 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV24
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[29:[bind(SV2,$thf( ^ [SX0: $i] : ~ ( ~ ( ~ ( ~ ( ~ ( SV24 @ SX0 ) ) ) ) ) ))]]) ).

thf(52,plain,
    ! [SV21: $i > $o] :
      ( ( ( ~ ~ ~ ~ ( SV21 @ c_2 ) )
        = $false )
      | ( ( ~ ( SV21 @ c_2 ) )
        = $true )
      | ( ( ~ ~ ( SV21
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ( SV21 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extuni,[status(esa)],[29:[bind(SV2,$thf( ^ [SX0: $i] : ~ ( ~ ( ~ ( ~ ( SV21 @ SX0 ) ) ) ) ))]]) ).

thf(55,plain,
    ! [SV18: $i > $o] :
      ( ( ( ~ ~ ~ ( SV18 @ c_2 ) )
        = $false )
      | ( ( ~ ( SV18 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV18
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ( SV18 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[29:[bind(SV2,$thf( ^ [SX0: $i] : ~ ( ~ ( ~ ( SV18 @ SX0 ) ) ) ))]]) ).

thf(56,plain,
    ! [SV15: $i > $o] :
      ( ( ( ~ ~ ( SV15 @ c_2 ) )
        = $false )
      | ( ( ~ ( SV15 @ c_2 ) )
        = $true )
      | ( ( ~ ~ ( SV15
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ( SV15 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extuni,[status(esa)],[29:[bind(SV2,$thf( ^ [SX0: $i] : ~ ( ~ ( SV15 @ SX0 ) ) ))]]) ).

thf(59,plain,
    ! [SV12: $i > $o] :
      ( ( ( ~ ( SV12 @ c_2 ) )
        = $false )
      | ( ( ~ ( SV12 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV12
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ( SV12 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[29:[bind(SV2,$thf( ^ [SX0: $i] : ~ ( SV12 @ SX0 ) ))]]) ).

thf(60,plain,
    ! [SV3: $i] :
      ( ( ( c_less_ @ ( absval @ SV3 ) @ c0 )
        = $false )
      | ( ( c_less_ @ ( absval @ SV3 ) @ c0 )
        = $false ) ),
    inference(extuni,[status(esa)],[48:[bind(SV1,$thf( absval @ SV3 ))]]) ).

thf(61,plain,
    ! [SV3: $i] :
      ( ( c_less_ @ ( absval @ SV3 ) @ c0 )
      = $false ),
    inference(extuni,[status(esa)],[20:[bind(SV1,$thf( absval @ SV3 ))]]) ).

thf(62,plain,
    ! [SV12: $i > $o] :
      ( ( ( SV12 @ c_2 )
        = $true )
      | ( ( ~ ( SV12 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV12
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ( SV12 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[59]) ).

thf(65,plain,
    ! [SV15: $i > $o] :
      ( ( ( ~ ( SV15 @ c_2 ) )
        = $true )
      | ( ( ~ ( SV15 @ c_2 ) )
        = $true )
      | ( ( ~ ~ ( SV15
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ( SV15 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[56]) ).

thf(66,plain,
    ! [SV18: $i > $o] :
      ( ( ( ~ ~ ( SV18 @ c_2 ) )
        = $true )
      | ( ( ~ ( SV18 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV18
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ( SV18 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(69,plain,
    ! [SV21: $i > $o] :
      ( ( ( ~ ~ ~ ( SV21 @ c_2 ) )
        = $true )
      | ( ( ~ ( SV21 @ c_2 ) )
        = $true )
      | ( ( ~ ~ ( SV21
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ( SV21 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[52]) ).

thf(70,plain,
    ! [SV24: $i > $o] :
      ( ( ( ~ ~ ~ ~ ( SV24 @ c_2 ) )
        = $true )
      | ( ( ~ ( SV24 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV24
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[51]) ).

thf(72,plain,
    ! [SV12: $i > $o] :
      ( ( ( SV12 @ c_2 )
        = $true )
      | ( ( SV12 @ c_2 )
        = $true )
      | ( ( ~ ~ ( SV12
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ( SV12 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[62]) ).

thf(75,plain,
    ! [SV15: $i > $o] :
      ( ( ( SV15 @ c_2 )
        = $false )
      | ( ( ~ ( SV15 @ c_2 ) )
        = $true )
      | ( ( ~ ~ ( SV15
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ( SV15 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(76,plain,
    ! [SV18: $i > $o] :
      ( ( ( ~ ( SV18 @ c_2 ) )
        = $false )
      | ( ( ~ ( SV18 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV18
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ( SV18 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[66]) ).

thf(79,plain,
    ! [SV21: $i > $o] :
      ( ( ( ~ ~ ( SV21 @ c_2 ) )
        = $false )
      | ( ( ~ ( SV21 @ c_2 ) )
        = $true )
      | ( ( ~ ~ ( SV21
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ( SV21 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(80,plain,
    ! [SV24: $i > $o] :
      ( ( ( ~ ~ ~ ( SV24 @ c_2 ) )
        = $false )
      | ( ( ~ ( SV24 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV24
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(82,plain,
    ! [SV12: $i > $o] :
      ( ( ( ~ ( SV12
              @ ( absval
                @ ( sK1_Xy
                  @ ^ [SX0: $i] :
                      ~ ( SV12 @ SX0 ) ) ) ) )
        = $true )
      | ( ( SV12 @ c_2 )
        = $true )
      | ( ( SV12 @ c_2 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[72]) ).

thf(85,plain,
    ! [SV15: $i > $o] :
      ( ( ( SV15 @ c_2 )
        = $false )
      | ( ( SV15 @ c_2 )
        = $false )
      | ( ( ~ ~ ( SV15
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ( SV15 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[75]) ).

thf(86,plain,
    ! [SV18: $i > $o] :
      ( ( ( SV18 @ c_2 )
        = $true )
      | ( ( ~ ( SV18 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV18
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ( SV18 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[76]) ).

thf(89,plain,
    ! [SV21: $i > $o] :
      ( ( ( ~ ( SV21 @ c_2 ) )
        = $true )
      | ( ( ~ ( SV21 @ c_2 ) )
        = $true )
      | ( ( ~ ~ ( SV21
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ( SV21 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[79]) ).

thf(90,plain,
    ! [SV24: $i > $o] :
      ( ( ( ~ ~ ( SV24 @ c_2 ) )
        = $true )
      | ( ( ~ ( SV24 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV24
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[80]) ).

thf(92,plain,
    ! [SV12: $i > $o] :
      ( ( ( SV12
          @ ( absval
            @ ( sK1_Xy
              @ ^ [SX0: $i] :
                  ~ ( SV12 @ SX0 ) ) ) )
        = $false )
      | ( ( SV12 @ c_2 )
        = $true )
      | ( ( SV12 @ c_2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[82]) ).

thf(95,plain,
    ! [SV15: $i > $o] :
      ( ( ( ~ ( SV15
              @ ( absval
                @ ( sK1_Xy
                  @ ^ [SX0: $i] :
                      ~ ~ ( SV15 @ SX0 ) ) ) ) )
        = $false )
      | ( ( SV15 @ c_2 )
        = $false )
      | ( ( SV15 @ c_2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(96,plain,
    ! [SV18: $i > $o] :
      ( ( ( SV18 @ c_2 )
        = $true )
      | ( ( SV18 @ c_2 )
        = $true )
      | ( ( ~ ~ ( SV18
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ( SV18 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[86]) ).

thf(99,plain,
    ! [SV21: $i > $o] :
      ( ( ( SV21 @ c_2 )
        = $false )
      | ( ( ~ ( SV21 @ c_2 ) )
        = $true )
      | ( ( ~ ~ ( SV21
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ( SV21 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[89]) ).

thf(100,plain,
    ! [SV24: $i > $o] :
      ( ( ( ~ ( SV24 @ c_2 ) )
        = $false )
      | ( ( ~ ( SV24 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV24
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(103,plain,
    ! [SV15: $i > $o] :
      ( ( ( SV15
          @ ( absval
            @ ( sK1_Xy
              @ ^ [SX0: $i] :
                  ~ ~ ( SV15 @ SX0 ) ) ) )
        = $true )
      | ( ( SV15 @ c_2 )
        = $false )
      | ( ( SV15 @ c_2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[95]) ).

thf(104,plain,
    ! [SV18: $i > $o] :
      ( ( ( ~ ( SV18
              @ ( absval
                @ ( sK1_Xy
                  @ ^ [SX0: $i] :
                      ~ ~ ~ ( SV18 @ SX0 ) ) ) ) )
        = $true )
      | ( ( SV18 @ c_2 )
        = $true )
      | ( ( SV18 @ c_2 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[96]) ).

thf(107,plain,
    ! [SV21: $i > $o] :
      ( ( ( SV21 @ c_2 )
        = $false )
      | ( ( SV21 @ c_2 )
        = $false )
      | ( ( ~ ~ ( SV21
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ( SV21 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(108,plain,
    ! [SV24: $i > $o] :
      ( ( ( SV24 @ c_2 )
        = $true )
      | ( ( ~ ( SV24 @ c_2 ) )
        = $false )
      | ( ( ~ ~ ( SV24
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[100]) ).

thf(110,plain,
    ! [SV18: $i > $o] :
      ( ( ( SV18
          @ ( absval
            @ ( sK1_Xy
              @ ^ [SX0: $i] :
                  ~ ~ ~ ( SV18 @ SX0 ) ) ) )
        = $false )
      | ( ( SV18 @ c_2 )
        = $true )
      | ( ( SV18 @ c_2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[104]) ).

thf(113,plain,
    ! [SV21: $i > $o] :
      ( ( ( ~ ( SV21
              @ ( absval
                @ ( sK1_Xy
                  @ ^ [SX0: $i] :
                      ~ ~ ~ ~ ( SV21 @ SX0 ) ) ) ) )
        = $false )
      | ( ( SV21 @ c_2 )
        = $false )
      | ( ( SV21 @ c_2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[107]) ).

thf(114,plain,
    ! [SV24: $i > $o] :
      ( ( ( SV24 @ c_2 )
        = $true )
      | ( ( SV24 @ c_2 )
        = $true )
      | ( ( ~ ~ ( SV24
                @ ( absval
                  @ ( sK1_Xy
                    @ ^ [SX0: $i] :
                        ~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[108]) ).

thf(117,plain,
    ! [SV21: $i > $o] :
      ( ( ( SV21
          @ ( absval
            @ ( sK1_Xy
              @ ^ [SX0: $i] :
                  ~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
        = $true )
      | ( ( SV21 @ c_2 )
        = $false )
      | ( ( SV21 @ c_2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[113]) ).

thf(118,plain,
    ! [SV24: $i > $o] :
      ( ( ( ~ ( SV24
              @ ( absval
                @ ( sK1_Xy
                  @ ^ [SX0: $i] :
                      ~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) ) )
        = $true )
      | ( ( SV24 @ c_2 )
        = $true )
      | ( ( SV24 @ c_2 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[114]) ).

thf(120,plain,
    ! [SV24: $i > $o] :
      ( ( ( SV24
          @ ( absval
            @ ( sK1_Xy
              @ ^ [SX0: $i] :
                  ~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
        = $false )
      | ( ( SV24 @ c_2 )
        = $true )
      | ( ( SV24 @ c_2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[118]) ).

thf(122,plain,
    ! [SV5: $i > $o] :
      ( ( ( SV5 @ c_2 )
        = $true )
      | ( ( ~ ( SV5
              @ ( absval
                @ ( sK1_Xy
                  @ ^ [SX0: $i] :
                      ~ ( SV5 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(123,plain,
    ! [SV5: $i > $o] :
      ( ( ( SV5
          @ ( absval
            @ ( sK1_Xy
              @ ^ [SX0: $i] :
                  ~ ( SV5 @ SX0 ) ) ) )
        = $false )
      | ( ( SV5 @ c_2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[122]) ).

thf(124,plain,
    ( ( ( absval
        @ ( sK1_Xy
          @ ^ [SX0: $i] : ( SX0 = c_2 ) ) )
      = c_2 )
    = $true ),
    inference(extuni,[status(esa)],[24]) ).

thf(125,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ ( absval @ ( sK1_Xy @ SV2 ) ) )
        = $true )
      | ( ( SV2 @ c_2 )
        = $false ) ),
    inference(sim,[status(thm)],[49]) ).

thf(126,plain,
    ! [SV12: $i > $o] :
      ( ( ( SV12
          @ ( absval
            @ ( sK1_Xy
              @ ^ [SX0: $i] :
                  ~ ( SV12 @ SX0 ) ) ) )
        = $false )
      | ( ( SV12 @ c_2 )
        = $true ) ),
    inference(sim,[status(thm)],[92]) ).

thf(127,plain,
    ! [SV15: $i > $o] :
      ( ( ( SV15
          @ ( absval
            @ ( sK1_Xy
              @ ^ [SX0: $i] :
                  ~ ~ ( SV15 @ SX0 ) ) ) )
        = $true )
      | ( ( SV15 @ c_2 )
        = $false ) ),
    inference(sim,[status(thm)],[103]) ).

thf(128,plain,
    ! [SV18: $i > $o] :
      ( ( ( SV18
          @ ( absval
            @ ( sK1_Xy
              @ ^ [SX0: $i] :
                  ~ ~ ~ ( SV18 @ SX0 ) ) ) )
        = $false )
      | ( ( SV18 @ c_2 )
        = $true ) ),
    inference(sim,[status(thm)],[110]) ).

thf(129,plain,
    ! [SV21: $i > $o] :
      ( ( ( SV21
          @ ( absval
            @ ( sK1_Xy
              @ ^ [SX0: $i] :
                  ~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
        = $true )
      | ( ( SV21 @ c_2 )
        = $false ) ),
    inference(sim,[status(thm)],[117]) ).

thf(130,plain,
    ! [SV24: $i > $o] :
      ( ( ( SV24
          @ ( absval
            @ ( sK1_Xy
              @ ^ [SX0: $i] :
                  ~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
        = $false )
      | ( ( SV24 @ c_2 )
        = $true ) ),
    inference(sim,[status(thm)],[120]) ).

thf(131,plain,
    ! [SV3: $i] :
      ( ( c_less_ @ ( absval @ SV3 ) @ c0 )
      = $false ),
    inference(sim,[status(thm)],[60]) ).

thf(132,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[11,131,130,129,128,127,126,125,124,123,61,20,18]) ).

thf(133,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[132]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM802^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n012.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jul  5 07:51:30 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 0
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.35  (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.48  
% 0.19/0.48  ********************************
% 0.19/0.48  *   All subproblems solved!    *
% 0.19/0.48  ********************************
% 0.19/0.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:132,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.19/0.48  
% 0.19/0.48  %**** Beginning of derivation protocol ****
% 0.19/0.48  % SZS output start CNFRefutation
% See solution above
% 0.19/0.48  
% 0.19/0.48  %**** End of derivation protocol ****
% 0.19/0.48  %**** no. of clauses in derivation: 87 ****
% 0.19/0.48  %**** clause counter: 132 ****
% 0.19/0.48  
% 0.19/0.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:132,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------