TSTP Solution File: SYO324^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO324^5 : 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 : n017.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 : Thu Jul 21 17:33:23 EDT 2022

% Result   : Theorem 26.04s 26.28s
% Output   : CNFRefutation 26.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   92 (  24 unt;   3 typ;   0 def)
%            Number of atoms       :  516 ( 186 equ;   0 cnn)
%            Maximal formula atoms :    3 (   5 avg)
%            Number of connectives : 1342 ( 337   ~; 240   |;  25   &; 735   @)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  215 ( 215   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   2 con; 0-3 aty)
%            Number of variables   :  364 (  69   ^ 268   !;  27   ?; 364   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_sK1_Xh,type,
    sK1_Xh: ( $i > $o ) > $i ).

thf(tp_sK2_SY12,type,
    sK2_SY12: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(tp_sK3_SY14,type,
    sK3_SY14: $i > $o ).

thf(1,conjecture,
    ! [Xh: ( $i > $o ) > $i] :
      ( ? [Xp: $i > $o,Xq: $i > $o] :
          ( ! [Xq_31: $i > $o] :
              ( ~ ( Xq_31 @ ( Xh @ Xp ) )
              | ( Xq_31 @ ( Xh @ Xq ) ) )
          & ? [Xx: $i] :
              ~ ( ( Xp @ Xx )
              <=> ( Xq @ Xx ) ) )
      | ! [Xt: $i > $o] :
          ( ( Xt @ ( Xh @ Xt ) )
          | ? [Xq: $i > $o] :
              ( ( Xq
                @ ( Xh
                  @ ^ [Xz: $i] :
                    ? [Xt0: $i > $o] :
                      ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
                      & ! [Xq0: $i > $o] :
                          ( ~ ( Xq0 @ Xz )
                          | ( Xq0 @ ( Xh @ Xt0 ) ) ) ) ) )
              & ~ ( Xq @ ( Xh @ Xt ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM143_EXPANDB) ).

thf(2,negated_conjecture,
    ( ( ! [Xh: ( $i > $o ) > $i] :
          ( ? [Xp: $i > $o,Xq: $i > $o] :
              ( ! [Xq_31: $i > $o] :
                  ( ~ ( Xq_31 @ ( Xh @ Xp ) )
                  | ( Xq_31 @ ( Xh @ Xq ) ) )
              & ? [Xx: $i] :
                  ~ ( ( Xp @ Xx )
                  <=> ( Xq @ Xx ) ) )
          | ! [Xt: $i > $o] :
              ( ( Xt @ ( Xh @ Xt ) )
              | ? [Xq: $i > $o] :
                  ( ( Xq
                    @ ( Xh
                      @ ^ [Xz: $i] :
                        ? [Xt0: $i > $o] :
                          ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
                          & ! [Xq0: $i > $o] :
                              ( ~ ( Xq0 @ Xz )
                              | ( Xq0 @ ( Xh @ Xt0 ) ) ) ) ) )
                  & ~ ( Xq @ ( Xh @ Xt ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xh: ( $i > $o ) > $i] :
          ( ? [Xp: $i > $o,Xq: $i > $o] :
              ( ! [Xq_31: $i > $o] :
                  ( ~ ( Xq_31 @ ( Xh @ Xp ) )
                  | ( Xq_31 @ ( Xh @ Xq ) ) )
              & ? [Xx: $i] :
                  ~ ( ( Xp @ Xx )
                  <=> ( Xq @ Xx ) ) )
          | ! [Xt: $i > $o] :
              ( ( Xt @ ( Xh @ Xt ) )
              | ? [Xq: $i > $o] :
                  ( ( Xq
                    @ ( Xh
                      @ ^ [Xz: $i] :
                        ? [Xt0: $i > $o] :
                          ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
                          & ! [Xq0: $i > $o] :
                              ( ~ ( Xq0 @ Xz )
                              | ( Xq0 @ ( Xh @ Xt0 ) ) ) ) ) )
                  & ~ ( Xq @ ( Xh @ Xt ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ? [SY10: $i > $o,SY11: $i > $o] :
          ( ! [SY12: $i > $o] :
              ( ~ ( SY12 @ ( sK1_Xh @ SY10 ) )
              | ( SY12 @ ( sK1_Xh @ SY11 ) ) )
          & ? [Xx: $i] :
              ~ ( ( SY10 @ Xx )
              <=> ( SY11 @ Xx ) ) )
      | ! [SY14: $i > $o] :
          ( ( SY14 @ ( sK1_Xh @ SY14 ) )
          | ? [SY15: $i > $o] :
              ( ( SY15
                @ ( sK1_Xh
                  @ ^ [SY16: $i] :
                    ? [SY17: $i > $o] :
                      ( ~ ( SY17 @ ( sK1_Xh @ SY17 ) )
                      & ! [SY18: $i > $o] :
                          ( ~ ( SY18 @ SY16 )
                          | ( SY18 @ ( sK1_Xh @ SY17 ) ) ) ) ) )
              & ~ ( SY15 @ ( sK1_Xh @ SY14 ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ~ ( ? [SY10: $i > $o,SY11: $i > $o] :
              ( ! [SY12: $i > $o] :
                  ( ~ ( SY12 @ ( sK1_Xh @ SY10 ) )
                  | ( SY12 @ ( sK1_Xh @ SY11 ) ) )
              & ? [Xx: $i] :
                  ~ ( ( SY10 @ Xx )
                  <=> ( SY11 @ Xx ) ) )
          | ! [SY14: $i > $o] :
              ( ( SY14 @ ( sK1_Xh @ SY14 ) )
              | ? [SY15: $i > $o] :
                  ( ( SY15
                    @ ( sK1_Xh
                      @ ^ [SY16: $i] :
                        ? [SY17: $i > $o] :
                          ( ~ ( SY17 @ ( sK1_Xh @ SY17 ) )
                          & ! [SY18: $i > $o] :
                              ( ~ ( SY18 @ SY16 )
                              | ( SY18 @ ( sK1_Xh @ SY17 ) ) ) ) ) )
                  & ~ ( SY15 @ ( sK1_Xh @ SY14 ) ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ! [SY19: $i > $o] :
          ( ~ ( SY19
              @ ( sK1_Xh
                @ ^ [SY16: $i] :
                  ? [SY17: $i > $o] :
                    ( ~ ( SY17 @ ( sK1_Xh @ SY17 ) )
                    & ! [SY18: $i > $o] :
                        ( ~ ( SY18 @ SY16 )
                        | ( SY18 @ ( sK1_Xh @ SY17 ) ) ) ) ) )
          | ( SY19 @ ( sK1_Xh @ sK3_SY14 ) ) )
      & ~ ( sK3_SY14 @ ( sK1_Xh @ sK3_SY14 ) )
      & ! [SY10: $i > $o,SY11: $i > $o] :
          ( ( ( sK2_SY12 @ SY11 @ SY10 @ ( sK1_Xh @ SY10 ) )
            & ~ ( sK2_SY12 @ SY11 @ SY10 @ ( sK1_Xh @ SY11 ) ) )
          | ( ! [Xx: $i] :
                ( ~ ( SY10 @ Xx )
                | ( SY11 @ Xx ) )
            & ! [Xx: $i] :
                ( ~ ( SY11 @ Xx )
                | ( SY10 @ Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(7,plain,
    ( ( ! [SY19: $i > $o] :
          ( ~ ( SY19
              @ ( sK1_Xh
                @ ^ [SY16: $i] :
                  ? [SY17: $i > $o] :
                    ( ~ ( SY17 @ ( sK1_Xh @ SY17 ) )
                    & ! [SY18: $i > $o] :
                        ( ~ ( SY18 @ SY16 )
                        | ( SY18 @ ( sK1_Xh @ SY17 ) ) ) ) ) )
          | ( SY19 @ ( sK1_Xh @ sK3_SY14 ) ) )
      & ~ ( sK3_SY14 @ ( sK1_Xh @ sK3_SY14 ) )
      & ! [SY10: $i > $o,SY11: $i > $o] :
          ( ( ( sK2_SY12 @ SY11 @ SY10 @ ( sK1_Xh @ SY10 ) )
            & ~ ( sK2_SY12 @ SY11 @ SY10 @ ( sK1_Xh @ SY11 ) ) )
          | ( ! [Xx: $i] :
                ( ~ ( SY10 @ Xx )
                | ( SY11 @ Xx ) )
            & ! [Xx: $i] :
                ( ~ ( SY11 @ Xx )
                | ( SY10 @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i > $o] :
                      ( ~ ( SX0
                          @ ( sK1_Xh
                            @ ^ [SX1: $i] :
                                ~ ! [SX2: $i > $o] :
                                    ~ ~ ( ~ ~ ( SX2 @ ( sK1_Xh @ SX2 ) )
                                        | ~ ! [SX3: $i > $o] :
                                              ( ~ ( SX3 @ SX1 )
                                              | ( SX3 @ ( sK1_Xh @ SX2 ) ) ) ) ) )
                      | ( SX0 @ ( sK1_Xh @ sK3_SY14 ) ) )
                | ~ ~ ( sK3_SY14 @ ( sK1_Xh @ sK3_SY14 ) ) )
          | ~ ! [SX0: $i > $o,SX1: $i > $o] :
                ( ~ ( ~ ( sK2_SY12 @ SX1 @ SX0 @ ( sK1_Xh @ SX0 ) )
                    | ~ ~ ( sK2_SY12 @ SX1 @ SX0 @ ( sK1_Xh @ SX1 ) ) )
                | ~ ( ~ ! [SX2: $i] :
                          ( ~ ( SX0 @ SX2 )
                          | ( SX1 @ SX2 ) )
                    | ~ ! [SX2: $i] :
                          ( ~ ( SX1 @ SX2 )
                          | ( SX0 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i > $o] :
                  ( ~ ( SX0
                      @ ( sK1_Xh
                        @ ^ [SX1: $i] :
                            ~ ! [SX2: $i > $o] :
                                ~ ~ ( ~ ~ ( SX2 @ ( sK1_Xh @ SX2 ) )
                                    | ~ ! [SX3: $i > $o] :
                                          ( ~ ( SX3 @ SX1 )
                                          | ( SX3 @ ( sK1_Xh @ SX2 ) ) ) ) ) )
                  | ( SX0 @ ( sK1_Xh @ sK3_SY14 ) ) )
            | ~ ~ ( sK3_SY14 @ ( sK1_Xh @ sK3_SY14 ) ) )
      | ~ ! [SX0: $i > $o,SX1: $i > $o] :
            ( ~ ( ~ ( sK2_SY12 @ SX1 @ SX0 @ ( sK1_Xh @ SX0 ) )
                | ~ ~ ( sK2_SY12 @ SX1 @ SX0 @ ( sK1_Xh @ SX1 ) ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( SX0 @ SX2 )
                      | ( SX1 @ SX2 ) )
                | ~ ! [SX2: $i] :
                      ( ~ ( SX1 @ SX2 )
                      | ( SX0 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i > $o] :
                  ( ~ ( SX0
                      @ ( sK1_Xh
                        @ ^ [SX1: $i] :
                            ~ ! [SX2: $i > $o] :
                                ~ ~ ( ~ ~ ( SX2 @ ( sK1_Xh @ SX2 ) )
                                    | ~ ! [SX3: $i > $o] :
                                          ( ~ ( SX3 @ SX1 )
                                          | ( SX3 @ ( sK1_Xh @ SX2 ) ) ) ) ) )
                  | ( SX0 @ ( sK1_Xh @ sK3_SY14 ) ) )
            | ~ ~ ( sK3_SY14 @ ( sK1_Xh @ sK3_SY14 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
            ( ~ ( ~ ( sK2_SY12 @ SX1 @ SX0 @ ( sK1_Xh @ SX0 ) )
                | ~ ~ ( sK2_SY12 @ SX1 @ SX0 @ ( sK1_Xh @ SX1 ) ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( SX0 @ SX2 )
                      | ( SX1 @ SX2 ) )
                | ~ ! [SX2: $i] :
                      ( ~ ( SX1 @ SX2 )
                      | ( SX0 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ~ ( ~ ! [SX0: $i > $o] :
                ( ~ ( SX0
                    @ ( sK1_Xh
                      @ ^ [SX1: $i] :
                          ~ ! [SX2: $i > $o] :
                              ~ ~ ( ~ ~ ( SX2 @ ( sK1_Xh @ SX2 ) )
                                  | ~ ! [SX3: $i > $o] :
                                        ( ~ ( SX3 @ SX1 )
                                        | ( SX3 @ ( sK1_Xh @ SX2 ) ) ) ) ) )
                | ( SX0 @ ( sK1_Xh @ sK3_SY14 ) ) )
          | ~ ~ ( sK3_SY14 @ ( sK1_Xh @ sK3_SY14 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ! [SX0: $i > $o,SX1: $i > $o] :
          ( ~ ( ~ ( sK2_SY12 @ SX1 @ SX0 @ ( sK1_Xh @ SX0 ) )
              | ~ ~ ( sK2_SY12 @ SX1 @ SX0 @ ( sK1_Xh @ SX1 ) ) )
          | ~ ( ~ ! [SX2: $i] :
                    ( ~ ( SX0 @ SX2 )
                    | ( SX1 @ SX2 ) )
              | ~ ! [SX2: $i] :
                    ( ~ ( SX1 @ SX2 )
                    | ( SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ! [SX0: $i > $o] :
            ( ~ ( SX0
                @ ( sK1_Xh
                  @ ^ [SX1: $i] :
                      ~ ! [SX2: $i > $o] :
                          ~ ~ ( ~ ~ ( SX2 @ ( sK1_Xh @ SX2 ) )
                              | ~ ! [SX3: $i > $o] :
                                    ( ~ ( SX3 @ SX1 )
                                    | ( SX3 @ ( sK1_Xh @ SX2 ) ) ) ) ) )
            | ( SX0 @ ( sK1_Xh @ sK3_SY14 ) ) )
      | ~ ~ ( sK3_SY14 @ ( sK1_Xh @ sK3_SY14 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV1: $i > $o] :
      ( ( ! [SY23: $i > $o] :
            ( ~ ( ~ ( sK2_SY12 @ SY23 @ SV1 @ ( sK1_Xh @ SV1 ) )
                | ~ ~ ( sK2_SY12 @ SY23 @ SV1 @ ( sK1_Xh @ SY23 ) ) )
            | ~ ( ~ ! [SY24: $i] :
                      ( ~ ( SV1 @ SY24 )
                      | ( SY23 @ SY24 ) )
                | ~ ! [SY25: $i] :
                      ( ~ ( SY23 @ SY25 )
                      | ( SV1 @ SY25 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ! [SX0: $i > $o] :
            ( ~ ( SX0
                @ ( sK1_Xh
                  @ ^ [SX1: $i] :
                      ~ ! [SX2: $i > $o] :
                          ~ ~ ( ~ ~ ( SX2 @ ( sK1_Xh @ SX2 ) )
                              | ~ ! [SX3: $i > $o] :
                                    ( ~ ( SX3 @ SX1 )
                                    | ( SX3 @ ( sK1_Xh @ SX2 ) ) ) ) ) )
            | ( SX0 @ ( sK1_Xh @ sK3_SY14 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ~ ( sK3_SY14 @ ( sK1_Xh @ sK3_SY14 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ~ ( ~ ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
            | ~ ~ ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) ) )
        | ~ ( ~ ! [SY26: $i] :
                  ( ~ ( SV1 @ SY26 )
                  | ( SV2 @ SY26 ) )
            | ~ ! [SY27: $i] :
                  ( ~ ( SV2 @ SY27 )
                  | ( SV1 @ SY27 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ( SX0
              @ ( sK1_Xh
                @ ^ [SX1: $i] :
                    ~ ! [SX2: $i > $o] :
                        ~ ~ ( ~ ~ ( SX2 @ ( sK1_Xh @ SX2 ) )
                            | ~ ! [SX3: $i > $o] :
                                  ( ~ ( SX3 @ SX1 )
                                  | ( SX3 @ ( sK1_Xh @ SX2 ) ) ) ) ) )
          | ( SX0 @ ( sK1_Xh @ sK3_SY14 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ~ ( sK3_SY14 @ ( sK1_Xh @ sK3_SY14 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ( ~ ( ~ ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
              | ~ ~ ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY26: $i] :
                    ( ~ ( SV1 @ SY26 )
                    | ( SV2 @ SY26 ) )
              | ~ ! [SY27: $i] :
                    ( ~ ( SV2 @ SY27 )
                    | ( SV1 @ SY27 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV3: $i > $o] :
      ( ( ~ ( SV3
            @ ( sK1_Xh
              @ ^ [SX1: $i] :
                  ~ ! [SX2: $i > $o] :
                      ~ ~ ( ~ ~ ( SX2 @ ( sK1_Xh @ SX2 ) )
                          | ~ ! [SX3: $i > $o] :
                                ( ~ ( SX3 @ SX1 )
                                | ( SX3 @ ( sK1_Xh @ SX2 ) ) ) ) ) )
        | ( SV3 @ ( sK1_Xh @ sK3_SY14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(23,plain,
    ( ( sK3_SY14 @ ( sK1_Xh @ sK3_SY14 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ( ~ ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
          | ~ ~ ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY26: $i] :
                    ( ~ ( SV1 @ SY26 )
                    | ( SV2 @ SY26 ) )
              | ~ ! [SY27: $i] :
                    ( ~ ( SV2 @ SY27 )
                    | ( SV1 @ SY27 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(25,plain,
    ! [SV3: $i > $o] :
      ( ( ( ~ ( SV3
              @ ( sK1_Xh
                @ ^ [SX1: $i] :
                    ~ ! [SX2: $i > $o] :
                        ~ ~ ( ~ ~ ( SX2 @ ( sK1_Xh @ SX2 ) )
                            | ~ ! [SX3: $i > $o] :
                                  ( ~ ( SX3 @ SX1 )
                                  | ( SX3 @ ( sK1_Xh @ SX2 ) ) ) ) ) ) )
        = $true )
      | ( ( SV3 @ ( sK1_Xh @ sK3_SY14 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ( ~ ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY26: $i] :
                    ( ~ ( SV1 @ SY26 )
                    | ( SV2 @ SY26 ) )
              | ~ ! [SY27: $i] :
                    ( ~ ( SV2 @ SY27 )
                    | ( SV1 @ SY27 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(27,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ( ~ ~ ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY26: $i] :
                    ( ~ ( SV1 @ SY26 )
                    | ( SV2 @ SY26 ) )
              | ~ ! [SY27: $i] :
                    ( ~ ( SV2 @ SY27 )
                    | ( SV1 @ SY27 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(28,plain,
    ! [SV3: $i > $o] :
      ( ( ( SV3
          @ ( sK1_Xh
            @ ^ [SX1: $i] :
                ~ ! [SX2: $i > $o] :
                    ~ ~ ( ~ ~ ( SX2 @ ( sK1_Xh @ SX2 ) )
                        | ~ ! [SX3: $i > $o] :
                              ( ~ ( SX3 @ SX1 )
                              | ( SX3 @ ( sK1_Xh @ SX2 ) ) ) ) ) )
        = $false )
      | ( ( SV3 @ ( sK1_Xh @ sK3_SY14 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(29,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY26: $i] :
                    ( ~ ( SV1 @ SY26 )
                    | ( SV2 @ SY26 ) )
              | ~ ! [SY27: $i] :
                    ( ~ ( SV2 @ SY27 )
                    | ( SV1 @ SY27 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(30,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ( ~ ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY26: $i] :
                    ( ~ ( SV1 @ SY26 )
                    | ( SV2 @ SY26 ) )
              | ~ ! [SY27: $i] :
                    ( ~ ( SV2 @ SY27 )
                    | ( SV1 @ SY27 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV2: $i > $o,SV1: $i > $o] :
      ( ( ( ~ ! [SY26: $i] :
                ( ~ ( SV1 @ SY26 )
                | ( SV2 @ SY26 ) )
          | ~ ! [SY27: $i] :
                ( ~ ( SV2 @ SY27 )
                | ( SV1 @ SY27 ) ) )
        = $false )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(32,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY26: $i] :
                    ( ~ ( SV1 @ SY26 )
                    | ( SV2 @ SY26 ) )
              | ~ ! [SY27: $i] :
                    ( ~ ( SV2 @ SY27 )
                    | ( SV1 @ SY27 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(33,plain,
    ! [SV2: $i > $o,SV1: $i > $o] :
      ( ( ( ~ ! [SY26: $i] :
                ( ~ ( SV1 @ SY26 )
                | ( SV2 @ SY26 ) ) )
        = $false )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(34,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ( ~ ! [SY27: $i] :
                ( ~ ( SV2 @ SY27 )
                | ( SV1 @ SY27 ) ) )
        = $false )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(35,plain,
    ! [SV2: $i > $o,SV1: $i > $o] :
      ( ( ( ~ ! [SY26: $i] :
                ( ~ ( SV1 @ SY26 )
                | ( SV2 @ SY26 ) )
          | ~ ! [SY27: $i] :
                ( ~ ( SV2 @ SY27 )
                | ( SV1 @ SY27 ) ) )
        = $false )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(36,plain,
    ! [SV2: $i > $o,SV1: $i > $o] :
      ( ( ( ! [SY26: $i] :
              ( ~ ( SV1 @ SY26 )
              | ( SV2 @ SY26 ) ) )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(37,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ( ! [SY27: $i] :
              ( ~ ( SV2 @ SY27 )
              | ( SV1 @ SY27 ) ) )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(38,plain,
    ! [SV2: $i > $o,SV1: $i > $o] :
      ( ( ( ~ ! [SY26: $i] :
                ( ~ ( SV1 @ SY26 )
                | ( SV2 @ SY26 ) ) )
        = $false )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(39,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ( ~ ! [SY27: $i] :
                ( ~ ( SV2 @ SY27 )
                | ( SV1 @ SY27 ) ) )
        = $false )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(40,plain,
    ! [SV2: $i > $o,SV4: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV4 )
          | ( SV2 @ SV4 ) )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(41,plain,
    ! [SV1: $i > $o,SV5: $i,SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ SV5 )
          | ( SV1 @ SV5 ) )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(42,plain,
    ! [SV2: $i > $o,SV1: $i > $o] :
      ( ( ( ! [SY26: $i] :
              ( ~ ( SV1 @ SY26 )
              | ( SV2 @ SY26 ) ) )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV1: $i > $o,SV2: $i > $o] :
      ( ( ( ! [SY27: $i] :
              ( ~ ( SV2 @ SY27 )
              | ( SV1 @ SY27 ) ) )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV2: $i > $o,SV4: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV4 ) )
        = $true )
      | ( ( SV2 @ SV4 )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV1: $i > $o,SV5: $i,SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ SV5 ) )
        = $true )
      | ( ( SV1 @ SV5 )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[41]) ).

thf(46,plain,
    ! [SV2: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV6 )
          | ( SV2 @ SV6 ) )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(47,plain,
    ! [SV1: $i > $o,SV7: $i,SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ SV7 )
          | ( SV1 @ SV7 ) )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV2: $i > $o,SV4: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV4 )
        = $false )
      | ( ( SV2 @ SV4 )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(49,plain,
    ! [SV1: $i > $o,SV5: $i,SV2: $i > $o] :
      ( ( ( SV2 @ SV5 )
        = $false )
      | ( ( SV1 @ SV5 )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(50,plain,
    ! [SV2: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV6 ) )
        = $true )
      | ( ( SV2 @ SV6 )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[46]) ).

thf(51,plain,
    ! [SV1: $i > $o,SV7: $i,SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ SV7 ) )
        = $true )
      | ( ( SV1 @ SV7 )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[47]) ).

thf(52,plain,
    ! [SV2: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV6 )
        = $false )
      | ( ( SV2 @ SV6 )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(53,plain,
    ! [SV1: $i > $o,SV7: $i,SV2: $i > $o] :
      ( ( ( SV2 @ SV7 )
        = $false )
      | ( ( SV1 @ SV7 )
        = $true )
      | ( ( sK2_SY12 @ SV2 @ SV1 @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(54,plain,
    ( ( ( ( sK1_Xh
          @ ^ [SX0: $i] :
              ~ ! [SX1: $i > $o] :
                  ~ ~ ( ~ ~ ( SX1 @ ( sK1_Xh @ SX1 ) )
                      | ~ ! [SX2: $i > $o] :
                            ( ~ ( SX2 @ SX0 )
                            | ( SX2 @ ( sK1_Xh @ SX1 ) ) ) ) )
        = ( sK1_Xh
          @ ^ [SX0: $i] :
              ~ ! [SX1: $i > $o] :
                  ~ ~ ( ~ ~ ( SX1 @ ( sK1_Xh @ SX1 ) )
                      | ~ ! [SX2: $i > $o] :
                            ( ~ ( SX2 @ SX0 )
                            | ( SX2 @ ( sK1_Xh @ SX1 ) ) ) ) ) )
      = $false )
    | ( ( ( sK1_Xh @ sK3_SY14 )
        = ( sK1_Xh
          @ ^ [SX0: $i] :
              ~ ! [SX1: $i > $o] :
                  ~ ~ ( ~ ~ ( SX1 @ ( sK1_Xh @ SX1 ) )
                      | ~ ! [SX2: $i > $o] :
                            ( ~ ( SX2 @ SX0 )
                            | ( SX2 @ ( sK1_Xh @ SX1 ) ) ) ) ) )
      = $true ) ),
    inference(replace_leibnizEQ,[status(thm)],[28:[bind(SV3,$thf( ^ [SV8: $i] : ( SV8 = ( sK1_Xh @ ^ [SX1: $i] : ~ ( ! [SX2: $i > $o] : ~ ( ~ ( ~ ( ~ ( SX2 @ ( sK1_Xh @ SX2 ) ) ) | ~ ( ! [SX3: $i > $o] : ( ~ ( SX3 @ SX1 ) | ( SX3 @ ( sK1_Xh @ SX2 ) ) ) ) ) ) ) ) ) ))]]) ).

thf(55,plain,
    ( ( ( sK1_Xh @ sK3_SY14 )
      = ( sK1_Xh
        @ ^ [SX0: $i] :
            ~ ! [SX1: $i > $o] :
                ~ ~ ( ~ ~ ( SX1 @ ( sK1_Xh @ SX1 ) )
                    | ~ ! [SX2: $i > $o] :
                          ( ~ ( SX2 @ SX0 )
                          | ( SX2 @ ( sK1_Xh @ SX1 ) ) ) ) ) )
    = $true ),
    inference(sim,[status(thm)],[54]) ).

thf(57,plain,
    ! [SV4: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV4 )
        = $false )
      | ( $false = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] : $false
          @ SV1
          @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[48:[bind(SV2,$thf( ^ [SV11: $i] : $false ))]]) ).

thf(58,plain,
    ! [SV10: $i > $o,SV4: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV4 )
        = $false )
      | ( ( ~ ( SV10 @ SV4 ) )
        = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] :
              ~ ( SV10 @ SX0 )
          @ SV1
          @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[48:[bind(SV2,$thf( ^ [SV9: $i] : ~ ( SV10 @ SV9 ) ))]]) ).

thf(59,plain,
    ! [SV4: $i,SV2: $i > $o] :
      ( ( $true = $false )
      | ( ( SV2 @ SV4 )
        = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] : $true
          @ ( sK1_Xh
            @ ^ [SX0: $i] : $true ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[48:[bind(SV1,$thf( ^ [SV16: $i] : $true ))]]) ).

thf(61,plain,
    ! [SV2: $i > $o,SV4: $i,SV14: $i > $o] :
      ( ( ( ~ ( SV14 @ SV4 ) )
        = $false )
      | ( ( SV2 @ SV4 )
        = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] :
              ~ ( SV14 @ SX0 )
          @ ( sK1_Xh
            @ ^ [SX0: $i] :
                ~ ( SV14 @ SX0 ) ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[48:[bind(SV1,$thf( ^ [SV13: $i] : ~ ( SV14 @ SV13 ) ))]]) ).

thf(62,plain,
    ! [SV5: $i,SV1: $i > $o] :
      ( ( $true = $false )
      | ( ( SV1 @ SV5 )
        = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] : $true
          @ SV1
          @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[49:[bind(SV2,$thf( ^ [SV12: $i] : $true ))]]) ).

thf(64,plain,
    ! [SV1: $i > $o,SV5: $i,SV10: $i > $o] :
      ( ( ( ~ ( SV10 @ SV5 ) )
        = $false )
      | ( ( SV1 @ SV5 )
        = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] :
              ~ ( SV10 @ SX0 )
          @ SV1
          @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[49:[bind(SV2,$thf( ^ [SV9: $i] : ~ ( SV10 @ SV9 ) ))]]) ).

thf(66,plain,
    ! [SV5: $i,SV2: $i > $o] :
      ( ( ( SV2 @ SV5 )
        = $false )
      | ( $false = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] : $false
          @ ( sK1_Xh
            @ ^ [SX0: $i] : $false ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[49:[bind(SV1,$thf( ^ [SV15: $i] : $false ))]]) ).

thf(67,plain,
    ! [SV14: $i > $o,SV5: $i,SV2: $i > $o] :
      ( ( ( SV2 @ SV5 )
        = $false )
      | ( ( ~ ( SV14 @ SV5 ) )
        = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] :
              ~ ( SV14 @ SX0 )
          @ ( sK1_Xh
            @ ^ [SX0: $i] :
                ~ ( SV14 @ SX0 ) ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[49:[bind(SV1,$thf( ^ [SV13: $i] : ~ ( SV14 @ SV13 ) ))]]) ).

thf(69,plain,
    ! [SV6: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV6 )
        = $false )
      | ( $false = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] : $false
          @ SV1
          @ ( sK1_Xh
            @ ^ [SX0: $i] : $false ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[52:[bind(SV2,$thf( ^ [SV11: $i] : $false ))]]) ).

thf(70,plain,
    ! [SV10: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV6 )
        = $false )
      | ( ( ~ ( SV10 @ SV6 ) )
        = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] :
              ~ ( SV10 @ SX0 )
          @ SV1
          @ ( sK1_Xh
            @ ^ [SX0: $i] :
                ~ ( SV10 @ SX0 ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[52:[bind(SV2,$thf( ^ [SV9: $i] : ~ ( SV10 @ SV9 ) ))]]) ).

thf(71,plain,
    ! [SV6: $i,SV2: $i > $o] :
      ( ( $true = $false )
      | ( ( SV2 @ SV6 )
        = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] : $true
          @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[52:[bind(SV1,$thf( ^ [SV16: $i] : $true ))]]) ).

thf(73,plain,
    ! [SV2: $i > $o,SV6: $i,SV14: $i > $o] :
      ( ( ( ~ ( SV14 @ SV6 ) )
        = $false )
      | ( ( SV2 @ SV6 )
        = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] :
              ~ ( SV14 @ SX0 )
          @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[52:[bind(SV1,$thf( ^ [SV13: $i] : ~ ( SV14 @ SV13 ) ))]]) ).

thf(74,plain,
    ! [SV7: $i,SV1: $i > $o] :
      ( ( $true = $false )
      | ( ( SV1 @ SV7 )
        = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] : $true
          @ SV1
          @ ( sK1_Xh
            @ ^ [SX0: $i] : $true ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[53:[bind(SV2,$thf( ^ [SV12: $i] : $true ))]]) ).

thf(76,plain,
    ! [SV1: $i > $o,SV7: $i,SV10: $i > $o] :
      ( ( ( ~ ( SV10 @ SV7 ) )
        = $false )
      | ( ( SV1 @ SV7 )
        = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] :
              ~ ( SV10 @ SX0 )
          @ SV1
          @ ( sK1_Xh
            @ ^ [SX0: $i] :
                ~ ( SV10 @ SX0 ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[53:[bind(SV2,$thf( ^ [SV9: $i] : ~ ( SV10 @ SV9 ) ))]]) ).

thf(78,plain,
    ! [SV7: $i,SV2: $i > $o] :
      ( ( ( SV2 @ SV7 )
        = $false )
      | ( $false = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] : $false
          @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[53:[bind(SV1,$thf( ^ [SV15: $i] : $false ))]]) ).

thf(79,plain,
    ! [SV14: $i > $o,SV7: $i,SV2: $i > $o] :
      ( ( ( SV2 @ SV7 )
        = $false )
      | ( ( ~ ( SV14 @ SV7 ) )
        = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] :
              ~ ( SV14 @ SX0 )
          @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[53:[bind(SV1,$thf( ^ [SV13: $i] : ~ ( SV14 @ SV13 ) ))]]) ).

thf(80,plain,
    ! [SV1: $i > $o,SV4: $i,SV10: $i > $o] :
      ( ( ( SV10 @ SV4 )
        = $false )
      | ( ( SV1 @ SV4 )
        = $false )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] :
              ~ ( SV10 @ SX0 )
          @ SV1
          @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[58]) ).

thf(81,plain,
    ! [SV2: $i > $o,SV4: $i,SV14: $i > $o] :
      ( ( ( SV14 @ SV4 )
        = $true )
      | ( ( SV2 @ SV4 )
        = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] :
              ~ ( SV14 @ SX0 )
          @ ( sK1_Xh
            @ ^ [SX0: $i] :
                ~ ( SV14 @ SX0 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[61]) ).

thf(82,plain,
    ! [SV1: $i > $o,SV5: $i,SV10: $i > $o] :
      ( ( ( SV10 @ SV5 )
        = $true )
      | ( ( SV1 @ SV5 )
        = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] :
              ~ ( SV10 @ SX0 )
          @ SV1
          @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[64]) ).

thf(83,plain,
    ! [SV2: $i > $o,SV5: $i,SV14: $i > $o] :
      ( ( ( SV14 @ SV5 )
        = $false )
      | ( ( SV2 @ SV5 )
        = $false )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] :
              ~ ( SV14 @ SX0 )
          @ ( sK1_Xh
            @ ^ [SX0: $i] :
                ~ ( SV14 @ SX0 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(84,plain,
    ! [SV1: $i > $o,SV6: $i,SV10: $i > $o] :
      ( ( ( SV10 @ SV6 )
        = $false )
      | ( ( SV1 @ SV6 )
        = $false )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] :
              ~ ( SV10 @ SX0 )
          @ SV1
          @ ( sK1_Xh
            @ ^ [SX0: $i] :
                ~ ( SV10 @ SX0 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(85,plain,
    ! [SV2: $i > $o,SV6: $i,SV14: $i > $o] :
      ( ( ( SV14 @ SV6 )
        = $true )
      | ( ( SV2 @ SV6 )
        = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] :
              ~ ( SV14 @ SX0 )
          @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[73]) ).

thf(86,plain,
    ! [SV1: $i > $o,SV7: $i,SV10: $i > $o] :
      ( ( ( SV10 @ SV7 )
        = $true )
      | ( ( SV1 @ SV7 )
        = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] :
              ~ ( SV10 @ SX0 )
          @ SV1
          @ ( sK1_Xh
            @ ^ [SX0: $i] :
                ~ ( SV10 @ SX0 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[76]) ).

thf(87,plain,
    ! [SV2: $i > $o,SV7: $i,SV14: $i > $o] :
      ( ( ( SV14 @ SV7 )
        = $false )
      | ( ( SV2 @ SV7 )
        = $false )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] :
              ~ ( SV14 @ SX0 )
          @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(88,plain,
    ! [SV4: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV4 )
        = $false )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] : $false
          @ SV1
          @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(sim,[status(thm)],[57]) ).

thf(89,plain,
    ! [SV4: $i,SV2: $i > $o] :
      ( ( ( SV2 @ SV4 )
        = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] : $true
          @ ( sK1_Xh
            @ ^ [SX0: $i] : $true ) )
        = $true ) ),
    inference(sim,[status(thm)],[59]) ).

thf(90,plain,
    ! [SV5: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV5 )
        = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] : $true
          @ SV1
          @ ( sK1_Xh @ SV1 ) )
        = $true ) ),
    inference(sim,[status(thm)],[62]) ).

thf(91,plain,
    ! [SV5: $i,SV2: $i > $o] :
      ( ( ( SV2 @ SV5 )
        = $false )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] : $false
          @ ( sK1_Xh
            @ ^ [SX0: $i] : $false ) )
        = $true ) ),
    inference(sim,[status(thm)],[66]) ).

thf(92,plain,
    ! [SV6: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV6 )
        = $false )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] : $false
          @ SV1
          @ ( sK1_Xh
            @ ^ [SX0: $i] : $false ) )
        = $false ) ),
    inference(sim,[status(thm)],[69]) ).

thf(93,plain,
    ! [SV6: $i,SV2: $i > $o] :
      ( ( ( SV2 @ SV6 )
        = $true )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] : $true
          @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(sim,[status(thm)],[71]) ).

thf(94,plain,
    ! [SV7: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV7 )
        = $true )
      | ( ( sK2_SY12
          @ ^ [SX0: $i] : $true
          @ SV1
          @ ( sK1_Xh
            @ ^ [SX0: $i] : $true ) )
        = $false ) ),
    inference(sim,[status(thm)],[74]) ).

thf(95,plain,
    ! [SV7: $i,SV2: $i > $o] :
      ( ( ( SV2 @ SV7 )
        = $false )
      | ( ( sK2_SY12 @ SV2
          @ ^ [SX0: $i] : $false
          @ ( sK1_Xh @ SV2 ) )
        = $false ) ),
    inference(sim,[status(thm)],[78]) ).

thf(96,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[23,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,55,53,52,49,48]) ).

thf(97,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[96]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO324^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jul  9 04:32:46 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 0
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (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)........eprover: CPU time limit exceeded, terminating
% 25.17/25.43  .
% 26.04/26.28  
% 26.04/26.28  ********************************
% 26.04/26.28  *   All subproblems solved!    *
% 26.04/26.28  ********************************
% 26.04/26.28  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:96,loop_count:0,foatp_calls:2,translation:fof_full)
% 26.04/26.29  
% 26.04/26.29  %**** Beginning of derivation protocol ****
% 26.04/26.29  % SZS output start CNFRefutation
% See solution above
% 26.04/26.29  
% 26.04/26.29  %**** End of derivation protocol ****
% 26.04/26.29  %**** no. of clauses in derivation: 89 ****
% 26.04/26.29  %**** clause counter: 96 ****
% 26.04/26.29  
% 26.04/26.29  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:96,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------