TSTP Solution File: GEO498+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GEO498+1 : TPTP v8.1.0. Released v7.0.0.
% 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 : Sat Jul 16 05:10:23 EDT 2022

% Result   : Theorem 1.05s 1.23s
% Output   : CNFRefutation 1.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   36
% Syntax   : Number of formulae    :  105 (  59 unt;  28 typ;   0 def)
%            Number of atoms       :  325 ( 172 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  494 (  94   ~;  78   |;   4   &; 318   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   92 (  92   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   31 (  28 usr;  10 con; 0-8 aty)
%            Number of variables   :  164 (   0   ^ 164   !;   0   ?; 164   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_alpha,type,
    alpha: $i ).

thf(tp_beta,type,
    beta: $i ).

thf(tp_c63,type,
    c63: $i > $i > $i > $i ).

thf(tp_crossbar,type,
    crossbar: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_ext,type,
    ext: $i > $i > $i > $i > $i ).

thf(tp_gamma,type,
    gamma: $i ).

thf(tp_ins,type,
    ins: $i > $i > $i > $i > $i ).

thf(tp_insert,type,
    insert: $i > $i > $i > $i > $i ).

thf(tp_insert5,type,
    insert5: $i > $i > $i > $i > $i > $i ).

thf(tp_ip,type,
    ip: $i > $i > $i > $i > $i > $i ).

thf(tp_le,type,
    le: $i > $i > $i > $i > $o ).

thf(tp_pointOffLine,type,
    pointOffLine: $i > $i > $i ).

thf(tp_s,type,
    s: $i > $i > $i ).

thf(tp_sK1_Xa,type,
    sK1_Xa: $i ).

thf(tp_sK2_SY22,type,
    sK2_SY22: $i ).

thf(tp_sK3_SY25,type,
    sK3_SY25: $i ).

thf(tp_sK4_SY27,type,
    sK4_SY27: $i ).

thf(tp_s_afs,type,
    s_afs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_s_col,type,
    s_col: $i > $i > $i > $o ).

thf(tp_s_e,type,
    s_e: $i > $i > $i > $i > $o ).

thf(tp_s_e3,type,
    s_e3: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_s_fs,type,
    s_fs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_s_ifs,type,
    s_ifs: $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_s_kf,type,
    s_kf: $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_s_m,type,
    s_m: $i > $i > $i > $o ).

thf(tp_s_t,type,
    s_t: $i > $i > $i > $o ).

thf(tp_sameside,type,
    sameside: $i > $i > $i > $o ).

thf(tp_xb,type,
    xb: $i ).

thf(11,axiom,
    ! [Xa: $i,Xp: $i] :
      ( ( s @ Xa @ ( s @ Xa @ Xp ) )
      = Xp ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_7) ).

thf(12,axiom,
    ! [Xp: $i,Xa: $i,Xq: $i] :
      ( ~ ( s_m @ Xp @ Xa @ Xq )
      | ( Xq
        = ( s @ Xa @ Xp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_6) ).

thf(13,axiom,
    ! [Xp: $i,Xa: $i,Xr: $i,Xq: $i] :
      ( ~ ( s_m @ Xp @ Xa @ Xr )
      | ~ ( s_m @ Xp @ Xa @ Xq )
      | ( Xr = Xq ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_4b) ).

thf(14,axiom,
    ! [Xp: $i,Xa: $i] : ( s_m @ Xp @ Xa @ ( s @ Xa @ Xp ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_4a) ).

thf(15,axiom,
    ! [Xa: $i,Xm: $i] :
      ( ( s_m @ Xa @ Xm @ Xa )
      | ( Xm != Xa ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_3b) ).

thf(16,axiom,
    ! [Xa: $i,Xm: $i] :
      ( ~ ( s_m @ Xa @ Xm @ Xa )
      | ( Xm = Xa ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_3a) ).

thf(17,axiom,
    ! [Xa: $i,Xm: $i,Xb: $i] :
      ( ~ ( s_m @ Xa @ Xm @ Xb )
      | ( s_m @ Xb @ Xm @ Xa ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_2) ).

thf(110,conjecture,
    ! [Xa: $i,Xp: $i,Xr: $i,Xq: $i] :
      ( ( ( s @ Xa @ Xp )
       != Xr )
      | ( ( s @ Xa @ Xq )
       != Xr )
      | ( Xp = Xq ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz7_8) ).

thf(111,negated_conjecture,
    ( ( ! [Xa: $i,Xp: $i,Xr: $i,Xq: $i] :
          ( ( ( s @ Xa @ Xp )
           != Xr )
          | ( ( s @ Xa @ Xq )
           != Xr )
          | ( Xp = Xq ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[110]) ).

thf(112,plain,
    ( ( ! [Xa: $i,Xp: $i,Xr: $i,Xq: $i] :
          ( ( ( s @ Xa @ Xp )
           != Xr )
          | ( ( s @ Xa @ Xq )
           != Xr )
          | ( Xp = Xq ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[111]) ).

thf(113,plain,
    ( ( ! [Xp: $i,Xa: $i,Xr: $i,Xq: $i] :
          ( ~ ( s_m @ Xp @ Xa @ Xr )
          | ~ ( s_m @ Xp @ Xa @ Xq )
          | ( Xr = Xq ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(114,plain,
    ( ( ! [Xa: $i,Xm: $i] :
          ( ( s_m @ Xa @ Xm @ Xa )
          | ( Xm != Xa ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(115,plain,
    ( ( ! [Xa: $i,Xm: $i] :
          ( ~ ( s_m @ Xa @ Xm @ Xa )
          | ( Xm = Xa ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(116,plain,
    ( ( ! [Xa: $i,Xm: $i,Xb: $i] :
          ( ~ ( s_m @ Xa @ Xm @ Xb )
          | ( s_m @ Xb @ Xm @ Xa ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(117,plain,
    ( ( ! [Xa: $i,Xp: $i] :
          ( ( s @ Xa @ ( s @ Xa @ Xp ) )
          = Xp ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(118,plain,
    ( ( ! [Xp: $i,Xa: $i,Xq: $i] :
          ( ~ ( s_m @ Xp @ Xa @ Xq )
          | ( Xq
            = ( s @ Xa @ Xp ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(119,plain,
    ( ( ! [Xp: $i,Xa: $i] : ( s_m @ Xp @ Xa @ ( s @ Xa @ Xp ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(120,plain,
    ( ( ! [SY22: $i,SY23: $i,SY24: $i] :
          ( ( ( s @ sK1_Xa @ SY22 )
           != SY23 )
          | ( ( s @ sK1_Xa @ SY24 )
           != SY23 )
          | ( SY22 = SY24 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[112]) ).

thf(121,plain,
    ( ( ! [SY25: $i,SY26: $i] :
          ( ( ( s @ sK1_Xa @ sK2_SY22 )
           != SY25 )
          | ( ( s @ sK1_Xa @ SY26 )
           != SY25 )
          | ( sK2_SY22 = SY26 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[120]) ).

thf(122,plain,
    ( ( ! [SY27: $i] :
          ( ( ( s @ sK1_Xa @ sK2_SY22 )
           != sK3_SY25 )
          | ( ( s @ sK1_Xa @ SY27 )
           != sK3_SY25 )
          | ( sK2_SY22 = SY27 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[121]) ).

thf(123,plain,
    ( ( ( ( s @ sK1_Xa @ sK2_SY22 )
       != sK3_SY25 )
      | ( ( s @ sK1_Xa @ sK4_SY27 )
       != sK3_SY25 )
      | ( sK2_SY22 = sK4_SY27 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[122]) ).

thf(124,plain,
    ( ( ~ ( ( ( s @ sK1_Xa @ sK2_SY22 )
           != sK3_SY25 )
          | ( ( s @ sK1_Xa @ sK4_SY27 )
           != sK3_SY25 )
          | ( sK2_SY22 = sK4_SY27 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[123]) ).

thf(125,plain,
    ( ( ( sK2_SY22 != sK4_SY27 )
      & ( ( s @ sK1_Xa @ sK2_SY22 )
        = sK3_SY25 )
      & ( ( s @ sK1_Xa @ sK4_SY27 )
        = sK3_SY25 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[124]) ).

thf(126,plain,
    ( ( ! [Xp: $i,Xa: $i,Xr: $i,Xq: $i] :
          ( ( Xr = Xq )
          | ~ ( s_m @ Xp @ Xa @ Xr )
          | ~ ( s_m @ Xp @ Xa @ Xq ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[113]) ).

thf(127,plain,
    ( ( ! [Xa: $i,Xm: $i] :
          ( ( Xm != Xa )
          | ( s_m @ Xa @ Xm @ Xa ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[114]) ).

thf(128,plain,
    ( ( ! [Xp: $i,Xa: $i] : ( s_m @ Xp @ Xa @ ( s @ Xa @ Xp ) ) )
    = $true ),
    inference(copy,[status(thm)],[119]) ).

thf(129,plain,
    ( ( ! [Xp: $i,Xa: $i,Xq: $i] :
          ( ~ ( s_m @ Xp @ Xa @ Xq )
          | ( Xq
            = ( s @ Xa @ Xp ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[118]) ).

thf(130,plain,
    ( ( ! [Xa: $i,Xp: $i] :
          ( ( s @ Xa @ ( s @ Xa @ Xp ) )
          = Xp ) )
    = $true ),
    inference(copy,[status(thm)],[117]) ).

thf(131,plain,
    ( ( ! [Xa: $i,Xm: $i,Xb: $i] :
          ( ~ ( s_m @ Xa @ Xm @ Xb )
          | ( s_m @ Xb @ Xm @ Xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[116]) ).

thf(132,plain,
    ( ( ! [Xa: $i,Xm: $i] :
          ( ~ ( s_m @ Xa @ Xm @ Xa )
          | ( Xm = Xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[115]) ).

thf(133,plain,
    ( ( ! [Xa: $i,Xm: $i] :
          ( ( Xm != Xa )
          | ( s_m @ Xa @ Xm @ Xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[127]) ).

thf(134,plain,
    ( ( ! [Xp: $i,Xa: $i,Xr: $i,Xq: $i] :
          ( ( Xr = Xq )
          | ~ ( s_m @ Xp @ Xa @ Xr )
          | ~ ( s_m @ Xp @ Xa @ Xq ) ) )
    = $true ),
    inference(copy,[status(thm)],[126]) ).

thf(135,plain,
    ( ( ( sK2_SY22 != sK4_SY27 )
      & ( ( s @ sK1_Xa @ sK2_SY22 )
        = sK3_SY25 )
      & ( ( s @ sK1_Xa @ sK4_SY27 )
        = sK3_SY25 ) )
    = $true ),
    inference(copy,[status(thm)],[125]) ).

thf(136,plain,
    ( ( ~ ( ~ ( ( sK2_SY22 != sK4_SY27 ) )
          | ~ ~ ( ( ( s @ sK1_Xa @ sK2_SY22 )
                 != sK3_SY25 )
                | ( ( s @ sK1_Xa @ sK4_SY27 )
                 != sK3_SY25 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[135]) ).

thf(137,plain,
    ! [SV1: $i] :
      ( ( ! [SY28: $i] : ( s_m @ SV1 @ SY28 @ ( s @ SY28 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[128]) ).

thf(138,plain,
    ! [SV2: $i] :
      ( ( ! [SY29: $i,SY30: $i] :
            ( ~ ( s_m @ SV2 @ SY29 @ SY30 )
            | ( SY30
              = ( s @ SY29 @ SV2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(139,plain,
    ! [SV3: $i] :
      ( ( ! [SY31: $i] :
            ( ( s @ SV3 @ ( s @ SV3 @ SY31 ) )
            = SY31 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[130]) ).

thf(140,plain,
    ! [SV4: $i] :
      ( ( ! [SY32: $i,SY33: $i] :
            ( ~ ( s_m @ SV4 @ SY32 @ SY33 )
            | ( s_m @ SY33 @ SY32 @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[131]) ).

thf(141,plain,
    ! [SV5: $i] :
      ( ( ! [SY34: $i] :
            ( ~ ( s_m @ SV5 @ SY34 @ SV5 )
            | ( SY34 = SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[132]) ).

thf(142,plain,
    ! [SV6: $i] :
      ( ( ! [SY35: $i] :
            ( ( SY35 != SV6 )
            | ( s_m @ SV6 @ SY35 @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[133]) ).

thf(143,plain,
    ! [SV7: $i] :
      ( ( ! [SY36: $i,SY37: $i,SY38: $i] :
            ( ( SY37 = SY38 )
            | ~ ( s_m @ SV7 @ SY36 @ SY37 )
            | ~ ( s_m @ SV7 @ SY36 @ SY38 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[134]) ).

thf(144,plain,
    ( ( ~ ( ( sK2_SY22 != sK4_SY27 ) )
      | ~ ~ ( ( ( s @ sK1_Xa @ sK2_SY22 )
             != sK3_SY25 )
            | ( ( s @ sK1_Xa @ sK4_SY27 )
             != sK3_SY25 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[136]) ).

thf(145,plain,
    ! [SV8: $i,SV1: $i] :
      ( ( s_m @ SV1 @ SV8 @ ( s @ SV8 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[137]) ).

thf(146,plain,
    ! [SV9: $i,SV2: $i] :
      ( ( ! [SY39: $i] :
            ( ~ ( s_m @ SV2 @ SV9 @ SY39 )
            | ( SY39
              = ( s @ SV9 @ SV2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[138]) ).

thf(147,plain,
    ! [SV10: $i,SV3: $i] :
      ( ( ( s @ SV3 @ ( s @ SV3 @ SV10 ) )
        = SV10 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[139]) ).

thf(148,plain,
    ! [SV11: $i,SV4: $i] :
      ( ( ! [SY40: $i] :
            ( ~ ( s_m @ SV4 @ SV11 @ SY40 )
            | ( s_m @ SY40 @ SV11 @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(149,plain,
    ! [SV12: $i,SV5: $i] :
      ( ( ~ ( s_m @ SV5 @ SV12 @ SV5 )
        | ( SV12 = SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(150,plain,
    ! [SV6: $i,SV13: $i] :
      ( ( ( SV13 != SV6 )
        | ( s_m @ SV6 @ SV13 @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[142]) ).

thf(151,plain,
    ! [SV14: $i,SV7: $i] :
      ( ( ! [SY41: $i,SY42: $i] :
            ( ( SY41 = SY42 )
            | ~ ( s_m @ SV7 @ SV14 @ SY41 )
            | ~ ( s_m @ SV7 @ SV14 @ SY42 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[143]) ).

thf(152,plain,
    ( ( ~ ( ( sK2_SY22 != sK4_SY27 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[144]) ).

thf(153,plain,
    ( ( ~ ~ ( ( ( s @ sK1_Xa @ sK2_SY22 )
             != sK3_SY25 )
            | ( ( s @ sK1_Xa @ sK4_SY27 )
             != sK3_SY25 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[144]) ).

thf(154,plain,
    ! [SV15: $i,SV9: $i,SV2: $i] :
      ( ( ~ ( s_m @ SV2 @ SV9 @ SV15 )
        | ( SV15
          = ( s @ SV9 @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[146]) ).

thf(155,plain,
    ! [SV16: $i,SV11: $i,SV4: $i] :
      ( ( ~ ( s_m @ SV4 @ SV11 @ SV16 )
        | ( s_m @ SV16 @ SV11 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[148]) ).

thf(156,plain,
    ! [SV12: $i,SV5: $i] :
      ( ( ( ~ ( s_m @ SV5 @ SV12 @ SV5 ) )
        = $true )
      | ( ( SV12 = SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[149]) ).

thf(157,plain,
    ! [SV6: $i,SV13: $i] :
      ( ( ( ( SV13 != SV6 ) )
        = $true )
      | ( ( s_m @ SV6 @ SV13 @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[150]) ).

thf(158,plain,
    ! [SV14: $i,SV7: $i,SV17: $i] :
      ( ( ! [SY43: $i] :
            ( ( SV17 = SY43 )
            | ~ ( s_m @ SV7 @ SV14 @ SV17 )
            | ~ ( s_m @ SV7 @ SV14 @ SY43 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[151]) ).

thf(159,plain,
    ( ( ( sK2_SY22 != sK4_SY27 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[152]) ).

thf(160,plain,
    ( ( ~ ( ( ( s @ sK1_Xa @ sK2_SY22 )
           != sK3_SY25 )
          | ( ( s @ sK1_Xa @ sK4_SY27 )
           != sK3_SY25 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[153]) ).

thf(161,plain,
    ! [SV15: $i,SV9: $i,SV2: $i] :
      ( ( ( ~ ( s_m @ SV2 @ SV9 @ SV15 ) )
        = $true )
      | ( ( SV15
          = ( s @ SV9 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[154]) ).

thf(162,plain,
    ! [SV16: $i,SV11: $i,SV4: $i] :
      ( ( ( ~ ( s_m @ SV4 @ SV11 @ SV16 ) )
        = $true )
      | ( ( s_m @ SV16 @ SV11 @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[155]) ).

thf(163,plain,
    ! [SV12: $i,SV5: $i] :
      ( ( ( s_m @ SV5 @ SV12 @ SV5 )
        = $false )
      | ( ( SV12 = SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[156]) ).

thf(164,plain,
    ! [SV6: $i,SV13: $i] :
      ( ( ( SV13 = SV6 )
        = $false )
      | ( ( s_m @ SV6 @ SV13 @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[157]) ).

thf(165,plain,
    ! [SV14: $i,SV7: $i,SV18: $i,SV17: $i] :
      ( ( ( SV17 = SV18 )
        | ~ ( s_m @ SV7 @ SV14 @ SV17 )
        | ~ ( s_m @ SV7 @ SV14 @ SV18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[158]) ).

thf(166,plain,
    ( ( sK2_SY22 = sK4_SY27 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[159]) ).

thf(167,plain,
    ( ( ( ( s @ sK1_Xa @ sK2_SY22 )
       != sK3_SY25 )
      | ( ( s @ sK1_Xa @ sK4_SY27 )
       != sK3_SY25 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[160]) ).

thf(168,plain,
    ! [SV15: $i,SV9: $i,SV2: $i] :
      ( ( ( s_m @ SV2 @ SV9 @ SV15 )
        = $false )
      | ( ( SV15
          = ( s @ SV9 @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[161]) ).

thf(169,plain,
    ! [SV16: $i,SV11: $i,SV4: $i] :
      ( ( ( s_m @ SV4 @ SV11 @ SV16 )
        = $false )
      | ( ( s_m @ SV16 @ SV11 @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[162]) ).

thf(170,plain,
    ! [SV14: $i,SV7: $i,SV18: $i,SV17: $i] :
      ( ( ( SV17 = SV18 )
        = $true )
      | ( ( ~ ( s_m @ SV7 @ SV14 @ SV17 )
          | ~ ( s_m @ SV7 @ SV14 @ SV18 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[165]) ).

thf(171,plain,
    ( ( ( ( s @ sK1_Xa @ sK2_SY22 )
       != sK3_SY25 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[167]) ).

thf(172,plain,
    ( ( ( ( s @ sK1_Xa @ sK4_SY27 )
       != sK3_SY25 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[167]) ).

thf(173,plain,
    ! [SV18: $i,SV17: $i,SV14: $i,SV7: $i] :
      ( ( ( ~ ( s_m @ SV7 @ SV14 @ SV17 ) )
        = $true )
      | ( ( ~ ( s_m @ SV7 @ SV14 @ SV18 ) )
        = $true )
      | ( ( SV17 = SV18 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[170]) ).

thf(174,plain,
    ( ( ( s @ sK1_Xa @ sK2_SY22 )
      = sK3_SY25 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[171]) ).

thf(175,plain,
    ( ( ( s @ sK1_Xa @ sK4_SY27 )
      = sK3_SY25 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[172]) ).

thf(176,plain,
    ! [SV18: $i,SV17: $i,SV14: $i,SV7: $i] :
      ( ( ( s_m @ SV7 @ SV14 @ SV17 )
        = $false )
      | ( ( ~ ( s_m @ SV7 @ SV14 @ SV18 ) )
        = $true )
      | ( ( SV17 = SV18 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[173]) ).

thf(177,plain,
    ! [SV17: $i,SV18: $i,SV14: $i,SV7: $i] :
      ( ( ( s_m @ SV7 @ SV14 @ SV18 )
        = $false )
      | ( ( s_m @ SV7 @ SV14 @ SV17 )
        = $false )
      | ( ( SV17 = SV18 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[176]) ).

thf(178,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[145,177,175,174,169,168,166,164,163,147]) ).

thf(179,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[178]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO498+1 : TPTP v8.1.0. Released v7.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n017.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 : Sat Jun 18 12:35:27 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.43  ..
% 0.89/1.14  
% 0.89/1.14   No.of.Axioms: 109
% 0.89/1.14  
% 0.89/1.14   Length.of.Defs: 0
% 0.89/1.14  
% 0.89/1.14   Contains.Choice.Funs: false
% 1.01/1.19  ....
% 1.01/1.20  (rf:2,axioms:7,ps:3,u:5,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:111,loop_count:0,foatp_calls:0,translation:fof_full)...
% 1.05/1.23  
% 1.05/1.23  ********************************
% 1.05/1.23  *   All subproblems solved!    *
% 1.05/1.23  ********************************
% 1.05/1.23  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:7,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:178,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.05/1.24  
% 1.05/1.24  %**** Beginning of derivation protocol ****
% 1.05/1.24  % SZS output start CNFRefutation
% See solution above
% 1.05/1.24  
% 1.05/1.24  %**** End of derivation protocol ****
% 1.05/1.24  %**** no. of clauses in derivation: 77 ****
% 1.05/1.24  %**** clause counter: 178 ****
% 1.05/1.24  
% 1.05/1.24  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:7,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:178,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------