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Vampire---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : GEG018^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 07:49:27 AM UTC 2026

% Result   : Theorem 0.20s 0.28s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   59 (  56 unt;   0 typ;   0 def)
%            Number of atoms       :  570 (  55 equ;   0 cnn)
%            Maximal formula atoms :    4 (   9 avg)
%            Number of connectives : 1464 (  98   ~;  10   |; 116   &; 977   @)
%                                         (   0 <=>;  94  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Number of types       :    4 (   2 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   86 (  81 usr;  14 con; 0-4 aty)
%                                         ( 113  !!;  56  ??;   0 @@+;   0 @@-)
%            Number of variables   :  334 ( 309   ^;  18   !;   7   ?; 334   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    mu: $tType ).

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_7,type,
    reg: $tType ).

thf(func_def_0,type,
    meq_ind: mu > mu > $i > $o ).

thf(func_def_1,type,
    meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_3,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(func_def_4,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_5,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_6,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_7,type,
    mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_8,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_9,type,
    mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_10,type,
    mforall_ind: ( mu > $i > $o ) > $i > $o ).

thf(func_def_11,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(func_def_12,type,
    mexists_ind: ( mu > $i > $o ) > $i > $o ).

thf(func_def_13,type,
    mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(func_def_14,type,
    mtrue: $i > $o ).

thf(func_def_15,type,
    mfalse: $i > $o ).

thf(func_def_16,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_17,type,
    mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(func_def_18,type,
    mreflexive: ( $i > $i > $o ) > $o ).

thf(func_def_19,type,
    msymmetric: ( $i > $i > $o ) > $o ).

thf(func_def_20,type,
    mserial: ( $i > $i > $o ) > $o ).

thf(func_def_21,type,
    mtransitive: ( $i > $i > $o ) > $o ).

thf(func_def_22,type,
    meuclidean: ( $i > $i > $o ) > $o ).

thf(func_def_23,type,
    mpartially_functional: ( $i > $i > $o ) > $o ).

thf(func_def_24,type,
    mfunctional: ( $i > $i > $o ) > $o ).

thf(func_def_25,type,
    mweakly_dense: ( $i > $i > $o ) > $o ).

thf(func_def_26,type,
    mweakly_connected: ( $i > $i > $o ) > $o ).

thf(func_def_27,type,
    mweakly_directed: ( $i > $i > $o ) > $o ).

thf(func_def_28,type,
    mvalid: ( $i > $o ) > $o ).

thf(func_def_29,type,
    minvalid: ( $i > $o ) > $o ).

thf(func_def_30,type,
    msatisfiable: ( $i > $o ) > $o ).

thf(func_def_31,type,
    mcountersatisfiable: ( $i > $o ) > $o ).

thf(func_def_32,type,
    c: reg > reg > $o ).

thf(func_def_33,type,
    dc: reg > reg > $o ).

thf(func_def_34,type,
    p: reg > reg > $o ).

thf(func_def_35,type,
    eq: reg > reg > $o ).

thf(func_def_36,type,
    o: reg > reg > $o ).

thf(func_def_37,type,
    po: reg > reg > $o ).

thf(func_def_38,type,
    ec: reg > reg > $o ).

thf(func_def_39,type,
    pp: reg > reg > $o ).

thf(func_def_40,type,
    tpp: reg > reg > $o ).

thf(func_def_41,type,
    ntpp: reg > reg > $o ).

thf(func_def_42,type,
    catalunya: reg ).

thf(func_def_43,type,
    france: reg ).

thf(func_def_44,type,
    spain: reg ).

thf(func_def_45,type,
    paris: reg ).

thf(func_def_46,type,
    a: $i > $i > $o ).

thf(func_def_47,type,
    fool: $i > $i > $o ).

thf(func_def_48,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_49,type,
    vOR: $o > $o > $o ).

thf(func_def_50,type,
    vNOT: $o > $o ).

thf(func_def_51,type,
    db3: 
      !>[X0: $tType] : X0 ).

thf(func_def_52,type,
    db1: 
      !>[X0: $tType] : X0 ).

thf(func_def_53,type,
    db0: 
      !>[X0: $tType] : X0 ).

thf(func_def_54,type,
    db2: 
      !>[X0: $tType] : X0 ).

thf(func_def_55,type,
    vLAM: 
      !>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).

thf(func_def_58,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_59,type,
    vAND: $o > $o > $o ).

thf(func_def_60,type,
    vIMP: $o > $o > $o ).

thf(func_def_61,type,
    db4: 
      !>[X0: $tType] : X0 ).

thf(func_def_62,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_63,type,
    sK0: reg > reg ).

thf(func_def_64,type,
    sK1: reg > reg ).

thf(func_def_65,type,
    sK2: reg ).

thf(func_def_66,type,
    sK3: reg > reg ).

thf(func_def_67,type,
    sK4: reg > reg ).

thf(func_def_68,type,
    sK5: reg > reg ).

thf(func_def_69,type,
    sK6: reg > reg ).

thf(func_def_70,type,
    sK7: reg ).

thf(func_def_71,type,
    sK8: reg > reg ).

thf(func_def_72,type,
    sK9: reg > reg ).

thf(func_def_73,type,
    sK10: reg ).

thf(func_def_76,type,
    sK13: reg ).

thf(func_def_77,type,
    sK14: reg > reg ).

thf(func_def_78,type,
    sK15: reg > reg > reg ).

thf(func_def_79,type,
    sK16: reg > reg ).

thf(func_def_80,type,
    sK17: $i > ( $i > $o ) > $i ).

thf(func_def_81,type,
    sK18: $i > ( $i > $o ) > $i ).

thf(func_def_82,type,
    sK19: $i > ( $i > $o ) > $i ).

thf(f16,axiom,
    ( mbox
    = ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
        ! [X3: $i] :
          ( ( X1 @ X3 )
          | ~ ( X0 @ X2 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).

thf(f28,axiom,
    ( ( ^ [X0: $i > $o] :
        ! [X1: $i] : ( X0 @ X1 ) )
    = mvalid ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).

thf(f35,axiom,
    ( ( ^ [X0: reg,X1: reg] :
        ! [X2: reg] :
          ( ( c @ X2 @ X0 )
         => ( c @ X2 @ X1 ) ) )
    = p ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',p) ).

thf(f37,axiom,
    ( o
    = ( ^ [X0: reg,X1: reg] :
        ? [X2: reg] :
          ( ( p @ X2 @ X0 )
          & ( p @ X2 @ X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',o) ).

thf(f39,axiom,
    ( ( ^ [X0: reg,X1: reg] :
          ( ~ ( o @ X0 @ X1 )
          & ( c @ X0 @ X1 ) ) )
    = ec ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ec) ).

thf(f40,axiom,
    ( ( ^ [X0: reg,X1: reg] :
          ( ( p @ X0 @ X1 )
          & ~ ( p @ X1 @ X0 ) ) )
    = pp ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',pp) ).

thf(f42,axiom,
    ( ( ^ [X0: reg,X1: reg] :
          ( ( pp @ X0 @ X1 )
          & ~ ? [X2: reg] :
                ( ( ec @ X2 @ X1 )
                & ( ec @ X2 @ X0 ) ) ) )
    = ntpp ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ntpp) ).

thf(f49,conjecture,
    ( mvalid
    @ ( mbox @ fool
      @ ^ [X0: $i] :
          ~ ? [X1: reg] :
            ! [X2: reg] : ( ntpp @ X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(f50,negated_conjecture,
    ~ ( mvalid
      @ ( mbox @ fool
        @ ^ [X0: $i] :
            ~ ? [X1: reg] :
              ! [X2: reg] : ( ntpp @ X1 @ X2 ) ) ),
    inference(negated_conjecture,[status(cth)],[f49]) ).

thf(f51,plain,
    ( mbox
    = ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
        ! [X3: $i] :
          ( ( X1 @ X3 )
          | ~ ( X0 @ X2 @ X3 ) ) ) ),
    inference(rectify,[],[f16]) ).

thf(f52,plain,
    ( mbox
    = ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
          ( !! @ $i
          @ ^ [Y3: $i] :
              ( ~ ( Y0 @ Y2 @ Y3 )
              | ( Y1 @ Y3 ) ) ) ) ),
    inference(fool_elimination,[],[f51]) ).

thf(f88,plain,
    ( ( ^ [X0: $i > $o] :
        ! [X1: $i] : ( X0 @ X1 ) )
    = mvalid ),
    inference(rectify,[],[f28]) ).

thf(f89,plain,
    ( mvalid
    = ( ^ [Y0: $i > $o] :
          ( !! @ $i
          @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
    inference(fool_elimination,[],[f88]) ).

thf(f99,plain,
    ~ ( mvalid
      @ ( mbox @ fool
        @ ^ [X0: $i] :
            ~ ? [X1: reg] :
              ! [X2: reg] : ( ntpp @ X1 @ X2 ) ) ),
    inference(rectify,[],[f50]) ).

thf(f100,plain,
    ( $true
   != ( mvalid
      @ ( mbox @ fool
        @ ^ [Y0: $i] :
            ~ ( ?? @ reg
              @ ^ [Y1: reg] :
                  ( !! @ reg
                  @ ^ [Y2: reg] : ( ntpp @ Y1 @ Y2 ) ) ) ) ) ),
    inference(fool_elimination,[],[f99]) ).

thf(f102,plain,
    ( ( ^ [X0: reg,X1: reg] :
        ! [X2: reg] :
          ( ( c @ X2 @ X0 )
         => ( c @ X2 @ X1 ) ) )
    = p ),
    inference(rectify,[],[f35]) ).

thf(f103,plain,
    ( p
    = ( ^ [Y0: reg,Y1: reg] :
          ( !! @ reg
          @ ^ [Y2: reg] :
              ( ( c @ Y2 @ Y0 )
             => ( c @ Y2 @ Y1 ) ) ) ) ),
    inference(fool_elimination,[],[f102]) ).

thf(f107,plain,
    ( ( ^ [X0: reg,X1: reg] :
          ( ( p @ X0 @ X1 )
          & ~ ( p @ X1 @ X0 ) ) )
    = pp ),
    inference(rectify,[],[f40]) ).

thf(f108,plain,
    ( pp
    = ( ^ [Y0: reg,Y1: reg] :
          ( ~ ( p @ Y1 @ Y0 )
          & ( p @ Y0 @ Y1 ) ) ) ),
    inference(fool_elimination,[],[f107]) ).

thf(f109,plain,
    ( ( ^ [X0: reg,X1: reg] :
          ( ~ ( o @ X0 @ X1 )
          & ( c @ X0 @ X1 ) ) )
    = ec ),
    inference(rectify,[],[f39]) ).

thf(f110,plain,
    ( ec
    = ( ^ [Y0: reg,Y1: reg] :
          ( ( c @ Y0 @ Y1 )
          & ~ ( o @ Y0 @ Y1 ) ) ) ),
    inference(fool_elimination,[],[f109]) ).

thf(f116,plain,
    ( ( ^ [X0: reg,X1: reg] :
          ( ( pp @ X0 @ X1 )
          & ~ ? [X2: reg] :
                ( ( ec @ X2 @ X1 )
                & ( ec @ X2 @ X0 ) ) ) )
    = ntpp ),
    inference(rectify,[],[f42]) ).

thf(f117,plain,
    ( ntpp
    = ( ^ [Y0: reg,Y1: reg] :
          ( ~ ( ?? @ reg
              @ ^ [Y2: reg] :
                  ( ( ec @ Y2 @ Y0 )
                  & ( ec @ Y2 @ Y1 ) ) )
          & ( pp @ Y0 @ Y1 ) ) ) ),
    inference(fool_elimination,[],[f116]) ).

thf(f126,plain,
    ( o
    = ( ^ [X0: reg,X1: reg] :
        ? [X2: reg] :
          ( ( p @ X2 @ X0 )
          & ( p @ X2 @ X1 ) ) ) ),
    inference(rectify,[],[f37]) ).

thf(f127,plain,
    ( o
    = ( ^ [Y0: reg,Y1: reg] :
          ( ?? @ reg
          @ ^ [Y2: reg] :
              ( ( p @ Y2 @ Y1 )
              & ( p @ Y2 @ Y0 ) ) ) ) ),
    inference(fool_elimination,[],[f126]) ).

thf(f138,plain,
    ( $true
   != ( mvalid
      @ ( mbox @ fool
        @ ^ [Y0: $i] :
            ~ ( ?? @ reg
              @ ^ [Y1: reg] :
                  ( !! @ reg
                  @ ^ [Y2: reg] : ( ntpp @ Y1 @ Y2 ) ) ) ) ) ),
    inference(flattening,[],[f100]) ).

thf(f146,plain,
    ( pp
    = ( ^ [Y0: reg,Y1: reg] :
          ( ~ ( p @ Y1 @ Y0 )
          & ( p @ Y0 @ Y1 ) ) ) ),
    inference(cnf_transformation,[],[f108]) ).

thf(f151,plain,
    ( p
    = ( ^ [Y0: reg,Y1: reg] :
          ( !! @ reg
          @ ^ [Y2: reg] :
              ( ( c @ Y2 @ Y0 )
             => ( c @ Y2 @ Y1 ) ) ) ) ),
    inference(cnf_transformation,[],[f103]) ).

thf(f153,plain,
    ( o
    = ( ^ [Y0: reg,Y1: reg] :
          ( ?? @ reg
          @ ^ [Y2: reg] :
              ( ( p @ Y2 @ Y1 )
              & ( p @ Y2 @ Y0 ) ) ) ) ),
    inference(cnf_transformation,[],[f127]) ).

thf(f172,plain,
    ( $true
   != ( mvalid
      @ ( mbox @ fool
        @ ^ [Y0: $i] :
            ~ ( ?? @ reg
              @ ^ [Y1: reg] :
                  ( !! @ reg
                  @ ^ [Y2: reg] : ( ntpp @ Y1 @ Y2 ) ) ) ) ) ),
    inference(cnf_transformation,[],[f138]) ).

thf(f173,plain,
    ( ec
    = ( ^ [Y0: reg,Y1: reg] :
          ( ( c @ Y0 @ Y1 )
          & ~ ( o @ Y0 @ Y1 ) ) ) ),
    inference(cnf_transformation,[],[f110]) ).

thf(f174,plain,
    ( ntpp
    = ( ^ [Y0: reg,Y1: reg] :
          ( ~ ( ?? @ reg
              @ ^ [Y2: reg] :
                  ( ( ec @ Y2 @ Y0 )
                  & ( ec @ Y2 @ Y1 ) ) )
          & ( pp @ Y0 @ Y1 ) ) ) ),
    inference(cnf_transformation,[],[f117]) ).

thf(f179,plain,
    ( mvalid
    = ( ^ [Y0: $i > $o] :
          ( !! @ $i
          @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
    inference(cnf_transformation,[],[f89]) ).

thf(f180,plain,
    ( mbox
    = ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
          ( !! @ $i
          @ ^ [Y3: $i] :
              ( ~ ( Y0 @ Y2 @ Y3 )
              | ( Y1 @ Y3 ) ) ) ) ),
    inference(cnf_transformation,[],[f52]) ).

thf(f201,plain,
    ( o
    = ( ^ [Y0: reg,Y1: reg] :
          ( ?? @ reg
          @ ^ [Y2: reg] :
              ( ( ^ [Y3: reg,Y4: reg] :
                    ( !! @ reg
                    @ ^ [Y5: reg] :
                        ( ( c @ Y5 @ Y3 )
                       => ( c @ Y5 @ Y4 ) ) )
                @ Y2
                @ Y1 )
              & ( ^ [Y3: reg,Y4: reg] :
                    ( !! @ reg
                    @ ^ [Y5: reg] :
                        ( ( c @ Y5 @ Y3 )
                       => ( c @ Y5 @ Y4 ) ) )
                @ Y2
                @ Y0 ) ) ) ) ),
    inference(definition_unfolding,[],[f153,f151,f151]) ).

thf(f203,plain,
    ( ec
    = ( ^ [Y0: reg,Y1: reg] :
          ( ( c @ Y0 @ Y1 )
          & ~ ( ^ [Y2: reg,Y3: reg] :
                  ( ?? @ reg
                  @ ^ [Y4: reg] :
                      ( ( ^ [Y5: reg,Y6: reg] :
                            ( !! @ reg
                            @ ^ [Y7: reg] :
                                ( ( c @ Y7 @ Y5 )
                               => ( c @ Y7 @ Y6 ) ) )
                        @ Y4
                        @ Y3 )
                      & ( ^ [Y5: reg,Y6: reg] :
                            ( !! @ reg
                            @ ^ [Y7: reg] :
                                ( ( c @ Y7 @ Y5 )
                               => ( c @ Y7 @ Y6 ) ) )
                        @ Y4
                        @ Y2 ) ) )
              @ Y0
              @ Y1 ) ) ) ),
    inference(definition_unfolding,[],[f173,f201]) ).

thf(f204,plain,
    ( pp
    = ( ^ [Y0: reg,Y1: reg] :
          ( ~ ( ^ [Y2: reg,Y3: reg] :
                  ( !! @ reg
                  @ ^ [Y4: reg] :
                      ( ( c @ Y4 @ Y2 )
                     => ( c @ Y4 @ Y3 ) ) )
              @ Y1
              @ Y0 )
          & ( ^ [Y2: reg,Y3: reg] :
                ( !! @ reg
                @ ^ [Y4: reg] :
                    ( ( c @ Y4 @ Y2 )
                   => ( c @ Y4 @ Y3 ) ) )
            @ Y0
            @ Y1 ) ) ) ),
    inference(definition_unfolding,[],[f146,f151,f151]) ).

thf(f206,plain,
    ( ntpp
    = ( ^ [Y0: reg,Y1: reg] :
          ( ~ ( ?? @ reg
              @ ^ [Y2: reg] :
                  ( ( ^ [Y3: reg,Y4: reg] :
                        ( ( c @ Y3 @ Y4 )
                        & ~ ( ^ [Y5: reg,Y6: reg] :
                                ( ?? @ reg
                                @ ^ [Y7: reg] :
                                    ( ( ^ [Y8: reg,Y9: reg] :
                                          ( !! @ reg
                                          @ ^ [Y10: reg] :
                                              ( ( c @ Y10 @ Y8 )
                                             => ( c @ Y10 @ Y9 ) ) )
                                      @ Y7
                                      @ Y6 )
                                    & ( ^ [Y8: reg,Y9: reg] :
                                          ( !! @ reg
                                          @ ^ [Y10: reg] :
                                              ( ( c @ Y10 @ Y8 )
                                             => ( c @ Y10 @ Y9 ) ) )
                                      @ Y7
                                      @ Y5 ) ) )
                            @ Y3
                            @ Y4 ) )
                    @ Y2
                    @ Y0 )
                  & ( ^ [Y3: reg,Y4: reg] :
                        ( ( c @ Y3 @ Y4 )
                        & ~ ( ^ [Y5: reg,Y6: reg] :
                                ( ?? @ reg
                                @ ^ [Y7: reg] :
                                    ( ( ^ [Y8: reg,Y9: reg] :
                                          ( !! @ reg
                                          @ ^ [Y10: reg] :
                                              ( ( c @ Y10 @ Y8 )
                                             => ( c @ Y10 @ Y9 ) ) )
                                      @ Y7
                                      @ Y6 )
                                    & ( ^ [Y8: reg,Y9: reg] :
                                          ( !! @ reg
                                          @ ^ [Y10: reg] :
                                              ( ( c @ Y10 @ Y8 )
                                             => ( c @ Y10 @ Y9 ) ) )
                                      @ Y7
                                      @ Y5 ) ) )
                            @ Y3
                            @ Y4 ) )
                    @ Y2
                    @ Y1 ) ) )
          & ( ^ [Y2: reg,Y3: reg] :
                ( ~ ( ^ [Y4: reg,Y5: reg] :
                        ( !! @ reg
                        @ ^ [Y6: reg] :
                            ( ( c @ Y6 @ Y4 )
                           => ( c @ Y6 @ Y5 ) ) )
                    @ Y3
                    @ Y2 )
                & ( ^ [Y4: reg,Y5: reg] :
                      ( !! @ reg
                      @ ^ [Y6: reg] :
                          ( ( c @ Y6 @ Y4 )
                         => ( c @ Y6 @ Y5 ) ) )
                  @ Y2
                  @ Y3 ) )
            @ Y0
            @ Y1 ) ) ) ),
    inference(definition_unfolding,[],[f174,f203,f203,f204]) ).

thf(f211,plain,
    ( $true
   != ( ^ [Y0: $i > $o] :
          ( !! @ $i
          @ ^ [Y1: $i] : ( Y0 @ Y1 ) )
      @ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
            ( !! @ $i
            @ ^ [Y3: $i] :
                ( ~ ( Y0 @ Y2 @ Y3 )
                | ( Y1 @ Y3 ) ) )
        @ fool
        @ ^ [Y0: $i] :
            ~ ( ?? @ reg
              @ ^ [Y1: reg] :
                  ( !! @ reg
                  @ ^ [Y2: reg] :
                      ( ^ [Y3: reg,Y4: reg] :
                          ( ~ ( ?? @ reg
                              @ ^ [Y5: reg] :
                                  ( ( ^ [Y6: reg,Y7: reg] :
                                        ( ( c @ Y6 @ Y7 )
                                        & ~ ( ^ [Y8: reg,Y9: reg] :
                                                ( ?? @ reg
                                                @ ^ [Y10: reg] :
                                                    ( ( ^ [Y11: reg,Y12: reg] :
                                                          ( !! @ reg
                                                          @ ^ [Y13: reg] :
                                                              ( ( c @ Y13 @ Y11 )
                                                             => ( c @ Y13 @ Y12 ) ) )
                                                      @ Y10
                                                      @ Y9 )
                                                    & ( ^ [Y11: reg,Y12: reg] :
                                                          ( !! @ reg
                                                          @ ^ [Y13: reg] :
                                                              ( ( c @ Y13 @ Y11 )
                                                             => ( c @ Y13 @ Y12 ) ) )
                                                      @ Y10
                                                      @ Y8 ) ) )
                                            @ Y6
                                            @ Y7 ) )
                                    @ Y5
                                    @ Y3 )
                                  & ( ^ [Y6: reg,Y7: reg] :
                                        ( ( c @ Y6 @ Y7 )
                                        & ~ ( ^ [Y8: reg,Y9: reg] :
                                                ( ?? @ reg
                                                @ ^ [Y10: reg] :
                                                    ( ( ^ [Y11: reg,Y12: reg] :
                                                          ( !! @ reg
                                                          @ ^ [Y13: reg] :
                                                              ( ( c @ Y13 @ Y11 )
                                                             => ( c @ Y13 @ Y12 ) ) )
                                                      @ Y10
                                                      @ Y9 )
                                                    & ( ^ [Y11: reg,Y12: reg] :
                                                          ( !! @ reg
                                                          @ ^ [Y13: reg] :
                                                              ( ( c @ Y13 @ Y11 )
                                                             => ( c @ Y13 @ Y12 ) ) )
                                                      @ Y10
                                                      @ Y8 ) ) )
                                            @ Y6
                                            @ Y7 ) )
                                    @ Y5
                                    @ Y4 ) ) )
                          & ( ^ [Y5: reg,Y6: reg] :
                                ( ~ ( ^ [Y7: reg,Y8: reg] :
                                        ( !! @ reg
                                        @ ^ [Y9: reg] :
                                            ( ( c @ Y9 @ Y7 )
                                           => ( c @ Y9 @ Y8 ) ) )
                                    @ Y6
                                    @ Y5 )
                                & ( ^ [Y7: reg,Y8: reg] :
                                      ( !! @ reg
                                      @ ^ [Y9: reg] :
                                          ( ( c @ Y9 @ Y7 )
                                         => ( c @ Y9 @ Y8 ) ) )
                                  @ Y5
                                  @ Y6 ) )
                            @ Y3
                            @ Y4 ) )
                      @ Y1
                      @ Y2 ) ) ) ) ) ),
    inference(definition_unfolding,[],[f172,f179,f180,f206]) ).

thf(f344,plain,
    ( $true
   != ( !! @ $i
      @ ^ [Y0: $i] :
          ( !! @ $i
          @ ^ [Y1: $i] :
              ( ~ ( fool @ Y0 @ Y1 )
              | ~ ( ?? @ reg
                  @ ^ [Y2: reg] :
                      ( !! @ reg
                      @ ^ [Y3: reg] :
                          ( ~ ( ?? @ reg
                              @ ^ [Y4: reg] :
                                  ( ( c @ Y4 @ Y2 )
                                  & ~ ( ?? @ reg
                                      @ ^ [Y5: reg] :
                                          ( ( !! @ reg
                                            @ ^ [Y6: reg] :
                                                ( ( c @ Y6 @ Y5 )
                                               => ( c @ Y6 @ Y2 ) ) )
                                          & ( !! @ reg
                                            @ ^ [Y6: reg] :
                                                ( ( c @ Y6 @ Y5 )
                                               => ( c @ Y6 @ Y4 ) ) ) ) )
                                  & ( c @ Y4 @ Y3 )
                                  & ~ ( ?? @ reg
                                      @ ^ [Y5: reg] :
                                          ( ( !! @ reg
                                            @ ^ [Y6: reg] :
                                                ( ( c @ Y6 @ Y5 )
                                               => ( c @ Y6 @ Y3 ) ) )
                                          & ( !! @ reg
                                            @ ^ [Y6: reg] :
                                                ( ( c @ Y6 @ Y5 )
                                               => ( c @ Y6 @ Y4 ) ) ) ) ) ) )
                          & ~ ( !! @ reg
                              @ ^ [Y4: reg] :
                                  ( ( c @ Y4 @ Y3 )
                                 => ( c @ Y4 @ Y2 ) ) )
                          & ( !! @ reg
                            @ ^ [Y4: reg] :
                                ( ( c @ Y4 @ Y2 )
                               => ( c @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ),
    inference(beta-eta_normalization,[],[f211]) ).

thf(f345,plain,
    ( ( ^ [Y0: $i] :
          ( !! @ $i
          @ ^ [Y1: $i] :
              ( ~ ( fool @ Y0 @ Y1 )
              | ~ ( ?? @ reg
                  @ ^ [Y2: reg] :
                      ( !! @ reg
                      @ ^ [Y3: reg] :
                          ( ~ ( ?? @ reg
                              @ ^ [Y4: reg] :
                                  ( ( c @ Y4 @ Y2 )
                                  & ~ ( ?? @ reg
                                      @ ^ [Y5: reg] :
                                          ( ( !! @ reg
                                            @ ^ [Y6: reg] :
                                                ( ( c @ Y6 @ Y5 )
                                               => ( c @ Y6 @ Y2 ) ) )
                                          & ( !! @ reg
                                            @ ^ [Y6: reg] :
                                                ( ( c @ Y6 @ Y5 )
                                               => ( c @ Y6 @ Y4 ) ) ) ) )
                                  & ( c @ Y4 @ Y3 )
                                  & ~ ( ?? @ reg
                                      @ ^ [Y5: reg] :
                                          ( ( !! @ reg
                                            @ ^ [Y6: reg] :
                                                ( ( c @ Y6 @ Y5 )
                                               => ( c @ Y6 @ Y3 ) ) )
                                          & ( !! @ reg
                                            @ ^ [Y6: reg] :
                                                ( ( c @ Y6 @ Y5 )
                                               => ( c @ Y6 @ Y4 ) ) ) ) ) ) )
                          & ~ ( !! @ reg
                              @ ^ [Y4: reg] :
                                  ( ( c @ Y4 @ Y3 )
                                 => ( c @ Y4 @ Y2 ) ) )
                          & ( !! @ reg
                            @ ^ [Y4: reg] :
                                ( ( c @ Y4 @ Y2 )
                               => ( c @ Y4 @ Y3 ) ) ) ) ) ) ) )
      @ sK11 )
    = $false ),
    inference(sigma_proxy_clausification,[],[f344]) ).

thf(f346,plain,
    ( ( !! @ $i
      @ ^ [Y0: $i] :
          ( ~ ( fool @ sK11 @ Y0 )
          | ~ ( ?? @ reg
              @ ^ [Y1: reg] :
                  ( !! @ reg
                  @ ^ [Y2: reg] :
                      ( ~ ( ?? @ reg
                          @ ^ [Y3: reg] :
                              ( ( c @ Y3 @ Y1 )
                              & ~ ( ?? @ reg
                                  @ ^ [Y4: reg] :
                                      ( ( !! @ reg
                                        @ ^ [Y5: reg] :
                                            ( ( c @ Y5 @ Y4 )
                                           => ( c @ Y5 @ Y1 ) ) )
                                      & ( !! @ reg
                                        @ ^ [Y5: reg] :
                                            ( ( c @ Y5 @ Y4 )
                                           => ( c @ Y5 @ Y3 ) ) ) ) )
                              & ( c @ Y3 @ Y2 )
                              & ~ ( ?? @ reg
                                  @ ^ [Y4: reg] :
                                      ( ( !! @ reg
                                        @ ^ [Y5: reg] :
                                            ( ( c @ Y5 @ Y4 )
                                           => ( c @ Y5 @ Y2 ) ) )
                                      & ( !! @ reg
                                        @ ^ [Y5: reg] :
                                            ( ( c @ Y5 @ Y4 )
                                           => ( c @ Y5 @ Y3 ) ) ) ) ) ) )
                      & ~ ( !! @ reg
                          @ ^ [Y3: reg] :
                              ( ( c @ Y3 @ Y2 )
                             => ( c @ Y3 @ Y1 ) ) )
                      & ( !! @ reg
                        @ ^ [Y3: reg] :
                            ( ( c @ Y3 @ Y1 )
                           => ( c @ Y3 @ Y2 ) ) ) ) ) ) ) )
    = $false ),
    inference(beta-eta_normalization,[],[f345]) ).

thf(f347,plain,
    ( ( ^ [Y0: $i] :
          ( ~ ( fool @ sK11 @ Y0 )
          | ~ ( ?? @ reg
              @ ^ [Y1: reg] :
                  ( !! @ reg
                  @ ^ [Y2: reg] :
                      ( ~ ( ?? @ reg
                          @ ^ [Y3: reg] :
                              ( ( c @ Y3 @ Y1 )
                              & ~ ( ?? @ reg
                                  @ ^ [Y4: reg] :
                                      ( ( !! @ reg
                                        @ ^ [Y5: reg] :
                                            ( ( c @ Y5 @ Y4 )
                                           => ( c @ Y5 @ Y1 ) ) )
                                      & ( !! @ reg
                                        @ ^ [Y5: reg] :
                                            ( ( c @ Y5 @ Y4 )
                                           => ( c @ Y5 @ Y3 ) ) ) ) )
                              & ( c @ Y3 @ Y2 )
                              & ~ ( ?? @ reg
                                  @ ^ [Y4: reg] :
                                      ( ( !! @ reg
                                        @ ^ [Y5: reg] :
                                            ( ( c @ Y5 @ Y4 )
                                           => ( c @ Y5 @ Y2 ) ) )
                                      & ( !! @ reg
                                        @ ^ [Y5: reg] :
                                            ( ( c @ Y5 @ Y4 )
                                           => ( c @ Y5 @ Y3 ) ) ) ) ) ) )
                      & ~ ( !! @ reg
                          @ ^ [Y3: reg] :
                              ( ( c @ Y3 @ Y2 )
                             => ( c @ Y3 @ Y1 ) ) )
                      & ( !! @ reg
                        @ ^ [Y3: reg] :
                            ( ( c @ Y3 @ Y1 )
                           => ( c @ Y3 @ Y2 ) ) ) ) ) ) )
      @ sK12 )
    = $false ),
    inference(sigma_proxy_clausification,[],[f346]) ).

thf(f348,plain,
    ( ( ~ ( fool @ sK11 @ sK12 )
      | ~ ( ?? @ reg
          @ ^ [Y0: reg] :
              ( !! @ reg
              @ ^ [Y1: reg] :
                  ( ~ ( ?? @ reg
                      @ ^ [Y2: reg] :
                          ( ( c @ Y2 @ Y0 )
                          & ~ ( ?? @ reg
                              @ ^ [Y3: reg] :
                                  ( ( !! @ reg
                                    @ ^ [Y4: reg] :
                                        ( ( c @ Y4 @ Y3 )
                                       => ( c @ Y4 @ Y0 ) ) )
                                  & ( !! @ reg
                                    @ ^ [Y4: reg] :
                                        ( ( c @ Y4 @ Y3 )
                                       => ( c @ Y4 @ Y2 ) ) ) ) )
                          & ( c @ Y2 @ Y1 )
                          & ~ ( ?? @ reg
                              @ ^ [Y3: reg] :
                                  ( ( !! @ reg
                                    @ ^ [Y4: reg] :
                                        ( ( c @ Y4 @ Y3 )
                                       => ( c @ Y4 @ Y1 ) ) )
                                  & ( !! @ reg
                                    @ ^ [Y4: reg] :
                                        ( ( c @ Y4 @ Y3 )
                                       => ( c @ Y4 @ Y2 ) ) ) ) ) ) )
                  & ~ ( !! @ reg
                      @ ^ [Y2: reg] :
                          ( ( c @ Y2 @ Y1 )
                         => ( c @ Y2 @ Y0 ) ) )
                  & ( !! @ reg
                    @ ^ [Y2: reg] :
                        ( ( c @ Y2 @ Y0 )
                       => ( c @ Y2 @ Y1 ) ) ) ) ) ) )
    = $false ),
    inference(beta-eta_normalization,[],[f347]) ).

thf(f349,plain,
    ( $false
    = ( ~ ( ?? @ reg
          @ ^ [Y0: reg] :
              ( !! @ reg
              @ ^ [Y1: reg] :
                  ( ~ ( ?? @ reg
                      @ ^ [Y2: reg] :
                          ( ( c @ Y2 @ Y0 )
                          & ~ ( ?? @ reg
                              @ ^ [Y3: reg] :
                                  ( ( !! @ reg
                                    @ ^ [Y4: reg] :
                                        ( ( c @ Y4 @ Y3 )
                                       => ( c @ Y4 @ Y0 ) ) )
                                  & ( !! @ reg
                                    @ ^ [Y4: reg] :
                                        ( ( c @ Y4 @ Y3 )
                                       => ( c @ Y4 @ Y2 ) ) ) ) )
                          & ( c @ Y2 @ Y1 )
                          & ~ ( ?? @ reg
                              @ ^ [Y3: reg] :
                                  ( ( !! @ reg
                                    @ ^ [Y4: reg] :
                                        ( ( c @ Y4 @ Y3 )
                                       => ( c @ Y4 @ Y1 ) ) )
                                  & ( !! @ reg
                                    @ ^ [Y4: reg] :
                                        ( ( c @ Y4 @ Y3 )
                                       => ( c @ Y4 @ Y2 ) ) ) ) ) ) )
                  & ~ ( !! @ reg
                      @ ^ [Y2: reg] :
                          ( ( c @ Y2 @ Y1 )
                         => ( c @ Y2 @ Y0 ) ) )
                  & ( !! @ reg
                    @ ^ [Y2: reg] :
                        ( ( c @ Y2 @ Y0 )
                       => ( c @ Y2 @ Y1 ) ) ) ) ) ) ) ),
    inference(or_proxy_clausification,[],[f348]) ).

thf(f352,plain,
    ( $true
    = ( ?? @ reg
      @ ^ [Y0: reg] :
          ( !! @ reg
          @ ^ [Y1: reg] :
              ( ~ ( ?? @ reg
                  @ ^ [Y2: reg] :
                      ( ( c @ Y2 @ Y0 )
                      & ~ ( ?? @ reg
                          @ ^ [Y3: reg] :
                              ( ( !! @ reg
                                @ ^ [Y4: reg] :
                                    ( ( c @ Y4 @ Y3 )
                                   => ( c @ Y4 @ Y0 ) ) )
                              & ( !! @ reg
                                @ ^ [Y4: reg] :
                                    ( ( c @ Y4 @ Y3 )
                                   => ( c @ Y4 @ Y2 ) ) ) ) )
                      & ( c @ Y2 @ Y1 )
                      & ~ ( ?? @ reg
                          @ ^ [Y3: reg] :
                              ( ( !! @ reg
                                @ ^ [Y4: reg] :
                                    ( ( c @ Y4 @ Y3 )
                                   => ( c @ Y4 @ Y1 ) ) )
                              & ( !! @ reg
                                @ ^ [Y4: reg] :
                                    ( ( c @ Y4 @ Y3 )
                                   => ( c @ Y4 @ Y2 ) ) ) ) ) ) )
              & ~ ( !! @ reg
                  @ ^ [Y2: reg] :
                      ( ( c @ Y2 @ Y1 )
                     => ( c @ Y2 @ Y0 ) ) )
              & ( !! @ reg
                @ ^ [Y2: reg] :
                    ( ( c @ Y2 @ Y0 )
                   => ( c @ Y2 @ Y1 ) ) ) ) ) ) ),
    inference(not_proxy_clausification,[],[f349]) ).

thf(f353,plain,
    ( $true
    = ( ^ [Y0: reg] :
          ( !! @ reg
          @ ^ [Y1: reg] :
              ( ~ ( ?? @ reg
                  @ ^ [Y2: reg] :
                      ( ( c @ Y2 @ Y0 )
                      & ~ ( ?? @ reg
                          @ ^ [Y3: reg] :
                              ( ( !! @ reg
                                @ ^ [Y4: reg] :
                                    ( ( c @ Y4 @ Y3 )
                                   => ( c @ Y4 @ Y0 ) ) )
                              & ( !! @ reg
                                @ ^ [Y4: reg] :
                                    ( ( c @ Y4 @ Y3 )
                                   => ( c @ Y4 @ Y2 ) ) ) ) )
                      & ( c @ Y2 @ Y1 )
                      & ~ ( ?? @ reg
                          @ ^ [Y3: reg] :
                              ( ( !! @ reg
                                @ ^ [Y4: reg] :
                                    ( ( c @ Y4 @ Y3 )
                                   => ( c @ Y4 @ Y1 ) ) )
                              & ( !! @ reg
                                @ ^ [Y4: reg] :
                                    ( ( c @ Y4 @ Y3 )
                                   => ( c @ Y4 @ Y2 ) ) ) ) ) ) )
              & ~ ( !! @ reg
                  @ ^ [Y2: reg] :
                      ( ( c @ Y2 @ Y1 )
                     => ( c @ Y2 @ Y0 ) ) )
              & ( !! @ reg
                @ ^ [Y2: reg] :
                    ( ( c @ Y2 @ Y0 )
                   => ( c @ Y2 @ Y1 ) ) ) ) )
      @ sK13 ) ),
    inference(sigma_proxy_clausification,[],[f352]) ).

thf(f354,plain,
    ( $true
    = ( !! @ reg
      @ ^ [Y0: reg] :
          ( ~ ( ?? @ reg
              @ ^ [Y1: reg] :
                  ( ( c @ Y1 @ sK13 )
                  & ~ ( ?? @ reg
                      @ ^ [Y2: reg] :
                          ( ( !! @ reg
                            @ ^ [Y3: reg] :
                                ( ( c @ Y3 @ Y2 )
                               => ( c @ Y3 @ sK13 ) ) )
                          & ( !! @ reg
                            @ ^ [Y3: reg] :
                                ( ( c @ Y3 @ Y2 )
                               => ( c @ Y3 @ Y1 ) ) ) ) )
                  & ( c @ Y1 @ Y0 )
                  & ~ ( ?? @ reg
                      @ ^ [Y2: reg] :
                          ( ( !! @ reg
                            @ ^ [Y3: reg] :
                                ( ( c @ Y3 @ Y2 )
                               => ( c @ Y3 @ Y0 ) ) )
                          & ( !! @ reg
                            @ ^ [Y3: reg] :
                                ( ( c @ Y3 @ Y2 )
                               => ( c @ Y3 @ Y1 ) ) ) ) ) ) )
          & ~ ( !! @ reg
              @ ^ [Y1: reg] :
                  ( ( c @ Y1 @ Y0 )
                 => ( c @ Y1 @ sK13 ) ) )
          & ( !! @ reg
            @ ^ [Y1: reg] :
                ( ( c @ Y1 @ sK13 )
               => ( c @ Y1 @ Y0 ) ) ) ) ) ),
    inference(beta-eta_normalization,[],[f353]) ).

thf(f355,plain,
    ! [X1: reg] :
      ( $true
      = ( ^ [Y0: reg] :
            ( ~ ( ?? @ reg
                @ ^ [Y1: reg] :
                    ( ( c @ Y1 @ sK13 )
                    & ~ ( ?? @ reg
                        @ ^ [Y2: reg] :
                            ( ( !! @ reg
                              @ ^ [Y3: reg] :
                                  ( ( c @ Y3 @ Y2 )
                                 => ( c @ Y3 @ sK13 ) ) )
                            & ( !! @ reg
                              @ ^ [Y3: reg] :
                                  ( ( c @ Y3 @ Y2 )
                                 => ( c @ Y3 @ Y1 ) ) ) ) )
                    & ( c @ Y1 @ Y0 )
                    & ~ ( ?? @ reg
                        @ ^ [Y2: reg] :
                            ( ( !! @ reg
                              @ ^ [Y3: reg] :
                                  ( ( c @ Y3 @ Y2 )
                                 => ( c @ Y3 @ Y0 ) ) )
                            & ( !! @ reg
                              @ ^ [Y3: reg] :
                                  ( ( c @ Y3 @ Y2 )
                                 => ( c @ Y3 @ Y1 ) ) ) ) ) ) )
            & ~ ( !! @ reg
                @ ^ [Y1: reg] :
                    ( ( c @ Y1 @ Y0 )
                   => ( c @ Y1 @ sK13 ) ) )
            & ( !! @ reg
              @ ^ [Y1: reg] :
                  ( ( c @ Y1 @ sK13 )
                 => ( c @ Y1 @ Y0 ) ) ) )
        @ X1 ) ),
    inference(pi_proxy_clausification,[],[f354]) ).

thf(f356,plain,
    ! [X1: reg] :
      ( $true
      = ( ~ ( ?? @ reg
            @ ^ [Y0: reg] :
                ( ( c @ Y0 @ sK13 )
                & ~ ( ?? @ reg
                    @ ^ [Y1: reg] :
                        ( ( !! @ reg
                          @ ^ [Y2: reg] :
                              ( ( c @ Y2 @ Y1 )
                             => ( c @ Y2 @ sK13 ) ) )
                        & ( !! @ reg
                          @ ^ [Y2: reg] :
                              ( ( c @ Y2 @ Y1 )
                             => ( c @ Y2 @ Y0 ) ) ) ) )
                & ( c @ Y0 @ X1 )
                & ~ ( ?? @ reg
                    @ ^ [Y1: reg] :
                        ( ( !! @ reg
                          @ ^ [Y2: reg] :
                              ( ( c @ Y2 @ Y1 )
                             => ( c @ Y2 @ X1 ) ) )
                        & ( !! @ reg
                          @ ^ [Y2: reg] :
                              ( ( c @ Y2 @ Y1 )
                             => ( c @ Y2 @ Y0 ) ) ) ) ) ) )
        & ~ ( !! @ reg
            @ ^ [Y0: reg] :
                ( ( c @ Y0 @ X1 )
               => ( c @ Y0 @ sK13 ) ) )
        & ( !! @ reg
          @ ^ [Y0: reg] :
              ( ( c @ Y0 @ sK13 )
             => ( c @ Y0 @ X1 ) ) ) ) ),
    inference(beta-eta_normalization,[],[f355]) ).

thf(f357,plain,
    ! [X1: reg] :
      ( $true
      = ( ~ ( !! @ reg
            @ ^ [Y0: reg] :
                ( ( c @ Y0 @ X1 )
               => ( c @ Y0 @ sK13 ) ) )
        & ( !! @ reg
          @ ^ [Y0: reg] :
              ( ( c @ Y0 @ sK13 )
             => ( c @ Y0 @ X1 ) ) ) ) ),
    inference(and_proxy_clausification,[],[f356]) ).

thf(f396,plain,
    ! [X1: reg] :
      ( $true
      = ( ~ ( !! @ reg
            @ ^ [Y0: reg] :
                ( ( c @ Y0 @ X1 )
               => ( c @ Y0 @ sK13 ) ) ) ) ),
    inference(and_proxy_clausification,[],[f357]) ).

thf(f397,plain,
    ! [X1: reg] :
      ( ( !! @ reg
        @ ^ [Y0: reg] :
            ( ( c @ Y0 @ X1 )
           => ( c @ Y0 @ sK13 ) ) )
      = $false ),
    inference(not_proxy_clausification,[],[f396]) ).

thf(f398,plain,
    ! [X1: reg] :
      ( ( ^ [Y0: reg] :
            ( ( c @ Y0 @ X1 )
           => ( c @ Y0 @ sK13 ) )
        @ ( sK16 @ X1 ) )
      = $false ),
    inference(sigma_proxy_clausification,[],[f397]) ).

thf(f399,plain,
    ! [X1: reg] :
      ( ( ( c @ ( sK16 @ X1 ) @ X1 )
       => ( c @ ( sK16 @ X1 ) @ sK13 ) )
      = $false ),
    inference(beta-eta_normalization,[],[f398]) ).

thf(f400,plain,
    ! [X1: reg] :
      ( ( c @ ( sK16 @ X1 ) @ sK13 )
      = $false ),
    inference(imp_proxy_clausification,[],[f399]) ).

thf(f401,plain,
    ! [X1: reg] :
      ( $true
      = ( c @ ( sK16 @ X1 ) @ X1 ) ),
    inference(imp_proxy_clausification,[],[f399]) ).

thf(f578,plain,
    $true = $false,
    inference(constrained_superposition,[],[f401,f400]) ).

thf(f581,plain,
    $false,
    inference(trivial_inequality_removal,[],[f578]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : GEG018^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18  % Computer : n011.cluster.edu
% 0.09/0.18  % Model    : x86_64 x86_64
% 0.09/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18  % Memory   : 8046.5625MB
% 0.09/0.18  % OS       : Linux 6.8.0-71-generic
% 0.09/0.18  % CPULimit : 300
% 0.09/0.19  % WCLimit  : 300
% 0.09/0.19  % DateTime : Tue Sep 29 18:34:31 UTC 2026
% 0.09/0.19  % CPUTime  : 
% 0.09/0.19  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22  Running higher-order theorem proving
% 0.09/0.23  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.28  % (485150)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28  % (485161)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2988091045:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28  % (485157)lrs+10_16_si=on:nwc=1.5:random_seed=4074553781:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28  % (485156)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4170411719:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28  % (485158)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2363971380:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28  % (485158)Instruction limit reached! 
% 0.20/0.28  % (485158)------------------------------
% 0.20/0.28  % (485158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28  % (485158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28  % (485158)CaDiCaL version: 2.1.3
% 0.20/0.28  % (485158)Termination reason: Instruction limit
% 0.20/0.28  % (485158)Termination phase: Property scanning
% 0.20/0.28  % (485158)Time elapsed: 0.002 s
% 0.20/0.28  % (485158)Peak memory usage: 10 MB
% 0.20/0.28  % (485158)Instructions burned: 4 (million)
% 0.20/0.28  % (485161) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-485150-485161"...
% 0.20/0.28  % (485161)...printing done.
% 0.20/0.28  % (485161)Refutation found. Thanks to Tanya!
% 0.20/0.28  % SZS status Theorem for theBenchmark
% 0.20/0.28  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28  % (485161)------------------------------
% 0.20/0.28  % (485161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28  % (485161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28  % (485161)CaDiCaL version: 2.1.3
% 0.20/0.28  % (485161)Termination reason: Refutation
% 0.20/0.28  % (485161)Time elapsed: 0.012 s
% 0.20/0.28  % (485161)Peak memory usage: 12 MB
% 0.20/0.28  % (485161)Instructions burned: 42 (million)
% 0.20/0.28  % (485150)Success in time 0.044 s
% 0.20/0.28  % Vampire exiting
%------------------------------------------------------------------------------