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Vampire-SAT---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SWV427^2 : TPTP v9.3.1. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT

% Computer : n018.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 08:40:05 AM UTC 2026

% Result   : Theorem 30.22s 4.55s
% Output   : Refutation 30.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   41
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  107 (  74 unt;   0 typ;   0 def)
%            Number of atoms       :  893 ( 183 equ;   0 cnn)
%            Maximal formula atoms :   15 (   8 avg)
%            Number of connectives : 1177 (  31   ~; 134   |;   0   &; 841   @)
%                                         (   0 <=>;  90  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  152 ( 152   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   55 (  51 usr;   7 con; 0-4 aty)
%                                         (  81  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  315 ( 249   ^;  66   !;   0   ?; 315   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_6,type,
    individuals: $tType ).

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

thf(func_def_2,type,
    prop_b: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_34,type,
    vLAM: 
      !>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).

thf(func_def_35,type,
    vNOT: $o > $o ).

thf(func_def_36,type,
    db1: 
      !>[X0: $tType] : X0 ).

thf(func_def_37,type,
    db0: 
      !>[X0: $tType] : X0 ).

thf(func_def_38,type,
    vOR: $o > $o > $o ).

thf(func_def_39,type,
    db2: 
      !>[X0: $tType] : X0 ).

thf(func_def_40,type,
    vAND: $o > $o > $o ).

thf(func_def_41,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_42,type,
    vIMP: $o > $o > $o ).

thf(func_def_43,type,
    db3: 
      !>[X0: $tType] : X0 ).

thf(func_def_44,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_49,type,
    sK4: $i > ( $i > $o ) > $i ).

thf(func_def_50,type,
    sK5: $i > ( $i > $o ) > $i ).

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

thf(func_def_53,type,
    sK7: ( $i > $o ) > ( $i > $i ) > $i ).

thf(func_def_54,type,
    sK8: ( $i > $o ) > ( $i > $i ) > $i ).

thf(f3,axiom,
    ( mnot
    = ( ^ [X0: $i > $o,X1: $i] :
          ~ ( X0 @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).

thf(f4,axiom,
    ( mor
    = ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
          ( ( X1 @ X2 )
          | ( X0 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).

thf(f6,axiom,
    ( mimpl
    = ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mimpl) ).

thf(f8,axiom,
    ( mbox
    = ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
        ! [X3: $i] :
          ( ( X0 @ X2 @ X3 )
         => ( X1 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).

thf(f12,axiom,
    ( mvalid
    = ( ^ [X0: $i > $o] :
        ! [X1: $i] : ( X0 @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).

thf(f16,axiom,
    ( icl_atom
    = ( ^ [X0: $i > $o] : ( mbox @ rel @ X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_atom) ).

thf(f17,axiom,
    ( icl_princ
    = ( ^ [X0: $i > $o] : X0 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_princ) ).

thf(f20,axiom,
    ( icl_impl
    = ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_impl) ).

thf(f23,axiom,
    ( icl_says
    = ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mor @ X0 @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_says) ).

thf(f24,axiom,
    ( iclval
    = ( ^ [X0: $i > $o] : ( mvalid @ X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^0.ax',icl_s4_valid) ).

thf(f25,axiom,
    ! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV008^1.ax',refl_axiom) ).

thf(f27,conjecture,
    iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idem) ).

thf(f28,negated_conjecture,
    ~ ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f27]) ).

thf(f31,plain,
    ( mnot
    = ( ^ [X0: $i > $o,X1: $i] :
          ~ ( X0 @ X1 ) ) ),
    inference(rectify,[],[f3]) ).

thf(f32,plain,
    ( mnot
    = ( ^ [Y0: $i > $o,Y1: $i] :
          ~ ( Y0 @ Y1 ) ) ),
    inference(fool_elimination,[],[f31]) ).

thf(f33,plain,
    ( mor
    = ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
          ( ( X1 @ X2 )
          | ( X0 @ X2 ) ) ) ),
    inference(rectify,[],[f4]) ).

thf(f34,plain,
    ( mor
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y0 @ Y2 )
          | ( Y1 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f33]) ).

thf(f37,plain,
    ( mimpl
    = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
    inference(fool_elimination,[],[f6]) ).

thf(f39,plain,
    ( mbox
    = ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
        ! [X3: $i] :
          ( ( X0 @ X2 @ X3 )
         => ( X1 @ X3 ) ) ) ),
    inference(rectify,[],[f8]) ).

thf(f40,plain,
    ( mbox
    = ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
          ( !! @ $i
          @ ^ [Y3: $i] :
              ( ( Y0 @ Y2 @ Y3 )
             => ( Y1 @ Y3 ) ) ) ) ),
    inference(fool_elimination,[],[f39]) ).

thf(f47,plain,
    ( mvalid
    = ( ^ [X0: $i > $o] :
        ! [X1: $i] : ( X0 @ X1 ) ) ),
    inference(rectify,[],[f12]) ).

thf(f48,plain,
    ( mvalid
    = ( ^ [Y0: $i > $o] :
          ( !! @ $i
          @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
    inference(fool_elimination,[],[f47]) ).

thf(f55,plain,
    ( icl_atom
    = ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
    inference(fool_elimination,[],[f16]) ).

thf(f56,plain,
    ( icl_princ
    = ( ^ [Y0: $i > $o] : Y0 ) ),
    inference(fool_elimination,[],[f17]) ).

thf(f59,plain,
    ( icl_impl
    = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
    inference(fool_elimination,[],[f20]) ).

thf(f60,plain,
    ( icl_says
    = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
    inference(fool_elimination,[],[f23]) ).

thf(f61,plain,
    ( iclval
    = ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
    inference(fool_elimination,[],[f24]) ).

thf(f62,plain,
    ! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
    inference(rectify,[],[f25]) ).

thf(f63,plain,
    ! [X0: $i > $o] :
      ( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
      = $true ),
    inference(fool_elimination,[],[f62]) ).

thf(f66,plain,
    ~ ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) ),
    inference(rectify,[],[f28]) ).

thf(f67,plain,
    ( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) )
   != $true ),
    inference(fool_elimination,[],[f66]) ).

thf(f68,plain,
    ( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) )
   != $true ),
    inference(flattening,[],[f67]) ).

thf(f71,plain,
    ( mnot
    = ( ^ [Y0: $i > $o,Y1: $i] :
          ~ ( Y0 @ Y1 ) ) ),
    inference(cnf_transformation,[],[f32]) ).

thf(f72,plain,
    ( mor
    = ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
          ( ( Y0 @ Y2 )
          | ( Y1 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f34]) ).

thf(f74,plain,
    ( mimpl
    = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
    inference(cnf_transformation,[],[f37]) ).

thf(f76,plain,
    ( mbox
    = ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
          ( !! @ $i
          @ ^ [Y3: $i] :
              ( ( Y0 @ Y2 @ Y3 )
             => ( Y1 @ Y3 ) ) ) ) ),
    inference(cnf_transformation,[],[f40]) ).

thf(f80,plain,
    ( mvalid
    = ( ^ [Y0: $i > $o] :
          ( !! @ $i
          @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
    inference(cnf_transformation,[],[f48]) ).

thf(f84,plain,
    ( icl_atom
    = ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
    inference(cnf_transformation,[],[f55]) ).

thf(f85,plain,
    ( icl_princ
    = ( ^ [Y0: $i > $o] : Y0 ) ),
    inference(cnf_transformation,[],[f56]) ).

thf(f88,plain,
    ( icl_impl
    = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
    inference(cnf_transformation,[],[f59]) ).

thf(f91,plain,
    ( icl_says
    = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
    inference(cnf_transformation,[],[f60]) ).

thf(f92,plain,
    ( iclval
    = ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
    inference(cnf_transformation,[],[f61]) ).

thf(f93,plain,
    ! [X0: $i > $o] :
      ( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
      = $true ),
    inference(cnf_transformation,[],[f63]) ).

thf(f95,plain,
    ( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) )
   != $true ),
    inference(cnf_transformation,[],[f68]) ).

thf(f98,plain,
    ( mimpl
    = ( ^ [Y0: $i > $o,Y1: $i > $o] :
          ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
              ( ( Y2 @ Y4 )
              | ( Y3 @ Y4 ) )
          @ ( ^ [Y2: $i > $o,Y3: $i] :
                ~ ( Y2 @ Y3 )
            @ Y0 )
          @ Y1 ) ) ),
    inference(definition_unfolding,[],[f74,f72,f71]) ).

thf(f100,plain,
    ( icl_atom
    = ( ^ [Y0: $i > $o] :
          ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
              ( !! @ $i
              @ ^ [Y4: $i] :
                  ( ( Y1 @ Y3 @ Y4 )
                 => ( Y2 @ Y4 ) ) )
          @ rel
          @ Y0 ) ) ),
    inference(definition_unfolding,[],[f84,f76]) ).

thf(f103,plain,
    ( icl_impl
    = ( ^ [Y0: $i > $o,Y1: $i > $o] :
          ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
              ( !! @ $i
              @ ^ [Y5: $i] :
                  ( ( Y2 @ Y4 @ Y5 )
                 => ( Y3 @ Y5 ) ) )
          @ rel
          @ ( ^ [Y2: $i > $o,Y3: $i > $o] :
                ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
                    ( ( Y4 @ Y6 )
                    | ( Y5 @ Y6 ) )
                @ ( ^ [Y4: $i > $o,Y5: $i] :
                      ~ ( Y4 @ Y5 )
                  @ Y2 )
                @ Y3 )
            @ Y0
            @ Y1 ) ) ) ),
    inference(definition_unfolding,[],[f88,f76,f98]) ).

thf(f106,plain,
    ( icl_says
    = ( ^ [Y0: $i > $o,Y1: $i > $o] :
          ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
              ( !! @ $i
              @ ^ [Y5: $i] :
                  ( ( Y2 @ Y4 @ Y5 )
                 => ( Y3 @ Y5 ) ) )
          @ rel
          @ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
                ( ( Y2 @ Y4 )
                | ( Y3 @ Y4 ) )
            @ Y0
            @ Y1 ) ) ) ),
    inference(definition_unfolding,[],[f91,f76,f72]) ).

thf(f107,plain,
    ( iclval
    = ( ^ [Y0: $i > $o] :
          ( ^ [Y1: $i > $o] :
              ( !! @ $i
              @ ^ [Y2: $i] : ( Y1 @ Y2 ) )
          @ Y0 ) ) ),
    inference(definition_unfolding,[],[f92,f80]) ).

thf(f108,plain,
    ! [X0: $i > $o] :
      ( $true
      = ( ^ [Y0: $i > $o] :
            ( !! @ $i
            @ ^ [Y1: $i] : ( Y0 @ Y1 ) )
        @ ( ^ [Y0: $i > $o,Y1: $i > $o] :
              ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
                  ( ( Y2 @ Y4 )
                  | ( Y3 @ Y4 ) )
              @ ( ^ [Y2: $i > $o,Y3: $i] :
                    ~ ( Y2 @ Y3 )
                @ Y0 )
              @ Y1 )
          @ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
                ( !! @ $i
                @ ^ [Y3: $i] :
                    ( ( Y0 @ Y2 @ Y3 )
                   => ( Y1 @ Y3 ) ) )
            @ rel
            @ X0 )
          @ X0 ) ) ),
    inference(definition_unfolding,[],[f93,f80,f98,f76]) ).

thf(f110,plain,
    ( $true
   != ( ^ [Y0: $i > $o] :
          ( ^ [Y1: $i > $o] :
              ( !! @ $i
              @ ^ [Y2: $i] : ( Y1 @ Y2 ) )
          @ Y0 )
      @ ( ^ [Y0: $i > $o,Y1: $i > $o] :
            ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
                ( !! @ $i
                @ ^ [Y5: $i] :
                    ( ( Y2 @ Y4 @ Y5 )
                   => ( Y3 @ Y5 ) ) )
            @ rel
            @ ( ^ [Y2: $i > $o,Y3: $i > $o] :
                  ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
                      ( ( Y4 @ Y6 )
                      | ( Y5 @ Y6 ) )
                  @ ( ^ [Y4: $i > $o,Y5: $i] :
                        ~ ( Y4 @ Y5 )
                    @ Y2 )
                  @ Y3 )
              @ Y0
              @ Y1 ) )
        @ ( ^ [Y0: $i > $o,Y1: $i > $o] :
              ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
                  ( !! @ $i
                  @ ^ [Y5: $i] :
                      ( ( Y2 @ Y4 @ Y5 )
                     => ( Y3 @ Y5 ) ) )
              @ rel
              @ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
                    ( ( Y2 @ Y4 )
                    | ( Y3 @ Y4 ) )
                @ Y0
                @ Y1 ) )
          @ ( ^ [Y0: $i > $o] : Y0
            @ a )
          @ ( ^ [Y0: $i > $o,Y1: $i > $o] :
                ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
                    ( !! @ $i
                    @ ^ [Y5: $i] :
                        ( ( Y2 @ Y4 @ Y5 )
                       => ( Y3 @ Y5 ) ) )
                @ rel
                @ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
                      ( ( Y2 @ Y4 )
                      | ( Y3 @ Y4 ) )
                  @ Y0
                  @ Y1 ) )
            @ ( ^ [Y0: $i > $o] : Y0
              @ a )
            @ ( ^ [Y0: $i > $o] :
                  ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
                      ( !! @ $i
                      @ ^ [Y4: $i] :
                          ( ( Y1 @ Y3 @ Y4 )
                         => ( Y2 @ Y4 ) ) )
                  @ rel
                  @ Y0 )
              @ s ) ) )
        @ ( ^ [Y0: $i > $o,Y1: $i > $o] :
              ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
                  ( !! @ $i
                  @ ^ [Y5: $i] :
                      ( ( Y2 @ Y4 @ Y5 )
                     => ( Y3 @ Y5 ) ) )
              @ rel
              @ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
                    ( ( Y2 @ Y4 )
                    | ( Y3 @ Y4 ) )
                @ Y0
                @ Y1 ) )
          @ ( ^ [Y0: $i > $o] : Y0
            @ a )
          @ ( ^ [Y0: $i > $o] :
                ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
                    ( !! @ $i
                    @ ^ [Y4: $i] :
                        ( ( Y1 @ Y3 @ Y4 )
                       => ( Y2 @ Y4 ) ) )
                @ rel
                @ Y0 )
            @ s ) ) ) ) ),
    inference(definition_unfolding,[],[f95,f107,f103,f106,f85,f106,f85,f100,f106,f85,f100]) ).

thf(f111,plain,
    ( $true
   != ( !! @ $i
      @ ^ [Y0: $i] :
          ( !! @ $i
          @ ^ [Y1: $i] :
              ( ( rel @ Y0 @ Y1 )
             => ( ~ ( !! @ $i
                    @ ^ [Y2: $i] :
                        ( ( rel @ Y1 @ Y2 )
                       => ( ( a @ Y2 )
                          | ( !! @ $i
                            @ ^ [Y3: $i] :
                                ( ( rel @ Y2 @ Y3 )
                               => ( ( a @ Y3 )
                                  | ( !! @ $i
                                    @ ^ [Y4: $i] :
                                        ( ( rel @ Y3 @ Y4 )
                                       => ( s @ Y4 ) ) ) ) ) ) ) ) )
                | ( !! @ $i
                  @ ^ [Y2: $i] :
                      ( ( rel @ Y1 @ Y2 )
                     => ( ( a @ Y2 )
                        | ( !! @ $i
                          @ ^ [Y3: $i] :
                              ( ( rel @ Y2 @ Y3 )
                             => ( s @ Y3 ) ) ) ) ) ) ) ) ) ) ),
    inference(beta-eta_normalization,[],[f110]) ).

thf(f112,plain,
    ( $false
    = ( ^ [Y0: $i] :
          ( !! @ $i
          @ ^ [Y1: $i] :
              ( ( rel @ Y0 @ Y1 )
             => ( ~ ( !! @ $i
                    @ ^ [Y2: $i] :
                        ( ( rel @ Y1 @ Y2 )
                       => ( ( a @ Y2 )
                          | ( !! @ $i
                            @ ^ [Y3: $i] :
                                ( ( rel @ Y2 @ Y3 )
                               => ( ( a @ Y3 )
                                  | ( !! @ $i
                                    @ ^ [Y4: $i] :
                                        ( ( rel @ Y3 @ Y4 )
                                       => ( s @ Y4 ) ) ) ) ) ) ) ) )
                | ( !! @ $i
                  @ ^ [Y2: $i] :
                      ( ( rel @ Y1 @ Y2 )
                     => ( ( a @ Y2 )
                        | ( !! @ $i
                          @ ^ [Y3: $i] :
                              ( ( rel @ Y2 @ Y3 )
                             => ( s @ Y3 ) ) ) ) ) ) ) ) )
      @ sK0 ) ),
    inference(sigma_proxy_clausification,[],[f111]) ).

thf(f113,plain,
    ( $false
    = ( !! @ $i
      @ ^ [Y0: $i] :
          ( ( rel @ sK0 @ Y0 )
         => ( ~ ( !! @ $i
                @ ^ [Y1: $i] :
                    ( ( rel @ Y0 @ Y1 )
                   => ( ( a @ Y1 )
                      | ( !! @ $i
                        @ ^ [Y2: $i] :
                            ( ( rel @ Y1 @ Y2 )
                           => ( ( a @ Y2 )
                              | ( !! @ $i
                                @ ^ [Y3: $i] :
                                    ( ( rel @ Y2 @ Y3 )
                                   => ( s @ Y3 ) ) ) ) ) ) ) ) )
            | ( !! @ $i
              @ ^ [Y1: $i] :
                  ( ( rel @ Y0 @ Y1 )
                 => ( ( a @ Y1 )
                    | ( !! @ $i
                      @ ^ [Y2: $i] :
                          ( ( rel @ Y1 @ Y2 )
                         => ( s @ Y2 ) ) ) ) ) ) ) ) ) ),
    inference(beta-eta_normalization,[],[f112]) ).

thf(f114,plain,
    ( $false
    = ( ^ [Y0: $i] :
          ( ( rel @ sK0 @ Y0 )
         => ( ~ ( !! @ $i
                @ ^ [Y1: $i] :
                    ( ( rel @ Y0 @ Y1 )
                   => ( ( a @ Y1 )
                      | ( !! @ $i
                        @ ^ [Y2: $i] :
                            ( ( rel @ Y1 @ Y2 )
                           => ( ( a @ Y2 )
                              | ( !! @ $i
                                @ ^ [Y3: $i] :
                                    ( ( rel @ Y2 @ Y3 )
                                   => ( s @ Y3 ) ) ) ) ) ) ) ) )
            | ( !! @ $i
              @ ^ [Y1: $i] :
                  ( ( rel @ Y0 @ Y1 )
                 => ( ( a @ Y1 )
                    | ( !! @ $i
                      @ ^ [Y2: $i] :
                          ( ( rel @ Y1 @ Y2 )
                         => ( s @ Y2 ) ) ) ) ) ) ) )
      @ sK1 ) ),
    inference(sigma_proxy_clausification,[],[f113]) ).

thf(f115,plain,
    ( $false
    = ( ( rel @ sK0 @ sK1 )
     => ( ~ ( !! @ $i
            @ ^ [Y0: $i] :
                ( ( rel @ sK1 @ Y0 )
               => ( ( a @ Y0 )
                  | ( !! @ $i
                    @ ^ [Y1: $i] :
                        ( ( rel @ Y0 @ Y1 )
                       => ( ( a @ Y1 )
                          | ( !! @ $i
                            @ ^ [Y2: $i] :
                                ( ( rel @ Y1 @ Y2 )
                               => ( s @ Y2 ) ) ) ) ) ) ) ) )
        | ( !! @ $i
          @ ^ [Y0: $i] :
              ( ( rel @ sK1 @ Y0 )
             => ( ( a @ Y0 )
                | ( !! @ $i
                  @ ^ [Y1: $i] :
                      ( ( rel @ Y0 @ Y1 )
                     => ( s @ Y1 ) ) ) ) ) ) ) ) ),
    inference(beta-eta_normalization,[],[f114]) ).

thf(f116,plain,
    ( $false
    = ( ~ ( !! @ $i
          @ ^ [Y0: $i] :
              ( ( rel @ sK1 @ Y0 )
             => ( ( a @ Y0 )
                | ( !! @ $i
                  @ ^ [Y1: $i] :
                      ( ( rel @ Y0 @ Y1 )
                     => ( ( a @ Y1 )
                        | ( !! @ $i
                          @ ^ [Y2: $i] :
                              ( ( rel @ Y1 @ Y2 )
                             => ( s @ Y2 ) ) ) ) ) ) ) ) )
      | ( !! @ $i
        @ ^ [Y0: $i] :
            ( ( rel @ sK1 @ Y0 )
           => ( ( a @ Y0 )
              | ( !! @ $i
                @ ^ [Y1: $i] :
                    ( ( rel @ Y0 @ Y1 )
                   => ( s @ Y1 ) ) ) ) ) ) ) ),
    inference(imp_proxy_clausification,[],[f115]) ).

thf(f118,plain,
    ( $false
    = ( !! @ $i
      @ ^ [Y0: $i] :
          ( ( rel @ sK1 @ Y0 )
         => ( ( a @ Y0 )
            | ( !! @ $i
              @ ^ [Y1: $i] :
                  ( ( rel @ Y0 @ Y1 )
                 => ( s @ Y1 ) ) ) ) ) ) ),
    inference(or_proxy_clausification,[],[f116]) ).

thf(f119,plain,
    ( $false
    = ( ~ ( !! @ $i
          @ ^ [Y0: $i] :
              ( ( rel @ sK1 @ Y0 )
             => ( ( a @ Y0 )
                | ( !! @ $i
                  @ ^ [Y1: $i] :
                      ( ( rel @ Y0 @ Y1 )
                     => ( ( a @ Y1 )
                        | ( !! @ $i
                          @ ^ [Y2: $i] :
                              ( ( rel @ Y1 @ Y2 )
                             => ( s @ Y2 ) ) ) ) ) ) ) ) ) ) ),
    inference(or_proxy_clausification,[],[f116]) ).

thf(f120,plain,
    ( $true
    = ( !! @ $i
      @ ^ [Y0: $i] :
          ( ( rel @ sK1 @ Y0 )
         => ( ( a @ Y0 )
            | ( !! @ $i
              @ ^ [Y1: $i] :
                  ( ( rel @ Y0 @ Y1 )
                 => ( ( a @ Y1 )
                    | ( !! @ $i
                      @ ^ [Y2: $i] :
                          ( ( rel @ Y1 @ Y2 )
                         => ( s @ Y2 ) ) ) ) ) ) ) ) ) ),
    inference(not_proxy_clausification,[],[f119]) ).

thf(f121,plain,
    ! [X1: $i] :
      ( $true
      = ( ^ [Y0: $i] :
            ( ( rel @ sK1 @ Y0 )
           => ( ( a @ Y0 )
              | ( !! @ $i
                @ ^ [Y1: $i] :
                    ( ( rel @ Y0 @ Y1 )
                   => ( ( a @ Y1 )
                      | ( !! @ $i
                        @ ^ [Y2: $i] :
                            ( ( rel @ Y1 @ Y2 )
                           => ( s @ Y2 ) ) ) ) ) ) ) )
        @ X1 ) ),
    inference(pi_proxy_clausification,[],[f120]) ).

thf(f122,plain,
    ! [X1: $i] :
      ( $true
      = ( ( rel @ sK1 @ X1 )
       => ( ( a @ X1 )
          | ( !! @ $i
            @ ^ [Y0: $i] :
                ( ( rel @ X1 @ Y0 )
               => ( ( a @ Y0 )
                  | ( !! @ $i
                    @ ^ [Y1: $i] :
                        ( ( rel @ Y0 @ Y1 )
                       => ( s @ Y1 ) ) ) ) ) ) ) ) ),
    inference(beta-eta_normalization,[],[f121]) ).

thf(f123,plain,
    ! [X1: $i] :
      ( ( $false
        = ( rel @ sK1 @ X1 ) )
      | ( $true
        = ( ( a @ X1 )
          | ( !! @ $i
            @ ^ [Y0: $i] :
                ( ( rel @ X1 @ Y0 )
               => ( ( a @ Y0 )
                  | ( !! @ $i
                    @ ^ [Y1: $i] :
                        ( ( rel @ Y0 @ Y1 )
                       => ( s @ Y1 ) ) ) ) ) ) ) ) ),
    inference(imp_proxy_clausification,[],[f122]) ).

thf(f124,plain,
    ! [X1: $i] :
      ( ( $false
        = ( rel @ sK1 @ X1 ) )
      | ( $true
        = ( !! @ $i
          @ ^ [Y0: $i] :
              ( ( rel @ X1 @ Y0 )
             => ( ( a @ Y0 )
                | ( !! @ $i
                  @ ^ [Y1: $i] :
                      ( ( rel @ Y0 @ Y1 )
                     => ( s @ Y1 ) ) ) ) ) ) )
      | ( $true
        = ( a @ X1 ) ) ),
    inference(or_proxy_clausification,[],[f123]) ).

thf(f125,plain,
    ! [X2: $i,X1: $i] :
      ( ( $false
        = ( rel @ sK1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: $i] :
              ( ( rel @ X1 @ Y0 )
             => ( ( a @ Y0 )
                | ( !! @ $i
                  @ ^ [Y1: $i] :
                      ( ( rel @ Y0 @ Y1 )
                     => ( s @ Y1 ) ) ) ) )
          @ X2 ) )
      | ( $true
        = ( a @ X1 ) ) ),
    inference(pi_proxy_clausification,[],[f124]) ).

thf(f126,plain,
    ! [X2: $i,X1: $i] :
      ( ( $false
        = ( rel @ sK1 @ X1 ) )
      | ( $true
        = ( ( rel @ X1 @ X2 )
         => ( ( a @ X2 )
            | ( !! @ $i
              @ ^ [Y0: $i] :
                  ( ( rel @ X2 @ Y0 )
                 => ( s @ Y0 ) ) ) ) ) )
      | ( $true
        = ( a @ X1 ) ) ),
    inference(beta-eta_normalization,[],[f125]) ).

thf(f127,plain,
    ! [X2: $i,X1: $i] :
      ( ( $false
        = ( rel @ sK1 @ X1 ) )
      | ( $false
        = ( rel @ X1 @ X2 ) )
      | ( $true
        = ( a @ X1 ) )
      | ( $true
        = ( ( a @ X2 )
          | ( !! @ $i
            @ ^ [Y0: $i] :
                ( ( rel @ X2 @ Y0 )
               => ( s @ Y0 ) ) ) ) ) ),
    inference(imp_proxy_clausification,[],[f126]) ).

thf(f128,plain,
    ! [X2: $i,X1: $i] :
      ( ( $false
        = ( rel @ sK1 @ X1 ) )
      | ( $false
        = ( rel @ X1 @ X2 ) )
      | ( $true
        = ( a @ X1 ) )
      | ( $true
        = ( !! @ $i
          @ ^ [Y0: $i] :
              ( ( rel @ X2 @ Y0 )
             => ( s @ Y0 ) ) ) )
      | ( $true
        = ( a @ X2 ) ) ),
    inference(or_proxy_clausification,[],[f127]) ).

thf(f129,plain,
    ! [X2: $i,X3: $i,X1: $i] :
      ( ( $false
        = ( rel @ sK1 @ X1 ) )
      | ( $false
        = ( rel @ X1 @ X2 ) )
      | ( $true
        = ( a @ X1 ) )
      | ( $true
        = ( ^ [Y0: $i] :
              ( ( rel @ X2 @ Y0 )
             => ( s @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( a @ X2 ) ) ),
    inference(pi_proxy_clausification,[],[f128]) ).

thf(f130,plain,
    ! [X2: $i,X3: $i,X1: $i] :
      ( ( $false
        = ( rel @ sK1 @ X1 ) )
      | ( $false
        = ( rel @ X1 @ X2 ) )
      | ( $true
        = ( a @ X1 ) )
      | ( $true
        = ( ( rel @ X2 @ X3 )
         => ( s @ X3 ) ) )
      | ( $true
        = ( a @ X2 ) ) ),
    inference(beta-eta_normalization,[],[f129]) ).

thf(f131,plain,
    ! [X2: $i,X3: $i,X1: $i] :
      ( ( $false
        = ( rel @ sK1 @ X1 ) )
      | ( $false
        = ( rel @ X2 @ X3 ) )
      | ( $false
        = ( rel @ X1 @ X2 ) )
      | ( $true
        = ( a @ X1 ) )
      | ( $true
        = ( a @ X2 ) )
      | ( $true
        = ( s @ X3 ) ) ),
    inference(imp_proxy_clausification,[],[f130]) ).

thf(f132,plain,
    ( $false
    = ( ^ [Y0: $i] :
          ( ( rel @ sK1 @ Y0 )
         => ( ( a @ Y0 )
            | ( !! @ $i
              @ ^ [Y1: $i] :
                  ( ( rel @ Y0 @ Y1 )
                 => ( s @ Y1 ) ) ) ) )
      @ sK2 ) ),
    inference(sigma_proxy_clausification,[],[f118]) ).

thf(f133,plain,
    ( $false
    = ( ( rel @ sK1 @ sK2 )
     => ( ( a @ sK2 )
        | ( !! @ $i
          @ ^ [Y0: $i] :
              ( ( rel @ sK2 @ Y0 )
             => ( s @ Y0 ) ) ) ) ) ),
    inference(beta-eta_normalization,[],[f132]) ).

thf(f134,plain,
    ( $false
    = ( ( a @ sK2 )
      | ( !! @ $i
        @ ^ [Y0: $i] :
            ( ( rel @ sK2 @ Y0 )
           => ( s @ Y0 ) ) ) ) ),
    inference(imp_proxy_clausification,[],[f133]) ).

thf(f135,plain,
    ( $true
    = ( rel @ sK1 @ sK2 ) ),
    inference(imp_proxy_clausification,[],[f133]) ).

thf(f136,plain,
    ( $false
    = ( !! @ $i
      @ ^ [Y0: $i] :
          ( ( rel @ sK2 @ Y0 )
         => ( s @ Y0 ) ) ) ),
    inference(or_proxy_clausification,[],[f134]) ).

thf(f137,plain,
    ( $false
    = ( a @ sK2 ) ),
    inference(or_proxy_clausification,[],[f134]) ).

thf(f138,plain,
    ( $false
    = ( ^ [Y0: $i] :
          ( ( rel @ sK2 @ Y0 )
         => ( s @ Y0 ) )
      @ sK3 ) ),
    inference(sigma_proxy_clausification,[],[f136]) ).

thf(f139,plain,
    ( $false
    = ( ( rel @ sK2 @ sK3 )
     => ( s @ sK3 ) ) ),
    inference(beta-eta_normalization,[],[f138]) ).

thf(f140,plain,
    ( $false
    = ( s @ sK3 ) ),
    inference(imp_proxy_clausification,[],[f139]) ).

thf(f141,plain,
    ( $true
    = ( rel @ sK2 @ sK3 ) ),
    inference(imp_proxy_clausification,[],[f139]) ).

thf(f159,plain,
    ! [X0: $i > $o] :
      ( $true
      = ( !! @ $i
        @ ^ [Y0: $i] :
            ( ~ ( !! @ $i
                @ ^ [Y1: $i] :
                    ( ( rel @ Y0 @ Y1 )
                   => ( X0 @ Y1 ) ) )
            | ( X0 @ Y0 ) ) ) ),
    inference(beta-eta_normalization,[],[f108]) ).

thf(f160,plain,
    ! [X0: $i > $o,X1: $i] :
      ( $true
      = ( ^ [Y0: $i] :
            ( ~ ( !! @ $i
                @ ^ [Y1: $i] :
                    ( ( rel @ Y0 @ Y1 )
                   => ( X0 @ Y1 ) ) )
            | ( X0 @ Y0 ) )
        @ X1 ) ),
    inference(pi_proxy_clausification,[],[f159]) ).

thf(f161,plain,
    ! [X0: $i > $o,X1: $i] :
      ( $true
      = ( ~ ( !! @ $i
            @ ^ [Y0: $i] :
                ( ( rel @ X1 @ Y0 )
               => ( X0 @ Y0 ) ) )
        | ( X0 @ X1 ) ) ),
    inference(beta-eta_normalization,[],[f160]) ).

thf(f162,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( ( X0 @ X1 )
        = $true )
      | ( $true
        = ( ~ ( !! @ $i
              @ ^ [Y0: $i] :
                  ( ( rel @ X1 @ Y0 )
                 => ( X0 @ Y0 ) ) ) ) ) ),
    inference(or_proxy_clausification,[],[f161]) ).

thf(f163,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( ( X0 @ X1 )
        = $true )
      | ( $false
        = ( !! @ $i
          @ ^ [Y0: $i] :
              ( ( rel @ X1 @ Y0 )
             => ( X0 @ Y0 ) ) ) ) ),
    inference(not_proxy_clausification,[],[f162]) ).

thf(f164,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( ( X0 @ X1 )
        = $true )
      | ( $false
        = ( ^ [Y0: $i] :
              ( ( rel @ X1 @ Y0 )
             => ( X0 @ Y0 ) )
          @ ( sK5 @ X1 @ X0 ) ) ) ),
    inference(sigma_proxy_clausification,[],[f163]) ).

thf(f165,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( ( X0 @ X1 )
        = $true )
      | ( $false
        = ( ( rel @ X1 @ ( sK5 @ X1 @ X0 ) )
         => ( X0 @ ( sK5 @ X1 @ X0 ) ) ) ) ),
    inference(beta-eta_normalization,[],[f164]) ).

thf(f166,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( $false
        = ( X0 @ ( sK5 @ X1 @ X0 ) ) )
      | ( ( X0 @ X1 )
        = $true ) ),
    inference(imp_proxy_clausification,[],[f165]) ).

thf(f167,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( $true
        = ( rel @ X1 @ ( sK5 @ X1 @ X0 ) ) )
      | ( ( X0 @ X1 )
        = $true ) ),
    inference(imp_proxy_clausification,[],[f165]) ).

thf(f177,plain,
    ! [X0: $i] :
      ( ( sK5 @ X0
        @ ^ [Y0: $i] : ( Y0 != X0 ) )
      = X0 ),
    inference(leibniz_equality_elimination,[],[f166]) ).

thf(f587,plain,
    ! [X2: $i,X0: $i,X1: $i > $o] :
      ( ( $false = $true )
      | ( $true
        = ( X1 @ X0 ) )
      | ( $false
        = ( rel @ sK1 @ X0 ) )
      | ( $false
        = ( rel @ ( sK5 @ X0 @ X1 ) @ X2 ) )
      | ( $true
        = ( a @ X0 ) )
      | ( $true
        = ( a @ ( sK5 @ X0 @ X1 ) ) )
      | ( $true
        = ( s @ X2 ) ) ),
    inference(constrained_superposition,[],[f167,f131]) ).

thf(f606,plain,
    ! [X2: $i,X0: $i,X1: $i > $o] :
      ( ( $false
        = ( rel @ ( sK5 @ X0 @ X1 ) @ X2 ) )
      | ( $false
        = ( rel @ sK1 @ X0 ) )
      | ( $true
        = ( X1 @ X0 ) )
      | ( $true
        = ( a @ X0 ) )
      | ( $true
        = ( a @ ( sK5 @ X0 @ X1 ) ) )
      | ( $true
        = ( s @ X2 ) ) ),
    inference(trivial_inequality_removal,[],[f587]) ).

thf(f37242,plain,
    ! [X0: $i,X1: $i] :
      ( ( $false
        = ( rel @ X0 @ X1 ) )
      | ( $false
        = ( rel @ sK1 @ X0 ) )
      | ( $true
        = ( ^ [Y0: $i] : ( Y0 != X0 )
          @ X0 ) )
      | ( $true
        = ( a @ X0 ) )
      | ( $true
        = ( a @ X0 ) )
      | ( $true
        = ( s @ X1 ) ) ),
    inference(constrained_superposition,[],[f606,f177]) ).

thf(f37737,plain,
    ! [X0: $i,X1: $i] :
      ( ( $false
        = ( rel @ X0 @ X1 ) )
      | ( $false
        = ( rel @ sK1 @ X0 ) )
      | ( $true
        = ( ^ [Y0: $i] : ( Y0 != X0 )
          @ X0 ) )
      | ( $true
        = ( a @ X0 ) )
      | ( $true
        = ( s @ X1 ) ) ),
    inference(duplicate_literal_removal,[],[f37242]) ).

thf(f37738,plain,
    ! [X0: $i,X1: $i] :
      ( ( $false
        = ( rel @ X0 @ X1 ) )
      | ( $false
        = ( rel @ sK1 @ X0 ) )
      | ( $true
        = ( X0 != X0 ) )
      | ( $true
        = ( a @ X0 ) )
      | ( $true
        = ( s @ X1 ) ) ),
    inference(beta-eta_normalization,[],[f37737]) ).

thf(f37739,plain,
    ! [X0: $i,X1: $i] :
      ( ( $false
        = ( rel @ X0 @ X1 ) )
      | ( $false
        = ( rel @ sK1 @ X0 ) )
      | ( $false
        = ( X0 = X0 ) )
      | ( $true
        = ( a @ X0 ) )
      | ( $true
        = ( s @ X1 ) ) ),
    inference(not_proxy_clausification,[],[f37738]) ).

thf(f37740,plain,
    ! [X0: $i,X1: $i] :
      ( ( $false
        = ( rel @ X0 @ X1 ) )
      | ( $false
        = ( rel @ sK1 @ X0 ) )
      | ( X0 != X0 )
      | ( $true
        = ( a @ X0 ) )
      | ( $true
        = ( s @ X1 ) ) ),
    inference(equality_proxy_clausification,[],[f37739]) ).

thf(f37741,plain,
    ! [X0: $i,X1: $i] :
      ( ( $false
        = ( rel @ sK1 @ X0 ) )
      | ( $false
        = ( rel @ X0 @ X1 ) )
      | ( $true
        = ( a @ X0 ) )
      | ( $true
        = ( s @ X1 ) ) ),
    inference(trivial_inequality_removal,[],[f37740]) ).

thf(f37989,plain,
    ( ( $false = $true )
    | ( $false
      = ( rel @ sK1 @ sK2 ) )
    | ( $true
      = ( a @ sK2 ) )
    | ( $true
      = ( s @ sK3 ) ) ),
    inference(constrained_superposition,[],[f141,f37741]) ).

thf(f37994,plain,
    ( ( $false
      = ( rel @ sK1 @ sK2 ) )
    | ( $true
      = ( a @ sK2 ) )
    | ( $true
      = ( s @ sK3 ) ) ),
    inference(trivial_inequality_removal,[],[f37989]) ).

thf(f38357,plain,
    ( ( $false = $true )
    | ( $false
      = ( rel @ sK1 @ sK2 ) )
    | ( $true
      = ( s @ sK3 ) ) ),
    inference(forward_demodulation,[],[f37994,f137]) ).

thf(f38358,plain,
    ( ( $false
      = ( rel @ sK1 @ sK2 ) )
    | ( $true
      = ( s @ sK3 ) ) ),
    inference(trivial_inequality_removal,[],[f38357]) ).

thf(f38361,plain,
    ( ( $false = $true )
    | ( $false
      = ( rel @ sK1 @ sK2 ) ) ),
    inference(forward_demodulation,[],[f38358,f140]) ).

thf(f38362,plain,
    ( $false
    = ( rel @ sK1 @ sK2 ) ),
    inference(trivial_inequality_removal,[],[f38361]) ).

thf(f38513,plain,
    $false = $true,
    inference(constrained_superposition,[],[f135,f38362]) ).

thf(f38514,plain,
    $false,
    inference(trivial_inequality_removal,[],[f38513]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV427^2 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20  % Computer : n018.cluster.edu
% 0.09/0.20  % Model    : x86_64 x86_64
% 0.09/0.20  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20  % Memory   : 8046.5625MB
% 0.09/0.20  % OS       : Linux 6.8.0-71-generic
% 0.09/0.20  % CPULimit : 300
% 0.09/0.20  % WCLimit  : 300
% 0.09/0.20  % DateTime : Tue Sep 29 16:04:07 UTC 2026
% 0.09/0.20  % CPUTime  : 
% 0.09/0.20  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23  Running first-order model finding
% 0.09/0.23  Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.31/1.18  % (266699)Will run a generic schedule for satisfiability detection.
% 6.31/1.18  % (266705)% WARNING: option uhcvi not known.
% 6.31/1.18  % (266709)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=902814301:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.31/1.18  % (266704)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1999556344_2999 on theBenchmark for (2999ds/0Mi)
% 6.31/1.18  % (266705)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2829712239:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.31/1.18  % (266707)dis+10_1_sil=32000:sp=arity:random_seed=3414083669:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.31/1.18  % (266705)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.31/1.18  % Exception at run slice level
% 6.31/1.18  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.31/1.18  % (266705)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.31/1.18  % (266708)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1683758629:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.31/1.18  % (266708)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.31/1.18  % (266706)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=685721360:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.31/1.18  % (266710)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=859932978:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.31/1.18  % (266715)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4099091421:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.31/1.18  % Exception at run slice level
% 6.31/1.18  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.31/1.18  % (266709)Instruction limit reached! 
% 6.31/1.18  % (266709)------------------------------
% 6.31/1.18  % (266709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.31/1.18  % (266709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/1.18  % (266709)CaDiCaL version: 2.1.3
% 6.31/1.18  % (266709)Termination reason: Instruction limit
% 6.31/1.18  % (266709)Termination phase: Saturation
% 6.31/1.18  % (266709)Time elapsed: 0.036 s
% 6.31/1.18  % (266709)Peak memory usage: 13 MB
% 6.31/1.18  % (266709)Instructions burned: 135 (million)
% 6.31/1.18  % (266721)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3324604258:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 6.31/1.18  % (266720)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2789057720:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.31/1.18  % (266721)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.31/1.18  % (266721)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.31/1.18  % (266707)Instruction limit reached! 
% 6.31/1.18  % (266707)------------------------------
% 6.31/1.18  % (266707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.31/1.18  % (266707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/1.18  % (266707)CaDiCaL version: 2.1.3
% 6.31/1.18  % (266707)Termination reason: Instruction limit
% 6.31/1.18  % (266707)Termination phase: Saturation
% 6.31/1.18  % (266707)Time elapsed: 0.051 s
% 6.31/1.18  % (266707)Peak memory usage: 12 MB
% 6.31/1.18  % (266707)Instructions burned: 103 (million)
% 6.31/1.18  % (266724)ott-21_1_sil=16000:fs=off:random_seed=3776507672:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 6.31/1.18  % (266720)Instruction limit reached! 
% 6.31/1.18  % (266720)------------------------------
% 6.31/1.18  % (266720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.31/1.18  % (266720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.31/1.18  % (266720)CaDiCaL version: 2.1.3
% 6.31/1.18  % (266720)Termination reason: Instruction limit
% 6.31/1.18  % (266720)Termination phase: Saturation
% 6.31/1.18  % (266720)Time elapsed: 0.065 s
% 6.31/1.18  % (266720)Peak memory usage: 12 MB
% 6.31/1.18  % (266720)Instructions burned: 132 (million)
% 6.31/1.18  % (266708)Instruction limit reached! 
% 6.31/1.18  % (266708)------------------------------
% 20.96/3.23  % (266708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.96/3.23  % (266708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.96/3.23  % (266708)CaDiCaL version: 2.1.3
% 20.96/3.23  % (266708)Termination reason: Instruction limit
% 20.96/3.23  % (266708)Termination phase: Saturation
% 20.96/3.23  % (266708)Time elapsed: 0.103 s
% 20.96/3.23  % (266708)Peak memory usage: 12 MB
% 20.96/3.23  % (266708)Instructions burned: 116 (million)
% 20.96/3.23  % (266726)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2194428448:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 20.96/3.23  % (266727)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3198139768:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 20.96/3.23  % Exception at run slice level
% 20.96/3.23  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.96/3.23  % (266710)Instruction limit reached! 
% 20.96/3.23  % (266710)------------------------------
% 20.96/3.23  % (266710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.96/3.23  % (266710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.96/3.23  % (266710)CaDiCaL version: 2.1.3
% 20.96/3.23  % (266710)Termination reason: Instruction limit
% 20.96/3.23  % (266710)Termination phase: Saturation
% 20.96/3.23  % (266710)Time elapsed: 0.133 s
% 20.96/3.23  % (266710)Peak memory usage: 12 MB
% 20.96/3.23  % (266710)Instructions burned: 160 (million)
% 20.96/3.23  % (266724)Instruction limit reached! 
% 20.96/3.23  % (266724)------------------------------
% 20.96/3.23  % (266724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.96/3.23  % (266724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.96/3.23  % (266724)CaDiCaL version: 2.1.3
% 20.96/3.23  % (266724)Termination reason: Instruction limit
% 20.96/3.23  % (266724)Termination phase: Saturation
% 20.96/3.23  % (266724)Time elapsed: 0.084 s
% 20.96/3.23  % (266724)Peak memory usage: 12 MB
% 20.96/3.23  % (266724)Instructions burned: 180 (million)
% 20.96/3.23  % (266730)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3020785062:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 20.96/3.23  % (266731)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1634539097:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 20.96/3.23  % (266732)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3319072942:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 20.96/3.23  % (266732)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.96/3.23  % Exception at run slice level
% 20.96/3.23  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.96/3.23  % (266721)Instruction limit reached! 
% 20.96/3.23  % (266721)------------------------------
% 20.96/3.23  % (266721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.96/3.23  % (266721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.96/3.23  % (266721)CaDiCaL version: 2.1.3
% 20.96/3.23  % (266721)Termination reason: Instruction limit
% 20.96/3.23  % (266721)Termination phase: Saturation
% 20.96/3.23  % (266721)Time elapsed: 0.167 s
% 20.96/3.23  % (266721)Peak memory usage: 15 MB
% 20.96/3.23  % (266721)Instructions burned: 688 (million)
% 20.96/3.23  % (266736)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=265722355:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 20.96/3.23  % (266736)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 20.96/3.23  % (266737)fmb+10_1_sil=64000:random_seed=4010006677:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 20.96/3.23  % (266737)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 20.96/3.23  % Exception at run slice level
% 20.96/3.23  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.96/3.23  % (266740)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4047088819:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 20.96/3.23  % Exception at run slice level
% 20.96/3.23  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 20.96/3.23  % (266742)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2707605882:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 30.22/4.55  % Exception at run slice level
% 30.22/4.55  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 30.22/4.55  % (266744)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1743150300:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 30.22/4.55  % (266744)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 30.22/4.55  % (266726)Instruction limit reached! 
% 30.22/4.55  % (266726)------------------------------
% 30.22/4.55  % (266726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266726)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266726)Termination reason: Instruction limit
% 30.22/4.55  % (266726)Termination phase: Saturation
% 30.22/4.55  % (266726)Time elapsed: 0.235 s
% 30.22/4.55  % (266726)Peak memory usage: 13 MB
% 30.22/4.55  % (266726)Instructions burned: 479 (million)
% 30.22/4.55  % (266746)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=543603642:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 30.22/4.55  % (266746)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 30.22/4.55  % (266746)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 30.22/4.55  % (266732)Instruction limit reached! 
% 30.22/4.55  % (266732)------------------------------
% 30.22/4.55  % (266732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266732)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266732)Termination reason: Instruction limit
% 30.22/4.55  % (266732)Termination phase: Saturation
% 30.22/4.55  % (266732)Time elapsed: 0.370 s
% 30.22/4.55  % (266732)Peak memory usage: 18 MB
% 30.22/4.55  % (266732)Instructions burned: 693 (million)
% 30.22/4.55  % (266748)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=664659778:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 30.22/4.55  % Exception at run slice level
% 30.22/4.55  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 30.22/4.55  % (266750)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3911397184:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 30.22/4.55  % Exception at run slice level
% 30.22/4.55  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 30.22/4.55  % (266754)ott-2_1_sil=16000:newcnf=on:random_seed=208233640:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 30.22/4.55  % (266754)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 30.22/4.55  % (266736)Instruction limit reached! 
% 30.22/4.55  % (266736)------------------------------
% 30.22/4.55  % (266736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266736)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266736)Termination reason: Instruction limit
% 30.22/4.55  % (266736)Termination phase: Saturation
% 30.22/4.55  % (266736)Time elapsed: 0.463 s
% 30.22/4.55  % (266736)Peak memory usage: 15 MB
% 30.22/4.55  % (266736)Instructions burned: 880 (million)
% 30.22/4.55  % (266756)ott+10_1_sil=32000:tgt=ground:random_seed=1329139710:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 30.22/4.55  % (266730)Instruction limit reached! 
% 30.22/4.55  % (266730)------------------------------
% 30.22/4.55  % (266730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266730)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266730)Termination reason: Instruction limit
% 30.22/4.55  % (266730)Termination phase: Saturation
% 30.22/4.55  % (266730)Time elapsed: 0.705 s
% 30.22/4.55  % (266730)Peak memory usage: 15 MB
% 30.22/4.55  % (266730)Instructions burned: 1180 (million)
% 30.22/4.55  % (266758)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3159963948:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 30.22/4.55  % Exception at run slice level
% 30.22/4.55  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 30.22/4.55  % (266760)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2222442295:i=3512:aac=none_2990 on theBenchmark for (2990ds/3512Mi)
% 30.22/4.55  % (266760)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 30.22/4.55  % (266754)Instruction limit reached! 
% 30.22/4.55  % (266754)------------------------------
% 30.22/4.55  % (266754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266754)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266754)Termination reason: Instruction limit
% 30.22/4.55  % (266754)Termination phase: Saturation
% 30.22/4.55  % (266754)Time elapsed: 0.409 s
% 30.22/4.55  % (266754)Peak memory usage: 15 MB
% 30.22/4.55  % (266754)Instructions burned: 871 (million)
% 30.22/4.55  % (266762)dis+21_1_sil=32000:sas=cadical:random_seed=2632519653:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 30.22/4.55  % (266746)Instruction limit reached! 
% 30.22/4.55  % (266746)------------------------------
% 30.22/4.55  % (266746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266746)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266746)Termination reason: Instruction limit
% 30.22/4.55  % (266746)Termination phase: Saturation
% 30.22/4.55  % (266746)Time elapsed: 0.726 s
% 30.22/4.55  % (266746)Peak memory usage: 19 MB
% 30.22/4.55  % (266746)Instructions burned: 1472 (million)
% 30.22/4.55  % (266764)ott+11_1_sil=16000:gs=on:random_seed=735977305:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2988 on theBenchmark for (2988ds/2251Mi)
% 30.22/4.55  % (266764)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 30.22/4.55  % (266744)Instruction limit reached! 
% 30.22/4.55  % (266744)------------------------------
% 30.22/4.55  % (266744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266744)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266744)Termination reason: Instruction limit
% 30.22/4.55  % (266744)Termination phase: Saturation
% 30.22/4.55  % (266744)Time elapsed: 1.546 s
% 30.22/4.55  % (266744)Peak memory usage: 20 MB
% 30.22/4.55  % (266744)Instructions burned: 5133 (million)
% 30.22/4.55  % (266771)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=893238979:fmbsr=1.6:i=67534_2981 on theBenchmark for (2981ds/67534Mi)
% 30.22/4.55  % Exception at run slice level
% 30.22/4.55  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 30.22/4.55  % (266773)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=1905686606:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2981 on theBenchmark for (2981ds/4591Mi)
% 30.22/4.55  % (266764)Instruction limit reached! 
% 30.22/4.55  % (266764)------------------------------
% 30.22/4.55  % (266764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266764)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266764)Termination reason: Instruction limit
% 30.22/4.55  % (266764)Termination phase: Saturation
% 30.22/4.55  % (266764)Time elapsed: 0.977 s
% 30.22/4.55  % (266764)Peak memory usage: 15 MB
% 30.22/4.55  % (266764)Instructions burned: 2251 (million)
% 30.22/4.55  % (266775)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=349941257:i=29340_2978 on theBenchmark for (2978ds/29340Mi)
% 30.22/4.55  % (266773)Instruction limit reached! 
% 30.22/4.55  % (266773)------------------------------
% 30.22/4.55  % (266773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266773)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266773)Termination reason: Instruction limit
% 30.22/4.55  % (266773)Termination phase: Saturation
% 30.22/4.55  % (266773)Time elapsed: 1.103 s
% 30.22/4.55  % (266773)Peak memory usage: 29 MB
% 30.22/4.55  % (266773)Instructions burned: 4594 (million)
% 30.22/4.55  % (266784)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=1637216969:i=5211_2970 on theBenchmark for (2970ds/5211Mi)
% 30.22/4.55  % (266760)Instruction limit reached! 
% 30.22/4.55  % (266760)------------------------------
% 30.22/4.55  % (266760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266760)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266760)Termination reason: Instruction limit
% 30.22/4.55  % (266760)Termination phase: Saturation
% 30.22/4.55  % (266760)Time elapsed: 2.048 s
% 30.22/4.55  % (266760)Peak memory usage: 17 MB
% 30.22/4.55  % (266760)Instructions burned: 3514 (million)
% 30.22/4.55  % (266786)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=1620784429:i=5497:nm=2_2970 on theBenchmark for (2970ds/5497Mi)
% 30.22/4.55  % Exception at run slice level
% 30.22/4.55  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 30.22/4.55  % (266788)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=2573204387:fmbsr=2:i=46332_2970 on theBenchmark for (2970ds/46332Mi)
% 30.22/4.55  % Exception at run slice level
% 30.22/4.55  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 30.22/4.55  % (266790)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=1531715629:i=14071_2969 on theBenchmark for (2969ds/14071Mi)
% 30.22/4.55  % Exception at run slice level
% 30.22/4.55  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 30.22/4.55  % (266792)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3460133121:i=22565:add=on:rawr=on_2969 on theBenchmark for (2969ds/22565Mi)
% 30.22/4.55  % (266762)Instruction limit reached! 
% 30.22/4.55  % (266762)------------------------------
% 30.22/4.55  % (266762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266762)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266762)Termination reason: Instruction limit
% 30.22/4.55  % (266762)Termination phase: Saturation
% 30.22/4.55  % (266762)Time elapsed: 1.938 s
% 30.22/4.55  % (266762)Peak memory usage: 19 MB
% 30.22/4.55  % (266762)Instructions burned: 3774 (million)
% 30.22/4.55  % (266794)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=570390191:i=8173:av=off_2969 on theBenchmark for (2969ds/8173Mi)
% 30.22/4.55  % (266756)Instruction limit reached! 
% 30.22/4.55  % (266756)------------------------------
% 30.22/4.55  % (266756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266756)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266756)Termination reason: Instruction limit
% 30.22/4.55  % (266756)Termination phase: Saturation
% 30.22/4.55  % (266756)Time elapsed: 2.581 s
% 30.22/4.55  % (266756)Peak memory usage: 23 MB
% 30.22/4.55  % (266756)Instructions burned: 5114 (million)
% 30.22/4.55  % (266797)dis+10_16:1_sil=16000:random_seed=2170848719:i=9155:fsr=off_2966 on theBenchmark for (2966ds/9155Mi)
% 30.22/4.55  % (266705) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-266699-266705"...
% 30.22/4.55  % (266705)...printing done.
% 30.22/4.55  % (266705)Refutation found. Thanks to Tanya!
% 30.22/4.55  % SZS status Theorem for theBenchmark
% 30.22/4.55  % SZS output start Proof for theBenchmark
% See solution above
% 30.22/4.55  % (266705)------------------------------
% 30.22/4.55  % (266705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.22/4.55  % (266705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.22/4.55  % (266705)CaDiCaL version: 2.1.3
% 30.22/4.55  % (266705)Termination reason: Refutation
% 30.22/4.55  % (266705)Time elapsed: 4.269 s
% 30.22/4.55  % (266705)Peak memory usage: 23 MB
% 30.22/4.55  % (266705)Instructions burned: 8638 (million)
% 30.22/4.55  % (266699)Success in time 4.31 s
% 30.22/4.55  % Vampire exiting
%------------------------------------------------------------------------------