TSTP Solution File: SWV884-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWV884-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 11:05:52 EDT 2023

% Result   : Unsatisfiable 87.91s 66.00s
% Output   : CNFRefutation 87.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  120
% Syntax   : Number of formulae    :  133 (  11 unt; 113 typ;   0 def)
%            Number of atoms       :   31 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   27 (  16   ~;  11   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  186 ( 104   >;  82   *;   0   +;   0  <<)
%            Number of predicates  :   67 (  66 usr;   1 prp; 0-4 aty)
%            Number of functors    :   47 (  47 usr;   9 con; 0-5 aty)
%            Number of variables   :   31 (;  31   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_Fun_Oinj__on > c_lessequals > c_in > c_fequal > c_Ring__and__Field_Odvd__class_Odvd > c_HOL_Oord__class_Oless > c_Finite__Set_Ofinite > hBOOL > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring__1 > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Oidom > class_Ring__and__Field_Odvd > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Ocomm__ring__1 > class_Ring__and__Field_Ocomm__ring > class_Orderings_Otop > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Orderings_Obot > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add__meet > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Nat_Osemiring__char__0 > class_Lattices_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Obounded__lattice > class_Int_Onumber__ring > class_HOL_Oord > class_Finite__Set_Ofinite_Ofinite > class_Divides_Osemiring__div > class_Divides_Oring__div > class_Complete__Lattice_Ocomplete__lattice > c_Fun_Ofun__upd > c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1 > c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 > c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 > c_ATP__Linkup_Osko__Set__Ximage__iff__1__1 > c_ATP__Linkup_Osko__Set__Ximage__cong__1__1 > c_ATP__Linkup_Osko__Set__XimageE__1__1 > c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 > c_Set_Ovimage > c_Set_Oimage > c_Hilbert__Choice_Oinv__into > c_Set_Oinsert > c_Lattices_Olower__semilattice__class_Oinf > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_Divides_Odiv__class_Omod > c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2 > c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2 > tc_fun > hAPP > c_SetInterval_Oord__class_OatLeast > c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1 > c_Nat_Osemiring__1__class_Oof__nat > c_Inductive_Ocomplete__lattice__class_Ogfp > c_Finite__Set_Olinorder__class_OMin > c_Finite__Set_Olinorder__class_OMax > c_Finite__Set_Ocard > c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1 > c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1 > #nlpp > c_Suc > c_Orderings_Otop__class_Otop > c_Orderings_Obot__class_Obot > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1 > c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1 > c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1 > v_pn > v_na > v_mgt__call > v_U > v_G > tc_nat > tc_bool > tc_Com_Opname > t_a

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1,type,
    c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1: ( $i * $i ) > $i ).

tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
    class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).

tff(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1,type,
    c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(c_Set_Oinsert,type,
    c_Set_Oinsert: ( $i * $i * $i ) > $i ).

tff(class_Orderings_Olinorder,type,
    class_Orderings_Olinorder: $i > $o ).

tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).

tff(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1,type,
    c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(class_Int_Onumber__ring,type,
    class_Int_Onumber__ring: $i > $o ).

tff(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1,type,
    c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1: ( $i * $i ) > $i ).

tff(c_HOL_Oord__class_Oless,type,
    c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(c_Orderings_Otop__class_Otop,type,
    c_Orderings_Otop__class_Otop: $i > $i ).

tff(v_G,type,
    v_G: $i ).

tff(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1,type,
    c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

tff(class_Ring__and__Field_Oordered__semiring,type,
    class_Ring__and__Field_Oordered__semiring: $i > $o ).

tff(class_Ring__and__Field_Osemiring,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

tff(c_SetInterval_Oord__class_OatLeast,type,
    c_SetInterval_Oord__class_OatLeast: ( $i * $i ) > $i ).

tff(class_Ring__and__Field_Ocomm__semiring,type,
    class_Ring__and__Field_Ocomm__semiring: $i > $o ).

tff(class_Lattices_Obounded__lattice,type,
    class_Lattices_Obounded__lattice: $i > $o ).

tff(class_Ring__and__Field_Oring,type,
    class_Ring__and__Field_Oring: $i > $o ).

tff(class_Lattices_Olattice,type,
    class_Lattices_Olattice: $i > $o ).

tff(c_Nat_Osemiring__1__class_Oof__nat,type,
    c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).

tff(class_OrderedGroup_Oab__semigroup__add,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

tff(c_Finite__Set_Olinorder__class_OMin,type,
    c_Finite__Set_Olinorder__class_OMin: ( $i * $i ) > $i ).

tff(c_Finite__Set_Olinorder__class_OMax,type,
    c_Finite__Set_Olinorder__class_OMax: ( $i * $i ) > $i ).

tff(t_a,type,
    t_a: $i ).

tff(class_OrderedGroup_Olordered__ab__group__add__meet,type,
    class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).

tff(class_Ring__and__Field_Omult__zero,type,
    class_Ring__and__Field_Omult__zero: $i > $o ).

tff(class_OrderedGroup_Olordered__ab__group__add,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

tff(class_Orderings_Oorder,type,
    class_Orderings_Oorder: $i > $o ).

tff(class_Orderings_Opreorder,type,
    class_Orderings_Opreorder: $i > $o ).

tff(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2,type,
    c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2: ( $i * $i * $i ) > $i ).

tff(class_OrderedGroup_Oab__semigroup__mult,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

tff(c_Fun_Oinj__on,type,
    c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).

tff(class_Ring__and__Field_Ono__zero__divisors,type,
    class_Ring__and__Field_Ono__zero__divisors: $i > $o ).

tff(class_Ring__and__Field_Opordered__ring,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

tff(class_Ring__and__Field_Ozero__neq__one,type,
    class_Ring__and__Field_Ozero__neq__one: $i > $o ).

tff(c_Orderings_Obot__class_Obot,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

tff(c_Set_Ovimage,type,
    c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).

tff(c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1,type,
    c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1: $i > $i ).

tff(v_U,type,
    v_U: $i ).

tff(v_pn,type,
    v_pn: $i ).

tff(class_Ring__and__Field_Oordered__ring__strict,type,
    class_Ring__and__Field_Oordered__ring__strict: $i > $o ).

tff(c_Inductive_Ocomplete__lattice__class_Ogfp,type,
    c_Inductive_Ocomplete__lattice__class_Ogfp: ( $i * $i ) > $i ).

tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

tff(class_Orderings_Otop,type,
    class_Orderings_Otop: $i > $o ).

tff(c_Suc,type,
    c_Suc: $i > $i ).

tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
    class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).

tff(class_Ring__and__Field_Ocomm__ring__1,type,
    class_Ring__and__Field_Ocomm__ring__1: $i > $o ).

tff(class_Ring__and__Field_Oordered__idom,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

tff(class_Divides_Oring__div,type,
    class_Divides_Oring__div: $i > $o ).

tff(class_OrderedGroup_Ocancel__semigroup__add,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

tff(c_lessequals,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(c_in,type,
    c_in: ( $i * $i * $i ) > $o ).

tff(tc_nat,type,
    tc_nat: $i ).

tff(c_Divides_Odiv__class_Omod,type,
    c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).

tff(c_Finite__Set_Ocard,type,
    c_Finite__Set_Ocard: ( $i * $i ) > $i ).

tff(class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

tff(class_OrderedGroup_Ocomm__monoid__mult,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

tff(class_OrderedGroup_Ocomm__monoid__add,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

tff(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2,type,
    c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2: ( $i * $i * $i ) > $i ).

tff(c_Hilbert__Choice_Oinv__into,type,
    c_Hilbert__Choice_Oinv__into: ( $i * $i * $i * $i ) > $i ).

tff(tc_fun,type,
    tc_fun: ( $i * $i ) > $i ).

tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
    class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).

tff(class_Ring__and__Field_Oidom,type,
    class_Ring__and__Field_Oidom: $i > $o ).

tff(tc_bool,type,
    tc_bool: $i ).

tff(class_OrderedGroup_Omonoid__add,type,
    class_OrderedGroup_Omonoid__add: $i > $o ).

tff(c_Fun_Ofun__upd,type,
    c_Fun_Ofun__upd: ( $i * $i * $i * $i * $i ) > $i ).

tff(v_mgt__call,type,
    v_mgt__call: $i ).

tff(class_Ring__and__Field_Ocomm__ring,type,
    class_Ring__and__Field_Ocomm__ring: $i > $o ).

tff(class_Ring__and__Field_Oordered__semiring__strict,type,
    class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).

tff(tc_Com_Opname,type,
    tc_Com_Opname: $i ).

tff(v_na,type,
    v_na: $i ).

tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

tff(class_Nat_Osemiring__char__0,type,
    class_Nat_Osemiring__char__0: $i > $o ).

tff(c_HOL_Oplus__class_Oplus,type,
    c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).

tff(c_HOL_Otimes__class_Otimes,type,
    c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).

tff(c_Ring__and__Field_Odvd__class_Odvd,type,
    c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).

tff(c_HOL_Ozero__class_Ozero,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(c_HOL_Oone__class_Oone,type,
    c_HOL_Oone__class_Oone: $i > $i ).

tff(c_fequal,type,
    c_fequal: ( $i * $i * $i ) > $o ).

tff(class_OrderedGroup_Omonoid__mult,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

tff(class_HOL_Oord,type,
    class_HOL_Oord: $i > $o ).

tff(class_Ring__and__Field_Omult__mono1,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

tff(class_OrderedGroup_Oab__group__add,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

tff(hAPP,type,
    hAPP: ( $i * $i ) > $i ).

tff(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1,type,
    c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1: ( $i * $i ) > $i ).

tff(class_Finite__Set_Ofinite_Ofinite,type,
    class_Finite__Set_Ofinite_Ofinite: $i > $o ).

tff(c_ATP__Linkup_Osko__Set__XimageE__1__1,type,
    c_ATP__Linkup_Osko__Set__XimageE__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(class_Ring__and__Field_Oring__1,type,
    class_Ring__and__Field_Oring__1: $i > $o ).

tff(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1,type,
    c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1: $i > $i ).

tff(c_Finite__Set_Ofinite,type,
    c_Finite__Set_Ofinite: ( $i * $i ) > $o ).

tff(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1,type,
    c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1: $i > $i ).

tff(class_Ring__and__Field_Odvd,type,
    class_Ring__and__Field_Odvd: $i > $o ).

tff(class_OrderedGroup_Ogroup__add,type,
    class_OrderedGroup_Ogroup__add: $i > $o ).

tff(hBOOL,type,
    hBOOL: $i > $o ).

tff(class_Divides_Osemiring__div,type,
    class_Divides_Osemiring__div: $i > $o ).

tff(class_Ring__and__Field_Omult__mono,type,
    class_Ring__and__Field_Omult__mono: $i > $o ).

tff(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1,type,
    c_ATP__Linkup_Osko__Set__Ximage__cong__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(class_Lattices_Olower__semilattice,type,
    class_Lattices_Olower__semilattice: $i > $o ).

tff(class_Ring__and__Field_Ocomm__semiring__1,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(class_Ring__and__Field_Opordered__semiring,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
    class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).

tff(c_HOL_Ominus__class_Ominus,type,
    c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(class_Orderings_Obot,type,
    class_Orderings_Obot: $i > $o ).

tff(class_OrderedGroup_Opordered__ab__group__add,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

tff(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1,type,
    c_ATP__Linkup_Osko__Set__Ximage__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1,type,
    c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(c_Set_Oimage,type,
    c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).

tff(class_Ring__and__Field_Osemiring__1,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

tff(c_Lattices_Olower__semilattice__class_Oinf,type,
    c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).

tff(class_Ring__and__Field_Oordered__semidom,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

tff(class_Complete__Lattice_Ocomplete__lattice,type,
    class_Complete__Lattice_Ocomplete__lattice: $i > $o ).

tff(f_6834,axiom,
    c_in(v_pn,v_U,tc_Com_Opname),
    file(unknown,unknown) ).

tff(f_6622,axiom,
    ! [V_S,V_x,T_a] :
      ( hBOOL(hAPP(V_S,V_x))
      | ~ c_in(V_x,V_S,T_a) ),
    file(unknown,unknown) ).

tff(f_6617,axiom,
    ! [V_x,V_S,T_a] :
      ( c_in(V_x,V_S,T_a)
      | ~ hBOOL(hAPP(V_S,V_x)) ),
    file(unknown,unknown) ).

tff(f_6821,axiom,
    ! [T_a,V_A,V_f,T_b,V_x] :
      ( c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b)
      | ~ c_in(V_x,V_A,T_a) ),
    file(unknown,unknown) ).

tff(f_6831,axiom,
    c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    file(unknown,unknown) ).

tff(f_6430,axiom,
    ! [V_x,V_A,T_a,V_B] :
      ( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
      | ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
      | ~ c_in(V_x,V_B,T_a) ),
    file(unknown,unknown) ).

tff(f_6838,axiom,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    file(unknown,unknown) ).

tff(c_2120,plain,
    c_in(v_pn,v_U,tc_Com_Opname),
    inference(cnfTransformation,[status(thm)],[f_6834]) ).

tff(c_4031,plain,
    ! [V_x_3498,V_S_3499,T_a_3500] :
      ( ~ c_in(V_x_3498,V_S_3499,T_a_3500)
      | hBOOL(hAPP(V_S_3499,V_x_3498)) ),
    inference(cnfTransformation,[status(thm)],[f_6622]) ).

tff(c_4042,plain,
    hBOOL(hAPP(v_U,v_pn)),
    inference(resolution,[status(thm)],[c_2120,c_4031]) ).

tff(c_4511,plain,
    ! [V_S_3518,V_x_3519,T_a_3520] :
      ( ~ hBOOL(hAPP(V_S_3518,V_x_3519))
      | c_in(V_x_3519,V_S_3518,T_a_3520) ),
    inference(cnfTransformation,[status(thm)],[f_6617]) ).

tff(c_4518,plain,
    ! [T_a_3520] : c_in(v_pn,v_U,T_a_3520),
    inference(resolution,[status(thm)],[c_4042,c_4511]) ).

tff(c_2108,plain,
    ! [T_b_3301,T_a_3298,V_x_3302,V_f_3300,V_A_3299] :
      ( ~ c_in(V_x_3302,V_A_3299,T_a_3298)
      | c_in(hAPP(V_f_3300,V_x_3302),c_Set_Oimage(V_f_3300,V_A_3299,T_a_3298,T_b_3301),T_b_3301) ),
    inference(cnfTransformation,[status(thm)],[f_6821]) ).

tff(c_2114,plain,
    c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    inference(cnfTransformation,[status(thm)],[f_6831]) ).

tff(c_234939,plain,
    ! [V_x_6143,V_B_6144,T_a_6145,V_A_6146] :
      ( ~ c_in(V_x_6143,V_B_6144,T_a_6145)
      | ~ c_lessequals(V_A_6146,V_B_6144,tc_fun(T_a_6145,tc_bool))
      | c_lessequals(c_Set_Oinsert(V_x_6143,V_A_6146,T_a_6145),V_B_6144,tc_fun(T_a_6145,tc_bool)) ),
    inference(cnfTransformation,[status(thm)],[f_6430]) ).

tff(c_2124,plain,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    inference(cnfTransformation,[status(thm)],[f_6838]) ).

tff(c_234972,plain,
    ( ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a)
    | ~ c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
    inference(resolution,[status(thm)],[c_234939,c_2124]) ).

tff(c_235077,plain,
    ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
    inference(demodulation,[status(thm),theory(equality)],[c_2114,c_234972]) ).

tff(c_240651,plain,
    ~ c_in(v_pn,v_U,tc_Com_Opname),
    inference(resolution,[status(thm)],[c_2108,c_235077]) ).

tff(c_240655,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4518,c_240651]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWV884-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34  % Computer : n004.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 22:25:11 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 87.91/66.00  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 87.91/66.01  
% 87.91/66.01  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 87.98/66.04  
% 87.98/66.04  Inference rules
% 87.98/66.04  ----------------------
% 87.98/66.04  #Ref     : 82
% 87.98/66.04  #Sup     : 54285
% 87.98/66.04  #Fact    : 12
% 87.98/66.04  #Define  : 0
% 87.98/66.04  #Split   : 6
% 87.98/66.04  #Chain   : 0
% 87.98/66.04  #Close   : 0
% 87.98/66.04  
% 87.98/66.04  Ordering : KBO
% 87.98/66.04  
% 87.98/66.04  Simplification rules
% 87.98/66.04  ----------------------
% 87.98/66.04  #Subsume      : 17064
% 87.98/66.04  #Demod        : 33038
% 87.98/66.04  #Tautology    : 10686
% 87.98/66.04  #SimpNegUnit  : 1590
% 87.98/66.04  #BackRed      : 18
% 87.98/66.04  
% 87.98/66.04  #Partial instantiations: 0
% 87.98/66.04  #Strategies tried      : 1
% 87.98/66.04  
% 87.98/66.04  Timing (in seconds)
% 87.98/66.04  ----------------------
% 87.98/66.04  Preprocessing        : 2.01
% 87.98/66.04  Parsing              : 1.12
% 87.98/66.04  CNF conversion       : 0.16
% 87.98/66.04  Main loop            : 62.97
% 87.98/66.04  Inferencing          : 6.28
% 87.98/66.04  Reduction            : 31.63
% 87.98/66.04  Demodulation         : 23.76
% 87.98/66.04  BG Simplification    : 0.68
% 87.98/66.04  Subsumption          : 20.60
% 87.98/66.04  Abstraction          : 0.78
% 87.98/66.04  MUC search           : 0.00
% 87.98/66.04  Cooper               : 0.00
% 87.98/66.04  Total                : 65.03
% 87.98/66.04  Index Insertion      : 0.00
% 87.98/66.04  Index Deletion       : 0.00
% 87.98/66.04  Index Matching       : 0.00
% 87.98/66.04  BG Taut test         : 0.00
%------------------------------------------------------------------------------