TSTP Solution File: LCL777-1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL777-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n002.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 : Sun May  5 07:53:05 EDT 2024

% Result   : Unsatisfiable 0.20s 0.41s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   66
% Syntax   : Number of formulae    :  104 (  68 unt;   0 def)
%            Number of atoms       :  140 (   9 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   52 (  16   ~;   4   |;   0   &)
%                                         (  32 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :   47 (  45 usr;  33 prp; 0-3 aty)
%            Number of functors    :   21 (  21 usr;  10 con; 0-5 aty)
%            Number of variables   :   29 (  29   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f577,plain,
    $false,
    inference(avatar_sat_refutation,[],[f426,f431,f436,f441,f446,f451,f456,f461,f466,f471,f476,f481,f486,f491,f496,f501,f506,f511,f516,f521,f526,f531,f535,f539,f544,f548,f552,f556,f560,f564,f568,f573,f576]) ).

fof(f576,plain,
    ( ~ spl0_25
    | spl0_32 ),
    inference(avatar_split_clause,[],[f575,f570,f541]) ).

fof(f541,plain,
    ( spl0_25
  <=> hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f570,plain,
    ( spl0_32
  <=> hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f575,plain,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i))))
    | spl0_32 ),
    inference(forward_demodulation,[],[f574,f399]) ).

fof(f399,plain,
    ! [X44,X22,X25] : hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X22,tc_Lambda_OdB,tc_Lambda_OdB)),X44) = c_List_Ofoldl(c_Lambda_OdB_OApp,X25,c_List_Orotate1(c_List_Olist_OCons(X44,X22,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    inference(forward_demodulation,[],[f313,f288]) ).

fof(f288,axiom,
    ! [X0,X1,X30] : c_List_Orotate1(c_List_Olist_OCons(X1,X0,X30),X30) = c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X30),X30),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_1) ).

fof(f313,axiom,
    ! [X44,X22,X25] : hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X22,tc_Lambda_OdB,tc_Lambda_OdB)),X44) = c_List_Ofoldl(c_Lambda_OdB_OApp,X25,c_List_Oappend(X22,c_List_Olist_OCons(X44,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__last_0) ).

fof(f574,plain,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Orotate1(c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),v_ss,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
    | spl0_32 ),
    inference(forward_demodulation,[],[f572,f288]) ).

fof(f572,plain,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
    | spl0_32 ),
    inference(avatar_component_clause,[],[f570]) ).

fof(f573,plain,
    ~ spl0_32,
    inference(avatar_split_clause,[],[f365,f570]) ).

fof(f365,axiom,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

fof(f568,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f337,f566]) ).

fof(f566,plain,
    ( spl0_31
  <=> ! [X10] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X10))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f337,axiom,
    ! [X10] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X10))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).

fof(f564,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f224,f562]) ).

fof(f562,plain,
    ( spl0_30
  <=> ! [X10] : ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f224,axiom,
    ! [X10] : ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).

fof(f560,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f205,f558]) ).

fof(f558,plain,
    ( spl0_29
  <=> ! [X43,X3] : c_List_Olistsp(X43,c_List_Olist_ONil(X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f205,axiom,
    ! [X3,X43] : c_List_Olistsp(X43,c_List_Olist_ONil(X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).

fof(f556,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f187,f554]) ).

fof(f554,plain,
    ( spl0_28
  <=> ! [X34,X41] : c_Lambda_OdB_OVar(X34) != c_Lambda_OdB_OAbs(X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f187,axiom,
    ! [X41,X34] : c_Lambda_OdB_OVar(X34) != c_Lambda_OdB_OAbs(X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).

fof(f552,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f93,f550]) ).

fof(f550,plain,
    ( spl0_27
  <=> ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f93,axiom,
    ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).

fof(f548,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f53,f546]) ).

fof(f546,plain,
    ( spl0_26
  <=> ! [X27] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X27) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f53,axiom,
    ! [X27] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

fof(f544,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f362,f541]) ).

fof(f362,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f539,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f242,f537]) ).

fof(f537,plain,
    ( spl0_24
  <=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f242,axiom,
    ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

fof(f535,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f100,f533]) ).

fof(f533,plain,
    ( spl0_23
  <=> ! [X10] : c_Suc(X10) != X10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f100,axiom,
    ! [X10] : c_Suc(X10) != X10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

fof(f531,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f361,f528]) ).

fof(f528,plain,
    ( spl0_22
  <=> hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f361,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f526,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f364,f523]) ).

fof(f523,plain,
    ( spl0_21
  <=> hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,v_s),c_Lambda_OdB_OVar(v_i)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f364,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,v_s),c_Lambda_OdB_OVar(v_i)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f521,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f386,f518]) ).

fof(f518,plain,
    ( spl0_20
  <=> class_Int_Onumber__ring(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f386,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).

fof(f516,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f385,f513]) ).

fof(f513,plain,
    ( spl0_19
  <=> class_Int_Oring__char__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f385,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).

fof(f511,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f384,f508]) ).

fof(f508,plain,
    ( spl0_18
  <=> class_Orderings_Oorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f384,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).

fof(f506,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f383,f503]) ).

fof(f503,plain,
    ( spl0_17
  <=> class_Orderings_Olinorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f383,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).

fof(f501,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f382,f498]) ).

fof(f498,plain,
    ( spl0_16
  <=> class_Orderings_Opreorder(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f382,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).

fof(f496,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f381,f493]) ).

fof(f493,plain,
    ( spl0_15
  <=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f381,axiom,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).

fof(f491,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f380,f488]) ).

fof(f488,plain,
    ( spl0_14
  <=> class_Ring__and__Field_Osemiring__1(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f380,axiom,
    class_Ring__and__Field_Osemiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).

fof(f486,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f379,f483]) ).

fof(f483,plain,
    ( spl0_13
  <=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f379,axiom,
    class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).

fof(f481,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f378,f478]) ).

fof(f478,plain,
    ( spl0_12
  <=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f378,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).

fof(f476,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f377,f473]) ).

fof(f473,plain,
    ( spl0_11
  <=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f377,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).

fof(f471,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f376,f468]) ).

fof(f468,plain,
    ( spl0_10
  <=> class_Orderings_Oorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f376,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

fof(f466,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f375,f463]) ).

fof(f463,plain,
    ( spl0_9
  <=> class_Orderings_Opreorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f375,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

fof(f461,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f374,f458]) ).

fof(f458,plain,
    ( spl0_8
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f374,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f456,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f373,f453]) ).

fof(f453,plain,
    ( spl0_7
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f373,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f451,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f372,f448]) ).

fof(f448,plain,
    ( spl0_6
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f372,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f446,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f371,f443]) ).

fof(f443,plain,
    ( spl0_5
  <=> class_Nat_Osemiring__char__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f371,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

fof(f441,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f370,f438]) ).

fof(f438,plain,
    ( spl0_4
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f370,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

fof(f436,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f369,f433]) ).

fof(f433,plain,
    ( spl0_3
  <=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f369,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

fof(f431,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f368,f428]) ).

fof(f428,plain,
    ( spl0_2
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f368,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

fof(f426,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f363,f423]) ).

fof(f423,plain,
    ( spl0_1
  <=> hBOOL(hAPP(c_InductTermi_OIT,v_s)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f363,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : LCL777-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n002.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 13:58:12 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.36  % (10285)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.39  % (10288)WARNING: value z3 for option sas not known
% 0.13/0.39  % (10289)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.39  % (10290)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.39  % (10287)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.39  % (10291)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.39  % (10286)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.39  % (10288)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.39  % (10293)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.40  % (10290)First to succeed.
% 0.20/0.40  % (10290)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10285"
% 0.20/0.41  % (10290)Refutation found. Thanks to Tanya!
% 0.20/0.41  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.41  % (10290)------------------------------
% 0.20/0.41  % (10290)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.41  % (10290)Termination reason: Refutation
% 0.20/0.41  
% 0.20/0.41  % (10290)Memory used [KB]: 1261
% 0.20/0.41  % (10290)Time elapsed: 0.016 s
% 0.20/0.41  % (10290)Instructions burned: 28 (million)
% 0.20/0.41  % (10285)Success in time 0.046 s
%------------------------------------------------------------------------------