TSTP Solution File: LCL777-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL777-1 : 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 : n016.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 10:48:59 EDT 2023

% Result   : Unsatisfiable 5.86s 2.36s
% Output   : CNFRefutation 5.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   72
% Syntax   : Number of formulae    :   77 (   8 unt;  69 typ;   0 def)
%            Number of atoms       :    8 (   2 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  134 (  58   >;  76   *;   0   +;   0  <<)
%            Number of predicates  :   19 (  17 usr;   1 prp; 0-4 aty)
%            Number of functors    :   52 (  52 usr;  11 con; 0-5 aty)
%            Number of variables   :    6 (;   6   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_ListOrder_Ostep1 > c_Wellfounded_Oaccp > c_Type_Otypings > c_Type_Otyping > c_List_Olistsp > c_HOL_Oord__class_Oless > hBOOL > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__idom > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Nat_Osemiring__char__0 > class_Int_Oring__char__0 > class_Int_Onumber__ring > c_List_Osko__List__Xappend__eq__Cons__conv__1__1 > c_List_Osko__List__XCons__eq__append__conv__1__1 > c_List_Ofoldl > c_Type_Osko__Type__Xvar__app__types__1__1 > c_Type_Osko__Type__Xvar__app__typesE__1__1 > c_Type_Osko__Type__Xtypes__snocE__1__2 > c_List_Olist__update > c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 > c_Predicate_Oconversep > c_List_Otake > c_List_Osplice > c_List_Oreplicate > c_List_Onth > c_List_Olist_OCons > c_List_Odrop > c_List_Oappend > c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 > c_Lambda_Osubstn > c_Lambda_Osubst > c_Lambda_Oliftn > tc_fun > hAPP > c_Transitive__Closure_Ortranclp > c_Nat_Osize__class_Osize > c_Nat_Osemiring__1__class_Oof__nat > c_List_Otl > c_List_Orotate1 > c_List_Orev > c_List_Olast > c_List_Ohd > c_List_Obutlast > c_Int_Onumber__class_Onumber__of > #nlpp > tc_List_Olist > c_fequal > c_Suc > c_List_Olist_ONil > c_Lambda_OdB_OdB__size > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > v_ss > v_s > v_r > v_i > tc_nat > tc_bool > tc_Lambda_OdB > tc_Int_Oint > c_Lambda_OdB_OApp > c_Lambda_Obeta > c_InductTermi_OIT

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(class_Int_Oring__char__0,type,
    class_Int_Oring__char__0: $i > $o ).

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

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

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

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

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

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

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

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

tff(c_Type_Osko__Type__Xvar__app__typesE__1__1,type,
    c_Type_Osko__Type__Xvar__app__typesE__1__1: ( $i * $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(c_Type_Osko__Type__Xvar__app__types__1__1,type,
    c_Type_Osko__Type__Xvar__app__types__1__1: ( $i * $i * $i * $i ) > $i ).

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

tff(c_ListOrder_Ostep1,type,
    c_ListOrder_Ostep1: ( $i * $i * $i * $i ) > $o ).

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

tff(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1,type,
    c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: ( $i * $i * $i ) > $i ).

tff(c_Type_Osko__Type__Xtypes__snocE__1__2,type,
    c_Type_Osko__Type__Xtypes__snocE__1__2: ( $i * $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

tff(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1,type,
    c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: ( $i * $i * $i * $i ) > $i ).

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

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

tff(c_List_Osko__List__XCons__eq__append__conv__1__1,type,
    c_List_Osko__List__XCons__eq__append__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).

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

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

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

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

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

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

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_List_Osko__List__Xappend__eq__Cons__conv__1__1,type,
    c_List_Osko__List__Xappend__eq__Cons__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).

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

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

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

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

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

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

tff(c_List_Orotate1,type,
    c_List_Orotate1: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

tff(f_1574,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(unknown,unknown) ).

tff(f_1405,axiom,
    ! [V_t,V_ts,V_u] : ( hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_ts,c_List_Olist_OCons(V_u,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    file(unknown,unknown) ).

tff(f_1578,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(unknown,unknown) ).

tff(c_724,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)))),
    inference(cnfTransformation,[status(thm)],[f_1574]) ).

tff(c_626,plain,
    ! [V_t_934,V_ts_935,V_u_936] : ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_t_934,c_List_Oappend(V_ts_935,c_List_Olist_OCons(V_u_936,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t_934,V_ts_935,tc_Lambda_OdB,tc_Lambda_OdB)),V_u_936) ),
    inference(cnfTransformation,[status(thm)],[f_1405]) ).

tff(c_730,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))),
    inference(cnfTransformation,[status(thm)],[f_1578]) ).

tff(c_790,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)))),
    inference(demodulation,[status(thm),theory(equality)],[c_626,c_730]) ).

tff(c_792,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_724,c_790]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL777-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14  % 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
% 0.17/0.36  % Computer : n016.cluster.edu
% 0.17/0.36  % Model    : x86_64 x86_64
% 0.17/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36  % Memory   : 8042.1875MB
% 0.17/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36  % CPULimit : 300
% 0.17/0.36  % WCLimit  : 300
% 0.17/0.36  % DateTime : Thu Aug  3 14:28:52 EDT 2023
% 0.17/0.36  % CPUTime  : 
% 5.86/2.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.86/2.37  
% 5.86/2.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.86/2.39  
% 5.86/2.39  Inference rules
% 5.86/2.39  ----------------------
% 5.86/2.39  #Ref     : 0
% 5.86/2.39  #Sup     : 0
% 5.86/2.39  #Fact    : 0
% 5.86/2.39  #Define  : 0
% 5.86/2.39  #Split   : 0
% 5.86/2.39  #Chain   : 0
% 5.86/2.39  #Close   : 0
% 5.86/2.39  
% 5.86/2.39  Ordering : KBO
% 5.86/2.39  
% 5.86/2.39  Simplification rules
% 5.86/2.39  ----------------------
% 5.86/2.39  #Subsume      : 376
% 5.86/2.39  #Demod        : 17
% 5.86/2.39  #Tautology    : 11
% 5.86/2.39  #SimpNegUnit  : 0
% 5.86/2.39  #BackRed      : 0
% 5.86/2.39  
% 5.86/2.39  #Partial instantiations: 0
% 5.86/2.39  #Strategies tried      : 1
% 5.86/2.39  
% 5.86/2.39  Timing (in seconds)
% 5.86/2.39  ----------------------
% 5.86/2.39  Preprocessing        : 1.14
% 5.86/2.39  Parsing              : 0.62
% 5.86/2.39  CNF conversion       : 0.09
% 5.86/2.39  Main loop            : 0.17
% 5.86/2.39  Inferencing          : 0.00
% 5.86/2.39  Reduction            : 0.09
% 5.86/2.40  Demodulation         : 0.06
% 5.86/2.40  BG Simplification    : 0.09
% 5.86/2.40  Subsumption          : 0.06
% 5.86/2.40  Abstraction          : 0.02
% 5.86/2.40  MUC search           : 0.00
% 5.86/2.40  Cooper               : 0.00
% 5.86/2.40  Total                : 1.36
% 5.86/2.40  Index Insertion      : 0.00
% 5.86/2.40  Index Deletion       : 0.00
% 5.86/2.40  Index Matching       : 0.00
% 5.86/2.40  BG Taut test         : 0.00
%------------------------------------------------------------------------------