TSTP Solution File: LCL806-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL806-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %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 : Thu Aug 31 06:59:43 EDT 2023

% Result   : Unsatisfiable 0.20s 0.66s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  113
% Syntax   : Number of formulae    :  120 (   9 unt; 108 typ;   0 def)
%            Number of atoms       :   20 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   18 (  10   ~;   8   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  160 (  73   >;  87   *;   0   +;   0  <<)
%            Number of predicates  :   31 (  30 usr;   1 prp; 0-4 aty)
%            Number of functors    :   78 (  78 usr;  35 con; 0-5 aty)
%            Number of variables   :    9 (   2 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    c_Lambda_Obeta: $i ).

tff(decl_23,type,
    c_Lambda_OdB_OApp: $i ).

tff(decl_24,type,
    tc_Lambda_OdB: $i ).

tff(decl_25,type,
    c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_26,type,
    hAPP: ( $i * $i ) > $i ).

tff(decl_27,type,
    hBOOL: $i > $o ).

tff(decl_28,type,
    c_ListOrder_Ostep1: ( $i * $i * $i * $i ) > $o ).

tff(decl_29,type,
    tc_nat: $i ).

tff(decl_30,type,
    c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(decl_31,type,
    c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(decl_32,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(decl_33,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

tff(decl_34,type,
    c_HOL_Oplus__class_Oplus: $i > $i ).

tff(decl_35,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

tff(decl_36,type,
    c_Nat_Osemiring__1__class_Oof__nat__aux: ( $i * $i * $i * $i ) > $i ).

tff(decl_37,type,
    c_Suc: $i > $i ).

tff(decl_38,type,
    class_Ring__and__Field_Oidom: $i > $o ).

tff(decl_39,type,
    class_Int_Onumber__ring: $i > $o ).

tff(decl_40,type,
    class_OrderedGroup_Ogroup__add: $i > $o ).

tff(decl_41,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

tff(decl_42,type,
    c_HOL_Oone__class_Oone: $i > $i ).

tff(decl_43,type,
    c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: ( $i * $i * $i ) > $i ).

tff(decl_44,type,
    c_Lambda_OdB_OVar: $i > $i ).

tff(decl_45,type,
    c_Type_Oshift: $i > $i ).

tff(decl_46,type,
    c_Type_Otype_OFun: $i ).

tff(decl_47,type,
    c_Type_Otype_Otype__size: $i > $i ).

tff(decl_48,type,
    tc_Type_Otype: $i ).

tff(decl_49,type,
    c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).

tff(decl_50,type,
    c_Lambda_Osubst: $i ).

tff(decl_51,type,
    c_Type_Osko__Type__Xlist__app__typeE__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_52,type,
    c_Type_Otypings: ( $i * $i * $i ) > $o ).

tff(decl_53,type,
    c_Type_Otyping: $i ).

tff(decl_54,type,
    c_Type_Osko__Type__Xlist__app__typeD__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_55,type,
    c_Lambda_Osubstn: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).

tff(decl_57,type,
    c_COMBC: ( $i * $i * $i ) > $i ).

tff(decl_58,type,
    c_List_Ofoldr: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_59,type,
    v_ea______: $i ).

tff(decl_60,type,
    v_ia______: $i ).

tff(decl_61,type,
    v_T____: $i ).

tff(decl_62,type,
    v_n____: $i ).

tff(decl_63,type,
    v_rs____: $i ).

tff(decl_64,type,
    v_T_Ha______: $i ).

tff(decl_65,type,
    c_Nat_Ocompow: ( $i * $i * $i * $i ) > $i ).

tff(decl_66,type,
    c_Fun_Ocomp: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_67,type,
    c_Transitive__Closure_Ortranclp: ( $i * $i ) > $i ).

tff(decl_68,type,
    class_OrderedGroup_Omonoid__add: $i > $o ).

tff(decl_69,type,
    class_Ring__and__Field_Ozero__neq__one: $i > $o ).

tff(decl_70,type,
    c_Lambda_Oliftn: ( $i * $i * $i ) > $i ).

tff(decl_71,type,
    c_Lambda_OdB_OAbs: $i > $i ).

tff(decl_72,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

tff(decl_73,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

tff(decl_74,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

tff(decl_75,type,
    c_Lambda_Olift: $i ).

tff(decl_76,type,
    c_Type_Osko__Type__Xvar__app__typesE__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_77,type,
    c_InductTermi_OIT: $i ).

tff(decl_78,type,
    c_List_Olistsp: ( $i * $i * $i ) > $o ).

tff(decl_79,type,
    c_Type_Osko__Type__Xtyping__elims__3__1: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    c_Type_Osko__Type__Xtyping__elims__3__2: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    c_Type_Osko__Type__Xvar__app__types__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_82,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

tff(decl_83,type,
    class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).

tff(decl_84,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

tff(decl_85,type,
    v_i____: $i ).

tff(decl_86,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

tff(decl_87,type,
    class_Nat_Osemiring__char__0: $i > $o ).

tff(decl_88,type,
    class_OrderedGroup_Osemigroup__add: $i > $o ).

tff(decl_89,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(decl_90,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

tff(decl_91,type,
    c_COMBK: ( $i * $i * $i ) > $i ).

tff(decl_92,type,
    v_T_H_H____: $i ).

tff(decl_93,type,
    v_Ts____: $i ).

tff(decl_94,type,
    v_T_H____: $i ).

tff(decl_95,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

tff(decl_96,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

tff(decl_97,type,
    t_a: $i ).

tff(decl_98,type,
    v_x: $i ).

tff(decl_99,type,
    v_e____: $i ).

tff(decl_100,type,
    c_Type_Osko__Type__Xtyping__elims__2__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_101,type,
    c_Fun_Oid: $i > $i ).

tff(decl_102,type,
    c_Type_Osko__Type__Xabs__typeE__1__1: ( $i * $i ) > $i ).

tff(decl_103,type,
    c_Type_Osko__Type__Xabs__typeE__1__2: ( $i * $i ) > $i ).

tff(decl_104,type,
    v_u____: $i ).

tff(decl_105,type,
    v_a____: $i ).

tff(decl_106,type,
    v_as____: $i ).

tff(decl_107,type,
    c_List_Omap: ( $i * $i * $i * $i ) > $i ).

tff(decl_108,type,
    tc_fun: ( $i * $i ) > $i ).

tff(decl_109,type,
    v_bs____: $i ).

tff(decl_110,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_111,type,
    class_Orderings_Opreorder: $i > $o ).

tff(decl_112,type,
    class_Orderings_Olinorder: $i > $o ).

tff(decl_113,type,
    c_Fun_Ofcomp: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_114,type,
    v_b____: $i ).

tff(decl_115,type,
    v_sko__local__XCons__Xhyps__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_116,type,
    v_ua______: $i ).

tff(decl_117,type,
    v_sko__local__XCons__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_118,type,
    tc_bool: $i ).

tff(decl_119,type,
    c_COMBS: ( $i * $i * $i ) > $i ).

tff(decl_120,type,
    c_COMBB: ( $i * $i * $i ) > $i ).

tff(decl_121,type,
    c_and: $i ).

tff(decl_122,type,
    c_All: $i > $i ).

tff(decl_123,type,
    c_implies: $i ).

tff(decl_124,type,
    c_Ex: $i > $i ).

tff(decl_125,type,
    v_sko__CHAINED__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_126,type,
    v_xc: $i ).

tff(decl_127,type,
    v_xa: $i ).

tff(decl_128,type,
    v_xb: $i ).

tff(decl_129,type,
    c_fequal: ( $i * $i * $i ) > $o ).

cnf(cls_Cons_I1_J_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_b____),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_I1_J_0) ).

cnf(cls_conjecture_0,negated_conjecture,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_conjecture_3,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_conjecture_2,negated_conjecture,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_conjecture_1,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(c_0_5,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_b____),X4)) ),
    cls_Cons_I1_J_0 ).

cnf(c_0_6,negated_conjecture,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
    cls_conjecture_0 ).

cnf(c_0_7,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
    cls_conjecture_3 ).

cnf(c_0_8,negated_conjecture,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X1),v_xc)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X1),v_T____))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
    cls_conjecture_2 ).

cnf(c_0_10,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
    cls_conjecture_1 ).

cnf(c_0_11,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LCL806-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n016.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 Aug 25 06:04:40 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.66  % Version  : CSE_E---1.5
% 0.20/0.66  % Problem  : theBenchmark.p
% 0.20/0.66  % Proof found
% 0.20/0.66  % SZS status Theorem for theBenchmark.p
% 0.20/0.66  % SZS output start Proof
% See solution above
% 0.20/0.67  % Total time : 0.077000 s
% 0.20/0.67  % SZS output end Proof
% 0.20/0.67  % Total time : 0.091000 s
%------------------------------------------------------------------------------