TSTP Solution File: SWV822-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV822-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n006.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 21:48:17 EDT 2023

% Result   : Unsatisfiable 111.19s 111.22s
% Output   : CNFRefutation 111.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   87
% Syntax   : Number of formulae    :  107 (  10 unt;  79 typ;   0 def)
%            Number of atoms       :   59 (  10 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   58 (  27   ~;  31   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  105 (  67   >;  38   *;   0   +;   0  <<)
%            Number of predicates  :   48 (  46 usr;   1 prp; 0-4 aty)
%            Number of functors    :   33 (  33 usr;  12 con; 0-6 aty)
%            Number of variables   :   48 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

tff(decl_23,type,
    c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(decl_24,type,
    c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).

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

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

tff(decl_27,type,
    c_Suc: $i > $i ).

tff(decl_28,type,
    tc_nat: $i ).

tff(decl_29,type,
    class_Ring__and__Field_Oordered__ring__strict: $i > $o ).

tff(decl_30,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

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

tff(decl_32,type,
    c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).

tff(decl_33,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(decl_34,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

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

tff(decl_36,type,
    class_Ring__and__Field_Oidom: $i > $o ).

tff(decl_37,type,
    class_Int_Onumber__ring: $i > $o ).

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

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

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

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

tff(decl_42,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

tff(decl_43,type,
    class_Orderings_Olinorder: $i > $o ).

tff(decl_44,type,
    c_Orderings_Oord__class_Omax: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    c_Orderings_Oord__class_Omin: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    c_Com_Ocom_OSemi: ( $i * $i ) > $i ).

tff(decl_47,type,
    class_Ring__and__Field_Oring: $i > $o ).

tff(decl_48,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

tff(decl_49,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

tff(decl_50,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).

tff(decl_51,type,
    class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).

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

tff(decl_53,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_54,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

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

tff(decl_56,type,
    c_Option_Ooption_ONone: $i > $i ).

tff(decl_57,type,
    class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).

tff(decl_58,type,
    class_Ring__and__Field_Ono__zero__divisors: $i > $o ).

tff(decl_59,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

tff(decl_60,type,
    class_Ring__and__Field_Omult__zero: $i > $o ).

tff(decl_61,type,
    class_Divides_Oring__div: $i > $o ).

tff(decl_62,type,
    c_COMBI: ( $i * $i ) > $i ).

tff(decl_63,type,
    c_COMBK: ( $i * $i * $i * $i ) > $i ).

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

tff(decl_65,type,
    c_Com_OWT: $i > $o ).

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

tff(decl_67,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

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

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

tff(decl_70,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

tff(decl_71,type,
    class_Ring__and__Field_Omult__mono: $i > $o ).

tff(decl_72,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

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

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

tff(decl_75,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

tff(decl_76,type,
    class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).

tff(decl_77,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

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

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

tff(decl_80,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

tff(decl_81,type,
    class_Ring__and__Field_Ocomm__semiring: $i > $o ).

tff(decl_82,type,
    c_Option_Othe: ( $i * $i ) > $i ).

tff(decl_83,type,
    v_P: $i ).

tff(decl_84,type,
    v_Q: $i ).

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

tff(decl_86,type,
    t_b: $i ).

tff(decl_87,type,
    c_Com_Ocom_OBODY: $i > $i ).

tff(decl_88,type,
    c_Com_Obody: $i > $i ).

tff(decl_89,type,
    tc_Com_Ocom: $i ).

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

tff(decl_91,type,
    v_x: $i ).

tff(decl_92,type,
    c_Natural_Osko__Natural__Xevaln__elim__cases__6__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_93,type,
    c_Natural_Osko__Natural__Xevaln__max2__1__1: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_94,type,
    c_Com_Osko__Com__XWTs__elim__cases__7__1: $i > $i ).

tff(decl_95,type,
    hAPP: ( $i * $i ) > $i ).

tff(decl_96,type,
    v_xa: $i ).

tff(decl_97,type,
    hBOOL: $i > $o ).

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

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

tff(decl_100,type,
    v_xb: $i ).

cnf(cls_evaln_OBody_0,axiom,
    ( c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,c_Suc(X3),X4)
    | ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X1),tc_Com_Ocom),X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OBody_0) ).

cnf(cls_conjecture_4,negated_conjecture,
    ( c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)
    | c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

cnf(cls_evaln__elim__cases_I6_J_0,axiom,
    ( X1 = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X2,X1,X3,X4))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(X2),X3,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).

cnf(cls_nat_Oinject_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

cnf(cls_evaln__elim__cases_I6_J_1,axiom,
    ( c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X1),tc_Com_Ocom),X2,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X3,X2,X4),X4)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_1) ).

cnf(cls_conjecture_9,negated_conjecture,
    ( hBOOL(hAPP(hAPP(v_Q,X1),X2))
    | hBOOL(hAPP(hAPP(v_Q,X4),X5))
    | ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),X3,v_n,X2)
    | ~ hBOOL(hAPP(hAPP(v_P,X1),X3))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X6,c_Suc(v_n),X5)
    | ~ hBOOL(hAPP(hAPP(v_P,X4),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).

cnf(cls_conjecture_0,negated_conjecture,
    ( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
    | hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_conjecture_8,negated_conjecture,
    ( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))
    | ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).

cnf(c_0_8,axiom,
    ( c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,c_Suc(X3),X4)
    | ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X1),tc_Com_Ocom),X2,X3,X4) ),
    cls_evaln_OBody_0 ).

cnf(c_0_9,negated_conjecture,
    ( c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)
    | c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb) ),
    cls_conjecture_4 ).

cnf(c_0_10,axiom,
    ( X1 = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X2,X1,X3,X4))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(X2),X3,X1,X4) ),
    cls_evaln__elim__cases_I6_J_0 ).

cnf(c_0_11,negated_conjecture,
    c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_nat_Oinject_0 ).

cnf(c_0_13,negated_conjecture,
    c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb)) = c_Suc(v_n),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,axiom,
    ( c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X1),tc_Com_Ocom),X2,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X3,X2,X4),X4)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,X3,X4) ),
    cls_evaln__elim__cases_I6_J_1 ).

cnf(c_0_15,negated_conjecture,
    ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb) = X1
    | c_Suc(v_n) != c_Suc(X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb),v_xb),
    inference(spm,[status(thm)],[c_0_14,c_0_11]) ).

cnf(c_0_17,negated_conjecture,
    c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb) = v_n,
    inference(er,[status(thm)],[c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    ( hBOOL(hAPP(hAPP(v_Q,X1),X2))
    | hBOOL(hAPP(hAPP(v_Q,X4),X5))
    | ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),X3,v_n,X2)
    | ~ hBOOL(hAPP(hAPP(v_P,X1),X3))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X6,c_Suc(v_n),X5)
    | ~ hBOOL(hAPP(hAPP(v_P,X4),X6)) ),
    cls_conjecture_9 ).

cnf(c_0_19,negated_conjecture,
    c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb),
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    ( hBOOL(hAPP(hAPP(v_Q,X1),v_xb))
    | hBOOL(hAPP(hAPP(v_Q,X2),X3))
    | ~ hBOOL(hAPP(hAPP(v_P,X1),v_xa))
    | ~ hBOOL(hAPP(hAPP(v_P,X2),X4))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X4,c_Suc(v_n),X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,negated_conjecture,
    hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
    inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).

cnf(c_0_22,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb)),
    inference(fof_simplification,[status(thm)],[cls_conjecture_8]) ).

cnf(c_0_23,negated_conjecture,
    ( hBOOL(hAPP(hAPP(v_Q,X1),v_xb))
    | hBOOL(hAPP(hAPP(v_Q,X2),v_xb))
    | ~ hBOOL(hAPP(hAPP(v_P,X2),v_xa))
    | ~ hBOOL(hAPP(hAPP(v_P,X1),v_xa)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_11]) ).

cnf(c_0_24,negated_conjecture,
    hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
    c_0_21 ).

cnf(c_0_25,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb)),
    c_0_22 ).

cnf(c_0_26,negated_conjecture,
    ( hBOOL(hAPP(hAPP(v_Q,X1),v_xb))
    | ~ hBOOL(hAPP(hAPP(v_P,X1),v_xa)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).

cnf(c_0_27,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_25]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWV822-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n006.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 29 06:59:36 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 111.19/111.22  % Version  : CSE_E---1.5
% 111.19/111.22  % Problem  : theBenchmark.p
% 111.19/111.22  % Proof found
% 111.19/111.22  % SZS status Theorem for theBenchmark.p
% 111.19/111.22  % SZS output start Proof
% See solution above
% 111.19/111.22  % Total time : 110.647000 s
% 111.19/111.22  % SZS output end Proof
% 111.19/111.22  % Total time : 110.671000 s
%------------------------------------------------------------------------------