TSTP Solution File: COM133+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : COM133+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n031.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 : Wed Aug 30 18:36:37 EDT 2023

% Result   : Theorem 0.21s 0.72s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  113
% Syntax   : Number of formulae    :  141 (   8 unt; 107 typ;   0 def)
%            Number of atoms       :  123 (  50 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  147 (  58   ~;  53   |;  23   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  274 (  96   >; 178   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-4 aty)
%            Number of functors    :   98 (  98 usr;  11 con; 0-5 aty)
%            Number of variables   :  161 (  11 sgn;  94   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    visValue: $i > $o ).

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

tff(decl_27,type,
    vempty: $i ).

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

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

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

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

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

tff(decl_33,type,
    vlookup: ( $i * $i ) > $i ).

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

tff(decl_35,type,
    vgensym: $i > $i ).

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

tff(decl_37,type,
    vnoExp: $i ).

tff(decl_38,type,
    vsomeExp: $i > $i ).

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

tff(decl_40,type,
    vgetSomeExp: $i > $i ).

tff(decl_41,type,
    vreduce: $i > $i ).

tff(decl_42,type,
    varrow: ( $i * $i ) > $i ).

tff(decl_43,type,
    veabs: $i ).

tff(decl_44,type,
    epred1_4: ( $i * $i * $i * $i ) > $o ).

tff(decl_45,type,
    epred2_4: ( $i * $i * $i * $i ) > $o ).

tff(decl_46,type,
    epred3_2: ( $i * $i ) > $o ).

tff(decl_47,type,
    epred4_2: ( $i * $i ) > $o ).

tff(decl_48,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_54,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_57,type,
    esk10_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_58,type,
    esk11_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_59,type,
    esk12_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_60,type,
    esk13_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_61,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_62,type,
    esk15_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_63,type,
    esk16_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk17_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk18_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_66,type,
    esk19_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk20_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_71,type,
    esk24_3: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk25_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk26_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk27_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk28_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk29_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk30_3: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk31_3: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk32_0: $i ).

tff(decl_80,type,
    esk33_0: $i ).

tff(decl_81,type,
    esk34_0: $i ).

tff(decl_82,type,
    esk35_0: $i ).

tff(decl_83,type,
    esk36_0: $i ).

tff(decl_84,type,
    esk37_0: $i ).

tff(decl_85,type,
    esk38_0: $i ).

tff(decl_86,type,
    esk39_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk40_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk41_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_89,type,
    esk42_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_90,type,
    esk43_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_91,type,
    esk44_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk45_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_93,type,
    esk46_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_94,type,
    esk47_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_95,type,
    esk48_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_96,type,
    esk49_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_97,type,
    esk50_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_98,type,
    esk51_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_99,type,
    esk52_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_100,type,
    esk53_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_101,type,
    esk54_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_102,type,
    esk55_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_103,type,
    esk56_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_104,type,
    esk57_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_105,type,
    esk58_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_106,type,
    esk59_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_107,type,
    esk60_2: ( $i * $i ) > $i ).

tff(decl_108,type,
    esk61_2: ( $i * $i ) > $i ).

tff(decl_109,type,
    esk62_2: ( $i * $i ) > $i ).

tff(decl_110,type,
    esk63_2: ( $i * $i ) > $i ).

tff(decl_111,type,
    esk64_2: ( $i * $i ) > $i ).

tff(decl_112,type,
    esk65_2: ( $i * $i ) > $i ).

tff(decl_113,type,
    esk66_2: ( $i * $i ) > $i ).

tff(decl_114,type,
    esk67_2: ( $i * $i ) > $i ).

tff(decl_115,type,
    esk68_2: ( $i * $i ) > $i ).

tff(decl_116,type,
    esk69_2: ( $i * $i ) > $i ).

tff(decl_117,type,
    esk70_2: ( $i * $i ) > $i ).

tff(decl_118,type,
    esk71_2: ( $i * $i ) > $i ).

tff(decl_119,type,
    esk72_2: ( $i * $i ) > $i ).

tff(decl_120,type,
    esk73_2: ( $i * $i ) > $i ).

tff(decl_121,type,
    esk74_2: ( $i * $i ) > $i ).

tff(decl_122,type,
    esk75_2: ( $i * $i ) > $i ).

tff(decl_123,type,
    esk76_2: ( $i * $i ) > $i ).

tff(decl_124,type,
    esk77_2: ( $i * $i ) > $i ).

tff(decl_125,type,
    esk78_2: ( $i * $i ) > $i ).

tff(decl_126,type,
    esk79_2: ( $i * $i ) > $i ).

tff(decl_127,type,
    esk80_2: ( $i * $i ) > $i ).

tff(decl_128,type,
    esk81_2: ( $i * $i ) > $i ).

fof('T-subst-abs-2',axiom,
    ! [X15,X20,X9,X11,X21,X10,X34] :
      ( ( X9 != X21
        & ~ visFreeVar(X21,X11)
        & vtcheck(X20,X11,X15)
        & vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34) )
     => vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs-2') ).

fof('T-subst-abs-3',axiom,
    ! [X15,X20,X9,X11,X21,X10,X34] :
      ( ( X9 != X21
        & visFreeVar(X21,X11)
        & vtcheck(X20,X11,X15)
        & vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34) )
     => vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs-3') ).

fof('T-subst-abs',conjecture,
    ! [X15,X20,X9,X11,X21,X10,X34] :
      ( ( vtcheck(X20,X11,X15)
        & vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34) )
     => vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs') ).

fof(subst3,axiom,
    ! [X11,X9,X1,X4,X6,X19,X21,X15,X12] :
      ( ( X1 = X9
        & X4 = X11
        & X6 = vabs(X21,X15,X12) )
     => ( X9 = X21
       => ( X19 = vsubst(X1,X4,X6)
         => X19 = vabs(X21,X15,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst3) ).

fof('T-Strong',axiom,
    ! [X9,X10,X20,X11,X15] :
      ( ( ~ visFreeVar(X9,X11)
        & vtcheck(vbind(X9,X10,X20),X11,X15) )
     => vtcheck(X20,X11,X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Strong') ).

fof(isFreeVar1,axiom,
    ! [X15,X1,X4,X9,X14,X11] :
      ( ( X1 = X14
        & X4 = vabs(X9,X15,X11) )
     => ( ( ( X9 != X14
            & visFreeVar(X14,X11) )
         => visFreeVar(X1,X4) )
        & ( visFreeVar(X1,X4)
         => ( X9 != X14
            & visFreeVar(X14,X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isFreeVar1) ).

fof(c_0_6,plain,
    ! [X15,X20,X9,X11,X21,X10,X34] :
      ( ( X9 != X21
        & ~ visFreeVar(X21,X11)
        & vtcheck(X20,X11,X15)
        & vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34) )
     => vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
    inference(fof_simplification,[status(thm)],['T-subst-abs-2']) ).

fof(c_0_7,plain,
    ! [X331,X332,X333,X334,X335,X336,X337] :
      ( X333 = X335
      | ~ visFreeVar(X335,X334)
      | ~ vtcheck(X332,X334,X331)
      | ~ vtcheck(vbind(X333,X331,X332),vabs(X335,X336,veabs),X337)
      | vtcheck(X332,vsubst(X333,X334,vabs(X335,X336,veabs)),X337) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['T-subst-abs-3'])]) ).

fof(c_0_8,plain,
    ! [X324,X325,X326,X327,X328,X329,X330] :
      ( X326 = X328
      | visFreeVar(X328,X327)
      | ~ vtcheck(X325,X327,X324)
      | ~ vtcheck(vbind(X326,X324,X325),vabs(X328,X329,veabs),X330)
      | vtcheck(X325,vsubst(X326,X327,vabs(X328,X329,veabs)),X330) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X15,X20,X9,X11,X21,X10,X34] :
        ( ( vtcheck(X20,X11,X15)
          & vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34) )
       => vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
    inference(assume_negation,[status(cth)],['T-subst-abs']) ).

fof(c_0_10,plain,
    ! [X169,X170,X171,X172,X173,X174,X175,X176,X177] :
      ( X171 != X170
      | X172 != X169
      | X173 != vabs(X175,X176,X177)
      | X170 != X175
      | X174 != vsubst(X171,X172,X173)
      | X174 = vabs(X175,X176,X177) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst3])]) ).

cnf(c_0_11,plain,
    ( X1 = X2
    | vtcheck(X4,vsubst(X1,X3,vabs(X2,X6,veabs)),X7)
    | ~ visFreeVar(X2,X3)
    | ~ vtcheck(X4,X3,X5)
    | ~ vtcheck(vbind(X1,X5,X4),vabs(X2,X6,veabs),X7) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ( X1 = X2
    | visFreeVar(X2,X3)
    | vtcheck(X4,vsubst(X1,X3,vabs(X2,X6,veabs)),X7)
    | ~ vtcheck(X4,X3,X5)
    | ~ vtcheck(vbind(X1,X5,X4),vabs(X2,X6,veabs),X7) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_13,negated_conjecture,
    ( vtcheck(esk33_0,esk35_0,esk32_0)
    & vtcheck(vbind(esk34_0,esk32_0,esk33_0),vabs(esk36_0,esk37_0,veabs),esk38_0)
    & ~ vtcheck(esk33_0,vsubst(esk34_0,esk35_0,vabs(esk36_0,esk37_0,veabs)),esk38_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

cnf(c_0_14,plain,
    ( X9 = vabs(X6,X7,X8)
    | X1 != X2
    | X3 != X4
    | X5 != vabs(X6,X7,X8)
    | X2 != X6
    | X9 != vsubst(X1,X3,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_15,plain,
    ! [X9,X10,X20,X11,X15] :
      ( ( ~ visFreeVar(X9,X11)
        & vtcheck(vbind(X9,X10,X20),X11,X15) )
     => vtcheck(X20,X11,X15) ),
    inference(fof_simplification,[status(thm)],['T-Strong']) ).

fof(c_0_16,plain,
    ! [X72,X73,X74,X75,X76,X77] :
      ( ( X75 = X76
        | ~ visFreeVar(X76,X77)
        | visFreeVar(X73,X74)
        | X73 != X76
        | X74 != vabs(X75,X72,X77) )
      & ( X75 != X76
        | ~ visFreeVar(X73,X74)
        | X73 != X76
        | X74 != vabs(X75,X72,X77) )
      & ( visFreeVar(X76,X77)
        | ~ visFreeVar(X73,X74)
        | X73 != X76
        | X74 != vabs(X75,X72,X77) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar1])])]) ).

cnf(c_0_17,plain,
    ( X1 = X2
    | vtcheck(X3,vsubst(X1,X4,vabs(X2,X5,veabs)),X6)
    | ~ vtcheck(vbind(X1,X7,X3),vabs(X2,X5,veabs),X6)
    | ~ vtcheck(X3,X4,X7) ),
    inference(csr,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_18,negated_conjecture,
    vtcheck(esk33_0,esk35_0,esk32_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    ( X1 = vabs(X2,X3,X4)
    | X1 != vsubst(X2,X5,X6)
    | X6 != vabs(X2,X3,X4) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])])]) ).

fof(c_0_20,plain,
    ! [X301,X302,X303,X304,X305] :
      ( visFreeVar(X301,X304)
      | ~ vtcheck(vbind(X301,X302,X303),X304,X305)
      | vtcheck(X303,X304,X305) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).

cnf(c_0_21,plain,
    ( X1 != X2
    | ~ visFreeVar(X3,X4)
    | X3 != X2
    | X4 != vabs(X1,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    ( X1 = X2
    | vtcheck(esk33_0,vsubst(X1,esk35_0,vabs(X2,X3,veabs)),X4)
    | ~ vtcheck(vbind(X1,esk32_0,esk33_0),vabs(X2,X3,veabs),X4) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    vtcheck(vbind(esk34_0,esk32_0,esk33_0),vabs(esk36_0,esk37_0,veabs),esk38_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_24,negated_conjecture,
    ~ vtcheck(esk33_0,vsubst(esk34_0,esk35_0,vabs(esk36_0,esk37_0,veabs)),esk38_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_25,plain,
    ( vsubst(X1,X2,X3) = vabs(X1,X4,X5)
    | X3 != vabs(X1,X4,X5) ),
    inference(er,[status(thm)],[c_0_19]) ).

cnf(c_0_26,plain,
    ( visFreeVar(X1,X2)
    | vtcheck(X4,X2,X5)
    | ~ vtcheck(vbind(X1,X3,X4),X2,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_27,plain,
    ( X1 != vabs(X2,X3,X4)
    | ~ visFreeVar(X2,X1) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])]) ).

cnf(c_0_28,negated_conjecture,
    esk36_0 = esk34_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_29,plain,
    vsubst(X1,X2,vabs(X1,X3,X4)) = vabs(X1,X3,X4),
    inference(er,[status(thm)],[c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    ( vtcheck(esk33_0,vabs(esk36_0,esk37_0,veabs),esk38_0)
    | visFreeVar(esk34_0,vabs(esk36_0,esk37_0,veabs)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_23]) ).

cnf(c_0_31,plain,
    ~ visFreeVar(X1,vabs(X1,X2,X3)),
    inference(er,[status(thm)],[c_0_27]) ).

cnf(c_0_32,negated_conjecture,
    ~ vtcheck(esk33_0,vabs(esk34_0,esk37_0,veabs),esk38_0),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_28]),c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_31]),c_0_32]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : COM133+1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.18/0.35  % Computer : n031.cluster.edu
% 0.18/0.35  % Model    : x86_64 x86_64
% 0.18/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35  % Memory   : 8042.1875MB
% 0.18/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35  % CPULimit   : 300
% 0.18/0.35  % WCLimit    : 300
% 0.18/0.35  % DateTime   : Tue Aug 29 13:47:26 EDT 2023
% 0.18/0.35  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 0.21/0.72  % Version  : CSE_E---1.5
% 0.21/0.72  % Problem  : theBenchmark.p
% 0.21/0.72  % Proof found
% 0.21/0.72  % SZS status Theorem for theBenchmark.p
% 0.21/0.72  % SZS output start Proof
% See solution above
% 0.21/0.73  % Total time : 0.151000 s
% 0.21/0.73  % SZS output end Proof
% 0.21/0.73  % Total time : 0.157000 s
%------------------------------------------------------------------------------