TSTP Solution File: COM124+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : COM124+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 : n025.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 18:36:35 EDT 2023

% Result   : Theorem 4.41s 4.63s
% Output   : CNFRefutation 4.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :  117
% Syntax   : Number of formulae    :  175 (  16 unt; 107 typ;   0 def)
%            Number of atoms       :  204 (  66 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  227 (  91   ~;  88   |;  27   &)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    8 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  276 (  97   >; 179   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-4 aty)
%            Number of functors    :   97 (  97 usr;  10 con; 0-5 aty)
%            Number of variables   :  232 (  40 sgn; 102   !;   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,
    valphaEquivalent: ( $i * $i ) > $o ).

tff(decl_44,type,
    veabs: $i ).

tff(decl_45,type,
    epred1_4: ( $i * $i * $i * $i ) > $o ).

tff(decl_46,type,
    epred2_4: ( $i * $i * $i * $i ) > $o ).

tff(decl_47,type,
    epred3_2: ( $i * $i ) > $o ).

tff(decl_48,type,
    epred4_2: ( $i * $i ) > $o ).

tff(decl_49,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_54,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_57,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_58,type,
    esk10_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_59,type,
    esk11_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_60,type,
    esk12_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_61,type,
    esk13_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_62,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_63,type,
    esk15_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk16_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk17_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_66,type,
    esk18_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk19_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk20_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_69,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_71,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_72,type,
    esk24_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk25_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk26_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk27_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk28_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk29_3: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk30_3: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk31_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk32_0: $i ).

tff(decl_81,type,
    esk33_0: $i ).

tff(decl_82,type,
    esk34_0: $i ).

tff(decl_83,type,
    esk35_0: $i ).

tff(decl_84,type,
    esk36_0: $i ).

tff(decl_85,type,
    esk37_0: $i ).

tff(decl_86,type,
    esk38_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk39_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk40_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_89,type,
    esk41_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_90,type,
    esk42_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_91,type,
    esk43_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk44_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_93,type,
    esk45_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_94,type,
    esk46_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_95,type,
    esk47_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_96,type,
    esk48_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_97,type,
    esk49_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_98,type,
    esk50_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_99,type,
    esk51_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_100,type,
    esk52_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_101,type,
    esk53_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_102,type,
    esk54_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_103,type,
    esk55_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_104,type,
    esk56_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_105,type,
    esk57_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_106,type,
    esk58_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_107,type,
    esk59_2: ( $i * $i ) > $i ).

tff(decl_108,type,
    esk60_2: ( $i * $i ) > $i ).

tff(decl_109,type,
    esk61_2: ( $i * $i ) > $i ).

tff(decl_110,type,
    esk62_2: ( $i * $i ) > $i ).

tff(decl_111,type,
    esk63_2: ( $i * $i ) > $i ).

tff(decl_112,type,
    esk64_2: ( $i * $i ) > $i ).

tff(decl_113,type,
    esk65_2: ( $i * $i ) > $i ).

tff(decl_114,type,
    esk66_2: ( $i * $i ) > $i ).

tff(decl_115,type,
    esk67_2: ( $i * $i ) > $i ).

tff(decl_116,type,
    esk68_2: ( $i * $i ) > $i ).

tff(decl_117,type,
    esk69_2: ( $i * $i ) > $i ).

tff(decl_118,type,
    esk70_2: ( $i * $i ) > $i ).

tff(decl_119,type,
    esk71_2: ( $i * $i ) > $i ).

tff(decl_120,type,
    esk72_2: ( $i * $i ) > $i ).

tff(decl_121,type,
    esk73_2: ( $i * $i ) > $i ).

tff(decl_122,type,
    esk74_2: ( $i * $i ) > $i ).

tff(decl_123,type,
    esk75_2: ( $i * $i ) > $i ).

tff(decl_124,type,
    esk76_2: ( $i * $i ) > $i ).

tff(decl_125,type,
    esk77_2: ( $i * $i ) > $i ).

tff(decl_126,type,
    esk78_2: ( $i * $i ) > $i ).

tff(decl_127,type,
    esk79_2: ( $i * $i ) > $i ).

tff(decl_128,type,
    esk80_2: ( $i * $i ) > $i ).

fof('alpha-equiv-subst-abs',axiom,
    ! [X10,X9,X21,X11] :
      ( ~ visFreeVar(X21,X11)
     => valphaEquivalent(vabs(X9,X10,X11),vabs(X21,X10,vsubst(X9,vvar(X21),X11))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/COM001+1.ax','alpha-equiv-subst-abs') ).

fof('T-Weak-FreeVar-abs-2',conjecture,
    ! [X9,X10,X20,X21,X36,X15] :
      ( ( X9 = X21
        & ~ visFreeVar(X9,vabs(X21,X36,veabs))
        & vtcheck(X20,vabs(X21,X36,veabs),X15) )
     => vtcheck(vbind(X9,X10,X20),vabs(X21,X36,veabs),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-2') ).

fof('alpha-equiv-typing',axiom,
    ! [X11,X20,X12,X15] :
      ( ( vtcheck(X20,X11,X15)
        & valphaEquivalent(X11,X12) )
     => vtcheck(X20,X12,X15) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/COM001+1.ax','alpha-equiv-typing') ).

fof(isFreeVar2,axiom,
    ! [X1,X4,X12,X14,X13] :
      ( ( X1 = X14
        & X4 = vapp(X12,X13) )
     => ( ( ( visFreeVar(X14,X12)
            | visFreeVar(X14,X13) )
         => visFreeVar(X1,X4) )
        & ( visFreeVar(X1,X4)
         => ( visFreeVar(X14,X12)
            | visFreeVar(X14,X13) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isFreeVar2) ).

fof(isFreeVar0,axiom,
    ! [X1,X4,X9,X14] :
      ( ( X1 = X14
        & X4 = vvar(X9) )
     => ( ( X9 = X14
         => visFreeVar(X1,X4) )
        & ( visFreeVar(X1,X4)
         => X9 = X14 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isFreeVar0) ).

fof('alpha-equiv-sym',axiom,
    ! [X13,X12] :
      ( valphaEquivalent(X12,X13)
     => valphaEquivalent(X13,X12) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/COM001+1.ax','alpha-equiv-sym') ).

fof('T-Weak-FreeVar-abs-1-gen',axiom,
    ! [X9,X10,X20,X21,X36,X12,X15] :
      ( ( X9 != X21
        & ~ visFreeVar(X9,vabs(X21,X36,X12))
        & vtcheck(X20,vabs(X21,X36,X12),X15) )
     => vtcheck(vbind(X9,X10,X20),vabs(X21,X36,X12),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-1-gen') ).

fof('alpha-equiv-FreeVar',axiom,
    ! [X11,X9,X12] :
      ( ( ~ visFreeVar(X9,X11)
        & valphaEquivalent(X11,X12) )
     => ~ visFreeVar(X9,X12) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/COM001+1.ax','alpha-equiv-FreeVar') ).

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('gensym-is-fresh',axiom,
    ! [X14,X11] :
      ( vgensym(X11) = X14
     => ~ visFreeVar(X14,X11) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','gensym-is-fresh') ).

fof(c_0_10,plain,
    ! [X10,X9,X21,X11] :
      ( ~ visFreeVar(X21,X11)
     => valphaEquivalent(vabs(X9,X10,X11),vabs(X21,X10,vsubst(X9,vvar(X21),X11))) ),
    inference(fof_simplification,[status(thm)],['alpha-equiv-subst-abs']) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X9,X10,X20,X21,X36,X15] :
        ( ( X9 = X21
          & ~ visFreeVar(X9,vabs(X21,X36,veabs))
          & vtcheck(X20,vabs(X21,X36,veabs),X15) )
       => vtcheck(vbind(X9,X10,X20),vabs(X21,X36,veabs),X15) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['T-Weak-FreeVar-abs-2'])]) ).

fof(c_0_12,plain,
    ! [X308,X309,X310,X311] :
      ( ~ vtcheck(X309,X308,X311)
      | ~ valphaEquivalent(X308,X310)
      | vtcheck(X309,X310,X311) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['alpha-equiv-typing'])]) ).

fof(c_0_13,plain,
    ! [X304,X305,X306,X307] :
      ( visFreeVar(X306,X307)
      | valphaEquivalent(vabs(X305,X304,X307),vabs(X306,X304,vsubst(X305,vvar(X306),X307))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).

fof(c_0_14,negated_conjecture,
    ( esk32_0 = esk35_0
    & ~ visFreeVar(esk32_0,vabs(esk35_0,esk36_0,veabs))
    & vtcheck(esk34_0,vabs(esk35_0,esk36_0,veabs),esk37_0)
    & ~ vtcheck(vbind(esk32_0,esk33_0,esk34_0),vabs(esk35_0,esk36_0,veabs),esk37_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_15,plain,
    ! [X80,X81,X82,X83,X84] :
      ( ( ~ visFreeVar(X83,X82)
        | visFreeVar(X80,X81)
        | X80 != X83
        | X81 != vapp(X82,X84) )
      & ( ~ visFreeVar(X83,X84)
        | visFreeVar(X80,X81)
        | X80 != X83
        | X81 != vapp(X82,X84) )
      & ( ~ visFreeVar(X80,X81)
        | visFreeVar(X83,X82)
        | visFreeVar(X83,X84)
        | X80 != X83
        | X81 != vapp(X82,X84) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar2])])]) ).

fof(c_0_16,plain,
    ! [X70,X71,X72,X73] :
      ( ( X72 != X73
        | visFreeVar(X70,X71)
        | X70 != X73
        | X71 != vvar(X72) )
      & ( ~ visFreeVar(X70,X71)
        | X72 = X73
        | X70 != X73
        | X71 != vvar(X72) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar0])])]) ).

fof(c_0_17,plain,
    ! [X299,X300] :
      ( ~ valphaEquivalent(X300,X299)
      | valphaEquivalent(X299,X300) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['alpha-equiv-sym'])]) ).

fof(c_0_18,plain,
    ! [X9,X10,X20,X21,X36,X12,X15] :
      ( ( X9 != X21
        & ~ visFreeVar(X9,vabs(X21,X36,X12))
        & vtcheck(X20,vabs(X21,X36,X12),X15) )
     => vtcheck(vbind(X9,X10,X20),vabs(X21,X36,X12),X15) ),
    inference(fof_simplification,[status(thm)],['T-Weak-FreeVar-abs-1-gen']) ).

cnf(c_0_19,plain,
    ( vtcheck(X1,X4,X3)
    | ~ vtcheck(X1,X2,X3)
    | ~ valphaEquivalent(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    ( visFreeVar(X1,X2)
    | valphaEquivalent(vabs(X3,X4,X2),vabs(X1,X4,vsubst(X3,vvar(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,negated_conjecture,
    vtcheck(esk34_0,vabs(esk35_0,esk36_0,veabs),esk37_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,negated_conjecture,
    esk32_0 = esk35_0,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,plain,
    ( visFreeVar(X3,X4)
    | ~ visFreeVar(X1,X2)
    | X3 != X1
    | X4 != vapp(X5,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,plain,
    ( visFreeVar(X3,X4)
    | X1 != X2
    | X3 != X2
    | X4 != vvar(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_25,plain,
    ! [X11,X9,X12] :
      ( ( ~ visFreeVar(X9,X11)
        & valphaEquivalent(X11,X12) )
     => ~ visFreeVar(X9,X12) ),
    inference(fof_simplification,[status(thm)],['alpha-equiv-FreeVar']) ).

cnf(c_0_26,plain,
    ( valphaEquivalent(X2,X1)
    | ~ valphaEquivalent(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_27,plain,
    ! [X325,X326,X327,X328,X329,X330,X331] :
      ( X325 = X328
      | visFreeVar(X325,vabs(X328,X329,X330))
      | ~ vtcheck(X327,vabs(X328,X329,X330),X331)
      | vtcheck(vbind(X325,X326,X327),vabs(X328,X329,X330),X331) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).

cnf(c_0_28,plain,
    ( vtcheck(X1,vabs(X2,X3,vsubst(X4,vvar(X2),X5)),X6)
    | visFreeVar(X2,X5)
    | ~ vtcheck(X1,vabs(X4,X3,X5),X6) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_29,negated_conjecture,
    vtcheck(esk34_0,vabs(esk32_0,esk36_0,veabs),esk37_0),
    inference(rw,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_30,plain,
    ( visFreeVar(X3,X4)
    | ~ visFreeVar(X1,X2)
    | X3 != X1
    | X4 != vapp(X2,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_31,plain,
    ( visFreeVar(X1,X2)
    | X2 != vapp(X3,X4)
    | ~ visFreeVar(X1,X4) ),
    inference(er,[status(thm)],[c_0_23]) ).

cnf(c_0_32,plain,
    ( visFreeVar(X1,X2)
    | X2 != vvar(X1) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).

fof(c_0_33,plain,
    ! [X312,X313,X314] :
      ( visFreeVar(X313,X312)
      | ~ valphaEquivalent(X312,X314)
      | ~ visFreeVar(X313,X314) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).

cnf(c_0_34,plain,
    ( valphaEquivalent(vabs(X1,X2,vsubst(X3,vvar(X1),X4)),vabs(X3,X2,X4))
    | visFreeVar(X1,X4) ),
    inference(spm,[status(thm)],[c_0_26,c_0_20]) ).

cnf(c_0_35,plain,
    ( X1 = X2
    | visFreeVar(X1,vabs(X2,X3,X4))
    | vtcheck(vbind(X1,X7,X5),vabs(X2,X3,X4),X6)
    | ~ vtcheck(X5,vabs(X2,X3,X4),X6) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_36,negated_conjecture,
    ( vtcheck(esk34_0,vabs(X1,esk36_0,vsubst(esk32_0,vvar(X1),veabs)),esk37_0)
    | visFreeVar(X1,veabs) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

fof(c_0_37,plain,
    ! [X74,X75,X76,X77,X78,X79] :
      ( ( X77 = X78
        | ~ visFreeVar(X78,X79)
        | visFreeVar(X75,X76)
        | X75 != X78
        | X76 != vabs(X77,X74,X79) )
      & ( X77 != X78
        | ~ visFreeVar(X75,X76)
        | X75 != X78
        | X76 != vabs(X77,X74,X79) )
      & ( visFreeVar(X78,X79)
        | ~ visFreeVar(X75,X76)
        | X75 != X78
        | X76 != vabs(X77,X74,X79) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar1])])]) ).

cnf(c_0_38,plain,
    ( visFreeVar(X1,X2)
    | X2 != vapp(X3,X4)
    | ~ visFreeVar(X1,X3) ),
    inference(er,[status(thm)],[c_0_30]) ).

cnf(c_0_39,plain,
    ( visFreeVar(X1,vapp(X2,X3))
    | ~ visFreeVar(X1,X3) ),
    inference(er,[status(thm)],[c_0_31]) ).

cnf(c_0_40,plain,
    visFreeVar(X1,vvar(X1)),
    inference(er,[status(thm)],[c_0_32]) ).

cnf(c_0_41,plain,
    ( visFreeVar(X1,X2)
    | ~ valphaEquivalent(X2,X3)
    | ~ visFreeVar(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_42,plain,
    ( vtcheck(X1,vabs(X2,X3,X4),X5)
    | visFreeVar(X6,X4)
    | ~ vtcheck(X1,vabs(X6,X3,vsubst(X2,vvar(X6),X4)),X5) ),
    inference(spm,[status(thm)],[c_0_19,c_0_34]) ).

cnf(c_0_43,negated_conjecture,
    ( X1 = X2
    | vtcheck(vbind(X1,X3,esk34_0),vabs(X2,esk36_0,vsubst(esk32_0,vvar(X2),veabs)),esk37_0)
    | visFreeVar(X1,vabs(X2,esk36_0,vsubst(esk32_0,vvar(X2),veabs)))
    | visFreeVar(X2,veabs) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_44,plain,
    ( X1 != X2
    | ~ visFreeVar(X3,X4)
    | X3 != X2
    | X4 != vabs(X1,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_45,plain,
    ( visFreeVar(X1,vapp(X2,X3))
    | ~ visFreeVar(X1,X2) ),
    inference(er,[status(thm)],[c_0_38]) ).

cnf(c_0_46,plain,
    visFreeVar(X1,vapp(X2,vvar(X1))),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_47,negated_conjecture,
    ~ vtcheck(vbind(esk32_0,esk33_0,esk34_0),vabs(esk35_0,esk36_0,veabs),esk37_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_48,plain,
    ( visFreeVar(X1,vabs(X2,X3,X4))
    | visFreeVar(X5,X4)
    | ~ visFreeVar(X1,vabs(X5,X3,vsubst(X2,vvar(X5),X4))) ),
    inference(spm,[status(thm)],[c_0_41,c_0_20]) ).

cnf(c_0_49,negated_conjecture,
    ( X1 = X2
    | vtcheck(vbind(X1,X3,esk34_0),vabs(esk32_0,esk36_0,veabs),esk37_0)
    | visFreeVar(X1,vabs(X2,esk36_0,vsubst(esk32_0,vvar(X2),veabs)))
    | visFreeVar(X2,veabs) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_50,plain,
    ( X1 != vabs(X2,X3,X4)
    | ~ visFreeVar(X2,X1) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_44])]) ).

cnf(c_0_51,plain,
    visFreeVar(X1,vapp(vapp(X2,vvar(X1)),X3)),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

fof(c_0_52,plain,
    ! [X14,X11] :
      ( vgensym(X11) = X14
     => ~ visFreeVar(X14,X11) ),
    inference(fof_simplification,[status(thm)],['gensym-is-fresh']) ).

cnf(c_0_53,negated_conjecture,
    ~ vtcheck(vbind(esk32_0,esk33_0,esk34_0),vabs(esk32_0,esk36_0,veabs),esk37_0),
    inference(rw,[status(thm)],[c_0_47,c_0_22]) ).

cnf(c_0_54,negated_conjecture,
    ( X1 = X2
    | vtcheck(vbind(X1,X3,esk34_0),vabs(esk32_0,esk36_0,veabs),esk37_0)
    | visFreeVar(X1,vabs(esk32_0,esk36_0,veabs))
    | visFreeVar(X2,veabs) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_55,plain,
    ~ visFreeVar(X1,vabs(X1,X2,X3)),
    inference(er,[status(thm)],[c_0_50]) ).

cnf(c_0_56,plain,
    visFreeVar(X1,vapp(vapp(vapp(X2,vvar(X1)),X3),X4)),
    inference(spm,[status(thm)],[c_0_45,c_0_51]) ).

fof(c_0_57,plain,
    ! [X147,X148] :
      ( vgensym(X148) != X147
      | ~ visFreeVar(X147,X148) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])]) ).

cnf(c_0_58,negated_conjecture,
    ( esk32_0 = X1
    | visFreeVar(X1,veabs) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).

cnf(c_0_59,plain,
    visFreeVar(X1,vapp(vapp(vapp(vapp(X2,vvar(X1)),X3),X4),X5)),
    inference(spm,[status(thm)],[c_0_45,c_0_56]) ).

cnf(c_0_60,plain,
    ( vgensym(X1) != X2
    | ~ visFreeVar(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_61,negated_conjecture,
    ( esk32_0 = X1
    | visFreeVar(X1,vapp(veabs,X2)) ),
    inference(spm,[status(thm)],[c_0_45,c_0_58]) ).

cnf(c_0_62,plain,
    visFreeVar(X1,vapp(X2,vapp(vapp(vapp(vapp(X3,vvar(X1)),X4),X5),X6))),
    inference(spm,[status(thm)],[c_0_39,c_0_59]) ).

cnf(c_0_63,negated_conjecture,
    ( esk32_0 = X1
    | vgensym(vapp(veabs,X2)) != X1 ),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_64,plain,
    vgensym(vapp(X1,vapp(vapp(vapp(vapp(X2,vvar(X3)),X4),X5),X6))) != X3,
    inference(spm,[status(thm)],[c_0_60,c_0_62]) ).

cnf(c_0_65,negated_conjecture,
    vgensym(vapp(veabs,X1)) = esk32_0,
    inference(er,[status(thm)],[c_0_63]) ).

cnf(c_0_66,negated_conjecture,
    esk32_0 != X1,
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_67,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_22,c_0_66]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : COM124+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
% 0.14/0.34  % Computer : n025.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 29 13:40:10 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 4.41/4.63  % Version  : CSE_E---1.5
% 4.41/4.63  % Problem  : theBenchmark.p
% 4.41/4.63  % Proof found
% 4.41/4.63  % SZS status Theorem for theBenchmark.p
% 4.41/4.63  % SZS output start Proof
% See solution above
% 4.41/4.64  % Total time : 4.055000 s
% 4.41/4.64  % SZS output end Proof
% 4.41/4.64  % Total time : 4.061000 s
%------------------------------------------------------------------------------