TSTP Solution File: COM124+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : COM124+1 : TPTP v8.2.0. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n008.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 : Mon May 20 19:07:28 EDT 2024

% Result   : Theorem 18.73s 2.79s
% Output   : CNFRefutation 18.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   70 (  16 unt;   0 def)
%            Number of atoms       :  233 (  99 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  266 ( 103   ~;  99   |;  35   &)
%                                         (   0 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-3 aty)
%            Number of variables   :  251 (  20 sgn 138   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
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/sandbox/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/sandbox/benchmark/Axioms/COM001+1.ax','alpha-equiv-typing') ).

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/sandbox/benchmark/Axioms/COM001+1.ax','alpha-equiv-subst-abs') ).

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/sandbox/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-1-gen') ).

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

fof('alpha-equiv-FreeVar',axiom,
    ! [X11,X9,X12] :
      ( ( ~ visFreeVar(X9,X11)
        & valphaEquivalent(X11,X12) )
     => ~ visFreeVar(X9,X12) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/COM001+0.ax',isFreeVar1) ).

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

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/sandbox/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/sandbox/benchmark/Axioms/COM001+0.ax',isFreeVar0) ).

fof(subst2,axiom,
    ! [X1,X4,X6,X19,X12,X9,X11,X13] :
      ( ( X1 = X9
        & X4 = X11
        & X6 = vapp(X12,X13) )
     => ( X19 = vsubst(X1,X4,X6)
       => X19 = vapp(vsubst(X9,X11,X12),vsubst(X9,X11,X13)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',subst2) ).

fof(subst0,axiom,
    ! [X9,X21,X1,X4,X6,X19,X11] :
      ( ( X1 = X9
        & X4 = X11
        & X6 = vvar(X21) )
     => ( X9 = X21
       => ( X19 = vsubst(X1,X4,X6)
         => X19 = X11 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',subst0) ).

fof(c_0_12,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_13,plain,
    ! [X308,X309,X310,X311] :
      ( ~ vtcheck(X309,X308,X311)
      | ~ valphaEquivalent(X308,X310)
      | vtcheck(X309,X310,X311) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['alpha-equiv-typing'])])]) ).

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(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).

fof(c_0_15,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_16,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_17,plain,
    ( vtcheck(X1,X4,X3)
    | ~ vtcheck(X1,X2,X3)
    | ~ valphaEquivalent(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    vtcheck(esk34_0,vabs(esk35_0,esk36_0,veabs),esk37_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_19,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_15])]) ).

fof(c_0_20,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).

cnf(c_0_21,negated_conjecture,
    ( vtcheck(esk34_0,X1,esk37_0)
    | ~ valphaEquivalent(vabs(esk35_0,esk36_0,veabs),X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,plain,
    ( visFreeVar(X1,X2)
    | valphaEquivalent(vabs(X3,X4,X2),vabs(X1,X4,vsubst(X3,vvar(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_23,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_20]) ).

cnf(c_0_24,negated_conjecture,
    ( vtcheck(esk34_0,vabs(X1,esk36_0,vsubst(esk35_0,vvar(X1),veabs)),esk37_0)
    | visFreeVar(X1,veabs) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

fof(c_0_25,plain,
    ! [X299,X300] :
      ( ~ valphaEquivalent(X300,X299)
      | valphaEquivalent(X299,X300) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['alpha-equiv-sym'])])]) ).

fof(c_0_26,plain,
    ! [X11,X9,X12] :
      ( ( ~ visFreeVar(X9,X11)
        & valphaEquivalent(X11,X12) )
     => ~ visFreeVar(X9,X12) ),
    inference(fof_simplification,[status(thm)],['alpha-equiv-FreeVar']) ).

cnf(c_0_27,negated_conjecture,
    ( X1 = X2
    | vtcheck(vbind(X1,X3,esk34_0),vabs(X2,esk36_0,vsubst(esk35_0,vvar(X2),veabs)),esk37_0)
    | visFreeVar(X1,vabs(X2,esk36_0,vsubst(esk35_0,vvar(X2),veabs)))
    | visFreeVar(X2,veabs) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,plain,
    ( valphaEquivalent(X2,X1)
    | ~ valphaEquivalent(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_29,plain,
    ! [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) ) ) ) ),
    inference(fof_simplification,[status(thm)],[isFreeVar1]) ).

fof(c_0_30,plain,
    ! [X312,X313,X314] :
      ( visFreeVar(X313,X312)
      | ~ valphaEquivalent(X312,X314)
      | ~ visFreeVar(X313,X314) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).

cnf(c_0_31,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_32,negated_conjecture,
    esk32_0 = esk35_0,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_33,negated_conjecture,
    ( X1 = X2
    | vtcheck(vbind(X1,X3,esk34_0),X4,esk37_0)
    | visFreeVar(X1,vabs(X2,esk36_0,vsubst(esk35_0,vvar(X2),veabs)))
    | visFreeVar(X2,veabs)
    | ~ valphaEquivalent(vabs(X2,esk36_0,vsubst(esk35_0,vvar(X2),veabs)),X4) ),
    inference(spm,[status(thm)],[c_0_17,c_0_27]) ).

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_28,c_0_22]) ).

fof(c_0_35,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).

fof(c_0_36,plain,
    ! [X14,X11] :
      ( vgensym(X11) = X14
     => ~ visFreeVar(X14,X11) ),
    inference(fof_simplification,[status(thm)],['gensym-is-fresh']) ).

fof(c_0_37,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar2])])])]) ).

cnf(c_0_38,plain,
    ( visFreeVar(X1,X2)
    | ~ valphaEquivalent(X2,X3)
    | ~ visFreeVar(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_39,negated_conjecture,
    ~ vtcheck(vbind(esk35_0,esk33_0,esk34_0),vabs(esk35_0,esk36_0,veabs),esk37_0),
    inference(rw,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_40,negated_conjecture,
    ( X1 = X2
    | vtcheck(vbind(X1,X3,esk34_0),vabs(esk35_0,esk36_0,veabs),esk37_0)
    | visFreeVar(X1,vabs(X2,esk36_0,vsubst(esk35_0,vvar(X2),veabs)))
    | visFreeVar(X2,veabs) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_41,plain,
    ( X1 != X2
    | ~ visFreeVar(X3,X4)
    | X3 != X2
    | X4 != vabs(X1,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

fof(c_0_42,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar0])])])]) ).

fof(c_0_43,plain,
    ! [X147,X148] :
      ( vgensym(X148) != X147
      | ~ visFreeVar(X147,X148) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).

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

cnf(c_0_45,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_38,c_0_22]) ).

cnf(c_0_46,negated_conjecture,
    ( esk35_0 = X1
    | visFreeVar(esk35_0,vabs(X1,esk36_0,vsubst(esk35_0,vvar(X1),veabs)))
    | visFreeVar(X1,veabs) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_47,plain,
    ~ visFreeVar(X1,vabs(X1,X2,X3)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_41])])]) ).

cnf(c_0_48,plain,
    ( visFreeVar(X3,X4)
    | ~ visFreeVar(X1,X2)
    | X3 != X1
    | X4 != vapp(X5,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_49,plain,
    ( visFreeVar(X3,X4)
    | X1 != X2
    | X3 != X2
    | X4 != vvar(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

fof(c_0_50,plain,
    ! [X163,X164,X165,X166,X167,X168,X169,X170] :
      ( X163 != X168
      | X164 != X169
      | X165 != vapp(X167,X170)
      | X166 != vsubst(X163,X164,X165)
      | X166 = vapp(vsubst(X168,X169,X167),vsubst(X168,X169,X170)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst2])])]) ).

fof(c_0_51,plain,
    ! [X149,X150,X151,X152,X153,X154,X155] :
      ( X151 != X149
      | X152 != X155
      | X153 != vvar(X150)
      | X149 != X150
      | X154 != vsubst(X151,X152,X153)
      | X154 = X155 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst0])])]) ).

cnf(c_0_52,plain,
    ( vgensym(X1) != X2
    | ~ visFreeVar(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_53,plain,
    ( visFreeVar(X1,vapp(X2,X3))
    | ~ visFreeVar(X1,X2) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_44])]) ).

cnf(c_0_54,negated_conjecture,
    ( esk35_0 = X1
    | visFreeVar(X1,veabs) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).

cnf(c_0_55,plain,
    ( visFreeVar(X1,vapp(X2,X3))
    | ~ visFreeVar(X1,X3) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_48])]) ).

cnf(c_0_56,plain,
    visFreeVar(X1,vvar(X1)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_49])])]) ).

cnf(c_0_57,plain,
    ( X8 = vapp(vsubst(X2,X4,X6),vsubst(X2,X4,X7))
    | X1 != X2
    | X3 != X4
    | X5 != vapp(X6,X7)
    | X8 != vsubst(X1,X3,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_58,plain,
    ( X7 = X4
    | X1 != X2
    | X3 != X4
    | X5 != vvar(X6)
    | X2 != X6
    | X7 != vsubst(X1,X3,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_59,plain,
    ~ visFreeVar(vgensym(X1),X1),
    inference(er,[status(thm)],[c_0_52]) ).

cnf(c_0_60,negated_conjecture,
    ( esk35_0 = X1
    | visFreeVar(X1,vapp(veabs,X2)) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_61,plain,
    visFreeVar(X1,vapp(X2,vvar(X1))),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_62,plain,
    vapp(vsubst(X1,X2,X3),vsubst(X1,X2,X4)) = vsubst(X1,X2,vapp(X3,X4)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_57])])])]) ).

cnf(c_0_63,plain,
    vsubst(X1,X2,vvar(X1)) = X2,
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_58])])])])]) ).

cnf(c_0_64,negated_conjecture,
    vgensym(vapp(veabs,X1)) = esk35_0,
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_65,plain,
    visFreeVar(X1,vapp(X2,vapp(X3,vvar(X1)))),
    inference(spm,[status(thm)],[c_0_55,c_0_61]) ).

cnf(c_0_66,plain,
    vapp(vsubst(X1,X2,X3),X2) = vsubst(X1,X2,vapp(X3,vvar(X1))),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_67,negated_conjecture,
    ~ visFreeVar(esk35_0,vapp(veabs,X1)),
    inference(spm,[status(thm)],[c_0_59,c_0_64]) ).

cnf(c_0_68,plain,
    visFreeVar(X1,vapp(X2,vsubst(X3,vvar(X1),vapp(X4,vvar(X3))))),
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_69,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_67,c_0_68]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : COM124+1 : TPTP v8.2.0. Released v6.4.0.
% 0.06/0.11  % Command    : run_E %s %d THM
% 0.10/0.30  % Computer : n008.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Sun May 19 10:31:52 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.15/0.41  Running first-order theorem proving
% 0.15/0.41  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.73/2.79  # Version: 3.1.0
% 18.73/2.79  # Preprocessing class: FSLSSMSSSSSNFFN.
% 18.73/2.79  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.73/2.79  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 18.73/2.79  # Starting new_bool_3 with 300s (1) cores
% 18.73/2.79  # Starting new_bool_1 with 300s (1) cores
% 18.73/2.79  # Starting sh5l with 300s (1) cores
% 18.73/2.79  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 15104 completed with status 0
% 18.73/2.79  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 18.73/2.79  # Preprocessing class: FSLSSMSSSSSNFFN.
% 18.73/2.79  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.73/2.79  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 18.73/2.79  # No SInE strategy applied
% 18.73/2.79  # Search class: FGHSF-FSLF32-MFFFFFNN
% 18.73/2.79  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 18.73/2.79  # Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 811s (1) cores
% 18.73/2.79  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 18.73/2.79  # Starting new_bool_3 with 136s (1) cores
% 18.73/2.79  # Starting new_bool_1 with 136s (1) cores
% 18.73/2.79  # Starting sh5l with 136s (1) cores
% 18.73/2.79  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 15111 completed with status 0
% 18.73/2.79  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 18.73/2.79  # Preprocessing class: FSLSSMSSSSSNFFN.
% 18.73/2.79  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.73/2.79  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 18.73/2.79  # No SInE strategy applied
% 18.73/2.79  # Search class: FGHSF-FSLF32-MFFFFFNN
% 18.73/2.79  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 18.73/2.79  # Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 811s (1) cores
% 18.73/2.79  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 18.73/2.79  # Preprocessing time       : 0.008 s
% 18.73/2.79  # Presaturation interreduction done
% 18.73/2.79  
% 18.73/2.79  # Proof found!
% 18.73/2.79  # SZS status Theorem
% 18.73/2.79  # SZS output start CNFRefutation
% See solution above
% 18.73/2.79  # Parsed axioms                        : 64
% 18.73/2.79  # Removed by relevancy pruning/SinE    : 0
% 18.73/2.79  # Initial clauses                      : 431
% 18.73/2.79  # Removed in clause preprocessing      : 13
% 18.73/2.79  # Initial clauses in saturation        : 418
% 18.73/2.79  # Processed clauses                    : 5709
% 18.73/2.79  # ...of these trivial                  : 199
% 18.73/2.79  # ...subsumed                          : 2975
% 18.73/2.79  # ...remaining for further processing  : 2535
% 18.73/2.79  # Other redundant clauses eliminated   : 2523
% 18.73/2.79  # Clauses deleted for lack of memory   : 0
% 18.73/2.79  # Backward-subsumed                    : 212
% 18.73/2.79  # Backward-rewritten                   : 62
% 18.73/2.79  # Generated clauses                    : 109069
% 18.73/2.79  # ...of the previous two non-redundant : 100465
% 18.73/2.79  # ...aggressively subsumed             : 0
% 18.73/2.79  # Contextual simplify-reflections      : 6
% 18.73/2.79  # Paramodulations                      : 106503
% 18.73/2.79  # Factorizations                       : 4
% 18.73/2.79  # NegExts                              : 0
% 18.73/2.79  # Equation resolutions                 : 2593
% 18.73/2.79  # Disequality decompositions           : 0
% 18.73/2.79  # Total rewrite steps                  : 10839
% 18.73/2.79  # ...of those cached                   : 8584
% 18.73/2.79  # Propositional unsat checks           : 0
% 18.73/2.79  #    Propositional check models        : 0
% 18.73/2.79  #    Propositional check unsatisfiable : 0
% 18.73/2.79  #    Propositional clauses             : 0
% 18.73/2.79  #    Propositional clauses after purity: 0
% 18.73/2.79  #    Propositional unsat core size     : 0
% 18.73/2.79  #    Propositional preprocessing time  : 0.000
% 18.73/2.79  #    Propositional encoding time       : 0.000
% 18.73/2.79  #    Propositional solver time         : 0.000
% 18.73/2.79  #    Success case prop preproc time    : 0.000
% 18.73/2.79  #    Success case prop encoding time   : 0.000
% 18.73/2.79  #    Success case prop solver time     : 0.000
% 18.73/2.79  # Current number of processed clauses  : 1769
% 18.73/2.79  #    Positive orientable unit clauses  : 190
% 18.73/2.79  #    Positive unorientable unit clauses: 4
% 18.73/2.79  #    Negative unit clauses             : 55
% 18.73/2.79  #    Non-unit-clauses                  : 1520
% 18.73/2.79  # Current number of unprocessed clauses: 89245
% 18.73/2.79  # ...number of literals in the above   : 454039
% 18.73/2.79  # Current number of archived formulas  : 0
% 18.73/2.79  # Current number of archived clauses   : 672
% 18.73/2.79  # Clause-clause subsumption calls (NU) : 358082
% 18.73/2.79  # Rec. Clause-clause subsumption calls : 119528
% 18.73/2.79  # Non-unit clause-clause subsumptions  : 2192
% 18.73/2.79  # Unit Clause-clause subsumption calls : 9898
% 18.73/2.79  # Rewrite failures with RHS unbound    : 106
% 18.73/2.79  # BW rewrite match attempts            : 1950
% 18.73/2.79  # BW rewrite match successes           : 13
% 18.73/2.79  # Condensation attempts                : 0
% 18.73/2.79  # Condensation successes               : 0
% 18.73/2.79  # Termbank termtop insertions          : 4833124
% 18.73/2.79  # Search garbage collected termcells   : 4104
% 18.73/2.79  
% 18.73/2.79  # -------------------------------------------------
% 18.73/2.79  # User time                : 2.252 s
% 18.73/2.79  # System time              : 0.060 s
% 18.73/2.79  # Total time               : 2.312 s
% 18.73/2.79  # Maximum resident set size: 2872 pages
% 18.73/2.79  
% 18.73/2.79  # -------------------------------------------------
% 18.73/2.79  # User time                : 11.389 s
% 18.73/2.79  # System time              : 0.119 s
% 18.73/2.79  # Total time               : 11.508 s
% 18.73/2.79  # Maximum resident set size: 1832 pages
% 18.73/2.79  % E---3.1 exiting
% 18.73/2.79  % E exiting
%------------------------------------------------------------------------------