TSTP Solution File: NUM536+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM536+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n028.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 10:38:30 EDT 2023

% Result   : Theorem 5.60s 5.69s
% Output   : CNFRefutation 5.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   52 (  10 unt;  15 typ;   0 def)
%            Number of atoms       :  235 (  56 equ)
%            Maximal formula atoms :   54 (   6 avg)
%            Number of connectives :  338 ( 140   ~; 166   |;  24   &)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  12   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   69 (   0 sgn;  24   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aSet0: $i > $o ).

tff(decl_23,type,
    aElement0: $i > $o ).

tff(decl_24,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(decl_25,type,
    isFinite0: $i > $o ).

tff(decl_26,type,
    slcrc0: $i ).

tff(decl_27,type,
    isCountable0: $i > $o ).

tff(decl_28,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff(decl_29,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_30,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff(decl_31,type,
    xx: $i ).

tff(decl_32,type,
    xS: $i ).

tff(decl_33,type,
    esk1_1: $i > $i ).

tff(decl_34,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_36,type,
    esk4_3: ( $i * $i * $i ) > $i ).

fof(mDefDiff,axiom,
    ! [X1,X2] :
      ( ( aSet0(X1)
        & aElement0(X2) )
     => ! [X3] :
          ( X3 = sdtmndt0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aElement0(X4)
                  & aElementOf0(X4,X1)
                  & X4 != X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).

fof(m__679,hypothesis,
    ( aElement0(xx)
    & aSet0(xS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__679) ).

fof(mDefCons,axiom,
    ! [X1,X2] :
      ( ( aSet0(X1)
        & aElement0(X2) )
     => ! [X3] :
          ( X3 = sdtpldt0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aElement0(X4)
                  & ( aElementOf0(X4,X1)
                    | X4 = X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).

fof(mEOfElem,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).

fof(m__,conjecture,
    sdtmndt0(sdtpldt0(xS,xx),xx) = xS,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(m__679_02,hypothesis,
    ~ aElementOf0(xx,xS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__679_02) ).

fof(c_0_6,plain,
    ! [X33,X34,X35,X36,X37,X38] :
      ( ( aSet0(X35)
        | X35 != sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( aElement0(X36)
        | ~ aElementOf0(X36,X35)
        | X35 != sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( aElementOf0(X36,X33)
        | ~ aElementOf0(X36,X35)
        | X35 != sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( X36 != X34
        | ~ aElementOf0(X36,X35)
        | X35 != sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( ~ aElement0(X37)
        | ~ aElementOf0(X37,X33)
        | X37 = X34
        | aElementOf0(X37,X35)
        | X35 != sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( ~ aElementOf0(esk4_3(X33,X34,X38),X38)
        | ~ aElement0(esk4_3(X33,X34,X38))
        | ~ aElementOf0(esk4_3(X33,X34,X38),X33)
        | esk4_3(X33,X34,X38) = X34
        | ~ aSet0(X38)
        | X38 = sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( aElement0(esk4_3(X33,X34,X38))
        | aElementOf0(esk4_3(X33,X34,X38),X38)
        | ~ aSet0(X38)
        | X38 = sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( aElementOf0(esk4_3(X33,X34,X38),X33)
        | aElementOf0(esk4_3(X33,X34,X38),X38)
        | ~ aSet0(X38)
        | X38 = sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( esk4_3(X33,X34,X38) != X34
        | aElementOf0(esk4_3(X33,X34,X38),X38)
        | ~ aSet0(X38)
        | X38 = sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])])]) ).

cnf(c_0_7,plain,
    ( aElementOf0(esk4_3(X1,X2,X3),X1)
    | aElementOf0(esk4_3(X1,X2,X3),X3)
    | X3 = sdtmndt0(X1,X2)
    | ~ aSet0(X3)
    | ~ aSet0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_8,hypothesis,
    aElement0(xx),
    inference(split_conjunct,[status(thm)],[m__679]) ).

fof(c_0_9,plain,
    ! [X26,X27,X28,X29,X30,X31] :
      ( ( aSet0(X28)
        | X28 != sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( aElement0(X29)
        | ~ aElementOf0(X29,X28)
        | X28 != sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( aElementOf0(X29,X26)
        | X29 = X27
        | ~ aElementOf0(X29,X28)
        | X28 != sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( ~ aElementOf0(X30,X26)
        | ~ aElement0(X30)
        | aElementOf0(X30,X28)
        | X28 != sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( X30 != X27
        | ~ aElement0(X30)
        | aElementOf0(X30,X28)
        | X28 != sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( ~ aElementOf0(esk3_3(X26,X27,X31),X26)
        | ~ aElement0(esk3_3(X26,X27,X31))
        | ~ aElementOf0(esk3_3(X26,X27,X31),X31)
        | ~ aSet0(X31)
        | X31 = sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( esk3_3(X26,X27,X31) != X27
        | ~ aElement0(esk3_3(X26,X27,X31))
        | ~ aElementOf0(esk3_3(X26,X27,X31),X31)
        | ~ aSet0(X31)
        | X31 = sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( aElement0(esk3_3(X26,X27,X31))
        | aElementOf0(esk3_3(X26,X27,X31),X31)
        | ~ aSet0(X31)
        | X31 = sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( aElementOf0(esk3_3(X26,X27,X31),X26)
        | esk3_3(X26,X27,X31) = X27
        | aElementOf0(esk3_3(X26,X27,X31),X31)
        | ~ aSet0(X31)
        | X31 = sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefCons])])])])])]) ).

cnf(c_0_10,hypothesis,
    ( X1 = sdtmndt0(X2,xx)
    | aElementOf0(esk4_3(X2,xx,X1),X1)
    | aElementOf0(esk4_3(X2,xx,X1),X2)
    | ~ aSet0(X1)
    | ~ aSet0(X2) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,hypothesis,
    aSet0(xS),
    inference(split_conjunct,[status(thm)],[m__679]) ).

cnf(c_0_12,plain,
    ( aSet0(X1)
    | X1 != sdtpldt0(X2,X3)
    | ~ aSet0(X2)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( aElementOf0(X1,X2)
    | X1 = X3
    | ~ aElementOf0(X1,X4)
    | X4 != sdtpldt0(X2,X3)
    | ~ aSet0(X2)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,hypothesis,
    ( sdtmndt0(X1,xx) = xS
    | aElementOf0(esk4_3(X1,xx,xS),xS)
    | aElementOf0(esk4_3(X1,xx,xS),X1)
    | ~ aSet0(X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,plain,
    ( aSet0(sdtpldt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aSet0(X1) ),
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
    ( X1 = X2
    | aElementOf0(X1,X3)
    | ~ aElementOf0(X1,sdtpldt0(X3,X2))
    | ~ aElement0(X2)
    | ~ aSet0(X3) ),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_17,hypothesis,
    ( sdtmndt0(sdtpldt0(X1,X2),xx) = xS
    | aElementOf0(esk4_3(sdtpldt0(X1,X2),xx,xS),sdtpldt0(X1,X2))
    | aElementOf0(esk4_3(sdtpldt0(X1,X2),xx,xS),xS)
    | ~ aElement0(X2)
    | ~ aSet0(X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

fof(c_0_18,plain,
    ! [X5,X6] :
      ( ~ aSet0(X5)
      | ~ aElementOf0(X6,X5)
      | aElement0(X6) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).

cnf(c_0_19,hypothesis,
    ( esk4_3(sdtpldt0(X1,X2),xx,xS) = X2
    | sdtmndt0(sdtpldt0(X1,X2),xx) = xS
    | aElementOf0(esk4_3(sdtpldt0(X1,X2),xx,xS),xS)
    | aElementOf0(esk4_3(sdtpldt0(X1,X2),xx,xS),X1)
    | ~ aElement0(X2)
    | ~ aSet0(X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_20,negated_conjecture,
    sdtmndt0(sdtpldt0(xS,xx),xx) != xS,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_21,plain,
    ( esk4_3(X1,X2,X3) = X2
    | X3 = sdtmndt0(X1,X2)
    | ~ aElementOf0(esk4_3(X1,X2,X3),X3)
    | ~ aElement0(esk4_3(X1,X2,X3))
    | ~ aElementOf0(esk4_3(X1,X2,X3),X1)
    | ~ aSet0(X3)
    | ~ aSet0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_22,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,hypothesis,
    ( esk4_3(sdtpldt0(X1,xx),xx,xS) = xx
    | sdtmndt0(sdtpldt0(X1,xx),xx) = xS
    | aElementOf0(esk4_3(sdtpldt0(X1,xx),xx,xS),xS)
    | aElementOf0(esk4_3(sdtpldt0(X1,xx),xx,xS),X1)
    | ~ aSet0(X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_8]) ).

cnf(c_0_24,negated_conjecture,
    sdtmndt0(sdtpldt0(xS,xx),xx) != xS,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,plain,
    ( aElementOf0(X1,X3)
    | ~ aElementOf0(X1,X2)
    | ~ aElement0(X1)
    | X3 != sdtpldt0(X2,X4)
    | ~ aSet0(X2)
    | ~ aElement0(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_26,plain,
    ( esk4_3(X1,X2,X3) = X2
    | X3 = sdtmndt0(X1,X2)
    | ~ aElementOf0(esk4_3(X1,X2,X3),X3)
    | ~ aElementOf0(esk4_3(X1,X2,X3),X1)
    | ~ aElement0(X2)
    | ~ aSet0(X3)
    | ~ aSet0(X1) ),
    inference(csr,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_27,hypothesis,
    ( esk4_3(sdtpldt0(xS,xx),xx,xS) = xx
    | aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),xS) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_11]),c_0_24]) ).

cnf(c_0_28,plain,
    ( aElementOf0(X1,X2)
    | X2 != sdtpldt0(X3,X4)
    | ~ aElementOf0(X1,X3)
    | ~ aElement0(X4)
    | ~ aSet0(X3) ),
    inference(csr,[status(thm)],[c_0_25,c_0_22]) ).

cnf(c_0_29,hypothesis,
    ( esk4_3(sdtpldt0(xS,xx),xx,xS) = xx
    | ~ aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
    | ~ aSet0(sdtpldt0(xS,xx)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_8]),c_0_11])]),c_0_24]) ).

cnf(c_0_30,plain,
    ( aElementOf0(X1,sdtpldt0(X2,X3))
    | ~ aElementOf0(X1,X2)
    | ~ aElement0(X3)
    | ~ aSet0(X2) ),
    inference(er,[status(thm)],[c_0_28]) ).

fof(c_0_31,hypothesis,
    ~ aElementOf0(xx,xS),
    inference(fof_simplification,[status(thm)],[m__679_02]) ).

cnf(c_0_32,plain,
    ( aElementOf0(esk4_3(X1,X2,X3),X3)
    | X3 = sdtmndt0(X1,X2)
    | esk4_3(X1,X2,X3) != X2
    | ~ aSet0(X3)
    | ~ aSet0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_33,hypothesis,
    ( esk4_3(sdtpldt0(xS,xx),xx,xS) = xx
    | ~ aSet0(sdtpldt0(xS,xx)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_8]),c_0_11])]),c_0_27]) ).

cnf(c_0_34,hypothesis,
    ~ aElementOf0(xx,xS),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_35,hypothesis,
    ~ aSet0(sdtpldt0(xS,xx)),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_8]),c_0_11])]),c_0_24]),c_0_34]) ).

cnf(c_0_36,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_15]),c_0_8]),c_0_11])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM536+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n028.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   : Fri Aug 25 15:17:21 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 5.60/5.69  % Version  : CSE_E---1.5
% 5.60/5.69  % Problem  : theBenchmark.p
% 5.60/5.69  % Proof found
% 5.60/5.69  % SZS status Theorem for theBenchmark.p
% 5.60/5.69  % SZS output start Proof
% See solution above
% 5.60/5.69  % Total time : 5.131000 s
% 5.60/5.69  % SZS output end Proof
% 5.60/5.69  % Total time : 5.133000 s
%------------------------------------------------------------------------------