TSTP Solution File: NUN086+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUN086+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n015.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 12:45:59 EDT 2023

% Result   : Theorem 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   94 (  35 unt;  24 typ;   0 def)
%            Number of atoms       :  185 (  65 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  182 (  67   ~;  51   |;  64   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   38 (  23   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;   1 con; 0-2 aty)
%            Number of variables   :  148 (  12 sgn;  44   !;  31   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    r1: $i > $o ).

tff(decl_23,type,
    r2: ( $i * $i ) > $o ).

tff(decl_24,type,
    r3: ( $i * $i * $i ) > $o ).

tff(decl_25,type,
    r4: ( $i * $i * $i ) > $o ).

tff(decl_26,type,
    esk1_0: $i ).

tff(decl_27,type,
    esk2_1: $i > $i ).

tff(decl_28,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_29,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_31,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_32,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_33,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_34,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk13_1: $i > $i ).

tff(decl_39,type,
    esk14_1: $i > $i ).

tff(decl_40,type,
    esk15_1: $i > $i ).

tff(decl_41,type,
    esk16_1: $i > $i ).

tff(decl_42,type,
    esk17_1: $i > $i ).

tff(decl_43,type,
    esk18_1: $i > $i ).

tff(decl_44,type,
    esk19_1: $i > $i ).

tff(decl_45,type,
    esk20_1: $i > $i ).

fof(axiom_2,axiom,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( ~ r2(X3,X5)
        & X5 != X4 )
      | ( r2(X3,X5)
        & X5 = X4 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).

fof(axiom_1,axiom,
    ? [X1] :
    ! [X2] :
      ( ( ~ r1(X2)
        & X2 != X1 )
      | ( r1(X2)
        & X2 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).

fof(axiom_5a,axiom,
    ! [X33] :
    ? [X34] :
      ( ? [X35] :
          ( r1(X35)
          & r4(X33,X35,X34) )
      & ? [X36] :
          ( r1(X36)
          & X34 = X36 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).

fof(zerotimesoneeqzero,conjecture,
    ? [X39] :
      ( ? [X22] :
          ( ? [X23] :
              ( r1(X23)
              & r2(X23,X22) )
          & ? [X16] :
              ( r1(X16)
              & r4(X16,X22,X39) ) )
      & ? [X17] :
          ( r1(X17)
          & X39 = X17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zerotimesoneeqzero) ).

fof(axiom_2a,axiom,
    ! [X20,X21] :
    ? [X22] :
      ( ? [X23] :
          ( ? [X24] :
              ( r2(X21,X24)
              & r4(X20,X24,X23) )
          & X23 = X22 )
      & ? [X25] :
          ( r3(X25,X20,X22)
          & r4(X20,X21,X25) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).

fof(axiom_4,axiom,
    ! [X10,X11] :
    ? [X12] :
    ! [X13] :
      ( ( ~ r4(X10,X11,X13)
        & X13 != X12 )
      | ( r4(X10,X11,X13)
        & X13 = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4) ).

fof(axiom_3,axiom,
    ! [X6,X7] :
    ? [X8] :
    ! [X9] :
      ( ( ~ r3(X6,X7,X9)
        & X9 != X8 )
      | ( r3(X6,X7,X9)
        & X9 = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3) ).

fof(axiom_4a,axiom,
    ! [X30] :
    ? [X31] :
      ( ? [X32] :
          ( r1(X32)
          & r3(X30,X32,X31) )
      & X31 = X30 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).

fof(axiom_1a,axiom,
    ! [X14,X15] :
    ? [X16] :
      ( ? [X17] :
          ( ? [X18] :
              ( r2(X15,X18)
              & r3(X14,X18,X17) )
          & X17 = X16 )
      & ? [X19] :
          ( r2(X19,X16)
          & r3(X14,X15,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).

fof(c_0_9,plain,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( ~ r2(X3,X5)
        & X5 != X4 )
      | ( r2(X3,X5)
        & X5 = X4 ) ),
    inference(fof_simplification,[status(thm)],[axiom_2]) ).

fof(c_0_10,plain,
    ? [X1] :
    ! [X2] :
      ( ( ~ r1(X2)
        & X2 != X1 )
      | ( r1(X2)
        & X2 = X1 ) ),
    inference(fof_simplification,[status(thm)],[axiom_1]) ).

fof(c_0_11,plain,
    ! [X76] :
      ( r1(esk16_1(X76))
      & r4(X76,esk16_1(X76),esk15_1(X76))
      & r1(esk17_1(X76))
      & esk15_1(X76) = esk17_1(X76) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).

fof(c_0_12,negated_conjecture,
    ~ ? [X39] :
        ( ? [X22] :
            ( ? [X23] :
                ( r1(X23)
                & r2(X23,X22) )
            & ? [X16] :
                ( r1(X16)
                & r4(X16,X22,X39) ) )
        & ? [X17] :
            ( r1(X17)
            & X39 = X17 ) ),
    inference(assume_negation,[status(cth)],[zerotimesoneeqzero]) ).

fof(c_0_13,plain,
    ! [X63,X64] :
      ( r2(X64,esk11_2(X63,X64))
      & r4(X63,esk11_2(X63,X64),esk10_2(X63,X64))
      & esk10_2(X63,X64) = esk9_2(X63,X64)
      & r3(esk12_2(X63,X64),X63,esk9_2(X63,X64))
      & r4(X63,X64,esk12_2(X63,X64)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).

fof(c_0_14,plain,
    ! [X46,X48] :
      ( ( r2(X46,X48)
        | ~ r2(X46,X48) )
      & ( X48 = esk2_1(X46)
        | ~ r2(X46,X48) )
      & ( r2(X46,X48)
        | X48 != esk2_1(X46) )
      & ( X48 = esk2_1(X46)
        | X48 != esk2_1(X46) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_9])])]) ).

fof(c_0_15,plain,
    ! [X45] :
      ( ( r1(X45)
        | ~ r1(X45) )
      & ( X45 = esk1_0
        | ~ r1(X45) )
      & ( r1(X45)
        | X45 != esk1_0 )
      & ( X45 = esk1_0
        | X45 != esk1_0 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_10])])]) ).

cnf(c_0_16,plain,
    r1(esk17_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    esk15_1(X1) = esk17_1(X1),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_18,negated_conjecture,
    ! [X87,X88,X89,X90,X91] :
      ( ~ r1(X89)
      | ~ r2(X89,X88)
      | ~ r1(X90)
      | ~ r4(X90,X88,X87)
      | ~ r1(X91)
      | X87 != X91 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

cnf(c_0_19,plain,
    r4(X1,esk11_2(X1,X2),esk10_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    esk10_2(X1,X2) = esk9_2(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    ( X1 = esk2_1(X2)
    | ~ r2(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    r2(X1,esk11_2(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_23,plain,
    ! [X10,X11] :
    ? [X12] :
    ! [X13] :
      ( ( ~ r4(X10,X11,X13)
        & X13 != X12 )
      | ( r4(X10,X11,X13)
        & X13 = X12 ) ),
    inference(fof_simplification,[status(thm)],[axiom_4]) ).

cnf(c_0_24,plain,
    ( X1 = esk1_0
    | ~ r1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_25,plain,
    r1(esk16_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_26,plain,
    r1(esk15_1(X1)),
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_27,negated_conjecture,
    ( ~ r1(X1)
    | ~ r2(X1,X2)
    | ~ r1(X3)
    | ~ r4(X3,X2,X4)
    | ~ r1(X5)
    | X4 != X5 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_28,plain,
    r4(X1,esk11_2(X1,X2),esk9_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_29,plain,
    esk11_2(X1,X2) = esk2_1(X2),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

fof(c_0_30,plain,
    ! [X6,X7] :
    ? [X8] :
    ! [X9] :
      ( ( ~ r3(X6,X7,X9)
        & X9 != X8 )
      | ( r3(X6,X7,X9)
        & X9 = X8 ) ),
    inference(fof_simplification,[status(thm)],[axiom_3]) ).

fof(c_0_31,plain,
    ! [X53,X54,X56] :
      ( ( r4(X53,X54,X56)
        | ~ r4(X53,X54,X56) )
      & ( X56 = esk4_2(X53,X54)
        | ~ r4(X53,X54,X56) )
      & ( r4(X53,X54,X56)
        | X56 != esk4_2(X53,X54) )
      & ( X56 = esk4_2(X53,X54)
        | X56 != esk4_2(X53,X54) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_23])])]) ).

cnf(c_0_32,plain,
    r4(X1,esk16_1(X1),esk15_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_33,plain,
    esk16_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_34,plain,
    esk15_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_24,c_0_26]) ).

fof(c_0_35,plain,
    ! [X73] :
      ( r1(esk14_1(X73))
      & r3(X73,esk14_1(X73),esk13_1(X73))
      & esk13_1(X73) = X73 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).

cnf(c_0_36,negated_conjecture,
    ( ~ r4(X1,X2,X3)
    | ~ r2(X4,X2)
    | ~ r1(X3)
    | ~ r1(X1)
    | ~ r1(X4) ),
    inference(er,[status(thm)],[c_0_27]) ).

cnf(c_0_37,plain,
    r4(X1,esk2_1(X2),esk9_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_38,plain,
    ( r2(X1,X2)
    | X2 != esk2_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_39,plain,
    ! [X49,X50,X52] :
      ( ( r3(X49,X50,X52)
        | ~ r3(X49,X50,X52) )
      & ( X52 = esk3_2(X49,X50)
        | ~ r3(X49,X50,X52) )
      & ( r3(X49,X50,X52)
        | X52 != esk3_2(X49,X50) )
      & ( X52 = esk3_2(X49,X50)
        | X52 != esk3_2(X49,X50) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_30])])]) ).

fof(c_0_40,plain,
    ! [X57,X58] :
      ( r2(X58,esk7_2(X57,X58))
      & r3(X57,esk7_2(X57,X58),esk6_2(X57,X58))
      & esk6_2(X57,X58) = esk5_2(X57,X58)
      & r2(esk8_2(X57,X58),esk5_2(X57,X58))
      & r3(X57,X58,esk8_2(X57,X58)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).

cnf(c_0_41,plain,
    ( X1 = esk4_2(X2,X3)
    | ~ r4(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_42,plain,
    r4(X1,esk1_0,esk1_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).

cnf(c_0_43,plain,
    r4(X1,X2,esk12_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_44,plain,
    r3(X1,esk14_1(X1),esk13_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_45,plain,
    esk13_1(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_46,plain,
    r1(esk14_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_47,negated_conjecture,
    ( ~ r2(X1,esk2_1(X2))
    | ~ r1(esk9_2(X3,X2))
    | ~ r1(X3)
    | ~ r1(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_48,plain,
    r2(X1,esk2_1(X1)),
    inference(er,[status(thm)],[c_0_38]) ).

cnf(c_0_49,plain,
    ( r1(X1)
    | X1 != esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_50,plain,
    ( X1 = esk3_2(X2,X3)
    | ~ r3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_51,plain,
    r3(X1,X2,esk8_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_52,plain,
    esk4_2(X1,esk1_0) = esk1_0,
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_53,plain,
    esk4_2(X1,X2) = esk12_2(X1,X2),
    inference(spm,[status(thm)],[c_0_41,c_0_43]) ).

cnf(c_0_54,plain,
    r3(X1,esk14_1(X1),X1),
    inference(rw,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_55,plain,
    esk14_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_24,c_0_46]) ).

cnf(c_0_56,negated_conjecture,
    ( ~ r1(esk9_2(X1,X2))
    | ~ r1(X1)
    | ~ r1(X2) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_57,plain,
    r1(esk1_0),
    inference(er,[status(thm)],[c_0_49]) ).

cnf(c_0_58,plain,
    esk3_2(X1,X2) = esk8_2(X1,X2),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_59,plain,
    r3(esk12_2(X1,X2),X1,esk9_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_60,plain,
    esk12_2(X1,esk1_0) = esk1_0,
    inference(rw,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_61,plain,
    r3(X1,esk1_0,X1),
    inference(rw,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_62,negated_conjecture,
    ( ~ r1(esk9_2(esk1_0,X1))
    | ~ r1(X1) ),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_63,plain,
    ( X1 = esk8_2(X2,X3)
    | ~ r3(X2,X3,X1) ),
    inference(rw,[status(thm)],[c_0_50,c_0_58]) ).

cnf(c_0_64,plain,
    r3(esk1_0,X1,esk9_2(X1,esk1_0)),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_65,plain,
    esk3_2(X1,esk1_0) = X1,
    inference(spm,[status(thm)],[c_0_50,c_0_61]) ).

cnf(c_0_66,negated_conjecture,
    ~ r1(esk9_2(esk1_0,esk1_0)),
    inference(spm,[status(thm)],[c_0_62,c_0_57]) ).

cnf(c_0_67,plain,
    esk9_2(X1,esk1_0) = esk8_2(esk1_0,X1),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_68,plain,
    esk8_2(X1,esk1_0) = X1,
    inference(rw,[status(thm)],[c_0_65,c_0_58]) ).

cnf(c_0_69,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_57])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUN086+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun Aug 27 09:44:24 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.60  % Version  : CSE_E---1.5
% 0.21/0.60  % Problem  : theBenchmark.p
% 0.21/0.60  % Proof found
% 0.21/0.60  % SZS status Theorem for theBenchmark.p
% 0.21/0.60  % SZS output start Proof
% See solution above
% 0.21/0.61  % Total time : 0.015000 s
% 0.21/0.61  % SZS output end Proof
% 0.21/0.61  % Total time : 0.018000 s
%------------------------------------------------------------------------------