TSTP Solution File: NUN076+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUN076+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n021.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 12:45:54 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   78 (  19 unt;  25 typ;   0 def)
%            Number of atoms       :  164 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  194 (  83   ~;  68   |;  43   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   40 (  24   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;   1 con; 0-2 aty)
%            Number of variables   :  124 (  15 sgn;  44   !;  25   ?;   0   :)

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

tff(decl_23,type,
    r1: $i > $o ).

tff(decl_24,type,
    r2: ( $i * $i ) > $o ).

tff(decl_25,type,
    r3: ( $i * $i * $i ) > $o ).

tff(decl_26,type,
    r4: ( $i * $i * $i ) > $o ).

tff(decl_27,type,
    esk1_0: $i ).

tff(decl_28,type,
    esk2_1: $i > $i ).

tff(decl_29,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_31,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_32,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_33,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_34,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk13_1: $i > $i ).

tff(decl_40,type,
    esk14_1: $i > $i ).

tff(decl_41,type,
    esk15_1: $i > $i ).

tff(decl_42,type,
    esk16_1: $i > $i ).

tff(decl_43,type,
    esk17_1: $i > $i ).

tff(decl_44,type,
    esk18_1: $i > $i ).

tff(decl_45,type,
    esk19_1: $i > $i ).

tff(decl_46,type,
    esk20_1: $i > $i ).

fof(axiom_1,axiom,
    ? [X1] :
    ! [X2] :
      ( ( id(X2,X1)
        & r1(X2) )
      | ( ~ r1(X2)
        & ~ id(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1) ).

fof(thereexistsanevennumberid,conjecture,
    ? [X63,X46,X47] :
      ( ? [X40] :
          ( id(X40,X63)
          & ? [X49] :
              ( r4(X49,X46,X40)
              & ? [X43] :
                  ( r2(X43,X49)
                  & ? [X58] :
                      ( r1(X58)
                      & r2(X58,X43) ) ) ) )
      & ? [X41] :
          ( id(X41,X63)
          & r3(X46,X47,X41) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thereexistsanevennumberid) ).

fof(axiom_6,axiom,
    ! [X15,X16] :
      ( ~ id(X15,X16)
      | id(X16,X15) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6) ).

fof(axiom_5a,axiom,
    ! [X57] :
    ? [X58] :
      ( ? [X59] :
          ( r1(X59)
          & r4(X57,X59,X58) )
      & ? [X60] :
          ( id(X58,X60)
          & r1(X60) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).

fof(axiom_8,axiom,
    ! [X20,X21] :
      ( ~ id(X20,X21)
      | ( ~ r1(X20)
        & ~ r1(X21) )
      | ( r1(X20)
        & r1(X21) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_8) ).

fof(axiom_7,axiom,
    ! [X17,X18,X19] :
      ( ~ id(X17,X18)
      | id(X17,X19)
      | ~ id(X18,X19) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7) ).

fof(axiom_4a,axiom,
    ! [X54] :
    ? [X55] :
      ( id(X55,X54)
      & ? [X56] :
          ( r1(X56)
          & r3(X54,X56,X55) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).

fof(axiom_2,axiom,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( id(X5,X4)
        & r2(X3,X5) )
      | ( ~ r2(X3,X5)
        & ~ id(X5,X4) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_2) ).

fof(axiom_5,axiom,
    ! [X14] : id(X14,X14),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).

fof(c_0_9,plain,
    ? [X1] :
    ! [X2] :
      ( ( id(X2,X1)
        & r1(X2) )
      | ( ~ r1(X2)
        & ~ id(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[axiom_1]) ).

fof(c_0_10,negated_conjecture,
    ~ ? [X63,X46,X47] :
        ( ? [X40] :
            ( id(X40,X63)
            & ? [X49] :
                ( r4(X49,X46,X40)
                & ? [X43] :
                    ( r2(X43,X49)
                    & ? [X58] :
                        ( r1(X58)
                        & r2(X58,X43) ) ) ) )
        & ? [X41] :
            ( id(X41,X63)
            & r3(X46,X47,X41) ) ),
    inference(assume_negation,[status(cth)],[thereexistsanevennumberid]) ).

fof(c_0_11,plain,
    ! [X15,X16] :
      ( ~ id(X15,X16)
      | id(X16,X15) ),
    inference(fof_simplification,[status(thm)],[axiom_6]) ).

fof(c_0_12,plain,
    ! [X69] :
      ( ( ~ r1(X69)
        | id(X69,esk1_0) )
      & ( ~ id(X69,esk1_0)
        | id(X69,esk1_0) )
      & ( ~ r1(X69)
        | r1(X69) )
      & ( ~ id(X69,esk1_0)
        | r1(X69) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_9])])]) ).

fof(c_0_13,plain,
    ! [X124] :
      ( r1(esk16_1(X124))
      & r4(X124,esk16_1(X124),esk15_1(X124))
      & id(esk15_1(X124),esk17_1(X124))
      & r1(esk17_1(X124)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).

fof(c_0_14,plain,
    ! [X20,X21] :
      ( ~ id(X20,X21)
      | ( ~ r1(X20)
        & ~ r1(X21) )
      | ( r1(X20)
        & r1(X21) ) ),
    inference(fof_simplification,[status(thm)],[axiom_8]) ).

fof(c_0_15,negated_conjecture,
    ! [X135,X136,X137,X138,X139,X140,X141,X142] :
      ( ~ id(X138,X135)
      | ~ r4(X139,X136,X138)
      | ~ r2(X140,X139)
      | ~ r1(X141)
      | ~ r2(X141,X140)
      | ~ id(X142,X135)
      | ~ r3(X136,X137,X142) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_16,plain,
    ! [X17,X18,X19] :
      ( ~ id(X17,X18)
      | id(X17,X19)
      | ~ id(X18,X19) ),
    inference(fof_simplification,[status(thm)],[axiom_7]) ).

fof(c_0_17,plain,
    ! [X82,X83] :
      ( ~ id(X82,X83)
      | id(X83,X82) ),
    inference(variable_rename,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ( id(X1,esk1_0)
    | ~ r1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    r1(esk16_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_20,plain,
    ! [X87,X88] :
      ( ( r1(X87)
        | ~ r1(X87)
        | ~ id(X87,X88) )
      & ( r1(X88)
        | ~ r1(X87)
        | ~ id(X87,X88) )
      & ( r1(X87)
        | ~ r1(X88)
        | ~ id(X87,X88) )
      & ( r1(X88)
        | ~ r1(X88)
        | ~ id(X87,X88) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_14])]) ).

cnf(c_0_21,negated_conjecture,
    ( ~ id(X1,X2)
    | ~ r4(X3,X4,X1)
    | ~ r2(X5,X3)
    | ~ r1(X6)
    | ~ r2(X6,X5)
    | ~ id(X7,X2)
    | ~ r3(X4,X8,X7) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,plain,
    r4(X1,esk16_1(X1),esk15_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_23,plain,
    ! [X121] :
      ( id(esk13_1(X121),X121)
      & r1(esk14_1(X121))
      & r3(X121,esk14_1(X121),esk13_1(X121)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).

fof(c_0_24,plain,
    ! [X84,X85,X86] :
      ( ~ id(X84,X85)
      | id(X84,X86)
      | ~ id(X85,X86) ),
    inference(variable_rename,[status(thm)],[c_0_16]) ).

cnf(c_0_25,plain,
    ( id(X2,X1)
    | ~ id(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_26,plain,
    id(esk16_1(X1),esk1_0),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_27,plain,
    ( r1(X1)
    | ~ r1(X2)
    | ~ id(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,plain,
    id(esk15_1(X1),esk17_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_29,plain,
    r1(esk17_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_30,negated_conjecture,
    ( ~ r3(esk16_1(X1),X2,X3)
    | ~ r2(X4,X5)
    | ~ r2(X5,X1)
    | ~ r1(X4)
    | ~ id(esk15_1(X1),X6)
    | ~ id(X3,X6) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_31,plain,
    r3(X1,esk14_1(X1),esk13_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_32,plain,
    ( id(X1,X3)
    | ~ id(X1,X2)
    | ~ id(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_33,plain,
    id(esk1_0,esk16_1(X1)),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_34,plain,
    r1(esk15_1(X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).

fof(c_0_35,plain,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( id(X5,X4)
        & r2(X3,X5) )
      | ( ~ r2(X3,X5)
        & ~ id(X5,X4) ) ),
    inference(fof_simplification,[status(thm)],[axiom_2]) ).

cnf(c_0_36,negated_conjecture,
    ( ~ r2(X1,X2)
    | ~ r2(X2,X3)
    | ~ r1(X1)
    | ~ id(esk13_1(esk16_1(X3)),X4)
    | ~ id(esk15_1(X3),X4) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_37,plain,
    id(esk13_1(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_38,plain,
    ( id(X1,esk16_1(X2))
    | ~ id(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,plain,
    id(esk15_1(X1),esk1_0),
    inference(spm,[status(thm)],[c_0_18,c_0_34]) ).

fof(c_0_40,plain,
    ! [X70,X72] :
      ( ( ~ r2(X70,X72)
        | id(X72,esk2_1(X70)) )
      & ( ~ id(X72,esk2_1(X70))
        | id(X72,esk2_1(X70)) )
      & ( ~ r2(X70,X72)
        | r2(X70,X72) )
      & ( ~ id(X72,esk2_1(X70))
        | r2(X70,X72) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_35])])]) ).

fof(c_0_41,plain,
    ! [X81] : id(X81,X81),
    inference(variable_rename,[status(thm)],[axiom_5]) ).

cnf(c_0_42,negated_conjecture,
    ( ~ r2(X1,X2)
    | ~ r2(X2,X3)
    | ~ r1(X1)
    | ~ id(esk15_1(X3),esk16_1(X3)) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_43,plain,
    id(esk15_1(X1),esk16_1(X2)),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_44,plain,
    ( r2(X2,X1)
    | ~ id(X1,esk2_1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_45,plain,
    id(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_46,negated_conjecture,
    ( ~ r2(X1,X2)
    | ~ r2(X2,X3)
    | ~ r1(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).

cnf(c_0_47,plain,
    r2(X1,esk2_1(X1)),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_48,negated_conjecture,
    ( ~ r2(esk2_1(X1),X2)
    | ~ r1(X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_49,plain,
    r2(X1,esk13_1(esk2_1(X1))),
    inference(spm,[status(thm)],[c_0_44,c_0_37]) ).

cnf(c_0_50,plain,
    r1(esk14_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_51,negated_conjecture,
    ~ r1(X1),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_52,plain,
    $false,
    inference(sr,[status(thm)],[c_0_50,c_0_51]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUN076+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n021.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   : Sun Aug 27 09:44:57 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.028000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.031000 s
%------------------------------------------------------------------------------