TSTP Solution File: NUN062+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n010.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 12:45:47 EDT 2023

% Result   : Theorem 4.14s 4.20s
% Output   : CNFRefutation 4.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   59 (  10 unt;  27 typ;   0 def)
%            Number of atoms       :  101 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  124 (  55   ~;  42   |;  27   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  25   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   22 (  22 usr;   2 con; 0-2 aty)
%            Number of variables   :   73 (   4 sgn;  34   !;  12   ?;   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 ).

tff(decl_47,type,
    esk21_0: $i ).

tff(decl_48,type,
    esk22_2: ( $i * $i ) > $i ).

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(infiniteNumbersid,conjecture,
    ! [X38] :
    ? [X46,X63] :
      ( ! [X40] :
          ( ~ id(X63,X40)
          | ~ r1(X40) )
      & ? [X47] :
          ( id(X47,X46)
          & r3(X38,X63,X47) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',infiniteNumbersid) ).

fof(axiom_7a,axiom,
    ! [X65,X66] :
      ( ! [X67] :
          ( ~ id(X67,X66)
          | ~ r1(X67) )
      | ~ r2(X65,X66) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).

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

fof(axiom_1a,axiom,
    ! [X38,X39] :
    ? [X40] :
      ( ? [X41] :
          ( id(X41,X40)
          & ? [X42] :
              ( r2(X39,X42)
              & r3(X38,X42,X41) ) )
      & ? [X43] :
          ( r2(X43,X40)
          & r3(X38,X39,X43) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).

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(c_0_6,plain,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( id(X5,X4)
        & r2(X3,X5) )
      | ( ~ r2(X3,X5)
        & ~ id(X5,X4) ) ),
    inference(fof_simplification,[status(thm)],[axiom_2]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X38] :
      ? [X46,X63] :
        ( ! [X40] :
            ( ~ id(X63,X40)
            | ~ r1(X40) )
        & ? [X47] :
            ( id(X47,X46)
            & r3(X38,X63,X47) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[infiniteNumbersid])]) ).

fof(c_0_8,plain,
    ! [X65,X66] :
      ( ! [X67] :
          ( ~ id(X67,X66)
          | ~ r1(X67) )
      | ~ r2(X65,X66) ),
    inference(fof_simplification,[status(thm)],[axiom_7a]) ).

fof(c_0_9,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_6])])]) ).

fof(c_0_10,plain,
    ! [X81] : id(X81,X81),
    inference(variable_rename,[status(thm)],[axiom_5]) ).

fof(c_0_11,negated_conjecture,
    ! [X136,X137,X139] :
      ( ( id(X137,esk22_2(X136,X137))
        | ~ id(X139,X136)
        | ~ r3(esk21_0,X137,X139) )
      & ( r1(esk22_2(X136,X137))
        | ~ id(X139,X136)
        | ~ r3(esk21_0,X137,X139) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).

fof(c_0_12,plain,
    ! [X105,X106] :
      ( id(esk6_2(X105,X106),esk5_2(X105,X106))
      & r2(X106,esk7_2(X105,X106))
      & r3(X105,esk7_2(X105,X106),esk6_2(X105,X106))
      & r2(esk8_2(X105,X106),esk5_2(X105,X106))
      & r3(X105,X106,esk8_2(X105,X106)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).

fof(c_0_13,plain,
    ! [X132,X133,X134] :
      ( ~ id(X134,X133)
      | ~ r1(X134)
      | ~ r2(X132,X133) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).

cnf(c_0_14,plain,
    ( r2(X2,X1)
    | ~ id(X1,esk2_1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    id(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_16,plain,
    ! [X20,X21] :
      ( ~ id(X20,X21)
      | ( ~ r1(X20)
        & ~ r1(X21) )
      | ( r1(X20)
        & r1(X21) ) ),
    inference(fof_simplification,[status(thm)],[axiom_8]) ).

cnf(c_0_17,negated_conjecture,
    ( id(X1,esk22_2(X2,X1))
    | ~ id(X3,X2)
    | ~ r3(esk21_0,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    r3(X1,X2,esk8_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,negated_conjecture,
    ( r1(esk22_2(X1,X2))
    | ~ id(X3,X1)
    | ~ r3(esk21_0,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_20,plain,
    ( ~ id(X1,X2)
    | ~ r1(X1)
    | ~ r2(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    r2(X1,esk2_1(X1)),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

fof(c_0_22,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_16])]) ).

cnf(c_0_23,negated_conjecture,
    ( id(X1,esk22_2(X2,X1))
    | ~ id(esk8_2(esk21_0,X1),X2) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_24,negated_conjecture,
    ( r1(esk22_2(X1,X2))
    | ~ id(esk8_2(esk21_0,X2),X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_18]) ).

cnf(c_0_25,plain,
    ( ~ r1(X1)
    | ~ id(X1,esk2_1(X2)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    ( r1(X1)
    | ~ r1(X2)
    | ~ id(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    id(X1,esk22_2(esk8_2(esk21_0,X1),X1)),
    inference(spm,[status(thm)],[c_0_23,c_0_15]) ).

cnf(c_0_28,negated_conjecture,
    r1(esk22_2(esk8_2(esk21_0,X1),X1)),
    inference(spm,[status(thm)],[c_0_24,c_0_15]) ).

cnf(c_0_29,plain,
    ~ r1(esk2_1(X1)),
    inference(spm,[status(thm)],[c_0_25,c_0_15]) ).

cnf(c_0_30,negated_conjecture,
    r1(X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).

cnf(c_0_31,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n010.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sun Aug 27 09:03:04 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 4.14/4.20  % Version  : CSE_E---1.5
% 4.14/4.20  % Problem  : theBenchmark.p
% 4.14/4.20  % Proof found
% 4.14/4.20  % SZS status Theorem for theBenchmark.p
% 4.14/4.20  % SZS output start Proof
% See solution above
% 4.14/4.20  % Total time : 3.644000 s
% 4.14/4.20  % SZS output end Proof
% 4.14/4.20  % Total time : 3.647000 s
%------------------------------------------------------------------------------