TSTP Solution File: SET804+4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET804+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n007.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 14:35:37 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   58 (   9 unt;  34 typ;   0 def)
%            Number of atoms       :   80 (  11 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :   90 (  34   ~;  30   |;  18   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   79 (  29   >;  50   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-4 aty)
%            Number of functors    :   21 (  21 usr;   5 con; 0-4 aty)
%            Number of variables   :   50 (   2 sgn;  30   !;   2   ?;   0   :)

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

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

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

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

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

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

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

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

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

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

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

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

tff(decl_34,type,
    epred1_2: ( $i * $i ) > $o ).

tff(decl_35,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_38,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_40,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_41,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_42,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk9_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk10_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk11_0: $i ).

tff(decl_46,type,
    esk12_0: $i ).

tff(decl_47,type,
    esk13_0: $i ).

tff(decl_48,type,
    esk14_0: $i ).

tff(decl_49,type,
    esk15_0: $i ).

tff(decl_50,type,
    esk16_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk20_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk21_2: ( $i * $i ) > $i ).

fof(thIV16,conjecture,
    ! [X1,X2] :
      ( order(X1,X2)
     => ! [X8,X9] :
          ( ( min(X8,X1,X2)
            & min(X9,X1,X2)
            & X8 != X9 )
         => ~ ? [X6] : least(X6,X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV16) ).

fof(min,axiom,
    ! [X1,X2,X6] :
      ( min(X6,X1,X2)
    <=> ( member(X6,X2)
        & ! [X3] :
            ( ( member(X3,X2)
              & apply(X1,X3,X6) )
           => X6 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',min) ).

fof(least,axiom,
    ! [X1,X2,X6] :
      ( least(X6,X1,X2)
    <=> ( member(X6,X2)
        & ! [X3] :
            ( member(X3,X2)
           => apply(X1,X6,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',least) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
        ( order(X1,X2)
       => ! [X8,X9] :
            ( ( min(X8,X1,X2)
              & min(X9,X1,X2)
              & X8 != X9 )
           => ~ ? [X6] : least(X6,X1,X2) ) ),
    inference(assume_negation,[status(cth)],[thIV16]) ).

fof(c_0_4,plain,
    ! [X60,X61,X62,X63,X64,X65,X66] :
      ( ( member(X62,X61)
        | ~ min(X62,X60,X61) )
      & ( ~ member(X63,X61)
        | ~ apply(X60,X63,X62)
        | X62 = X63
        | ~ min(X62,X60,X61) )
      & ( member(esk8_3(X64,X65,X66),X65)
        | ~ member(X66,X65)
        | min(X66,X64,X65) )
      & ( apply(X64,esk8_3(X64,X65,X66),X66)
        | ~ member(X66,X65)
        | min(X66,X64,X65) )
      & ( X66 != esk8_3(X64,X65,X66)
        | ~ member(X66,X65)
        | min(X66,X64,X65) ) ),
    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)],[min])])])])])]) ).

fof(c_0_5,negated_conjecture,
    ( order(esk11_0,esk12_0)
    & min(esk13_0,esk11_0,esk12_0)
    & min(esk14_0,esk11_0,esk12_0)
    & esk13_0 != esk14_0
    & least(esk15_0,esk11_0,esk12_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_6,plain,
    ! [X44,X45,X46,X47,X48,X49,X50] :
      ( ( member(X46,X45)
        | ~ least(X46,X44,X45) )
      & ( ~ member(X47,X45)
        | apply(X44,X46,X47)
        | ~ least(X46,X44,X45) )
      & ( member(esk6_3(X48,X49,X50),X49)
        | ~ member(X50,X49)
        | least(X50,X48,X49) )
      & ( ~ apply(X48,X50,esk6_3(X48,X49,X50))
        | ~ member(X50,X49)
        | least(X50,X48,X49) ) ),
    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)],[least])])])])])]) ).

cnf(c_0_7,plain,
    ( X4 = X1
    | ~ member(X1,X2)
    | ~ apply(X3,X1,X4)
    | ~ min(X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    min(esk14_0,esk11_0,esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( apply(X3,X4,X1)
    | ~ member(X1,X2)
    | ~ least(X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    least(esk15_0,esk11_0,esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,plain,
    ( member(X1,X2)
    | ~ least(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,plain,
    ( member(X1,X2)
    | ~ min(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_13,negated_conjecture,
    ( X1 = esk14_0
    | ~ apply(esk11_0,X1,esk14_0)
    | ~ member(X1,esk12_0) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    ( apply(esk11_0,esk15_0,X1)
    | ~ member(X1,esk12_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    member(esk15_0,esk12_0),
    inference(spm,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    member(esk14_0,esk12_0),
    inference(spm,[status(thm)],[c_0_12,c_0_8]) ).

cnf(c_0_17,negated_conjecture,
    min(esk13_0,esk11_0,esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_18,negated_conjecture,
    esk15_0 = esk14_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).

cnf(c_0_19,negated_conjecture,
    ( X1 = esk13_0
    | ~ apply(esk11_0,X1,esk13_0)
    | ~ member(X1,esk12_0) ),
    inference(spm,[status(thm)],[c_0_7,c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    ( apply(esk11_0,esk14_0,X1)
    | ~ member(X1,esk12_0) ),
    inference(rw,[status(thm)],[c_0_14,c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    member(esk13_0,esk12_0),
    inference(spm,[status(thm)],[c_0_12,c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    esk13_0 != esk14_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_23,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16]),c_0_21])]),c_0_22]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET804+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n007.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   : Sat Aug 26 12:09:11 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.59  start to proof: theBenchmark
% 0.20/0.61  % Version  : CSE_E---1.5
% 0.20/0.61  % Problem  : theBenchmark.p
% 0.20/0.61  % Proof found
% 0.20/0.61  % SZS status Theorem for theBenchmark.p
% 0.20/0.61  % SZS output start Proof
% See solution above
% 0.20/0.62  % Total time : 0.019000 s
% 0.20/0.62  % SZS output end Proof
% 0.20/0.62  % Total time : 0.022000 s
%------------------------------------------------------------------------------