TSTP Solution File: SET814+4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET814+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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 14:35:39 EDT 2023

% Result   : Theorem 152.58s 152.55s
% Output   : CNFRefutation 152.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   64 (   4 unt;  35 typ;   0 def)
%            Number of atoms       :   92 (   0 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  104 (  41   ~;  42   |;  13   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   60 (  31   >;  29   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   27 (  27 usr;   4 con; 0-3 aty)
%            Number of variables   :   59 (   0 sgn;  28   !;   1   ?;   0   :)

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

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

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

tff(decl_25,type,
    power_set: $i > $i ).

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

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

tff(decl_28,type,
    empty_set: $i ).

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

tff(decl_30,type,
    singleton: $i > $i ).

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

tff(decl_32,type,
    sum: $i > $i ).

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

tff(decl_34,type,
    on: $i ).

tff(decl_35,type,
    set: $i > $o ).

tff(decl_36,type,
    member_predicate: $i ).

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

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

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

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

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

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

tff(decl_43,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_44,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_45,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_46,type,
    esk4_1: $i > $i ).

tff(decl_47,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk14_0: $i ).

fof(thI3,axiom,
    ! [X1,X2,X9] :
      ( ( subset(X1,X2)
        & subset(X2,X9) )
     => subset(X1,X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI3) ).

fof(ordinal_number,axiom,
    ! [X1] :
      ( member(X1,on)
    <=> ( set(X1)
        & strict_well_order(member_predicate,X1)
        & ! [X3] :
            ( member(X3,X1)
           => subset(X3,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',ordinal_number) ).

fof(thV14,conjecture,
    ! [X1] :
      ( member(X1,on)
     => subset(sum(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV14) ).

fof(sum,axiom,
    ! [X3,X1] :
      ( member(X3,sum(X1))
    <=> ? [X5] :
          ( member(X5,X1)
          & member(X3,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).

fof(subset,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).

fof(c_0_5,plain,
    ! [X93,X94,X95] :
      ( ~ subset(X93,X94)
      | ~ subset(X94,X95)
      | subset(X93,X95) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thI3])]) ).

fof(c_0_6,plain,
    ! [X47,X48,X49] :
      ( ( set(X47)
        | ~ member(X47,on) )
      & ( strict_well_order(member_predicate,X47)
        | ~ member(X47,on) )
      & ( ~ member(X48,X47)
        | subset(X48,X47)
        | ~ member(X47,on) )
      & ( member(esk4_1(X49),X49)
        | ~ set(X49)
        | ~ strict_well_order(member_predicate,X49)
        | member(X49,on) )
      & ( ~ subset(esk4_1(X49),X49)
        | ~ set(X49)
        | ~ strict_well_order(member_predicate,X49)
        | member(X49,on) ) ),
    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)],[ordinal_number])])])])])]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1] :
        ( member(X1,on)
       => subset(sum(X1),X1) ),
    inference(assume_negation,[status(cth)],[thV14]) ).

cnf(c_0_8,plain,
    ( subset(X1,X3)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( subset(X1,X2)
    | ~ member(X1,X2)
    | ~ member(X2,on) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_10,negated_conjecture,
    ( member(esk14_0,on)
    & ~ subset(sum(esk14_0),esk14_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_11,plain,
    ( subset(X1,X2)
    | ~ member(X2,on)
    | ~ member(X3,X2)
    | ~ subset(X1,X3) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    member(esk14_0,on),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_13,plain,
    ! [X35,X36,X38,X39,X40] :
      ( ( member(esk2_2(X35,X36),X36)
        | ~ member(X35,sum(X36)) )
      & ( member(X35,esk2_2(X35,X36))
        | ~ member(X35,sum(X36)) )
      & ( ~ member(X40,X39)
        | ~ member(X38,X40)
        | member(X38,sum(X39)) ) ),
    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)],[sum])])])])])]) ).

fof(c_0_14,plain,
    ! [X10,X11,X12,X13,X14] :
      ( ( ~ subset(X10,X11)
        | ~ member(X12,X10)
        | member(X12,X11) )
      & ( member(esk1_2(X13,X14),X13)
        | subset(X13,X14) )
      & ( ~ member(esk1_2(X13,X14),X14)
        | subset(X13,X14) ) ),
    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)],[subset])])])])])]) ).

cnf(c_0_15,negated_conjecture,
    ( subset(X1,esk14_0)
    | ~ member(X2,esk14_0)
    | ~ subset(X1,X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,plain,
    ( member(esk2_2(X1,X2),X2)
    | ~ member(X1,sum(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,plain,
    ( member(X1,esk2_2(X1,X2))
    | ~ member(X1,sum(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,negated_conjecture,
    ( subset(X1,esk14_0)
    | ~ member(X2,sum(esk14_0))
    | ~ subset(X1,esk2_2(X2,esk14_0)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_22,plain,
    subset(X1,X1),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,plain,
    ( member(X1,X2)
    | ~ member(X1,sum(X3))
    | ~ subset(esk2_2(X1,X3),X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,negated_conjecture,
    ( subset(esk2_2(X1,esk14_0),esk14_0)
    | ~ member(X1,sum(esk14_0)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_25,negated_conjecture,
    ( member(X1,esk14_0)
    | ~ member(X1,sum(esk14_0)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_26,negated_conjecture,
    ( member(esk1_2(sum(esk14_0),X1),esk14_0)
    | subset(sum(esk14_0),X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_18]) ).

cnf(c_0_27,negated_conjecture,
    ~ subset(sum(esk14_0),esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_26]),c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET814+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n008.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 12:40:32 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 152.58/152.55  % Version  : CSE_E---1.5
% 152.58/152.55  % Problem  : theBenchmark.p
% 152.58/152.55  % Proof found
% 152.58/152.55  % SZS status Theorem for theBenchmark.p
% 152.58/152.55  % SZS output start Proof
% See solution above
% 152.58/152.55  % Total time : 151.983000 s
% 152.58/152.55  % SZS output end Proof
% 152.58/152.55  % Total time : 151.993000 s
%------------------------------------------------------------------------------