TSTP Solution File: SET934+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET934+1 : 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 : 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 14:36:21 EDT 2023

% Result   : Theorem 153.20s 153.16s
% Output   : CNFRefutation 153.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   67 (  18 unt;  12 typ;   0 def)
%            Number of atoms       :  139 (  18 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :  135 (  51   ~;  66   |;  11   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   8   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :  148 (  10 sgn;  47   !;   0   ?;   0   :)

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

tff(decl_23,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_24,type,
    powerset: $i > $i ).

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

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

tff(decl_27,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk2_3: ( $i * $i * $i ) > $i ).

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

tff(decl_30,type,
    esk4_0: $i ).

tff(decl_31,type,
    esk5_0: $i ).

tff(decl_32,type,
    esk6_0: $i ).

tff(decl_33,type,
    esk7_0: $i ).

fof(d1_zfmisc_1,axiom,
    ! [X1,X2] :
      ( X2 = powerset(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> subset(X3,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(t1_xboole_1,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X2,X3) )
     => subset(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

fof(t7_xboole_1,axiom,
    ! [X1,X2] : subset(X1,set_union2(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).

fof(d2_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_union2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            | in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(commutativity_k2_xboole_0,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(t81_zfmisc_1,conjecture,
    ! [X1,X2] : subset(set_union2(powerset(X1),powerset(X2)),powerset(set_union2(X1,X2))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).

fof(c_0_7,plain,
    ! [X9,X10,X11,X12,X13,X14] :
      ( ( ~ in(X11,X10)
        | subset(X11,X9)
        | X10 != powerset(X9) )
      & ( ~ subset(X12,X9)
        | in(X12,X10)
        | X10 != powerset(X9) )
      & ( ~ in(esk1_2(X13,X14),X14)
        | ~ subset(esk1_2(X13,X14),X13)
        | X14 = powerset(X13) )
      & ( in(esk1_2(X13,X14),X14)
        | subset(esk1_2(X13,X14),X13)
        | X14 = powerset(X13) ) ),
    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)],[d1_zfmisc_1])])])])])]) ).

fof(c_0_8,plain,
    ! [X25,X26,X27,X28,X29] :
      ( ( ~ subset(X25,X26)
        | ~ in(X27,X25)
        | in(X27,X26) )
      & ( in(esk3_2(X28,X29),X28)
        | subset(X28,X29) )
      & ( ~ in(esk3_2(X28,X29),X29)
        | subset(X28,X29) ) ),
    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)],[d3_tarski])])])])])]) ).

cnf(c_0_9,plain,
    ( in(X1,X3)
    | ~ subset(X1,X2)
    | X3 != powerset(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,plain,
    ! [X39,X40,X41] :
      ( ~ subset(X39,X40)
      | ~ subset(X40,X41)
      | subset(X39,X41) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).

fof(c_0_11,plain,
    ! [X42,X43] : subset(X42,set_union2(X42,X43)),
    inference(variable_rename,[status(thm)],[t7_xboole_1]) ).

fof(c_0_12,plain,
    ! [X16,X17,X18,X19,X20,X21,X22,X23] :
      ( ( ~ in(X19,X18)
        | in(X19,X16)
        | in(X19,X17)
        | X18 != set_union2(X16,X17) )
      & ( ~ in(X20,X16)
        | in(X20,X18)
        | X18 != set_union2(X16,X17) )
      & ( ~ in(X20,X17)
        | in(X20,X18)
        | X18 != set_union2(X16,X17) )
      & ( ~ in(esk2_3(X21,X22,X23),X21)
        | ~ in(esk2_3(X21,X22,X23),X23)
        | X23 = set_union2(X21,X22) )
      & ( ~ in(esk2_3(X21,X22,X23),X22)
        | ~ in(esk2_3(X21,X22,X23),X23)
        | X23 = set_union2(X21,X22) )
      & ( in(esk2_3(X21,X22,X23),X23)
        | in(esk2_3(X21,X22,X23),X21)
        | in(esk2_3(X21,X22,X23),X22)
        | X23 = set_union2(X21,X22) ) ),
    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)],[d2_xboole_0])])])])])]) ).

fof(c_0_13,plain,
    ! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
    inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).

cnf(c_0_14,plain,
    ( subset(X1,X2)
    | ~ in(esk3_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,plain,
    ( in(X1,powerset(X2))
    | ~ subset(X1,X2) ),
    inference(er,[status(thm)],[c_0_9]) ).

cnf(c_0_16,plain,
    ( subset(X1,X3)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    subset(X1,set_union2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ( subset(X1,X3)
    | ~ in(X1,X2)
    | X2 != powerset(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_19,plain,
    ( in(X1,X3)
    | in(X1,X4)
    | ~ in(X1,X2)
    | X2 != set_union2(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_22,plain,
    ( subset(X1,powerset(X2))
    | ~ subset(esk3_2(X1,powerset(X2)),X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_23,plain,
    ( subset(X1,set_union2(X2,X3))
    | ~ subset(X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_24,plain,
    ( subset(X1,X2)
    | ~ in(X1,powerset(X2)) ),
    inference(er,[status(thm)],[c_0_18]) ).

cnf(c_0_25,plain,
    ( in(esk3_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_26,plain,
    ( in(X1,X2)
    | in(X1,X3)
    | ~ in(X1,set_union2(X3,X2)) ),
    inference(er,[status(thm)],[c_0_19]) ).

cnf(c_0_27,plain,
    subset(X1,set_union2(X2,X1)),
    inference(spm,[status(thm)],[c_0_17,c_0_20]) ).

cnf(c_0_28,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[c_0_21,c_0_17]) ).

cnf(c_0_29,plain,
    ( subset(X1,powerset(set_union2(X2,X3)))
    | ~ subset(esk3_2(X1,powerset(set_union2(X2,X3))),X2) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_30,plain,
    ( subset(esk3_2(powerset(X1),X2),X1)
    | subset(powerset(X1),X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_31,plain,
    ( subset(set_union2(X1,X2),X3)
    | in(esk3_2(set_union2(X1,X2),X3),X1)
    | in(esk3_2(set_union2(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_25]) ).

cnf(c_0_32,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_27]) ).

cnf(c_0_33,plain,
    ( subset(X1,set_union2(X2,X3))
    | ~ in(esk3_2(X1,set_union2(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_28]) ).

cnf(c_0_34,plain,
    subset(powerset(X1),powerset(set_union2(X1,X2))),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_35,plain,
    ( subset(X1,set_union2(X2,X3))
    | ~ subset(X1,X3) ),
    inference(spm,[status(thm)],[c_0_16,c_0_27]) ).

cnf(c_0_36,plain,
    ( subset(set_union2(X1,X2),X2)
    | in(esk3_2(set_union2(X1,X2),X2),X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_31]) ).

cnf(c_0_37,plain,
    ( subset(X1,set_union2(X2,X3))
    | ~ in(esk3_2(X1,set_union2(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_14,c_0_32]) ).

cnf(c_0_38,plain,
    ( subset(set_union2(X1,X2),set_union2(X2,X3))
    | in(esk3_2(set_union2(X1,X2),set_union2(X2,X3)),X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_31]) ).

cnf(c_0_39,plain,
    ( in(X1,powerset(set_union2(X2,X3)))
    | ~ in(X1,powerset(X2)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_34]) ).

cnf(c_0_40,plain,
    ( subset(X1,powerset(set_union2(X2,X3)))
    | ~ subset(esk3_2(X1,powerset(set_union2(X2,X3))),X3) ),
    inference(spm,[status(thm)],[c_0_22,c_0_35]) ).

cnf(c_0_41,plain,
    ( subset(esk3_2(set_union2(powerset(X1),X2),X2),X1)
    | subset(set_union2(powerset(X1),X2),X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_36]) ).

cnf(c_0_42,plain,
    subset(set_union2(X1,X2),set_union2(X2,X1)),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_43,plain,
    ( subset(X1,set_union2(powerset(set_union2(X2,X3)),X4))
    | ~ in(esk3_2(X1,set_union2(powerset(set_union2(X2,X3)),X4)),powerset(X2)) ),
    inference(spm,[status(thm)],[c_0_33,c_0_39]) ).

cnf(c_0_44,plain,
    ( subset(set_union2(X1,X2),set_union2(X3,X2))
    | in(esk3_2(set_union2(X1,X2),set_union2(X3,X2)),X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_31]) ).

fof(c_0_45,negated_conjecture,
    ~ ! [X1,X2] : subset(set_union2(powerset(X1),powerset(X2)),powerset(set_union2(X1,X2))),
    inference(assume_negation,[status(cth)],[t81_zfmisc_1]) ).

cnf(c_0_46,plain,
    subset(set_union2(powerset(X1),powerset(set_union2(X2,X1))),powerset(set_union2(X2,X1))),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_47,plain,
    ( subset(X1,set_union2(X2,X3))
    | ~ subset(X1,set_union2(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_16,c_0_42]) ).

cnf(c_0_48,plain,
    subset(set_union2(powerset(X1),X2),set_union2(powerset(set_union2(X1,X3)),X2)),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

fof(c_0_49,negated_conjecture,
    ~ subset(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).

cnf(c_0_50,plain,
    ( subset(X1,powerset(set_union2(X2,X3)))
    | ~ subset(X1,set_union2(powerset(X3),powerset(set_union2(X2,X3)))) ),
    inference(spm,[status(thm)],[c_0_16,c_0_46]) ).

cnf(c_0_51,plain,
    subset(set_union2(powerset(X1),X2),set_union2(X2,powerset(set_union2(X1,X3)))),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_52,negated_conjecture,
    ~ subset(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_53,plain,
    subset(set_union2(powerset(X1),powerset(X2)),powerset(set_union2(X1,X2))),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_54,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET934+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/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 16:23:41 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 153.20/153.16  % Version  : CSE_E---1.5
% 153.20/153.16  % Problem  : theBenchmark.p
% 153.20/153.16  % Proof found
% 153.20/153.16  % SZS status Theorem for theBenchmark.p
% 153.20/153.16  % SZS output start Proof
% See solution above
% 153.20/153.17  % Total time : 152.600000 s
% 153.20/153.17  % SZS output end Proof
% 153.20/153.17  % Total time : 152.611000 s
%------------------------------------------------------------------------------