TSTP Solution File: SET200+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n018.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 14:33:36 EDT 2023

% Result   : Theorem 0.20s 0.63s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   34 (   4 unt;   9 typ;   0 def)
%            Number of atoms       :   64 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   60 (  21   ~;  26   |;   8   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   5   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   55 (   2 sgn;  22   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_26,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_27,type,
    esk3_0: $i ).

tff(decl_28,type,
    esk4_0: $i ).

tff(decl_29,type,
    esk5_0: $i ).

tff(decl_30,type,
    esk6_0: $i ).

fof(prove_th34,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( subset(X1,X2)
        & subset(X3,X4) )
     => subset(union(X1,X3),union(X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th34) ).

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

fof(union_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( subset(X1,X2)
          & subset(X3,X4) )
       => subset(union(X1,X3),union(X2,X4)) ),
    inference(assume_negation,[status(cth)],[prove_th34]) ).

fof(c_0_4,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( ~ subset(X8,X9)
        | ~ member(X10,X8)
        | member(X10,X9) )
      & ( member(esk1_2(X11,X12),X11)
        | subset(X11,X12) )
      & ( ~ member(esk1_2(X11,X12),X12)
        | subset(X11,X12) ) ),
    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_defn])])])])])]) ).

fof(c_0_5,plain,
    ! [X5,X6,X7] :
      ( ( ~ member(X7,union(X5,X6))
        | member(X7,X5)
        | member(X7,X6) )
      & ( ~ member(X7,X5)
        | member(X7,union(X5,X6)) )
      & ( ~ member(X7,X6)
        | member(X7,union(X5,X6)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).

fof(c_0_6,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    & subset(esk5_0,esk6_0)
    & ~ subset(union(esk3_0,esk5_0),union(esk4_0,esk6_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_7,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

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

cnf(c_0_9,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_10,negated_conjecture,
    subset(esk5_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,negated_conjecture,
    subset(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_13,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    ( member(X1,esk6_0)
    | ~ member(X1,esk5_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_15,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_16,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_17,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_7,c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    ( member(X1,esk4_0)
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_12]) ).

cnf(c_0_19,negated_conjecture,
    ( subset(X1,union(X2,esk6_0))
    | ~ member(esk1_2(X1,union(X2,esk6_0)),esk5_0) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_20,plain,
    ( subset(union(X1,X2),X3)
    | member(esk1_2(union(X1,X2),X3),X1)
    | member(esk1_2(union(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    ( subset(X1,union(esk4_0,X2))
    | ~ member(esk1_2(X1,union(esk4_0,X2)),esk3_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    ( subset(union(X1,esk5_0),union(X2,esk6_0))
    | member(esk1_2(union(X1,esk5_0),union(X2,esk6_0)),X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,negated_conjecture,
    ~ subset(union(esk3_0,esk5_0),union(esk4_0,esk6_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n018.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 14:27:00 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.63  % Version  : CSE_E---1.5
% 0.20/0.63  % Problem  : theBenchmark.p
% 0.20/0.63  % Proof found
% 0.20/0.63  % SZS status Theorem for theBenchmark.p
% 0.20/0.63  % SZS output start Proof
% See solution above
% 0.20/0.63  % Total time : 0.062000 s
% 0.20/0.63  % SZS output end Proof
% 0.20/0.63  % Total time : 0.065000 s
%------------------------------------------------------------------------------