TSTP Solution File: SET201+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET201+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n025.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 0.19s 0.75s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   42 (  10 unt;   9 typ;   0 def)
%            Number of atoms       :   74 (   3 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   66 (  25   ~;  27   |;   9   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 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  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   64 (   6 sgn;  26   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    intersection: ( $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_th41,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( subset(X1,X2)
        & subset(X3,X4) )
     => subset(intersection(X1,X3),intersection(X2,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th41) ).

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

fof(intersection_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).

fof(commutativity_of_intersection,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( subset(X1,X2)
          & subset(X3,X4) )
       => subset(intersection(X1,X3),intersection(X2,X4)) ),
    inference(assume_negation,[status(cth)],[prove_th41]) ).

fof(c_0_5,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_6,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    & subset(esk5_0,esk6_0)
    & ~ subset(intersection(esk3_0,esk5_0),intersection(esk4_0,esk6_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_7,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    subset(esk5_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X5,X6,X7] :
      ( ( member(X7,X5)
        | ~ member(X7,intersection(X5,X6)) )
      & ( member(X7,X6)
        | ~ member(X7,intersection(X5,X6)) )
      & ( ~ member(X7,X5)
        | ~ member(X7,X6)
        | member(X7,intersection(X5,X6)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).

cnf(c_0_10,negated_conjecture,
    subset(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,negated_conjecture,
    ( member(X1,esk6_0)
    | ~ member(X1,esk5_0) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_13,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_15,negated_conjecture,
    ( member(X1,esk4_0)
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_7,c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    ( subset(X1,esk6_0)
    | ~ member(esk1_2(X1,esk6_0),esk5_0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,plain,
    ( subset(intersection(X1,X2),X3)
    | member(esk1_2(intersection(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    ( subset(X1,esk4_0)
    | ~ member(esk1_2(X1,esk4_0),esk3_0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_15]) ).

fof(c_0_19,plain,
    ! [X14,X15] : intersection(X14,X15) = intersection(X15,X14),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

cnf(c_0_20,negated_conjecture,
    subset(intersection(X1,esk5_0),esk6_0),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    subset(intersection(X1,esk3_0),esk4_0),
    inference(spm,[status(thm)],[c_0_18,c_0_17]) ).

cnf(c_0_22,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_23,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_24,negated_conjecture,
    ( member(X1,esk6_0)
    | ~ member(X1,intersection(X2,esk5_0)) ),
    inference(spm,[status(thm)],[c_0_7,c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    subset(intersection(esk3_0,X1),esk4_0),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,plain,
    ( subset(X1,intersection(X2,X3))
    | ~ member(esk1_2(X1,intersection(X2,X3)),X3)
    | ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    ( subset(intersection(X1,esk5_0),X2)
    | member(esk1_2(intersection(X1,esk5_0),X2),esk6_0) ),
    inference(spm,[status(thm)],[c_0_24,c_0_14]) ).

cnf(c_0_28,negated_conjecture,
    ( member(X1,esk4_0)
    | ~ member(X1,intersection(esk3_0,X2)) ),
    inference(spm,[status(thm)],[c_0_7,c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    ( subset(intersection(X1,esk5_0),intersection(X2,esk6_0))
    | ~ member(esk1_2(intersection(X1,esk5_0),intersection(X2,esk6_0)),X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    ( subset(intersection(esk3_0,X1),X2)
    | member(esk1_2(intersection(esk3_0,X1),X2),esk4_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_14]) ).

cnf(c_0_31,negated_conjecture,
    ~ subset(intersection(esk3_0,esk5_0),intersection(esk4_0,esk6_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_32,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET201+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n025.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   : Sat Aug 26 08:58:37 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.59  start to proof: theBenchmark
% 0.19/0.75  % Version  : CSE_E---1.5
% 0.19/0.75  % Problem  : theBenchmark.p
% 0.19/0.75  % Proof found
% 0.19/0.75  % SZS status Theorem for theBenchmark.p
% 0.19/0.75  % SZS output start Proof
% See solution above
% 0.19/0.75  % Total time : 0.153000 s
% 0.19/0.75  % SZS output end Proof
% 0.19/0.75  % Total time : 0.156000 s
%------------------------------------------------------------------------------