TSTP Solution File: SET974+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET974+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 : n009.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 14:36:29 EDT 2023

% Result   : Theorem 0.60s 0.64s
% Output   : CNFRefutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   38 (   4 unt;  17 typ;   0 def)
%            Number of atoms       :   53 (   2 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   61 (  29   ~;  17   |;  13   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  11   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-5 aty)
%            Number of variables   :   66 (  11 sgn;  31   !;   2   ?;   0   :)

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

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

tff(decl_24,type,
    set_intersection2: ( $i * $i ) > $i ).

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

tff(decl_26,type,
    singleton: $i > $i ).

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

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

tff(decl_29,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk1_0: $i ).

tff(decl_31,type,
    esk2_0: $i ).

tff(decl_32,type,
    esk3_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_33,type,
    esk4_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_34,type,
    esk5_0: $i ).

tff(decl_35,type,
    esk6_0: $i ).

tff(decl_36,type,
    esk7_0: $i ).

tff(decl_37,type,
    esk8_0: $i ).

tff(decl_38,type,
    esk9_2: ( $i * $i ) > $i ).

fof(t4_xboole_0,axiom,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).

fof(t104_zfmisc_1,axiom,
    ! [X1,X2,X3,X4,X5] :
      ~ ( in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5)))
        & ! [X6,X7] :
            ~ ( X1 = ordered_pair(X6,X7)
              & in(X6,set_intersection2(X2,X4))
              & in(X7,set_intersection2(X3,X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).

fof(t127_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( disjoint(X1,X2)
        | disjoint(X3,X4) )
     => disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).

fof(c_0_3,plain,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).

fof(c_0_4,plain,
    ! [X34,X35,X37,X38,X39] :
      ( ( disjoint(X34,X35)
        | in(esk9_2(X34,X35),set_intersection2(X34,X35)) )
      & ( ~ in(X39,set_intersection2(X37,X38))
        | ~ disjoint(X37,X38) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).

fof(c_0_5,plain,
    ! [X23,X24,X25,X26,X27] :
      ( ( X23 = ordered_pair(esk3_5(X23,X24,X25,X26,X27),esk4_5(X23,X24,X25,X26,X27))
        | ~ in(X23,set_intersection2(cartesian_product2(X24,X25),cartesian_product2(X26,X27))) )
      & ( in(esk3_5(X23,X24,X25,X26,X27),set_intersection2(X24,X26))
        | ~ in(X23,set_intersection2(cartesian_product2(X24,X25),cartesian_product2(X26,X27))) )
      & ( in(esk4_5(X23,X24,X25,X26,X27),set_intersection2(X25,X27))
        | ~ in(X23,set_intersection2(cartesian_product2(X24,X25),cartesian_product2(X26,X27))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t104_zfmisc_1])])])]) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( disjoint(X1,X2)
          | disjoint(X3,X4) )
       => disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    inference(assume_negation,[status(cth)],[t127_zfmisc_1]) ).

cnf(c_0_7,plain,
    ( ~ in(X1,set_intersection2(X2,X3))
    | ~ disjoint(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    ( in(esk3_5(X1,X2,X3,X4,X5),set_intersection2(X2,X4))
    | ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_9,negated_conjecture,
    ( ( disjoint(esk5_0,esk6_0)
      | disjoint(esk7_0,esk8_0) )
    & ~ disjoint(cartesian_product2(esk5_0,esk7_0),cartesian_product2(esk6_0,esk8_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

cnf(c_0_10,plain,
    ( ~ disjoint(X1,X2)
    | ~ in(X3,set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X5))) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    ( disjoint(X1,X2)
    | in(esk9_2(X1,X2),set_intersection2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_12,plain,
    ( in(esk4_5(X1,X2,X3,X4,X5),set_intersection2(X3,X5))
    | ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_13,negated_conjecture,
    ~ disjoint(cartesian_product2(esk5_0,esk7_0),cartesian_product2(esk6_0,esk8_0)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
    | ~ disjoint(X1,X3) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,plain,
    ( ~ disjoint(X1,X2)
    | ~ in(X3,set_intersection2(cartesian_product2(X4,X1),cartesian_product2(X5,X2))) ),
    inference(spm,[status(thm)],[c_0_7,c_0_12]) ).

cnf(c_0_16,negated_conjecture,
    ( disjoint(esk5_0,esk6_0)
    | disjoint(esk7_0,esk8_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_17,negated_conjecture,
    ~ disjoint(esk5_0,esk6_0),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,plain,
    ( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
    | ~ disjoint(X2,X4) ),
    inference(spm,[status(thm)],[c_0_15,c_0_11]) ).

cnf(c_0_19,negated_conjecture,
    disjoint(esk7_0,esk8_0),
    inference(sr,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_19])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat Aug 26 12:39:50 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.50/0.62  start to proof: theBenchmark
% 0.60/0.64  % Version  : CSE_E---1.5
% 0.60/0.64  % Problem  : theBenchmark.p
% 0.60/0.64  % Proof found
% 0.60/0.64  % SZS status Theorem for theBenchmark.p
% 0.60/0.64  % SZS output start Proof
% See solution above
% 0.60/0.65  % Total time : 0.009000 s
% 0.60/0.65  % SZS output end Proof
% 0.60/0.65  % Total time : 0.011000 s
%------------------------------------------------------------------------------