TSTP Solution File: SEU127+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU127+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 16:22:35 EDT 2023

% Result   : Theorem 0.22s 0.71s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   36 (  10 unt;  17 typ;   0 def)
%            Number of atoms       :   55 (  11 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :   56 (  20   ~;  24   |;   8   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  12   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-3 aty)
%            Number of variables   :   48 (   4 sgn;  28   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    empty_set: $i ).

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

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

tff(decl_29,type,
    esk1_1: $i > $i ).

tff(decl_30,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_31,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_32,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_33,type,
    esk5_0: $i ).

tff(decl_34,type,
    esk6_0: $i ).

tff(decl_35,type,
    esk7_0: $i ).

tff(decl_36,type,
    esk8_0: $i ).

tff(decl_37,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk10_2: ( $i * $i ) > $i ).

fof(d3_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_intersection2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

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(t17_xboole_1,conjecture,
    ! [X1,X2] : subset(set_intersection2(X1,X2),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(c_0_4,plain,
    ! [X32,X33,X34,X35,X36,X37,X38,X39] :
      ( ( in(X35,X32)
        | ~ in(X35,X34)
        | X34 != set_intersection2(X32,X33) )
      & ( in(X35,X33)
        | ~ in(X35,X34)
        | X34 != set_intersection2(X32,X33) )
      & ( ~ in(X36,X32)
        | ~ in(X36,X33)
        | in(X36,X34)
        | X34 != set_intersection2(X32,X33) )
      & ( ~ in(esk4_3(X37,X38,X39),X39)
        | ~ in(esk4_3(X37,X38,X39),X37)
        | ~ in(esk4_3(X37,X38,X39),X38)
        | X39 = set_intersection2(X37,X38) )
      & ( in(esk4_3(X37,X38,X39),X37)
        | in(esk4_3(X37,X38,X39),X39)
        | X39 = set_intersection2(X37,X38) )
      & ( in(esk4_3(X37,X38,X39),X38)
        | in(esk4_3(X37,X38,X39),X39)
        | X39 = set_intersection2(X37,X38) ) ),
    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_xboole_0])])])])])]) ).

cnf(c_0_5,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_intersection2(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

fof(c_0_6,plain,
    ! [X26,X27,X28,X29,X30] :
      ( ( ~ subset(X26,X27)
        | ~ in(X28,X26)
        | in(X28,X27) )
      & ( in(esk3_2(X29,X30),X29)
        | subset(X29,X30) )
      & ( ~ in(esk3_2(X29,X30),X30)
        | subset(X29,X30) ) ),
    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_7,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X3,X2)) ),
    inference(er,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    ( in(esk3_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X1,X2] : subset(set_intersection2(X1,X2),X1),
    inference(assume_negation,[status(cth)],[t17_xboole_1]) ).

cnf(c_0_10,plain,
    ( subset(X1,X2)
    | ~ in(esk3_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( subset(set_intersection2(X1,X2),X3)
    | in(esk3_2(set_intersection2(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

fof(c_0_12,plain,
    ! [X9,X10] : set_intersection2(X9,X10) = set_intersection2(X10,X9),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

fof(c_0_13,negated_conjecture,
    ~ subset(set_intersection2(esk7_0,esk8_0),esk7_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

cnf(c_0_14,plain,
    subset(set_intersection2(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,negated_conjecture,
    ~ subset(set_intersection2(esk7_0,esk8_0),esk7_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    subset(set_intersection2(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem    : SEU127+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36  % Computer : n004.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Wed Aug 23 16:40:38 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.22/0.65  start to proof: theBenchmark
% 0.22/0.71  % Version  : CSE_E---1.5
% 0.22/0.71  % Problem  : theBenchmark.p
% 0.22/0.71  % Proof found
% 0.22/0.71  % SZS status Theorem for theBenchmark.p
% 0.22/0.71  % SZS output start Proof
% See solution above
% 0.22/0.71  % Total time : 0.054000 s
% 0.22/0.71  % SZS output end Proof
% 0.22/0.71  % Total time : 0.057000 s
%------------------------------------------------------------------------------