TSTP Solution File: SEU224+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU224+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n001.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 16:23:31 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   61 (  10 unt;  26 typ;   0 def)
%            Number of atoms       :  142 (  28 equ)
%            Maximal formula atoms :   27 (   4 avg)
%            Number of connectives :  176 (  69   ~;  72   |;  23   &)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  14   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  12 con; 0-3 aty)
%            Number of variables   :   70 (   6 sgn;  38   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

tff(decl_31,type,
    relation_empty_yielding: $i > $o ).

tff(decl_32,type,
    relation_dom: $i > $i ).

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

tff(decl_34,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_35,type,
    esk2_1: $i > $i ).

tff(decl_36,type,
    esk3_0: $i ).

tff(decl_37,type,
    esk4_0: $i ).

tff(decl_38,type,
    esk5_0: $i ).

tff(decl_39,type,
    esk6_0: $i ).

tff(decl_40,type,
    esk7_0: $i ).

tff(decl_41,type,
    esk8_0: $i ).

tff(decl_42,type,
    esk9_0: $i ).

tff(decl_43,type,
    esk10_0: $i ).

tff(decl_44,type,
    esk11_0: $i ).

tff(decl_45,type,
    esk12_0: $i ).

tff(decl_46,type,
    esk13_0: $i ).

tff(decl_47,type,
    esk14_3: ( $i * $i * $i ) > $i ).

fof(l82_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
      <=> ( in(X2,relation_dom(X3))
          & in(X2,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).

fof(t68_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( X2 = relation_dom_restriction(X3,X1)
          <=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
              & ! [X4] :
                  ( in(X4,relation_dom(X2))
                 => apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).

fof(fc4_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & function(X1) )
     => ( relation(relation_dom_restriction(X1,X2))
        & function(relation_dom_restriction(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).

fof(dt_k7_relat_1,axiom,
    ! [X1,X2] :
      ( relation(X1)
     => relation(relation_dom_restriction(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).

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/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

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

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
        <=> ( in(X2,relation_dom(X3))
            & in(X2,X1) ) ) ),
    inference(assume_negation,[status(cth)],[l82_funct_1]) ).

fof(c_0_7,plain,
    ! [X50,X51,X52,X53] :
      ( ( relation_dom(X51) = set_intersection2(relation_dom(X52),X50)
        | X51 != relation_dom_restriction(X52,X50)
        | ~ relation(X52)
        | ~ function(X52)
        | ~ relation(X51)
        | ~ function(X51) )
      & ( ~ in(X53,relation_dom(X51))
        | apply(X51,X53) = apply(X52,X53)
        | X51 != relation_dom_restriction(X52,X50)
        | ~ relation(X52)
        | ~ function(X52)
        | ~ relation(X51)
        | ~ function(X51) )
      & ( in(esk14_3(X50,X51,X52),relation_dom(X51))
        | relation_dom(X51) != set_intersection2(relation_dom(X52),X50)
        | X51 = relation_dom_restriction(X52,X50)
        | ~ relation(X52)
        | ~ function(X52)
        | ~ relation(X51)
        | ~ function(X51) )
      & ( apply(X51,esk14_3(X50,X51,X52)) != apply(X52,esk14_3(X50,X51,X52))
        | relation_dom(X51) != set_intersection2(relation_dom(X52),X50)
        | X51 = relation_dom_restriction(X52,X50)
        | ~ relation(X52)
        | ~ function(X52)
        | ~ relation(X51)
        | ~ function(X51) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_funct_1])])])])]) ).

fof(c_0_8,plain,
    ! [X29,X30] :
      ( ( relation(relation_dom_restriction(X29,X30))
        | ~ relation(X29)
        | ~ function(X29) )
      & ( function(relation_dom_restriction(X29,X30))
        | ~ relation(X29)
        | ~ function(X29) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).

fof(c_0_9,plain,
    ! [X21,X22] :
      ( ~ relation(X21)
      | relation(relation_dom_restriction(X21,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).

fof(c_0_10,plain,
    ! [X12,X13,X14,X15,X16,X17,X18,X19] :
      ( ( in(X15,X12)
        | ~ in(X15,X14)
        | X14 != set_intersection2(X12,X13) )
      & ( in(X15,X13)
        | ~ in(X15,X14)
        | X14 != set_intersection2(X12,X13) )
      & ( ~ in(X16,X12)
        | ~ in(X16,X13)
        | in(X16,X14)
        | X14 != set_intersection2(X12,X13) )
      & ( ~ in(esk1_3(X17,X18,X19),X19)
        | ~ in(esk1_3(X17,X18,X19),X17)
        | ~ in(esk1_3(X17,X18,X19),X18)
        | X19 = set_intersection2(X17,X18) )
      & ( in(esk1_3(X17,X18,X19),X17)
        | in(esk1_3(X17,X18,X19),X19)
        | X19 = set_intersection2(X17,X18) )
      & ( in(esk1_3(X17,X18,X19),X18)
        | in(esk1_3(X17,X18,X19),X19)
        | X19 = set_intersection2(X17,X18) ) ),
    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])])])])])]) ).

fof(c_0_11,negated_conjecture,
    ( relation(esk5_0)
    & function(esk5_0)
    & ( ~ in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0)))
      | ~ in(esk4_0,relation_dom(esk5_0))
      | ~ in(esk4_0,esk3_0) )
    & ( in(esk4_0,relation_dom(esk5_0))
      | in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0))) )
    & ( in(esk4_0,esk3_0)
      | in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

cnf(c_0_12,plain,
    ( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
    | X1 != relation_dom_restriction(X2,X3)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( function(relation_dom_restriction(X1,X2))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( relation(relation_dom_restriction(X1,X2))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_15,plain,
    ! [X10,X11] : set_intersection2(X10,X11) = set_intersection2(X11,X10),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

cnf(c_0_16,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_intersection2(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,negated_conjecture,
    ( in(esk4_0,esk3_0)
    | in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_13]),c_0_14]) ).

cnf(c_0_19,negated_conjecture,
    relation(esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_20,negated_conjecture,
    function(esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_21,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X2,X3)) ),
    inference(er,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_intersection2(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0)))
    | ~ in(esk4_0,relation_dom(esk5_0))
    | ~ in(esk4_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_25,negated_conjecture,
    in(esk4_0,esk3_0),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]),c_0_21]),c_0_22]) ).

cnf(c_0_26,negated_conjecture,
    ( in(esk4_0,relation_dom(esk5_0))
    | in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_27,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X3,X2)) ),
    inference(er,[status(thm)],[c_0_23]) ).

cnf(c_0_28,negated_conjecture,
    ( ~ in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0)))
    | ~ in(esk4_0,relation_dom(esk5_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).

cnf(c_0_29,negated_conjecture,
    in(esk4_0,relation_dom(esk5_0)),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_18]),c_0_19]),c_0_20])]),c_0_21]),c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    ~ in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).

cnf(c_0_31,plain,
    ( in(X1,X4)
    | ~ in(X1,X2)
    | ~ in(X1,X3)
    | X4 != set_intersection2(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_32,negated_conjecture,
    ~ in(esk4_0,set_intersection2(esk3_0,relation_dom(esk5_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_18]),c_0_21]),c_0_19]),c_0_20])]) ).

cnf(c_0_33,plain,
    ( in(X1,set_intersection2(X2,X3))
    | ~ in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_29]),c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU224+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n001.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
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Wed Aug 23 15:58:39 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.61  % Version  : CSE_E---1.5
% 0.20/0.61  % Problem  : theBenchmark.p
% 0.20/0.61  % Proof found
% 0.20/0.61  % SZS status Theorem for theBenchmark.p
% 0.20/0.61  % SZS output start Proof
% See solution above
% 0.20/0.62  % Total time : 0.020000 s
% 0.20/0.62  % SZS output end Proof
% 0.20/0.62  % Total time : 0.024000 s
%------------------------------------------------------------------------------