TSTP Solution File: SEU009+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU009+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 : n008.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 16:22:07 EDT 2023

% Result   : Theorem 0.21s 0.67s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   56 (  11 unt;  26 typ;   0 def)
%            Number of atoms       :  126 (  15 equ)
%            Maximal formula atoms :   19 (   4 avg)
%            Number of connectives :  162 (  66   ~;  66   |;  20   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  16   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  10 con; 0-2 aty)
%            Number of variables   :   42 (   2 sgn;  22   !;   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,
    relation_composition: ( $i * $i ) > $i ).

tff(decl_27,type,
    identity_relation: $i > $i ).

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

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

tff(decl_30,type,
    relation_empty_yielding: $i > $o ).

tff(decl_31,type,
    powerset: $i > $i ).

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

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

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

tff(decl_35,type,
    esk1_1: $i > $i ).

tff(decl_36,type,
    esk2_0: $i ).

tff(decl_37,type,
    esk3_0: $i ).

tff(decl_38,type,
    esk4_1: $i > $i ).

tff(decl_39,type,
    esk5_0: $i ).

tff(decl_40,type,
    esk6_0: $i ).

tff(decl_41,type,
    esk7_1: $i > $i ).

tff(decl_42,type,
    esk8_0: $i ).

tff(decl_43,type,
    esk9_0: $i ).

tff(decl_44,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_45,type,
    esk11_0: $i ).

tff(decl_46,type,
    esk12_0: $i ).

tff(decl_47,type,
    esk13_0: $i ).

fof(t40_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
      <=> ( in(X2,relation_dom(X3))
          & in(apply(X3,X2),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_1) ).

fof(t34_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ( X2 = identity_relation(X1)
      <=> ( relation_dom(X2) = X1
          & ! [X3] :
              ( in(X3,X1)
             => apply(X2,X3) = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).

fof(dt_k6_relat_1,axiom,
    ! [X1] : relation(identity_relation(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).

fof(fc2_funct_1,axiom,
    ! [X1] :
      ( relation(identity_relation(X1))
      & function(identity_relation(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).

fof(t21_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( in(X1,relation_dom(relation_composition(X3,X2)))
          <=> ( in(X1,relation_dom(X3))
              & in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
        <=> ( in(X2,relation_dom(X3))
            & in(apply(X3,X2),X1) ) ) ),
    inference(assume_negation,[status(cth)],[t40_funct_1]) ).

fof(c_0_6,plain,
    ! [X41,X42,X43] :
      ( ( relation_dom(X42) = X41
        | X42 != identity_relation(X41)
        | ~ relation(X42)
        | ~ function(X42) )
      & ( ~ in(X43,X41)
        | apply(X42,X43) = X43
        | X42 != identity_relation(X41)
        | ~ relation(X42)
        | ~ function(X42) )
      & ( in(esk10_2(X41,X42),X41)
        | relation_dom(X42) != X41
        | X42 = identity_relation(X41)
        | ~ relation(X42)
        | ~ function(X42) )
      & ( apply(X42,esk10_2(X41,X42)) != esk10_2(X41,X42)
        | relation_dom(X42) != X41
        | X42 = identity_relation(X41)
        | ~ relation(X42)
        | ~ function(X42) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).

fof(c_0_7,plain,
    ! [X10] : relation(identity_relation(X10)),
    inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).

fof(c_0_8,plain,
    ! [X18] :
      ( relation(identity_relation(X18))
      & function(identity_relation(X18)) ),
    inference(variable_rename,[status(thm)],[fc2_funct_1]) ).

fof(c_0_9,plain,
    ! [X36,X37,X38] :
      ( ( in(X36,relation_dom(X38))
        | ~ in(X36,relation_dom(relation_composition(X38,X37)))
        | ~ relation(X38)
        | ~ function(X38)
        | ~ relation(X37)
        | ~ function(X37) )
      & ( in(apply(X38,X36),relation_dom(X37))
        | ~ in(X36,relation_dom(relation_composition(X38,X37)))
        | ~ relation(X38)
        | ~ function(X38)
        | ~ relation(X37)
        | ~ function(X37) )
      & ( ~ in(X36,relation_dom(X38))
        | ~ in(apply(X38,X36),relation_dom(X37))
        | in(X36,relation_dom(relation_composition(X38,X37)))
        | ~ relation(X38)
        | ~ function(X38)
        | ~ relation(X37)
        | ~ function(X37) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])]) ).

fof(c_0_10,negated_conjecture,
    ( relation(esk13_0)
    & function(esk13_0)
    & ( ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
      | ~ in(esk12_0,relation_dom(esk13_0))
      | ~ in(apply(esk13_0,esk12_0),esk11_0) )
    & ( in(esk12_0,relation_dom(esk13_0))
      | in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) )
    & ( in(apply(esk13_0,esk12_0),esk11_0)
      | in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).

cnf(c_0_11,plain,
    ( relation_dom(X1) = X2
    | X1 != identity_relation(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,plain,
    relation(identity_relation(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    function(identity_relation(X1)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ( in(X1,relation_dom(X2))
    | ~ in(X1,relation_dom(relation_composition(X2,X3)))
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    ( in(esk12_0,relation_dom(esk13_0))
    | in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    relation(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,negated_conjecture,
    function(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,plain,
    ( in(apply(X1,X2),relation_dom(X3))
    | ~ in(X2,relation_dom(relation_composition(X1,X3)))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_19,plain,
    relation_dom(identity_relation(X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_11]),c_0_12]),c_0_13])]) ).

cnf(c_0_20,negated_conjecture,
    ( ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
    | ~ in(esk12_0,relation_dom(esk13_0))
    | ~ in(apply(esk13_0,esk12_0),esk11_0) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_21,negated_conjecture,
    in(esk12_0,relation_dom(esk13_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_12]),c_0_16]),c_0_13]),c_0_17])]) ).

cnf(c_0_22,plain,
    ( in(apply(X1,X2),X3)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_dom(relation_composition(X1,identity_relation(X3)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_12]),c_0_13])]) ).

cnf(c_0_23,negated_conjecture,
    ( in(apply(esk13_0,esk12_0),esk11_0)
    | in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
    | ~ in(apply(esk13_0,esk12_0),esk11_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).

cnf(c_0_25,negated_conjecture,
    in(apply(esk13_0,esk12_0),esk11_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_16]),c_0_17])]) ).

cnf(c_0_26,plain,
    ( in(X1,relation_dom(relation_composition(X2,X3)))
    | ~ in(X1,relation_dom(X2))
    | ~ in(apply(X2,X1),relation_dom(X3))
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_27,negated_conjecture,
    ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).

cnf(c_0_28,plain,
    ( in(X1,relation_dom(relation_composition(X2,identity_relation(X3))))
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(apply(X2,X1),X3)
    | ~ in(X1,relation_dom(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_12]),c_0_13])]) ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_16]),c_0_17]),c_0_25]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n008.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
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 14:52:02 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.67  % Version  : CSE_E---1.5
% 0.21/0.67  % Problem  : theBenchmark.p
% 0.21/0.67  % Proof found
% 0.21/0.67  % SZS status Theorem for theBenchmark.p
% 0.21/0.67  % SZS output start Proof
% See solution above
% 0.21/0.68  % Total time : 0.079000 s
% 0.21/0.68  % SZS output end Proof
% 0.21/0.68  % Total time : 0.082000 s
%------------------------------------------------------------------------------