TSTP Solution File: SEU046+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU046+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 : n002.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 16:22:15 EDT 2023

% Result   : Theorem 0.24s 0.67s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   57 (   6 unt;  30 typ;   0 def)
%            Number of atoms       :  159 (  17 equ)
%            Maximal formula atoms :   79 (   5 avg)
%            Number of connectives :  220 (  88   ~;  96   |;  24   &)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   29 (  19   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   22 (  22 usr;  11 con; 0-3 aty)
%            Number of variables   :   52 (   5 sgn;  35   !;   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,
    subset: ( $i * $i ) > $o ).

tff(decl_28,type,
    relation_rng_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,
    powerset: $i > $i ).

tff(decl_33,type,
    relation_dom: $i > $i ).

tff(decl_34,type,
    relation_rng: $i > $i ).

tff(decl_35,type,
    apply: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk2_1: $i > $i ).

tff(decl_38,type,
    esk3_0: $i ).

tff(decl_39,type,
    esk4_0: $i ).

tff(decl_40,type,
    esk5_1: $i > $i ).

tff(decl_41,type,
    esk6_0: $i ).

tff(decl_42,type,
    esk7_0: $i ).

tff(decl_43,type,
    esk8_0: $i ).

tff(decl_44,type,
    esk9_1: $i > $i ).

tff(decl_45,type,
    esk10_0: $i ).

tff(decl_46,type,
    esk11_0: $i ).

tff(decl_47,type,
    esk12_0: $i ).

tff(decl_48,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk14_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk15_0: $i ).

tff(decl_51,type,
    esk16_0: $i ).

fof(t89_funct_1,conjecture,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
        & subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_funct_1) ).

fof(t118_relat_1,axiom,
    ! [X1,X2] :
      ( relation(X2)
     => subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).

fof(t85_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( X2 = relation_rng_restriction(X1,X3)
          <=> ( ! [X4] :
                  ( in(X4,relation_dom(X2))
                <=> ( in(X4,relation_dom(X3))
                    & in(apply(X3,X4),X1) ) )
              & ! [X4] :
                  ( in(X4,relation_dom(X2))
                 => apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).

fof(fc5_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ( relation(relation_rng_restriction(X1,X2))
        & function(relation_rng_restriction(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).

fof(dt_k8_relat_1,axiom,
    ! [X1,X2] :
      ( relation(X2)
     => relation(relation_rng_restriction(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).

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(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( relation(X2)
          & function(X2) )
       => ( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
          & subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ) ),
    inference(assume_negation,[status(cth)],[t89_funct_1]) ).

fof(c_0_7,negated_conjecture,
    ( relation(esk16_0)
    & function(esk16_0)
    & ( ~ subset(relation_dom(relation_rng_restriction(esk15_0,esk16_0)),relation_dom(esk16_0))
      | ~ subset(relation_rng(relation_rng_restriction(esk15_0,esk16_0)),relation_rng(esk16_0)) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_8,plain,
    ! [X40,X41] :
      ( ~ relation(X41)
      | subset(relation_rng(relation_rng_restriction(X40,X41)),relation_rng(X41)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_relat_1])]) ).

fof(c_0_9,plain,
    ! [X57,X58,X59,X60,X61,X62] :
      ( ( in(X60,relation_dom(X59))
        | ~ in(X60,relation_dom(X58))
        | X58 != relation_rng_restriction(X57,X59)
        | ~ relation(X59)
        | ~ function(X59)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( in(apply(X59,X60),X57)
        | ~ in(X60,relation_dom(X58))
        | X58 != relation_rng_restriction(X57,X59)
        | ~ relation(X59)
        | ~ function(X59)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( ~ in(X61,relation_dom(X59))
        | ~ in(apply(X59,X61),X57)
        | in(X61,relation_dom(X58))
        | X58 != relation_rng_restriction(X57,X59)
        | ~ relation(X59)
        | ~ function(X59)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( ~ in(X62,relation_dom(X58))
        | apply(X58,X62) = apply(X59,X62)
        | X58 != relation_rng_restriction(X57,X59)
        | ~ relation(X59)
        | ~ function(X59)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( in(esk14_3(X57,X58,X59),relation_dom(X58))
        | ~ in(esk13_3(X57,X58,X59),relation_dom(X58))
        | ~ in(esk13_3(X57,X58,X59),relation_dom(X59))
        | ~ in(apply(X59,esk13_3(X57,X58,X59)),X57)
        | X58 = relation_rng_restriction(X57,X59)
        | ~ relation(X59)
        | ~ function(X59)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( apply(X58,esk14_3(X57,X58,X59)) != apply(X59,esk14_3(X57,X58,X59))
        | ~ in(esk13_3(X57,X58,X59),relation_dom(X58))
        | ~ in(esk13_3(X57,X58,X59),relation_dom(X59))
        | ~ in(apply(X59,esk13_3(X57,X58,X59)),X57)
        | X58 = relation_rng_restriction(X57,X59)
        | ~ relation(X59)
        | ~ function(X59)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( in(esk14_3(X57,X58,X59),relation_dom(X58))
        | in(esk13_3(X57,X58,X59),relation_dom(X59))
        | in(esk13_3(X57,X58,X59),relation_dom(X58))
        | X58 = relation_rng_restriction(X57,X59)
        | ~ relation(X59)
        | ~ function(X59)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( apply(X58,esk14_3(X57,X58,X59)) != apply(X59,esk14_3(X57,X58,X59))
        | in(esk13_3(X57,X58,X59),relation_dom(X59))
        | in(esk13_3(X57,X58,X59),relation_dom(X58))
        | X58 = relation_rng_restriction(X57,X59)
        | ~ relation(X59)
        | ~ function(X59)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( in(esk14_3(X57,X58,X59),relation_dom(X58))
        | in(apply(X59,esk13_3(X57,X58,X59)),X57)
        | in(esk13_3(X57,X58,X59),relation_dom(X58))
        | X58 = relation_rng_restriction(X57,X59)
        | ~ relation(X59)
        | ~ function(X59)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( apply(X58,esk14_3(X57,X58,X59)) != apply(X59,esk14_3(X57,X58,X59))
        | in(apply(X59,esk13_3(X57,X58,X59)),X57)
        | in(esk13_3(X57,X58,X59),relation_dom(X58))
        | X58 = relation_rng_restriction(X57,X59)
        | ~ relation(X59)
        | ~ function(X59)
        | ~ relation(X58)
        | ~ function(X58) ) ),
    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)],[t85_funct_1])])])])])]) ).

fof(c_0_10,plain,
    ! [X21,X22] :
      ( ( relation(relation_rng_restriction(X21,X22))
        | ~ relation(X22)
        | ~ function(X22) )
      & ( function(relation_rng_restriction(X21,X22))
        | ~ relation(X22)
        | ~ function(X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc5_funct_1])])]) ).

fof(c_0_11,plain,
    ! [X16,X17] :
      ( ~ relation(X17)
      | relation(relation_rng_restriction(X16,X17)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).

cnf(c_0_12,negated_conjecture,
    ( ~ subset(relation_dom(relation_rng_restriction(esk15_0,esk16_0)),relation_dom(esk16_0))
    | ~ subset(relation_rng(relation_rng_restriction(esk15_0,esk16_0)),relation_rng(esk16_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( subset(relation_rng(relation_rng_restriction(X2,X1)),relation_rng(X1))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    relation(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_15,plain,
    ! [X10,X11,X12,X13,X14] :
      ( ( ~ subset(X10,X11)
        | ~ in(X12,X10)
        | in(X12,X11) )
      & ( in(esk1_2(X13,X14),X13)
        | subset(X13,X14) )
      & ( ~ in(esk1_2(X13,X14),X14)
        | subset(X13,X14) ) ),
    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_16,plain,
    ( in(X1,relation_dom(X2))
    | ~ in(X1,relation_dom(X3))
    | X3 != relation_rng_restriction(X4,X2)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_17,plain,
    ( function(relation_rng_restriction(X1,X2))
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,plain,
    ( relation(relation_rng_restriction(X2,X1))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,negated_conjecture,
    ~ subset(relation_dom(relation_rng_restriction(esk15_0,esk16_0)),relation_dom(esk16_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).

cnf(c_0_20,plain,
    ( in(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,plain,
    ( subset(X1,X2)
    | ~ in(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,plain,
    ( in(X1,relation_dom(X2))
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(X1,relation_dom(relation_rng_restriction(X3,X2))) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]),c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    in(esk1_2(relation_dom(relation_rng_restriction(esk15_0,esk16_0)),relation_dom(esk16_0)),relation_dom(relation_rng_restriction(esk15_0,esk16_0))),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,negated_conjecture,
    function(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_25,negated_conjecture,
    ~ in(esk1_2(relation_dom(relation_rng_restriction(esk15_0,esk16_0)),relation_dom(esk16_0)),relation_dom(esk16_0)),
    inference(spm,[status(thm)],[c_0_19,c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]),c_0_24])]),c_0_25]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16  % Problem    : SEU046+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.17  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.39  % Computer : n002.cluster.edu
% 0.17/0.39  % Model    : x86_64 x86_64
% 0.17/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39  % Memory   : 8042.1875MB
% 0.17/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39  % CPULimit   : 300
% 0.17/0.39  % WCLimit    : 300
% 0.17/0.39  % DateTime   : Wed Aug 23 16:46:01 EDT 2023
% 0.17/0.39  % CPUTime  : 
% 0.24/0.65  start to proof: theBenchmark
% 0.24/0.67  % Version  : CSE_E---1.5
% 0.24/0.67  % Problem  : theBenchmark.p
% 0.24/0.67  % Proof found
% 0.24/0.67  % SZS status Theorem for theBenchmark.p
% 0.24/0.67  % SZS output start Proof
% See solution above
% 0.24/0.68  % Total time : 0.015000 s
% 0.24/0.68  % SZS output end Proof
% 0.24/0.68  % Total time : 0.018000 s
%------------------------------------------------------------------------------