TSTP Solution File: SEU030+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU030+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n026.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 16:22:11 EDT 2023

% Result   : Theorem 0.20s 0.64s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   59 (  13 unt;  28 typ;   0 def)
%            Number of atoms       :  131 (  42 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  159 (  59   ~;  56   |;  29   &)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  17   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  11 con; 0-2 aty)
%            Number of variables   :   30 (   0 sgn;  18   !;   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,
    function_inverse: $i > $i ).

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

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

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

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

tff(decl_32,type,
    relation_empty_yielding: $i > $o ).

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

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

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

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

tff(decl_37,type,
    esk1_1: $i > $i ).

tff(decl_38,type,
    esk2_0: $i ).

tff(decl_39,type,
    esk3_0: $i ).

tff(decl_40,type,
    esk4_1: $i > $i ).

tff(decl_41,type,
    esk5_0: $i ).

tff(decl_42,type,
    esk6_0: $i ).

tff(decl_43,type,
    esk7_0: $i ).

tff(decl_44,type,
    esk8_1: $i > $i ).

tff(decl_45,type,
    esk9_0: $i ).

tff(decl_46,type,
    esk10_0: $i ).

tff(decl_47,type,
    esk11_0: $i ).

tff(decl_48,type,
    esk12_0: $i ).

tff(decl_49,type,
    esk13_0: $i ).

fof(t63_funct_1,conjecture,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ( ( one_to_one(X1)
              & relation_rng(X1) = relation_dom(X2)
              & relation_composition(X1,X2) = identity_relation(relation_dom(X1)) )
           => X2 = function_inverse(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_1) ).

fof(l72_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ! [X4] :
              ( ( relation(X4)
                & function(X4) )
             => ( ( relation_rng(X2) = X1
                  & relation_composition(X2,X3) = identity_relation(relation_dom(X4))
                  & relation_composition(X3,X4) = identity_relation(X1) )
               => X4 = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l72_funct_1) ).

fof(t61_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
       => ( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
          & relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).

fof(t55_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( one_to_one(X1)
       => ( relation_rng(X1) = relation_dom(function_inverse(X1))
          & relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).

fof(dt_k2_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( relation(function_inverse(X1))
        & function(function_inverse(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1] :
        ( ( relation(X1)
          & function(X1) )
       => ! [X2] :
            ( ( relation(X2)
              & function(X2) )
           => ( ( one_to_one(X1)
                & relation_rng(X1) = relation_dom(X2)
                & relation_composition(X1,X2) = identity_relation(relation_dom(X1)) )
             => X2 = function_inverse(X1) ) ) ),
    inference(assume_negation,[status(cth)],[t63_funct_1]) ).

fof(c_0_6,plain,
    ! [X28,X29,X30,X31] :
      ( ~ relation(X29)
      | ~ function(X29)
      | ~ relation(X30)
      | ~ function(X30)
      | ~ relation(X31)
      | ~ function(X31)
      | relation_rng(X29) != X28
      | relation_composition(X29,X30) != identity_relation(relation_dom(X31))
      | relation_composition(X30,X31) != identity_relation(X28)
      | X31 = X29 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l72_funct_1])])]) ).

fof(c_0_7,plain,
    ! [X58] :
      ( ( relation_composition(X58,function_inverse(X58)) = identity_relation(relation_dom(X58))
        | ~ one_to_one(X58)
        | ~ relation(X58)
        | ~ function(X58) )
      & ( relation_composition(function_inverse(X58),X58) = identity_relation(relation_rng(X58))
        | ~ one_to_one(X58)
        | ~ relation(X58)
        | ~ function(X58) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t61_funct_1])])]) ).

fof(c_0_8,negated_conjecture,
    ( relation(esk12_0)
    & function(esk12_0)
    & relation(esk13_0)
    & function(esk13_0)
    & one_to_one(esk12_0)
    & relation_rng(esk12_0) = relation_dom(esk13_0)
    & relation_composition(esk12_0,esk13_0) = identity_relation(relation_dom(esk12_0))
    & esk13_0 != function_inverse(esk12_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_9,plain,
    ! [X54] :
      ( ( relation_rng(X54) = relation_dom(function_inverse(X54))
        | ~ one_to_one(X54)
        | ~ relation(X54)
        | ~ function(X54) )
      & ( relation_dom(X54) = relation_rng(function_inverse(X54))
        | ~ one_to_one(X54)
        | ~ relation(X54)
        | ~ function(X54) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).

fof(c_0_10,plain,
    ! [X10] :
      ( ( relation(function_inverse(X10))
        | ~ relation(X10)
        | ~ function(X10) )
      & ( function(function_inverse(X10))
        | ~ relation(X10)
        | ~ function(X10) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).

cnf(c_0_11,plain,
    ( X3 = X1
    | ~ relation(X1)
    | ~ function(X1)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X3)
    | ~ function(X3)
    | relation_rng(X1) != X4
    | relation_composition(X1,X2) != identity_relation(relation_dom(X3))
    | relation_composition(X2,X3) != identity_relation(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,plain,
    ( relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1))
    | ~ one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,negated_conjecture,
    one_to_one(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    relation(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    function(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_16,plain,
    ( relation_dom(X1) = relation_rng(function_inverse(X1))
    | ~ one_to_one(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

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

cnf(c_0_18,plain,
    ( function(function_inverse(X1))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_19,plain,
    ( X1 = X2
    | relation_composition(X1,X3) != identity_relation(relation_dom(X2))
    | relation_composition(X3,X2) != identity_relation(relation_rng(X1))
    | ~ relation(X2)
    | ~ relation(X3)
    | ~ relation(X1)
    | ~ function(X2)
    | ~ function(X3)
    | ~ function(X1) ),
    inference(er,[status(thm)],[c_0_11]) ).

cnf(c_0_20,negated_conjecture,
    relation_composition(function_inverse(esk12_0),esk12_0) = identity_relation(relation_rng(esk12_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).

cnf(c_0_21,negated_conjecture,
    relation_rng(function_inverse(esk12_0)) = relation_dom(esk12_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_13]),c_0_14]),c_0_15])]) ).

cnf(c_0_22,negated_conjecture,
    relation(function_inverse(esk12_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15])]) ).

cnf(c_0_23,negated_conjecture,
    function(function_inverse(esk12_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_15])]) ).

cnf(c_0_24,negated_conjecture,
    ( function_inverse(esk12_0) = X1
    | identity_relation(relation_dom(X1)) != identity_relation(relation_rng(esk12_0))
    | relation_composition(esk12_0,X1) != identity_relation(relation_dom(esk12_0))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_14]),c_0_22]),c_0_15]),c_0_23])]) ).

cnf(c_0_25,negated_conjecture,
    relation_rng(esk12_0) = relation_dom(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_26,negated_conjecture,
    relation_composition(esk12_0,esk13_0) = identity_relation(relation_dom(esk12_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_27,negated_conjecture,
    relation(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_28,negated_conjecture,
    function(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_29,negated_conjecture,
    esk13_0 != function_inverse(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_30,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU030+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n026.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Wed Aug 23 13:33:16 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.54  start to proof: theBenchmark
% 0.20/0.64  % Version  : CSE_E---1.5
% 0.20/0.64  % Problem  : theBenchmark.p
% 0.20/0.64  % Proof found
% 0.20/0.64  % SZS status Theorem for theBenchmark.p
% 0.20/0.64  % SZS output start Proof
% See solution above
% 0.20/0.65  % Total time : 0.092000 s
% 0.20/0.65  % SZS output end Proof
% 0.20/0.65  % Total time : 0.096000 s
%------------------------------------------------------------------------------