TSTP Solution File: SET994+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET994+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 : n018.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 14:36:33 EDT 2023

% Result   : Theorem 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   69 (  20 unt;  25 typ;   0 def)
%            Number of atoms       :  109 (  41 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   95 (  30   ~;  32   |;  21   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  15   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  10 con; 0-2 aty)
%            Number of variables   :   49 (   4 sgn;  24   !;   3   ?;   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,
    element: ( $i * $i ) > $o ).

tff(decl_27,type,
    empty_set: $i ).

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

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

tff(decl_30,type,
    relation_dom: $i > $i ).

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

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

tff(decl_33,type,
    n0: $i ).

tff(decl_34,type,
    n1: $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_1: $i > $i ).

tff(decl_45,type,
    esk11_1: $i > $i ).

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

fof(t6_boole,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(t16_funct_1,conjecture,
    ! [X1] :
      ( ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ! [X3] :
              ( ( relation(X3)
                & function(X3) )
             => ( ( relation_dom(X2) = X1
                  & relation_dom(X3) = X1 )
               => X2 = X3 ) ) )
     => X1 = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).

fof(s3_funct_1__e4_14__funct_1,axiom,
    ! [X1] :
    ? [X2] :
      ( relation(X2)
      & function(X2)
      & relation_dom(X2) = X1
      & ! [X3] :
          ( in(X3,X1)
         => apply(X2,X3) = n0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e4_14__funct_1) ).

fof(spc0_boole,axiom,
    empty(n0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc0_boole) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(existence_m1_subset_1,axiom,
    ! [X1] :
    ? [X2] : element(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(s3_funct_1__e7_14__funct_1,axiom,
    ! [X1] :
    ? [X2] :
      ( relation(X2)
      & function(X2)
      & relation_dom(X2) = X1
      & ! [X3] :
          ( in(X3,X1)
         => apply(X2,X3) = n1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e7_14__funct_1) ).

fof(spc1_boole,axiom,
    ~ empty(n1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc1_boole) ).

fof(fc12_relat_1,axiom,
    ( empty(empty_set)
    & relation(empty_set)
    & relation_empty_yielding(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).

fof(c_0_9,plain,
    ! [X45] :
      ( ~ empty(X45)
      | X45 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1] :
        ( ! [X2] :
            ( ( relation(X2)
              & function(X2) )
           => ! [X3] :
                ( ( relation(X3)
                  & function(X3) )
               => ( ( relation_dom(X2) = X1
                    & relation_dom(X3) = X1 )
                 => X2 = X3 ) ) )
       => X1 = empty_set ),
    inference(assume_negation,[status(cth)],[t16_funct_1]) ).

fof(c_0_11,plain,
    ! [X24,X26] :
      ( relation(esk10_1(X24))
      & function(esk10_1(X24))
      & relation_dom(esk10_1(X24)) = X24
      & ( ~ in(X26,X24)
        | apply(esk10_1(X24),X26) = n0 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s3_funct_1__e4_14__funct_1])])])]) ).

cnf(c_0_12,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    empty(n0),
    inference(split_conjunct,[status(thm)],[spc0_boole]) ).

fof(c_0_14,plain,
    ! [X35,X36] :
      ( ~ element(X35,X36)
      | empty(X36)
      | in(X35,X36) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

fof(c_0_15,plain,
    ! [X8] : element(esk1_1(X8),X8),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).

fof(c_0_16,negated_conjecture,
    ! [X31,X32] :
      ( ( ~ relation(X31)
        | ~ function(X31)
        | ~ relation(X32)
        | ~ function(X32)
        | relation_dom(X31) != esk12_0
        | relation_dom(X32) != esk12_0
        | X31 = X32 )
      & esk12_0 != empty_set ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).

fof(c_0_17,plain,
    ! [X27,X29] :
      ( relation(esk11_1(X27))
      & function(esk11_1(X27))
      & relation_dom(esk11_1(X27)) = X27
      & ( ~ in(X29,X27)
        | apply(esk11_1(X27),X29) = n1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s3_funct_1__e7_14__funct_1])])])]) ).

cnf(c_0_18,plain,
    ( apply(esk10_1(X2),X1) = n0
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,plain,
    n0 = empty_set,
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_20,plain,
    ( empty(X2)
    | in(X1,X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,plain,
    element(esk1_1(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,negated_conjecture,
    ( X1 = X2
    | ~ relation(X1)
    | ~ function(X1)
    | ~ relation(X2)
    | ~ function(X2)
    | relation_dom(X1) != esk12_0
    | relation_dom(X2) != esk12_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    relation_dom(esk11_1(X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24,plain,
    relation(esk11_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,plain,
    function(esk11_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_26,plain,
    ( apply(esk10_1(X1),X2) = empty_set
    | ~ in(X2,X1) ),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_27,plain,
    ( empty(X1)
    | in(esk1_1(X1),X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    ( X1 = esk11_1(esk12_0)
    | relation_dom(X1) != esk12_0
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(er,[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_24]),c_0_25])])]) ).

cnf(c_0_29,plain,
    relation_dom(esk10_1(X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_30,plain,
    relation(esk10_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_31,plain,
    function(esk10_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_32,plain,
    ( apply(esk11_1(X2),X1) = n1
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_33,plain,
    ( apply(esk10_1(X1),esk1_1(X1)) = empty_set
    | empty(X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_34,negated_conjecture,
    esk10_1(esk12_0) = esk11_1(esk12_0),
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])])]) ).

cnf(c_0_35,plain,
    ( apply(esk11_1(X1),esk1_1(X1)) = n1
    | empty(X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_27]) ).

cnf(c_0_36,negated_conjecture,
    ( apply(esk11_1(esk12_0),esk1_1(esk12_0)) = empty_set
    | empty(esk12_0) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

fof(c_0_37,plain,
    ~ empty(n1),
    inference(fof_simplification,[status(thm)],[spc1_boole]) ).

cnf(c_0_38,negated_conjecture,
    ( n1 = empty_set
    | empty(esk12_0) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_39,negated_conjecture,
    esk12_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_40,plain,
    ~ empty(n1),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_41,negated_conjecture,
    n1 = empty_set,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_38]),c_0_39]) ).

cnf(c_0_42,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).

cnf(c_0_43,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET994+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n018.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   : Sat Aug 26 09:51:59 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.60  % Version  : CSE_E---1.5
% 0.21/0.60  % Problem  : theBenchmark.p
% 0.21/0.60  % Proof found
% 0.21/0.60  % SZS status Theorem for theBenchmark.p
% 0.21/0.60  % SZS output start Proof
% See solution above
% 0.21/0.60  % Total time : 0.010000 s
% 0.21/0.60  % SZS output end Proof
% 0.21/0.60  % Total time : 0.013000 s
%------------------------------------------------------------------------------