TSTP Solution File: SET995+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET995+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 : 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 14:36:34 EDT 2023

% Result   : Theorem 0.19s 0.73s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   62 (  11 unt;  30 typ;   0 def)
%            Number of atoms       :  158 (  65 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  202 (  76   ~;  82   |;  29   &)
%                                         (   4 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  20   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;  10 con; 0-3 aty)
%            Number of variables   :   52 (   0 sgn;  30   !;   1   ?;   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,
    singleton: $i > $i ).

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

tff(decl_28,type,
    relation_dom: $i > $i ).

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

tff(decl_35,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_37,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk5_1: $i > $i ).

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

tff(decl_41,type,
    esk7_0: $i ).

tff(decl_42,type,
    esk8_1: $i > $i ).

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

tff(decl_44,type,
    esk10_0: $i ).

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

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

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

tff(decl_48,type,
    esk14_0: $i ).

tff(decl_49,type,
    esk15_0: $i ).

tff(decl_50,type,
    esk16_0: $i ).

tff(decl_51,type,
    esk17_2: ( $i * $i ) > $i ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(t17_funct_1,conjecture,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( ( relation_dom(X2) = relation_dom(X3)
              & relation_rng(X2) = singleton(X1)
              & relation_rng(X3) = singleton(X1) )
           => X2 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_1) ).

fof(d5_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( X2 = relation_rng(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,relation_dom(X1))
                  & X3 = apply(X1,X4) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).

fof(t9_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ( ( relation_dom(X1) = relation_dom(X2)
              & ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X1,X3) = apply(X2,X3) ) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).

fof(c_0_4,plain,
    ! [X9,X10,X11,X12,X13,X14] :
      ( ( ~ in(X11,X10)
        | X11 = X9
        | X10 != singleton(X9) )
      & ( X12 != X9
        | in(X12,X10)
        | X10 != singleton(X9) )
      & ( ~ in(esk1_2(X13,X14),X14)
        | esk1_2(X13,X14) != X13
        | X14 = singleton(X13) )
      & ( in(esk1_2(X13,X14),X14)
        | esk1_2(X13,X14) = X13
        | X14 = singleton(X13) ) ),
    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)],[d1_tarski])])])])])]) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( relation(X2)
          & function(X2) )
       => ! [X3] :
            ( ( relation(X3)
              & function(X3) )
           => ( ( relation_dom(X2) = relation_dom(X3)
                & relation_rng(X2) = singleton(X1)
                & relation_rng(X3) = singleton(X1) )
             => X2 = X3 ) ) ),
    inference(assume_negation,[status(cth)],[t17_funct_1]) ).

cnf(c_0_6,plain,
    ( X1 = X3
    | ~ in(X1,X2)
    | X2 != singleton(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

fof(c_0_7,negated_conjecture,
    ( relation(esk15_0)
    & function(esk15_0)
    & relation(esk16_0)
    & function(esk16_0)
    & relation_dom(esk15_0) = relation_dom(esk16_0)
    & relation_rng(esk15_0) = singleton(esk14_0)
    & relation_rng(esk16_0) = singleton(esk14_0)
    & esk15_0 != esk16_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_8,plain,
    ! [X16,X17,X18,X20,X21,X22,X24] :
      ( ( in(esk2_3(X16,X17,X18),relation_dom(X16))
        | ~ in(X18,X17)
        | X17 != relation_rng(X16)
        | ~ relation(X16)
        | ~ function(X16) )
      & ( X18 = apply(X16,esk2_3(X16,X17,X18))
        | ~ in(X18,X17)
        | X17 != relation_rng(X16)
        | ~ relation(X16)
        | ~ function(X16) )
      & ( ~ in(X21,relation_dom(X16))
        | X20 != apply(X16,X21)
        | in(X20,X17)
        | X17 != relation_rng(X16)
        | ~ relation(X16)
        | ~ function(X16) )
      & ( ~ in(esk3_2(X16,X22),X22)
        | ~ in(X24,relation_dom(X16))
        | esk3_2(X16,X22) != apply(X16,X24)
        | X22 = relation_rng(X16)
        | ~ relation(X16)
        | ~ function(X16) )
      & ( in(esk4_2(X16,X22),relation_dom(X16))
        | in(esk3_2(X16,X22),X22)
        | X22 = relation_rng(X16)
        | ~ relation(X16)
        | ~ function(X16) )
      & ( esk3_2(X16,X22) = apply(X16,esk4_2(X16,X22))
        | in(esk3_2(X16,X22),X22)
        | X22 = relation_rng(X16)
        | ~ relation(X16)
        | ~ function(X16) ) ),
    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)],[d5_funct_1])])])])])]) ).

cnf(c_0_9,plain,
    ( X1 = X2
    | ~ in(X1,singleton(X2)) ),
    inference(er,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    relation_rng(esk15_0) = singleton(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( in(X3,X4)
    | ~ in(X1,relation_dom(X2))
    | X3 != apply(X2,X1)
    | X4 != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    relation_rng(esk16_0) = singleton(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_13,plain,
    ! [X65,X66] :
      ( ( in(esk17_2(X65,X66),relation_dom(X65))
        | relation_dom(X65) != relation_dom(X66)
        | X65 = X66
        | ~ relation(X66)
        | ~ function(X66)
        | ~ relation(X65)
        | ~ function(X65) )
      & ( apply(X65,esk17_2(X65,X66)) != apply(X66,esk17_2(X65,X66))
        | relation_dom(X65) != relation_dom(X66)
        | X65 = X66
        | ~ relation(X66)
        | ~ function(X66)
        | ~ relation(X65)
        | ~ function(X65) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_funct_1])])])])]) ).

cnf(c_0_14,negated_conjecture,
    ( X1 = esk14_0
    | ~ in(X1,relation_rng(esk15_0)) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_15,plain,
    ( in(apply(X1,X2),relation_rng(X1))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X2,relation_dom(X1)) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_11])]) ).

cnf(c_0_16,negated_conjecture,
    relation(esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_17,negated_conjecture,
    function(esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_18,negated_conjecture,
    relation_rng(esk16_0) = relation_rng(esk15_0),
    inference(rw,[status(thm)],[c_0_12,c_0_10]) ).

cnf(c_0_19,negated_conjecture,
    relation(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_20,negated_conjecture,
    function(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_21,negated_conjecture,
    relation_dom(esk15_0) = relation_dom(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_22,plain,
    ( in(esk17_2(X1,X2),relation_dom(X1))
    | X1 = X2
    | relation_dom(X1) != relation_dom(X2)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_23,plain,
    ( X1 = X2
    | apply(X1,esk17_2(X1,X2)) != apply(X2,esk17_2(X1,X2))
    | relation_dom(X1) != relation_dom(X2)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_24,negated_conjecture,
    ( apply(esk15_0,X1) = esk14_0
    | ~ in(X1,relation_dom(esk15_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).

cnf(c_0_25,negated_conjecture,
    ( in(apply(esk16_0,X1),relation_rng(esk15_0))
    | ~ in(X1,relation_dom(esk15_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_18]),c_0_19]),c_0_20]),c_0_21])]) ).

cnf(c_0_26,negated_conjecture,
    ( X1 = esk15_0
    | in(esk17_2(X1,esk15_0),relation_dom(X1))
    | relation_dom(X1) != relation_dom(esk15_0)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_17])]) ).

cnf(c_0_27,negated_conjecture,
    esk15_0 != esk16_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_28,negated_conjecture,
    ( X1 = esk15_0
    | apply(X1,esk17_2(X1,esk15_0)) != esk14_0
    | relation_dom(X1) != relation_dom(esk15_0)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(esk17_2(X1,esk15_0),relation_dom(esk15_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_16]),c_0_17])]) ).

cnf(c_0_29,negated_conjecture,
    ( apply(esk16_0,X1) = esk14_0
    | ~ in(X1,relation_dom(esk15_0)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    in(esk17_2(esk16_0,esk15_0),relation_dom(esk15_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_19]),c_0_20])]),c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[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_28,c_0_29]),c_0_21]),c_0_19]),c_0_20]),c_0_30])]),c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET995+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
% 0.12/0.33  % Computer : n001.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sat Aug 26 09:06:15 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.73  % Version  : CSE_E---1.5
% 0.19/0.73  % Problem  : theBenchmark.p
% 0.19/0.73  % Proof found
% 0.19/0.73  % SZS status Theorem for theBenchmark.p
% 0.19/0.73  % SZS output start Proof
% See solution above
% 0.19/0.73  % Total time : 0.166000 s
% 0.19/0.73  % SZS output end Proof
% 0.19/0.73  % Total time : 0.170000 s
%------------------------------------------------------------------------------