TSTP Solution File: SEU203+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU203+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n013.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 16:23:18 EDT 2023

% Result   : Theorem 13.93s 13.99s
% Output   : CNFRefutation 13.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  103 (  13 unt;  25 typ;   0 def)
%            Number of atoms       :  279 (  42 equ)
%            Maximal formula atoms :   26 (   3 avg)
%            Number of connectives :  364 ( 163   ~; 167   |;  20   &)
%                                         (   6 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   32 (  16   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;   9 con; 0-4 aty)
%            Number of variables   :  158 (   9 sgn;  54   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    in: ( $i * $i ) > $o ).

tff(decl_23,type,
    empty: $i > $o ).

tff(decl_24,type,
    relation: $i > $o ).

tff(decl_25,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_26,type,
    relation_image: ( $i * $i ) > $i ).

tff(decl_27,type,
    ordered_pair: ( $i * $i ) > $i ).

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

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

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

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

tff(decl_32,type,
    esk1_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_33,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_34,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_35,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_36,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk7_1: $i > $i ).

tff(decl_39,type,
    esk8_0: $i ).

tff(decl_40,type,
    esk9_0: $i ).

tff(decl_41,type,
    esk10_0: $i ).

tff(decl_42,type,
    esk11_0: $i ).

tff(decl_43,type,
    esk12_0: $i ).

tff(decl_44,type,
    esk13_0: $i ).

tff(decl_45,type,
    esk14_0: $i ).

tff(decl_46,type,
    esk15_0: $i ).

fof(t143_relat_1,conjecture,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(X1,relation_image(X3,X2))
      <=> ? [X4] :
            ( in(X4,relation_dom(X3))
            & in(ordered_pair(X4,X1),X3)
            & in(X4,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).

fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(d13_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2,X3] :
          ( X3 = relation_image(X1,X2)
        <=> ! [X4] :
              ( in(X4,X3)
            <=> ? [X5] :
                  ( in(ordered_pair(X5,X4),X1)
                  & in(X5,X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(d4_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( X2 = relation_dom(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).

fof(t7_boole,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & empty(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(cc1_relat_1,axiom,
    ! [X1] :
      ( empty(X1)
     => relation(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).

fof(fc7_relat_1,axiom,
    ! [X1] :
      ( empty(X1)
     => ( empty(relation_dom(X1))
        & relation(relation_dom(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).

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

fof(t1_subset,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => element(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( relation(X3)
       => ( in(X1,relation_image(X3,X2))
        <=> ? [X4] :
              ( in(X4,relation_dom(X3))
              & in(ordered_pair(X4,X1),X3)
              & in(X4,X2) ) ) ),
    inference(assume_negation,[status(cth)],[t143_relat_1]) ).

fof(c_0_11,negated_conjecture,
    ! [X51] :
      ( relation(esk14_0)
      & ( ~ in(esk12_0,relation_image(esk14_0,esk13_0))
        | ~ in(X51,relation_dom(esk14_0))
        | ~ in(ordered_pair(X51,esk12_0),esk14_0)
        | ~ in(X51,esk13_0) )
      & ( in(esk15_0,relation_dom(esk14_0))
        | in(esk12_0,relation_image(esk14_0,esk13_0)) )
      & ( in(ordered_pair(esk15_0,esk12_0),esk14_0)
        | in(esk12_0,relation_image(esk14_0,esk13_0)) )
      & ( in(esk15_0,esk13_0)
        | in(esk12_0,relation_image(esk14_0,esk13_0)) ) ),
    inference(distribute,[status(thm)],[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_12,plain,
    ! [X33,X34] : ordered_pair(X33,X34) = unordered_pair(unordered_pair(X33,X34),singleton(X33)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_13,plain,
    ! [X11,X12,X13,X14,X16,X17,X18,X19,X21] :
      ( ( in(ordered_pair(esk1_4(X11,X12,X13,X14),X14),X11)
        | ~ in(X14,X13)
        | X13 != relation_image(X11,X12)
        | ~ relation(X11) )
      & ( in(esk1_4(X11,X12,X13,X14),X12)
        | ~ in(X14,X13)
        | X13 != relation_image(X11,X12)
        | ~ relation(X11) )
      & ( ~ in(ordered_pair(X17,X16),X11)
        | ~ in(X17,X12)
        | in(X16,X13)
        | X13 != relation_image(X11,X12)
        | ~ relation(X11) )
      & ( ~ in(esk2_3(X11,X18,X19),X19)
        | ~ in(ordered_pair(X21,esk2_3(X11,X18,X19)),X11)
        | ~ in(X21,X18)
        | X19 = relation_image(X11,X18)
        | ~ relation(X11) )
      & ( in(ordered_pair(esk3_3(X11,X18,X19),esk2_3(X11,X18,X19)),X11)
        | in(esk2_3(X11,X18,X19),X19)
        | X19 = relation_image(X11,X18)
        | ~ relation(X11) )
      & ( in(esk3_3(X11,X18,X19),X18)
        | in(esk2_3(X11,X18,X19),X19)
        | X19 = relation_image(X11,X18)
        | ~ relation(X11) ) ),
    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)],[d13_relat_1])])])])])]) ).

cnf(c_0_14,negated_conjecture,
    ( ~ in(esk12_0,relation_image(esk14_0,esk13_0))
    | ~ in(X1,relation_dom(esk14_0))
    | ~ in(ordered_pair(X1,esk12_0),esk14_0)
    | ~ in(X1,esk13_0) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_16,plain,
    ! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

fof(c_0_17,plain,
    ! [X23,X24,X25,X27,X28,X29,X31] :
      ( ( ~ in(X25,X24)
        | in(ordered_pair(X25,esk4_3(X23,X24,X25)),X23)
        | X24 != relation_dom(X23)
        | ~ relation(X23) )
      & ( ~ in(ordered_pair(X27,X28),X23)
        | in(X27,X24)
        | X24 != relation_dom(X23)
        | ~ relation(X23) )
      & ( ~ in(esk5_2(X23,X29),X29)
        | ~ in(ordered_pair(esk5_2(X23,X29),X31),X23)
        | X29 = relation_dom(X23)
        | ~ relation(X23) )
      & ( in(esk5_2(X23,X29),X29)
        | in(ordered_pair(esk5_2(X23,X29),esk6_2(X23,X29)),X23)
        | X29 = relation_dom(X23)
        | ~ relation(X23) ) ),
    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)],[d4_relat_1])])])])])]) ).

cnf(c_0_18,plain,
    ( in(ordered_pair(esk1_4(X1,X2,X3,X4),X4),X1)
    | ~ in(X4,X3)
    | X3 != relation_image(X1,X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    ( ~ in(X1,esk13_0)
    | ~ in(X1,relation_dom(esk14_0))
    | ~ in(esk12_0,relation_image(esk14_0,esk13_0))
    | ~ in(unordered_pair(unordered_pair(X1,esk12_0),singleton(X1)),esk14_0) ),
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,plain,
    ( in(X1,X4)
    | ~ in(ordered_pair(X1,X2),X3)
    | X4 != relation_dom(X3)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_22,plain,
    ! [X58,X59] :
      ( ~ in(X58,X59)
      | ~ empty(X59) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).

cnf(c_0_23,plain,
    ( in(unordered_pair(unordered_pair(esk1_4(X1,X2,X3,X4),X4),singleton(esk1_4(X1,X2,X3,X4))),X1)
    | X3 != relation_image(X1,X2)
    | ~ relation(X1)
    | ~ in(X4,X3) ),
    inference(rw,[status(thm)],[c_0_18,c_0_15]) ).

fof(c_0_24,plain,
    ! [X8] :
      ( ~ empty(X8)
      | relation(X8) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,esk12_0)),esk14_0)
    | ~ in(esk12_0,relation_image(esk14_0,esk13_0))
    | ~ in(X1,relation_dom(esk14_0))
    | ~ in(X1,esk13_0) ),
    inference(rw,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    ( in(esk15_0,relation_dom(esk14_0))
    | in(esk12_0,relation_image(esk14_0,esk13_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_27,plain,
    ( in(X1,X4)
    | X4 != relation_dom(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
    inference(rw,[status(thm)],[c_0_21,c_0_15]) ).

cnf(c_0_28,negated_conjecture,
    ( in(esk15_0,esk13_0)
    | in(esk12_0,relation_image(esk14_0,esk13_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_29,plain,
    ( ~ in(X1,X2)
    | ~ empty(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_30,plain,
    ( in(unordered_pair(singleton(esk1_4(X1,X2,X3,X4)),unordered_pair(X4,esk1_4(X1,X2,X3,X4))),X1)
    | X3 != relation_image(X1,X2)
    | ~ relation(X1)
    | ~ in(X4,X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_20]),c_0_20]) ).

cnf(c_0_31,plain,
    ( relation(X1)
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_32,negated_conjecture,
    ( in(esk15_0,relation_dom(esk14_0))
    | ~ in(unordered_pair(singleton(X1),unordered_pair(X1,esk12_0)),esk14_0)
    | ~ in(X1,relation_dom(esk14_0))
    | ~ in(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_33,plain,
    ( in(X1,X2)
    | X2 != relation_dom(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X3) ),
    inference(rw,[status(thm)],[c_0_27,c_0_20]) ).

cnf(c_0_34,negated_conjecture,
    ( in(esk15_0,esk13_0)
    | ~ in(unordered_pair(singleton(X1),unordered_pair(X1,esk12_0)),esk14_0)
    | ~ in(X1,relation_dom(esk14_0))
    | ~ in(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_28]) ).

cnf(c_0_35,negated_conjecture,
    ( in(ordered_pair(esk15_0,esk12_0),esk14_0)
    | in(esk12_0,relation_image(esk14_0,esk13_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_36,plain,
    ( X1 != relation_image(X2,X3)
    | ~ empty(X2)
    | ~ in(X4,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).

cnf(c_0_37,negated_conjecture,
    ( in(esk15_0,relation_dom(esk14_0))
    | ~ in(unordered_pair(singleton(X1),unordered_pair(esk12_0,X1)),esk14_0)
    | ~ in(X1,relation_dom(esk14_0))
    | ~ in(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_32,c_0_20]) ).

cnf(c_0_38,negated_conjecture,
    relation(esk14_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_39,plain,
    ( in(X1,X2)
    | X2 != relation_dom(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(singleton(X1),unordered_pair(X4,X1)),X3) ),
    inference(spm,[status(thm)],[c_0_33,c_0_20]) ).

cnf(c_0_40,negated_conjecture,
    ( in(esk15_0,esk13_0)
    | ~ in(unordered_pair(singleton(X1),unordered_pair(esk12_0,X1)),esk14_0)
    | ~ in(X1,relation_dom(esk14_0))
    | ~ in(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_34,c_0_20]) ).

cnf(c_0_41,negated_conjecture,
    ( in(esk12_0,relation_image(esk14_0,esk13_0))
    | in(unordered_pair(unordered_pair(esk15_0,esk12_0),singleton(esk15_0)),esk14_0) ),
    inference(rw,[status(thm)],[c_0_35,c_0_15]) ).

cnf(c_0_42,plain,
    ( ~ empty(X1)
    | ~ in(X2,relation_image(X1,X3)) ),
    inference(er,[status(thm)],[c_0_36]) ).

fof(c_0_43,plain,
    ! [X43] :
      ( ( empty(relation_dom(X43))
        | ~ empty(X43) )
      & ( relation(relation_dom(X43))
        | ~ empty(X43) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).

cnf(c_0_44,negated_conjecture,
    ( in(esk15_0,relation_dom(esk14_0))
    | X1 != relation_image(esk14_0,X2)
    | ~ in(esk1_4(esk14_0,X2,X1,esk12_0),relation_dom(esk14_0))
    | ~ in(esk1_4(esk14_0,X2,X1,esk12_0),esk13_0)
    | ~ in(esk12_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_30]),c_0_38])]) ).

cnf(c_0_45,plain,
    ( in(esk1_4(X1,X2,X3,X4),X5)
    | X3 != relation_image(X1,X2)
    | X5 != relation_dom(X1)
    | ~ relation(X1)
    | ~ in(X4,X3) ),
    inference(spm,[status(thm)],[c_0_39,c_0_30]) ).

cnf(c_0_46,negated_conjecture,
    ( in(esk15_0,esk13_0)
    | X1 != relation_image(esk14_0,X2)
    | ~ in(esk1_4(esk14_0,X2,X1,esk12_0),relation_dom(esk14_0))
    | ~ in(esk1_4(esk14_0,X2,X1,esk12_0),esk13_0)
    | ~ in(esk12_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_30]),c_0_38])]) ).

cnf(c_0_47,negated_conjecture,
    ( in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0)
    | in(esk12_0,relation_image(esk14_0,esk13_0)) ),
    inference(rw,[status(thm)],[c_0_41,c_0_20]) ).

fof(c_0_48,plain,
    ! [X55,X56] :
      ( ~ element(X55,X56)
      | empty(X56)
      | in(X55,X56) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

cnf(c_0_49,negated_conjecture,
    ( in(esk15_0,relation_dom(esk14_0))
    | ~ empty(esk14_0) ),
    inference(spm,[status(thm)],[c_0_42,c_0_26]) ).

cnf(c_0_50,plain,
    ( empty(relation_dom(X1))
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_51,negated_conjecture,
    ( in(esk15_0,relation_dom(esk14_0))
    | X1 != relation_image(esk14_0,X2)
    | ~ in(esk1_4(esk14_0,X2,X1,esk12_0),esk13_0)
    | ~ in(esk12_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_38])]) ).

cnf(c_0_52,plain,
    ( in(esk1_4(X1,X2,X3,X4),X2)
    | ~ in(X4,X3)
    | X3 != relation_image(X1,X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_53,negated_conjecture,
    ( in(esk15_0,esk13_0)
    | X1 != relation_image(esk14_0,X2)
    | ~ in(esk1_4(esk14_0,X2,X1,esk12_0),esk13_0)
    | ~ in(esk12_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_45]),c_0_38])]) ).

cnf(c_0_54,plain,
    ( in(X2,X5)
    | ~ in(ordered_pair(X1,X2),X3)
    | ~ in(X1,X4)
    | X5 != relation_image(X3,X4)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_55,negated_conjecture,
    ( in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0)
    | ~ in(unordered_pair(singleton(X1),unordered_pair(X1,esk12_0)),esk14_0)
    | ~ in(X1,relation_dom(esk14_0))
    | ~ in(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_47]) ).

cnf(c_0_56,plain,
    ( empty(X2)
    | in(X1,X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_57,negated_conjecture,
    ~ empty(esk14_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_49]),c_0_50]) ).

cnf(c_0_58,negated_conjecture,
    ( in(esk15_0,relation_dom(esk14_0))
    | X1 != relation_image(esk14_0,esk13_0)
    | ~ in(esk12_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_38])]) ).

cnf(c_0_59,negated_conjecture,
    ( in(esk15_0,esk13_0)
    | X1 != relation_image(esk14_0,esk13_0)
    | ~ in(esk12_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_52]),c_0_38])]) ).

cnf(c_0_60,plain,
    ( in(X2,X5)
    | X5 != relation_image(X3,X4)
    | ~ relation(X3)
    | ~ in(X1,X4)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
    inference(rw,[status(thm)],[c_0_54,c_0_15]) ).

cnf(c_0_61,negated_conjecture,
    ( in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0)
    | ~ element(unordered_pair(singleton(X1),unordered_pair(X1,esk12_0)),esk14_0)
    | ~ in(X1,relation_dom(esk14_0))
    | ~ in(X1,esk13_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).

cnf(c_0_62,negated_conjecture,
    in(esk15_0,relation_dom(esk14_0)),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_58]),c_0_26]) ).

cnf(c_0_63,negated_conjecture,
    in(esk15_0,esk13_0),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_28]) ).

cnf(c_0_64,negated_conjecture,
    ( in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0)
    | ~ in(unordered_pair(singleton(X1),unordered_pair(esk12_0,X1)),esk14_0)
    | ~ in(X1,relation_dom(esk14_0))
    | ~ in(X1,esk13_0) ),
    inference(spm,[status(thm)],[c_0_55,c_0_20]) ).

cnf(c_0_65,plain,
    ( in(X1,X2)
    | X2 != relation_image(X3,X4)
    | ~ relation(X3)
    | ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X1)),X3)
    | ~ in(X5,X4) ),
    inference(rw,[status(thm)],[c_0_60,c_0_20]) ).

cnf(c_0_66,negated_conjecture,
    ( in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0)
    | ~ element(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).

cnf(c_0_67,negated_conjecture,
    ( in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0)
    | X1 != relation_image(esk14_0,X2)
    | ~ in(esk1_4(esk14_0,X2,X1,esk12_0),relation_dom(esk14_0))
    | ~ in(esk1_4(esk14_0,X2,X1,esk12_0),esk13_0)
    | ~ in(esk12_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_30]),c_0_38])]) ).

cnf(c_0_68,negated_conjecture,
    ( in(esk12_0,X1)
    | X1 != relation_image(esk14_0,X2)
    | ~ element(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0)
    | ~ in(esk15_0,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_38])]) ).

cnf(c_0_69,negated_conjecture,
    ( in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0)
    | X1 != relation_image(esk14_0,X2)
    | ~ in(esk1_4(esk14_0,X2,X1,esk12_0),esk13_0)
    | ~ in(esk12_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_45]),c_0_38])]) ).

cnf(c_0_70,negated_conjecture,
    ( in(esk12_0,relation_image(esk14_0,X1))
    | ~ element(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0)
    | ~ in(esk15_0,X1) ),
    inference(er,[status(thm)],[c_0_68]) ).

fof(c_0_71,plain,
    ! [X53,X54] :
      ( ~ in(X53,X54)
      | element(X53,X54) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).

cnf(c_0_72,negated_conjecture,
    ( in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0)
    | X1 != relation_image(esk14_0,esk13_0)
    | ~ in(esk12_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_52]),c_0_38])]) ).

cnf(c_0_73,negated_conjecture,
    ( ~ element(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0)
    | ~ in(unordered_pair(singleton(X1),unordered_pair(X1,esk12_0)),esk14_0)
    | ~ in(X1,relation_dom(esk14_0))
    | ~ in(X1,esk13_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_70]),c_0_63])]) ).

cnf(c_0_74,plain,
    ( element(X1,X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

cnf(c_0_75,negated_conjecture,
    in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_72]),c_0_47]) ).

cnf(c_0_76,negated_conjecture,
    ~ element(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk12_0)),esk14_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_66]),c_0_62]),c_0_63])]) ).

cnf(c_0_77,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU203+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n013.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 12:29:47 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.61  start to proof: theBenchmark
% 13.93/13.99  % Version  : CSE_E---1.5
% 13.93/13.99  % Problem  : theBenchmark.p
% 13.93/13.99  % Proof found
% 13.93/13.99  % SZS status Theorem for theBenchmark.p
% 13.93/13.99  % SZS output start Proof
% See solution above
% 13.99/14.00  % Total time : 13.377000 s
% 13.99/14.00  % SZS output end Proof
% 13.99/14.00  % Total time : 13.381000 s
%------------------------------------------------------------------------------