TSTP Solution File: SEU228+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU228+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 : n031.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 16:23:34 EDT 2023

% Result   : Theorem 196.35s 196.32s
% Output   : CNFRefutation 196.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   94 (   6 unt;  36 typ;   0 def)
%            Number of atoms       :  355 (  86 equ)
%            Maximal formula atoms :   44 (   6 avg)
%            Number of connectives :  522 ( 225   ~; 245   |;  35   &)
%                                         (   8 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   45 (  25   >;  20   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   28 (  28 usr;  11 con; 0-4 aty)
%            Number of variables   :  186 (   5 sgn;  54   !;   2   ?;   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_image: ( $i * $i ) > $i ).

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

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

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

tff(decl_32,type,
    relation_rng: $i > $i ).

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

tff(decl_34,type,
    empty_set: $i ).

tff(decl_35,type,
    relation_empty_yielding: $i > $o ).

tff(decl_36,type,
    powerset: $i > $i ).

tff(decl_37,type,
    esk1_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_38,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_40,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_41,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_42,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_44,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_45,type,
    esk9_1: $i > $i ).

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

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

tff(decl_48,type,
    esk12_1: $i > $i ).

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

tff(decl_50,type,
    esk14_0: $i ).

tff(decl_51,type,
    esk15_0: $i ).

tff(decl_52,type,
    esk16_1: $i > $i ).

tff(decl_53,type,
    esk17_0: $i ).

tff(decl_54,type,
    esk18_0: $i ).

tff(decl_55,type,
    esk19_0: $i ).

tff(decl_56,type,
    esk20_0: $i ).

tff(decl_57,type,
    esk21_0: $i ).

fof(d12_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( X3 = relation_image(X1,X2)
        <=> ! [X4] :
              ( in(X4,X3)
            <=> ? [X5] :
                  ( in(X5,relation_dom(X1))
                  & in(X5,X2)
                  & X4 = apply(X1,X5) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_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(t147_funct_1,conjecture,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ( subset(X1,relation_rng(X2))
       => relation_image(X2,relation_inverse_image(X2,X1)) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(d13_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( X3 = relation_inverse_image(X1,X2)
        <=> ! [X4] :
              ( in(X4,X3)
            <=> ( in(X4,relation_dom(X1))
                & in(apply(X1,X4),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).

fof(d10_xboole_0,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).

fof(t145_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).

fof(c_0_7,plain,
    ! [X13,X14,X15,X16,X18,X19,X20,X21,X23] :
      ( ( in(esk1_4(X13,X14,X15,X16),relation_dom(X13))
        | ~ in(X16,X15)
        | X15 != relation_image(X13,X14)
        | ~ relation(X13)
        | ~ function(X13) )
      & ( in(esk1_4(X13,X14,X15,X16),X14)
        | ~ in(X16,X15)
        | X15 != relation_image(X13,X14)
        | ~ relation(X13)
        | ~ function(X13) )
      & ( X16 = apply(X13,esk1_4(X13,X14,X15,X16))
        | ~ in(X16,X15)
        | X15 != relation_image(X13,X14)
        | ~ relation(X13)
        | ~ function(X13) )
      & ( ~ in(X19,relation_dom(X13))
        | ~ in(X19,X14)
        | X18 != apply(X13,X19)
        | in(X18,X15)
        | X15 != relation_image(X13,X14)
        | ~ relation(X13)
        | ~ function(X13) )
      & ( ~ in(esk2_3(X13,X20,X21),X21)
        | ~ in(X23,relation_dom(X13))
        | ~ in(X23,X20)
        | esk2_3(X13,X20,X21) != apply(X13,X23)
        | X21 = relation_image(X13,X20)
        | ~ relation(X13)
        | ~ function(X13) )
      & ( in(esk3_3(X13,X20,X21),relation_dom(X13))
        | in(esk2_3(X13,X20,X21),X21)
        | X21 = relation_image(X13,X20)
        | ~ relation(X13)
        | ~ function(X13) )
      & ( in(esk3_3(X13,X20,X21),X20)
        | in(esk2_3(X13,X20,X21),X21)
        | X21 = relation_image(X13,X20)
        | ~ relation(X13)
        | ~ function(X13) )
      & ( esk2_3(X13,X20,X21) = apply(X13,esk3_3(X13,X20,X21))
        | in(esk2_3(X13,X20,X21),X21)
        | X21 = relation_image(X13,X20)
        | ~ relation(X13)
        | ~ function(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)],[d12_funct_1])])])])])]) ).

fof(c_0_8,plain,
    ! [X39,X40,X41,X43,X44,X45,X47] :
      ( ( in(esk6_3(X39,X40,X41),relation_dom(X39))
        | ~ in(X41,X40)
        | X40 != relation_rng(X39)
        | ~ relation(X39)
        | ~ function(X39) )
      & ( X41 = apply(X39,esk6_3(X39,X40,X41))
        | ~ in(X41,X40)
        | X40 != relation_rng(X39)
        | ~ relation(X39)
        | ~ function(X39) )
      & ( ~ in(X44,relation_dom(X39))
        | X43 != apply(X39,X44)
        | in(X43,X40)
        | X40 != relation_rng(X39)
        | ~ relation(X39)
        | ~ function(X39) )
      & ( ~ in(esk7_2(X39,X45),X45)
        | ~ in(X47,relation_dom(X39))
        | esk7_2(X39,X45) != apply(X39,X47)
        | X45 = relation_rng(X39)
        | ~ relation(X39)
        | ~ function(X39) )
      & ( in(esk8_2(X39,X45),relation_dom(X39))
        | in(esk7_2(X39,X45),X45)
        | X45 = relation_rng(X39)
        | ~ relation(X39)
        | ~ function(X39) )
      & ( esk7_2(X39,X45) = apply(X39,esk8_2(X39,X45))
        | in(esk7_2(X39,X45),X45)
        | X45 = relation_rng(X39)
        | ~ relation(X39)
        | ~ function(X39) ) ),
    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,
    ( in(X4,X5)
    | ~ in(X1,relation_dom(X2))
    | ~ in(X1,X3)
    | X4 != apply(X2,X1)
    | X5 != relation_image(X2,X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,plain,
    ( in(esk6_3(X1,X2,X3),relation_dom(X1))
    | ~ in(X3,X2)
    | X2 != relation_rng(X1)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,plain,
    ( in(X1,X2)
    | X1 != apply(X3,esk6_3(X3,X4,X5))
    | X2 != relation_image(X3,X6)
    | X4 != relation_rng(X3)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ in(esk6_3(X3,X4,X5),X6)
    | ~ in(X5,X4) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_12,plain,
    ( X1 = apply(X2,esk6_3(X2,X3,X1))
    | ~ in(X1,X3)
    | X3 != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_13,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( relation(X2)
          & function(X2) )
       => ( subset(X1,relation_rng(X2))
         => relation_image(X2,relation_inverse_image(X2,X1)) = X1 ) ),
    inference(assume_negation,[status(cth)],[t147_funct_1]) ).

cnf(c_0_14,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_15,plain,
    ( in(esk1_4(X1,X2,X3,X4),relation_dom(X1))
    | ~ in(X4,X3)
    | X3 != relation_image(X1,X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_16,plain,
    ( in(X1,X2)
    | X2 != relation_image(X3,X4)
    | X5 != relation_rng(X3)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ in(esk6_3(X3,X5,X1),X4)
    | ~ in(X1,X5) ),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12])]) ).

fof(c_0_17,plain,
    ! [X33,X34,X35,X36,X37] :
      ( ( ~ subset(X33,X34)
        | ~ in(X35,X33)
        | in(X35,X34) )
      & ( in(esk5_2(X36,X37),X36)
        | subset(X36,X37) )
      & ( ~ in(esk5_2(X36,X37),X37)
        | subset(X36,X37) ) ),
    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])])])])])]) ).

fof(c_0_18,negated_conjecture,
    ( relation(esk21_0)
    & function(esk21_0)
    & subset(esk20_0,relation_rng(esk21_0))
    & relation_image(esk21_0,relation_inverse_image(esk21_0,esk20_0)) != esk20_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).

cnf(c_0_19,plain,
    ( in(X1,X2)
    | X1 != apply(X3,esk1_4(X3,X4,X5,X6))
    | X5 != relation_image(X3,X4)
    | X2 != relation_rng(X3)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ in(X6,X5) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
    ( X1 = apply(X2,esk1_4(X2,X3,X4,X1))
    | ~ in(X1,X4)
    | X4 != relation_image(X2,X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_21,plain,
    ( in(X1,X2)
    | X2 != relation_image(X3,relation_dom(X3))
    | X4 != relation_rng(X3)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ in(X1,X4) ),
    inference(spm,[status(thm)],[c_0_16,c_0_10]) ).

cnf(c_0_22,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    subset(esk20_0,relation_rng(esk21_0)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,plain,
    ( in(X1,X2)
    | X3 != relation_image(X4,X5)
    | X2 != relation_rng(X4)
    | ~ relation(X4)
    | ~ function(X4)
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20])]) ).

cnf(c_0_25,plain,
    ( in(X1,relation_image(X2,relation_dom(X2)))
    | X3 != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    ( in(X1,relation_rng(esk21_0))
    | ~ in(X1,esk20_0) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_27,plain,
    ! [X25,X26,X27,X28,X29,X30,X31] :
      ( ( in(X28,relation_dom(X25))
        | ~ in(X28,X27)
        | X27 != relation_inverse_image(X25,X26)
        | ~ relation(X25)
        | ~ function(X25) )
      & ( in(apply(X25,X28),X26)
        | ~ in(X28,X27)
        | X27 != relation_inverse_image(X25,X26)
        | ~ relation(X25)
        | ~ function(X25) )
      & ( ~ in(X29,relation_dom(X25))
        | ~ in(apply(X25,X29),X26)
        | in(X29,X27)
        | X27 != relation_inverse_image(X25,X26)
        | ~ relation(X25)
        | ~ function(X25) )
      & ( ~ in(esk4_3(X25,X30,X31),X31)
        | ~ in(esk4_3(X25,X30,X31),relation_dom(X25))
        | ~ in(apply(X25,esk4_3(X25,X30,X31)),X30)
        | X31 = relation_inverse_image(X25,X30)
        | ~ relation(X25)
        | ~ function(X25) )
      & ( in(esk4_3(X25,X30,X31),relation_dom(X25))
        | in(esk4_3(X25,X30,X31),X31)
        | X31 = relation_inverse_image(X25,X30)
        | ~ relation(X25)
        | ~ function(X25) )
      & ( in(apply(X25,esk4_3(X25,X30,X31)),X30)
        | in(esk4_3(X25,X30,X31),X31)
        | X31 = relation_inverse_image(X25,X30)
        | ~ relation(X25)
        | ~ function(X25) ) ),
    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_funct_1])])])])])]) ).

cnf(c_0_28,plain,
    ( in(X1,X2)
    | X2 != relation_rng(X3)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ in(X1,relation_image(X3,X4)) ),
    inference(er,[status(thm)],[c_0_24]) ).

cnf(c_0_29,negated_conjecture,
    ( in(X1,relation_image(X2,relation_dom(X2)))
    | relation_rng(esk21_0) != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(X1,esk20_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,plain,
    ( in(X1,X4)
    | ~ in(X1,relation_dom(X2))
    | ~ in(apply(X2,X1),X3)
    | X4 != relation_inverse_image(X2,X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ( in(X1,X2)
    | relation_rng(esk21_0) != relation_rng(X3)
    | X2 != relation_rng(X3)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ in(X1,esk20_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_32,plain,
    ( in(esk5_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_33,plain,
    ( in(X1,X2)
    | X1 != apply(X3,esk1_4(X3,X4,X5,X6))
    | X2 != relation_image(X3,X7)
    | X5 != relation_image(X3,X4)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ in(esk1_4(X3,X4,X5,X6),X7)
    | ~ in(X6,X5) ),
    inference(spm,[status(thm)],[c_0_9,c_0_15]) ).

cnf(c_0_34,plain,
    ( in(esk1_4(X1,X2,X3,X4),X5)
    | X5 != relation_inverse_image(X1,X6)
    | X3 != relation_image(X1,X2)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X4,X6)
    | ~ in(X4,X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_15]) ).

cnf(c_0_35,negated_conjecture,
    ( subset(esk20_0,X1)
    | in(esk5_2(esk20_0,X1),X2)
    | relation_rng(esk21_0) != relation_rng(X3)
    | X2 != relation_rng(X3)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_36,plain,
    ( in(X1,X2)
    | X2 != relation_image(X3,X4)
    | X5 != relation_image(X3,X6)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ in(esk1_4(X3,X6,X5,X1),X4)
    | ~ in(X1,X5) ),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_20])]) ).

cnf(c_0_37,plain,
    ( in(esk1_4(X1,X2,X3,X4),relation_inverse_image(X1,X5))
    | X3 != relation_image(X1,X2)
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(X4,X5)
    | ~ in(X4,X3) ),
    inference(er,[status(thm)],[c_0_34]) ).

cnf(c_0_38,negated_conjecture,
    ( subset(esk20_0,X1)
    | in(esk5_2(esk20_0,X1),relation_rng(X2))
    | relation_rng(esk21_0) != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(er,[status(thm)],[c_0_35]) ).

cnf(c_0_39,negated_conjecture,
    relation(esk21_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_40,negated_conjecture,
    function(esk21_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_41,plain,
    ( in(X1,X2)
    | X2 != relation_image(X3,relation_inverse_image(X3,X4))
    | X5 != relation_image(X3,X6)
    | ~ relation(X3)
    | ~ function(X3)
    | ~ in(X1,X5)
    | ~ in(X1,X4) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_42,negated_conjecture,
    ( subset(esk20_0,X1)
    | in(esk5_2(esk20_0,X1),relation_rng(esk21_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_38]),c_0_39]),c_0_40])]) ).

cnf(c_0_43,plain,
    ( in(X1,relation_image(X2,relation_inverse_image(X2,X3)))
    | X4 != relation_image(X2,X5)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(X1,X4)
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_41]) ).

cnf(c_0_44,negated_conjecture,
    ( subset(esk20_0,X1)
    | in(esk5_2(esk20_0,X1),relation_image(X2,relation_dom(X2)))
    | relation_rng(esk21_0) != relation_rng(X2)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_42]) ).

cnf(c_0_45,plain,
    ( in(X1,relation_image(X2,relation_inverse_image(X2,X3)))
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(X1,relation_image(X2,X4))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_43]) ).

cnf(c_0_46,negated_conjecture,
    ( subset(esk20_0,X1)
    | in(esk5_2(esk20_0,X1),relation_image(esk21_0,relation_dom(esk21_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_44]),c_0_39]),c_0_40])]) ).

fof(c_0_47,plain,
    ! [X11,X12] :
      ( ( subset(X11,X12)
        | X11 != X12 )
      & ( subset(X12,X11)
        | X11 != X12 )
      & ( ~ subset(X11,X12)
        | ~ subset(X12,X11)
        | X11 = X12 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).

fof(c_0_48,plain,
    ! [X69,X70] :
      ( ~ relation(X70)
      | ~ function(X70)
      | subset(relation_image(X70,relation_inverse_image(X70,X69)),X69) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t145_funct_1])]) ).

cnf(c_0_49,negated_conjecture,
    ( subset(esk20_0,X1)
    | in(esk5_2(esk20_0,X1),relation_image(esk21_0,relation_inverse_image(esk21_0,X2)))
    | ~ in(esk5_2(esk20_0,X1),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_39]),c_0_40])]) ).

cnf(c_0_50,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_51,plain,
    ( subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_52,plain,
    ( subset(X1,X2)
    | ~ in(esk5_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_53,negated_conjecture,
    ( subset(esk20_0,X1)
    | in(esk5_2(esk20_0,X1),relation_image(esk21_0,relation_inverse_image(esk21_0,esk20_0))) ),
    inference(spm,[status(thm)],[c_0_49,c_0_32]) ).

cnf(c_0_54,plain,
    ( relation_image(X1,relation_inverse_image(X1,X2)) = X2
    | ~ subset(X2,relation_image(X1,relation_inverse_image(X1,X2)))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_55,negated_conjecture,
    subset(esk20_0,relation_image(esk21_0,relation_inverse_image(esk21_0,esk20_0))),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_56,negated_conjecture,
    relation_image(esk21_0,relation_inverse_image(esk21_0,esk20_0)) != esk20_0,
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_57,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_54,c_0_55]),c_0_39]),c_0_40])]),c_0_56]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem    : SEU228+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.15  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36  % Computer : n031.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Wed Aug 23 22:58:20 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.21/0.60  start to proof: theBenchmark
% 196.35/196.32  % Version  : CSE_E---1.5
% 196.35/196.32  % Problem  : theBenchmark.p
% 196.35/196.32  % Proof found
% 196.35/196.32  % SZS status Theorem for theBenchmark.p
% 196.35/196.32  % SZS output start Proof
% See solution above
% 196.35/196.33  % Total time : 195.734000 s
% 196.35/196.33  % SZS output end Proof
% 196.35/196.33  % Total time : 195.746000 s
%------------------------------------------------------------------------------