TSTP Solution File: SEU299+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU299+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 16:24:14 EDT 2023
% Result : Theorem 2.58s 2.64s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 58
% Syntax : Number of formulae : 160 ( 12 unt; 55 typ; 0 def)
% Number of atoms : 852 ( 209 equ)
% Maximal formula atoms : 166 ( 8 avg)
% Number of connectives : 1262 ( 515 ~; 595 |; 108 &)
% ( 5 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 66 ( 38 >; 28 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 17 con; 0-4 aty)
% Number of variables : 282 ( 2 sgn; 70 !; 16 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ordinal: $i > $o ).
tff(decl_23,type,
in: ( $i * $i ) > $o ).
tff(decl_24,type,
succ: $i > $i ).
tff(decl_25,type,
omega: $i ).
tff(decl_26,type,
powerset: $i > $i ).
tff(decl_27,type,
element: ( $i * $i ) > $o ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
subset: ( $i * $i ) > $o ).
tff(decl_30,type,
empty: $i > $o ).
tff(decl_31,type,
finite: $i > $o ).
tff(decl_32,type,
relation: $i > $o ).
tff(decl_33,type,
function: $i > $o ).
tff(decl_34,type,
one_to_one: $i > $o ).
tff(decl_35,type,
epsilon_transitive: $i > $o ).
tff(decl_36,type,
epsilon_connected: $i > $o ).
tff(decl_37,type,
natural: $i > $o ).
tff(decl_38,type,
relation_empty_yielding: $i > $o ).
tff(decl_39,type,
epred1_3: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
esk1_0: $i ).
tff(decl_41,type,
esk2_1: $i > $i ).
tff(decl_42,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk5_1: $i > $i ).
tff(decl_45,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk7_0: $i ).
tff(decl_47,type,
esk8_1: $i > $i ).
tff(decl_48,type,
esk9_1: $i > $i ).
tff(decl_49,type,
esk10_0: $i ).
tff(decl_50,type,
esk11_0: $i ).
tff(decl_51,type,
esk12_0: $i ).
tff(decl_52,type,
esk13_0: $i ).
tff(decl_53,type,
esk14_0: $i ).
tff(decl_54,type,
esk15_0: $i ).
tff(decl_55,type,
esk16_0: $i ).
tff(decl_56,type,
esk17_0: $i ).
tff(decl_57,type,
esk18_0: $i ).
tff(decl_58,type,
esk19_0: $i ).
tff(decl_59,type,
esk20_0: $i ).
tff(decl_60,type,
esk21_1: $i > $i ).
tff(decl_61,type,
esk22_1: $i > $i ).
tff(decl_62,type,
esk23_0: $i ).
tff(decl_63,type,
esk24_0: $i ).
tff(decl_64,type,
esk25_1: $i > $i ).
tff(decl_65,type,
esk26_1: $i > $i ).
tff(decl_66,type,
esk27_1: $i > $i ).
tff(decl_67,type,
esk28_1: $i > $i ).
tff(decl_68,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk32_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk33_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_73,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
esk35_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_75,type,
esk36_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk37_4: ( $i * $i * $i * $i ) > $i ).
fof(s1_tarski__e18_27__finset_1__1,axiom,
! [X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& ( in(X5,omega)
=> ! [X6] :
( element(X6,powerset(powerset(X5)))
=> ~ ( X6 != empty_set
& ! [X7] :
~ ( in(X7,X6)
& ! [X8] :
( ( in(X8,X6)
& subset(X7,X8) )
=> X8 = X7 ) ) ) ) ) )
& X2 = X4
& ? [X9] :
( ordinal(X9)
& X4 = X9
& ( in(X9,omega)
=> ! [X10] :
( element(X10,powerset(powerset(X9)))
=> ~ ( X10 != empty_set
& ! [X11] :
~ ( in(X11,X10)
& ! [X12] :
( ( in(X12,X10)
& subset(X11,X12) )
=> X12 = X11 ) ) ) ) ) ) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,succ(X1))
& X4 = X3
& ? [X13] :
( ordinal(X13)
& X3 = X13
& ( in(X13,omega)
=> ! [X14] :
( element(X14,powerset(powerset(X13)))
=> ~ ( X14 != empty_set
& ! [X15] :
~ ( in(X15,X14)
& ! [X16] :
( ( in(X16,X14)
& subset(X15,X16) )
=> X16 = X15 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e18_27__finset_1__1) ).
fof(s1_xboole_0__e18_27__finset_1__1,conjecture,
! [X1] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( X5 != empty_set
& ! [X6] :
~ ( in(X6,X5)
& ! [X7] :
( ( in(X7,X5)
& subset(X6,X7) )
=> X7 = X6 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e18_27__finset_1__1) ).
fof(c_0_2,plain,
! [X2,X3,X4] :
( epred1_3(X4,X3,X2)
<=> ( X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& ( in(X5,omega)
=> ! [X6] :
( element(X6,powerset(powerset(X5)))
=> ~ ( X6 != empty_set
& ! [X7] :
~ ( in(X7,X6)
& ! [X8] :
( ( in(X8,X6)
& subset(X7,X8) )
=> X8 = X7 ) ) ) ) ) )
& X2 = X4
& ? [X9] :
( ordinal(X9)
& X4 = X9
& ( in(X9,omega)
=> ! [X10] :
( element(X10,powerset(powerset(X9)))
=> ~ ( X10 != empty_set
& ! [X11] :
~ ( in(X11,X10)
& ! [X12] :
( ( in(X12,X10)
& subset(X11,X12) )
=> X12 = X11 ) ) ) ) ) ) ) ),
introduced(definition) ).
fof(c_0_3,axiom,
! [X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( epred1_3(X4,X3,X2)
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,succ(X1))
& X4 = X3
& ? [X13] :
( ordinal(X13)
& X3 = X13
& ( in(X13,omega)
=> ! [X14] :
( element(X14,powerset(powerset(X13)))
=> ~ ( X14 != empty_set
& ! [X15] :
~ ( in(X15,X14)
& ! [X16] :
( ( in(X16,X14)
& subset(X15,X16) )
=> X16 = X15 ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[s1_tarski__e18_27__finset_1__1,c_0_2]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( X5 != empty_set
& ! [X6] :
~ ( in(X6,X5)
& ! [X7] :
( ( in(X7,X5)
& subset(X6,X7) )
=> X7 = X6 ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[s1_xboole_0__e18_27__finset_1__1]) ).
fof(c_0_5,plain,
! [X70,X75,X78,X80,X81,X82,X83,X85] :
( ( in(esk29_2(X70,X75),succ(X70))
| ~ in(X75,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( esk29_2(X70,X75) = X75
| ~ in(X75,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( ordinal(esk30_2(X70,X75))
| ~ in(X75,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( X75 = esk30_2(X70,X75)
| ~ in(X75,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( in(esk31_3(X70,X75,X78),X78)
| X78 = empty_set
| ~ element(X78,powerset(powerset(esk30_2(X70,X75))))
| ~ in(esk30_2(X70,X75),omega)
| ~ in(X75,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( ~ in(X80,X78)
| ~ subset(esk31_3(X70,X75,X78),X80)
| X80 = esk31_3(X70,X75,X78)
| X78 = empty_set
| ~ element(X78,powerset(powerset(esk30_2(X70,X75))))
| ~ in(esk30_2(X70,X75),omega)
| ~ in(X75,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( in(X83,omega)
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( element(esk32_3(X70,X81,X83),powerset(powerset(X83)))
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( esk32_3(X70,X81,X83) != empty_set
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( in(esk33_4(X70,X81,X83,X85),esk32_3(X70,X81,X83))
| ~ in(X85,esk32_3(X70,X81,X83))
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( subset(X85,esk33_4(X70,X81,X83,X85))
| ~ in(X85,esk32_3(X70,X81,X83))
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( esk33_4(X70,X81,X83,X85) != X85
| ~ in(X85,esk32_3(X70,X81,X83))
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ ordinal(X70) )
& ( in(esk29_2(X70,X75),succ(X70))
| ~ in(X75,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) )
& ( esk29_2(X70,X75) = X75
| ~ in(X75,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) )
& ( ordinal(esk30_2(X70,X75))
| ~ in(X75,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) )
& ( X75 = esk30_2(X70,X75)
| ~ in(X75,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) )
& ( in(esk31_3(X70,X75,X78),X78)
| X78 = empty_set
| ~ element(X78,powerset(powerset(esk30_2(X70,X75))))
| ~ in(esk30_2(X70,X75),omega)
| ~ in(X75,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) )
& ( ~ in(X80,X78)
| ~ subset(esk31_3(X70,X75,X78),X80)
| X80 = esk31_3(X70,X75,X78)
| X78 = empty_set
| ~ element(X78,powerset(powerset(esk30_2(X70,X75))))
| ~ in(esk30_2(X70,X75),omega)
| ~ in(X75,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) )
& ( in(X83,omega)
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) )
& ( element(esk32_3(X70,X81,X83),powerset(powerset(X83)))
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) )
& ( esk32_3(X70,X81,X83) != empty_set
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) )
& ( in(esk33_4(X70,X81,X83,X85),esk32_3(X70,X81,X83))
| ~ in(X85,esk32_3(X70,X81,X83))
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) )
& ( subset(X85,esk33_4(X70,X81,X83,X85))
| ~ in(X85,esk32_3(X70,X81,X83))
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) )
& ( esk33_4(X70,X81,X83,X85) != X85
| ~ in(X85,esk32_3(X70,X81,X83))
| ~ ordinal(X83)
| X81 != X83
| ~ in(X82,succ(X70))
| X82 != X81
| in(X81,esk28_1(X70))
| esk26_1(X70) != esk27_1(X70)
| ~ ordinal(X70) ) ),
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)],[c_0_3])])])])])]) ).
fof(c_0_6,negated_conjecture,
! [X18,X20,X22,X25,X27] :
( ordinal(esk1_0)
& ( in(X20,omega)
| ~ ordinal(X20)
| esk2_1(X18) != X20
| ~ in(esk2_1(X18),succ(esk1_0))
| ~ in(esk2_1(X18),X18) )
& ( element(esk3_2(X18,X20),powerset(powerset(X20)))
| ~ ordinal(X20)
| esk2_1(X18) != X20
| ~ in(esk2_1(X18),succ(esk1_0))
| ~ in(esk2_1(X18),X18) )
& ( esk3_2(X18,X20) != empty_set
| ~ ordinal(X20)
| esk2_1(X18) != X20
| ~ in(esk2_1(X18),succ(esk1_0))
| ~ in(esk2_1(X18),X18) )
& ( in(esk4_3(X18,X20,X22),esk3_2(X18,X20))
| ~ in(X22,esk3_2(X18,X20))
| ~ ordinal(X20)
| esk2_1(X18) != X20
| ~ in(esk2_1(X18),succ(esk1_0))
| ~ in(esk2_1(X18),X18) )
& ( subset(X22,esk4_3(X18,X20,X22))
| ~ in(X22,esk3_2(X18,X20))
| ~ ordinal(X20)
| esk2_1(X18) != X20
| ~ in(esk2_1(X18),succ(esk1_0))
| ~ in(esk2_1(X18),X18) )
& ( esk4_3(X18,X20,X22) != X22
| ~ in(X22,esk3_2(X18,X20))
| ~ ordinal(X20)
| esk2_1(X18) != X20
| ~ in(esk2_1(X18),succ(esk1_0))
| ~ in(esk2_1(X18),X18) )
& ( in(esk2_1(X18),succ(esk1_0))
| in(esk2_1(X18),X18) )
& ( ordinal(esk5_1(X18))
| in(esk2_1(X18),X18) )
& ( esk2_1(X18) = esk5_1(X18)
| in(esk2_1(X18),X18) )
& ( in(esk6_2(X18,X25),X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(esk5_1(X18))))
| ~ in(esk5_1(X18),omega)
| in(esk2_1(X18),X18) )
& ( ~ in(X27,X25)
| ~ subset(esk6_2(X18,X25),X27)
| X27 = esk6_2(X18,X25)
| X25 = empty_set
| ~ element(X25,powerset(powerset(esk5_1(X18))))
| ~ in(esk5_1(X18),omega)
| in(esk2_1(X18),X18) ) ),
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_4])])])])]) ).
cnf(c_0_7,plain,
( subset(X1,esk33_4(X2,X3,X4,X1))
| in(X3,esk28_1(X2))
| epred1_3(esk27_1(X2),esk26_1(X2),esk25_1(X2))
| ~ in(X1,esk32_3(X2,X3,X4))
| ~ ordinal(X4)
| X3 != X4
| ~ in(X5,succ(X2))
| X5 != X3
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( in(X2,esk28_1(X1))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| esk33_4(X1,X2,X3,X4) != X4
| ~ in(X4,esk32_3(X1,X2,X3))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X5,succ(X1))
| X5 != X2
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( in(esk33_4(X1,X2,X3,X4),esk32_3(X1,X2,X3))
| in(X2,esk28_1(X1))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| ~ in(X4,esk32_3(X1,X2,X3))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X5,succ(X1))
| X5 != X2
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( ordinal(esk5_1(X1))
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
( esk2_1(X1) = esk5_1(X1)
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( in(X2,esk28_1(X1))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| esk32_3(X1,X2,X3) != empty_set
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,succ(X1))
| X4 != X2
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( X1 = esk6_2(X3,X2)
| X2 = empty_set
| in(esk2_1(X3),X3)
| ~ in(X1,X2)
| ~ subset(esk6_2(X3,X2),X1)
| ~ element(X2,powerset(powerset(esk5_1(X3))))
| ~ in(esk5_1(X3),omega) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| subset(X2,esk33_4(X1,X3,X3,X2))
| in(X3,esk28_1(X1))
| ~ in(X2,esk32_3(X1,X3,X3))
| ~ in(X3,succ(X1))
| ~ ordinal(X3)
| ~ ordinal(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_7])]) ).
cnf(c_0_15,plain,
( epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| in(X2,esk28_1(X1))
| esk33_4(X1,X2,X2,X3) != X3
| ~ in(X3,esk32_3(X1,X2,X2))
| ~ in(X2,succ(X1))
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_8])]) ).
cnf(c_0_16,plain,
( epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| in(esk33_4(X1,X2,X2,X3),esk32_3(X1,X2,X2))
| in(X2,esk28_1(X1))
| ~ in(X3,esk32_3(X1,X2,X2))
| ~ in(X2,succ(X1))
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_17,negated_conjecture,
( in(esk2_1(X1),succ(esk1_0))
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
ordinal(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( in(esk2_1(X1),X1)
| ordinal(esk2_1(X1)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_20,plain,
( epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| in(X2,esk28_1(X1))
| esk32_3(X1,X2,X2) != empty_set
| ~ in(X2,succ(X1))
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_12])]) ).
cnf(c_0_21,negated_conjecture,
( X1 = empty_set
| epred1_3(esk27_1(X2),esk26_1(X2),esk25_1(X2))
| in(X3,esk28_1(X2))
| in(esk2_1(X4),X4)
| ~ element(X1,powerset(powerset(esk5_1(X4))))
| ~ in(esk33_4(X2,X3,X3,esk6_2(X4,X1)),X1)
| ~ in(esk6_2(X4,X1),esk32_3(X2,X3,X3))
| ~ in(esk5_1(X4),omega)
| ~ in(X3,succ(X2))
| ~ ordinal(X3)
| ~ ordinal(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| in(esk33_4(esk1_0,esk2_1(X1),esk2_1(X1),X2),esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)))
| in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X1),X1)
| ~ in(X2,esk32_3(esk1_0,esk2_1(X1),esk2_1(X1))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( in(esk6_2(X1,X2),X2)
| X2 = empty_set
| in(esk2_1(X1),X1)
| ~ element(X2,powerset(powerset(esk5_1(X1))))
| ~ in(esk5_1(X1),omega) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X1),X1)
| esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)) != empty_set ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_25,plain,
( in(X1,omega)
| in(X2,esk28_1(X4))
| epred1_3(esk27_1(X4),esk26_1(X4),esk25_1(X4))
| ~ ordinal(X1)
| X2 != X1
| ~ in(X3,succ(X4))
| X3 != X2
| ~ ordinal(X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_26,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X1),X1)
| in(esk2_1(X2),X2)
| ~ element(esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)),powerset(powerset(esk5_1(X2))))
| ~ in(esk5_1(X2),omega) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_18])]),c_0_19]),c_0_17]),c_0_23]),c_0_24]) ).
cnf(c_0_27,plain,
( element(esk32_3(X1,X2,X3),powerset(powerset(X3)))
| in(X2,esk28_1(X1))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,succ(X1))
| X4 != X2
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_28,plain,
( epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| in(X2,esk28_1(X1))
| in(X2,omega)
| ~ in(X2,succ(X1))
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
( subset(X1,esk4_3(X2,X3,X1))
| ~ in(X1,esk3_2(X2,X3))
| ~ ordinal(X3)
| esk2_1(X2) != X3
| ~ in(esk2_1(X2),succ(esk1_0))
| ~ in(esk2_1(X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_30,negated_conjecture,
( esk4_3(X1,X2,X3) != X3
| ~ in(X3,esk3_2(X1,X2))
| ~ ordinal(X2)
| esk2_1(X1) != X2
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_31,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X2),X2)
| in(esk2_1(X1),X1)
| ~ element(esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)),powerset(powerset(esk2_1(X2))))
| ~ in(esk2_1(X2),omega) ),
inference(spm,[status(thm)],[c_0_26,c_0_11]) ).
cnf(c_0_32,plain,
( epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| element(esk32_3(X1,X2,X2),powerset(powerset(X2)))
| in(X2,esk28_1(X1))
| ~ in(X2,succ(X1))
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_27])]) ).
cnf(c_0_33,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X1),omega)
| in(esk2_1(X1),X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_34,plain,
( X1 = esk31_3(X3,X4,X2)
| X2 = empty_set
| epred1_3(esk27_1(X3),esk26_1(X3),esk25_1(X3))
| ~ in(X1,X2)
| ~ subset(esk31_3(X3,X4,X2),X1)
| ~ element(X2,powerset(powerset(esk30_2(X3,X4))))
| ~ in(esk30_2(X3,X4),omega)
| ~ in(X4,esk28_1(X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_35,negated_conjecture,
( subset(X1,esk4_3(X2,esk2_1(X2),X1))
| ~ in(esk2_1(X2),succ(esk1_0))
| ~ in(X1,esk3_2(X2,esk2_1(X2)))
| ~ in(esk2_1(X2),X2)
| ~ ordinal(esk2_1(X2)) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( esk4_3(X1,esk2_1(X1),X2) != X2
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(X2,esk3_2(X1,esk2_1(X1)))
| ~ in(esk2_1(X1),X1)
| ~ ordinal(esk2_1(X1)) ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( in(esk4_3(X1,X2,X3),esk3_2(X1,X2))
| ~ in(X3,esk3_2(X1,X2))
| ~ ordinal(X2)
| esk2_1(X1) != X2
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_38,negated_conjecture,
( esk3_2(X1,X2) != empty_set
| ~ ordinal(X2)
| esk2_1(X1) != X2
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_39,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X1),X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_18])]),c_0_19]),c_0_33]),c_0_17]) ).
cnf(c_0_40,negated_conjecture,
( X1 = empty_set
| epred1_3(esk27_1(X2),esk26_1(X2),esk25_1(X2))
| ~ element(X1,powerset(powerset(esk30_2(X2,X3))))
| ~ in(esk4_3(X4,esk2_1(X4),esk31_3(X2,X3,X1)),X1)
| ~ in(esk31_3(X2,X3,X1),esk3_2(X4,esk2_1(X4)))
| ~ in(esk2_1(X4),succ(esk1_0))
| ~ in(esk30_2(X2,X3),omega)
| ~ in(X3,esk28_1(X2))
| ~ in(esk2_1(X4),X4)
| ~ ordinal(esk2_1(X4))
| ~ ordinal(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( in(esk4_3(X1,esk2_1(X1),X2),esk3_2(X1,esk2_1(X1)))
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(X2,esk3_2(X1,esk2_1(X1)))
| ~ in(esk2_1(X1),X1)
| ~ ordinal(esk2_1(X1)) ),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
( in(esk31_3(X1,X2,X3),X3)
| X3 = empty_set
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| ~ element(X3,powerset(powerset(esk30_2(X1,X2))))
| ~ in(esk30_2(X1,X2),omega)
| ~ in(X2,esk28_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_43,negated_conjecture,
( esk3_2(X1,esk2_1(X1)) != empty_set
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(esk2_1(X1),X1)
| ~ ordinal(esk2_1(X1)) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
( X1 = esk30_2(X2,X1)
| epred1_3(esk27_1(X2),esk26_1(X2),esk25_1(X2))
| ~ in(X1,esk28_1(X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_45,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| in(esk2_1(esk28_1(esk1_0)),esk28_1(esk1_0)) ),
inference(ef,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| ~ element(esk3_2(X2,esk2_1(X2)),powerset(powerset(esk30_2(X1,X3))))
| ~ in(esk2_1(X2),succ(esk1_0))
| ~ in(esk30_2(X1,X3),omega)
| ~ in(X3,esk28_1(X1))
| ~ in(esk2_1(X2),X2)
| ~ ordinal(esk2_1(X2))
| ~ ordinal(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( esk30_2(esk1_0,esk2_1(esk28_1(esk1_0))) = esk2_1(esk28_1(esk1_0))
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_18])]) ).
cnf(c_0_48,negated_conjecture,
( element(esk3_2(X1,X2),powerset(powerset(X2)))
| ~ ordinal(X2)
| esk2_1(X1) != X2
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_49,plain,
( ordinal(esk30_2(X1,X2))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| ~ in(X2,esk28_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_50,plain,
( esk29_2(X1,X2) = X2
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| ~ in(X2,esk28_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_51,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| ~ element(esk3_2(X1,esk2_1(X1)),powerset(powerset(esk2_1(esk28_1(esk1_0)))))
| ~ in(esk2_1(esk28_1(esk1_0)),omega)
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(esk2_1(X1),X1)
| ~ ordinal(esk2_1(X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_18])]),c_0_45]) ).
cnf(c_0_52,negated_conjecture,
( element(esk3_2(X1,esk2_1(X1)),powerset(powerset(esk2_1(X1))))
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(esk2_1(X1),X1)
| ~ ordinal(esk2_1(X1)) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| ordinal(esk2_1(esk28_1(esk1_0))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_47]),c_0_18])]),c_0_19]) ).
cnf(c_0_54,plain,
( in(esk29_2(X1,X2),succ(X1))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| ~ in(X2,esk28_1(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_55,negated_conjecture,
( esk29_2(esk1_0,esk2_1(esk28_1(esk1_0))) = esk2_1(esk28_1(esk1_0))
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_45]),c_0_18])]) ).
cnf(c_0_56,plain,
( subset(X1,esk33_4(X2,X3,X4,X1))
| in(X3,esk28_1(X2))
| ~ in(X1,esk32_3(X2,X3,X4))
| ~ ordinal(X4)
| X3 != X4
| ~ in(X5,succ(X2))
| X5 != X3
| esk26_1(X2) != esk27_1(X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_57,plain,
( in(X2,esk28_1(X1))
| esk33_4(X1,X2,X3,X4) != X4
| ~ in(X4,esk32_3(X1,X2,X3))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X5,succ(X1))
| X5 != X2
| esk26_1(X1) != esk27_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_58,plain,
( in(esk33_4(X1,X2,X3,X4),esk32_3(X1,X2,X3))
| in(X2,esk28_1(X1))
| ~ in(X4,esk32_3(X1,X2,X3))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X5,succ(X1))
| X5 != X2
| esk26_1(X1) != esk27_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_59,plain,
( in(X2,esk28_1(X1))
| esk32_3(X1,X2,X3) != empty_set
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,succ(X1))
| X4 != X2
| esk26_1(X1) != esk27_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_60,plain,
! [X2,X3,X4] :
( epred1_3(X4,X3,X2)
=> ( X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& ( in(X5,omega)
=> ! [X6] :
( element(X6,powerset(powerset(X5)))
=> ~ ( X6 != empty_set
& ! [X7] :
~ ( in(X7,X6)
& ! [X8] :
( ( in(X8,X6)
& subset(X7,X8) )
=> X8 = X7 ) ) ) ) ) )
& X2 = X4
& ? [X9] :
( ordinal(X9)
& X4 = X9
& ( in(X9,omega)
=> ! [X10] :
( element(X10,powerset(powerset(X9)))
=> ~ ( X10 != empty_set
& ! [X11] :
~ ( in(X11,X10)
& ! [X12] :
( ( in(X12,X10)
& subset(X11,X12) )
=> X12 = X11 ) ) ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_2]) ).
cnf(c_0_61,negated_conjecture,
( in(X1,omega)
| ~ ordinal(X1)
| esk2_1(X2) != X1
| ~ in(esk2_1(X2),succ(esk1_0))
| ~ in(esk2_1(X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_62,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| ~ in(esk2_1(esk28_1(esk1_0)),succ(esk1_0))
| ~ in(esk2_1(esk28_1(esk1_0)),omega) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_45]) ).
cnf(c_0_63,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| in(esk2_1(esk28_1(esk1_0)),succ(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_18])]),c_0_17]) ).
cnf(c_0_64,plain,
( subset(X1,esk33_4(X2,X3,X3,X1))
| in(X3,esk28_1(X2))
| esk26_1(X2) != esk27_1(X2)
| ~ in(X1,esk32_3(X2,X3,X3))
| ~ in(X3,succ(X2))
| ~ ordinal(X3)
| ~ ordinal(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_56])]) ).
cnf(c_0_65,plain,
( in(X1,esk28_1(X2))
| esk33_4(X2,X1,X1,X3) != X3
| esk26_1(X2) != esk27_1(X2)
| ~ in(X3,esk32_3(X2,X1,X1))
| ~ in(X1,succ(X2))
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_57])]) ).
cnf(c_0_66,plain,
( in(esk33_4(X1,X2,X2,X3),esk32_3(X1,X2,X2))
| in(X2,esk28_1(X1))
| esk26_1(X1) != esk27_1(X1)
| ~ in(X3,esk32_3(X1,X2,X2))
| ~ in(X2,succ(X1))
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_58])]) ).
cnf(c_0_67,plain,
( in(X1,esk28_1(X2))
| esk32_3(X2,X1,X1) != empty_set
| esk26_1(X2) != esk27_1(X2)
| ~ in(X1,succ(X2))
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_59])]) ).
fof(c_0_68,plain,
! [X87,X88,X89,X91,X93,X95,X97] :
( ( X87 = X88
| ~ epred1_3(X89,X88,X87) )
& ( ordinal(esk34_3(X87,X88,X89))
| ~ epred1_3(X89,X88,X87) )
& ( X88 = esk34_3(X87,X88,X89)
| ~ epred1_3(X89,X88,X87) )
& ( in(esk35_4(X87,X88,X89,X91),X91)
| X91 = empty_set
| ~ element(X91,powerset(powerset(esk34_3(X87,X88,X89))))
| ~ in(esk34_3(X87,X88,X89),omega)
| ~ epred1_3(X89,X88,X87) )
& ( ~ in(X93,X91)
| ~ subset(esk35_4(X87,X88,X89,X91),X93)
| X93 = esk35_4(X87,X88,X89,X91)
| X91 = empty_set
| ~ element(X91,powerset(powerset(esk34_3(X87,X88,X89))))
| ~ in(esk34_3(X87,X88,X89),omega)
| ~ epred1_3(X89,X88,X87) )
& ( X87 = X89
| ~ epred1_3(X89,X88,X87) )
& ( ordinal(esk36_3(X87,X88,X89))
| ~ epred1_3(X89,X88,X87) )
& ( X89 = esk36_3(X87,X88,X89)
| ~ epred1_3(X89,X88,X87) )
& ( in(esk37_4(X87,X88,X89,X95),X95)
| X95 = empty_set
| ~ element(X95,powerset(powerset(esk36_3(X87,X88,X89))))
| ~ in(esk36_3(X87,X88,X89),omega)
| ~ epred1_3(X89,X88,X87) )
& ( ~ in(X97,X95)
| ~ subset(esk37_4(X87,X88,X89,X95),X97)
| X97 = esk37_4(X87,X88,X89,X95)
| X95 = empty_set
| ~ element(X95,powerset(powerset(esk36_3(X87,X88,X89))))
| ~ in(esk36_3(X87,X88,X89),omega)
| ~ epred1_3(X89,X88,X87) ) ),
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_60])])])])]) ).
cnf(c_0_69,negated_conjecture,
( in(esk2_1(X1),omega)
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(esk2_1(X1),X1)
| ~ ordinal(esk2_1(X1)) ),
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_70,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| ~ in(esk2_1(esk28_1(esk1_0)),omega) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
( X1 = empty_set
| in(X2,esk28_1(X3))
| in(esk2_1(X4),X4)
| esk26_1(X3) != esk27_1(X3)
| ~ element(X1,powerset(powerset(esk5_1(X4))))
| ~ in(esk33_4(X3,X2,X2,esk6_2(X4,X1)),X1)
| ~ in(esk6_2(X4,X1),esk32_3(X3,X2,X2))
| ~ in(esk5_1(X4),omega)
| ~ in(X2,succ(X3))
| ~ ordinal(X2)
| ~ ordinal(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_64]),c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( in(esk33_4(esk1_0,esk2_1(X1),esk2_1(X1),X2),esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)))
| in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X1),X1)
| esk26_1(esk1_0) != esk27_1(esk1_0)
| ~ in(X2,esk32_3(esk1_0,esk2_1(X1),esk2_1(X1))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_73,negated_conjecture,
( in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X1),X1)
| esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)) != empty_set
| esk26_1(esk1_0) != esk27_1(esk1_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_74,plain,
( in(X1,omega)
| in(X2,esk28_1(X4))
| ~ ordinal(X1)
| X2 != X1
| ~ in(X3,succ(X4))
| X3 != X2
| esk26_1(X4) != esk27_1(X4)
| ~ ordinal(X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_75,plain,
( X1 = X2
| ~ epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_76,negated_conjecture,
epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_63]),c_0_53]),c_0_45]),c_0_70]) ).
cnf(c_0_77,negated_conjecture,
( in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X1),X1)
| in(esk2_1(X2),X2)
| esk26_1(esk1_0) != esk27_1(esk1_0)
| ~ element(esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)),powerset(powerset(esk5_1(X2))))
| ~ in(esk5_1(X2),omega) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_18])]),c_0_19]),c_0_17]),c_0_23]),c_0_73]) ).
cnf(c_0_78,plain,
( element(esk32_3(X1,X2,X3),powerset(powerset(X3)))
| in(X2,esk28_1(X1))
| ~ ordinal(X3)
| X2 != X3
| ~ in(X4,succ(X1))
| X4 != X2
| esk26_1(X1) != esk27_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_79,plain,
( in(X1,esk28_1(X2))
| in(X1,omega)
| esk26_1(X2) != esk27_1(X2)
| ~ in(X1,succ(X2))
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_74])]) ).
cnf(c_0_80,plain,
esk25_1(esk1_0) = esk26_1(esk1_0),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X2),X2)
| in(esk2_1(X1),X1)
| esk26_1(esk1_0) != esk27_1(esk1_0)
| ~ element(esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)),powerset(powerset(esk2_1(X2))))
| ~ in(esk2_1(X2),omega) ),
inference(spm,[status(thm)],[c_0_77,c_0_11]) ).
cnf(c_0_82,plain,
( element(esk32_3(X1,X2,X2),powerset(powerset(X2)))
| in(X2,esk28_1(X1))
| esk26_1(X1) != esk27_1(X1)
| ~ in(X2,succ(X1))
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_78])]) ).
cnf(c_0_83,negated_conjecture,
( in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X1),omega)
| in(esk2_1(X1),X1)
| esk26_1(esk1_0) != esk27_1(esk1_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_84,plain,
( X1 = X2
| ~ epred1_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_85,negated_conjecture,
epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk26_1(esk1_0)),
inference(rw,[status(thm)],[c_0_76,c_0_80]) ).
cnf(c_0_86,negated_conjecture,
( in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X1),X1)
| esk26_1(esk1_0) != esk27_1(esk1_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_18])]),c_0_19]),c_0_83]),c_0_17]) ).
cnf(c_0_87,plain,
esk26_1(esk1_0) = esk27_1(esk1_0),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
( in(esk2_1(X1),esk28_1(esk1_0))
| in(esk2_1(X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]) ).
cnf(c_0_89,plain,
( esk29_2(X1,X2) = X2
| ~ in(X2,esk28_1(X1))
| esk26_1(X1) != esk27_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_90,negated_conjecture,
in(esk2_1(esk28_1(esk1_0)),esk28_1(esk1_0)),
inference(ef,[status(thm)],[c_0_88]) ).
cnf(c_0_91,plain,
( X1 = esk30_2(X2,X1)
| ~ in(X1,esk28_1(X2))
| esk26_1(X2) != esk27_1(X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_92,plain,
( X1 = esk31_3(X3,X4,X2)
| X2 = empty_set
| ~ in(X1,X2)
| ~ subset(esk31_3(X3,X4,X2),X1)
| ~ element(X2,powerset(powerset(esk30_2(X3,X4))))
| ~ in(esk30_2(X3,X4),omega)
| ~ in(X4,esk28_1(X3))
| esk26_1(X3) != esk27_1(X3)
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_93,plain,
( in(esk29_2(X1,X2),succ(X1))
| ~ in(X2,esk28_1(X1))
| esk26_1(X1) != esk27_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_94,negated_conjecture,
esk29_2(esk1_0,esk2_1(esk28_1(esk1_0))) = esk2_1(esk28_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_87]),c_0_18])]) ).
cnf(c_0_95,plain,
( ordinal(esk30_2(X1,X2))
| ~ in(X2,esk28_1(X1))
| esk26_1(X1) != esk27_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_96,negated_conjecture,
esk30_2(esk1_0,esk2_1(esk28_1(esk1_0))) = esk2_1(esk28_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_90]),c_0_87]),c_0_18])]) ).
cnf(c_0_97,negated_conjecture,
( X1 = empty_set
| esk26_1(X2) != esk27_1(X2)
| ~ element(X1,powerset(powerset(esk30_2(X2,X3))))
| ~ in(esk4_3(X4,esk2_1(X4),esk31_3(X2,X3,X1)),X1)
| ~ in(esk31_3(X2,X3,X1),esk3_2(X4,esk2_1(X4)))
| ~ in(esk2_1(X4),succ(esk1_0))
| ~ in(esk30_2(X2,X3),omega)
| ~ in(X3,esk28_1(X2))
| ~ in(esk2_1(X4),X4)
| ~ ordinal(esk2_1(X4))
| ~ ordinal(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_35]),c_0_36]) ).
cnf(c_0_98,plain,
( in(esk31_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ element(X3,powerset(powerset(esk30_2(X1,X2))))
| ~ in(esk30_2(X1,X2),omega)
| ~ in(X2,esk28_1(X1))
| esk26_1(X1) != esk27_1(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_99,negated_conjecture,
in(esk2_1(esk28_1(esk1_0)),succ(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_87]),c_0_90]),c_0_18])]) ).
cnf(c_0_100,negated_conjecture,
ordinal(esk2_1(esk28_1(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_87]),c_0_90]),c_0_18])]) ).
cnf(c_0_101,negated_conjecture,
( esk26_1(X1) != esk27_1(X1)
| ~ element(esk3_2(X2,esk2_1(X2)),powerset(powerset(esk30_2(X1,X3))))
| ~ in(esk2_1(X2),succ(esk1_0))
| ~ in(esk30_2(X1,X3),omega)
| ~ in(X3,esk28_1(X1))
| ~ in(esk2_1(X2),X2)
| ~ ordinal(esk2_1(X2))
| ~ ordinal(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_41]),c_0_98]),c_0_43]) ).
cnf(c_0_102,negated_conjecture,
in(esk2_1(esk28_1(esk1_0)),omega),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_99]),c_0_90]),c_0_100])]) ).
cnf(c_0_103,negated_conjecture,
( ~ element(esk3_2(X1,esk2_1(X1)),powerset(powerset(esk2_1(esk28_1(esk1_0)))))
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(esk2_1(X1),X1)
| ~ ordinal(esk2_1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_96]),c_0_87]),c_0_90]),c_0_18])]),c_0_102])]) ).
cnf(c_0_104,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_52]),c_0_99]),c_0_90]),c_0_100])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU299+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n029.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 : Wed Aug 23 23:39:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.62 start to proof: theBenchmark
% 2.58/2.64 % Version : CSE_E---1.5
% 2.58/2.64 % Problem : theBenchmark.p
% 2.58/2.64 % Proof found
% 2.58/2.64 % SZS status Theorem for theBenchmark.p
% 2.58/2.64 % SZS output start Proof
% See solution above
% 2.58/2.65 % Total time : 2.006000 s
% 2.58/2.65 % SZS output end Proof
% 2.58/2.65 % Total time : 2.009000 s
%------------------------------------------------------------------------------