%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU299+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:37 PM UTC 2026
% Result : Theorem 0.19s 2.32s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 106 ( 12 unt; 0 def)
% Number of atoms : 864 ( 212 equ)
% Maximal formula atoms : 166 ( 8 avg)
% Number of connectives : 1277 ( 519 ~; 595 |; 114 &)
% ( 6 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 3 con; 0-4 aty)
% Number of variables : 289 ( 2 sgn 75 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_xboole_0__e18_27__finset_1__1,conjecture,
! [X1] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( ! [X6] :
~ ( ! [X7] :
( ( subset(X6,X7)
& in(X7,X5) )
=> X7 = X6 )
& in(X6,X5) )
& X5 != empty_set ) ) )
& X3 = X4
& ordinal(X4) )
& in(X3,succ(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e18_27__finset_1__1) ).
fof(s1_tarski__e18_27__finset_1__1,axiom,
! [X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( ( ? [X9] :
( ( in(X9,omega)
=> ! [X10] :
( element(X10,powerset(powerset(X9)))
=> ~ ( ! [X11] :
~ ( ! [X12] :
( ( subset(X11,X12)
& in(X12,X10) )
=> X12 = X11 )
& in(X11,X10) )
& X10 != empty_set ) ) )
& X4 = X9
& ordinal(X9) )
& X2 = X4
& ? [X5] :
( ( in(X5,omega)
=> ! [X6] :
( element(X6,powerset(powerset(X5)))
=> ~ ( ! [X7] :
~ ( ! [X8] :
( ( subset(X7,X8)
& in(X8,X6) )
=> X8 = X7 )
& in(X7,X6) )
& X6 != empty_set ) ) )
& X3 = X5
& ordinal(X5) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X13] :
( ( in(X13,omega)
=> ! [X14] :
( element(X14,powerset(powerset(X13)))
=> ~ ( ! [X15] :
~ ( ! [X16] :
( ( subset(X15,X16)
& in(X16,X14) )
=> X16 = X15 )
& in(X15,X14) )
& X14 != empty_set ) ) )
& X3 = X13
& ordinal(X13) )
& X4 = X3
& in(X4,succ(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e18_27__finset_1__1) ).
fof(c_0_2,plain,
! [X2,X3,X4] :
( epred1_3(X4,X3,X2)
<=> ( ? [X9] :
( ( in(X9,omega)
=> ! [X10] :
( element(X10,powerset(powerset(X9)))
=> ~ ( ! [X11] :
~ ( ! [X12] :
( ( subset(X11,X12)
& in(X12,X10) )
=> X12 = X11 )
& in(X11,X10) )
& X10 != empty_set ) ) )
& X4 = X9
& ordinal(X9) )
& X2 = X4
& ? [X5] :
( ( in(X5,omega)
=> ! [X6] :
( element(X6,powerset(powerset(X5)))
=> ~ ( ! [X7] :
~ ( ! [X8] :
( ( subset(X7,X8)
& in(X8,X6) )
=> X8 = X7 )
& in(X7,X6) )
& X6 != empty_set ) ) )
& X3 = X5
& ordinal(X5) )
& X2 = X3 ) ),
introduced(definition) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( ! [X6] :
~ ( ! [X7] :
( ( subset(X6,X7)
& in(X7,X5) )
=> X7 = X6 )
& in(X6,X5) )
& X5 != empty_set ) ) )
& X3 = X4
& ordinal(X4) )
& in(X3,succ(X1)) ) ) ),
inference(assume_negation,[status(cth)],[s1_xboole_0__e18_27__finset_1__1]) ).
fof(c_0_4,plain,
! [X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( epred1_3(X4,X3,X2)
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X13] :
( ( in(X13,omega)
=> ! [X14] :
( element(X14,powerset(powerset(X13)))
=> ~ ( ! [X15] :
~ ( ! [X16] :
( ( subset(X15,X16)
& in(X16,X14) )
=> X16 = X15 )
& in(X15,X14) )
& X14 != empty_set ) ) )
& X3 = X13
& ordinal(X13) )
& X4 = X3
& in(X4,succ(X1)) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[s1_tarski__e18_27__finset_1__1]),c_0_2]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( ! [X6] :
~ ( ! [X7] :
( ( subset(X6,X7)
& in(X7,X5) )
=> X7 = X6 )
& in(X6,X5) )
& X5 != empty_set ) ) )
& X3 = X4
& ordinal(X4) )
& in(X3,succ(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_6,plain,
! [X70,X75,X78,X80,X81,X82,X83,X85] :
( ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| ~ in(X85,esk32_3(X70,X81,X83))
| esk33_4(X70,X81,X83,X85) != X85 )
& ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| ~ in(X85,esk32_3(X70,X81,X83))
| subset(X85,esk33_4(X70,X81,X83,X85)) )
& ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| ~ in(X85,esk32_3(X70,X81,X83))
| in(esk33_4(X70,X81,X83,X85),esk32_3(X70,X81,X83)) )
& ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| esk32_3(X70,X81,X83) != empty_set )
& ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| element(esk32_3(X70,X81,X83),powerset(powerset(X83))) )
& ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| in(X83,omega) )
& ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| ~ in(X75,esk28_1(X70))
| ~ in(esk30_2(X70,X75),omega)
| ~ element(X78,powerset(powerset(esk30_2(X70,X75))))
| X78 = empty_set
| X80 = esk31_3(X70,X75,X78)
| ~ subset(esk31_3(X70,X75,X78),X80)
| ~ in(X80,X78) )
& ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| ~ in(X75,esk28_1(X70))
| ~ in(esk30_2(X70,X75),omega)
| ~ element(X78,powerset(powerset(esk30_2(X70,X75))))
| X78 = empty_set
| in(esk31_3(X70,X75,X78),X78) )
& ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| ~ in(X75,esk28_1(X70))
| X75 = esk30_2(X70,X75) )
& ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| ~ in(X75,esk28_1(X70))
| ordinal(esk30_2(X70,X75)) )
& ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| ~ in(X75,esk28_1(X70))
| esk29_2(X70,X75) = X75 )
& ( ~ ordinal(X70)
| esk26_1(X70) != esk27_1(X70)
| ~ in(X75,esk28_1(X70))
| in(esk29_2(X70,X75),succ(X70)) )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| ~ in(X85,esk32_3(X70,X81,X83))
| esk33_4(X70,X81,X83,X85) != X85 )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| ~ in(X85,esk32_3(X70,X81,X83))
| subset(X85,esk33_4(X70,X81,X83,X85)) )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| ~ in(X85,esk32_3(X70,X81,X83))
| in(esk33_4(X70,X81,X83,X85),esk32_3(X70,X81,X83)) )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| esk32_3(X70,X81,X83) != empty_set )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| element(esk32_3(X70,X81,X83),powerset(powerset(X83))) )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| in(X81,esk28_1(X70))
| X82 != X81
| ~ in(X82,succ(X70))
| X81 != X83
| ~ ordinal(X83)
| in(X83,omega) )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ in(X75,esk28_1(X70))
| ~ in(esk30_2(X70,X75),omega)
| ~ element(X78,powerset(powerset(esk30_2(X70,X75))))
| X78 = empty_set
| X80 = esk31_3(X70,X75,X78)
| ~ subset(esk31_3(X70,X75,X78),X80)
| ~ in(X80,X78) )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ in(X75,esk28_1(X70))
| ~ in(esk30_2(X70,X75),omega)
| ~ element(X78,powerset(powerset(esk30_2(X70,X75))))
| X78 = empty_set
| in(esk31_3(X70,X75,X78),X78) )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ in(X75,esk28_1(X70))
| X75 = esk30_2(X70,X75) )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ in(X75,esk28_1(X70))
| ordinal(esk30_2(X70,X75)) )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ in(X75,esk28_1(X70))
| esk29_2(X70,X75) = X75 )
& ( ~ ordinal(X70)
| epred1_3(esk27_1(X70),esk26_1(X70),esk25_1(X70))
| ~ in(X75,esk28_1(X70))
| in(esk29_2(X70,X75),succ(X70)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_4])])])])])])]) ).
fof(c_0_7,negated_conjecture,
! [X18,X20,X22,X25,X27] :
( ( in(esk2_1(X18),X18)
| ~ in(esk5_1(X18),omega)
| ~ element(X25,powerset(powerset(esk5_1(X18))))
| X25 = empty_set
| X27 = esk6_2(X18,X25)
| ~ subset(esk6_2(X18,X25),X27)
| ~ in(X27,X25) )
& ( in(esk2_1(X18),X18)
| ~ in(esk5_1(X18),omega)
| ~ element(X25,powerset(powerset(esk5_1(X18))))
| X25 = empty_set
| in(esk6_2(X18,X25),X25) )
& ( in(esk2_1(X18),X18)
| esk2_1(X18) = esk5_1(X18) )
& ( in(esk2_1(X18),X18)
| ordinal(esk5_1(X18)) )
& ( in(esk2_1(X18),X18)
| in(esk2_1(X18),succ(esk1_0)) )
& ( ~ in(esk2_1(X18),X18)
| ~ in(esk2_1(X18),succ(esk1_0))
| esk2_1(X18) != X20
| ~ ordinal(X20)
| ~ in(X22,esk3_2(X18,X20))
| esk4_3(X18,X20,X22) != X22 )
& ( ~ in(esk2_1(X18),X18)
| ~ in(esk2_1(X18),succ(esk1_0))
| esk2_1(X18) != X20
| ~ ordinal(X20)
| ~ in(X22,esk3_2(X18,X20))
| subset(X22,esk4_3(X18,X20,X22)) )
& ( ~ in(esk2_1(X18),X18)
| ~ in(esk2_1(X18),succ(esk1_0))
| esk2_1(X18) != X20
| ~ ordinal(X20)
| ~ in(X22,esk3_2(X18,X20))
| in(esk4_3(X18,X20,X22),esk3_2(X18,X20)) )
& ( ~ in(esk2_1(X18),X18)
| ~ in(esk2_1(X18),succ(esk1_0))
| esk2_1(X18) != X20
| ~ ordinal(X20)
| esk3_2(X18,X20) != empty_set )
& ( ~ in(esk2_1(X18),X18)
| ~ in(esk2_1(X18),succ(esk1_0))
| esk2_1(X18) != X20
| ~ ordinal(X20)
| element(esk3_2(X18,X20),powerset(powerset(X20))) )
& ( ~ in(esk2_1(X18),X18)
| ~ in(esk2_1(X18),succ(esk1_0))
| esk2_1(X18) != X20
| ~ ordinal(X20)
| in(X20,omega) )
& ordinal(esk1_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).
cnf(c_0_8,plain,
( ~ ordinal(X2)
| X5 != X3
| ~ in(X5,succ(X2))
| X3 != X4
| ~ ordinal(X4)
| ~ in(X1,esk32_3(X2,X3,X4))
| epred1_3(esk27_1(X2),esk26_1(X2),esk25_1(X2))
| in(X3,esk28_1(X2))
| subset(X1,esk33_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( ~ ordinal(X1)
| X5 != X2
| ~ in(X5,succ(X1))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X4,esk32_3(X1,X2,X3))
| esk33_4(X1,X2,X3,X4) != X4
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| in(X2,esk28_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ ordinal(X1)
| X5 != X2
| ~ in(X5,succ(X1))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X4,esk32_3(X1,X2,X3))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| in(X2,esk28_1(X1))
| in(esk33_4(X1,X2,X3,X4),esk32_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
( in(esk2_1(X1),X1)
| ordinal(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( in(esk2_1(X1),X1)
| esk2_1(X1) = esk5_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( ~ ordinal(X1)
| X4 != X2
| ~ in(X4,succ(X1))
| X2 != X3
| ~ ordinal(X3)
| esk32_3(X1,X2,X3) != empty_set
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| in(X2,esk28_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( ~ in(esk5_1(X3),omega)
| ~ element(X2,powerset(powerset(esk5_1(X3))))
| ~ subset(esk6_2(X3,X2),X1)
| ~ in(X1,X2)
| in(esk2_1(X3),X3)
| X2 = empty_set
| X1 = esk6_2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( ~ ordinal(X1)
| ~ ordinal(X3)
| ~ in(X3,succ(X1))
| ~ in(X2,esk32_3(X1,X3,X3))
| in(X3,esk28_1(X1))
| subset(X2,esk33_4(X1,X3,X3,X2))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_8])]) ).
cnf(c_0_16,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X2,succ(X1))
| ~ in(X3,esk32_3(X1,X2,X2))
| esk33_4(X1,X2,X2,X3) != X3
| in(X2,esk28_1(X1))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_17,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X2,succ(X1))
| ~ in(X3,esk32_3(X1,X2,X2))
| in(X2,esk28_1(X1))
| in(esk33_4(X1,X2,X2,X3),esk32_3(X1,X2,X2))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).
cnf(c_0_18,negated_conjecture,
( in(esk2_1(X1),X1)
| in(esk2_1(X1),succ(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
ordinal(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
( ordinal(esk2_1(X1))
| in(esk2_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_21,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X2,succ(X1))
| esk32_3(X1,X2,X2) != empty_set
| in(X2,esk28_1(X1))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_13])]) ).
cnf(c_0_22,negated_conjecture,
( ~ ordinal(X2)
| ~ ordinal(X3)
| ~ in(X3,succ(X2))
| ~ in(esk5_1(X4),omega)
| ~ in(esk6_2(X4,X1),esk32_3(X2,X3,X3))
| ~ in(esk33_4(X2,X3,X3,esk6_2(X4,X1)),X1)
| ~ element(X1,powerset(powerset(esk5_1(X4))))
| in(esk2_1(X4),X4)
| in(X3,esk28_1(X2))
| epred1_3(esk27_1(X2),esk26_1(X2),esk25_1(X2))
| X1 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(X2,esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)))
| in(esk2_1(X1),X1)
| in(esk2_1(X1),esk28_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)))
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(esk5_1(X1),omega)
| ~ element(X2,powerset(powerset(esk5_1(X1))))
| in(esk2_1(X1),X1)
| X2 = empty_set
| in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
( esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)) != empty_set
| in(esk2_1(X1),X1)
| in(esk2_1(X1),esk28_1(esk1_0))
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_26,plain,
( ~ ordinal(X4)
| X3 != X2
| ~ in(X3,succ(X4))
| X2 != X1
| ~ ordinal(X1)
| epred1_3(esk27_1(X4),esk26_1(X4),esk25_1(X4))
| in(X2,esk28_1(X4))
| in(X1,omega) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(esk5_1(X2),omega)
| ~ element(esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)),powerset(powerset(esk5_1(X2))))
| in(esk2_1(X2),X2)
| in(esk2_1(X1),X1)
| in(esk2_1(X1),esk28_1(esk1_0))
| 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(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19])]),c_0_20]),c_0_18]),c_0_24]),c_0_25]) ).
cnf(c_0_28,plain,
( ~ ordinal(X1)
| X4 != X2
| ~ in(X4,succ(X1))
| X2 != X3
| ~ ordinal(X3)
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| in(X2,esk28_1(X1))
| element(esk32_3(X1,X2,X3),powerset(powerset(X3))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_29,plain,
( ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X2,succ(X1))
| in(X2,omega)
| in(X2,esk28_1(X1))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_26])]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(esk2_1(X2),X2)
| ~ in(esk2_1(X2),succ(esk1_0))
| esk2_1(X2) != X3
| ~ ordinal(X3)
| ~ in(X1,esk3_2(X2,X3))
| subset(X1,esk4_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_31,negated_conjecture,
( ~ in(esk2_1(X1),X1)
| ~ in(esk2_1(X1),succ(esk1_0))
| esk2_1(X1) != X2
| ~ ordinal(X2)
| ~ in(X3,esk3_2(X1,X2))
| esk4_3(X1,X2,X3) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(esk2_1(X2),omega)
| ~ element(esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)),powerset(powerset(esk2_1(X2))))
| in(esk2_1(X1),X1)
| in(esk2_1(X2),X2)
| in(esk2_1(X1),esk28_1(esk1_0))
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_12]) ).
cnf(c_0_33,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X2,succ(X1))
| in(X2,esk28_1(X1))
| element(esk32_3(X1,X2,X2),powerset(powerset(X2)))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_28])]) ).
cnf(c_0_34,negated_conjecture,
( in(esk2_1(X1),X1)
| in(esk2_1(X1),omega)
| in(esk2_1(X1),esk28_1(esk1_0))
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_35,plain,
( ~ ordinal(X3)
| ~ in(X4,esk28_1(X3))
| ~ in(esk30_2(X3,X4),omega)
| ~ element(X2,powerset(powerset(esk30_2(X3,X4))))
| ~ subset(esk31_3(X3,X4,X2),X1)
| ~ in(X1,X2)
| epred1_3(esk27_1(X3),esk26_1(X3),esk25_1(X3))
| X2 = empty_set
| X1 = esk31_3(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_36,negated_conjecture,
( ~ ordinal(esk2_1(X2))
| ~ in(esk2_1(X2),X2)
| ~ in(X1,esk3_2(X2,esk2_1(X2)))
| ~ in(esk2_1(X2),succ(esk1_0))
| subset(X1,esk4_3(X2,esk2_1(X2),X1)) ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( ~ ordinal(esk2_1(X1))
| ~ in(esk2_1(X1),X1)
| ~ in(X2,esk3_2(X1,esk2_1(X1)))
| ~ in(esk2_1(X1),succ(esk1_0))
| esk4_3(X1,esk2_1(X1),X2) != X2 ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_38,negated_conjecture,
( ~ in(esk2_1(X1),X1)
| ~ in(esk2_1(X1),succ(esk1_0))
| esk2_1(X1) != X2
| ~ ordinal(X2)
| ~ in(X3,esk3_2(X1,X2))
| in(esk4_3(X1,X2,X3),esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_39,negated_conjecture,
( ~ in(esk2_1(X1),X1)
| ~ in(esk2_1(X1),succ(esk1_0))
| esk2_1(X1) != X2
| ~ ordinal(X2)
| esk3_2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_40,negated_conjecture,
( in(esk2_1(X1),X1)
| in(esk2_1(X1),esk28_1(esk1_0))
| 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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_19])]),c_0_20]),c_0_34]),c_0_18]) ).
cnf(c_0_41,negated_conjecture,
( ~ ordinal(X2)
| ~ ordinal(esk2_1(X4))
| ~ in(esk2_1(X4),X4)
| ~ in(X3,esk28_1(X2))
| ~ in(esk30_2(X2,X3),omega)
| ~ in(esk2_1(X4),succ(esk1_0))
| ~ in(esk31_3(X2,X3,X1),esk3_2(X4,esk2_1(X4)))
| ~ in(esk4_3(X4,esk2_1(X4),esk31_3(X2,X3,X1)),X1)
| ~ element(X1,powerset(powerset(esk30_2(X2,X3))))
| epred1_3(esk27_1(X2),esk26_1(X2),esk25_1(X2))
| X1 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( ~ ordinal(esk2_1(X1))
| ~ in(esk2_1(X1),X1)
| ~ in(X2,esk3_2(X1,esk2_1(X1)))
| ~ in(esk2_1(X1),succ(esk1_0))
| in(esk4_3(X1,esk2_1(X1),X2),esk3_2(X1,esk2_1(X1))) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
( ~ ordinal(X1)
| ~ in(X2,esk28_1(X1))
| ~ in(esk30_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk30_2(X1,X2))))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| X3 = empty_set
| in(esk31_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_44,negated_conjecture,
( ~ ordinal(esk2_1(X1))
| ~ in(esk2_1(X1),X1)
| ~ in(esk2_1(X1),succ(esk1_0))
| esk3_2(X1,esk2_1(X1)) != empty_set ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
( ~ ordinal(X2)
| ~ in(X1,esk28_1(X2))
| epred1_3(esk27_1(X2),esk26_1(X2),esk25_1(X2))
| X1 = esk30_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_46,negated_conjecture,
( in(esk2_1(esk28_1(esk1_0)),esk28_1(esk1_0))
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(ef,[status(thm)],[c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( ~ ordinal(X1)
| ~ ordinal(esk2_1(X2))
| ~ in(esk2_1(X2),X2)
| ~ in(X3,esk28_1(X1))
| ~ in(esk30_2(X1,X3),omega)
| ~ in(esk2_1(X2),succ(esk1_0))
| ~ element(esk3_2(X2,esk2_1(X2)),powerset(powerset(esk30_2(X1,X3))))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| 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(spm,[status(thm)],[c_0_45,c_0_46]),c_0_19])]) ).
cnf(c_0_49,negated_conjecture,
( ~ in(esk2_1(X1),X1)
| ~ in(esk2_1(X1),succ(esk1_0))
| esk2_1(X1) != X2
| ~ ordinal(X2)
| element(esk3_2(X1,X2),powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_50,plain,
( ~ ordinal(X1)
| ~ in(X2,esk28_1(X1))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| ordinal(esk30_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_51,plain,
( ~ ordinal(X1)
| ~ in(X2,esk28_1(X1))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| esk29_2(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_52,negated_conjecture,
( ~ ordinal(esk2_1(X1))
| ~ in(esk2_1(X1),X1)
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ in(esk2_1(esk28_1(esk1_0)),omega)
| ~ element(esk3_2(X1,esk2_1(X1)),powerset(powerset(esk2_1(esk28_1(esk1_0)))))
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_19])]),c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( ~ ordinal(esk2_1(X1))
| ~ in(esk2_1(X1),X1)
| ~ in(esk2_1(X1),succ(esk1_0))
| element(esk3_2(X1,esk2_1(X1)),powerset(powerset(esk2_1(X1)))) ),
inference(er,[status(thm)],[c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( ordinal(esk2_1(esk28_1(esk1_0)))
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_48]),c_0_19])]),c_0_20]) ).
cnf(c_0_55,plain,
( ~ ordinal(X1)
| ~ in(X2,esk28_1(X1))
| epred1_3(esk27_1(X1),esk26_1(X1),esk25_1(X1))
| in(esk29_2(X1,X2),succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_56,negated_conjecture,
( epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0))
| 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(spm,[status(thm)],[c_0_51,c_0_46]),c_0_19])]) ).
cnf(c_0_57,plain,
( ~ ordinal(X2)
| esk26_1(X2) != esk27_1(X2)
| X5 != X3
| ~ in(X5,succ(X2))
| X3 != X4
| ~ ordinal(X4)
| ~ in(X1,esk32_3(X2,X3,X4))
| in(X3,esk28_1(X2))
| subset(X1,esk33_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_58,plain,
( ~ ordinal(X1)
| esk26_1(X1) != esk27_1(X1)
| X5 != X2
| ~ in(X5,succ(X1))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X4,esk32_3(X1,X2,X3))
| esk33_4(X1,X2,X3,X4) != X4
| in(X2,esk28_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_59,plain,
( ~ ordinal(X1)
| esk26_1(X1) != esk27_1(X1)
| X5 != X2
| ~ in(X5,succ(X1))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X4,esk32_3(X1,X2,X3))
| in(X2,esk28_1(X1))
| in(esk33_4(X1,X2,X3,X4),esk32_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_60,plain,
( ~ ordinal(X1)
| esk26_1(X1) != esk27_1(X1)
| X4 != X2
| ~ in(X4,succ(X1))
| X2 != X3
| ~ ordinal(X3)
| esk32_3(X1,X2,X3) != empty_set
| in(X2,esk28_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_61,plain,
! [X2,X3,X4] :
( epred1_3(X4,X3,X2)
=> ( ? [X9] :
( ( in(X9,omega)
=> ! [X10] :
( element(X10,powerset(powerset(X9)))
=> ~ ( ! [X11] :
~ ( ! [X12] :
( ( subset(X11,X12)
& in(X12,X10) )
=> X12 = X11 )
& in(X11,X10) )
& X10 != empty_set ) ) )
& X4 = X9
& ordinal(X9) )
& X2 = X4
& ? [X5] :
( ( in(X5,omega)
=> ! [X6] :
( element(X6,powerset(powerset(X5)))
=> ~ ( ! [X7] :
~ ( ! [X8] :
( ( subset(X7,X8)
& in(X8,X6) )
=> X8 = X7 )
& in(X7,X6) )
& X6 != empty_set ) ) )
& X3 = X5
& ordinal(X5) )
& X2 = X3 ) ),
inference(split_equiv,[status(thm)],[c_0_2]) ).
cnf(c_0_62,negated_conjecture,
( ~ in(esk2_1(X2),X2)
| ~ in(esk2_1(X2),succ(esk1_0))
| esk2_1(X2) != X1
| ~ ordinal(X1)
| in(X1,omega) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_63,negated_conjecture,
( ~ in(esk2_1(esk28_1(esk1_0)),omega)
| ~ in(esk2_1(esk28_1(esk1_0)),succ(esk1_0))
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_46]) ).
cnf(c_0_64,negated_conjecture,
( in(esk2_1(esk28_1(esk1_0)),succ(esk1_0))
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_19])]),c_0_18]) ).
cnf(c_0_65,plain,
( ~ ordinal(X2)
| ~ ordinal(X3)
| ~ in(X3,succ(X2))
| ~ in(X1,esk32_3(X2,X3,X3))
| esk26_1(X2) != esk27_1(X2)
| in(X3,esk28_1(X2))
| subset(X1,esk33_4(X2,X3,X3,X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_57])]) ).
cnf(c_0_66,plain,
( ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X1,succ(X2))
| ~ in(X3,esk32_3(X2,X1,X1))
| esk26_1(X2) != esk27_1(X2)
| esk33_4(X2,X1,X1,X3) != X3
| in(X1,esk28_1(X2)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_58])]) ).
cnf(c_0_67,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X2,succ(X1))
| ~ in(X3,esk32_3(X1,X2,X2))
| esk26_1(X1) != esk27_1(X1)
| in(X2,esk28_1(X1))
| in(esk33_4(X1,X2,X2,X3),esk32_3(X1,X2,X2)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_59])]) ).
cnf(c_0_68,plain,
( ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X1,succ(X2))
| esk26_1(X2) != esk27_1(X2)
| esk32_3(X2,X1,X1) != empty_set
| in(X1,esk28_1(X2)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_60])]) ).
fof(c_0_69,plain,
! [X87,X88,X89,X91,X93,X95,X97] :
( ( ~ epred1_3(X89,X88,X87)
| ~ in(esk36_3(X87,X88,X89),omega)
| ~ element(X95,powerset(powerset(esk36_3(X87,X88,X89))))
| X95 = empty_set
| X97 = esk37_4(X87,X88,X89,X95)
| ~ subset(esk37_4(X87,X88,X89,X95),X97)
| ~ in(X97,X95) )
& ( ~ epred1_3(X89,X88,X87)
| ~ in(esk36_3(X87,X88,X89),omega)
| ~ element(X95,powerset(powerset(esk36_3(X87,X88,X89))))
| X95 = empty_set
| in(esk37_4(X87,X88,X89,X95),X95) )
& ( ~ epred1_3(X89,X88,X87)
| X89 = esk36_3(X87,X88,X89) )
& ( ~ epred1_3(X89,X88,X87)
| ordinal(esk36_3(X87,X88,X89)) )
& ( ~ epred1_3(X89,X88,X87)
| X87 = X89 )
& ( ~ epred1_3(X89,X88,X87)
| ~ in(esk34_3(X87,X88,X89),omega)
| ~ element(X91,powerset(powerset(esk34_3(X87,X88,X89))))
| X91 = empty_set
| X93 = esk35_4(X87,X88,X89,X91)
| ~ subset(esk35_4(X87,X88,X89,X91),X93)
| ~ in(X93,X91) )
& ( ~ epred1_3(X89,X88,X87)
| ~ in(esk34_3(X87,X88,X89),omega)
| ~ element(X91,powerset(powerset(esk34_3(X87,X88,X89))))
| X91 = empty_set
| in(esk35_4(X87,X88,X89,X91),X91) )
& ( ~ epred1_3(X89,X88,X87)
| X88 = esk34_3(X87,X88,X89) )
& ( ~ epred1_3(X89,X88,X87)
| ordinal(esk34_3(X87,X88,X89)) )
& ( ~ epred1_3(X89,X88,X87)
| X87 = X88 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])])])]) ).
cnf(c_0_70,negated_conjecture,
( ~ ordinal(esk2_1(X1))
| ~ in(esk2_1(X1),X1)
| ~ in(esk2_1(X1),succ(esk1_0))
| in(esk2_1(X1),omega) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_71,negated_conjecture,
( ~ in(esk2_1(esk28_1(esk1_0)),omega)
| epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk25_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,negated_conjecture,
( ~ ordinal(X3)
| ~ ordinal(X2)
| ~ in(X2,succ(X3))
| ~ in(esk5_1(X4),omega)
| ~ in(esk6_2(X4,X1),esk32_3(X3,X2,X2))
| ~ in(esk33_4(X3,X2,X2,esk6_2(X4,X1)),X1)
| ~ element(X1,powerset(powerset(esk5_1(X4))))
| esk26_1(X3) != esk27_1(X3)
| in(esk2_1(X4),X4)
| in(X2,esk28_1(X3))
| X1 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_65]),c_0_66]) ).
cnf(c_0_73,negated_conjecture,
( ~ in(X2,esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)))
| esk26_1(esk1_0) != esk27_1(esk1_0)
| in(esk2_1(X1),X1)
| in(esk2_1(X1),esk28_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))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_74,negated_conjecture,
( esk26_1(esk1_0) != esk27_1(esk1_0)
| esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)) != empty_set
| in(esk2_1(X1),X1)
| in(esk2_1(X1),esk28_1(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_75,plain,
( ~ ordinal(X4)
| esk26_1(X4) != esk27_1(X4)
| X3 != X2
| ~ in(X3,succ(X4))
| X2 != X1
| ~ ordinal(X1)
| in(X2,esk28_1(X4))
| in(X1,omega) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_76,plain,
( ~ epred1_3(X3,X2,X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_77,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_70,c_0_64]),c_0_54]),c_0_46]),c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( ~ in(esk5_1(X2),omega)
| ~ element(esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)),powerset(powerset(esk5_1(X2))))
| esk26_1(esk1_0) != esk27_1(esk1_0)
| in(esk2_1(X2),X2)
| in(esk2_1(X1),X1)
| in(esk2_1(X1),esk28_1(esk1_0)) ),
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_72,c_0_73]),c_0_19])]),c_0_20]),c_0_18]),c_0_24]),c_0_74]) ).
cnf(c_0_79,plain,
( ~ ordinal(X1)
| esk26_1(X1) != esk27_1(X1)
| X4 != X2
| ~ in(X4,succ(X1))
| X2 != X3
| ~ ordinal(X3)
| in(X2,esk28_1(X1))
| element(esk32_3(X1,X2,X3),powerset(powerset(X3))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_80,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X1,succ(X2))
| esk26_1(X2) != esk27_1(X2)
| in(X1,omega)
| in(X1,esk28_1(X2)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_75])]) ).
cnf(c_0_81,plain,
esk25_1(esk1_0) = esk26_1(esk1_0),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,negated_conjecture,
( ~ in(esk2_1(X2),omega)
| ~ element(esk32_3(esk1_0,esk2_1(X1),esk2_1(X1)),powerset(powerset(esk2_1(X2))))
| esk26_1(esk1_0) != esk27_1(esk1_0)
| in(esk2_1(X1),X1)
| in(esk2_1(X2),X2)
| in(esk2_1(X1),esk28_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_78,c_0_12]) ).
cnf(c_0_83,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ~ in(X2,succ(X1))
| esk26_1(X1) != esk27_1(X1)
| in(X2,esk28_1(X1))
| element(esk32_3(X1,X2,X2),powerset(powerset(X2))) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_79])]) ).
cnf(c_0_84,negated_conjecture,
( esk26_1(esk1_0) != esk27_1(esk1_0)
| in(esk2_1(X1),X1)
| in(esk2_1(X1),omega)
| in(esk2_1(X1),esk28_1(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_85,plain,
( ~ epred1_3(X2,X3,X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_86,negated_conjecture,
epred1_3(esk27_1(esk1_0),esk26_1(esk1_0),esk26_1(esk1_0)),
inference(rw,[status(thm)],[c_0_77,c_0_81]) ).
cnf(c_0_87,negated_conjecture,
( esk26_1(esk1_0) != esk27_1(esk1_0)
| in(esk2_1(X1),X1)
| in(esk2_1(X1),esk28_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_82,c_0_83]),c_0_19])]),c_0_20]),c_0_84]),c_0_18]) ).
cnf(c_0_88,plain,
esk26_1(esk1_0) = esk27_1(esk1_0),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_89,negated_conjecture,
( in(esk2_1(X1),X1)
| in(esk2_1(X1),esk28_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88])]) ).
cnf(c_0_90,plain,
( ~ ordinal(X1)
| esk26_1(X1) != esk27_1(X1)
| ~ in(X2,esk28_1(X1))
| esk29_2(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_91,negated_conjecture,
in(esk2_1(esk28_1(esk1_0)),esk28_1(esk1_0)),
inference(ef,[status(thm)],[c_0_89]) ).
cnf(c_0_92,plain,
( ~ ordinal(X2)
| esk26_1(X2) != esk27_1(X2)
| ~ in(X1,esk28_1(X2))
| X1 = esk30_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_93,plain,
( ~ ordinal(X3)
| esk26_1(X3) != esk27_1(X3)
| ~ in(X4,esk28_1(X3))
| ~ in(esk30_2(X3,X4),omega)
| ~ element(X2,powerset(powerset(esk30_2(X3,X4))))
| ~ subset(esk31_3(X3,X4,X2),X1)
| ~ in(X1,X2)
| X2 = empty_set
| X1 = esk31_3(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_94,plain,
( ~ ordinal(X1)
| esk26_1(X1) != esk27_1(X1)
| ~ in(X2,esk28_1(X1))
| in(esk29_2(X1,X2),succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_95,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_90,c_0_91]),c_0_88]),c_0_19])]) ).
cnf(c_0_96,plain,
( ~ ordinal(X1)
| esk26_1(X1) != esk27_1(X1)
| ~ in(X2,esk28_1(X1))
| ordinal(esk30_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_97,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_92,c_0_91]),c_0_88]),c_0_19])]) ).
cnf(c_0_98,negated_conjecture,
( ~ ordinal(X2)
| ~ ordinal(esk2_1(X4))
| ~ in(esk2_1(X4),X4)
| ~ in(X3,esk28_1(X2))
| ~ in(esk30_2(X2,X3),omega)
| ~ in(esk2_1(X4),succ(esk1_0))
| ~ in(esk31_3(X2,X3,X1),esk3_2(X4,esk2_1(X4)))
| ~ in(esk4_3(X4,esk2_1(X4),esk31_3(X2,X3,X1)),X1)
| ~ element(X1,powerset(powerset(esk30_2(X2,X3))))
| esk26_1(X2) != esk27_1(X2)
| X1 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_36]),c_0_37]) ).
cnf(c_0_99,plain,
( ~ ordinal(X1)
| esk26_1(X1) != esk27_1(X1)
| ~ in(X2,esk28_1(X1))
| ~ in(esk30_2(X1,X2),omega)
| ~ element(X3,powerset(powerset(esk30_2(X1,X2))))
| X3 = empty_set
| in(esk31_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_100,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_94,c_0_95]),c_0_88]),c_0_91]),c_0_19])]) ).
cnf(c_0_101,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_96,c_0_97]),c_0_88]),c_0_91]),c_0_19])]) ).
cnf(c_0_102,negated_conjecture,
( ~ ordinal(X1)
| ~ ordinal(esk2_1(X2))
| ~ in(esk2_1(X2),X2)
| ~ in(X3,esk28_1(X1))
| ~ in(esk30_2(X1,X3),omega)
| ~ in(esk2_1(X2),succ(esk1_0))
| ~ element(esk3_2(X2,esk2_1(X2)),powerset(powerset(esk30_2(X1,X3))))
| esk26_1(X1) != esk27_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_42]),c_0_99]),c_0_44]) ).
cnf(c_0_103,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_70,c_0_100]),c_0_91]),c_0_101])]) ).
cnf(c_0_104,negated_conjecture,
( ~ ordinal(esk2_1(X1))
| ~ in(esk2_1(X1),X1)
| ~ in(esk2_1(X1),succ(esk1_0))
| ~ element(esk3_2(X1,esk2_1(X1)),powerset(powerset(esk2_1(esk28_1(esk1_0))))) ),
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_102,c_0_97]),c_0_88]),c_0_91]),c_0_19])]),c_0_103])]) ).
cnf(c_0_105,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_104,c_0_53]),c_0_100]),c_0_91]),c_0_101])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU299+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 06:11:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/2.32 % Version: 3.5.1
% 0.19/2.32 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/2.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/2.32 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/2.32 % Starting new_bool_3 with 300s (1) cores
% 0.19/2.32 % Starting new_bool_1 with 300s (1) cores
% 0.19/2.32 % Starting sh5l with 300s (1) cores
% 0.19/2.32 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1142429 completed with status 0
% 0.19/2.32 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.19/2.32 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/2.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/2.32 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/2.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/2.32 % No SInE strategy applied
% 0.19/2.32 % Search class: FGHSM-FSMM31-MFFFFFNN
% 0.19/2.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/2.32 % Starting SubtermCWHack with 136s (1) cores
% 0.19/2.32 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.19/2.32 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.19/2.32 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.19/2.32 % Starting new_bool_3 with 136s (1) cores
% 0.19/2.32 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with pid 1142439 completed with status 0
% 0.19/2.32 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y
% 0.19/2.32 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/2.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/2.32 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/2.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/2.32 % No SInE strategy applied
% 0.19/2.32 % Search class: FGHSM-FSMM31-MFFFFFNN
% 0.19/2.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/2.32 % Starting SubtermCWHack with 136s (1) cores
% 0.19/2.32 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.19/2.32 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.19/2.32 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.19/2.32 % Preprocessing time : 0.003 s
% 0.19/2.32 % Presaturation interreduction done
% 0.19/2.32
% 0.19/2.32 % Proof found!
% 0.19/2.32 % SZS status Theorem
% 0.19/2.32 % SZS output start CNFRefutation
% See solution above
% 0.19/2.32 % Parsed axioms : 47
% 0.19/2.32 % Removed by relevancy pruning/SinE : 0
% 0.19/2.32 % Initial clauses : 163
% 0.19/2.32 % Removed in clause preprocessing : 8
% 0.19/2.32 % Initial clauses in saturation : 155
% 0.19/2.32 % Processed clauses : 7554
% 0.19/2.32 % ...of these trivial : 86
% 0.19/2.32 % ...subsumed : 4697
% 0.19/2.32 % ...remaining for further processing : 2771
% 0.19/2.32 % Other redundant clauses eliminated : 30
% 0.19/2.32 % Clauses deleted for lack of memory : 0
% 0.19/2.32 % Backward-subsumed : 883
% 0.19/2.32 % Backward-rewritten : 622
% 0.19/2.32 % Generated clauses : 33740
% 0.19/2.32 % ...of the previous two non-redundant : 31992
% 0.19/2.32 % ...aggressively subsumed : 0
% 0.19/2.32 % Contextual simplify-reflections : 523
% 0.19/2.32 % Paramodulations : 33714
% 0.19/2.32 % Factorizations : 8
% 0.19/2.32 % NegExts : 0
% 0.19/2.32 % Equation resolutions : 30
% 0.19/2.32 % Disequality decompositions : 0
% 0.19/2.32 % Total rewrite steps : 9242
% 0.19/2.32 % ...of those cached : 9194
% 0.19/2.32 % Propositional unsat checks : 0
% 0.19/2.32 % Propositional check models : 0
% 0.19/2.32 % Propositional check unsatisfiable : 0
% 0.19/2.32 % Propositional clauses : 0
% 0.19/2.32 % Propositional clauses after purity: 0
% 0.19/2.32 % Propositional unsat core size : 0
% 0.19/2.32 % Propositional preprocessing time : 0.000
% 0.19/2.32 % Propositional encoding time : 0.000
% 0.19/2.32 % Propositional solver time : 0.000
% 0.19/2.32 % Success case prop preproc time : 0.000
% 0.19/2.32 % Success case prop encoding time : 0.000
% 0.19/2.32 % Success case prop solver time : 0.000
% 0.19/2.32 % Current number of processed clauses : 1106
% 0.19/2.32 % Positive orientable unit clauses : 77
% 0.19/2.32 % Positive unorientable unit clauses: 0
% 0.19/2.32 % Negative unit clauses : 16
% 0.19/2.32 % Non-unit-clauses : 1013
% 0.19/2.32 % Current number of unprocessed clauses: 24258
% 0.19/2.32 % ...number of literals in the above : 215259
% 0.19/2.32 % Current number of archived formulas : 0
% 0.19/2.32 % Current number of archived clauses : 1647
% 0.19/2.32 % Clause-clause subsumption calls (NU) : 795722
% 0.19/2.32 % Rec. Clause-clause subsumption calls : 51835
% 0.19/2.32 % Non-unit clause-clause subsumptions : 4632
% 0.19/2.32 % Unit Clause-clause subsumption calls : 6123
% 0.19/2.32 % Rewrite failures with RHS unbound : 0
% 0.19/2.32 % BW rewrite match attempts : 18
% 0.19/2.32 % BW rewrite match successes : 12
% 0.19/2.32 % Condensation attempts : 0
% 0.19/2.32 % Condensation successes : 0
% 0.19/2.32 % Termbank termtop insertions : 1242466
% 0.19/2.32 % Search garbage collected termcells : 1657
% 0.19/2.32
% 0.19/2.32 % -------------------------------------------------
% 0.19/2.32 % User time : 1.794 s
% 0.19/2.32 % System time : 0.032 s
% 0.19/2.32 % Total time : 1.826 s
% 0.19/2.32 % Maximum resident set size: 3688 pages
% 0.19/2.32
% 0.19/2.32 % -------------------------------------------------
% 0.19/2.32 % User time : 8.627 s
% 0.19/2.32 % System time : 0.117 s
% 0.19/2.32 % Total time : 8.744 s
% 0.19/2.32 % Maximum resident set size: 4608 pages
% 0.19/2.32 % E exiting
%------------------------------------------------------------------------------