%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU298+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.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 : Tue May 5 05:11:24 PM UTC 2026
% Result : Theorem 1.51s 1.76s
% Output : CNFRefutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 69 ( 6 unt; 0 def)
% Number of atoms : 469 ( 154 equ)
% Maximal formula atoms : 196 ( 6 avg)
% Number of connectives : 675 ( 275 ~; 338 |; 54 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-3 aty)
% Number of variables : 131 ( 0 sgn 20 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_tarski__e4_27_3_1__finset_1__1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& element(X2,powerset(powerset(succ(X1)))) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6] :
( in(X6,X2)
& X4 = set_difference(X6,singleton(X1)) )
& X3 = X5
& ? [X7] :
( in(X7,X2)
& X5 = set_difference(X7,singleton(X1)) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,powerset(X1))
& X5 = X4
& ? [X8] :
( in(X8,X2)
& X4 = set_difference(X8,singleton(X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_27_3_1__finset_1__1) ).
fof(s1_xboole_0__e4_27_3_1__finset_1,conjecture,
! [X1,X2] :
( ( ordinal(X1)
& element(X2,powerset(powerset(succ(X1)))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(X1))
& ? [X5] :
( in(X5,X2)
& X4 = set_difference(X5,singleton(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_27_3_1__finset_1) ).
fof(c_0_2,plain,
! [X119,X120,X127,X130,X131,X132] :
( ( in(esk27_3(X119,X120,X127),powerset(X119))
| ~ in(X127,esk26_2(X119,X120))
| esk21_2(X119,X120) = esk22_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( esk27_3(X119,X120,X127) = X127
| ~ in(X127,esk26_2(X119,X120))
| esk21_2(X119,X120) = esk22_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk28_3(X119,X120,X127),X120)
| ~ in(X127,esk26_2(X119,X120))
| esk21_2(X119,X120) = esk22_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( X127 = set_difference(esk28_3(X119,X120,X127),singleton(X119))
| ~ in(X127,esk26_2(X119,X120))
| esk21_2(X119,X120) = esk22_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( ~ in(X131,powerset(X119))
| X131 != X130
| ~ in(X132,X120)
| X130 != set_difference(X132,singleton(X119))
| in(X130,esk26_2(X119,X120))
| esk21_2(X119,X120) = esk22_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk27_3(X119,X120,X127),powerset(X119))
| ~ in(X127,esk26_2(X119,X120))
| in(esk24_2(X119,X120),X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( esk27_3(X119,X120,X127) = X127
| ~ in(X127,esk26_2(X119,X120))
| in(esk24_2(X119,X120),X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk28_3(X119,X120,X127),X120)
| ~ in(X127,esk26_2(X119,X120))
| in(esk24_2(X119,X120),X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( X127 = set_difference(esk28_3(X119,X120,X127),singleton(X119))
| ~ in(X127,esk26_2(X119,X120))
| in(esk24_2(X119,X120),X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( ~ in(X131,powerset(X119))
| X131 != X130
| ~ in(X132,X120)
| X130 != set_difference(X132,singleton(X119))
| in(X130,esk26_2(X119,X120))
| in(esk24_2(X119,X120),X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk27_3(X119,X120,X127),powerset(X119))
| ~ in(X127,esk26_2(X119,X120))
| esk22_2(X119,X120) = set_difference(esk24_2(X119,X120),singleton(X119))
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( esk27_3(X119,X120,X127) = X127
| ~ in(X127,esk26_2(X119,X120))
| esk22_2(X119,X120) = set_difference(esk24_2(X119,X120),singleton(X119))
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk28_3(X119,X120,X127),X120)
| ~ in(X127,esk26_2(X119,X120))
| esk22_2(X119,X120) = set_difference(esk24_2(X119,X120),singleton(X119))
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( X127 = set_difference(esk28_3(X119,X120,X127),singleton(X119))
| ~ in(X127,esk26_2(X119,X120))
| esk22_2(X119,X120) = set_difference(esk24_2(X119,X120),singleton(X119))
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( ~ in(X131,powerset(X119))
| X131 != X130
| ~ in(X132,X120)
| X130 != set_difference(X132,singleton(X119))
| in(X130,esk26_2(X119,X120))
| esk22_2(X119,X120) = set_difference(esk24_2(X119,X120),singleton(X119))
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk27_3(X119,X120,X127),powerset(X119))
| ~ in(X127,esk26_2(X119,X120))
| esk21_2(X119,X120) = esk23_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( esk27_3(X119,X120,X127) = X127
| ~ in(X127,esk26_2(X119,X120))
| esk21_2(X119,X120) = esk23_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk28_3(X119,X120,X127),X120)
| ~ in(X127,esk26_2(X119,X120))
| esk21_2(X119,X120) = esk23_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( X127 = set_difference(esk28_3(X119,X120,X127),singleton(X119))
| ~ in(X127,esk26_2(X119,X120))
| esk21_2(X119,X120) = esk23_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( ~ in(X131,powerset(X119))
| X131 != X130
| ~ in(X132,X120)
| X130 != set_difference(X132,singleton(X119))
| in(X130,esk26_2(X119,X120))
| esk21_2(X119,X120) = esk23_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk27_3(X119,X120,X127),powerset(X119))
| ~ in(X127,esk26_2(X119,X120))
| in(esk25_2(X119,X120),X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( esk27_3(X119,X120,X127) = X127
| ~ in(X127,esk26_2(X119,X120))
| in(esk25_2(X119,X120),X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk28_3(X119,X120,X127),X120)
| ~ in(X127,esk26_2(X119,X120))
| in(esk25_2(X119,X120),X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( X127 = set_difference(esk28_3(X119,X120,X127),singleton(X119))
| ~ in(X127,esk26_2(X119,X120))
| in(esk25_2(X119,X120),X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( ~ in(X131,powerset(X119))
| X131 != X130
| ~ in(X132,X120)
| X130 != set_difference(X132,singleton(X119))
| in(X130,esk26_2(X119,X120))
| in(esk25_2(X119,X120),X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk27_3(X119,X120,X127),powerset(X119))
| ~ in(X127,esk26_2(X119,X120))
| esk23_2(X119,X120) = set_difference(esk25_2(X119,X120),singleton(X119))
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( esk27_3(X119,X120,X127) = X127
| ~ in(X127,esk26_2(X119,X120))
| esk23_2(X119,X120) = set_difference(esk25_2(X119,X120),singleton(X119))
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk28_3(X119,X120,X127),X120)
| ~ in(X127,esk26_2(X119,X120))
| esk23_2(X119,X120) = set_difference(esk25_2(X119,X120),singleton(X119))
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( X127 = set_difference(esk28_3(X119,X120,X127),singleton(X119))
| ~ in(X127,esk26_2(X119,X120))
| esk23_2(X119,X120) = set_difference(esk25_2(X119,X120),singleton(X119))
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( ~ in(X131,powerset(X119))
| X131 != X130
| ~ in(X132,X120)
| X130 != set_difference(X132,singleton(X119))
| in(X130,esk26_2(X119,X120))
| esk23_2(X119,X120) = set_difference(esk25_2(X119,X120),singleton(X119))
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk27_3(X119,X120,X127),powerset(X119))
| ~ in(X127,esk26_2(X119,X120))
| esk22_2(X119,X120) != esk23_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( esk27_3(X119,X120,X127) = X127
| ~ in(X127,esk26_2(X119,X120))
| esk22_2(X119,X120) != esk23_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( in(esk28_3(X119,X120,X127),X120)
| ~ in(X127,esk26_2(X119,X120))
| esk22_2(X119,X120) != esk23_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( X127 = set_difference(esk28_3(X119,X120,X127),singleton(X119))
| ~ in(X127,esk26_2(X119,X120))
| esk22_2(X119,X120) != esk23_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) )
& ( ~ in(X131,powerset(X119))
| X131 != X130
| ~ in(X132,X120)
| X130 != set_difference(X132,singleton(X119))
| in(X130,esk26_2(X119,X120))
| esk22_2(X119,X120) != esk23_2(X119,X120)
| ~ ordinal(X119)
| ~ element(X120,powerset(powerset(succ(X119)))) ) ),
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)],[s1_tarski__e4_27_3_1__finset_1__1])])])])])]) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
( ( ordinal(X1)
& element(X2,powerset(powerset(succ(X1)))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(X1))
& ? [X5] :
( in(X5,X2)
& X4 = set_difference(X5,singleton(X1)) ) ) ) ),
inference(assume_negation,[status(cth)],[s1_xboole_0__e4_27_3_1__finset_1]) ).
cnf(c_0_4,plain,
( in(X3,esk26_2(X2,X5))
| esk21_2(X2,X5) = esk22_2(X2,X5)
| ~ in(X1,powerset(X2))
| X1 != X3
| ~ in(X4,X5)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X5,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
fof(c_0_5,negated_conjecture,
! [X71,X73] :
( ordinal(esk1_0)
& element(esk2_0,powerset(powerset(succ(esk1_0))))
& ( ~ in(esk3_1(X71),X71)
| ~ in(esk3_1(X71),powerset(esk1_0))
| ~ in(X73,esk2_0)
| esk3_1(X71) != set_difference(X73,singleton(esk1_0)) )
& ( in(esk3_1(X71),powerset(esk1_0))
| in(esk3_1(X71),X71) )
& ( in(esk4_1(X71),esk2_0)
| in(esk3_1(X71),X71) )
& ( esk3_1(X71) = set_difference(esk4_1(X71),singleton(esk1_0))
| in(esk3_1(X71),X71) ) ),
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_3])])])])]) ).
cnf(c_0_6,plain,
( esk21_2(X1,X2) = esk22_2(X1,X2)
| in(X3,esk26_2(X1,X2))
| X3 != set_difference(X4,singleton(X1))
| ~ in(X3,powerset(X1))
| ~ in(X4,X2)
| ~ element(X2,powerset(powerset(succ(X1))))
| ~ ordinal(X1) ),
inference(er,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
element(esk2_0,powerset(powerset(succ(esk1_0)))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
ordinal(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| in(X1,esk26_2(esk1_0,esk2_0))
| X1 != set_difference(X2,singleton(esk1_0))
| ~ in(X1,powerset(esk1_0))
| ~ in(X2,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).
cnf(c_0_10,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| in(set_difference(X1,singleton(esk1_0)),esk26_2(esk1_0,esk2_0))
| ~ in(set_difference(X1,singleton(esk1_0)),powerset(esk1_0))
| ~ in(X1,esk2_0) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_11,negated_conjecture,
( esk3_1(X1) = set_difference(esk4_1(X1),singleton(esk1_0))
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
( in(esk4_1(X1),esk2_0)
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( in(esk3_1(X1),powerset(esk1_0))
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,plain,
( esk27_3(X1,X2,X3) = X3
| esk21_2(X1,X2) = esk22_2(X1,X2)
| ~ in(X3,esk26_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| in(esk3_1(X1),esk26_2(esk1_0,esk2_0))
| in(esk3_1(X1),X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]) ).
cnf(c_0_16,plain,
( in(X3,esk26_2(X2,X5))
| esk21_2(X2,X5) = esk23_2(X2,X5)
| ~ in(X1,powerset(X2))
| X1 != X3
| ~ in(X4,X5)
| X3 != set_difference(X4,singleton(X2))
| ~ ordinal(X2)
| ~ element(X5,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_17,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| esk27_3(esk1_0,esk2_0,X1) = X1
| ~ in(X1,esk26_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_7]),c_0_8])]) ).
cnf(c_0_18,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| in(esk3_1(esk26_2(esk1_0,esk2_0)),esk26_2(esk1_0,esk2_0)) ),
inference(ef,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( esk21_2(X1,X2) = esk23_2(X1,X2)
| in(X3,esk26_2(X1,X2))
| X3 != set_difference(X4,singleton(X1))
| ~ in(X3,powerset(X1))
| ~ in(X4,X2)
| ~ element(X2,powerset(powerset(succ(X1))))
| ~ ordinal(X1) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( in(esk27_3(X1,X2,X3),powerset(X1))
| esk21_2(X1,X2) = esk22_2(X1,X2)
| ~ in(X3,esk26_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_21,negated_conjecture,
( esk27_3(esk1_0,esk2_0,esk3_1(esk26_2(esk1_0,esk2_0))) = esk3_1(esk26_2(esk1_0,esk2_0))
| esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk23_2(esk1_0,esk2_0)
| in(X1,esk26_2(esk1_0,esk2_0))
| X1 != set_difference(X2,singleton(esk1_0))
| ~ in(X1,powerset(esk1_0))
| ~ in(X2,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_7]),c_0_8])]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(esk3_1(X1),X1)
| ~ in(esk3_1(X1),powerset(esk1_0))
| ~ in(X2,esk2_0)
| esk3_1(X1) != set_difference(X2,singleton(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_24,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| in(esk3_1(esk26_2(esk1_0,esk2_0)),powerset(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_7]),c_0_8])]),c_0_18]) ).
cnf(c_0_25,plain,
( in(X3,esk26_2(X2,X5))
| ~ in(X1,powerset(X2))
| X1 != X3
| ~ in(X4,X5)
| X3 != set_difference(X4,singleton(X2))
| esk22_2(X2,X5) != esk23_2(X2,X5)
| ~ ordinal(X2)
| ~ element(X5,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_26,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk23_2(esk1_0,esk2_0)
| in(set_difference(X1,singleton(esk1_0)),esk26_2(esk1_0,esk2_0))
| ~ in(set_difference(X1,singleton(esk1_0)),powerset(esk1_0))
| ~ in(X1,esk2_0) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| esk3_1(esk26_2(esk1_0,esk2_0)) != set_difference(X1,singleton(esk1_0))
| ~ in(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_18]) ).
cnf(c_0_28,plain,
( X1 = set_difference(esk28_3(X2,X3,X1),singleton(X2))
| esk21_2(X2,X3) = esk22_2(X2,X3)
| ~ in(X1,esk26_2(X2,X3))
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_29,plain,
( in(esk28_3(X1,X2,X3),X2)
| esk21_2(X1,X2) = esk22_2(X1,X2)
| ~ in(X3,esk26_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_30,plain,
( in(X1,esk26_2(X2,X3))
| esk23_2(X2,X3) != esk22_2(X2,X3)
| X1 != set_difference(X4,singleton(X2))
| ~ in(X1,powerset(X2))
| ~ in(X4,X3)
| ~ element(X3,powerset(powerset(succ(X2))))
| ~ ordinal(X2) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( esk27_3(X1,X2,X3) = X3
| esk21_2(X1,X2) = esk23_2(X1,X2)
| ~ in(X3,esk26_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_32,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk23_2(esk1_0,esk2_0)
| in(esk3_1(X1),esk26_2(esk1_0,esk2_0))
| in(esk3_1(X1),X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_11]),c_0_12]),c_0_13]) ).
cnf(c_0_33,plain,
( esk27_3(X1,X2,X3) = X3
| ~ in(X3,esk26_2(X1,X2))
| esk22_2(X1,X2) != esk23_2(X1,X2)
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_34,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| esk21_2(esk1_0,X1) = esk22_2(esk1_0,X1)
| esk3_1(esk26_2(esk1_0,esk2_0)) != X2
| ~ in(esk28_3(esk1_0,X1,X2),esk2_0)
| ~ in(X2,esk26_2(esk1_0,X1))
| ~ element(X1,powerset(powerset(succ(esk1_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_8])]) ).
cnf(c_0_35,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| in(esk28_3(esk1_0,esk2_0,X1),esk2_0)
| ~ in(X1,esk26_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_7]),c_0_8])]) ).
cnf(c_0_36,negated_conjecture,
( in(X1,esk26_2(esk1_0,esk2_0))
| esk23_2(esk1_0,esk2_0) != esk22_2(esk1_0,esk2_0)
| X1 != set_difference(X2,singleton(esk1_0))
| ~ in(X1,powerset(esk1_0))
| ~ in(X2,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_7]),c_0_8])]) ).
cnf(c_0_37,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk23_2(esk1_0,esk2_0)
| esk27_3(esk1_0,esk2_0,X1) = X1
| ~ in(X1,esk26_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_7]),c_0_8])]) ).
cnf(c_0_38,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk23_2(esk1_0,esk2_0)
| in(esk3_1(esk26_2(esk1_0,esk2_0)),esk26_2(esk1_0,esk2_0)) ),
inference(ef,[status(thm)],[c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( esk27_3(esk1_0,esk2_0,X1) = X1
| esk23_2(esk1_0,esk2_0) != esk22_2(esk1_0,esk2_0)
| ~ in(X1,esk26_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_7]),c_0_8])]) ).
cnf(c_0_40,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| esk3_1(esk26_2(esk1_0,esk2_0)) != X1
| ~ in(X1,esk26_2(esk1_0,esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_7]),c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( in(set_difference(X1,singleton(esk1_0)),esk26_2(esk1_0,esk2_0))
| esk23_2(esk1_0,esk2_0) != esk22_2(esk1_0,esk2_0)
| ~ in(set_difference(X1,singleton(esk1_0)),powerset(esk1_0))
| ~ in(X1,esk2_0) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
( in(esk27_3(X1,X2,X3),powerset(X1))
| esk21_2(X1,X2) = esk23_2(X1,X2)
| ~ in(X3,esk26_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_43,negated_conjecture,
( esk27_3(esk1_0,esk2_0,esk3_1(esk26_2(esk1_0,esk2_0))) = esk3_1(esk26_2(esk1_0,esk2_0))
| esk21_2(esk1_0,esk2_0) = esk23_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
( in(esk27_3(X1,X2,X3),powerset(X1))
| ~ in(X3,esk26_2(X1,X2))
| esk22_2(X1,X2) != esk23_2(X1,X2)
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_45,negated_conjecture,
( esk27_3(esk1_0,esk2_0,esk3_1(esk26_2(esk1_0,esk2_0))) = esk3_1(esk26_2(esk1_0,esk2_0))
| in(esk3_1(esk26_2(esk1_0,esk2_0)),powerset(esk1_0))
| esk23_2(esk1_0,esk2_0) != esk22_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_13]) ).
cnf(c_0_46,negated_conjecture,
esk21_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_40,c_0_18]) ).
cnf(c_0_47,negated_conjecture,
( in(esk3_1(X1),esk26_2(esk1_0,esk2_0))
| in(esk3_1(X1),X1)
| esk23_2(esk1_0,esk2_0) != esk22_2(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_11]),c_0_12]),c_0_13]) ).
cnf(c_0_48,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk23_2(esk1_0,esk2_0)
| in(esk3_1(esk26_2(esk1_0,esk2_0)),powerset(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_7]),c_0_8])]),c_0_38]) ).
cnf(c_0_49,negated_conjecture,
( in(esk3_1(esk26_2(esk1_0,esk2_0)),powerset(esk1_0))
| esk23_2(esk1_0,esk2_0) != esk22_2(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_7]),c_0_8])]),c_0_13]) ).
cnf(c_0_50,negated_conjecture,
( in(esk3_1(X1),esk26_2(esk1_0,esk2_0))
| in(esk3_1(X1),X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_46]),c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk23_2(esk1_0,esk2_0)
| esk3_1(esk26_2(esk1_0,esk2_0)) != set_difference(X1,singleton(esk1_0))
| ~ in(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_48]),c_0_38]) ).
cnf(c_0_52,negated_conjecture,
( esk3_1(esk26_2(esk1_0,esk2_0)) != set_difference(X1,singleton(esk1_0))
| esk23_2(esk1_0,esk2_0) != esk22_2(esk1_0,esk2_0)
| ~ in(esk3_1(esk26_2(esk1_0,esk2_0)),esk26_2(esk1_0,esk2_0))
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
in(esk3_1(esk26_2(esk1_0,esk2_0)),esk26_2(esk1_0,esk2_0)),
inference(ef,[status(thm)],[c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( esk23_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| esk3_1(esk26_2(esk1_0,esk2_0)) != set_difference(X1,singleton(esk1_0))
| ~ in(X1,esk2_0) ),
inference(rw,[status(thm)],[c_0_51,c_0_46]) ).
cnf(c_0_55,plain,
( in(esk28_3(X1,X2,X3),X2)
| esk21_2(X1,X2) = esk23_2(X1,X2)
| ~ in(X3,esk26_2(X1,X2))
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_56,plain,
( in(esk28_3(X1,X2,X3),X2)
| ~ in(X3,esk26_2(X1,X2))
| esk22_2(X1,X2) != esk23_2(X1,X2)
| ~ ordinal(X1)
| ~ element(X2,powerset(powerset(succ(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_57,negated_conjecture,
( esk3_1(esk26_2(esk1_0,esk2_0)) != set_difference(X1,singleton(esk1_0))
| ~ in(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]),c_0_54]) ).
cnf(c_0_58,plain,
( X1 = set_difference(esk28_3(X2,X3,X1),singleton(X2))
| esk21_2(X2,X3) = esk23_2(X2,X3)
| ~ in(X1,esk26_2(X2,X3))
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_59,negated_conjecture,
( esk21_2(esk1_0,esk2_0) = esk23_2(esk1_0,esk2_0)
| in(esk28_3(esk1_0,esk2_0,X1),esk2_0)
| ~ in(X1,esk26_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_7]),c_0_8])]) ).
cnf(c_0_60,negated_conjecture,
( in(esk28_3(esk1_0,esk2_0,X1),esk2_0)
| esk23_2(esk1_0,esk2_0) != esk22_2(esk1_0,esk2_0)
| ~ in(X1,esk26_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_7]),c_0_8])]) ).
cnf(c_0_61,negated_conjecture,
( esk21_2(esk1_0,X1) = esk23_2(esk1_0,X1)
| esk3_1(esk26_2(esk1_0,esk2_0)) != X2
| ~ in(esk28_3(esk1_0,X1,X2),esk2_0)
| ~ in(X2,esk26_2(esk1_0,X1))
| ~ element(X1,powerset(powerset(succ(esk1_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_8])]) ).
cnf(c_0_62,negated_conjecture,
( in(esk28_3(esk1_0,esk2_0,X1),esk2_0)
| ~ in(X1,esk26_2(esk1_0,esk2_0)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_46]),c_0_60]) ).
cnf(c_0_63,plain,
( X1 = set_difference(esk28_3(X2,X3,X1),singleton(X2))
| ~ in(X1,esk26_2(X2,X3))
| esk22_2(X2,X3) != esk23_2(X2,X3)
| ~ ordinal(X2)
| ~ element(X3,powerset(powerset(succ(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_64,negated_conjecture,
( esk23_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0)
| esk3_1(esk26_2(esk1_0,esk2_0)) != X1
| ~ in(X1,esk26_2(esk1_0,esk2_0)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_7]),c_0_46]),c_0_62]) ).
cnf(c_0_65,negated_conjecture,
( esk23_2(esk1_0,X1) != esk22_2(esk1_0,X1)
| esk3_1(esk26_2(esk1_0,esk2_0)) != X2
| ~ in(esk28_3(esk1_0,X1,X2),esk2_0)
| ~ in(X2,esk26_2(esk1_0,X1))
| ~ element(X1,powerset(powerset(succ(esk1_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_63]),c_0_8])]) ).
cnf(c_0_66,negated_conjecture,
esk23_2(esk1_0,esk2_0) = esk22_2(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_64,c_0_53]) ).
cnf(c_0_67,negated_conjecture,
( esk3_1(esk26_2(esk1_0,esk2_0)) != X1
| ~ in(X1,esk26_2(esk1_0,esk2_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_7]),c_0_66])]),c_0_62]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_67,c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU298+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.28 % Computer : n024.cluster.edu
% 0.06/0.28 % Model : x86_64 x86_64
% 0.06/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.28 % Memory : 8042.1875MB
% 0.06/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.28 % CPULimit : 300
% 0.06/0.28 % WCLimit : 300
% 0.06/0.28 % DateTime : Mon May 4 21:55:26 EDT 2026
% 0.06/0.28 % CPUTime :
% 0.06/0.28 % start to proof: theBenchmark
% 1.51/1.76 % Version : CSE_E---1.7
% 1.51/1.76 % Problem : theBenchmark.p
% 1.51/1.76 % SZS status Theorem for theBenchmark.p
% 1.51/1.76 % SZS output start CNFRefutation
% See solution above
% 1.51/1.76 % Total time : 1.361s
%------------------------------------------------------------------------------