%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU272+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 02:24:31 PM UTC 2026
% Result : Theorem 2.79s 0.91s
% Output : CNFRefutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 73 ( 13 unt; 0 def)
% Number of atoms : 497 ( 144 equ)
% Maximal formula atoms : 252 ( 6 avg)
% Number of connectives : 679 ( 255 ~; 341 |; 75 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 68 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 123 ( 0 sgn 20 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_xboole_0__e8_6__wellord2__1,conjecture,
! [X1,X2] :
( ordinal(X2)
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5] :
( in(X5,X1)
& X4 = X5
& ordinal(X5) )
& in(X4,succ(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
fof(s1_tarski__e8_6__wellord2__1,axiom,
! [X1,X2] :
( ordinal(X2)
=> ( ! [X3,X4,X5] :
( ( ? [X7] :
( in(X7,X1)
& X5 = X7
& ordinal(X7) )
& X3 = X5
& ? [X6] :
( in(X6,X1)
& X4 = X6
& ordinal(X6) )
& X3 = X4 )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( ? [X8] :
( in(X8,X1)
& X4 = X8
& ordinal(X8) )
& X5 = X4
& in(X5,succ(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e8_6__wellord2__1) ).
fof(c_0_2,negated_conjecture,
~ ! [X1,X2] :
( ordinal(X2)
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5] :
( in(X5,X1)
& X4 = X5
& ordinal(X5) )
& in(X4,succ(X2)) ) ) ),
inference(assume_negation,[status(cth)],[s1_xboole_0__e8_6__wellord2__1]) ).
fof(c_0_3,plain,
! [X27,X28,X35,X38,X39,X40] :
( ( ~ ordinal(X28)
| esk10_2(X27,X28) != esk11_2(X27,X28)
| in(X38,esk14_2(X27,X28))
| ~ in(X40,X27)
| X38 != X40
| ~ ordinal(X40)
| X39 != X38
| ~ in(X39,succ(X28)) )
& ( ~ ordinal(X28)
| esk10_2(X27,X28) != esk11_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| in(esk16_3(X27,X28,X35),X27) )
& ( ~ ordinal(X28)
| esk10_2(X27,X28) != esk11_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| X35 = esk16_3(X27,X28,X35) )
& ( ~ ordinal(X28)
| esk10_2(X27,X28) != esk11_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| ordinal(esk16_3(X27,X28,X35)) )
& ( ~ ordinal(X28)
| esk10_2(X27,X28) != esk11_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| esk15_3(X27,X28,X35) = X35 )
& ( ~ ordinal(X28)
| esk10_2(X27,X28) != esk11_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| in(esk15_3(X27,X28,X35),succ(X28)) )
& ( ~ ordinal(X28)
| in(esk13_2(X27,X28),X27)
| in(X38,esk14_2(X27,X28))
| ~ in(X40,X27)
| X38 != X40
| ~ ordinal(X40)
| X39 != X38
| ~ in(X39,succ(X28)) )
& ( ~ ordinal(X28)
| in(esk13_2(X27,X28),X27)
| ~ in(X35,esk14_2(X27,X28))
| in(esk16_3(X27,X28,X35),X27) )
& ( ~ ordinal(X28)
| in(esk13_2(X27,X28),X27)
| ~ in(X35,esk14_2(X27,X28))
| X35 = esk16_3(X27,X28,X35) )
& ( ~ ordinal(X28)
| in(esk13_2(X27,X28),X27)
| ~ in(X35,esk14_2(X27,X28))
| ordinal(esk16_3(X27,X28,X35)) )
& ( ~ ordinal(X28)
| in(esk13_2(X27,X28),X27)
| ~ in(X35,esk14_2(X27,X28))
| esk15_3(X27,X28,X35) = X35 )
& ( ~ ordinal(X28)
| in(esk13_2(X27,X28),X27)
| ~ in(X35,esk14_2(X27,X28))
| in(esk15_3(X27,X28,X35),succ(X28)) )
& ( ~ ordinal(X28)
| esk11_2(X27,X28) = esk13_2(X27,X28)
| in(X38,esk14_2(X27,X28))
| ~ in(X40,X27)
| X38 != X40
| ~ ordinal(X40)
| X39 != X38
| ~ in(X39,succ(X28)) )
& ( ~ ordinal(X28)
| esk11_2(X27,X28) = esk13_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| in(esk16_3(X27,X28,X35),X27) )
& ( ~ ordinal(X28)
| esk11_2(X27,X28) = esk13_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| X35 = esk16_3(X27,X28,X35) )
& ( ~ ordinal(X28)
| esk11_2(X27,X28) = esk13_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| ordinal(esk16_3(X27,X28,X35)) )
& ( ~ ordinal(X28)
| esk11_2(X27,X28) = esk13_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| esk15_3(X27,X28,X35) = X35 )
& ( ~ ordinal(X28)
| esk11_2(X27,X28) = esk13_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| in(esk15_3(X27,X28,X35),succ(X28)) )
& ( ~ ordinal(X28)
| ordinal(esk13_2(X27,X28))
| in(X38,esk14_2(X27,X28))
| ~ in(X40,X27)
| X38 != X40
| ~ ordinal(X40)
| X39 != X38
| ~ in(X39,succ(X28)) )
& ( ~ ordinal(X28)
| ordinal(esk13_2(X27,X28))
| ~ in(X35,esk14_2(X27,X28))
| in(esk16_3(X27,X28,X35),X27) )
& ( ~ ordinal(X28)
| ordinal(esk13_2(X27,X28))
| ~ in(X35,esk14_2(X27,X28))
| X35 = esk16_3(X27,X28,X35) )
& ( ~ ordinal(X28)
| ordinal(esk13_2(X27,X28))
| ~ in(X35,esk14_2(X27,X28))
| ordinal(esk16_3(X27,X28,X35)) )
& ( ~ ordinal(X28)
| ordinal(esk13_2(X27,X28))
| ~ in(X35,esk14_2(X27,X28))
| esk15_3(X27,X28,X35) = X35 )
& ( ~ ordinal(X28)
| ordinal(esk13_2(X27,X28))
| ~ in(X35,esk14_2(X27,X28))
| in(esk15_3(X27,X28,X35),succ(X28)) )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk11_2(X27,X28)
| in(X38,esk14_2(X27,X28))
| ~ in(X40,X27)
| X38 != X40
| ~ ordinal(X40)
| X39 != X38
| ~ in(X39,succ(X28)) )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk11_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| in(esk16_3(X27,X28,X35),X27) )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk11_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| X35 = esk16_3(X27,X28,X35) )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk11_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| ordinal(esk16_3(X27,X28,X35)) )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk11_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| esk15_3(X27,X28,X35) = X35 )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk11_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| in(esk15_3(X27,X28,X35),succ(X28)) )
& ( ~ ordinal(X28)
| in(esk12_2(X27,X28),X27)
| in(X38,esk14_2(X27,X28))
| ~ in(X40,X27)
| X38 != X40
| ~ ordinal(X40)
| X39 != X38
| ~ in(X39,succ(X28)) )
& ( ~ ordinal(X28)
| in(esk12_2(X27,X28),X27)
| ~ in(X35,esk14_2(X27,X28))
| in(esk16_3(X27,X28,X35),X27) )
& ( ~ ordinal(X28)
| in(esk12_2(X27,X28),X27)
| ~ in(X35,esk14_2(X27,X28))
| X35 = esk16_3(X27,X28,X35) )
& ( ~ ordinal(X28)
| in(esk12_2(X27,X28),X27)
| ~ in(X35,esk14_2(X27,X28))
| ordinal(esk16_3(X27,X28,X35)) )
& ( ~ ordinal(X28)
| in(esk12_2(X27,X28),X27)
| ~ in(X35,esk14_2(X27,X28))
| esk15_3(X27,X28,X35) = X35 )
& ( ~ ordinal(X28)
| in(esk12_2(X27,X28),X27)
| ~ in(X35,esk14_2(X27,X28))
| in(esk15_3(X27,X28,X35),succ(X28)) )
& ( ~ ordinal(X28)
| esk10_2(X27,X28) = esk12_2(X27,X28)
| in(X38,esk14_2(X27,X28))
| ~ in(X40,X27)
| X38 != X40
| ~ ordinal(X40)
| X39 != X38
| ~ in(X39,succ(X28)) )
& ( ~ ordinal(X28)
| esk10_2(X27,X28) = esk12_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| in(esk16_3(X27,X28,X35),X27) )
& ( ~ ordinal(X28)
| esk10_2(X27,X28) = esk12_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| X35 = esk16_3(X27,X28,X35) )
& ( ~ ordinal(X28)
| esk10_2(X27,X28) = esk12_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| ordinal(esk16_3(X27,X28,X35)) )
& ( ~ ordinal(X28)
| esk10_2(X27,X28) = esk12_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| esk15_3(X27,X28,X35) = X35 )
& ( ~ ordinal(X28)
| esk10_2(X27,X28) = esk12_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| in(esk15_3(X27,X28,X35),succ(X28)) )
& ( ~ ordinal(X28)
| ordinal(esk12_2(X27,X28))
| in(X38,esk14_2(X27,X28))
| ~ in(X40,X27)
| X38 != X40
| ~ ordinal(X40)
| X39 != X38
| ~ in(X39,succ(X28)) )
& ( ~ ordinal(X28)
| ordinal(esk12_2(X27,X28))
| ~ in(X35,esk14_2(X27,X28))
| in(esk16_3(X27,X28,X35),X27) )
& ( ~ ordinal(X28)
| ordinal(esk12_2(X27,X28))
| ~ in(X35,esk14_2(X27,X28))
| X35 = esk16_3(X27,X28,X35) )
& ( ~ ordinal(X28)
| ordinal(esk12_2(X27,X28))
| ~ in(X35,esk14_2(X27,X28))
| ordinal(esk16_3(X27,X28,X35)) )
& ( ~ ordinal(X28)
| ordinal(esk12_2(X27,X28))
| ~ in(X35,esk14_2(X27,X28))
| esk15_3(X27,X28,X35) = X35 )
& ( ~ ordinal(X28)
| ordinal(esk12_2(X27,X28))
| ~ in(X35,esk14_2(X27,X28))
| in(esk15_3(X27,X28,X35),succ(X28)) )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk10_2(X27,X28)
| in(X38,esk14_2(X27,X28))
| ~ in(X40,X27)
| X38 != X40
| ~ ordinal(X40)
| X39 != X38
| ~ in(X39,succ(X28)) )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk10_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| in(esk16_3(X27,X28,X35),X27) )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk10_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| X35 = esk16_3(X27,X28,X35) )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk10_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| ordinal(esk16_3(X27,X28,X35)) )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk10_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| esk15_3(X27,X28,X35) = X35 )
& ( ~ ordinal(X28)
| esk9_2(X27,X28) = esk10_2(X27,X28)
| ~ in(X35,esk14_2(X27,X28))
| in(esk15_3(X27,X28,X35),succ(X28)) ) ),
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)],[s1_tarski__e8_6__wellord2__1])])])])])])]) ).
fof(c_0_4,negated_conjecture,
! [X11,X13] :
( ( in(esk3_1(X11),X11)
| in(esk4_1(X11),esk1_0) )
& ( in(esk3_1(X11),X11)
| esk3_1(X11) = esk4_1(X11) )
& ( in(esk3_1(X11),X11)
| ordinal(esk4_1(X11)) )
& ( in(esk3_1(X11),X11)
| in(esk3_1(X11),succ(esk2_0)) )
& ( ~ in(X13,esk1_0)
| esk3_1(X11) != X13
| ~ ordinal(X13)
| ~ in(esk3_1(X11),succ(esk2_0))
| ~ in(esk3_1(X11),X11) )
& ordinal(esk2_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_2])])])])])]) ).
cnf(c_0_5,plain,
( ~ ordinal(X2)
| ~ in(X4,X5)
| X3 != X4
| ~ ordinal(X4)
| X1 != X3
| ~ in(X1,succ(X2))
| esk9_2(X5,X2) = esk10_2(X5,X2)
| in(X3,esk14_2(X5,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
( in(esk3_1(X1),X1)
| ordinal(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( in(esk3_1(X1),X1)
| esk3_1(X1) = esk4_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( ~ ordinal(X2)
| ~ ordinal(X3)
| ~ in(X3,X1)
| ~ in(X3,succ(X2))
| in(X3,esk14_2(X1,X2))
| esk9_2(X1,X2) = esk10_2(X1,X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_5])]) ).
cnf(c_0_9,negated_conjecture,
( in(esk3_1(X1),X1)
| in(esk3_1(X1),succ(esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
ordinal(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
( ordinal(esk3_1(X1))
| in(esk3_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( in(esk3_1(X1),X1)
| in(esk4_1(X1),esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
( ~ in(esk3_1(X2),X1)
| in(esk3_1(X2),X2)
| in(esk3_1(X2),esk14_2(X1,esk2_0))
| esk9_2(X1,esk2_0) = esk10_2(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),c_0_11]) ).
cnf(c_0_14,negated_conjecture,
( in(esk3_1(X1),X1)
| in(esk3_1(X1),esk1_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( in(esk3_1(X1),X1)
| in(esk3_1(X1),esk14_2(esk1_0,esk2_0))
| esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( ~ ordinal(X2)
| ~ in(X3,esk14_2(X1,X2))
| esk9_2(X1,X2) = esk10_2(X1,X2)
| in(esk15_3(X1,X2,X3),succ(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_17,negated_conjecture,
( in(esk3_1(esk14_2(esk1_0,esk2_0)),esk14_2(esk1_0,esk2_0))
| esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0) ),
inference(ef,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
( ~ ordinal(X2)
| ~ in(X3,esk14_2(X1,X2))
| esk9_2(X1,X2) = esk10_2(X1,X2)
| esk15_3(X1,X2,X3) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_19,plain,
( ~ ordinal(X2)
| ~ in(X3,esk14_2(X1,X2))
| esk9_2(X1,X2) = esk10_2(X1,X2)
| ordinal(esk16_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_20,plain,
( ~ ordinal(X3)
| ~ in(X1,esk14_2(X2,X3))
| esk9_2(X2,X3) = esk10_2(X2,X3)
| X1 = esk16_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_21,plain,
( ~ ordinal(X2)
| ~ in(X3,esk14_2(X1,X2))
| esk9_2(X1,X2) = esk10_2(X1,X2)
| in(esk16_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_22,plain,
( ~ ordinal(X2)
| esk10_2(X5,X2) != esk11_2(X5,X2)
| ~ in(X4,X5)
| X3 != X4
| ~ ordinal(X4)
| X1 != X3
| ~ in(X1,succ(X2))
| in(X3,esk14_2(X5,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_23,plain,
( ~ ordinal(X2)
| ~ in(X4,X5)
| X3 != X4
| ~ ordinal(X4)
| X1 != X3
| ~ in(X1,succ(X2))
| esk9_2(X5,X2) = esk11_2(X5,X2)
| in(X3,esk14_2(X5,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(X2,esk1_0)
| esk3_1(X1) != X2
| ~ ordinal(X2)
| ~ in(esk3_1(X1),succ(esk2_0))
| ~ in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_25,negated_conjecture,
( in(esk15_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))),succ(esk2_0))
| esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_10])]) ).
cnf(c_0_26,negated_conjecture,
( esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| esk15_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))) = esk3_1(esk14_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_10])]) ).
cnf(c_0_27,negated_conjecture,
( ordinal(esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))))
| esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_10])]) ).
cnf(c_0_28,negated_conjecture,
( esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))) = esk3_1(esk14_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_17]),c_0_10])]) ).
cnf(c_0_29,negated_conjecture,
( in(esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))),esk1_0)
| esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_10])]) ).
cnf(c_0_30,plain,
( ~ ordinal(X3)
| ~ ordinal(X1)
| ~ in(X1,X2)
| ~ in(X1,succ(X3))
| esk11_2(X2,X3) != esk10_2(X2,X3)
| in(X1,esk14_2(X2,X3)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_22])]) ).
cnf(c_0_31,plain,
( ~ ordinal(X2)
| esk10_2(X1,X2) != esk11_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| in(esk15_3(X1,X2,X3),succ(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_32,plain,
( ~ ordinal(X2)
| esk10_2(X1,X2) != esk11_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| esk15_3(X1,X2,X3) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_33,plain,
( ~ ordinal(X2)
| ~ ordinal(X3)
| ~ in(X3,X1)
| ~ in(X3,succ(X2))
| in(X3,esk14_2(X1,X2))
| esk9_2(X1,X2) = esk11_2(X1,X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_23])]) ).
cnf(c_0_34,negated_conjecture,
( ~ ordinal(esk3_1(X1))
| ~ in(esk3_1(X1),X1)
| ~ in(esk3_1(X1),esk1_0)
| ~ in(esk3_1(X1),succ(esk2_0)) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_35,negated_conjecture,
( in(esk3_1(esk14_2(esk1_0,esk2_0)),succ(esk2_0))
| esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_36,negated_conjecture,
( ordinal(esk3_1(esk14_2(esk1_0,esk2_0)))
| esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
( in(esk3_1(esk14_2(esk1_0,esk2_0)),esk1_0)
| esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( ~ in(esk3_1(X1),X2)
| esk11_2(X2,esk2_0) != esk10_2(X2,esk2_0)
| in(esk3_1(X1),X1)
| in(esk3_1(X1),esk14_2(X2,esk2_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_9]),c_0_10])]),c_0_11]) ).
cnf(c_0_39,plain,
( ~ ordinal(X2)
| ~ in(X1,esk14_2(X3,X2))
| esk11_2(X3,X2) != esk10_2(X3,X2)
| in(X1,succ(X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( ~ in(esk3_1(X2),X1)
| in(esk3_1(X2),X2)
| in(esk3_1(X2),esk14_2(X1,esk2_0))
| esk9_2(X1,esk2_0) = esk11_2(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_9]),c_0_10])]),c_0_11]) ).
cnf(c_0_41,negated_conjecture,
esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37]),c_0_17]) ).
cnf(c_0_42,negated_conjecture,
( esk11_2(esk1_0,esk2_0) != esk10_2(esk1_0,esk2_0)
| in(esk3_1(X1),X1)
| in(esk3_1(X1),esk14_2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_38,c_0_14]) ).
cnf(c_0_43,negated_conjecture,
( ~ ordinal(X2)
| esk11_2(X1,X2) != esk10_2(X1,X2)
| in(esk3_1(esk14_2(X1,X2)),succ(X2))
| in(esk3_1(esk14_2(X1,X2)),succ(esk2_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_9]) ).
cnf(c_0_44,negated_conjecture,
( in(esk3_1(X1),X1)
| in(esk3_1(X1),esk14_2(esk1_0,esk2_0)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_14]),c_0_41]),c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( esk11_2(X1,esk2_0) != esk10_2(X1,esk2_0)
| in(esk3_1(esk14_2(X1,esk2_0)),succ(esk2_0)) ),
inference(spm,[status(thm)],[c_0_43,c_0_10]) ).
cnf(c_0_46,plain,
( ~ ordinal(X3)
| esk10_2(X2,X3) != esk11_2(X2,X3)
| ~ in(X1,esk14_2(X2,X3))
| X1 = esk16_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_47,negated_conjecture,
in(esk3_1(esk14_2(esk1_0,esk2_0)),esk14_2(esk1_0,esk2_0)),
inference(ef,[status(thm)],[c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( ~ ordinal(esk3_1(esk14_2(X1,esk2_0)))
| ~ in(esk3_1(esk14_2(X1,esk2_0)),esk1_0)
| ~ in(esk3_1(esk14_2(X1,esk2_0)),esk14_2(X1,esk2_0))
| esk11_2(X1,esk2_0) != esk10_2(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_49,plain,
( ~ ordinal(X2)
| esk10_2(X1,X2) != esk11_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| ordinal(esk16_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_50,negated_conjecture,
( esk11_2(esk1_0,esk2_0) != esk10_2(esk1_0,esk2_0)
| esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))) = esk3_1(esk14_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_10])]) ).
cnf(c_0_51,negated_conjecture,
( ~ ordinal(esk3_1(esk14_2(esk1_0,esk2_0)))
| ~ in(esk3_1(esk14_2(esk1_0,esk2_0)),esk1_0)
| esk11_2(esk1_0,esk2_0) != esk10_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( esk11_2(esk1_0,esk2_0) != esk10_2(esk1_0,esk2_0)
| ordinal(esk3_1(esk14_2(esk1_0,esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_47]),c_0_10])]) ).
cnf(c_0_53,plain,
( ~ ordinal(X2)
| ~ in(X3,esk14_2(X1,X2))
| esk9_2(X1,X2) = esk11_2(X1,X2)
| in(esk15_3(X1,X2,X3),succ(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_54,plain,
( ~ ordinal(X2)
| esk10_2(X1,X2) != esk11_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| in(esk16_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_55,negated_conjecture,
( ~ in(esk3_1(esk14_2(esk1_0,esk2_0)),esk1_0)
| esk11_2(esk1_0,esk2_0) != esk10_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
( ~ ordinal(X2)
| ~ in(X3,esk14_2(X1,X2))
| esk9_2(X1,X2) = esk11_2(X1,X2)
| in(esk16_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_57,plain,
( ~ ordinal(X2)
| ~ in(X3,esk14_2(X1,X2))
| esk9_2(X1,X2) = esk11_2(X1,X2)
| ordinal(esk16_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_58,negated_conjecture,
( in(esk15_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))),succ(esk2_0))
| esk11_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_47]),c_0_41]),c_0_10])]) ).
cnf(c_0_59,negated_conjecture,
esk11_2(esk1_0,esk2_0) != esk10_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_54,c_0_50]),c_0_47]),c_0_10])]),c_0_55]) ).
cnf(c_0_60,plain,
( ~ ordinal(X2)
| ~ in(X3,esk14_2(X1,X2))
| esk9_2(X1,X2) = esk11_2(X1,X2)
| esk15_3(X1,X2,X3) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_61,negated_conjecture,
( in(esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))),esk1_0)
| esk11_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_47]),c_0_41]),c_0_10])]) ).
cnf(c_0_62,plain,
( ~ ordinal(X3)
| ~ in(X1,esk14_2(X2,X3))
| esk9_2(X2,X3) = esk11_2(X2,X3)
| X1 = esk16_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_63,negated_conjecture,
( ordinal(esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))))
| esk11_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_47]),c_0_41]),c_0_10])]) ).
cnf(c_0_64,negated_conjecture,
in(esk15_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))),succ(esk2_0)),
inference(sr,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
esk15_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))) = esk3_1(esk14_2(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_47]),c_0_41]),c_0_10])]),c_0_59]) ).
cnf(c_0_66,negated_conjecture,
in(esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))),esk1_0),
inference(sr,[status(thm)],[c_0_61,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))) = esk3_1(esk14_2(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_47]),c_0_41]),c_0_10])]),c_0_59]) ).
cnf(c_0_68,negated_conjecture,
ordinal(esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0)))),
inference(sr,[status(thm)],[c_0_63,c_0_59]) ).
cnf(c_0_69,negated_conjecture,
in(esk3_1(esk14_2(esk1_0,esk2_0)),succ(esk2_0)),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,negated_conjecture,
in(esk3_1(esk14_2(esk1_0,esk2_0)),esk1_0),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,negated_conjecture,
ordinal(esk3_1(esk14_2(esk1_0,esk2_0))),
inference(rw,[status(thm)],[c_0_68,c_0_67]) ).
cnf(c_0_72,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_34,c_0_69]),c_0_70]),c_0_47]),c_0_71])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU272+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.43 % Computer : n019.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Mon Sep 21 06:05:49 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 2.79/0.91 % Version: 3.5.1
% 2.79/0.91 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.79/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.79/0.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.79/0.91 % Starting new_bool_3 with 300s (1) cores
% 2.79/0.91 % Starting new_bool_1 with 300s (1) cores
% 2.79/0.91 % Starting sh5l with 300s (1) cores
% 2.79/0.91 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1845507 completed with status 0
% 2.79/0.91 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.79/0.91 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.79/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.79/0.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.79/0.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.79/0.91 % No SInE strategy applied
% 2.79/0.91 % Search class: FGHSF-FFMM31-SFFFFFNN
% 2.79/0.91 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.79/0.91 % Starting SubtermCWHack with 136s (1) cores
% 2.79/0.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.79/0.91 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 2.79/0.91 % Starting new_bool_3 with 136s (1) cores
% 2.79/0.91 % Starting new_bool_1 with 136s (1) cores
% 2.79/0.91 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1845513 completed with status 0
% 2.79/0.91 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.79/0.91 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.79/0.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.79/0.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.79/0.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.79/0.91 % No SInE strategy applied
% 2.79/0.91 % Search class: FGHSF-FFMM31-SFFFFFNN
% 2.79/0.91 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.79/0.91 % Starting SubtermCWHack with 136s (1) cores
% 2.79/0.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.79/0.91 % Preprocessing time : 0.003 s
% 2.79/0.91 % Presaturation interreduction done
% 2.79/0.91
% 2.79/0.91 % Proof found!
% 2.79/0.91 % SZS status Theorem
% 2.79/0.91 % SZS output start CNFRefutation
% See solution above
% 2.79/0.91 % Parsed axioms : 14
% 2.79/0.91 % Removed by relevancy pruning/SinE : 0
% 2.79/0.91 % Initial clauses : 83
% 2.79/0.91 % Removed in clause preprocessing : 1
% 2.79/0.91 % Initial clauses in saturation : 82
% 2.79/0.91 % Processed clauses : 938
% 2.79/0.91 % ...of these trivial : 9
% 2.79/0.91 % ...subsumed : 256
% 2.79/0.91 % ...remaining for further processing : 673
% 2.79/0.91 % Other redundant clauses eliminated : 19
% 2.79/0.91 % Clauses deleted for lack of memory : 0
% 2.79/0.91 % Backward-subsumed : 43
% 2.79/0.91 % Backward-rewritten : 104
% 2.79/0.91 % Generated clauses : 7058
% 2.79/0.91 % ...of the previous two non-redundant : 6777
% 2.79/0.91 % ...aggressively subsumed : 0
% 2.79/0.91 % Contextual simplify-reflections : 37
% 2.79/0.91 % Paramodulations : 7025
% 2.79/0.91 % Factorizations : 20
% 2.79/0.91 % NegExts : 0
% 2.79/0.91 % Equation resolutions : 19
% 2.79/0.91 % Disequality decompositions : 0
% 2.79/0.91 % Total rewrite steps : 1572
% 2.79/0.91 % ...of those cached : 1550
% 2.79/0.91 % Propositional unsat checks : 0
% 2.79/0.91 % Propositional check models : 0
% 2.79/0.91 % Propositional check unsatisfiable : 0
% 2.79/0.91 % Propositional clauses : 0
% 2.79/0.91 % Propositional clauses after purity: 0
% 2.79/0.91 % Propositional unsat core size : 0
% 2.79/0.91 % Propositional preprocessing time : 0.000
% 2.79/0.91 % Propositional encoding time : 0.000
% 2.79/0.91 % Propositional solver time : 0.000
% 2.79/0.91 % Success case prop preproc time : 0.000
% 2.79/0.91 % Success case prop encoding time : 0.000
% 2.79/0.91 % Success case prop solver time : 0.000
% 2.79/0.91 % Current number of processed clauses : 432
% 2.79/0.91 % Positive orientable unit clauses : 24
% 2.79/0.91 % Positive unorientable unit clauses: 0
% 2.79/0.91 % Negative unit clauses : 11
% 2.79/0.91 % Non-unit-clauses : 397
% 2.79/0.91 % Current number of unprocessed clauses: 5808
% 2.79/0.91 % ...number of literals in the above : 26660
% 2.79/0.91 % Current number of archived formulas : 0
% 2.79/0.91 % Current number of archived clauses : 231
% 2.79/0.91 % Clause-clause subsumption calls (NU) : 20647
% 2.79/0.91 % Rec. Clause-clause subsumption calls : 8545
% 2.79/0.91 % Non-unit clause-clause subsumptions : 302
% 2.79/0.91 % Unit Clause-clause subsumption calls : 3037
% 2.79/0.91 % Rewrite failures with RHS unbound : 0
% 2.79/0.91 % BW rewrite match attempts : 30
% 2.79/0.91 % BW rewrite match successes : 12
% 2.79/0.91 % Condensation attempts : 0
% 2.79/0.91 % Condensation successes : 0
% 2.79/0.91 % Termbank termtop insertions : 216468
% 2.79/0.91 % Search garbage collected termcells : 767
% 2.79/0.91
% 2.79/0.91 % -------------------------------------------------
% 2.79/0.91 % User time : 0.288 s
% 2.79/0.91 % System time : 0.020 s
% 2.79/0.91 % Total time : 0.308 s
% 2.79/0.91 % Maximum resident set size: 3644 pages
% 2.79/0.91
% 2.79/0.91 % -------------------------------------------------
% 2.79/0.91 % User time : 1.690 s
% 2.79/0.91 % System time : 0.085 s
% 2.79/0.91 % Total time : 1.774 s
% 2.79/0.91 % Maximum resident set size: 4608 pages
% 2.79/0.91 % E exiting
%------------------------------------------------------------------------------