%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU272+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:11:19 PM UTC 2026
% Result : Theorem 9.25s 6.13s
% Output : CNFRefutation 9.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 72 ( 13 unt; 0 def)
% Number of atoms : 495 ( 143 equ)
% Maximal formula atoms : 252 ( 6 avg)
% Number of connectives : 678 ( 255 ~; 340 |; 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)
<=> ( in(X4,succ(X2))
& ? [X5] :
( ordinal(X5)
& X4 = X5
& in(X5,X1) ) ) ) ),
file('/export/starexec/sandbox2/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] :
( ( X3 = X4
& ? [X6] :
( ordinal(X6)
& X4 = X6
& in(X6,X1) )
& X3 = X5
& ? [X7] :
( ordinal(X7)
& X5 = X7
& in(X7,X1) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,succ(X2))
& X5 = X4
& ? [X8] :
( ordinal(X8)
& X4 = X8
& in(X8,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e8_6__wellord2__1) ).
fof(c_0_2,negated_conjecture,
~ ! [X1,X2] :
( ordinal(X2)
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,succ(X2))
& ? [X5] :
( ordinal(X5)
& X4 = X5
& in(X5,X1) ) ) ) ),
inference(assume_negation,[status(cth)],[s1_xboole_0__e8_6__wellord2__1]) ).
fof(c_0_3,plain,
! [X55,X56,X63,X66,X67,X68] :
( ( in(esk15_3(X55,X56,X63),succ(X56))
| ~ in(X63,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk10_2(X55,X56)
| ~ ordinal(X56) )
& ( esk15_3(X55,X56,X63) = X63
| ~ in(X63,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk10_2(X55,X56)
| ~ ordinal(X56) )
& ( ordinal(esk16_3(X55,X56,X63))
| ~ in(X63,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk10_2(X55,X56)
| ~ ordinal(X56) )
& ( X63 = esk16_3(X55,X56,X63)
| ~ in(X63,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk10_2(X55,X56)
| ~ ordinal(X56) )
& ( in(esk16_3(X55,X56,X63),X55)
| ~ in(X63,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk10_2(X55,X56)
| ~ ordinal(X56) )
& ( ~ in(X67,succ(X56))
| X67 != X66
| ~ ordinal(X68)
| X66 != X68
| ~ in(X68,X55)
| in(X66,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk10_2(X55,X56)
| ~ ordinal(X56) )
& ( in(esk15_3(X55,X56,X63),succ(X56))
| ~ in(X63,esk14_2(X55,X56))
| ordinal(esk12_2(X55,X56))
| ~ ordinal(X56) )
& ( esk15_3(X55,X56,X63) = X63
| ~ in(X63,esk14_2(X55,X56))
| ordinal(esk12_2(X55,X56))
| ~ ordinal(X56) )
& ( ordinal(esk16_3(X55,X56,X63))
| ~ in(X63,esk14_2(X55,X56))
| ordinal(esk12_2(X55,X56))
| ~ ordinal(X56) )
& ( X63 = esk16_3(X55,X56,X63)
| ~ in(X63,esk14_2(X55,X56))
| ordinal(esk12_2(X55,X56))
| ~ ordinal(X56) )
& ( in(esk16_3(X55,X56,X63),X55)
| ~ in(X63,esk14_2(X55,X56))
| ordinal(esk12_2(X55,X56))
| ~ ordinal(X56) )
& ( ~ in(X67,succ(X56))
| X67 != X66
| ~ ordinal(X68)
| X66 != X68
| ~ in(X68,X55)
| in(X66,esk14_2(X55,X56))
| ordinal(esk12_2(X55,X56))
| ~ ordinal(X56) )
& ( in(esk15_3(X55,X56,X63),succ(X56))
| ~ in(X63,esk14_2(X55,X56))
| esk10_2(X55,X56) = esk12_2(X55,X56)
| ~ ordinal(X56) )
& ( esk15_3(X55,X56,X63) = X63
| ~ in(X63,esk14_2(X55,X56))
| esk10_2(X55,X56) = esk12_2(X55,X56)
| ~ ordinal(X56) )
& ( ordinal(esk16_3(X55,X56,X63))
| ~ in(X63,esk14_2(X55,X56))
| esk10_2(X55,X56) = esk12_2(X55,X56)
| ~ ordinal(X56) )
& ( X63 = esk16_3(X55,X56,X63)
| ~ in(X63,esk14_2(X55,X56))
| esk10_2(X55,X56) = esk12_2(X55,X56)
| ~ ordinal(X56) )
& ( in(esk16_3(X55,X56,X63),X55)
| ~ in(X63,esk14_2(X55,X56))
| esk10_2(X55,X56) = esk12_2(X55,X56)
| ~ ordinal(X56) )
& ( ~ in(X67,succ(X56))
| X67 != X66
| ~ ordinal(X68)
| X66 != X68
| ~ in(X68,X55)
| in(X66,esk14_2(X55,X56))
| esk10_2(X55,X56) = esk12_2(X55,X56)
| ~ ordinal(X56) )
& ( in(esk15_3(X55,X56,X63),succ(X56))
| ~ in(X63,esk14_2(X55,X56))
| in(esk12_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( esk15_3(X55,X56,X63) = X63
| ~ in(X63,esk14_2(X55,X56))
| in(esk12_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( ordinal(esk16_3(X55,X56,X63))
| ~ in(X63,esk14_2(X55,X56))
| in(esk12_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( X63 = esk16_3(X55,X56,X63)
| ~ in(X63,esk14_2(X55,X56))
| in(esk12_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( in(esk16_3(X55,X56,X63),X55)
| ~ in(X63,esk14_2(X55,X56))
| in(esk12_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( ~ in(X67,succ(X56))
| X67 != X66
| ~ ordinal(X68)
| X66 != X68
| ~ in(X68,X55)
| in(X66,esk14_2(X55,X56))
| in(esk12_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( in(esk15_3(X55,X56,X63),succ(X56))
| ~ in(X63,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk11_2(X55,X56)
| ~ ordinal(X56) )
& ( esk15_3(X55,X56,X63) = X63
| ~ in(X63,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk11_2(X55,X56)
| ~ ordinal(X56) )
& ( ordinal(esk16_3(X55,X56,X63))
| ~ in(X63,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk11_2(X55,X56)
| ~ ordinal(X56) )
& ( X63 = esk16_3(X55,X56,X63)
| ~ in(X63,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk11_2(X55,X56)
| ~ ordinal(X56) )
& ( in(esk16_3(X55,X56,X63),X55)
| ~ in(X63,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk11_2(X55,X56)
| ~ ordinal(X56) )
& ( ~ in(X67,succ(X56))
| X67 != X66
| ~ ordinal(X68)
| X66 != X68
| ~ in(X68,X55)
| in(X66,esk14_2(X55,X56))
| esk9_2(X55,X56) = esk11_2(X55,X56)
| ~ ordinal(X56) )
& ( in(esk15_3(X55,X56,X63),succ(X56))
| ~ in(X63,esk14_2(X55,X56))
| ordinal(esk13_2(X55,X56))
| ~ ordinal(X56) )
& ( esk15_3(X55,X56,X63) = X63
| ~ in(X63,esk14_2(X55,X56))
| ordinal(esk13_2(X55,X56))
| ~ ordinal(X56) )
& ( ordinal(esk16_3(X55,X56,X63))
| ~ in(X63,esk14_2(X55,X56))
| ordinal(esk13_2(X55,X56))
| ~ ordinal(X56) )
& ( X63 = esk16_3(X55,X56,X63)
| ~ in(X63,esk14_2(X55,X56))
| ordinal(esk13_2(X55,X56))
| ~ ordinal(X56) )
& ( in(esk16_3(X55,X56,X63),X55)
| ~ in(X63,esk14_2(X55,X56))
| ordinal(esk13_2(X55,X56))
| ~ ordinal(X56) )
& ( ~ in(X67,succ(X56))
| X67 != X66
| ~ ordinal(X68)
| X66 != X68
| ~ in(X68,X55)
| in(X66,esk14_2(X55,X56))
| ordinal(esk13_2(X55,X56))
| ~ ordinal(X56) )
& ( in(esk15_3(X55,X56,X63),succ(X56))
| ~ in(X63,esk14_2(X55,X56))
| esk11_2(X55,X56) = esk13_2(X55,X56)
| ~ ordinal(X56) )
& ( esk15_3(X55,X56,X63) = X63
| ~ in(X63,esk14_2(X55,X56))
| esk11_2(X55,X56) = esk13_2(X55,X56)
| ~ ordinal(X56) )
& ( ordinal(esk16_3(X55,X56,X63))
| ~ in(X63,esk14_2(X55,X56))
| esk11_2(X55,X56) = esk13_2(X55,X56)
| ~ ordinal(X56) )
& ( X63 = esk16_3(X55,X56,X63)
| ~ in(X63,esk14_2(X55,X56))
| esk11_2(X55,X56) = esk13_2(X55,X56)
| ~ ordinal(X56) )
& ( in(esk16_3(X55,X56,X63),X55)
| ~ in(X63,esk14_2(X55,X56))
| esk11_2(X55,X56) = esk13_2(X55,X56)
| ~ ordinal(X56) )
& ( ~ in(X67,succ(X56))
| X67 != X66
| ~ ordinal(X68)
| X66 != X68
| ~ in(X68,X55)
| in(X66,esk14_2(X55,X56))
| esk11_2(X55,X56) = esk13_2(X55,X56)
| ~ ordinal(X56) )
& ( in(esk15_3(X55,X56,X63),succ(X56))
| ~ in(X63,esk14_2(X55,X56))
| in(esk13_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( esk15_3(X55,X56,X63) = X63
| ~ in(X63,esk14_2(X55,X56))
| in(esk13_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( ordinal(esk16_3(X55,X56,X63))
| ~ in(X63,esk14_2(X55,X56))
| in(esk13_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( X63 = esk16_3(X55,X56,X63)
| ~ in(X63,esk14_2(X55,X56))
| in(esk13_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( in(esk16_3(X55,X56,X63),X55)
| ~ in(X63,esk14_2(X55,X56))
| in(esk13_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( ~ in(X67,succ(X56))
| X67 != X66
| ~ ordinal(X68)
| X66 != X68
| ~ in(X68,X55)
| in(X66,esk14_2(X55,X56))
| in(esk13_2(X55,X56),X55)
| ~ ordinal(X56) )
& ( in(esk15_3(X55,X56,X63),succ(X56))
| ~ in(X63,esk14_2(X55,X56))
| esk10_2(X55,X56) != esk11_2(X55,X56)
| ~ ordinal(X56) )
& ( esk15_3(X55,X56,X63) = X63
| ~ in(X63,esk14_2(X55,X56))
| esk10_2(X55,X56) != esk11_2(X55,X56)
| ~ ordinal(X56) )
& ( ordinal(esk16_3(X55,X56,X63))
| ~ in(X63,esk14_2(X55,X56))
| esk10_2(X55,X56) != esk11_2(X55,X56)
| ~ ordinal(X56) )
& ( X63 = esk16_3(X55,X56,X63)
| ~ in(X63,esk14_2(X55,X56))
| esk10_2(X55,X56) != esk11_2(X55,X56)
| ~ ordinal(X56) )
& ( in(esk16_3(X55,X56,X63),X55)
| ~ in(X63,esk14_2(X55,X56))
| esk10_2(X55,X56) != esk11_2(X55,X56)
| ~ ordinal(X56) )
& ( ~ in(X67,succ(X56))
| X67 != X66
| ~ ordinal(X68)
| X66 != X68
| ~ in(X68,X55)
| in(X66,esk14_2(X55,X56))
| esk10_2(X55,X56) != esk11_2(X55,X56)
| ~ ordinal(X56) ) ),
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__e8_6__wellord2__1])])])])])]) ).
fof(c_0_4,negated_conjecture,
! [X39,X41] :
( ordinal(esk2_0)
& ( ~ in(esk3_1(X39),X39)
| ~ in(esk3_1(X39),succ(esk2_0))
| ~ ordinal(X41)
| esk3_1(X39) != X41
| ~ in(X41,esk1_0) )
& ( in(esk3_1(X39),succ(esk2_0))
| in(esk3_1(X39),X39) )
& ( ordinal(esk4_1(X39))
| in(esk3_1(X39),X39) )
& ( esk3_1(X39) = esk4_1(X39)
| in(esk3_1(X39),X39) )
& ( in(esk4_1(X39),esk1_0)
| in(esk3_1(X39),X39) ) ),
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_2])])])])]) ).
cnf(c_0_5,plain,
( in(X3,esk14_2(X5,X2))
| esk9_2(X5,X2) = esk10_2(X5,X2)
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
( ordinal(esk4_1(X1))
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( esk3_1(X1) = esk4_1(X1)
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( esk9_2(X1,X2) = esk10_2(X1,X2)
| in(X3,esk14_2(X1,X2))
| ~ in(X3,succ(X2))
| ~ in(X3,X1)
| ~ ordinal(X3)
| ~ ordinal(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_5])]) ).
cnf(c_0_9,negated_conjecture,
( in(esk3_1(X1),succ(esk2_0))
| in(esk3_1(X1),X1) ),
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,
( in(esk3_1(X1),X1)
| ordinal(esk3_1(X1)) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( in(esk4_1(X1),esk1_0)
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
( esk9_2(X1,esk2_0) = esk10_2(X1,esk2_0)
| in(esk3_1(X2),esk14_2(X1,esk2_0))
| in(esk3_1(X2),X2)
| ~ in(esk3_1(X2),X1) ),
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),esk1_0)
| in(esk3_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| in(esk3_1(X1),esk14_2(esk1_0,esk2_0))
| in(esk3_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( in(esk15_3(X1,X2,X3),succ(X2))
| esk9_2(X1,X2) = esk10_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_17,negated_conjecture,
( esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| in(esk3_1(esk14_2(esk1_0,esk2_0)),esk14_2(esk1_0,esk2_0)) ),
inference(ef,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
( esk15_3(X1,X2,X3) = X3
| esk9_2(X1,X2) = esk10_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_19,plain,
( ordinal(esk16_3(X1,X2,X3))
| esk9_2(X1,X2) = esk10_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_20,plain,
( X1 = esk16_3(X2,X3,X1)
| esk9_2(X2,X3) = esk10_2(X2,X3)
| ~ in(X1,esk14_2(X2,X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_21,plain,
( in(esk16_3(X1,X2,X3),X1)
| esk9_2(X1,X2) = esk10_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_22,plain,
( in(X3,esk14_2(X5,X2))
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| esk10_2(X5,X2) != esk11_2(X5,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_23,plain,
( in(X3,esk14_2(X5,X2))
| esk9_2(X5,X2) = esk11_2(X5,X2)
| ~ in(X1,succ(X2))
| X1 != X3
| ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X5)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(esk3_1(X1),X1)
| ~ in(esk3_1(X1),succ(esk2_0))
| ~ ordinal(X2)
| esk3_1(X1) != X2
| ~ in(X2,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_25,negated_conjecture,
( esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| in(esk15_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))),succ(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,
( esk15_3(esk1_0,esk2_0,esk3_1(esk14_2(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_18,c_0_17]),c_0_10])]) ).
cnf(c_0_27,negated_conjecture,
( esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| ordinal(esk16_3(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_19,c_0_17]),c_0_10])]) ).
cnf(c_0_28,negated_conjecture,
( esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(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_20,c_0_17]),c_0_10])]) ).
cnf(c_0_29,negated_conjecture,
( esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| in(esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))),esk1_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,
( in(X1,esk14_2(X2,X3))
| esk11_2(X2,X3) != esk10_2(X2,X3)
| ~ in(X1,succ(X3))
| ~ in(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_22])]) ).
cnf(c_0_31,plain,
( in(esk15_3(X1,X2,X3),succ(X2))
| ~ in(X3,esk14_2(X1,X2))
| esk10_2(X1,X2) != esk11_2(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_32,plain,
( esk15_3(X1,X2,X3) = X3
| ~ in(X3,esk14_2(X1,X2))
| esk10_2(X1,X2) != esk11_2(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_33,plain,
( esk9_2(X1,X2) = esk11_2(X1,X2)
| in(X3,esk14_2(X1,X2))
| ~ in(X3,succ(X2))
| ~ in(X3,X1)
| ~ ordinal(X3)
| ~ ordinal(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_23])]) ).
cnf(c_0_34,negated_conjecture,
( ~ in(esk3_1(X1),succ(esk2_0))
| ~ in(esk3_1(X1),esk1_0)
| ~ in(esk3_1(X1),X1)
| ~ ordinal(esk3_1(X1)) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_35,negated_conjecture,
( esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| in(esk3_1(esk14_2(esk1_0,esk2_0)),succ(esk2_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_36,negated_conjecture,
( esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| ordinal(esk3_1(esk14_2(esk1_0,esk2_0))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
( esk9_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| in(esk3_1(esk14_2(esk1_0,esk2_0)),esk1_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( in(esk3_1(X1),esk14_2(X2,esk2_0))
| in(esk3_1(X1),X1)
| esk11_2(X2,esk2_0) != esk10_2(X2,esk2_0)
| ~ in(esk3_1(X1),X2) ),
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,
( in(X1,succ(X2))
| esk11_2(X3,X2) != esk10_2(X3,X2)
| ~ in(X1,esk14_2(X3,X2))
| ~ ordinal(X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( esk9_2(X1,esk2_0) = esk11_2(X1,esk2_0)
| in(esk3_1(X2),esk14_2(X1,esk2_0))
| in(esk3_1(X2),X2)
| ~ in(esk3_1(X2),X1) ),
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,
( in(esk3_1(X1),esk14_2(esk1_0,esk2_0))
| in(esk3_1(X1),X1)
| esk11_2(esk1_0,esk2_0) != esk10_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_14]) ).
cnf(c_0_43,negated_conjecture,
( in(esk3_1(esk14_2(X1,X2)),succ(esk2_0))
| in(esk3_1(esk14_2(X1,X2)),succ(X2))
| esk11_2(X1,X2) != esk10_2(X1,X2)
| ~ ordinal(X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_9]) ).
cnf(c_0_44,negated_conjecture,
( in(esk3_1(X1),esk14_2(esk1_0,esk2_0))
| in(esk3_1(X1),X1) ),
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,
( in(esk3_1(esk14_2(X1,esk2_0)),succ(esk2_0))
| esk11_2(X1,esk2_0) != esk10_2(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_10]) ).
cnf(c_0_46,plain,
( X1 = esk16_3(X2,X3,X1)
| ~ in(X1,esk14_2(X2,X3))
| esk10_2(X2,X3) != esk11_2(X2,X3)
| ~ ordinal(X3) ),
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,
( esk11_2(X1,esk2_0) != esk10_2(X1,esk2_0)
| ~ in(esk3_1(esk14_2(X1,esk2_0)),esk14_2(X1,esk2_0))
| ~ in(esk3_1(esk14_2(X1,esk2_0)),esk1_0)
| ~ ordinal(esk3_1(esk14_2(X1,esk2_0))) ),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_49,plain,
( ordinal(esk16_3(X1,X2,X3))
| ~ in(X3,esk14_2(X1,X2))
| esk10_2(X1,X2) != esk11_2(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_50,negated_conjecture,
( esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(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(spm,[status(thm)],[c_0_46,c_0_47]),c_0_10])]) ).
cnf(c_0_51,negated_conjecture,
( esk11_2(esk1_0,esk2_0) != esk10_2(esk1_0,esk2_0)
| ~ in(esk3_1(esk14_2(esk1_0,esk2_0)),esk1_0)
| ~ ordinal(esk3_1(esk14_2(esk1_0,esk2_0))) ),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( ordinal(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_49,c_0_50]),c_0_47]),c_0_10])]) ).
cnf(c_0_53,plain,
( in(esk16_3(X1,X2,X3),X1)
| ~ in(X3,esk14_2(X1,X2))
| esk10_2(X1,X2) != esk11_2(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_54,negated_conjecture,
( esk11_2(esk1_0,esk2_0) != esk10_2(esk1_0,esk2_0)
| ~ in(esk3_1(esk14_2(esk1_0,esk2_0)),esk1_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,plain,
( in(esk16_3(X1,X2,X3),X1)
| esk9_2(X1,X2) = esk11_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_56,plain,
( ordinal(esk16_3(X1,X2,X3))
| esk9_2(X1,X2) = esk11_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_57,plain,
( in(esk15_3(X1,X2,X3),succ(X2))
| esk9_2(X1,X2) = esk11_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_58,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_53,c_0_50]),c_0_47]),c_0_10])]),c_0_54]) ).
cnf(c_0_59,plain,
( esk15_3(X1,X2,X3) = X3
| esk9_2(X1,X2) = esk11_2(X1,X2)
| ~ in(X3,esk14_2(X1,X2))
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_60,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| in(esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_47]),c_0_41]),c_0_10])]) ).
cnf(c_0_61,plain,
( X1 = esk16_3(X2,X3,X1)
| esk9_2(X2,X3) = esk11_2(X2,X3)
| ~ in(X1,esk14_2(X2,X3))
| ~ ordinal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_62,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk10_2(esk1_0,esk2_0)
| ordinal(esk16_3(esk1_0,esk2_0,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_56,c_0_47]),c_0_41]),c_0_10])]) ).
cnf(c_0_63,negated_conjecture,
in(esk15_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0))),succ(esk2_0)),
inference(sr,[status(thm)],[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])]),c_0_58]) ).
cnf(c_0_64,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_59,c_0_47]),c_0_41]),c_0_10])]),c_0_58]) ).
cnf(c_0_65,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_60,c_0_58]) ).
cnf(c_0_66,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_61,c_0_47]),c_0_41]),c_0_10])]),c_0_58]) ).
cnf(c_0_67,negated_conjecture,
ordinal(esk16_3(esk1_0,esk2_0,esk3_1(esk14_2(esk1_0,esk2_0)))),
inference(sr,[status(thm)],[c_0_62,c_0_58]) ).
cnf(c_0_68,negated_conjecture,
in(esk3_1(esk14_2(esk1_0,esk2_0)),succ(esk2_0)),
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
in(esk3_1(esk14_2(esk1_0,esk2_0)),esk1_0),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,negated_conjecture,
ordinal(esk3_1(esk14_2(esk1_0,esk2_0))),
inference(rw,[status(thm)],[c_0_67,c_0_66]) ).
cnf(c_0_71,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_68]),c_0_69]),c_0_47]),c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU272+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n031.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:56:24 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 9.25/6.13 % Version : CSE_E---1.7
% 9.25/6.13 % Problem : theBenchmark.p
% 9.25/6.13 % SZS status Theorem for theBenchmark.p
% 9.25/6.13 % SZS output start CNFRefutation
% See solution above
% 9.25/6.17 % Total time : 4.369s
%------------------------------------------------------------------------------