%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM386+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n014.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 04:57:13 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 101 ( 38 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 115 ( 45 ~; 54 |; 10 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 58 ( 4 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t13_ordinal1,conjecture,
! [X1,X2] :
( in(X1,succ(X2))
<=> ( in(X1,X2)
| X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( in(X1,succ(X2))
<=> ( in(X1,X2)
| X1 = X2 ) ),
inference(assume_negation,[status(cth)],[t13_ordinal1]) ).
fof(c_0_5,negated_conjecture,
( ( ~ in(esk14_0,esk15_0)
| ~ in(esk14_0,succ(esk15_0)) )
& ( esk14_0 != esk15_0
| ~ in(esk14_0,succ(esk15_0)) )
& ( in(esk14_0,succ(esk15_0))
| in(esk14_0,esk15_0)
| esk14_0 = esk15_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X60] : succ(X60) = set_union2(X60,singleton(X60)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_7,plain,
! [X68,X69,X70,X71,X72,X73,X74,X75] :
( ( ~ in(X71,X70)
| in(X71,X68)
| in(X71,X69)
| X70 != set_union2(X68,X69) )
& ( ~ in(X72,X68)
| in(X72,X70)
| X70 != set_union2(X68,X69) )
& ( ~ in(X72,X69)
| in(X72,X70)
| X70 != set_union2(X68,X69) )
& ( ~ in(esk2_3(X73,X74,X75),X73)
| ~ in(esk2_3(X73,X74,X75),X75)
| X75 = set_union2(X73,X74) )
& ( ~ in(esk2_3(X73,X74,X75),X74)
| ~ in(esk2_3(X73,X74,X75),X75)
| X75 = set_union2(X73,X74) )
& ( in(esk2_3(X73,X74,X75),X75)
| in(esk2_3(X73,X74,X75),X73)
| in(esk2_3(X73,X74,X75),X74)
| X75 = set_union2(X73,X74) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_8,negated_conjecture,
( ~ in(esk14_0,esk15_0)
| ~ in(esk14_0,succ(esk15_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X61,X62,X63,X64,X65,X66] :
( ( ~ in(X63,X62)
| X63 = X61
| X62 != singleton(X61) )
& ( X64 != X61
| in(X64,X62)
| X62 != singleton(X61) )
& ( ~ in(esk1_2(X65,X66),X66)
| esk1_2(X65,X66) != X65
| X66 = singleton(X65) )
& ( in(esk1_2(X65,X66),X66)
| esk1_2(X65,X66) = X65
| X66 = singleton(X65) ) ),
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)],[d1_tarski])])])])])]) ).
cnf(c_0_12,negated_conjecture,
( in(esk14_0,succ(esk15_0))
| in(esk14_0,esk15_0)
| esk14_0 = esk15_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( ~ in(esk14_0,esk15_0)
| ~ in(esk14_0,set_union2(esk15_0,singleton(esk15_0))) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( esk14_0 != esk15_0
| ~ in(esk14_0,succ(esk15_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( esk15_0 = esk14_0
| in(esk14_0,esk15_0)
| in(esk14_0,set_union2(esk15_0,singleton(esk15_0))) ),
inference(rw,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_20,negated_conjecture,
~ in(esk14_0,esk15_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( esk15_0 != esk14_0
| ~ in(esk14_0,set_union2(esk15_0,singleton(esk15_0))) ),
inference(rw,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_22,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( esk14_0 = esk15_0
| in(esk14_0,set_union2(esk15_0,singleton(esk15_0))) ),
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
~ in(esk14_0,singleton(esk15_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
esk14_0 = esk15_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_20]),c_0_26]) ).
cnf(c_0_29,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_27])]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM386+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n014.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:31:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.374s
%------------------------------------------------------------------------------