%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU160+2 : 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 : 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 05:10:51 PM UTC 2026
% Result : Theorem 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 56 ( 32 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 49 ( 18 ~; 24 |; 4 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 2 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t39_zfmisc_1,conjecture,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(l4_zfmisc_1,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
inference(assume_negation,[status(cth)],[t39_zfmisc_1]) ).
fof(c_0_6,lemma,
! [X319,X320] :
( ( ~ subset(X319,singleton(X320))
| X319 = empty_set
| X319 = singleton(X320) )
& ( X319 != empty_set
| subset(X319,singleton(X320)) )
& ( X319 != singleton(X320)
| subset(X319,singleton(X320)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(c_0_7,lemma,
! [X403] : unordered_pair(X403,X403) = singleton(X403),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_8,negated_conjecture,
( ( esk20_0 != empty_set
| ~ subset(esk20_0,singleton(esk21_0)) )
& ( esk20_0 != singleton(esk21_0)
| ~ subset(esk20_0,singleton(esk21_0)) )
& ( subset(esk20_0,singleton(esk21_0))
| esk20_0 = empty_set
| esk20_0 = singleton(esk21_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_9,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( subset(esk20_0,singleton(esk21_0))
| esk20_0 = empty_set
| esk20_0 = singleton(esk21_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( esk20_0 != singleton(esk21_0)
| ~ subset(esk20_0,singleton(esk21_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,lemma,
( X1 = empty_set
| X1 = unordered_pair(X2,X2)
| ~ subset(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( esk20_0 = empty_set
| esk20_0 = unordered_pair(esk21_0,esk21_0)
| subset(esk20_0,unordered_pair(esk21_0,esk21_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_10]) ).
fof(c_0_15,plain,
! [X329] : subset(X329,X329),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_16,negated_conjecture,
( esk20_0 != empty_set
| ~ subset(esk20_0,singleton(esk21_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( esk20_0 != unordered_pair(esk21_0,esk21_0)
| ~ subset(esk20_0,unordered_pair(esk21_0,esk21_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_10]),c_0_10]) ).
cnf(c_0_18,negated_conjecture,
( unordered_pair(esk21_0,esk21_0) = esk20_0
| esk20_0 = empty_set ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,lemma,
! [X356] : subset(empty_set,X356),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_21,negated_conjecture,
( esk20_0 != empty_set
| ~ subset(esk20_0,unordered_pair(esk21_0,esk21_0)) ),
inference(rw,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_22,negated_conjecture,
esk20_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_23,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU160+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n014.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:46:36 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Theorem for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------