%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET889+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 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 : n003.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 05:08:55 PM UTC 2026
% Result : Theorem 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 106 ( 67 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 105 ( 33 ~; 57 |; 10 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 75 ( 7 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(l4_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t30_zfmisc_1,conjecture,
! [X1] : powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
fof(c_0_6,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44] :
( ( ~ in(X40,X39)
| X40 = X37
| X40 = X38
| X39 != unordered_pair(X37,X38) )
& ( X41 != X37
| in(X41,X39)
| X39 != unordered_pair(X37,X38) )
& ( X41 != X38
| in(X41,X39)
| X39 != unordered_pair(X37,X38) )
& ( esk2_3(X42,X43,X44) != X42
| ~ in(esk2_3(X42,X43,X44),X44)
| X44 = unordered_pair(X42,X43) )
& ( esk2_3(X42,X43,X44) != X43
| ~ in(esk2_3(X42,X43,X44),X44)
| X44 = unordered_pair(X42,X43) )
& ( in(esk2_3(X42,X43,X44),X44)
| esk2_3(X42,X43,X44) = X42
| esk2_3(X42,X43,X44) = X43
| X44 = unordered_pair(X42,X43) ) ),
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_tarski])])])])])]) ).
fof(c_0_7,plain,
! [X46,X47] :
( ( ~ subset(X46,singleton(X47))
| X46 = empty_set
| X46 = singleton(X47) )
& ( X46 != empty_set
| subset(X46,singleton(X47)) )
& ( X46 != singleton(X47)
| subset(X46,singleton(X47)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(c_0_8,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( ~ in(X32,X31)
| subset(X32,X30)
| X31 != powerset(X30) )
& ( ~ subset(X33,X30)
| in(X33,X31)
| X31 != powerset(X30) )
& ( ~ in(esk1_2(X34,X35),X35)
| ~ subset(esk1_2(X34,X35),X34)
| X35 = powerset(X34) )
& ( in(esk1_2(X34,X35),X35)
| subset(esk1_2(X34,X35),X34)
| X35 = powerset(X34) ) ),
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_zfmisc_1])])])])])]) ).
cnf(c_0_9,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( in(esk1_2(X1,X2),X2)
| subset(esk1_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( esk1_2(singleton(X1),X2) = singleton(X1)
| esk1_2(singleton(X1),X2) = empty_set
| X2 = powerset(singleton(X1))
| in(esk1_2(singleton(X1),X2),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( esk1_2(singleton(X1),unordered_pair(X2,X3)) = singleton(X1)
| esk1_2(singleton(X1),unordered_pair(X2,X3)) = empty_set
| esk1_2(singleton(X1),unordered_pair(X2,X3)) = X3
| esk1_2(singleton(X1),unordered_pair(X2,X3)) = X2
| unordered_pair(X2,X3) = powerset(singleton(X1)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_15,plain,
! [X28,X29] : unordered_pair(X28,X29) = unordered_pair(X29,X28),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_16,plain,
( esk1_2(singleton(X1),unordered_pair(X2,empty_set)) = singleton(X1)
| esk1_2(singleton(X1),unordered_pair(X2,empty_set)) = empty_set
| esk1_2(singleton(X1),unordered_pair(X2,empty_set)) = X2
| unordered_pair(X2,empty_set) = powerset(singleton(X1)) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_14])]) ).
cnf(c_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X50] : subset(X50,X50),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_19,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] : powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
inference(assume_negation,[status(cth)],[t30_zfmisc_1]) ).
cnf(c_0_21,plain,
( X2 = powerset(X1)
| ~ in(esk1_2(X1,X2),X2)
| ~ subset(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,plain,
( esk1_2(singleton(X1),unordered_pair(empty_set,singleton(X1))) = singleton(X1)
| esk1_2(singleton(X1),unordered_pair(empty_set,singleton(X1))) = empty_set
| powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_16])]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_23,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_19])]) ).
cnf(c_0_25,plain,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_27,negated_conjecture,
powerset(singleton(esk6_0)) != unordered_pair(empty_set,singleton(esk6_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_28,plain,
( esk1_2(singleton(X1),unordered_pair(empty_set,singleton(X1))) = empty_set
| powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_29,plain,
subset(empty_set,singleton(X1)),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_26])]) ).
cnf(c_0_31,negated_conjecture,
powerset(singleton(esk6_0)) != unordered_pair(empty_set,singleton(esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET889+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 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
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:38:26 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------