%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU147+3 : 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 : n011.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 05:10:47 PM UTC 2026
% Result : Theorem 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 65 ( 34 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 65 ( 23 ~; 31 |; 6 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 1 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(t3_xboole_1,axiom,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_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(t1_zfmisc_1,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_5,plain,
! [X22,X23,X24,X25,X26,X27] :
( ( ~ in(X24,X23)
| X24 = X22
| X23 != singleton(X22) )
& ( X25 != X22
| in(X25,X23)
| X23 != singleton(X22) )
& ( ~ in(esk1_2(X26,X27),X27)
| esk1_2(X26,X27) != X26
| X27 = singleton(X26) )
& ( in(esk1_2(X26,X27),X27)
| esk1_2(X26,X27) = X26
| X27 = singleton(X26) ) ),
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])])])])])]) ).
fof(c_0_6,plain,
! [X42] :
( ~ subset(X42,empty_set)
| X42 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(c_0_7,plain,
! [X29,X30,X31,X32,X33,X34] :
( ( ~ in(X31,X30)
| subset(X31,X29)
| X30 != powerset(X29) )
& ( ~ subset(X32,X29)
| in(X32,X30)
| X30 != powerset(X29) )
& ( ~ in(esk2_2(X33,X34),X34)
| ~ subset(esk2_2(X33,X34),X33)
| X34 = powerset(X33) )
& ( in(esk2_2(X33,X34),X34)
| subset(esk2_2(X33,X34),X33)
| X34 = powerset(X33) ) ),
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_8,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( in(esk2_2(X1,X2),X2)
| subset(esk2_2(X1,X2),X1)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( esk2_2(empty_set,X1) = empty_set
| X1 = powerset(empty_set)
| in(esk2_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_13,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t1_zfmisc_1])]) ).
cnf(c_0_14,plain,
( esk2_2(empty_set,singleton(X1)) = empty_set
| esk2_2(empty_set,singleton(X1)) = X1
| singleton(X1) = powerset(empty_set) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X38] : subset(X38,X38),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_17,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,plain,
( X2 = powerset(X1)
| ~ in(esk2_2(X1,X2),X2)
| ~ subset(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
esk2_2(empty_set,singleton(empty_set)) = empty_set,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_14])]),c_0_15]) ).
cnf(c_0_20,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_17])]) ).
cnf(c_0_22,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU147+3 : 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
% 0.15/0.33 % Computer : n011.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 02:45:33 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Theorem for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------