%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU337+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n006.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 05:11:31 PM UTC 2026
% Result : Theorem 3.86s 3.21s
% Output : CNFRefutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 57 ( 4 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 57 ( 22 ~; 20 |; 4 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t17_tops_2,conjecture,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( open_subsets(X2,X1)
<=> closed_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tops_2) ).
fof(dt_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(t16_tops_2,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( closed_subsets(X2,X1)
<=> open_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tops_2) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( open_subsets(X2,X1)
<=> closed_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t17_tops_2]) ).
fof(c_0_5,plain,
! [X2125,X2126] :
( ~ element(X2126,powerset(powerset(X2125)))
| element(complements_of_subsets(X2125,X2126),powerset(powerset(X2125))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
fof(c_0_6,negated_conjecture,
( top_str(esk383_0)
& element(esk384_0,powerset(powerset(the_carrier(esk383_0))))
& ( ~ open_subsets(esk384_0,esk383_0)
| ~ closed_subsets(complements_of_subsets(the_carrier(esk383_0),esk384_0),esk383_0) )
& ( open_subsets(esk384_0,esk383_0)
| closed_subsets(complements_of_subsets(the_carrier(esk383_0),esk384_0),esk383_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X2255,X2256] :
( ~ element(X2256,powerset(powerset(X2255)))
| complements_of_subsets(X2255,complements_of_subsets(X2255,X2256)) = X2256 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
fof(c_0_8,lemma,
! [X3003,X3004] :
( ( ~ closed_subsets(X3004,X3003)
| open_subsets(complements_of_subsets(the_carrier(X3003),X3004),X3003)
| ~ element(X3004,powerset(powerset(the_carrier(X3003))))
| ~ top_str(X3003) )
& ( ~ open_subsets(complements_of_subsets(the_carrier(X3003),X3004),X3003)
| closed_subsets(X3004,X3003)
| ~ element(X3004,powerset(powerset(the_carrier(X3003))))
| ~ top_str(X3003) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_tops_2])])])]) ).
cnf(c_0_9,plain,
( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
element(esk384_0,powerset(powerset(the_carrier(esk383_0)))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,lemma,
( closed_subsets(X2,X1)
| ~ open_subsets(complements_of_subsets(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
element(complements_of_subsets(the_carrier(esk383_0),esk384_0),powerset(powerset(the_carrier(esk383_0)))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
complements_of_subsets(the_carrier(esk383_0),complements_of_subsets(the_carrier(esk383_0),esk384_0)) = esk384_0,
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
top_str(esk383_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( open_subsets(esk384_0,esk383_0)
| closed_subsets(complements_of_subsets(the_carrier(esk383_0),esk384_0),esk383_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
( ~ open_subsets(esk384_0,esk383_0)
| ~ closed_subsets(complements_of_subsets(the_carrier(esk383_0),esk384_0),esk383_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
closed_subsets(complements_of_subsets(the_carrier(esk383_0),esk384_0),esk383_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_19,lemma,
( open_subsets(complements_of_subsets(the_carrier(X2),X1),X2)
| ~ closed_subsets(X1,X2)
| ~ element(X1,powerset(powerset(the_carrier(X2))))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
~ open_subsets(esk384_0,esk383_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_14]),c_0_15]),c_0_13])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.21 % Problem : SEU337+2 : TPTP v9.2.1. Released v3.3.0.
% 0.02/0.21 % 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
% 0.13/0.43 % Computer : n006.cluster.edu
% 0.13/0.43 % Model : x86_64 x86_64
% 0.13/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.43 % Memory : 8042.1875MB
% 0.13/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.43 % CPULimit : 300
% 0.13/0.43 % WCLimit : 300
% 0.13/0.43 % DateTime : Tue May 5 02:58:31 EDT 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.47 % start to proof: theBenchmark
% 3.86/3.21 % Version : CSE_E---1.7
% 3.86/3.21 % Problem : theBenchmark.p
% 3.86/3.21 % SZS status Theorem for theBenchmark.p
% 3.86/3.21 % SZS output start CNFRefutation
% See solution above
% 3.86/3.22 % Total time : 2.475s
%------------------------------------------------------------------------------