%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU320+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 : n017.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 05:11:28 PM UTC 2026
% Result : Theorem 3.40s 3.06s
% Output : CNFRefutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 70 ( 9 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 26 ~; 24 |; 4 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t30_tops_1,conjecture,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( open_subset(X2,X1)
<=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(t29_tops_1,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( closed_subset(X2,X1)
<=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( open_subset(X2,X1)
<=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t30_tops_1]) ).
fof(c_0_6,plain,
! [X1908,X1909] :
( ~ element(X1909,powerset(X1908))
| element(subset_complement(X1908,X1909),powerset(X1908)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
fof(c_0_7,negated_conjecture,
( top_str(esk322_0)
& element(esk323_0,powerset(the_carrier(esk322_0)))
& ( ~ open_subset(esk323_0,esk322_0)
| ~ closed_subset(subset_complement(the_carrier(esk322_0),esk323_0),esk322_0) )
& ( open_subset(esk323_0,esk322_0)
| closed_subset(subset_complement(the_carrier(esk322_0),esk323_0),esk322_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X1807,X1808] :
( ~ element(X1808,powerset(X1807))
| subset_complement(X1807,X1808) = set_difference(X1807,X1808) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(c_0_9,plain,
! [X2055,X2056] :
( ~ element(X2056,powerset(X2055))
| subset_complement(X2055,subset_complement(X2055,X2056)) = X2056 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
cnf(c_0_10,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
element(esk323_0,powerset(the_carrier(esk322_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,lemma,
! [X2748,X2749] :
( ( ~ closed_subset(X2749,X2748)
| open_subset(subset_complement(the_carrier(X2748),X2749),X2748)
| ~ element(X2749,powerset(the_carrier(X2748)))
| ~ top_str(X2748) )
& ( ~ open_subset(subset_complement(the_carrier(X2748),X2749),X2748)
| closed_subset(X2749,X2748)
| ~ element(X2749,powerset(the_carrier(X2748)))
| ~ top_str(X2748) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t29_tops_1])])])]) ).
cnf(c_0_15,negated_conjecture,
element(subset_complement(the_carrier(esk322_0),esk323_0),powerset(the_carrier(esk322_0))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
subset_complement(the_carrier(esk322_0),esk323_0) = set_difference(the_carrier(esk322_0),esk323_0),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
subset_complement(the_carrier(esk322_0),subset_complement(the_carrier(esk322_0),esk323_0)) = esk323_0,
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( open_subset(esk323_0,esk322_0)
| closed_subset(subset_complement(the_carrier(esk322_0),esk323_0),esk322_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( ~ open_subset(esk323_0,esk322_0)
| ~ closed_subset(subset_complement(the_carrier(esk322_0),esk323_0),esk322_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,lemma,
( closed_subset(X2,X1)
| ~ open_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
element(set_difference(the_carrier(esk322_0),esk323_0),powerset(the_carrier(esk322_0))),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
subset_complement(the_carrier(esk322_0),set_difference(the_carrier(esk322_0),esk323_0)) = esk323_0,
inference(rw,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_23,negated_conjecture,
top_str(esk322_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
( closed_subset(set_difference(the_carrier(esk322_0),esk323_0),esk322_0)
| open_subset(esk323_0,esk322_0) ),
inference(rw,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( ~ closed_subset(set_difference(the_carrier(esk322_0),esk323_0),esk322_0)
| ~ open_subset(esk323_0,esk322_0) ),
inference(rw,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_26,negated_conjecture,
closed_subset(set_difference(the_carrier(esk322_0),esk323_0),esk322_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_27,lemma,
( open_subset(subset_complement(the_carrier(X2),X1),X2)
| ~ closed_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,negated_conjecture,
~ open_subset(esk323_0,esk322_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_29,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_27,c_0_26]),c_0_22]),c_0_23]),c_0_21])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU320+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n017.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:55:42 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 3.40/3.06 % Version : CSE_E---1.7
% 3.40/3.06 % Problem : theBenchmark.p
% 3.40/3.06 % SZS status Theorem for theBenchmark.p
% 3.40/3.06 % SZS output start CNFRefutation
% See solution above
% 3.40/3.07 % Total time : 2.534s
%------------------------------------------------------------------------------