%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU319+1 : 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 : n024.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 1.12s 1.64s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 66 ( 3 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 74 ( 30 ~; 28 |; 4 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d6_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( closed_subset(X2,X1)
<=> open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_pre_topc) ).
fof(t17_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(dt_l1_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(t29_tops_1,conjecture,
! [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_4,plain,
! [X30,X31] :
( ( ~ closed_subset(X31,X30)
| open_subset(subset_difference(the_carrier(X30),cast_as_carrier_subset(X30),X31),X30)
| ~ element(X31,powerset(the_carrier(X30)))
| ~ top_str(X30) )
& ( ~ open_subset(subset_difference(the_carrier(X30),cast_as_carrier_subset(X30),X31),X30)
| closed_subset(X31,X30)
| ~ element(X31,powerset(the_carrier(X30)))
| ~ top_str(X30) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_pre_topc])])])]) ).
fof(c_0_5,plain,
! [X49,X50] :
( ~ one_sorted_str(X49)
| ~ element(X50,powerset(the_carrier(X49)))
| subset_complement(the_carrier(X49),X50) = subset_difference(the_carrier(X49),cast_as_carrier_subset(X49),X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_pre_topc])])]) ).
fof(c_0_6,plain,
! [X38] :
( ~ top_str(X38)
| one_sorted_str(X38) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_pre_topc])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( closed_subset(X2,X1)
<=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t29_tops_1]) ).
cnf(c_0_8,plain,
( closed_subset(X2,X1)
| ~ open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
( subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( one_sorted_str(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( top_str(esk4_0)
& element(esk5_0,powerset(the_carrier(esk4_0)))
& ( ~ closed_subset(esk5_0,esk4_0)
| ~ open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0) )
& ( closed_subset(esk5_0,esk4_0)
| open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( closed_subset(X1,X2)
| ~ open_subset(subset_complement(the_carrier(X2),X1),X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( closed_subset(esk5_0,esk4_0)
| open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
element(esk5_0,powerset(the_carrier(esk4_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
top_str(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( ~ closed_subset(esk5_0,esk4_0)
| ~ open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
closed_subset(esk5_0,esk4_0),
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])]) ).
cnf(c_0_18,plain,
( open_subset(subset_difference(the_carrier(X2),cast_as_carrier_subset(X2),X1),X2)
| ~ closed_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_19,negated_conjecture,
~ open_subset(subset_complement(the_carrier(esk4_0),esk5_0),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_20,plain,
( open_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ closed_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_9]),c_0_10]) ).
cnf(c_0_21,negated_conjecture,
$false,
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_20]),c_0_17]),c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU319+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.08 % 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
% 0.06/0.27 % Computer : n024.cluster.edu
% 0.06/0.27 % Model : x86_64 x86_64
% 0.06/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.27 % Memory : 8042.1875MB
% 0.06/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.27 % CPULimit : 300
% 0.06/0.27 % WCLimit : 300
% 0.06/0.27 % DateTime : Mon May 4 21:56:41 EDT 2026
% 0.06/0.27 % CPUTime :
% 0.06/0.28 % start to proof: theBenchmark
% 1.12/1.64 % Version : CSE_E---1.7
% 1.12/1.64 % Problem : theBenchmark.p
% 1.12/1.64 % SZS status Theorem for theBenchmark.p
% 1.12/1.64 % SZS output start CNFRefutation
% See solution above
% 1.12/1.64 % Total time : 1.360s
%------------------------------------------------------------------------------