%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU319+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 : n019.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 4.29s 3.17s
% Output : CNFRefutation 4.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 80 ( 12 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 78 ( 31 ~; 29 |; 4 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 30 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
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(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,lemma,
! [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(c_0_6,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]) ).
fof(c_0_7,plain,
! [X1940] :
( ~ top_str(X1940)
| one_sorted_str(X1940) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_pre_topc])]) ).
fof(c_0_8,negated_conjecture,
( top_str(esk321_0)
& element(esk322_0,powerset(the_carrier(esk321_0)))
& ( ~ closed_subset(esk322_0,esk321_0)
| ~ open_subset(subset_complement(the_carrier(esk321_0),esk322_0),esk321_0) )
& ( closed_subset(esk322_0,esk321_0)
| open_subset(subset_complement(the_carrier(esk321_0),esk322_0),esk321_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X1701] :
( ~ one_sorted_str(X1701)
| cast_as_carrier_subset(X1701) = the_carrier(X1701) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])]) ).
cnf(c_0_10,plain,
( one_sorted_str(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
top_str(esk321_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X1805,X1806] :
( ~ element(X1806,powerset(X1805))
| subset_complement(X1805,X1806) = set_difference(X1805,X1806) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(c_0_13,plain,
! [X1812,X1813] :
( ( ~ closed_subset(X1813,X1812)
| open_subset(subset_difference(the_carrier(X1812),cast_as_carrier_subset(X1812),X1813),X1812)
| ~ element(X1813,powerset(the_carrier(X1812)))
| ~ top_str(X1812) )
& ( ~ open_subset(subset_difference(the_carrier(X1812),cast_as_carrier_subset(X1812),X1813),X1812)
| closed_subset(X1813,X1812)
| ~ element(X1813,powerset(the_carrier(X1812)))
| ~ top_str(X1812) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_pre_topc])])])]) ).
cnf(c_0_14,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
one_sorted_str(esk321_0),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_16,lemma,
! [X2647,X2648] :
( ~ one_sorted_str(X2647)
| ~ element(X2648,powerset(the_carrier(X2647)))
| subset_complement(the_carrier(X2647),X2648) = subset_difference(the_carrier(X2647),cast_as_carrier_subset(X2647),X2648) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_pre_topc])])]) ).
cnf(c_0_17,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
element(esk322_0,powerset(the_carrier(esk321_0))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,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_13]) ).
cnf(c_0_20,negated_conjecture,
cast_as_carrier_subset(esk321_0) = the_carrier(esk321_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,lemma,
( 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_16]) ).
cnf(c_0_22,negated_conjecture,
subset_complement(the_carrier(esk321_0),esk322_0) = set_difference(the_carrier(esk321_0),esk322_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( closed_subset(esk322_0,esk321_0)
| open_subset(subset_complement(the_carrier(esk321_0),esk322_0),esk321_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,negated_conjecture,
( ~ closed_subset(esk322_0,esk321_0)
| ~ open_subset(subset_complement(the_carrier(esk321_0),esk322_0),esk321_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
( closed_subset(esk322_0,esk321_0)
| ~ open_subset(subset_difference(the_carrier(esk321_0),the_carrier(esk321_0),esk322_0),esk321_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_20]),c_0_11])]) ).
cnf(c_0_26,negated_conjecture,
subset_difference(the_carrier(esk321_0),the_carrier(esk321_0),esk322_0) = set_difference(the_carrier(esk321_0),esk322_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_20]),c_0_22]),c_0_15])]) ).
cnf(c_0_27,negated_conjecture,
( closed_subset(esk322_0,esk321_0)
| open_subset(set_difference(the_carrier(esk321_0),esk322_0),esk321_0) ),
inference(rw,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( ~ closed_subset(esk322_0,esk321_0)
| ~ open_subset(set_difference(the_carrier(esk321_0),esk322_0),esk321_0) ),
inference(rw,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
closed_subset(esk322_0,esk321_0),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_30,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_13]) ).
cnf(c_0_31,negated_conjecture,
~ open_subset(set_difference(the_carrier(esk321_0),esk322_0),esk321_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_29]),c_0_20]),c_0_26]),c_0_11]),c_0_18])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU319+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.14/0.32 % Computer : n019.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
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:57:14 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 4.29/3.17 % Version : CSE_E---1.7
% 4.29/3.17 % Problem : theBenchmark.p
% 4.29/3.17 % SZS status Theorem for theBenchmark.p
% 4.29/3.17 % SZS output start CNFRefutation
% See solution above
% 4.29/3.18 % Total time : 2.536s
%------------------------------------------------------------------------------