TSTP Solution File: SEU323+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 : Thu Aug 31 16:24:27 EDT 2023
% Result : Theorem 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 25
% Syntax : Number of formulae : 45 ( 5 unt; 19 typ; 0 def)
% Number of atoms : 83 ( 3 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 96 ( 39 ~; 36 |; 11 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 15 >; 7 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn; 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
topological_space: $i > $o ).
tff(decl_23,type,
top_str: $i > $o ).
tff(decl_24,type,
closed_subset: ( $i * $i ) > $o ).
tff(decl_25,type,
the_carrier: $i > $i ).
tff(decl_26,type,
powerset: $i > $i ).
tff(decl_27,type,
element: ( $i * $i ) > $o ).
tff(decl_28,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_29,type,
open_subset: ( $i * $i ) > $o ).
tff(decl_30,type,
subset: ( $i * $i ) > $o ).
tff(decl_31,type,
one_sorted_str: $i > $o ).
tff(decl_32,type,
topstr_closure: ( $i * $i ) > $i ).
tff(decl_33,type,
interior: ( $i * $i ) > $i ).
tff(decl_34,type,
esk1_1: $i > $i ).
tff(decl_35,type,
esk2_0: $i ).
tff(decl_36,type,
esk3_0: $i ).
tff(decl_37,type,
esk4_1: $i > $i ).
tff(decl_38,type,
esk5_1: $i > $i ).
tff(decl_39,type,
esk6_0: $i ).
tff(decl_40,type,
esk7_0: $i ).
fof(fc3_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& closed_subset(X2,X1)
& element(X2,powerset(the_carrier(X1))) )
=> open_subset(subset_complement(the_carrier(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tops_1) ).
fof(d1_tops_1,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
fof(fc2_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> closed_subset(topstr_closure(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_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(t51_tops_1,conjecture,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1) ).
fof(dt_k6_pre_topc,axiom,
! [X1,X2] :
( ( top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> element(topstr_closure(X1,X2),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(c_0_6,plain,
! [X3,X4] :
( ~ topological_space(X3)
| ~ top_str(X3)
| ~ closed_subset(X4,X3)
| ~ element(X4,powerset(the_carrier(X3)))
| open_subset(subset_complement(the_carrier(X3),X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_tops_1])]) ).
fof(c_0_7,plain,
! [X29,X30] :
( ~ top_str(X29)
| ~ element(X30,powerset(the_carrier(X29)))
| interior(X29,X30) = subset_complement(the_carrier(X29),topstr_closure(X29,subset_complement(the_carrier(X29),X30))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tops_1])])]) ).
cnf(c_0_8,plain,
( open_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ closed_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X15,X16] :
( ~ topological_space(X15)
| ~ top_str(X15)
| ~ element(X16,powerset(the_carrier(X15)))
| closed_subset(topstr_closure(X15,X16),X15) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_tops_1])]) ).
fof(c_0_11,plain,
! [X11,X12] :
( ~ element(X12,powerset(X11))
| element(subset_complement(X11,X12),powerset(X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
inference(assume_negation,[status(cth)],[t51_tops_1]) ).
cnf(c_0_13,plain,
( open_subset(interior(X1,X2),X1)
| ~ element(topstr_closure(X1,subset_complement(the_carrier(X1),X2)),powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ closed_subset(topstr_closure(X1,subset_complement(the_carrier(X1),X2)),X1)
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
( closed_subset(topstr_closure(X1,X2),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X13,X14] :
( ~ top_str(X13)
| ~ element(X14,powerset(the_carrier(X13)))
| element(topstr_closure(X13,X14),powerset(the_carrier(X13))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_pre_topc])]) ).
fof(c_0_17,negated_conjecture,
( topological_space(esk6_0)
& top_str(esk6_0)
& element(esk7_0,powerset(the_carrier(esk6_0)))
& ~ open_subset(interior(esk6_0,esk7_0),esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_18,plain,
( open_subset(interior(X1,X2),X1)
| ~ element(topstr_closure(X1,subset_complement(the_carrier(X1),X2)),powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_19,plain,
( element(topstr_closure(X1,X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
~ open_subset(interior(esk6_0,esk7_0),esk6_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( open_subset(interior(X1,X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15]) ).
cnf(c_0_22,negated_conjecture,
element(esk7_0,powerset(the_carrier(esk6_0))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
top_str(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
topological_space(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,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_20,c_0_21]),c_0_22]),c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 01:40:47 EDT 2023
% 0.18/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark.p
% 0.19/0.60 % SZS output start Proof
% See solution above
% 0.19/0.60 % Total time : 0.011000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.013000 s
%------------------------------------------------------------------------------