TSTP Solution File: SEU341+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU341+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 : n011.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 16:24:35 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 40
% Syntax : Number of formulae : 72 ( 12 unt; 34 typ; 0 def)
% Number of atoms : 167 ( 7 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 201 ( 72 ~; 66 |; 34 &)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 27 >; 8 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 67 ( 1 sgn; 44 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
v1_membered: $i > $o ).
tff(decl_24,type,
element: ( $i * $i ) > $o ).
tff(decl_25,type,
v1_xcmplx_0: $i > $o ).
tff(decl_26,type,
v2_membered: $i > $o ).
tff(decl_27,type,
v1_xreal_0: $i > $o ).
tff(decl_28,type,
v3_membered: $i > $o ).
tff(decl_29,type,
v1_rat_1: $i > $o ).
tff(decl_30,type,
v4_membered: $i > $o ).
tff(decl_31,type,
v1_int_1: $i > $o ).
tff(decl_32,type,
v5_membered: $i > $o ).
tff(decl_33,type,
natural: $i > $o ).
tff(decl_34,type,
empty: $i > $o ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
empty_carrier: $i > $o ).
tff(decl_37,type,
topological_space: $i > $o ).
tff(decl_38,type,
top_str: $i > $o ).
tff(decl_39,type,
the_carrier: $i > $i ).
tff(decl_40,type,
point_neighbourhood: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
interior: ( $i * $i ) > $i ).
tff(decl_42,type,
one_sorted_str: $i > $o ).
tff(decl_43,type,
empty_set: $i ).
tff(decl_44,type,
subset: ( $i * $i ) > $o ).
tff(decl_45,type,
open_subset: ( $i * $i ) > $o ).
tff(decl_46,type,
esk1_0: $i ).
tff(decl_47,type,
esk2_0: $i ).
tff(decl_48,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk4_1: $i > $i ).
tff(decl_50,type,
esk5_0: $i ).
tff(decl_51,type,
esk6_1: $i > $i ).
tff(decl_52,type,
esk7_1: $i > $i ).
tff(decl_53,type,
esk8_0: $i ).
tff(decl_54,type,
esk9_0: $i ).
tff(decl_55,type,
esk10_0: $i ).
fof(dt_m1_connsp_2,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ! [X3] :
( point_neighbourhood(X3,X1,X2)
=> element(X3,powerset(the_carrier(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
fof(t5_connsp_2,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(existence_m1_connsp_2,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ? [X3] : point_neighbourhood(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_connsp_2) ).
fof(d1_connsp_2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(t55_tops_1,axiom,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( top_str(X2)
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ! [X4] :
( element(X4,powerset(the_carrier(X2)))
=> ( ( open_subset(X4,X2)
=> interior(X2,X4) = X4 )
& ( interior(X1,X3) = X3
=> open_subset(X3,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(c_0_6,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ! [X3] :
( point_neighbourhood(X3,X1,X2)
=> element(X3,powerset(the_carrier(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_connsp_2]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t5_connsp_2])]) ).
fof(c_0_8,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ? [X3] : point_neighbourhood(X3,X1,X2) ),
inference(fof_simplification,[status(thm)],[existence_m1_connsp_2]) ).
fof(c_0_9,plain,
! [X38,X39,X40] :
( empty_carrier(X38)
| ~ topological_space(X38)
| ~ top_str(X38)
| ~ element(X39,the_carrier(X38))
| ~ point_neighbourhood(X40,X38,X39)
| element(X40,powerset(the_carrier(X38))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,negated_conjecture,
( ~ empty_carrier(esk8_0)
& topological_space(esk8_0)
& top_str(esk8_0)
& element(esk9_0,powerset(the_carrier(esk8_0)))
& element(esk10_0,the_carrier(esk8_0))
& open_subset(esk9_0,esk8_0)
& in(esk10_0,esk9_0)
& ~ point_neighbourhood(esk9_0,esk8_0,esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,plain,
! [X43,X44] :
( empty_carrier(X43)
| ~ topological_space(X43)
| ~ top_str(X43)
| ~ element(X44,the_carrier(X43))
| point_neighbourhood(esk3_2(X43,X44),X43,X44) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_12,plain,
( empty_carrier(X1)
| element(X3,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ point_neighbourhood(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
element(esk10_0,the_carrier(esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
top_str(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
topological_space(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
~ empty_carrier(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( empty_carrier(X1)
| point_neighbourhood(esk3_2(X1,X2),X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_connsp_2]) ).
fof(c_0_19,plain,
! [X64,X65,X66,X67] :
( ( ~ open_subset(X67,X65)
| interior(X65,X67) = X67
| ~ element(X67,powerset(the_carrier(X65)))
| ~ element(X66,powerset(the_carrier(X64)))
| ~ top_str(X65)
| ~ topological_space(X64)
| ~ top_str(X64) )
& ( interior(X64,X66) != X66
| open_subset(X66,X64)
| ~ element(X67,powerset(the_carrier(X65)))
| ~ element(X66,powerset(the_carrier(X64)))
| ~ top_str(X65)
| ~ topological_space(X64)
| ~ top_str(X64) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_tops_1])])])]) ).
cnf(c_0_20,negated_conjecture,
( element(X1,powerset(the_carrier(esk8_0)))
| ~ point_neighbourhood(X1,esk8_0,esk10_0) ),
inference(sr,[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_21,negated_conjecture,
point_neighbourhood(esk3_2(esk8_0,esk10_0),esk8_0,esk10_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
fof(c_0_22,plain,
! [X32,X33,X34] :
( ( ~ point_neighbourhood(X34,X32,X33)
| in(X33,interior(X32,X34))
| ~ element(X34,powerset(the_carrier(X32)))
| ~ element(X33,the_carrier(X32))
| empty_carrier(X32)
| ~ topological_space(X32)
| ~ top_str(X32) )
& ( ~ in(X33,interior(X32,X34))
| point_neighbourhood(X34,X32,X33)
| ~ element(X34,powerset(the_carrier(X32)))
| ~ element(X33,the_carrier(X32))
| empty_carrier(X32)
| ~ topological_space(X32)
| ~ top_str(X32) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
cnf(c_0_23,plain,
( interior(X2,X1) = X1
| ~ open_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X4)))
| ~ top_str(X2)
| ~ topological_space(X4)
| ~ top_str(X4) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
element(esk3_2(esk8_0,esk10_0),powerset(the_carrier(esk8_0))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_25,plain,
! [X61,X62,X63] :
( ~ in(X61,X62)
| ~ element(X62,powerset(X63))
| element(X61,X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_26,plain,
( point_neighbourhood(X3,X2,X1)
| empty_carrier(X2)
| ~ in(X1,interior(X2,X3))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ element(X1,the_carrier(X2))
| ~ topological_space(X2)
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
element(esk9_0,powerset(the_carrier(esk8_0))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,negated_conjecture,
( interior(X1,X2) = X2
| ~ open_subset(X2,X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_14]),c_0_15])]) ).
cnf(c_0_29,negated_conjecture,
open_subset(esk9_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( point_neighbourhood(esk9_0,esk8_0,X1)
| ~ element(X1,the_carrier(esk8_0))
| ~ in(X1,interior(esk8_0,esk9_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_32,negated_conjecture,
interior(esk8_0,esk9_0) = esk9_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_29]),c_0_14])]) ).
cnf(c_0_33,negated_conjecture,
( element(X1,the_carrier(esk8_0))
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( point_neighbourhood(esk9_0,esk8_0,X1)
| ~ in(X1,esk9_0) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_35,negated_conjecture,
in(esk10_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_36,negated_conjecture,
~ point_neighbourhood(esk9_0,esk8_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU341+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
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 16:06:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.024000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.028000 s
%------------------------------------------------------------------------------