TSTP Solution File: SEU388+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU388+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n008.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 16:25:22 EDT 2023
% Result : Theorem 0.19s 0.67s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 108
% Syntax : Number of formulae : 133 ( 8 unt; 105 typ; 0 def)
% Number of atoms : 118 ( 13 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 142 ( 52 ~; 53 |; 23 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 113 ( 85 >; 28 *; 0 +; 0 <<)
% Number of predicates : 51 ( 49 usr; 1 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 20 con; 0-3 aty)
% Number of variables : 41 ( 0 sgn; 22 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
rel_str: $i > $o ).
tff(decl_23,type,
strict_rel_str: $i > $o ).
tff(decl_24,type,
the_carrier: $i > $i ).
tff(decl_25,type,
the_InternalRel: $i > $i ).
tff(decl_26,type,
rel_str_of: ( $i * $i ) > $i ).
tff(decl_27,type,
in: ( $i * $i ) > $o ).
tff(decl_28,type,
empty_carrier: $i > $o ).
tff(decl_29,type,
reflexive_relstr: $i > $o ).
tff(decl_30,type,
complete_relstr: $i > $o ).
tff(decl_31,type,
up_complete_relstr: $i > $o ).
tff(decl_32,type,
join_complete_relstr: $i > $o ).
tff(decl_33,type,
lower_bounded_relstr: $i > $o ).
tff(decl_34,type,
transitive_relstr: $i > $o ).
tff(decl_35,type,
antisymmetric_relstr: $i > $o ).
tff(decl_36,type,
with_suprema_relstr: $i > $o ).
tff(decl_37,type,
with_infima_relstr: $i > $o ).
tff(decl_38,type,
upper_bounded_relstr: $i > $o ).
tff(decl_39,type,
bounded_relstr: $i > $o ).
tff(decl_40,type,
empty: $i > $o ).
tff(decl_41,type,
finite: $i > $o ).
tff(decl_42,type,
relation: $i > $o ).
tff(decl_43,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_44,type,
powerset: $i > $i ).
tff(decl_45,type,
element: ( $i * $i ) > $o ).
tff(decl_46,type,
topological_space: $i > $o ).
tff(decl_47,type,
top_str: $i > $o ).
tff(decl_48,type,
open_subset: ( $i * $i ) > $o ).
tff(decl_49,type,
closed_subset: ( $i * $i ) > $o ).
tff(decl_50,type,
boundary_set: ( $i * $i ) > $o ).
tff(decl_51,type,
trivial_carrier: $i > $o ).
tff(decl_52,type,
nowhere_dense: ( $i * $i ) > $o ).
tff(decl_53,type,
connected_relstr: $i > $o ).
tff(decl_54,type,
v1_membered: $i > $o ).
tff(decl_55,type,
v2_membered: $i > $o ).
tff(decl_56,type,
v3_membered: $i > $o ).
tff(decl_57,type,
v4_membered: $i > $o ).
tff(decl_58,type,
v5_membered: $i > $o ).
tff(decl_59,type,
neighborhood_system: ( $i * $i ) > $i ).
tff(decl_60,type,
a_2_0_yellow19: ( $i * $i ) > $i ).
tff(decl_61,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_62,type,
cast_as_carrier_subset: $i > $i ).
tff(decl_63,type,
boole_POSet: $i > $i ).
tff(decl_64,type,
one_sorted_str: $i > $o ).
tff(decl_65,type,
point_neighbourhood: ( $i * $i * $i ) > $o ).
tff(decl_66,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_67,type,
empty_set: $i ).
tff(decl_68,type,
relation_empty_yielding: $i > $o ).
tff(decl_69,type,
lower_relstr_subset: ( $i * $i ) > $o ).
tff(decl_70,type,
upper_relstr_subset: ( $i * $i ) > $o ).
tff(decl_71,type,
v1_yellow_3: $i > $o ).
tff(decl_72,type,
distributive_relstr: $i > $o ).
tff(decl_73,type,
heyting_relstr: $i > $o ).
tff(decl_74,type,
complemented_relstr: $i > $o ).
tff(decl_75,type,
boolean_relstr: $i > $o ).
tff(decl_76,type,
directed_subset: ( $i * $i ) > $o ).
tff(decl_77,type,
filtered_subset: ( $i * $i ) > $o ).
tff(decl_78,type,
directed_relstr: $i > $o ).
tff(decl_79,type,
dense: ( $i * $i ) > $o ).
tff(decl_80,type,
subset: ( $i * $i ) > $o ).
tff(decl_81,type,
esk1_0: $i ).
tff(decl_82,type,
esk2_0: $i ).
tff(decl_83,type,
esk3_0: $i ).
tff(decl_84,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_85,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_86,type,
esk6_1: $i > $i ).
tff(decl_87,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_88,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
esk9_1: $i > $i ).
tff(decl_90,type,
esk10_1: $i > $i ).
tff(decl_91,type,
esk11_0: $i ).
tff(decl_92,type,
esk12_0: $i ).
tff(decl_93,type,
esk13_0: $i ).
tff(decl_94,type,
esk14_0: $i ).
tff(decl_95,type,
esk15_0: $i ).
tff(decl_96,type,
esk16_1: $i > $i ).
tff(decl_97,type,
esk17_1: $i > $i ).
tff(decl_98,type,
esk18_1: $i > $i ).
tff(decl_99,type,
esk19_0: $i ).
tff(decl_100,type,
esk20_0: $i ).
tff(decl_101,type,
esk21_0: $i ).
tff(decl_102,type,
esk22_0: $i ).
tff(decl_103,type,
esk23_1: $i > $i ).
tff(decl_104,type,
esk24_1: $i > $i ).
tff(decl_105,type,
esk25_1: $i > $i ).
tff(decl_106,type,
esk26_1: $i > $i ).
tff(decl_107,type,
esk27_0: $i ).
tff(decl_108,type,
esk28_1: $i > $i ).
tff(decl_109,type,
esk29_0: $i ).
tff(decl_110,type,
esk30_0: $i ).
tff(decl_111,type,
esk31_1: $i > $i ).
tff(decl_112,type,
esk32_1: $i > $i ).
tff(decl_113,type,
esk33_1: $i > $i ).
tff(decl_114,type,
esk34_1: $i > $i ).
tff(decl_115,type,
esk35_0: $i ).
tff(decl_116,type,
esk36_1: $i > $i ).
tff(decl_117,type,
esk37_1: $i > $i ).
tff(decl_118,type,
esk38_1: $i > $i ).
tff(decl_119,type,
esk39_1: $i > $i ).
tff(decl_120,type,
esk40_1: $i > $i ).
tff(decl_121,type,
esk41_1: $i > $i ).
tff(decl_122,type,
esk42_1: $i > $i ).
tff(decl_123,type,
esk43_2: ( $i * $i ) > $i ).
tff(decl_124,type,
esk44_0: $i ).
tff(decl_125,type,
esk45_0: $i ).
tff(decl_126,type,
esk46_0: $i ).
fof(d1_yellow19,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow19) ).
fof(t3_yellow19,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( in(X3,neighborhood_system(X1,X2))
<=> point_neighbourhood(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_yellow19) ).
fof(fraenkel_a_2_0_yellow19,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& topological_space(X2)
& top_str(X2)
& element(X3,the_carrier(X2)) )
=> ( in(X1,a_2_0_yellow19(X2,X3))
<=> ? [X4] :
( point_neighbourhood(X4,X2,X3)
& X1 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_yellow19) ).
fof(c_0_3,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d1_yellow19]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( in(X3,neighborhood_system(X1,X2))
<=> point_neighbourhood(X3,X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t3_yellow19])]) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& topological_space(X2)
& top_str(X2)
& element(X3,the_carrier(X2)) )
=> ( in(X1,a_2_0_yellow19(X2,X3))
<=> ? [X4] :
( point_neighbourhood(X4,X2,X3)
& X1 = X4 ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_yellow19]) ).
fof(c_0_6,plain,
! [X41,X42] :
( empty_carrier(X41)
| ~ topological_space(X41)
| ~ top_str(X41)
| ~ element(X42,the_carrier(X41))
| neighborhood_system(X41,X42) = a_2_0_yellow19(X41,X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_7,negated_conjecture,
( ~ empty_carrier(esk44_0)
& topological_space(esk44_0)
& top_str(esk44_0)
& element(esk45_0,the_carrier(esk44_0))
& ( ~ in(esk46_0,neighborhood_system(esk44_0,esk45_0))
| ~ point_neighbourhood(esk46_0,esk44_0,esk45_0) )
& ( in(esk46_0,neighborhood_system(esk44_0,esk45_0))
| point_neighbourhood(esk46_0,esk44_0,esk45_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X93,X94,X95,X97] :
( ( point_neighbourhood(esk8_3(X93,X94,X95),X94,X95)
| ~ in(X93,a_2_0_yellow19(X94,X95))
| empty_carrier(X94)
| ~ topological_space(X94)
| ~ top_str(X94)
| ~ element(X95,the_carrier(X94)) )
& ( X93 = esk8_3(X93,X94,X95)
| ~ in(X93,a_2_0_yellow19(X94,X95))
| empty_carrier(X94)
| ~ topological_space(X94)
| ~ top_str(X94)
| ~ element(X95,the_carrier(X94)) )
& ( ~ point_neighbourhood(X97,X94,X95)
| X93 != X97
| in(X93,a_2_0_yellow19(X94,X95))
| empty_carrier(X94)
| ~ topological_space(X94)
| ~ top_str(X94)
| ~ element(X95,the_carrier(X94)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
cnf(c_0_9,plain,
( empty_carrier(X1)
| neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
element(esk45_0,the_carrier(esk44_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
top_str(esk44_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
topological_space(esk44_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
~ empty_carrier(esk44_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( point_neighbourhood(esk8_3(X1,X2,X3),X2,X3)
| empty_carrier(X2)
| ~ in(X1,a_2_0_yellow19(X2,X3))
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
a_2_0_yellow19(esk44_0,esk45_0) = neighborhood_system(esk44_0,esk45_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]),c_0_13]) ).
cnf(c_0_16,plain,
( X1 = esk8_3(X1,X2,X3)
| empty_carrier(X2)
| ~ in(X1,a_2_0_yellow19(X2,X3))
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( point_neighbourhood(esk8_3(X1,esk44_0,esk45_0),esk44_0,esk45_0)
| ~ in(X1,neighborhood_system(esk44_0,esk45_0)) ),
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_14,c_0_15]),c_0_11]),c_0_12]),c_0_10])]),c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( in(esk46_0,neighborhood_system(esk44_0,esk45_0))
| point_neighbourhood(esk46_0,esk44_0,esk45_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( esk8_3(X1,esk44_0,esk45_0) = X1
| ~ in(X1,neighborhood_system(esk44_0,esk45_0)) ),
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_16,c_0_15]),c_0_11]),c_0_12]),c_0_10])]),c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( point_neighbourhood(esk8_3(esk46_0,esk44_0,esk45_0),esk44_0,esk45_0)
| point_neighbourhood(esk46_0,esk44_0,esk45_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( esk8_3(esk46_0,esk44_0,esk45_0) = esk46_0
| point_neighbourhood(esk46_0,esk44_0,esk45_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_22,plain,
( in(X4,a_2_0_yellow19(X2,X3))
| empty_carrier(X2)
| ~ point_neighbourhood(X1,X2,X3)
| X4 != X1
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(esk46_0,neighborhood_system(esk44_0,esk45_0))
| ~ point_neighbourhood(esk46_0,esk44_0,esk45_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
point_neighbourhood(esk46_0,esk44_0,esk45_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( empty_carrier(X1)
| in(X2,a_2_0_yellow19(X1,X3))
| ~ point_neighbourhood(X2,X1,X3)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X3,the_carrier(X1)) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ in(esk46_0,neighborhood_system(esk44_0,esk45_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[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_25,c_0_24]),c_0_15]),c_0_11]),c_0_12]),c_0_10])]),c_0_13]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU388+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n008.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 : Thu Aug 24 00:18:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 0.19/0.67 % Version : CSE_E---1.5
% 0.19/0.67 % Problem : theBenchmark.p
% 0.19/0.67 % Proof found
% 0.19/0.67 % SZS status Theorem for theBenchmark.p
% 0.19/0.67 % SZS output start Proof
% See solution above
% 0.19/0.67 % Total time : 0.115000 s
% 0.19/0.67 % SZS output end Proof
% 0.19/0.67 % Total time : 0.121000 s
%------------------------------------------------------------------------------