TSTP Solution File: SEU394+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU394+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 : n020.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 16:25:24 EDT 2023
% Result : Theorem 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 104
% Syntax : Number of formulae : 136 ( 14 unt; 97 typ; 0 def)
% Number of atoms : 139 ( 15 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 167 ( 67 ~; 43 |; 41 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 113 ( 79 >; 34 *; 0 +; 0 <<)
% Number of predicates : 44 ( 42 usr; 1 prp; 0-3 aty)
% Number of functors : 55 ( 55 usr; 18 con; 0-4 aty)
% Number of variables : 46 ( 1 sgn; 32 !; 0 ?; 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,
one_sorted_str: $i > $o ).
tff(decl_28,type,
net_str: ( $i * $i ) > $o ).
tff(decl_29,type,
strict_net_str: ( $i * $i ) > $o ).
tff(decl_30,type,
the_mapping: ( $i * $i ) > $i ).
tff(decl_31,type,
net_str_of: ( $i * $i * $i * $i ) > $i ).
tff(decl_32,type,
in: ( $i * $i ) > $o ).
tff(decl_33,type,
empty_carrier: $i > $o ).
tff(decl_34,type,
reflexive_relstr: $i > $o ).
tff(decl_35,type,
complete_relstr: $i > $o ).
tff(decl_36,type,
up_complete_relstr: $i > $o ).
tff(decl_37,type,
join_complete_relstr: $i > $o ).
tff(decl_38,type,
lower_bounded_relstr: $i > $o ).
tff(decl_39,type,
transitive_relstr: $i > $o ).
tff(decl_40,type,
antisymmetric_relstr: $i > $o ).
tff(decl_41,type,
with_suprema_relstr: $i > $o ).
tff(decl_42,type,
with_infima_relstr: $i > $o ).
tff(decl_43,type,
upper_bounded_relstr: $i > $o ).
tff(decl_44,type,
bounded_relstr: $i > $o ).
tff(decl_45,type,
empty: $i > $o ).
tff(decl_46,type,
finite: $i > $o ).
tff(decl_47,type,
relation: $i > $o ).
tff(decl_48,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_49,type,
powerset: $i > $i ).
tff(decl_50,type,
element: ( $i * $i ) > $o ).
tff(decl_51,type,
trivial_carrier: $i > $o ).
tff(decl_52,type,
connected_relstr: $i > $o ).
tff(decl_53,type,
filter_of_net_str: ( $i * $i ) > $i ).
tff(decl_54,type,
a_2_1_yellow19: ( $i * $i ) > $i ).
tff(decl_55,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_56,type,
function: $i > $o ).
tff(decl_57,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_58,type,
cast_as_carrier_subset: $i > $i ).
tff(decl_59,type,
boole_POSet: $i > $i ).
tff(decl_60,type,
filtered_subset: ( $i * $i ) > $o ).
tff(decl_61,type,
upper_relstr_subset: ( $i * $i ) > $o ).
tff(decl_62,type,
net_of_bool_filter: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_64,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_65,type,
empty_set: $i ).
tff(decl_66,type,
relation_empty_yielding: $i > $o ).
tff(decl_67,type,
lower_relstr_subset: ( $i * $i ) > $o ).
tff(decl_68,type,
singleton: $i > $i ).
tff(decl_69,type,
v1_yellow_3: $i > $o ).
tff(decl_70,type,
distributive_relstr: $i > $o ).
tff(decl_71,type,
heyting_relstr: $i > $o ).
tff(decl_72,type,
complemented_relstr: $i > $o ).
tff(decl_73,type,
boolean_relstr: $i > $o ).
tff(decl_74,type,
directed_subset: ( $i * $i ) > $o ).
tff(decl_75,type,
directed_relstr: $i > $o ).
tff(decl_76,type,
proper_element: ( $i * $i ) > $o ).
tff(decl_77,type,
is_eventually_in: ( $i * $i * $i ) > $o ).
tff(decl_78,type,
subset: ( $i * $i ) > $o ).
tff(decl_79,type,
esk1_0: $i ).
tff(decl_80,type,
esk2_0: $i ).
tff(decl_81,type,
esk3_1: $i > $i ).
tff(decl_82,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_83,type,
esk5_1: $i > $i ).
tff(decl_84,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_85,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
esk8_1: $i > $i ).
tff(decl_87,type,
esk9_1: $i > $i ).
tff(decl_88,type,
esk10_0: $i ).
tff(decl_89,type,
esk11_0: $i ).
tff(decl_90,type,
esk12_0: $i ).
tff(decl_91,type,
esk13_0: $i ).
tff(decl_92,type,
esk14_0: $i ).
tff(decl_93,type,
esk15_1: $i > $i ).
tff(decl_94,type,
esk16_1: $i > $i ).
tff(decl_95,type,
esk17_0: $i ).
tff(decl_96,type,
esk18_0: $i ).
tff(decl_97,type,
esk19_0: $i ).
tff(decl_98,type,
esk20_0: $i ).
tff(decl_99,type,
esk21_1: $i > $i ).
tff(decl_100,type,
esk22_1: $i > $i ).
tff(decl_101,type,
esk23_1: $i > $i ).
tff(decl_102,type,
esk24_0: $i ).
tff(decl_103,type,
esk25_1: $i > $i ).
tff(decl_104,type,
esk26_0: $i ).
tff(decl_105,type,
esk27_0: $i ).
tff(decl_106,type,
esk28_1: $i > $i ).
tff(decl_107,type,
esk29_1: $i > $i ).
tff(decl_108,type,
esk30_1: $i > $i ).
tff(decl_109,type,
esk31_1: $i > $i ).
tff(decl_110,type,
esk32_0: $i ).
tff(decl_111,type,
esk33_1: $i > $i ).
tff(decl_112,type,
esk34_1: $i > $i ).
tff(decl_113,type,
esk35_1: $i > $i ).
tff(decl_114,type,
esk36_1: $i > $i ).
tff(decl_115,type,
esk37_1: $i > $i ).
tff(decl_116,type,
esk38_0: $i ).
tff(decl_117,type,
esk39_0: $i ).
tff(decl_118,type,
esk40_2: ( $i * $i ) > $i ).
fof(t14_yellow19,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> set_difference(X2,singleton(empty_set)) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_yellow19) ).
fof(t15_yellow19,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_yellow19) ).
fof(t2_yellow19,axiom,
! [X1] :
( ~ empty(X1)
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(X1))
& upper_relstr_subset(X2,boole_POSet(X1))
& proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
& element(X2,powerset(the_carrier(boole_POSet(X1)))) )
=> ! [X3] :
~ ( in(X3,X2)
& empty(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_yellow19) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(t65_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(fc2_pre_topc,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(c_0_7,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> set_difference(X2,singleton(empty_set)) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
inference(fof_simplification,[status(thm)],[t14_yellow19]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t15_yellow19])]) ).
fof(c_0_9,plain,
! [X1] :
( ~ empty(X1)
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(X1))
& upper_relstr_subset(X2,boole_POSet(X1))
& proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
& element(X2,powerset(the_carrier(boole_POSet(X1)))) )
=> ! [X3] :
~ ( in(X3,X2)
& empty(X3) ) ) ),
inference(fof_simplification,[status(thm)],[t2_yellow19]) ).
fof(c_0_10,plain,
! [X181,X182] :
( empty_carrier(X181)
| ~ one_sorted_str(X181)
| empty(X182)
| ~ filtered_subset(X182,boole_POSet(cast_as_carrier_subset(X181)))
| ~ upper_relstr_subset(X182,boole_POSet(cast_as_carrier_subset(X181)))
| ~ element(X182,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X181)))))
| set_difference(X182,singleton(empty_set)) = filter_of_net_str(X181,net_of_bool_filter(X181,cast_as_carrier_subset(X181),X182)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,negated_conjecture,
( ~ empty_carrier(esk38_0)
& one_sorted_str(esk38_0)
& ~ empty(esk39_0)
& filtered_subset(esk39_0,boole_POSet(cast_as_carrier_subset(esk38_0)))
& upper_relstr_subset(esk39_0,boole_POSet(cast_as_carrier_subset(esk38_0)))
& proper_element(esk39_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk38_0)))))
& element(esk39_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk38_0)))))
& esk39_0 != filter_of_net_str(esk38_0,net_of_bool_filter(esk38_0,cast_as_carrier_subset(esk38_0),esk39_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X192,X193,X194] :
( empty(X192)
| empty(X193)
| ~ filtered_subset(X193,boole_POSet(X192))
| ~ upper_relstr_subset(X193,boole_POSet(X192))
| ~ proper_element(X193,powerset(the_carrier(boole_POSet(X192))))
| ~ element(X193,powerset(the_carrier(boole_POSet(X192))))
| ~ in(X194,X193)
| ~ empty(X194) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,plain,
! [X208,X209] :
( ~ in(X208,X209)
| ~ empty(X209) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_14,plain,
( empty_carrier(X1)
| empty(X2)
| set_difference(X2,singleton(empty_set)) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2))
| ~ one_sorted_str(X1)
| ~ filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
| ~ upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
| ~ element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
upper_relstr_subset(esk39_0,boole_POSet(cast_as_carrier_subset(esk38_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
filtered_subset(esk39_0,boole_POSet(cast_as_carrier_subset(esk38_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
element(esk39_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk38_0))))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
one_sorted_str(esk38_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
~ empty(esk39_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
~ empty_carrier(esk38_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_21,plain,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[t65_zfmisc_1]) ).
cnf(c_0_22,plain,
( empty(X1)
| empty(X2)
| ~ filtered_subset(X2,boole_POSet(X1))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ in(X3,X2)
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,negated_conjecture,
esk39_0 != filter_of_net_str(esk38_0,net_of_bool_filter(esk38_0,cast_as_carrier_subset(esk38_0),esk39_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,negated_conjecture,
filter_of_net_str(esk38_0,net_of_bool_filter(esk38_0,cast_as_carrier_subset(esk38_0),esk39_0)) = set_difference(esk39_0,singleton(empty_set)),
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(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]),c_0_18])]),c_0_19]),c_0_20]) ).
fof(c_0_26,plain,
! [X205,X206] :
( ( set_difference(X205,singleton(X206)) != X205
| ~ in(X206,X205) )
& ( in(X206,X205)
| set_difference(X205,singleton(X206)) = X205 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
fof(c_0_27,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_pre_topc]) ).
cnf(c_0_28,plain,
( empty(X1)
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ empty(X3)
| ~ in(X3,X2) ),
inference(csr,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
proper_element(esk39_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk38_0))))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
set_difference(esk39_0,singleton(empty_set)) != esk39_0,
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( in(X1,X2)
| set_difference(X2,singleton(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X84] :
( empty_carrier(X84)
| ~ one_sorted_str(X84)
| ~ empty(cast_as_carrier_subset(X84)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
cnf(c_0_33,negated_conjecture,
( empty(cast_as_carrier_subset(esk38_0))
| ~ empty(X1)
| ~ in(X1,esk39_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_34,negated_conjecture,
in(empty_set,esk39_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_36,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(cast_as_carrier_subset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
empty(cast_as_carrier_subset(esk38_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_18])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU394+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 18:02:45 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.52 start to proof: theBenchmark
% 0.19/0.64 % Version : CSE_E---1.5
% 0.19/0.64 % Problem : theBenchmark.p
% 0.19/0.64 % Proof found
% 0.19/0.64 % SZS status Theorem for theBenchmark.p
% 0.19/0.64 % SZS output start Proof
% See solution above
% 0.19/0.65 % Total time : 0.115000 s
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65 % Total time : 0.121000 s
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