TSTP Solution File: SEU391+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU391+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 : n006.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 16:25:23 EDT 2023
% Result : Theorem 0.21s 0.63s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 89
% Syntax : Number of formulae : 121 ( 9 unt; 86 typ; 0 def)
% Number of atoms : 152 ( 14 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 182 ( 65 ~; 74 |; 29 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 67 >; 23 *; 0 +; 0 <<)
% Number of predicates : 40 ( 38 usr; 1 prp; 0-3 aty)
% Number of functors : 48 ( 48 usr; 19 con; 0-3 aty)
% Number of variables : 45 ( 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,
trivial_carrier: $i > $o ).
tff(decl_47,type,
connected_relstr: $i > $o ).
tff(decl_48,type,
one_sorted_str: $i > $o ).
tff(decl_49,type,
net_str: ( $i * $i ) > $o ).
tff(decl_50,type,
filter_of_net_str: ( $i * $i ) > $i ).
tff(decl_51,type,
a_2_1_yellow19: ( $i * $i ) > $i ).
tff(decl_52,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_53,type,
cast_as_carrier_subset: $i > $i ).
tff(decl_54,type,
boole_POSet: $i > $i ).
tff(decl_55,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_56,type,
empty_set: $i ).
tff(decl_57,type,
relation_empty_yielding: $i > $o ).
tff(decl_58,type,
lower_relstr_subset: ( $i * $i ) > $o ).
tff(decl_59,type,
upper_relstr_subset: ( $i * $i ) > $o ).
tff(decl_60,type,
v1_yellow_3: $i > $o ).
tff(decl_61,type,
distributive_relstr: $i > $o ).
tff(decl_62,type,
heyting_relstr: $i > $o ).
tff(decl_63,type,
complemented_relstr: $i > $o ).
tff(decl_64,type,
boolean_relstr: $i > $o ).
tff(decl_65,type,
directed_subset: ( $i * $i ) > $o ).
tff(decl_66,type,
filtered_subset: ( $i * $i ) > $o ).
tff(decl_67,type,
directed_relstr: $i > $o ).
tff(decl_68,type,
is_eventually_in: ( $i * $i * $i ) > $o ).
tff(decl_69,type,
subset: ( $i * $i ) > $o ).
tff(decl_70,type,
esk1_0: $i ).
tff(decl_71,type,
esk2_0: $i ).
tff(decl_72,type,
esk3_1: $i > $i ).
tff(decl_73,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk5_1: $i > $i ).
tff(decl_75,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_76,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk8_1: $i > $i ).
tff(decl_78,type,
esk9_1: $i > $i ).
tff(decl_79,type,
esk10_0: $i ).
tff(decl_80,type,
esk11_0: $i ).
tff(decl_81,type,
esk12_0: $i ).
tff(decl_82,type,
esk13_0: $i ).
tff(decl_83,type,
esk14_0: $i ).
tff(decl_84,type,
esk15_1: $i > $i ).
tff(decl_85,type,
esk16_1: $i > $i ).
tff(decl_86,type,
esk17_0: $i ).
tff(decl_87,type,
esk18_0: $i ).
tff(decl_88,type,
esk19_0: $i ).
tff(decl_89,type,
esk20_0: $i ).
tff(decl_90,type,
esk21_1: $i > $i ).
tff(decl_91,type,
esk22_1: $i > $i ).
tff(decl_92,type,
esk23_1: $i > $i ).
tff(decl_93,type,
esk24_0: $i ).
tff(decl_94,type,
esk25_1: $i > $i ).
tff(decl_95,type,
esk26_0: $i ).
tff(decl_96,type,
esk27_0: $i ).
tff(decl_97,type,
esk28_1: $i > $i ).
tff(decl_98,type,
esk29_1: $i > $i ).
tff(decl_99,type,
esk30_0: $i ).
tff(decl_100,type,
esk31_1: $i > $i ).
tff(decl_101,type,
esk32_1: $i > $i ).
tff(decl_102,type,
esk33_1: $i > $i ).
tff(decl_103,type,
esk34_1: $i > $i ).
tff(decl_104,type,
esk35_0: $i ).
tff(decl_105,type,
esk36_0: $i ).
tff(decl_106,type,
esk37_0: $i ).
tff(decl_107,type,
esk38_2: ( $i * $i ) > $i ).
fof(d3_yellow19,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> filter_of_net_str(X1,X2) = a_2_1_yellow19(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_yellow19) ).
fof(t11_yellow19,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( in(X3,filter_of_net_str(X1,X2))
<=> ( is_eventually_in(X1,X2,X3)
& element(X3,powerset(the_carrier(X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_yellow19) ).
fof(fraenkel_a_2_1_yellow19,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& one_sorted_str(X2)
& ~ empty_carrier(X3)
& net_str(X3,X2) )
=> ( in(X1,a_2_1_yellow19(X2,X3))
<=> ? [X4] :
( element(X4,powerset(the_carrier(X2)))
& X1 = X4
& is_eventually_in(X2,X3,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).
fof(c_0_3,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> filter_of_net_str(X1,X2) = a_2_1_yellow19(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d3_yellow19]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ! [X3] :
( in(X3,filter_of_net_str(X1,X2))
<=> ( is_eventually_in(X1,X2,X3)
& element(X3,powerset(the_carrier(X1))) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t11_yellow19])]) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& one_sorted_str(X2)
& ~ empty_carrier(X3)
& net_str(X3,X2) )
=> ( in(X1,a_2_1_yellow19(X2,X3))
<=> ? [X4] :
( element(X4,powerset(the_carrier(X2)))
& X1 = X4
& is_eventually_in(X2,X3,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_1_yellow19]) ).
fof(c_0_6,plain,
! [X29,X30] :
( empty_carrier(X29)
| ~ one_sorted_str(X29)
| empty_carrier(X30)
| ~ net_str(X30,X29)
| filter_of_net_str(X29,X30) = a_2_1_yellow19(X29,X30) ),
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(esk35_0)
& one_sorted_str(esk35_0)
& ~ empty_carrier(esk36_0)
& net_str(esk36_0,esk35_0)
& ( ~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0))
| ~ is_eventually_in(esk35_0,esk36_0,esk37_0)
| ~ element(esk37_0,powerset(the_carrier(esk35_0))) )
& ( is_eventually_in(esk35_0,esk36_0,esk37_0)
| in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) )
& ( element(esk37_0,powerset(the_carrier(esk35_0)))
| in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_8,plain,
! [X74,X75,X76,X78] :
( ( element(esk7_3(X74,X75,X76),powerset(the_carrier(X75)))
| ~ in(X74,a_2_1_yellow19(X75,X76))
| empty_carrier(X75)
| ~ one_sorted_str(X75)
| empty_carrier(X76)
| ~ net_str(X76,X75) )
& ( X74 = esk7_3(X74,X75,X76)
| ~ in(X74,a_2_1_yellow19(X75,X76))
| empty_carrier(X75)
| ~ one_sorted_str(X75)
| empty_carrier(X76)
| ~ net_str(X76,X75) )
& ( is_eventually_in(X75,X76,esk7_3(X74,X75,X76))
| ~ in(X74,a_2_1_yellow19(X75,X76))
| empty_carrier(X75)
| ~ one_sorted_str(X75)
| empty_carrier(X76)
| ~ net_str(X76,X75) )
& ( ~ element(X78,powerset(the_carrier(X75)))
| X74 != X78
| ~ is_eventually_in(X75,X76,X78)
| in(X74,a_2_1_yellow19(X75,X76))
| empty_carrier(X75)
| ~ one_sorted_str(X75)
| empty_carrier(X76)
| ~ net_str(X76,X75) ) ),
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)
| empty_carrier(X2)
| filter_of_net_str(X1,X2) = a_2_1_yellow19(X1,X2)
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
net_str(esk36_0,esk35_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
one_sorted_str(esk35_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
~ empty_carrier(esk36_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
~ empty_carrier(esk35_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( is_eventually_in(X1,X2,esk7_3(X3,X1,X2))
| empty_carrier(X1)
| empty_carrier(X2)
| ~ in(X3,a_2_1_yellow19(X1,X2))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
a_2_1_yellow19(esk35_0,esk36_0) = filter_of_net_str(esk35_0,esk36_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[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 = esk7_3(X1,X2,X3)
| empty_carrier(X2)
| empty_carrier(X3)
| ~ in(X1,a_2_1_yellow19(X2,X3))
| ~ one_sorted_str(X2)
| ~ net_str(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( is_eventually_in(esk35_0,esk36_0,esk7_3(X1,esk35_0,esk36_0))
| ~ in(X1,filter_of_net_str(esk35_0,esk36_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_11]),c_0_15])]),c_0_12]),c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( is_eventually_in(esk35_0,esk36_0,esk37_0)
| in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( esk7_3(X1,esk35_0,esk36_0) = X1
| ~ in(X1,filter_of_net_str(esk35_0,esk36_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_10]),c_0_11]),c_0_15])]),c_0_12]),c_0_13]) ).
cnf(c_0_20,plain,
( element(esk7_3(X1,X2,X3),powerset(the_carrier(X2)))
| empty_carrier(X2)
| empty_carrier(X3)
| ~ in(X1,a_2_1_yellow19(X2,X3))
| ~ one_sorted_str(X2)
| ~ net_str(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( is_eventually_in(esk35_0,esk36_0,esk7_3(esk37_0,esk35_0,esk36_0))
| is_eventually_in(esk35_0,esk36_0,esk37_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( esk7_3(esk37_0,esk35_0,esk36_0) = esk37_0
| is_eventually_in(esk35_0,esk36_0,esk37_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( element(esk7_3(X1,esk35_0,esk36_0),powerset(the_carrier(esk35_0)))
| ~ in(X1,filter_of_net_str(esk35_0,esk36_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_10]),c_0_11]),c_0_15])]),c_0_12]),c_0_13]) ).
cnf(c_0_24,negated_conjecture,
( element(esk37_0,powerset(the_carrier(esk35_0)))
| in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
( ~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0))
| ~ is_eventually_in(esk35_0,esk36_0,esk37_0)
| ~ element(esk37_0,powerset(the_carrier(esk35_0))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
is_eventually_in(esk35_0,esk36_0,esk37_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( element(esk7_3(esk37_0,esk35_0,esk36_0),powerset(the_carrier(esk35_0)))
| element(esk37_0,powerset(the_carrier(esk35_0))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( esk7_3(esk37_0,esk35_0,esk36_0) = esk37_0
| element(esk37_0,powerset(the_carrier(esk35_0))) ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_29,plain,
( in(X3,a_2_1_yellow19(X2,X4))
| empty_carrier(X2)
| empty_carrier(X4)
| ~ element(X1,powerset(the_carrier(X2)))
| X3 != X1
| ~ is_eventually_in(X2,X4,X1)
| ~ one_sorted_str(X2)
| ~ net_str(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_30,negated_conjecture,
( ~ element(esk37_0,powerset(the_carrier(esk35_0)))
| ~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_31,negated_conjecture,
element(esk37_0,powerset(the_carrier(esk35_0))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| in(X3,a_2_1_yellow19(X2,X1))
| ~ is_eventually_in(X2,X1,X3)
| ~ net_str(X1,X2)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(the_carrier(X2))) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[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_32,c_0_26]),c_0_15]),c_0_10]),c_0_11]),c_0_31])]),c_0_13]),c_0_12]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU391+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
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 19:52:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.55 start to proof: theBenchmark
% 0.21/0.63 % Version : CSE_E---1.5
% 0.21/0.63 % Problem : theBenchmark.p
% 0.21/0.63 % Proof found
% 0.21/0.63 % SZS status Theorem for theBenchmark.p
% 0.21/0.63 % SZS output start Proof
% See solution above
% 0.21/0.64 % Total time : 0.069000 s
% 0.21/0.64 % SZS output end Proof
% 0.21/0.64 % Total time : 0.075000 s
%------------------------------------------------------------------------------