TSTP Solution File: SEU387+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU387+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 : n019.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 16:25:21 EDT 2023
% Result : Theorem 0.20s 0.65s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 80
% Syntax : Number of formulae : 110 ( 18 unt; 73 typ; 0 def)
% Number of atoms : 183 ( 7 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 213 ( 67 ~; 47 |; 88 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 68 ( 54 >; 14 *; 0 +; 0 <<)
% Number of predicates : 37 ( 35 usr; 1 prp; 0-3 aty)
% Number of functors : 38 ( 38 usr; 19 con; 0-2 aty)
% Number of variables : 39 ( 8 sgn; 25 !; 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,
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,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_49,type,
bottom_of_relstr: $i > $i ).
tff(decl_50,type,
boole_POSet: $i > $i ).
tff(decl_51,type,
one_sorted_str: $i > $o ).
tff(decl_52,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_53,type,
empty_set: $i ).
tff(decl_54,type,
relation_empty_yielding: $i > $o ).
tff(decl_55,type,
v1_yellow_3: $i > $o ).
tff(decl_56,type,
distributive_relstr: $i > $o ).
tff(decl_57,type,
heyting_relstr: $i > $o ).
tff(decl_58,type,
complemented_relstr: $i > $o ).
tff(decl_59,type,
boolean_relstr: $i > $o ).
tff(decl_60,type,
directed_relstr: $i > $o ).
tff(decl_61,type,
filtered_subset: ( $i * $i ) > $o ).
tff(decl_62,type,
upper_relstr_subset: ( $i * $i ) > $o ).
tff(decl_63,type,
proper_element: ( $i * $i ) > $o ).
tff(decl_64,type,
subset: ( $i * $i ) > $o ).
tff(decl_65,type,
esk1_0: $i ).
tff(decl_66,type,
esk2_0: $i ).
tff(decl_67,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk4_1: $i > $i ).
tff(decl_69,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk6_1: $i > $i ).
tff(decl_71,type,
esk7_0: $i ).
tff(decl_72,type,
esk8_0: $i ).
tff(decl_73,type,
esk9_0: $i ).
tff(decl_74,type,
esk10_0: $i ).
tff(decl_75,type,
esk11_0: $i ).
tff(decl_76,type,
esk12_1: $i > $i ).
tff(decl_77,type,
esk13_0: $i ).
tff(decl_78,type,
esk14_0: $i ).
tff(decl_79,type,
esk15_0: $i ).
tff(decl_80,type,
esk16_0: $i ).
tff(decl_81,type,
esk17_1: $i > $i ).
tff(decl_82,type,
esk18_1: $i > $i ).
tff(decl_83,type,
esk19_0: $i ).
tff(decl_84,type,
esk20_1: $i > $i ).
tff(decl_85,type,
esk21_0: $i ).
tff(decl_86,type,
esk22_0: $i ).
tff(decl_87,type,
esk23_1: $i > $i ).
tff(decl_88,type,
esk24_1: $i > $i ).
tff(decl_89,type,
esk25_1: $i > $i ).
tff(decl_90,type,
esk26_0: $i ).
tff(decl_91,type,
esk27_1: $i > $i ).
tff(decl_92,type,
esk28_0: $i ).
tff(decl_93,type,
esk29_0: $i ).
tff(decl_94,type,
esk30_0: $i ).
fof(t2_yellow19,conjecture,
! [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(t8_waybel_7,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& transitive_relstr(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,X1)
& upper_relstr_subset(X2,X1)
& element(X2,powerset(the_carrier(X1))) )
=> ( proper_element(X2,powerset(the_carrier(X1)))
<=> ~ in(bottom_of_relstr(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_waybel_7) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(fc1_waybel_7,axiom,
! [X1] :
( ~ empty_carrier(boole_POSet(X1))
& strict_rel_str(boole_POSet(X1))
& reflexive_relstr(boole_POSet(X1))
& transitive_relstr(boole_POSet(X1))
& antisymmetric_relstr(boole_POSet(X1))
& lower_bounded_relstr(boole_POSet(X1))
& upper_bounded_relstr(boole_POSet(X1))
& bounded_relstr(boole_POSet(X1))
& up_complete_relstr(boole_POSet(X1))
& join_complete_relstr(boole_POSet(X1))
& ~ v1_yellow_3(boole_POSet(X1))
& distributive_relstr(boole_POSet(X1))
& heyting_relstr(boole_POSet(X1))
& complemented_relstr(boole_POSet(X1))
& boolean_relstr(boole_POSet(X1))
& with_suprema_relstr(boole_POSet(X1))
& with_infima_relstr(boole_POSet(X1))
& complete_relstr(boole_POSet(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_waybel_7) ).
fof(t18_yellow_1,axiom,
! [X1] : bottom_of_relstr(boole_POSet(X1)) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_yellow_1) ).
fof(dt_k3_yellow_1,axiom,
! [X1] :
( strict_rel_str(boole_POSet(X1))
& rel_str(boole_POSet(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
fof(c_0_7,negated_conjecture,
~ ! [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)],[inference(assume_negation,[status(cth)],[t2_yellow19])]) ).
fof(c_0_8,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& transitive_relstr(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,X1)
& upper_relstr_subset(X2,X1)
& element(X2,powerset(the_carrier(X1))) )
=> ( proper_element(X2,powerset(the_carrier(X1)))
<=> ~ in(bottom_of_relstr(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t8_waybel_7]) ).
fof(c_0_9,plain,
! [X114] :
( ~ empty(X114)
| X114 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_10,negated_conjecture,
( ~ empty(esk28_0)
& ~ empty(esk29_0)
& filtered_subset(esk29_0,boole_POSet(esk28_0))
& upper_relstr_subset(esk29_0,boole_POSet(esk28_0))
& proper_element(esk29_0,powerset(the_carrier(boole_POSet(esk28_0))))
& element(esk29_0,powerset(the_carrier(boole_POSet(esk28_0))))
& in(esk30_0,esk29_0)
& empty(esk30_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,plain,
! [X119,X120] :
( ( ~ proper_element(X120,powerset(the_carrier(X119)))
| ~ in(bottom_of_relstr(X119),X120)
| empty(X120)
| ~ filtered_subset(X120,X119)
| ~ upper_relstr_subset(X120,X119)
| ~ element(X120,powerset(the_carrier(X119)))
| empty_carrier(X119)
| ~ reflexive_relstr(X119)
| ~ transitive_relstr(X119)
| ~ antisymmetric_relstr(X119)
| ~ lower_bounded_relstr(X119)
| ~ rel_str(X119) )
& ( in(bottom_of_relstr(X119),X120)
| proper_element(X120,powerset(the_carrier(X119)))
| empty(X120)
| ~ filtered_subset(X120,X119)
| ~ upper_relstr_subset(X120,X119)
| ~ element(X120,powerset(the_carrier(X119)))
| empty_carrier(X119)
| ~ reflexive_relstr(X119)
| ~ transitive_relstr(X119)
| ~ antisymmetric_relstr(X119)
| ~ lower_bounded_relstr(X119)
| ~ rel_str(X119) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_12,plain,
! [X115,X116] :
( ~ in(X115,X116)
| ~ empty(X116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_13,plain,
! [X1] :
( ~ empty_carrier(boole_POSet(X1))
& strict_rel_str(boole_POSet(X1))
& reflexive_relstr(boole_POSet(X1))
& transitive_relstr(boole_POSet(X1))
& antisymmetric_relstr(boole_POSet(X1))
& lower_bounded_relstr(boole_POSet(X1))
& upper_bounded_relstr(boole_POSet(X1))
& bounded_relstr(boole_POSet(X1))
& up_complete_relstr(boole_POSet(X1))
& join_complete_relstr(boole_POSet(X1))
& ~ v1_yellow_3(boole_POSet(X1))
& distributive_relstr(boole_POSet(X1))
& heyting_relstr(boole_POSet(X1))
& complemented_relstr(boole_POSet(X1))
& boolean_relstr(boole_POSet(X1))
& with_suprema_relstr(boole_POSet(X1))
& with_infima_relstr(boole_POSet(X1))
& complete_relstr(boole_POSet(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_waybel_7]) ).
cnf(c_0_14,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
empty(esk30_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( empty(X1)
| empty_carrier(X2)
| ~ proper_element(X1,powerset(the_carrier(X2)))
| ~ in(bottom_of_relstr(X2),X1)
| ~ filtered_subset(X1,X2)
| ~ upper_relstr_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ reflexive_relstr(X2)
| ~ transitive_relstr(X2)
| ~ antisymmetric_relstr(X2)
| ~ lower_bounded_relstr(X2)
| ~ rel_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X52] :
( ~ empty_carrier(boole_POSet(X52))
& strict_rel_str(boole_POSet(X52))
& reflexive_relstr(boole_POSet(X52))
& transitive_relstr(boole_POSet(X52))
& antisymmetric_relstr(boole_POSet(X52))
& lower_bounded_relstr(boole_POSet(X52))
& upper_bounded_relstr(boole_POSet(X52))
& bounded_relstr(boole_POSet(X52))
& up_complete_relstr(boole_POSet(X52))
& join_complete_relstr(boole_POSet(X52))
& ~ v1_yellow_3(boole_POSet(X52))
& distributive_relstr(boole_POSet(X52))
& heyting_relstr(boole_POSet(X52))
& complemented_relstr(boole_POSet(X52))
& boolean_relstr(boole_POSet(X52))
& with_suprema_relstr(boole_POSet(X52))
& with_infima_relstr(boole_POSet(X52))
& complete_relstr(boole_POSet(X52)) ),
inference(variable_rename,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X98] : bottom_of_relstr(boole_POSet(X98)) = empty_set,
inference(variable_rename,[status(thm)],[t18_yellow_1]) ).
cnf(c_0_20,negated_conjecture,
in(esk30_0,esk29_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
esk30_0 = empty_set,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_22,plain,
! [X32] :
( strict_rel_str(boole_POSet(X32))
& rel_str(boole_POSet(X32)) ),
inference(variable_rename,[status(thm)],[dt_k3_yellow_1]) ).
cnf(c_0_23,plain,
( empty_carrier(X1)
| ~ proper_element(X2,powerset(the_carrier(X1)))
| ~ upper_relstr_subset(X2,X1)
| ~ filtered_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ antisymmetric_relstr(X1)
| ~ transitive_relstr(X1)
| ~ lower_bounded_relstr(X1)
| ~ reflexive_relstr(X1)
| ~ in(bottom_of_relstr(X1),X2)
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
element(esk29_0,powerset(the_carrier(boole_POSet(esk28_0)))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,negated_conjecture,
proper_element(esk29_0,powerset(the_carrier(boole_POSet(esk28_0)))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
upper_relstr_subset(esk29_0,boole_POSet(esk28_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
filtered_subset(esk29_0,boole_POSet(esk28_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,plain,
antisymmetric_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
transitive_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,plain,
lower_bounded_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,plain,
reflexive_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,plain,
bottom_of_relstr(boole_POSet(X1)) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_33,negated_conjecture,
in(empty_set,esk29_0),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_34,plain,
rel_str(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,plain,
~ empty_carrier(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_36,negated_conjecture,
$false,
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_34])]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU387+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
% 0.13/0.35 % Computer : n019.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 15:55:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 0.20/0.65 % Version : CSE_E---1.5
% 0.20/0.65 % Problem : theBenchmark.p
% 0.20/0.65 % Proof found
% 0.20/0.65 % SZS status Theorem for theBenchmark.p
% 0.20/0.65 % SZS output start Proof
% See solution above
% 0.20/0.65 % Total time : 0.049000 s
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65 % Total time : 0.054000 s
%------------------------------------------------------------------------------