TSTP Solution File: SEU350+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU350+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 : n007.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 16:24:40 EDT 2023
% Result : Theorem 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 65
% Syntax : Number of formulae : 96 ( 10 unt; 60 typ; 0 def)
% Number of atoms : 138 ( 10 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 158 ( 56 ~; 52 |; 28 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 46 >; 19 *; 0 +; 0 <<)
% Number of predicates : 32 ( 30 usr; 1 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 14 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn; 33 !; 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,
latt_str: $i > $o ).
tff(decl_29,type,
empty_carrier: $i > $o ).
tff(decl_30,type,
lattice: $i > $o ).
tff(decl_31,type,
join_commutative: $i > $o ).
tff(decl_32,type,
join_associative: $i > $o ).
tff(decl_33,type,
meet_commutative: $i > $o ).
tff(decl_34,type,
meet_associative: $i > $o ).
tff(decl_35,type,
meet_absorbing: $i > $o ).
tff(decl_36,type,
join_absorbing: $i > $o ).
tff(decl_37,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_38,type,
powerset: $i > $i ).
tff(decl_39,type,
element: ( $i * $i ) > $o ).
tff(decl_40,type,
relation: $i > $o ).
tff(decl_41,type,
poset_of_lattice: $i > $i ).
tff(decl_42,type,
k2_lattice3: $i > $i ).
tff(decl_43,type,
cast_to_el_of_LattPOSet: ( $i * $i ) > $i ).
tff(decl_44,type,
cast_to_el_of_lattice: ( $i * $i ) > $i ).
tff(decl_45,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_46,type,
reflexive: $i > $o ).
tff(decl_47,type,
antisymmetric: $i > $o ).
tff(decl_48,type,
transitive: $i > $o ).
tff(decl_49,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_50,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_51,type,
reflexive_relstr: $i > $o ).
tff(decl_52,type,
transitive_relstr: $i > $o ).
tff(decl_53,type,
antisymmetric_relstr: $i > $o ).
tff(decl_54,type,
relation_of_lattice: $i > $i ).
tff(decl_55,type,
meet_semilatt_str: $i > $o ).
tff(decl_56,type,
one_sorted_str: $i > $o ).
tff(decl_57,type,
join_semilatt_str: $i > $o ).
tff(decl_58,type,
empty: $i > $o ).
tff(decl_59,type,
empty_set: $i ).
tff(decl_60,type,
subset: ( $i * $i ) > $o ).
tff(decl_61,type,
latt_element_smaller: ( $i * $i * $i ) > $o ).
tff(decl_62,type,
relstr_set_smaller: ( $i * $i * $i ) > $o ).
tff(decl_63,type,
esk1_0: $i ).
tff(decl_64,type,
esk2_0: $i ).
tff(decl_65,type,
esk3_0: $i ).
tff(decl_66,type,
esk4_0: $i ).
tff(decl_67,type,
esk5_0: $i ).
tff(decl_68,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk7_1: $i > $i ).
tff(decl_70,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_71,type,
esk9_0: $i ).
tff(decl_72,type,
esk10_1: $i > $i ).
tff(decl_73,type,
esk11_0: $i ).
tff(decl_74,type,
esk12_0: $i ).
tff(decl_75,type,
esk13_1: $i > $i ).
tff(decl_76,type,
esk14_0: $i ).
tff(decl_77,type,
esk15_0: $i ).
tff(decl_78,type,
esk16_1: $i > $i ).
tff(decl_79,type,
esk17_0: $i ).
tff(decl_80,type,
esk18_0: $i ).
tff(decl_81,type,
esk19_0: $i ).
fof(d4_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice3) ).
fof(t31_lattice3,conjecture,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_set_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_element_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice3) ).
fof(dt_k5_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(poset_of_lattice(X1))) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice3) ).
fof(d3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).
fof(t30_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice3) ).
fof(c_0_5,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d4_lattice3]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_set_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_element_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t31_lattice3])]) ).
fof(c_0_7,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(poset_of_lattice(X1))) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattice3]) ).
fof(c_0_8,plain,
! [X16,X17] :
( empty_carrier(X16)
| ~ lattice(X16)
| ~ latt_str(X16)
| ~ element(X17,the_carrier(poset_of_lattice(X16)))
| cast_to_el_of_lattice(X16,X17) = X17 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,negated_conjecture,
( ~ empty_carrier(esk18_0)
& lattice(esk18_0)
& latt_str(esk18_0)
& element(esk19_0,the_carrier(poset_of_lattice(esk18_0)))
& ( ~ relstr_set_smaller(poset_of_lattice(esk18_0),esk17_0,esk19_0)
| ~ latt_element_smaller(esk18_0,cast_to_el_of_lattice(esk18_0,esk19_0),esk17_0) )
& ( relstr_set_smaller(poset_of_lattice(esk18_0),esk17_0,esk19_0)
| latt_element_smaller(esk18_0,cast_to_el_of_lattice(esk18_0,esk19_0),esk17_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d3_lattice3]) ).
fof(c_0_11,plain,
! [X24,X25] :
( empty_carrier(X24)
| ~ lattice(X24)
| ~ latt_str(X24)
| ~ element(X25,the_carrier(poset_of_lattice(X24)))
| element(cast_to_el_of_lattice(X24,X25),the_carrier(X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
cnf(c_0_12,plain,
( empty_carrier(X1)
| cast_to_el_of_lattice(X1,X2) = X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(poset_of_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
element(esk19_0,the_carrier(poset_of_lattice(esk18_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
lattice(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
latt_str(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
~ empty_carrier(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_17,plain,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t30_lattice3]) ).
fof(c_0_18,plain,
! [X14,X15] :
( empty_carrier(X14)
| ~ lattice(X14)
| ~ latt_str(X14)
| ~ element(X15,the_carrier(X14))
| cast_to_el_of_LattPOSet(X14,X15) = X15 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_19,plain,
( empty_carrier(X1)
| element(cast_to_el_of_lattice(X1,X2),the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(poset_of_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
cast_to_el_of_lattice(esk18_0,esk19_0) = esk19_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]) ).
fof(c_0_21,plain,
! [X82,X83,X84] :
( ( ~ latt_element_smaller(X83,X84,X82)
| relstr_set_smaller(poset_of_lattice(X83),X82,cast_to_el_of_LattPOSet(X83,X84))
| ~ element(X84,the_carrier(X83))
| empty_carrier(X83)
| ~ lattice(X83)
| ~ latt_str(X83) )
& ( ~ relstr_set_smaller(poset_of_lattice(X83),X82,cast_to_el_of_LattPOSet(X83,X84))
| latt_element_smaller(X83,X84,X82)
| ~ element(X84,the_carrier(X83))
| empty_carrier(X83)
| ~ lattice(X83)
| ~ latt_str(X83) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_22,plain,
( empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X2) = X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
element(esk19_0,the_carrier(esk18_0)),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_13]),c_0_14]),c_0_15])]),c_0_16]),c_0_20]) ).
cnf(c_0_24,plain,
( relstr_set_smaller(poset_of_lattice(X1),X3,cast_to_el_of_LattPOSet(X1,X2))
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
cast_to_el_of_LattPOSet(esk18_0,esk19_0) = esk19_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk18_0),esk17_0,esk19_0)
| latt_element_smaller(esk18_0,cast_to_el_of_lattice(esk18_0,esk19_0),esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
( ~ relstr_set_smaller(poset_of_lattice(esk18_0),esk17_0,esk19_0)
| ~ latt_element_smaller(esk18_0,cast_to_el_of_lattice(esk18_0,esk19_0),esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk18_0),X1,esk19_0)
| ~ latt_element_smaller(esk18_0,esk19_0,X1) ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_14]),c_0_15])]),c_0_16]),c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk18_0),esk17_0,esk19_0)
| latt_element_smaller(esk18_0,esk19_0,esk17_0) ),
inference(rw,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_30,plain,
( latt_element_smaller(X1,X3,X2)
| empty_carrier(X1)
| ~ relstr_set_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,negated_conjecture,
( ~ relstr_set_smaller(poset_of_lattice(esk18_0),esk17_0,esk19_0)
| ~ latt_element_smaller(esk18_0,esk19_0,esk17_0) ),
inference(rw,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_32,negated_conjecture,
relstr_set_smaller(poset_of_lattice(esk18_0),esk17_0,esk19_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( latt_element_smaller(esk18_0,esk19_0,X1)
| ~ relstr_set_smaller(poset_of_lattice(esk18_0),X1,esk19_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_30,c_0_25]),c_0_23]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_34,negated_conjecture,
~ latt_element_smaller(esk18_0,esk19_0,esk17_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_32]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU350+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
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Wed Aug 23 16:10:39 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.60 % Version : CSE_E---1.5
% 0.19/0.60 % Problem : theBenchmark.p
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark.p
% 0.19/0.60 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.021000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.025000 s
%------------------------------------------------------------------------------