TSTP Solution File: SEU345+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU345+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 : n032.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 16:24:37 EDT 2023
% Result : Theorem 34.79s 34.88s
% Output : CNFRefutation 34.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 85
% Syntax : Number of formulae : 146 ( 24 unt; 70 typ; 0 def)
% Number of atoms : 277 ( 81 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 325 ( 124 ~; 133 |; 42 &)
% ( 5 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 102 ( 58 >; 44 *; 0 +; 0 <<)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-3 aty)
% Number of functors : 44 ( 44 usr; 12 con; 0-6 aty)
% Number of variables : 114 ( 11 sgn; 56 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
latt_str: $i > $o ).
tff(decl_23,type,
strict_latt_str: $i > $o ).
tff(decl_24,type,
the_carrier: $i > $i ).
tff(decl_25,type,
the_L_join: $i > $i ).
tff(decl_26,type,
the_L_meet: $i > $i ).
tff(decl_27,type,
latt_str_of: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
in: ( $i * $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,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_42,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_43,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_44,type,
meet_semilatt_str: $i > $o ).
tff(decl_45,type,
meet_commut: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
subset_union2: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
subset_intersection2: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
lower_bounded_semilattstr: $i > $o ).
tff(decl_49,type,
meet: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
bottom_of_semilattstr: $i > $i ).
tff(decl_51,type,
function: $i > $o ).
tff(decl_52,type,
apply_binary: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_54,type,
apply: ( $i * $i ) > $i ).
tff(decl_55,type,
boole_lattice: $i > $i ).
tff(decl_56,type,
join_semilatt_str: $i > $o ).
tff(decl_57,type,
join: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
apply_binary_as_element: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
singleton: $i > $i ).
tff(decl_60,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_61,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_62,type,
empty: $i > $o ).
tff(decl_63,type,
one_sorted_str: $i > $o ).
tff(decl_64,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_65,type,
empty_set: $i ).
tff(decl_66,type,
v1_binop_1: ( $i * $i ) > $o ).
tff(decl_67,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_68,type,
v2_binop_1: ( $i * $i ) > $o ).
tff(decl_69,type,
subset: ( $i * $i ) > $o ).
tff(decl_70,type,
esk1_1: $i > $i ).
tff(decl_71,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_72,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_73,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk6_0: $i ).
tff(decl_76,type,
esk7_0: $i ).
tff(decl_77,type,
esk8_0: $i ).
tff(decl_78,type,
esk9_0: $i ).
tff(decl_79,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_80,type,
esk11_1: $i > $i ).
tff(decl_81,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_82,type,
esk13_1: $i > $i ).
tff(decl_83,type,
esk14_0: $i ).
tff(decl_84,type,
esk15_1: $i > $i ).
tff(decl_85,type,
esk16_0: $i ).
tff(decl_86,type,
esk17_0: $i ).
tff(decl_87,type,
esk18_0: $i ).
tff(decl_88,type,
esk19_1: $i > $i ).
tff(decl_89,type,
esk20_0: $i ).
tff(decl_90,type,
esk21_0: $i ).
tff(decl_91,type,
esk22_0: $i ).
fof(d1_lattice3,axiom,
! [X1,X2] :
( ( strict_latt_str(X2)
& latt_str(X2) )
=> ( X2 = boole_lattice(X1)
<=> ( the_carrier(X2) = powerset(X1)
& ! [X3] :
( element(X3,powerset(X1))
=> ! [X4] :
( element(X4,powerset(X1))
=> ( apply_binary(the_L_join(X2),X3,X4) = subset_union2(X1,X3,X4)
& apply_binary(the_L_meet(X2),X3,X4) = subset_intersection2(X1,X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice3) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(d13_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
<=> ? [X2] :
( element(X2,the_carrier(X1))
& ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(fc1_lattice3,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice3) ).
fof(t1_lattice3,axiom,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_lattice3) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(d16_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( X2 = bottom_of_semilattstr(X1)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattices) ).
fof(dt_k5_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> element(bottom_of_semilattstr(X1),the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t3_lattice3,conjecture,
! [X1] :
( lower_bounded_semilattstr(boole_lattice(X1))
& bottom_of_semilattstr(boole_lattice(X1)) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_lattice3) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_15,plain,
! [X42,X43,X44,X45] :
( ( the_carrier(X43) = powerset(X42)
| X43 != boole_lattice(X42)
| ~ strict_latt_str(X43)
| ~ latt_str(X43) )
& ( apply_binary(the_L_join(X43),X44,X45) = subset_union2(X42,X44,X45)
| ~ element(X45,powerset(X42))
| ~ element(X44,powerset(X42))
| X43 != boole_lattice(X42)
| ~ strict_latt_str(X43)
| ~ latt_str(X43) )
& ( apply_binary(the_L_meet(X43),X44,X45) = subset_intersection2(X42,X44,X45)
| ~ element(X45,powerset(X42))
| ~ element(X44,powerset(X42))
| X43 != boole_lattice(X42)
| ~ strict_latt_str(X43)
| ~ latt_str(X43) )
& ( element(esk4_2(X42,X43),powerset(X42))
| the_carrier(X43) != powerset(X42)
| X43 = boole_lattice(X42)
| ~ strict_latt_str(X43)
| ~ latt_str(X43) )
& ( element(esk5_2(X42,X43),powerset(X42))
| the_carrier(X43) != powerset(X42)
| X43 = boole_lattice(X42)
| ~ strict_latt_str(X43)
| ~ latt_str(X43) )
& ( apply_binary(the_L_join(X43),esk4_2(X42,X43),esk5_2(X42,X43)) != subset_union2(X42,esk4_2(X42,X43),esk5_2(X42,X43))
| apply_binary(the_L_meet(X43),esk4_2(X42,X43),esk5_2(X42,X43)) != subset_intersection2(X42,esk4_2(X42,X43),esk5_2(X42,X43))
| the_carrier(X43) != powerset(X42)
| X43 = boole_lattice(X42)
| ~ strict_latt_str(X43)
| ~ latt_str(X43) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_lattice3])])])])]) ).
fof(c_0_16,plain,
! [X59] :
( strict_latt_str(boole_lattice(X59))
& latt_str(boole_lattice(X59)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
fof(c_0_17,plain,
! [X186] :
( ~ empty(X186)
| X186 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_18,plain,
! [X139] :
( element(esk15_1(X139),powerset(X139))
& empty(esk15_1(X139)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_19,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
<=> ? [X2] :
( element(X2,the_carrier(X1))
& ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d13_lattices]) ).
fof(c_0_20,plain,
! [X84] :
( ( meet_semilatt_str(X84)
| ~ latt_str(X84) )
& ( join_semilatt_str(X84)
| ~ latt_str(X84) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_21,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_lattice3]) ).
fof(c_0_22,plain,
! [X168,X169,X170] :
( ( join(boole_lattice(X168),X169,X170) = set_union2(X169,X170)
| ~ element(X170,the_carrier(boole_lattice(X168)))
| ~ element(X169,the_carrier(boole_lattice(X168))) )
& ( meet(boole_lattice(X168),X169,X170) = set_intersection2(X169,X170)
| ~ element(X170,the_carrier(boole_lattice(X168)))
| ~ element(X169,the_carrier(boole_lattice(X168))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_lattice3])])])]) ).
cnf(c_0_23,plain,
( the_carrier(X1) = powerset(X2)
| X1 != boole_lattice(X2)
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
strict_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
empty(esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_28,plain,
! [X30,X32,X33] :
( ( element(esk1_1(X30),the_carrier(X30))
| ~ lower_bounded_semilattstr(X30)
| empty_carrier(X30)
| ~ meet_semilatt_str(X30) )
& ( meet(X30,esk1_1(X30),X32) = esk1_1(X30)
| ~ element(X32,the_carrier(X30))
| ~ lower_bounded_semilattstr(X30)
| empty_carrier(X30)
| ~ meet_semilatt_str(X30) )
& ( meet(X30,X32,esk1_1(X30)) = esk1_1(X30)
| ~ element(X32,the_carrier(X30))
| ~ lower_bounded_semilattstr(X30)
| empty_carrier(X30)
| ~ meet_semilatt_str(X30) )
& ( element(esk2_2(X30,X33),the_carrier(X30))
| ~ element(X33,the_carrier(X30))
| lower_bounded_semilattstr(X30)
| empty_carrier(X30)
| ~ meet_semilatt_str(X30) )
& ( meet(X30,X33,esk2_2(X30,X33)) != X33
| meet(X30,esk2_2(X30,X33),X33) != X33
| ~ element(X33,the_carrier(X30))
| lower_bounded_semilattstr(X30)
| empty_carrier(X30)
| ~ meet_semilatt_str(X30) ) ),
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_19])])])])]) ).
cnf(c_0_29,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_30,plain,
! [X102] :
( ~ empty_carrier(boole_lattice(X102))
& strict_latt_str(boole_lattice(X102)) ),
inference(variable_rename,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
( meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3)
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
the_carrier(boole_lattice(X1)) = powerset(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_33,plain,
element(esk15_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_34,plain,
esk15_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_35,plain,
! [X173] : set_intersection2(X173,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
cnf(c_0_36,plain,
( element(esk2_2(X1,X2),the_carrier(X1))
| lower_bounded_semilattstr(X1)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
meet_semilatt_str(boole_lattice(X1)),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_38,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_39,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( X2 = bottom_of_semilattstr(X1)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d16_lattices]) ).
fof(c_0_40,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> element(bottom_of_semilattstr(X1),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattices]) ).
fof(c_0_41,plain,
! [X189,X190] :
( ~ empty(X189)
| X189 = X190
| ~ empty(X190) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
cnf(c_0_42,plain,
( meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).
cnf(c_0_43,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| element(esk2_2(boole_lattice(X1),X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_32]),c_0_37])]),c_0_38]) ).
fof(c_0_46,plain,
! [X19,X20] : set_intersection2(X19,X20) = set_intersection2(X20,X19),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_47,plain,
! [X35,X36,X37] :
( ( meet(X35,X36,X37) = X36
| ~ element(X37,the_carrier(X35))
| X36 != bottom_of_semilattstr(X35)
| ~ element(X36,the_carrier(X35))
| ~ lower_bounded_semilattstr(X35)
| empty_carrier(X35)
| ~ meet_semilatt_str(X35) )
& ( meet(X35,X37,X36) = X36
| ~ element(X37,the_carrier(X35))
| X36 != bottom_of_semilattstr(X35)
| ~ element(X36,the_carrier(X35))
| ~ lower_bounded_semilattstr(X35)
| empty_carrier(X35)
| ~ meet_semilatt_str(X35) )
& ( element(esk3_2(X35,X36),the_carrier(X35))
| X36 = bottom_of_semilattstr(X35)
| ~ element(X36,the_carrier(X35))
| ~ lower_bounded_semilattstr(X35)
| empty_carrier(X35)
| ~ meet_semilatt_str(X35) )
& ( meet(X35,X36,esk3_2(X35,X36)) != X36
| meet(X35,esk3_2(X35,X36),X36) != X36
| X36 = bottom_of_semilattstr(X35)
| ~ element(X36,the_carrier(X35))
| ~ lower_bounded_semilattstr(X35)
| empty_carrier(X35)
| ~ meet_semilatt_str(X35) ) ),
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_39])])])])]) ).
fof(c_0_48,plain,
! [X78] :
( empty_carrier(X78)
| ~ meet_semilatt_str(X78)
| element(bottom_of_semilattstr(X78),the_carrier(X78)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])]) ).
cnf(c_0_49,plain,
( lower_bounded_semilattstr(X1)
| empty_carrier(X1)
| meet(X1,X2,esk2_2(X1,X2)) != X2
| meet(X1,esk2_2(X1,X2),X2) != X2
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_50,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,plain,
( meet(boole_lattice(X1),X2,empty_set) = empty_set
| ~ element(X2,powerset(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_52,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| element(esk2_2(boole_lattice(X1),empty_set),powerset(X1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_43]) ).
cnf(c_0_53,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_54,negated_conjecture,
~ ! [X1] :
( lower_bounded_semilattstr(boole_lattice(X1))
& bottom_of_semilattstr(boole_lattice(X1)) = empty_set ),
inference(assume_negation,[status(cth)],[t3_lattice3]) ).
cnf(c_0_55,plain,
( meet(X1,X2,X3) = X2
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| X2 != bottom_of_semilattstr(X1)
| ~ element(X2,the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,plain,
( empty_carrier(X1)
| element(bottom_of_semilattstr(X1),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
( lower_bounded_semilattstr(X1)
| empty_carrier(X1)
| meet(X1,esk2_2(X1,X2),X2) != X2
| ~ empty(meet(X1,X2,esk2_2(X1,X2)))
| ~ empty(X2)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_58,plain,
( meet(boole_lattice(X1),esk2_2(boole_lattice(X1),empty_set),empty_set) = empty_set
| lower_bounded_semilattstr(boole_lattice(X1)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_60,plain,
( meet(boole_lattice(X1),X2,esk2_2(boole_lattice(X1),empty_set)) = set_intersection2(X2,esk2_2(boole_lattice(X1),empty_set))
| lower_bounded_semilattstr(boole_lattice(X1))
| ~ element(X2,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_52]) ).
cnf(c_0_61,plain,
set_intersection2(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_44,c_0_53]) ).
fof(c_0_62,negated_conjecture,
( ~ lower_bounded_semilattstr(boole_lattice(esk22_0))
| bottom_of_semilattstr(boole_lattice(esk22_0)) != empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])]) ).
cnf(c_0_63,plain,
( meet(X1,bottom_of_semilattstr(X1),X2) = bottom_of_semilattstr(X1)
| empty_carrier(X1)
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_55]),c_0_56]) ).
cnf(c_0_64,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| ~ empty(meet(boole_lattice(X1),empty_set,esk2_2(boole_lattice(X1),empty_set))) ),
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_57,c_0_58]),c_0_59]),c_0_37]),c_0_32]),c_0_43])]),c_0_38]) ).
cnf(c_0_65,plain,
( meet(boole_lattice(X1),empty_set,esk2_2(boole_lattice(X1),empty_set)) = empty_set
| lower_bounded_semilattstr(boole_lattice(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_43]),c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( ~ lower_bounded_semilattstr(boole_lattice(esk22_0))
| bottom_of_semilattstr(boole_lattice(esk22_0)) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_67,plain,
( meet(boole_lattice(X1),bottom_of_semilattstr(boole_lattice(X1)),X2) = bottom_of_semilattstr(boole_lattice(X1))
| ~ lower_bounded_semilattstr(boole_lattice(X1))
| ~ element(X2,powerset(X1)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_32]),c_0_37])]),c_0_38]) ).
cnf(c_0_68,plain,
lower_bounded_semilattstr(boole_lattice(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_59])]) ).
cnf(c_0_69,plain,
element(bottom_of_semilattstr(boole_lattice(X1)),powerset(X1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_32]),c_0_37])]),c_0_38]) ).
cnf(c_0_70,negated_conjecture,
( ~ empty(bottom_of_semilattstr(boole_lattice(esk22_0)))
| ~ lower_bounded_semilattstr(boole_lattice(esk22_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_50])]),c_0_59])]) ).
cnf(c_0_71,plain,
( meet(boole_lattice(X1),bottom_of_semilattstr(boole_lattice(X1)),X2) = bottom_of_semilattstr(boole_lattice(X1))
| ~ element(X2,powerset(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_72,plain,
meet(boole_lattice(X1),bottom_of_semilattstr(boole_lattice(X1)),empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_51,c_0_69]) ).
cnf(c_0_73,negated_conjecture,
~ empty(bottom_of_semilattstr(boole_lattice(esk22_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_68])]) ).
cnf(c_0_74,plain,
bottom_of_semilattstr(boole_lattice(X1)) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_43]),c_0_72]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74]),c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU345+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.08 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.06/0.26 % Computer : n032.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Wed Aug 23 21:47:26 EDT 2023
% 0.06/0.26 % CPUTime :
% 0.11/0.43 start to proof: theBenchmark
% 34.79/34.88 % Version : CSE_E---1.5
% 34.79/34.88 % Problem : theBenchmark.p
% 34.79/34.88 % Proof found
% 34.79/34.88 % SZS status Theorem for theBenchmark.p
% 34.79/34.88 % SZS output start Proof
% See solution above
% 34.84/34.89 % Total time : 34.449000 s
% 34.84/34.89 % SZS output end Proof
% 34.84/34.89 % Total time : 34.453000 s
%------------------------------------------------------------------------------