TSTP Solution File: SEU369+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU369+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 : n001.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 16:25:11 EDT 2023
% Result : Theorem 0.76s 0.86s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 113
% Syntax : Number of formulae : 180 ( 22 unt; 99 typ; 0 def)
% Number of atoms : 352 ( 27 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 402 ( 131 ~; 137 |; 99 &)
% ( 8 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 103 ( 74 >; 29 *; 0 +; 0 <<)
% Number of predicates : 52 ( 50 usr; 1 prp; 0-3 aty)
% Number of functors : 49 ( 49 usr; 25 con; 0-3 aty)
% Number of variables : 112 ( 7 sgn; 67 !; 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,
latt_str: $i > $o ).
tff(decl_28,type,
strict_latt_str: $i > $o ).
tff(decl_29,type,
the_L_join: $i > $i ).
tff(decl_30,type,
the_L_meet: $i > $i ).
tff(decl_31,type,
latt_str_of: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
in: ( $i * $i ) > $o ).
tff(decl_33,type,
empty_carrier: $i > $o ).
tff(decl_34,type,
lattice: $i > $o ).
tff(decl_35,type,
complete_latt_str: $i > $o ).
tff(decl_36,type,
join_commutative: $i > $o ).
tff(decl_37,type,
join_associative: $i > $o ).
tff(decl_38,type,
meet_commutative: $i > $o ).
tff(decl_39,type,
meet_associative: $i > $o ).
tff(decl_40,type,
meet_absorbing: $i > $o ).
tff(decl_41,type,
join_absorbing: $i > $o ).
tff(decl_42,type,
lower_bounded_semilattstr: $i > $o ).
tff(decl_43,type,
upper_bounded_semilattstr: $i > $o ).
tff(decl_44,type,
bounded_lattstr: $i > $o ).
tff(decl_45,type,
with_suprema_relstr: $i > $o ).
tff(decl_46,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_47,type,
powerset: $i > $i ).
tff(decl_48,type,
element: ( $i * $i ) > $o ).
tff(decl_49,type,
relation: $i > $o ).
tff(decl_50,type,
complete_relstr: $i > $o ).
tff(decl_51,type,
with_infima_relstr: $i > $o ).
tff(decl_52,type,
reflexive_relstr: $i > $o ).
tff(decl_53,type,
trivial_carrier: $i > $o ).
tff(decl_54,type,
transitive_relstr: $i > $o ).
tff(decl_55,type,
antisymmetric_relstr: $i > $o ).
tff(decl_56,type,
bounded_relstr: $i > $o ).
tff(decl_57,type,
lower_bounded_relstr: $i > $o ).
tff(decl_58,type,
upper_bounded_relstr: $i > $o ).
tff(decl_59,type,
boolean_lattstr: $i > $o ).
tff(decl_60,type,
distributive_lattstr: $i > $o ).
tff(decl_61,type,
complemented_lattstr: $i > $o ).
tff(decl_62,type,
modular_lattstr: $i > $o ).
tff(decl_63,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_64,type,
poset_of_lattice: $i > $i ).
tff(decl_65,type,
k2_lattice3: $i > $i ).
tff(decl_66,type,
boole_POSet: $i > $i ).
tff(decl_67,type,
boole_lattice: $i > $i ).
tff(decl_68,type,
cast_to_el_of_LattPOSet: ( $i * $i ) > $i ).
tff(decl_69,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_70,type,
singleton: $i > $i ).
tff(decl_71,type,
related: ( $i * $i * $i ) > $o ).
tff(decl_72,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_73,type,
function: $i > $o ).
tff(decl_74,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_75,type,
reflexive: $i > $o ).
tff(decl_76,type,
antisymmetric: $i > $o ).
tff(decl_77,type,
transitive: $i > $o ).
tff(decl_78,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_79,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_80,type,
relation_of_lattice: $i > $i ).
tff(decl_81,type,
meet_semilatt_str: $i > $o ).
tff(decl_82,type,
one_sorted_str: $i > $o ).
tff(decl_83,type,
join_semilatt_str: $i > $o ).
tff(decl_84,type,
empty: $i > $o ).
tff(decl_85,type,
empty_set: $i ).
tff(decl_86,type,
below_refl: ( $i * $i * $i ) > $o ).
tff(decl_87,type,
below: ( $i * $i * $i ) > $o ).
tff(decl_88,type,
related_reflexive: ( $i * $i * $i ) > $o ).
tff(decl_89,type,
subset: ( $i * $i ) > $o ).
tff(decl_90,type,
esk1_0: $i ).
tff(decl_91,type,
esk2_0: $i ).
tff(decl_92,type,
esk3_0: $i ).
tff(decl_93,type,
esk4_0: $i ).
tff(decl_94,type,
esk5_0: $i ).
tff(decl_95,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_96,type,
esk7_1: $i > $i ).
tff(decl_97,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_98,type,
esk9_0: $i ).
tff(decl_99,type,
esk10_0: $i ).
tff(decl_100,type,
esk11_0: $i ).
tff(decl_101,type,
esk12_0: $i ).
tff(decl_102,type,
esk13_0: $i ).
tff(decl_103,type,
esk14_0: $i ).
tff(decl_104,type,
esk15_1: $i > $i ).
tff(decl_105,type,
esk16_0: $i ).
tff(decl_106,type,
esk17_0: $i ).
tff(decl_107,type,
esk18_0: $i ).
tff(decl_108,type,
esk19_0: $i ).
tff(decl_109,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_110,type,
esk21_1: $i > $i ).
tff(decl_111,type,
esk22_0: $i ).
tff(decl_112,type,
esk23_0: $i ).
tff(decl_113,type,
esk24_0: $i ).
tff(decl_114,type,
esk25_0: $i ).
tff(decl_115,type,
esk26_1: $i > $i ).
tff(decl_116,type,
esk27_0: $i ).
tff(decl_117,type,
esk28_0: $i ).
tff(decl_118,type,
esk29_0: $i ).
tff(decl_119,type,
esk30_0: $i ).
tff(decl_120,type,
esk31_0: $i ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_u1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(t2_yellow_1,conjecture,
! [X1,X2] :
( element(X2,the_carrier(boole_POSet(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_POSet(X1)))
=> ( related_reflexive(boole_POSet(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_yellow_1) ).
fof(free_g1_orders_2,axiom,
! [X1,X2] :
( relation_of2(X2,X1,X1)
=> ! [X3,X4] :
( rel_str_of(X1,X2) = rel_str_of(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(abstractness_v1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( strict_rel_str(X1)
=> X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(d2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice3) ).
fof(dt_k3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(d2_yellow_1,axiom,
! [X1] : boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_yellow_1) ).
fof(fc1_knaster,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& lattice(boole_lattice(X1))
& distributive_lattstr(boole_lattice(X1))
& modular_lattstr(boole_lattice(X1))
& lower_bounded_semilattstr(boole_lattice(X1))
& upper_bounded_semilattstr(boole_lattice(X1))
& bounded_lattstr(boole_lattice(X1))
& complemented_lattstr(boole_lattice(X1))
& boolean_lattstr(boole_lattice(X1))
& complete_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_knaster) ).
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/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(t7_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
fof(redefinition_r3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(t2_lattice3,axiom,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( below(boole_lattice(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).
fof(c_0_14,plain,
! [X139,X140,X141] :
( ( ~ relation_of2_as_subset(X141,X139,X140)
| relation_of2(X141,X139,X140) )
& ( ~ relation_of2(X141,X139,X140)
| relation_of2_as_subset(X141,X139,X140) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_15,plain,
! [X60] :
( ~ rel_str(X60)
| relation_of2_as_subset(the_InternalRel(X60),the_carrier(X60),the_carrier(X60)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X2] :
( element(X2,the_carrier(boole_POSet(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_POSet(X1)))
=> ( related_reflexive(boole_POSet(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
inference(assume_negation,[status(cth)],[t2_yellow_1]) ).
fof(c_0_17,plain,
! [X103,X104,X105,X106] :
( ( X103 = X105
| rel_str_of(X103,X104) != rel_str_of(X105,X106)
| ~ relation_of2(X104,X103,X103) )
& ( X104 = X106
| rel_str_of(X103,X104) != rel_str_of(X105,X106)
| ~ relation_of2(X104,X103,X103) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_orders_2])])])]) ).
fof(c_0_18,plain,
! [X7] :
( ~ rel_str(X7)
| ~ strict_rel_str(X7)
| X7 = rel_str_of(the_carrier(X7),the_InternalRel(X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])]) ).
cnf(c_0_19,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
inference(fof_simplification,[status(thm)],[d2_lattice3]) ).
fof(c_0_22,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_lattice3]) ).
fof(c_0_23,negated_conjecture,
( element(esk30_0,the_carrier(boole_POSet(esk29_0)))
& element(esk31_0,the_carrier(boole_POSet(esk29_0)))
& ( ~ related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0)
| ~ subset(esk30_0,esk31_0) )
& ( related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0)
| subset(esk30_0,esk31_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_24,plain,
! [X32] : boole_POSet(X32) = poset_of_lattice(boole_lattice(X32)),
inference(variable_rename,[status(thm)],[d2_yellow_1]) ).
cnf(c_0_25,plain,
( X1 = X2
| rel_str_of(X1,X3) != rel_str_of(X2,X4)
| ~ relation_of2(X3,X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ strict_rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
( relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_28,plain,
! [X31] :
( empty_carrier(X31)
| ~ lattice(X31)
| ~ latt_str(X31)
| poset_of_lattice(X31) = rel_str_of(the_carrier(X31),k2_lattice3(X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
fof(c_0_29,plain,
! [X47] :
( ( strict_rel_str(poset_of_lattice(X47))
| empty_carrier(X47)
| ~ lattice(X47)
| ~ latt_str(X47) )
& ( reflexive_relstr(poset_of_lattice(X47))
| empty_carrier(X47)
| ~ lattice(X47)
| ~ latt_str(X47) )
& ( transitive_relstr(poset_of_lattice(X47))
| empty_carrier(X47)
| ~ lattice(X47)
| ~ latt_str(X47) )
& ( antisymmetric_relstr(poset_of_lattice(X47))
| empty_carrier(X47)
| ~ lattice(X47)
| ~ latt_str(X47) )
& ( rel_str(poset_of_lattice(X47))
| empty_carrier(X47)
| ~ lattice(X47)
| ~ latt_str(X47) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
fof(c_0_30,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& lattice(boole_lattice(X1))
& distributive_lattstr(boole_lattice(X1))
& modular_lattstr(boole_lattice(X1))
& lower_bounded_semilattstr(boole_lattice(X1))
& upper_bounded_semilattstr(boole_lattice(X1))
& bounded_lattstr(boole_lattice(X1))
& complemented_lattstr(boole_lattice(X1))
& boolean_lattstr(boole_lattice(X1))
& complete_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_knaster]) ).
fof(c_0_31,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]) ).
cnf(c_0_32,negated_conjecture,
element(esk31_0,the_carrier(boole_POSet(esk29_0))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
( the_carrier(rel_str_of(X1,X2)) = X1
| ~ strict_rel_str(rel_str_of(X1,X2))
| ~ rel_str(rel_str_of(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26])]),c_0_27]) ).
cnf(c_0_35,plain,
( empty_carrier(X1)
| poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( strict_rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_38,plain,
! [X75] :
( ~ empty_carrier(boole_lattice(X75))
& strict_latt_str(boole_lattice(X75))
& join_commutative(boole_lattice(X75))
& join_associative(boole_lattice(X75))
& meet_commutative(boole_lattice(X75))
& meet_associative(boole_lattice(X75))
& meet_absorbing(boole_lattice(X75))
& join_absorbing(boole_lattice(X75))
& lattice(boole_lattice(X75))
& distributive_lattstr(boole_lattice(X75))
& modular_lattstr(boole_lattice(X75))
& lower_bounded_semilattstr(boole_lattice(X75))
& upper_bounded_semilattstr(boole_lattice(X75))
& bounded_lattstr(boole_lattice(X75))
& complemented_lattstr(boole_lattice(X75))
& boolean_lattstr(boole_lattice(X75))
& complete_latt_str(boole_lattice(X75)) ),
inference(variable_rename,[status(thm)],[c_0_30]) ).
fof(c_0_39,plain,
! [X45] :
( strict_latt_str(boole_lattice(X45))
& latt_str(boole_lattice(X45)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
fof(c_0_40,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t7_lattice3]) ).
fof(c_0_41,plain,
! [X33,X34] :
( empty_carrier(X33)
| ~ lattice(X33)
| ~ latt_str(X33)
| ~ element(X34,the_carrier(X33))
| cast_to_el_of_LattPOSet(X33,X34) = X34 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
cnf(c_0_42,negated_conjecture,
element(esk31_0,the_carrier(poset_of_lattice(boole_lattice(esk29_0)))),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_43,plain,
( the_carrier(poset_of_lattice(X1)) = the_carrier(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37]) ).
cnf(c_0_44,plain,
lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,negated_conjecture,
element(esk30_0,the_carrier(boole_POSet(esk29_0))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_48,plain,
! [X176,X177,X178] :
( ( ~ below_refl(X176,X177,X178)
| related_reflexive(poset_of_lattice(X176),cast_to_el_of_LattPOSet(X176,X177),cast_to_el_of_LattPOSet(X176,X178))
| ~ element(X178,the_carrier(X176))
| ~ element(X177,the_carrier(X176))
| empty_carrier(X176)
| ~ lattice(X176)
| ~ latt_str(X176) )
& ( ~ related_reflexive(poset_of_lattice(X176),cast_to_el_of_LattPOSet(X176,X177),cast_to_el_of_LattPOSet(X176,X178))
| below_refl(X176,X177,X178)
| ~ element(X178,the_carrier(X176))
| ~ element(X177,the_carrier(X176))
| empty_carrier(X176)
| ~ lattice(X176)
| ~ latt_str(X176) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
cnf(c_0_49,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_41]) ).
cnf(c_0_50,negated_conjecture,
element(esk31_0,the_carrier(boole_lattice(esk29_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]),c_0_46]) ).
cnf(c_0_51,negated_conjecture,
element(esk30_0,the_carrier(poset_of_lattice(boole_lattice(esk29_0)))),
inference(rw,[status(thm)],[c_0_47,c_0_33]) ).
cnf(c_0_52,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_53,negated_conjecture,
cast_to_el_of_LattPOSet(boole_lattice(esk29_0),esk31_0) = esk31_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_44]),c_0_45])]),c_0_46]) ).
cnf(c_0_54,negated_conjecture,
element(esk30_0,the_carrier(boole_lattice(esk29_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_43]),c_0_44]),c_0_45])]),c_0_46]) ).
fof(c_0_55,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_lattices]) ).
cnf(c_0_56,negated_conjecture,
( below_refl(boole_lattice(esk29_0),X1,esk31_0)
| ~ related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),cast_to_el_of_LattPOSet(boole_lattice(esk29_0),X1),esk31_0)
| ~ element(X1,the_carrier(boole_lattice(esk29_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_52,c_0_53]),c_0_50]),c_0_44]),c_0_45])]),c_0_46]) ).
cnf(c_0_57,negated_conjecture,
cast_to_el_of_LattPOSet(boole_lattice(esk29_0),esk30_0) = esk30_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_54]),c_0_44]),c_0_45])]),c_0_46]) ).
cnf(c_0_58,negated_conjecture,
( related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0)
| subset(esk30_0,esk31_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_59,plain,
! [X142,X143,X144] :
( ( ~ below_refl(X142,X143,X144)
| below(X142,X143,X144)
| empty_carrier(X142)
| ~ meet_commutative(X142)
| ~ meet_absorbing(X142)
| ~ join_absorbing(X142)
| ~ latt_str(X142)
| ~ element(X143,the_carrier(X142))
| ~ element(X144,the_carrier(X142)) )
& ( ~ below(X142,X143,X144)
| below_refl(X142,X143,X144)
| empty_carrier(X142)
| ~ meet_commutative(X142)
| ~ meet_absorbing(X142)
| ~ join_absorbing(X142)
| ~ latt_str(X142)
| ~ element(X143,the_carrier(X142))
| ~ element(X144,the_carrier(X142)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
cnf(c_0_60,negated_conjecture,
( below_refl(boole_lattice(esk29_0),esk30_0,esk31_0)
| ~ related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_54])]) ).
cnf(c_0_61,negated_conjecture,
( subset(esk30_0,esk31_0)
| related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0) ),
inference(rw,[status(thm)],[c_0_58,c_0_33]) ).
fof(c_0_62,plain,
! [X157,X158,X159] :
( ( ~ below(boole_lattice(X157),X158,X159)
| subset(X158,X159)
| ~ element(X159,the_carrier(boole_lattice(X157)))
| ~ element(X158,the_carrier(boole_lattice(X157))) )
& ( ~ subset(X158,X159)
| below(boole_lattice(X157),X158,X159)
| ~ element(X159,the_carrier(boole_lattice(X157)))
| ~ element(X158,the_carrier(boole_lattice(X157))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_lattice3])])])]) ).
cnf(c_0_63,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,negated_conjecture,
( subset(esk30_0,esk31_0)
| below_refl(boole_lattice(esk29_0),esk30_0,esk31_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
join_absorbing(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_66,plain,
meet_absorbing(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_67,plain,
meet_commutative(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_68,plain,
( subset(X2,X3)
| ~ below(boole_lattice(X1),X2,X3)
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,negated_conjecture,
( subset(esk30_0,esk31_0)
| below(boole_lattice(esk29_0),esk30_0,esk31_0) ),
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(spm,[status(thm)],[c_0_63,c_0_64]),c_0_50]),c_0_54]),c_0_65]),c_0_66]),c_0_67]),c_0_45])]),c_0_46]) ).
cnf(c_0_70,plain,
( below(boole_lattice(X3),X1,X2)
| ~ subset(X1,X2)
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3))) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,negated_conjecture,
subset(esk30_0,esk31_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_50]),c_0_54])]) ).
cnf(c_0_72,negated_conjecture,
( below(boole_lattice(X1),esk30_0,esk31_0)
| ~ element(esk31_0,the_carrier(boole_lattice(X1)))
| ~ element(esk30_0,the_carrier(boole_lattice(X1))) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_73,negated_conjecture,
( ~ related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0)
| ~ subset(esk30_0,esk31_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_74,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ below(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_75,negated_conjecture,
below(boole_lattice(esk29_0),esk30_0,esk31_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_50]),c_0_54])]) ).
cnf(c_0_76,negated_conjecture,
( ~ subset(esk30_0,esk31_0)
| ~ related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0) ),
inference(rw,[status(thm)],[c_0_73,c_0_33]) ).
cnf(c_0_77,plain,
( related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_78,negated_conjecture,
below_refl(boole_lattice(esk29_0),esk30_0,esk31_0),
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(spm,[status(thm)],[c_0_74,c_0_75]),c_0_50]),c_0_54]),c_0_65]),c_0_66]),c_0_67]),c_0_45])]),c_0_46]) ).
cnf(c_0_79,negated_conjecture,
~ related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_71])]) ).
cnf(c_0_80,negated_conjecture,
$false,
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_57]),c_0_53]),c_0_50]),c_0_54]),c_0_44]),c_0_45])]),c_0_79]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU369+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
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 18:54:39 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.76/0.86 % Version : CSE_E---1.5
% 0.76/0.86 % Problem : theBenchmark.p
% 0.76/0.86 % Proof found
% 0.76/0.86 % SZS status Theorem for theBenchmark.p
% 0.76/0.86 % SZS output start Proof
% See solution above
% 0.76/0.87 % Total time : 0.292000 s
% 0.76/0.87 % SZS output end Proof
% 0.76/0.87 % Total time : 0.298000 s
%------------------------------------------------------------------------------