TSTP Solution File: SEU346+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU346+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 : n023.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 16:24:38 EDT 2023
% Result : Theorem 30.61s 30.70s
% Output : CNFRefutation 30.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 103
% Syntax : Number of formulae : 216 ( 14 unt; 78 typ; 0 def)
% Number of atoms : 682 ( 39 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 885 ( 341 ~; 365 |; 121 &)
% ( 8 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 98 ( 61 >; 37 *; 0 +; 0 <<)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 17 con; 0-4 aty)
% Number of variables : 256 ( 6 sgn; 121 !; 1 ?; 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,
join_commutative: $i > $o ).
tff(decl_36,type,
join_associative: $i > $o ).
tff(decl_37,type,
meet_commutative: $i > $o ).
tff(decl_38,type,
meet_associative: $i > $o ).
tff(decl_39,type,
meet_absorbing: $i > $o ).
tff(decl_40,type,
join_absorbing: $i > $o ).
tff(decl_41,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_42,type,
powerset: $i > $i ).
tff(decl_43,type,
element: ( $i * $i ) > $o ).
tff(decl_44,type,
relation: $i > $o ).
tff(decl_45,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_46,type,
poset_of_lattice: $i > $i ).
tff(decl_47,type,
k2_lattice3: $i > $i ).
tff(decl_48,type,
cast_to_el_of_LattPOSet: ( $i * $i ) > $i ).
tff(decl_49,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_50,type,
singleton: $i > $i ).
tff(decl_51,type,
related: ( $i * $i * $i ) > $o ).
tff(decl_52,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_53,type,
function: $i > $o ).
tff(decl_54,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_55,type,
k10_filter_1: ( $i * $i * $i * $i ) > $i ).
tff(decl_56,type,
k8_filter_1: ( $i * $i ) > $i ).
tff(decl_57,type,
empty: $i > $o ).
tff(decl_58,type,
ordered_pair_as_product_element: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
reflexive: $i > $o ).
tff(decl_60,type,
antisymmetric: $i > $o ).
tff(decl_61,type,
transitive: $i > $o ).
tff(decl_62,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_63,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_64,type,
reflexive_relstr: $i > $o ).
tff(decl_65,type,
transitive_relstr: $i > $o ).
tff(decl_66,type,
antisymmetric_relstr: $i > $o ).
tff(decl_67,type,
relation_of_lattice: $i > $i ).
tff(decl_68,type,
meet_semilatt_str: $i > $o ).
tff(decl_69,type,
one_sorted_str: $i > $o ).
tff(decl_70,type,
join_semilatt_str: $i > $o ).
tff(decl_71,type,
empty_set: $i ).
tff(decl_72,type,
v1_binop_1: ( $i * $i ) > $o ).
tff(decl_73,type,
v2_binop_1: ( $i * $i ) > $o ).
tff(decl_74,type,
below_refl: ( $i * $i * $i ) > $o ).
tff(decl_75,type,
below: ( $i * $i * $i ) > $o ).
tff(decl_76,type,
related_reflexive: ( $i * $i * $i ) > $o ).
tff(decl_77,type,
subset: ( $i * $i ) > $o ).
tff(decl_78,type,
esk1_0: $i ).
tff(decl_79,type,
esk2_0: $i ).
tff(decl_80,type,
esk3_0: $i ).
tff(decl_81,type,
esk4_0: $i ).
tff(decl_82,type,
esk5_0: $i ).
tff(decl_83,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_84,type,
esk7_1: $i > $i ).
tff(decl_85,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_86,type,
esk9_0: $i ).
tff(decl_87,type,
esk10_1: $i > $i ).
tff(decl_88,type,
esk11_0: $i ).
tff(decl_89,type,
esk12_0: $i ).
tff(decl_90,type,
esk13_1: $i > $i ).
tff(decl_91,type,
esk14_0: $i ).
tff(decl_92,type,
esk15_0: $i ).
tff(decl_93,type,
esk16_0: $i ).
tff(decl_94,type,
esk17_1: $i > $i ).
tff(decl_95,type,
esk18_0: $i ).
tff(decl_96,type,
esk19_0: $i ).
tff(decl_97,type,
esk20_0: $i ).
tff(decl_98,type,
esk21_0: $i ).
tff(decl_99,type,
esk22_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(t32_filter_1,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_1) ).
fof(reflexivity_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,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
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(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(cc1_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
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(fc1_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(d9_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( related(X1,X2,X3)
<=> in(ordered_pair(X2,X3),the_InternalRel(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
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(redefinition_k2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> k2_lattice3(X1) = relation_of_lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(redefinition_k1_domain_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(dt_k4_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(X1)) )
=> element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_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/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
fof(t7_lattice3,conjecture,
! [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_orders_2,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& rel_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( related_reflexive(X1,X2,X3)
<=> related(X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
fof(fc4_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(poset_of_lattice(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)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice3) ).
fof(c_0_25,plain,
! [X122,X123,X124] :
( ( ~ relation_of2_as_subset(X124,X122,X123)
| relation_of2(X124,X122,X123) )
& ( ~ relation_of2(X124,X122,X123)
| relation_of2_as_subset(X124,X122,X123) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_26,plain,
! [X54] :
( ~ rel_str(X54)
| relation_of2_as_subset(the_InternalRel(X54),the_carrier(X54),the_carrier(X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])]) ).
fof(c_0_27,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t32_filter_1]) ).
fof(c_0_28,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,X2) ),
inference(fof_simplification,[status(thm)],[reflexivity_r3_lattices]) ).
fof(c_0_29,plain,
! [X89,X90,X91,X92] :
( ( X89 = X91
| rel_str_of(X89,X90) != rel_str_of(X91,X92)
| ~ relation_of2(X90,X89,X89) )
& ( X90 = X92
| rel_str_of(X89,X90) != rel_str_of(X91,X92)
| ~ relation_of2(X90,X89,X89) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_orders_2])])])]) ).
cnf(c_0_30,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X154,X155] :
( ~ in(X154,X155)
| ~ empty(X155) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_33,plain,
! [X142,X143,X144] :
( ( ~ in(ordered_pair_as_product_element(the_carrier(X142),the_carrier(X142),X143,X144),relation_of_lattice(X142))
| below_refl(X142,X143,X144)
| ~ element(X144,the_carrier(X142))
| ~ element(X143,the_carrier(X142))
| empty_carrier(X142)
| ~ lattice(X142)
| ~ latt_str(X142) )
& ( ~ below_refl(X142,X143,X144)
| in(ordered_pair_as_product_element(the_carrier(X142),the_carrier(X142),X143,X144),relation_of_lattice(X142))
| ~ element(X144,the_carrier(X142))
| ~ element(X143,the_carrier(X142))
| empty_carrier(X142)
| ~ lattice(X142)
| ~ latt_str(X142) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
fof(c_0_34,plain,
! [X132,X133,X134] :
( empty_carrier(X132)
| ~ meet_commutative(X132)
| ~ meet_absorbing(X132)
| ~ join_absorbing(X132)
| ~ latt_str(X132)
| ~ element(X133,the_carrier(X132))
| ~ element(X134,the_carrier(X132))
| below_refl(X132,X133,X133) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).
fof(c_0_35,plain,
! [X64] : element(esk7_1(X64),X64),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_36,plain,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
cnf(c_0_37,plain,
( X1 = X2
| rel_str_of(X3,X1) != rel_str_of(X4,X2)
| ~ relation_of2(X1,X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_39,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])]) ).
fof(c_0_40,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]) ).
cnf(c_0_41,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| 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_33]) ).
cnf(c_0_43,plain,
( empty_carrier(X1)
| below_refl(X1,X2,X2)
| ~ 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_34]) ).
cnf(c_0_44,plain,
element(esk7_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_45,plain,
! [X11] :
( ( ~ empty_carrier(X11)
| empty_carrier(X11)
| ~ lattice(X11)
| ~ latt_str(X11) )
& ( join_commutative(X11)
| empty_carrier(X11)
| ~ lattice(X11)
| ~ latt_str(X11) )
& ( join_associative(X11)
| empty_carrier(X11)
| ~ lattice(X11)
| ~ latt_str(X11) )
& ( meet_commutative(X11)
| empty_carrier(X11)
| ~ lattice(X11)
| ~ latt_str(X11) )
& ( meet_associative(X11)
| empty_carrier(X11)
| ~ lattice(X11)
| ~ latt_str(X11) )
& ( meet_absorbing(X11)
| empty_carrier(X11)
| ~ lattice(X11)
| ~ latt_str(X11) )
& ( join_absorbing(X11)
| empty_carrier(X11)
| ~ lattice(X11)
| ~ latt_str(X11) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
fof(c_0_46,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_47,plain,
! [X23,X24,X25] :
( ( ~ related(X23,X24,X25)
| in(ordered_pair(X24,X25),the_InternalRel(X23))
| ~ element(X25,the_carrier(X23))
| ~ element(X24,the_carrier(X23))
| ~ rel_str(X23) )
& ( ~ in(ordered_pair(X24,X25),the_InternalRel(X23))
| related(X23,X24,X25)
| ~ element(X25,the_carrier(X23))
| ~ element(X24,the_carrier(X23))
| ~ rel_str(X23) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])]) ).
fof(c_0_48,plain,
! [X21,X22] : ordered_pair(X21,X22) = unordered_pair(unordered_pair(X21,X22),singleton(X21)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_49,plain,
( the_InternalRel(X1) = X2
| rel_str_of(the_carrier(X1),the_InternalRel(X1)) != rel_str_of(X3,X2)
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_50,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_39]) ).
fof(c_0_51,plain,
! [X18] :
( empty_carrier(X18)
| ~ lattice(X18)
| ~ latt_str(X18)
| poset_of_lattice(X18) = rel_str_of(the_carrier(X18),k2_lattice3(X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])]) ).
fof(c_0_52,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]) ).
cnf(c_0_53,plain,
( empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ empty(relation_of_lattice(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_54,plain,
( below_refl(X1,X2,X2)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_55,plain,
( meet_commutative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_56,plain,
( meet_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,plain,
( join_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_58,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> k2_lattice3(X1) = relation_of_lattice(X1) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_lattice3]) ).
fof(c_0_59,plain,
! [X138,X139] :
( ~ in(X138,X139)
| element(X138,X139) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_60,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_domain_1]) ).
fof(c_0_61,plain,
! [X71] :
( empty_carrier(X71)
| ~ one_sorted_str(X71)
| ~ empty(the_carrier(X71)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])]) ).
fof(c_0_62,plain,
! [X46] :
( ~ meet_semilatt_str(X46)
| one_sorted_str(X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
cnf(c_0_63,plain,
( related(X3,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X3))
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ rel_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_64,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_65,plain,
! [X140,X141] :
( ~ element(X140,X141)
| empty(X141)
| in(X140,X141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_66,plain,
( the_InternalRel(X1) = X2
| X1 != rel_str_of(X3,X2)
| ~ strict_rel_str(X1)
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_67,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_51]) ).
fof(c_0_68,plain,
! [X40] :
( ( strict_rel_str(poset_of_lattice(X40))
| empty_carrier(X40)
| ~ lattice(X40)
| ~ latt_str(X40) )
& ( reflexive_relstr(poset_of_lattice(X40))
| empty_carrier(X40)
| ~ lattice(X40)
| ~ latt_str(X40) )
& ( transitive_relstr(poset_of_lattice(X40))
| empty_carrier(X40)
| ~ lattice(X40)
| ~ latt_str(X40) )
& ( antisymmetric_relstr(poset_of_lattice(X40))
| empty_carrier(X40)
| ~ lattice(X40)
| ~ latt_str(X40) )
& ( rel_str(poset_of_lattice(X40))
| empty_carrier(X40)
| ~ lattice(X40)
| ~ latt_str(X40) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
cnf(c_0_69,plain,
( empty_carrier(X1)
| ~ empty(relation_of_lattice(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_56]),c_0_57]) ).
fof(c_0_70,plain,
! [X121] :
( empty_carrier(X121)
| ~ lattice(X121)
| ~ latt_str(X121)
| k2_lattice3(X121) = relation_of_lattice(X121) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])]) ).
cnf(c_0_71,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_72,plain,
! [X117,X118,X119,X120] :
( empty(X117)
| empty(X118)
| ~ element(X119,X117)
| ~ element(X120,X118)
| ordered_pair_as_product_element(X117,X118,X119,X120) = ordered_pair(X119,X120) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])]) ).
cnf(c_0_73,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_74,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_75,plain,
! [X49] :
( ( meet_semilatt_str(X49)
| ~ latt_str(X49) )
& ( join_semilatt_str(X49)
| ~ latt_str(X49) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_76,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(X1)) )
=> element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k4_lattice3]) ).
fof(c_0_77,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_78,negated_conjecture,
~ ! [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)],[inference(assume_negation,[status(cth)],[t7_lattice3])]) ).
cnf(c_0_79,plain,
( related(X3,X1,X2)
| ~ rel_str(X3)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X3)) ),
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_80,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_81,plain,
( the_InternalRel(X1) = k2_lattice3(X2)
| empty_carrier(X2)
| X1 != poset_of_lattice(X2)
| ~ lattice(X2)
| ~ latt_str(X2)
| ~ strict_rel_str(X1)
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_82,plain,
( rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_83,plain,
( strict_rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_84,plain,
( empty_carrier(X1)
| ~ empty(relation_of_lattice(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_44]) ).
cnf(c_0_85,plain,
( empty_carrier(X1)
| k2_lattice3(X1) = relation_of_lattice(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_86,plain,
( element(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_42]) ).
cnf(c_0_87,plain,
( empty(X1)
| empty(X2)
| ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4)
| ~ element(X3,X1)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_88,plain,
( empty_carrier(X1)
| ~ meet_semilatt_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_89,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
fof(c_0_90,plain,
! [X41,X42] :
( empty_carrier(X41)
| ~ lattice(X41)
| ~ latt_str(X41)
| ~ element(X42,the_carrier(X41))
| element(cast_to_el_of_LattPOSet(X41,X42),the_carrier(poset_of_lattice(X41))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])]) ).
fof(c_0_91,plain,
! [X19,X20] :
( empty_carrier(X19)
| ~ lattice(X19)
| ~ latt_str(X19)
| ~ element(X20,the_carrier(X19))
| cast_to_el_of_LattPOSet(X19,X20) = X20 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])]) ).
cnf(c_0_92,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_93,plain,
( in(ordered_pair(X2,X3),the_InternalRel(X1))
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_94,negated_conjecture,
( ~ empty_carrier(esk20_0)
& lattice(esk20_0)
& latt_str(esk20_0)
& element(esk21_0,the_carrier(esk20_0))
& element(esk22_0,the_carrier(esk20_0))
& ( ~ below_refl(esk20_0,esk21_0,esk22_0)
| ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) )
& ( below_refl(esk20_0,esk21_0,esk22_0)
| related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])]) ).
fof(c_0_95,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& rel_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( related_reflexive(X1,X2,X3)
<=> related(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_orders_2]) ).
cnf(c_0_96,plain,
( empty(the_InternalRel(X1))
| related(X1,X2,X3)
| ~ element(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_97,plain,
( the_InternalRel(poset_of_lattice(X1)) = k2_lattice3(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_81]),c_0_82]),c_0_83]) ).
cnf(c_0_98,plain,
( empty_carrier(X1)
| ~ empty(k2_lattice3(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_99,plain,
( element(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),k2_lattice3(X1))
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_85]) ).
cnf(c_0_100,plain,
( ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3))
| empty(X2)
| empty(X1)
| ~ element(X4,X2)
| ~ element(X3,X1) ),
inference(rw,[status(thm)],[c_0_87,c_0_64]) ).
cnf(c_0_101,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_102,plain,
( empty_carrier(X1)
| element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_103,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_91]) ).
fof(c_0_104,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(poset_of_lattice(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)) ) ),
inference(fof_simplification,[status(thm)],[fc4_lattice3]) ).
cnf(c_0_105,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),k2_lattice3(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_85]) ).
cnf(c_0_106,plain,
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(rw,[status(thm)],[c_0_93,c_0_64]) ).
cnf(c_0_107,negated_conjecture,
( ~ below_refl(esk20_0,esk21_0,esk22_0)
| ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_108,negated_conjecture,
element(esk22_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_109,negated_conjecture,
lattice(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_110,negated_conjecture,
latt_str(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_111,negated_conjecture,
~ empty_carrier(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
fof(c_0_112,plain,
! [X128,X129,X130] :
( ( ~ related_reflexive(X128,X129,X130)
| related(X128,X129,X130)
| empty_carrier(X128)
| ~ reflexive_relstr(X128)
| ~ rel_str(X128)
| ~ element(X129,the_carrier(X128))
| ~ element(X130,the_carrier(X128)) )
& ( ~ related(X128,X129,X130)
| related_reflexive(X128,X129,X130)
| empty_carrier(X128)
| ~ reflexive_relstr(X128)
| ~ rel_str(X128)
| ~ element(X129,the_carrier(X128))
| ~ element(X130,the_carrier(X128)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])]) ).
cnf(c_0_113,plain,
( related(poset_of_lattice(X1),X2,X3)
| empty_carrier(X1)
| ~ element(unordered_pair(unordered_pair(X2,X3),singleton(X2)),k2_lattice3(X1))
| ~ element(X3,the_carrier(poset_of_lattice(X1)))
| ~ element(X2,the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_82]),c_0_98]) ).
cnf(c_0_114,plain,
( element(unordered_pair(unordered_pair(X1,X2),singleton(X1)),k2_lattice3(X3))
| empty_carrier(X3)
| ~ below_refl(X3,X1,X2)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ lattice(X3)
| ~ latt_str(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_115,plain,
( element(X1,the_carrier(poset_of_lattice(X2)))
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
fof(c_0_116,plain,
! [X85] :
( ( ~ empty_carrier(poset_of_lattice(X85))
| empty_carrier(X85)
| ~ lattice(X85)
| ~ latt_str(X85) )
& ( strict_rel_str(poset_of_lattice(X85))
| empty_carrier(X85)
| ~ lattice(X85)
| ~ latt_str(X85) )
& ( reflexive_relstr(poset_of_lattice(X85))
| empty_carrier(X85)
| ~ lattice(X85)
| ~ latt_str(X85) )
& ( transitive_relstr(poset_of_lattice(X85))
| empty_carrier(X85)
| ~ lattice(X85)
| ~ latt_str(X85) )
& ( antisymmetric_relstr(poset_of_lattice(X85))
| empty_carrier(X85)
| ~ lattice(X85)
| ~ latt_str(X85) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_104])])]) ).
cnf(c_0_117,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ element(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),k2_lattice3(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_80]),c_0_98]) ).
cnf(c_0_118,plain,
( element(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X3))
| ~ related(X3,X1,X2)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ rel_str(X3) ),
inference(spm,[status(thm)],[c_0_71,c_0_106]) ).
cnf(c_0_119,negated_conjecture,
( below_refl(esk20_0,esk21_0,esk22_0)
| related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_120,negated_conjecture,
( ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),esk22_0)
| ~ below_refl(esk20_0,esk21_0,esk22_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_107,c_0_103]),c_0_108]),c_0_109]),c_0_110])]),c_0_111]) ).
cnf(c_0_121,negated_conjecture,
element(esk21_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_122,plain,
( related_reflexive(X1,X2,X3)
| empty_carrier(X1)
| ~ related(X1,X2,X3)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_123,plain,
( related(poset_of_lattice(X1),X2,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(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115]),c_0_115]) ).
cnf(c_0_124,plain,
( reflexive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_125,plain,
( empty_carrier(X1)
| ~ empty_carrier(poset_of_lattice(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_126,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ element(unordered_pair(unordered_pair(X2,X3),singleton(X2)),k2_lattice3(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_100]),c_0_101]) ).
cnf(c_0_127,plain,
( element(unordered_pair(unordered_pair(X1,X2),singleton(X1)),k2_lattice3(X3))
| empty_carrier(X3)
| ~ related(poset_of_lattice(X3),X1,X2)
| ~ element(X2,the_carrier(poset_of_lattice(X3)))
| ~ element(X1,the_carrier(poset_of_lattice(X3)))
| ~ lattice(X3)
| ~ latt_str(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_97]),c_0_82]) ).
cnf(c_0_128,negated_conjecture,
( related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),esk22_0)
| below_refl(esk20_0,esk21_0,esk22_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_119,c_0_103]),c_0_108]),c_0_109]),c_0_110])]),c_0_111]) ).
cnf(c_0_129,negated_conjecture,
( ~ related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| ~ below_refl(esk20_0,esk21_0,esk22_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_120,c_0_103]),c_0_121]),c_0_109]),c_0_110])]),c_0_111]) ).
cnf(c_0_130,plain,
( related_reflexive(poset_of_lattice(X1),X2,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(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_82]),c_0_115]),c_0_115]),c_0_124]),c_0_125]) ).
cnf(c_0_131,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ related(poset_of_lattice(X1),X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_115]),c_0_115]) ).
cnf(c_0_132,plain,
( related(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(X1,X2,X3)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_133,negated_conjecture,
( related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| below_refl(esk20_0,esk21_0,esk22_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_128,c_0_103]),c_0_121]),c_0_109]),c_0_110])]),c_0_111]) ).
cnf(c_0_134,negated_conjecture,
~ below_refl(esk20_0,esk21_0,esk22_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(spm,[status(thm)],[c_0_129,c_0_130]),c_0_108]),c_0_121]),c_0_109]),c_0_110])]),c_0_111]) ).
cnf(c_0_135,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(poset_of_lattice(X1),X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_82]),c_0_115]),c_0_115]),c_0_124]),c_0_125]) ).
cnf(c_0_136,negated_conjecture,
related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0),
inference(sr,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_137,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(spm,[status(thm)],[c_0_135,c_0_136]),c_0_108]),c_0_121]),c_0_109]),c_0_110])]),c_0_134]),c_0_111]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU346+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n023.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 18:07:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 30.61/30.70 % Version : CSE_E---1.5
% 30.61/30.70 % Problem : theBenchmark.p
% 30.61/30.70 % Proof found
% 30.61/30.70 % SZS status Theorem for theBenchmark.p
% 30.61/30.70 % SZS output start Proof
% See solution above
% 30.61/30.72 % Total time : 30.136000 s
% 30.61/30.72 % SZS output end Proof
% 30.61/30.72 % Total time : 30.143000 s
%------------------------------------------------------------------------------