TSTP Solution File: SEU346+1 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : SEU346+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.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 : Tue May 21 03:32:41 EDT 2024
% Result : Theorem 3.39s 0.90s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 145 ( 48 unt; 0 def)
% Number of atoms : 509 ( 52 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 579 ( 215 ~; 217 |; 94 &)
% ( 9 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-4 aty)
% Number of variables : 194 ( 5 sgn 111 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',dt_k3_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/sandbox2/benchmark/theBenchmark.p',t7_lattice3) ).
fof(d3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).
fof(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/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice3) ).
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(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/sandbox2/benchmark/theBenchmark.p',dt_u1_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(dt_k2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( reflexive(k2_lattice3(X1))
& antisymmetric(k2_lattice3(X1))
& transitive(k2_lattice3(X1))
& v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
& relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice3) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
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/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(fc1_orders_2,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& relation_of2(X2,X1,X1) )
=> ( ~ empty_carrier(rel_str_of(X1,X2))
& strict_rel_str(rel_str_of(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_orders_2) ).
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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_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/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
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/sandbox2/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(redefinition_k2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> k2_lattice3(X1) = relation_of_lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
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/sandbox2/benchmark/theBenchmark.p',t32_filter_1) ).
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/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(c_0_23,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_24,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])]) ).
fof(c_0_25,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
fof(c_0_26,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(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_27,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_28,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_29,plain,
! [X49] :
( ( meet_semilatt_str(X49)
| ~ latt_str(X49) )
& ( join_semilatt_str(X49)
| ~ latt_str(X49) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])])]) ).
fof(c_0_30,plain,
! [X54] :
( ~ rel_str(X54)
| relation_of2_as_subset(the_InternalRel(X54),the_carrier(X54),the_carrier(X54)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])])]) ).
cnf(c_0_31,plain,
( rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
lattice(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
latt_str(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,negated_conjecture,
~ empty_carrier(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_35,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(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
fof(c_0_36,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
fof(c_0_37,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_38,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_39,plain,
! [X46] :
( ~ meet_semilatt_str(X46)
| one_sorted_str(X46) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])])]) ).
cnf(c_0_40,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_41,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( reflexive(k2_lattice3(X1))
& antisymmetric(k2_lattice3(X1))
& transitive(k2_lattice3(X1))
& v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
& relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k2_lattice3]) ).
fof(c_0_42,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
cnf(c_0_43,plain,
( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,negated_conjecture,
rel_str(poset_of_lattice(esk20_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),c_0_34]) ).
fof(c_0_45,plain,
! [X7] :
( ~ rel_str(X7)
| ~ strict_rel_str(X7)
| X7 = rel_str_of(the_carrier(X7),the_InternalRel(X7)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])])]) ).
cnf(c_0_46,plain,
( strict_rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_47,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_35]) ).
cnf(c_0_48,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_36]) ).
fof(c_0_49,plain,
! [X1,X2] :
( ( ~ empty(X1)
& relation_of2(X2,X1,X1) )
=> ( ~ empty_carrier(rel_str_of(X1,X2))
& strict_rel_str(rel_str_of(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc1_orders_2]) ).
fof(c_0_50,plain,
! [X18] :
( empty_carrier(X18)
| ~ lattice(X18)
| ~ latt_str(X18)
| poset_of_lattice(X18) = rel_str_of(the_carrier(X18),k2_lattice3(X18)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
fof(c_0_51,plain,
! [X71] :
( empty_carrier(X71)
| ~ one_sorted_str(X71)
| ~ empty(the_carrier(X71)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
cnf(c_0_52,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_53,negated_conjecture,
meet_semilatt_str(esk20_0),
inference(spm,[status(thm)],[c_0_40,c_0_33]) ).
fof(c_0_54,plain,
! [X39] :
( ( reflexive(k2_lattice3(X39))
| empty_carrier(X39)
| ~ lattice(X39)
| ~ latt_str(X39) )
& ( antisymmetric(k2_lattice3(X39))
| empty_carrier(X39)
| ~ lattice(X39)
| ~ latt_str(X39) )
& ( transitive(k2_lattice3(X39))
| empty_carrier(X39)
| ~ lattice(X39)
| ~ latt_str(X39) )
& ( v1_partfun1(k2_lattice3(X39),the_carrier(X39),the_carrier(X39))
| empty_carrier(X39)
| ~ lattice(X39)
| ~ latt_str(X39) )
& ( relation_of2_as_subset(k2_lattice3(X39),the_carrier(X39),the_carrier(X39))
| empty_carrier(X39)
| ~ lattice(X39)
| ~ latt_str(X39) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
fof(c_0_55,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_56,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(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_orders_2])])])])]) ).
cnf(c_0_57,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_58,negated_conjecture,
relation_of2_as_subset(the_InternalRel(poset_of_lattice(esk20_0)),the_carrier(poset_of_lattice(esk20_0)),the_carrier(poset_of_lattice(esk20_0))),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_59,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_45]) ).
cnf(c_0_60,negated_conjecture,
strict_rel_str(poset_of_lattice(esk20_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_32]),c_0_33])]),c_0_34]) ).
fof(c_0_61,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_62,negated_conjecture,
( cast_to_el_of_LattPOSet(esk20_0,X1) = X1
| ~ element(X1,the_carrier(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_63,negated_conjecture,
element(esk22_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_64,negated_conjecture,
element(esk21_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_65,negated_conjecture,
( element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))
| ~ element(X1,the_carrier(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_32]),c_0_33])]),c_0_34]) ).
fof(c_0_66,plain,
! [X69,X70] :
( ( ~ empty_carrier(rel_str_of(X69,X70))
| empty(X69)
| ~ relation_of2(X70,X69,X69) )
& ( strict_rel_str(rel_str_of(X69,X70))
| empty(X69)
| ~ relation_of2(X70,X69,X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
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_50]) ).
cnf(c_0_68,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_69,negated_conjecture,
one_sorted_str(esk20_0),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_70,plain,
( relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_71,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
fof(c_0_72,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_73,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_56]) ).
cnf(c_0_74,negated_conjecture,
relation_of2(the_InternalRel(poset_of_lattice(esk20_0)),the_carrier(poset_of_lattice(esk20_0)),the_carrier(poset_of_lattice(esk20_0))),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_75,negated_conjecture,
rel_str_of(the_carrier(poset_of_lattice(esk20_0)),the_InternalRel(poset_of_lattice(esk20_0))) = poset_of_lattice(esk20_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_44])]) ).
fof(c_0_76,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_77,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])]) ).
cnf(c_0_78,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_26]) ).
cnf(c_0_79,negated_conjecture,
cast_to_el_of_LattPOSet(esk20_0,esk22_0) = esk22_0,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_80,negated_conjecture,
cast_to_el_of_LattPOSet(esk20_0,esk21_0) = esk21_0,
inference(spm,[status(thm)],[c_0_62,c_0_64]) ).
cnf(c_0_81,plain,
( reflexive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_82,negated_conjecture,
element(cast_to_el_of_LattPOSet(esk20_0,esk22_0),the_carrier(poset_of_lattice(esk20_0))),
inference(spm,[status(thm)],[c_0_65,c_0_63]) ).
cnf(c_0_83,negated_conjecture,
element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0))),
inference(spm,[status(thm)],[c_0_65,c_0_64]) ).
cnf(c_0_84,plain,
( empty(X1)
| ~ empty_carrier(rel_str_of(X1,X2))
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_85,negated_conjecture,
rel_str_of(the_carrier(esk20_0),k2_lattice3(esk20_0)) = poset_of_lattice(esk20_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_86,negated_conjecture,
~ empty(the_carrier(esk20_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_34]) ).
cnf(c_0_87,negated_conjecture,
relation_of2_as_subset(k2_lattice3(esk20_0),the_carrier(esk20_0),the_carrier(esk20_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_88,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_71]) ).
cnf(c_0_89,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_90,negated_conjecture,
( the_carrier(poset_of_lattice(esk20_0)) = X1
| rel_str_of(X1,X2) != poset_of_lattice(esk20_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
fof(c_0_91,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_92,plain,
! [X121] :
( empty_carrier(X121)
| ~ lattice(X121)
| ~ latt_str(X121)
| k2_lattice3(X121) = relation_of_lattice(X121) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])]) ).
fof(c_0_93,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(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])])]) ).
cnf(c_0_94,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_77]) ).
cnf(c_0_95,negated_conjecture,
( related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| below_refl(esk20_0,esk21_0,esk22_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_96,negated_conjecture,
reflexive_relstr(poset_of_lattice(esk20_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_97,negated_conjecture,
element(esk22_0,the_carrier(poset_of_lattice(esk20_0))),
inference(rw,[status(thm)],[c_0_82,c_0_79]) ).
cnf(c_0_98,negated_conjecture,
element(esk21_0,the_carrier(poset_of_lattice(esk20_0))),
inference(rw,[status(thm)],[c_0_83,c_0_80]) ).
cnf(c_0_99,negated_conjecture,
( ~ relation_of2(k2_lattice3(esk20_0),the_carrier(esk20_0),the_carrier(esk20_0))
| ~ empty_carrier(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_100,negated_conjecture,
relation_of2(k2_lattice3(esk20_0),the_carrier(esk20_0),the_carrier(esk20_0)),
inference(spm,[status(thm)],[c_0_57,c_0_87]) ).
cnf(c_0_101,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_88,c_0_89]) ).
cnf(c_0_102,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_56]) ).
cnf(c_0_103,negated_conjecture,
the_carrier(poset_of_lattice(esk20_0)) = the_carrier(esk20_0),
inference(spm,[status(thm)],[c_0_90,c_0_85]) ).
fof(c_0_104,plain,
! [X145,X146] :
( ( ~ element(X145,powerset(X146))
| subset(X145,X146) )
& ( ~ subset(X145,X146)
| element(X145,powerset(X146)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_105,plain,
! [X131] : subset(X131,X131),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_106,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_107,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(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])])])])]) ).
cnf(c_0_108,plain,
( empty_carrier(X1)
| k2_lattice3(X1) = relation_of_lattice(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_109,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_93]) ).
cnf(c_0_110,negated_conjecture,
( below_refl(esk20_0,esk21_0,esk22_0)
| related(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| empty_carrier(poset_of_lattice(esk20_0)) ),
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_94,c_0_95]),c_0_96]),c_0_97]),c_0_98]),c_0_44])]) ).
cnf(c_0_111,negated_conjecture,
~ empty_carrier(poset_of_lattice(esk20_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100])]) ).
cnf(c_0_112,negated_conjecture,
( ordered_pair_as_product_element(the_carrier(esk20_0),X1,esk21_0,X2) = unordered_pair(unordered_pair(esk21_0,X2),singleton(esk21_0))
| empty(X1)
| ~ element(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_64]),c_0_86]) ).
cnf(c_0_113,negated_conjecture,
( X1 = k2_lattice3(esk20_0)
| rel_str_of(X2,X1) != poset_of_lattice(esk20_0)
| ~ relation_of2(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_102,c_0_85]) ).
cnf(c_0_114,negated_conjecture,
rel_str_of(the_carrier(esk20_0),the_InternalRel(poset_of_lattice(esk20_0))) = poset_of_lattice(esk20_0),
inference(rw,[status(thm)],[c_0_75,c_0_103]) ).
cnf(c_0_115,negated_conjecture,
relation_of2(the_InternalRel(poset_of_lattice(esk20_0)),the_carrier(esk20_0),the_carrier(esk20_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_103]),c_0_103]) ).
cnf(c_0_116,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_93]) ).
cnf(c_0_117,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_118,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
fof(c_0_119,plain,
! [X72] : ~ empty(powerset(X72)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_106])]) ).
cnf(c_0_120,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_107]) ).
cnf(c_0_121,negated_conjecture,
relation_of_lattice(esk20_0) = k2_lattice3(esk20_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_122,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_109,c_0_89]) ).
cnf(c_0_123,negated_conjecture,
( below_refl(esk20_0,esk21_0,esk22_0)
| related(poset_of_lattice(esk20_0),esk21_0,esk22_0) ),
inference(sr,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_124,negated_conjecture,
unordered_pair(unordered_pair(esk21_0,esk22_0),singleton(esk21_0)) = ordered_pair_as_product_element(the_carrier(esk20_0),the_carrier(esk20_0),esk21_0,esk22_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_63]),c_0_86]) ).
cnf(c_0_125,negated_conjecture,
the_InternalRel(poset_of_lattice(esk20_0)) = k2_lattice3(esk20_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115])]) ).
cnf(c_0_126,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_116,c_0_89]) ).
cnf(c_0_127,negated_conjecture,
( ordered_pair_as_product_element(X1,the_carrier(esk20_0),X2,esk22_0) = unordered_pair(unordered_pair(X2,esk22_0),singleton(X2))
| empty(X1)
| ~ element(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_63]),c_0_86]) ).
cnf(c_0_128,plain,
element(X1,powerset(X1)),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_129,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_130,negated_conjecture,
( below_refl(esk20_0,X1,X2)
| ~ element(X2,the_carrier(esk20_0))
| ~ element(X1,the_carrier(esk20_0))
| ~ in(ordered_pair_as_product_element(the_carrier(esk20_0),the_carrier(esk20_0),X1,X2),k2_lattice3(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_131,negated_conjecture,
( below_refl(esk20_0,esk21_0,esk22_0)
| in(ordered_pair_as_product_element(the_carrier(esk20_0),the_carrier(esk20_0),esk21_0,esk22_0),k2_lattice3(esk20_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_97]),c_0_98]),c_0_44])]),c_0_124]),c_0_125]) ).
cnf(c_0_132,negated_conjecture,
( related(poset_of_lattice(esk20_0),X1,X2)
| ~ element(X2,the_carrier(esk20_0))
| ~ element(X1,the_carrier(esk20_0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),k2_lattice3(esk20_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_125]),c_0_103]),c_0_103]),c_0_44])]) ).
cnf(c_0_133,negated_conjecture,
unordered_pair(unordered_pair(X1,esk22_0),singleton(X1)) = ordered_pair_as_product_element(powerset(X1),the_carrier(esk20_0),X1,esk22_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_134,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_107]) ).
cnf(c_0_135,negated_conjecture,
below_refl(esk20_0,esk21_0,esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_63]),c_0_64])]) ).
cnf(c_0_136,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_26]) ).
cnf(c_0_137,negated_conjecture,
( related(poset_of_lattice(esk20_0),X1,esk22_0)
| ~ element(X1,the_carrier(esk20_0))
| ~ in(ordered_pair_as_product_element(powerset(X1),the_carrier(esk20_0),X1,esk22_0),k2_lattice3(esk20_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_63])]) ).
cnf(c_0_138,negated_conjecture,
ordered_pair_as_product_element(powerset(esk21_0),the_carrier(esk20_0),esk21_0,esk22_0) = ordered_pair_as_product_element(the_carrier(esk20_0),the_carrier(esk20_0),esk21_0,esk22_0),
inference(rw,[status(thm)],[c_0_124,c_0_133]) ).
cnf(c_0_139,negated_conjecture,
in(ordered_pair_as_product_element(the_carrier(esk20_0),the_carrier(esk20_0),esk21_0,esk22_0),k2_lattice3(esk20_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(spm,[status(thm)],[c_0_134,c_0_135]),c_0_121]),c_0_63]),c_0_64]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_140,negated_conjecture,
( ~ related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| ~ below_refl(esk20_0,esk21_0,esk22_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_79]),c_0_80]) ).
cnf(c_0_141,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_77]) ).
cnf(c_0_142,negated_conjecture,
related(poset_of_lattice(esk20_0),esk21_0,esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_64]),c_0_139])]) ).
cnf(c_0_143,negated_conjecture,
~ related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_135])]) ).
cnf(c_0_144,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_141,c_0_142]),c_0_96]),c_0_103]),c_0_63]),c_0_103]),c_0_64]),c_0_44])]),c_0_143]),c_0_111]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU346+1 : TPTP v8.2.0. Released v3.3.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun May 19 16:54:23 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order model finding
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.39/0.90 # Version: 3.1.0
% 3.39/0.90 # Preprocessing class: FSLSSMSSSSSNFFN.
% 3.39/0.90 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.39/0.90 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.39/0.90 # Starting new_bool_3 with 300s (1) cores
% 3.39/0.90 # Starting new_bool_1 with 300s (1) cores
% 3.39/0.90 # Starting sh5l with 300s (1) cores
% 3.39/0.90 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 11193 completed with status 0
% 3.39/0.90 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.39/0.90 # Preprocessing class: FSLSSMSSSSSNFFN.
% 3.39/0.90 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.39/0.90 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.39/0.90 # No SInE strategy applied
% 3.39/0.90 # Search class: FGHSM-FSLM31-SFFFFFNN
% 3.39/0.90 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.39/0.90 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 811s (1) cores
% 3.39/0.90 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.39/0.90 # Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 3.39/0.90 # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 3.39/0.90 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 3.39/0.90 # G-E--_208_C18_F1_AE_CS_SP_PI_S0a with pid 11200 completed with status 0
% 3.39/0.90 # Result found by G-E--_208_C18_F1_AE_CS_SP_PI_S0a
% 3.39/0.90 # Preprocessing class: FSLSSMSSSSSNFFN.
% 3.39/0.90 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.39/0.90 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.39/0.90 # No SInE strategy applied
% 3.39/0.90 # Search class: FGHSM-FSLM31-SFFFFFNN
% 3.39/0.90 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.39/0.90 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 811s (1) cores
% 3.39/0.90 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.39/0.90 # Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 3.39/0.90 # Preprocessing time : 0.003 s
% 3.39/0.90
% 3.39/0.90 # Proof found!
% 3.39/0.90 # SZS status Theorem
% 3.39/0.90 # SZS output start CNFRefutation
% See solution above
% 3.39/0.90 # Parsed axioms : 93
% 3.39/0.90 # Removed by relevancy pruning/SinE : 0
% 3.39/0.90 # Initial clauses : 182
% 3.39/0.90 # Removed in clause preprocessing : 13
% 3.39/0.90 # Initial clauses in saturation : 169
% 3.39/0.90 # Processed clauses : 2773
% 3.39/0.90 # ...of these trivial : 60
% 3.39/0.90 # ...subsumed : 901
% 3.39/0.90 # ...remaining for further processing : 1812
% 3.39/0.90 # Other redundant clauses eliminated : 0
% 3.39/0.90 # Clauses deleted for lack of memory : 0
% 3.39/0.90 # Backward-subsumed : 32
% 3.39/0.90 # Backward-rewritten : 101
% 3.39/0.90 # Generated clauses : 19140
% 3.39/0.90 # ...of the previous two non-redundant : 18871
% 3.39/0.90 # ...aggressively subsumed : 0
% 3.39/0.90 # Contextual simplify-reflections : 1
% 3.39/0.90 # Paramodulations : 19126
% 3.39/0.90 # Factorizations : 0
% 3.39/0.90 # NegExts : 0
% 3.39/0.90 # Equation resolutions : 9
% 3.39/0.90 # Disequality decompositions : 0
% 3.39/0.90 # Total rewrite steps : 3969
% 3.39/0.90 # ...of those cached : 3673
% 3.39/0.90 # Propositional unsat checks : 0
% 3.39/0.90 # Propositional check models : 0
% 3.39/0.90 # Propositional check unsatisfiable : 0
% 3.39/0.90 # Propositional clauses : 0
% 3.39/0.90 # Propositional clauses after purity: 0
% 3.39/0.90 # Propositional unsat core size : 0
% 3.39/0.90 # Propositional preprocessing time : 0.000
% 3.39/0.90 # Propositional encoding time : 0.000
% 3.39/0.90 # Propositional solver time : 0.000
% 3.39/0.90 # Success case prop preproc time : 0.000
% 3.39/0.90 # Success case prop encoding time : 0.000
% 3.39/0.90 # Success case prop solver time : 0.000
% 3.39/0.90 # Current number of processed clauses : 1674
% 3.39/0.90 # Positive orientable unit clauses : 438
% 3.39/0.90 # Positive unorientable unit clauses: 1
% 3.39/0.90 # Negative unit clauses : 48
% 3.39/0.90 # Non-unit-clauses : 1187
% 3.39/0.90 # Current number of unprocessed clauses: 16082
% 3.39/0.90 # ...number of literals in the above : 57243
% 3.39/0.90 # Current number of archived formulas : 0
% 3.39/0.90 # Current number of archived clauses : 139
% 3.39/0.90 # Clause-clause subsumption calls (NU) : 185394
% 3.39/0.90 # Rec. Clause-clause subsumption calls : 110063
% 3.39/0.90 # Non-unit clause-clause subsumptions : 794
% 3.39/0.90 # Unit Clause-clause subsumption calls : 17362
% 3.39/0.90 # Rewrite failures with RHS unbound : 0
% 3.39/0.90 # BW rewrite match attempts : 559
% 3.39/0.90 # BW rewrite match successes : 34
% 3.39/0.90 # Condensation attempts : 0
% 3.39/0.90 # Condensation successes : 0
% 3.39/0.90 # Termbank termtop insertions : 530276
% 3.39/0.90 # Search garbage collected termcells : 1948
% 3.39/0.90
% 3.39/0.90 # -------------------------------------------------
% 3.39/0.90 # User time : 0.394 s
% 3.39/0.90 # System time : 0.024 s
% 3.39/0.90 # Total time : 0.418 s
% 3.39/0.90 # Maximum resident set size: 2316 pages
% 3.39/0.90
% 3.39/0.90 # -------------------------------------------------
% 3.39/0.90 # User time : 1.996 s
% 3.39/0.90 # System time : 0.070 s
% 3.39/0.90 # Total time : 2.065 s
% 3.39/0.90 # Maximum resident set size: 1796 pages
% 3.39/0.90 % E---3.1 exiting
%------------------------------------------------------------------------------