%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU346+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:47 PM UTC 2026
% Result : Theorem 4.11s 1.11s
% Output : CNFRefutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 146 ( 48 unt; 0 def)
% Number of atoms : 516 ( 52 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 587 ( 217 ~; 217 |; 96 &)
% ( 10 <=>; 47 =>; 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 : 197 ( 5 sgn 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_lattice3,conjecture,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(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(dt_k3_lattice3,axiom,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ( rel_str(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& strict_rel_str(poset_of_lattice(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(d3_lattice3,axiom,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(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] :
( ( element(X2,the_carrier(X1))
& latt_str(X1)
& lattice(X1)
& ~ empty_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)
=> ( join_semilatt_str(X1)
& meet_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] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(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] :
( ( one_sorted_str(X1)
& ~ empty_carrier(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] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ( relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
& v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
& transitive(k2_lattice3(X1))
& antisymmetric(k2_lattice3(X1))
& reflexive(k2_lattice3(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] :
( ( relation_of2(X2,X1,X1)
& ~ empty(X1) )
=> ( strict_rel_str(rel_str_of(X1,X2))
& ~ empty_carrier(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] :
( ( element(X4,X2)
& element(X3,X1)
& ~ empty(X2)
& ~ empty(X1) )
=> 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)
=> ( X2 = X4
& X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(redefinition_r3_orders_2,axiom,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& rel_str(X1)
& reflexive_relstr(X1)
& ~ empty_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] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> k2_lattice3(X1) = relation_of_lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
fof(t32_filter_1,axiom,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(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,negated_conjecture,
~ ! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(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(assume_negation,[status(cth)],[t7_lattice3]) ).
fof(c_0_24,plain,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ( rel_str(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& strict_rel_str(poset_of_lattice(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_lattice3]) ).
fof(c_0_25,negated_conjecture,
~ ! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(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)],[c_0_23]) ).
fof(c_0_26,plain,
! [X40] :
( ( ~ latt_str(X40)
| ~ lattice(X40)
| empty_carrier(X40)
| rel_str(poset_of_lattice(X40)) )
& ( ~ latt_str(X40)
| ~ lattice(X40)
| empty_carrier(X40)
| antisymmetric_relstr(poset_of_lattice(X40)) )
& ( ~ latt_str(X40)
| ~ lattice(X40)
| empty_carrier(X40)
| transitive_relstr(poset_of_lattice(X40)) )
& ( ~ latt_str(X40)
| ~ lattice(X40)
| empty_carrier(X40)
| reflexive_relstr(poset_of_lattice(X40)) )
& ( ~ latt_str(X40)
| ~ lattice(X40)
| empty_carrier(X40)
| strict_rel_str(poset_of_lattice(X40)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_27,negated_conjecture,
( ( 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))
| ~ below_refl(esk20_0,esk21_0,esk22_0) )
& element(esk22_0,the_carrier(esk20_0))
& element(esk21_0,the_carrier(esk20_0))
& latt_str(esk20_0)
& lattice(esk20_0)
& ~ empty_carrier(esk20_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
fof(c_0_28,plain,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(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_29,plain,
! [X1,X2] :
( ( element(X2,the_carrier(X1))
& latt_str(X1)
& lattice(X1)
& ~ empty_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_30,plain,
! [X49] :
( ( ~ latt_str(X49)
| join_semilatt_str(X49) )
& ( ~ latt_str(X49)
| meet_semilatt_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_31,plain,
! [X54] :
( relation_of2_as_subset(the_InternalRel(X54),the_carrier(X54),the_carrier(X54))
| ~ rel_str(X54) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])])]) ).
cnf(c_0_32,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| rel_str(poset_of_lattice(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
lattice(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
latt_str(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
~ empty_carrier(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_36,plain,
! [X19,X20] :
( cast_to_el_of_LattPOSet(X19,X20) = X20
| ~ element(X20,the_carrier(X19))
| ~ latt_str(X19)
| ~ lattice(X19)
| empty_carrier(X19) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
fof(c_0_37,plain,
! [X41,X42] :
( element(cast_to_el_of_LattPOSet(X41,X42),the_carrier(poset_of_lattice(X41)))
| ~ element(X42,the_carrier(X41))
| ~ latt_str(X41)
| ~ lattice(X41)
| empty_carrier(X41) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
fof(c_0_38,plain,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
inference(fof_simplification,[status(thm)],[d2_lattice3]) ).
fof(c_0_39,plain,
! [X1] :
( ( one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_40,plain,
! [X46] :
( one_sorted_str(X46)
| ~ meet_semilatt_str(X46) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])])]) ).
cnf(c_0_41,plain,
( ~ latt_str(X1)
| meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_42,plain,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ( relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
& v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
& transitive(k2_lattice3(X1))
& antisymmetric(k2_lattice3(X1))
& reflexive(k2_lattice3(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k2_lattice3]) ).
fof(c_0_43,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_44,plain,
( ~ rel_str(X1)
| relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_45,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_32,c_0_33]),c_0_34])]),c_0_35]) ).
fof(c_0_46,plain,
! [X7] :
( X7 = rel_str_of(the_carrier(X7),the_InternalRel(X7))
| ~ strict_rel_str(X7)
| ~ rel_str(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])])]) ).
cnf(c_0_47,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| strict_rel_str(poset_of_lattice(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_48,plain,
( ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| cast_to_el_of_LattPOSet(X1,X2) = X2
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,plain,
( ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1)))
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_50,plain,
! [X1,X2] :
( ( relation_of2(X2,X1,X1)
& ~ empty(X1) )
=> ( strict_rel_str(rel_str_of(X1,X2))
& ~ empty_carrier(rel_str_of(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc1_orders_2]) ).
fof(c_0_51,plain,
! [X18] :
( poset_of_lattice(X18) = rel_str_of(the_carrier(X18),k2_lattice3(X18))
| ~ latt_str(X18)
| ~ lattice(X18)
| empty_carrier(X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
fof(c_0_52,plain,
! [X71] :
( ~ empty(the_carrier(X71))
| ~ one_sorted_str(X71)
| empty_carrier(X71) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
cnf(c_0_53,plain,
( ~ meet_semilatt_str(X1)
| one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_54,negated_conjecture,
meet_semilatt_str(esk20_0),
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
fof(c_0_55,plain,
! [X39] :
( ( ~ latt_str(X39)
| ~ lattice(X39)
| empty_carrier(X39)
| relation_of2_as_subset(k2_lattice3(X39),the_carrier(X39),the_carrier(X39)) )
& ( ~ latt_str(X39)
| ~ lattice(X39)
| empty_carrier(X39)
| v1_partfun1(k2_lattice3(X39),the_carrier(X39),the_carrier(X39)) )
& ( ~ latt_str(X39)
| ~ lattice(X39)
| empty_carrier(X39)
| transitive(k2_lattice3(X39)) )
& ( ~ latt_str(X39)
| ~ lattice(X39)
| empty_carrier(X39)
| antisymmetric(k2_lattice3(X39)) )
& ( ~ latt_str(X39)
| ~ lattice(X39)
| empty_carrier(X39)
| reflexive(k2_lattice3(X39)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
fof(c_0_56,plain,
! [X1,X2,X3,X4] :
( ( element(X4,X2)
& element(X3,X1)
& ~ empty(X2)
& ~ empty(X1) )
=> 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_57,plain,
! [X89,X90,X91,X92] :
( ( ~ relation_of2(X90,X89,X89)
| rel_str_of(X89,X90) != rel_str_of(X91,X92)
| X90 = X92 )
& ( ~ relation_of2(X90,X89,X89)
| rel_str_of(X89,X90) != rel_str_of(X91,X92)
| X89 = X91 ) ),
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_58,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_59,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_44,c_0_45]) ).
cnf(c_0_60,plain,
( ~ strict_rel_str(X1)
| ~ rel_str(X1)
| X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_61,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_47,c_0_33]),c_0_34])]),c_0_35]) ).
fof(c_0_62,plain,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& rel_str(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1) )
=> ( related_reflexive(X1,X2,X3)
<=> related(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_orders_2]) ).
cnf(c_0_63,negated_conjecture,
( ~ element(X1,the_carrier(esk20_0))
| cast_to_el_of_LattPOSet(esk20_0,X1) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_64,negated_conjecture,
element(esk22_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_65,negated_conjecture,
element(esk21_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_66,negated_conjecture,
( ~ element(X1,the_carrier(esk20_0))
| element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_33]),c_0_34])]),c_0_35]) ).
fof(c_0_67,plain,
! [X69,X70] :
( ( ~ relation_of2(X70,X69,X69)
| empty(X69)
| strict_rel_str(rel_str_of(X69,X70)) )
& ( ~ relation_of2(X70,X69,X69)
| empty(X69)
| ~ empty_carrier(rel_str_of(X69,X70)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])]) ).
cnf(c_0_68,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1))
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_69,plain,
( ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_70,negated_conjecture,
one_sorted_str(esk20_0),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_71,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_72,plain,
! [X117,X118,X119,X120] :
( ordered_pair_as_product_element(X117,X118,X119,X120) = ordered_pair(X119,X120)
| ~ element(X120,X118)
| ~ element(X119,X117)
| empty(X118)
| empty(X117) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])]) ).
fof(c_0_73,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_74,plain,
( ~ relation_of2(X3,X1,X1)
| rel_str_of(X1,X3) != rel_str_of(X2,X4)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_75,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_58,c_0_59]) ).
cnf(c_0_76,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_60,c_0_61]),c_0_45])]) ).
fof(c_0_77,plain,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> k2_lattice3(X1) = relation_of_lattice(X1) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_lattice3]) ).
fof(c_0_78,plain,
! [X128,X129,X130] :
( ( ~ element(X130,the_carrier(X128))
| ~ element(X129,the_carrier(X128))
| ~ rel_str(X128)
| ~ reflexive_relstr(X128)
| empty_carrier(X128)
| related_reflexive(X128,X129,X130)
| ~ related(X128,X129,X130) )
& ( ~ element(X130,the_carrier(X128))
| ~ element(X129,the_carrier(X128))
| ~ rel_str(X128)
| ~ reflexive_relstr(X128)
| empty_carrier(X128)
| related(X128,X129,X130)
| ~ related_reflexive(X128,X129,X130) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).
cnf(c_0_79,negated_conjecture,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_80,negated_conjecture,
cast_to_el_of_LattPOSet(esk20_0,esk22_0) = esk22_0,
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_81,negated_conjecture,
cast_to_el_of_LattPOSet(esk20_0,esk21_0) = esk21_0,
inference(spm,[status(thm)],[c_0_63,c_0_65]) ).
cnf(c_0_82,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| reflexive_relstr(poset_of_lattice(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_83,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_66,c_0_64]) ).
cnf(c_0_84,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_66,c_0_65]) ).
cnf(c_0_85,plain,
( ~ relation_of2(X2,X1,X1)
| ~ empty_carrier(rel_str_of(X1,X2))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_86,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_68,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_87,negated_conjecture,
~ empty(the_carrier(esk20_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_35]) ).
cnf(c_0_88,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_71,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_89,plain,
( ~ element(X4,X2)
| ~ element(X3,X1)
| ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4)
| empty(X2)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_90,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_91,negated_conjecture,
( rel_str_of(X1,X2) != poset_of_lattice(esk20_0)
| the_carrier(poset_of_lattice(esk20_0)) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
fof(c_0_92,plain,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(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_93,plain,
! [X121] :
( k2_lattice3(X121) = relation_of_lattice(X121)
| ~ latt_str(X121)
| ~ lattice(X121)
| empty_carrier(X121) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])]) ).
fof(c_0_94,plain,
! [X23,X24,X25] :
( ( ~ rel_str(X23)
| ~ element(X24,the_carrier(X23))
| ~ element(X25,the_carrier(X23))
| related(X23,X24,X25)
| ~ in(ordered_pair(X24,X25),the_InternalRel(X23)) )
& ( ~ rel_str(X23)
| ~ element(X24,the_carrier(X23))
| ~ element(X25,the_carrier(X23))
| in(ordered_pair(X24,X25),the_InternalRel(X23))
| ~ related(X23,X24,X25) ) ),
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_95,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1)
| ~ reflexive_relstr(X1)
| ~ related_reflexive(X1,X2,X3)
| empty_carrier(X1)
| related(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_96,negated_conjecture,
( below_refl(esk20_0,esk21_0,esk22_0)
| related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_97,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_82,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_98,negated_conjecture,
element(esk22_0,the_carrier(poset_of_lattice(esk20_0))),
inference(rw,[status(thm)],[c_0_83,c_0_80]) ).
cnf(c_0_99,negated_conjecture,
element(esk21_0,the_carrier(poset_of_lattice(esk20_0))),
inference(rw,[status(thm)],[c_0_84,c_0_81]) ).
cnf(c_0_100,negated_conjecture,
( ~ empty_carrier(poset_of_lattice(esk20_0))
| ~ relation_of2(k2_lattice3(esk20_0),the_carrier(esk20_0),the_carrier(esk20_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
cnf(c_0_101,negated_conjecture,
relation_of2(k2_lattice3(esk20_0),the_carrier(esk20_0),the_carrier(esk20_0)),
inference(spm,[status(thm)],[c_0_58,c_0_88]) ).
cnf(c_0_102,plain,
( ~ element(X3,X1)
| ~ element(X4,X2)
| empty(X1)
| empty(X2)
| ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)) ),
inference(rw,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_103,plain,
( ~ relation_of2(X1,X3,X3)
| rel_str_of(X3,X1) != rel_str_of(X4,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_104,negated_conjecture,
the_carrier(poset_of_lattice(esk20_0)) = the_carrier(esk20_0),
inference(spm,[status(thm)],[c_0_91,c_0_86]) ).
fof(c_0_105,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_106,plain,
! [X131] : subset(X131,X131),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_107,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_108,plain,
! [X142,X143,X144] :
( ( ~ latt_str(X142)
| ~ lattice(X142)
| empty_carrier(X142)
| ~ element(X143,the_carrier(X142))
| ~ element(X144,the_carrier(X142))
| in(ordered_pair_as_product_element(the_carrier(X142),the_carrier(X142),X143,X144),relation_of_lattice(X142))
| ~ below_refl(X142,X143,X144) )
& ( ~ latt_str(X142)
| ~ lattice(X142)
| empty_carrier(X142)
| ~ element(X143,the_carrier(X142))
| ~ element(X144,the_carrier(X142))
| below_refl(X142,X143,X144)
| ~ in(ordered_pair_as_product_element(the_carrier(X142),the_carrier(X142),X143,X144),relation_of_lattice(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_92])])])])]) ).
cnf(c_0_109,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| k2_lattice3(X1) = relation_of_lattice(X1)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_110,plain,
( ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ related(X1,X2,X3)
| in(ordered_pair(X2,X3),the_InternalRel(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_111,negated_conjecture,
( empty_carrier(poset_of_lattice(esk20_0))
| related(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| below_refl(esk20_0,esk21_0,esk22_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_95,c_0_96]),c_0_97]),c_0_98]),c_0_99]),c_0_45])]) ).
cnf(c_0_112,negated_conjecture,
~ empty_carrier(poset_of_lattice(esk20_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]) ).
cnf(c_0_113,negated_conjecture,
( ~ element(X2,X1)
| empty(X1)
| ordered_pair_as_product_element(the_carrier(esk20_0),X1,esk21_0,X2) = unordered_pair(unordered_pair(esk21_0,X2),singleton(esk21_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_65]),c_0_87]) ).
cnf(c_0_114,negated_conjecture,
( ~ relation_of2(X1,X2,X2)
| rel_str_of(X2,X1) != poset_of_lattice(esk20_0)
| X1 = k2_lattice3(esk20_0) ),
inference(spm,[status(thm)],[c_0_103,c_0_86]) ).
cnf(c_0_115,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_76,c_0_104]) ).
cnf(c_0_116,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_75,c_0_104]),c_0_104]) ).
cnf(c_0_117,plain,
( ~ rel_str(X3)
| ~ element(X1,the_carrier(X3))
| ~ element(X2,the_carrier(X3))
| ~ in(ordered_pair(X1,X2),the_InternalRel(X3))
| related(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_118,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_119,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
fof(c_0_120,plain,
! [X72] : ~ empty(powerset(X72)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_107])]) ).
cnf(c_0_121,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_122,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_109,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_123,plain,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ related(X1,X2,X3)
| ~ rel_str(X1)
| in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1)) ),
inference(rw,[status(thm)],[c_0_110,c_0_90]) ).
cnf(c_0_124,negated_conjecture,
( related(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| below_refl(esk20_0,esk21_0,esk22_0) ),
inference(sr,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_125,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_113,c_0_64]),c_0_87]) ).
cnf(c_0_126,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_114,c_0_115]),c_0_116])]) ).
cnf(c_0_127,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X3))
| ~ element(X1,the_carrier(X3))
| ~ element(X2,the_carrier(X3))
| ~ rel_str(X3)
| related(X3,X1,X2) ),
inference(rw,[status(thm)],[c_0_117,c_0_90]) ).
cnf(c_0_128,negated_conjecture,
( ~ element(X2,X1)
| empty(X1)
| ordered_pair_as_product_element(X1,the_carrier(esk20_0),X2,esk22_0) = unordered_pair(unordered_pair(X2,esk22_0),singleton(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_64]),c_0_87]) ).
cnf(c_0_129,plain,
element(X1,powerset(X1)),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_130,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_131,negated_conjecture,
( ~ in(ordered_pair_as_product_element(the_carrier(esk20_0),the_carrier(esk20_0),X1,X2),k2_lattice3(esk20_0))
| ~ element(X1,the_carrier(esk20_0))
| ~ element(X2,the_carrier(esk20_0))
| below_refl(esk20_0,X1,X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_132,negated_conjecture,
( in(ordered_pair_as_product_element(the_carrier(esk20_0),the_carrier(esk20_0),esk21_0,esk22_0),k2_lattice3(esk20_0))
| below_refl(esk20_0,esk21_0,esk22_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_123,c_0_124]),c_0_98]),c_0_99]),c_0_45])]),c_0_125]),c_0_126]) ).
cnf(c_0_133,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),k2_lattice3(esk20_0))
| ~ element(X1,the_carrier(esk20_0))
| ~ element(X2,the_carrier(esk20_0))
| related(poset_of_lattice(esk20_0),X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_126]),c_0_104]),c_0_104]),c_0_45])]) ).
cnf(c_0_134,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_128,c_0_129]),c_0_130]) ).
cnf(c_0_135,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_136,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_131,c_0_132]),c_0_64]),c_0_65])]) ).
cnf(c_0_137,negated_conjecture,
( ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_138,negated_conjecture,
( ~ in(ordered_pair_as_product_element(powerset(X1),the_carrier(esk20_0),X1,esk22_0),k2_lattice3(esk20_0))
| ~ element(X1,the_carrier(esk20_0))
| related(poset_of_lattice(esk20_0),X1,esk22_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_64])]) ).
cnf(c_0_139,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_125,c_0_134]) ).
cnf(c_0_140,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_135,c_0_136]),c_0_122]),c_0_64]),c_0_65]),c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_141,negated_conjecture,
( ~ below_refl(esk20_0,esk21_0,esk22_0)
| ~ related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_80]),c_0_81]) ).
cnf(c_0_142,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1)
| ~ reflexive_relstr(X1)
| ~ related(X1,X2,X3)
| empty_carrier(X1)
| related_reflexive(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_143,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_138,c_0_139]),c_0_65]),c_0_140])]) ).
cnf(c_0_144,negated_conjecture,
~ related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_136])]) ).
cnf(c_0_145,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_142,c_0_143]),c_0_97]),c_0_104]),c_0_64]),c_0_104]),c_0_65]),c_0_45])]),c_0_144]),c_0_112]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU346+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 % Computer : n012.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 21 06:13:51 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.11/1.11 % Version: 3.5.1
% 4.11/1.11 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.11/1.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.11/1.11 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.11/1.11 % Starting new_bool_3 with 300s (1) cores
% 4.11/1.11 % Starting new_bool_1 with 300s (1) cores
% 4.11/1.11 % Starting sh5l with 300s (1) cores
% 4.11/1.11 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1720529 completed with status 0
% 4.11/1.11 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 4.11/1.11 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.11/1.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.11/1.11 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.11/1.11 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.11/1.11 % No SInE strategy applied
% 4.11/1.11 % Search class: FGHSM-FSLM31-SFFFFFNN
% 4.11/1.11 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.11/1.11 % Starting SubtermCWHack with 136s (1) cores
% 4.11/1.11 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.11/1.11 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_S0e with 136s (1) cores
% 4.11/1.11 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 4.11/1.11 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 4.11/1.11 % G-E--_208_C18_F1_AE_CS_SP_PI_S0a with pid 1720539 completed with status 0
% 4.11/1.11 % Result found by G-E--_208_C18_F1_AE_CS_SP_PI_S0a
% 4.11/1.11 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.11/1.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.11/1.11 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.11/1.11 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.11/1.11 % No SInE strategy applied
% 4.11/1.11 % Search class: FGHSM-FSLM31-SFFFFFNN
% 4.11/1.11 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.11/1.11 % Starting SubtermCWHack with 136s (1) cores
% 4.11/1.11 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.11/1.11 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_S0e with 136s (1) cores
% 4.11/1.11 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 4.11/1.11 % Preprocessing time : 0.003 s
% 4.11/1.11
% 4.11/1.11 % Proof found!
% 4.11/1.11 % SZS status Theorem
% 4.11/1.11 % SZS output start CNFRefutation
% See solution above
% 4.11/1.11 % Parsed axioms : 93
% 4.11/1.11 % Removed by relevancy pruning/SinE : 0
% 4.11/1.11 % Initial clauses : 182
% 4.11/1.11 % Removed in clause preprocessing : 13
% 4.11/1.11 % Initial clauses in saturation : 169
% 4.11/1.11 % Processed clauses : 2773
% 4.11/1.11 % ...of these trivial : 60
% 4.11/1.11 % ...subsumed : 901
% 4.11/1.11 % ...remaining for further processing : 1812
% 4.11/1.11 % Other redundant clauses eliminated : 0
% 4.11/1.11 % Clauses deleted for lack of memory : 0
% 4.11/1.11 % Backward-subsumed : 32
% 4.11/1.11 % Backward-rewritten : 101
% 4.11/1.11 % Generated clauses : 19140
% 4.11/1.11 % ...of the previous two non-redundant : 18871
% 4.11/1.11 % ...aggressively subsumed : 0
% 4.11/1.11 % Contextual simplify-reflections : 1
% 4.11/1.11 % Paramodulations : 19126
% 4.11/1.11 % Factorizations : 0
% 4.11/1.11 % NegExts : 0
% 4.11/1.11 % Equation resolutions : 9
% 4.11/1.11 % Disequality decompositions : 0
% 4.11/1.11 % Total rewrite steps : 3969
% 4.11/1.11 % ...of those cached : 3673
% 4.11/1.11 % Propositional unsat checks : 0
% 4.11/1.11 % Propositional check models : 0
% 4.11/1.11 % Propositional check unsatisfiable : 0
% 4.11/1.11 % Propositional clauses : 0
% 4.11/1.11 % Propositional clauses after purity: 0
% 4.11/1.11 % Propositional unsat core size : 0
% 4.11/1.11 % Propositional preprocessing time : 0.000
% 4.11/1.11 % Propositional encoding time : 0.000
% 4.11/1.11 % Propositional solver time : 0.000
% 4.11/1.11 % Success case prop preproc time : 0.000
% 4.11/1.11 % Success case prop encoding time : 0.000
% 4.11/1.11 % Success case prop solver time : 0.000
% 4.11/1.11 % Current number of processed clauses : 1674
% 4.11/1.11 % Positive orientable unit clauses : 438
% 4.11/1.11 % Positive unorientable unit clauses: 1
% 4.11/1.11 % Negative unit clauses : 48
% 4.11/1.11 % Non-unit-clauses : 1187
% 4.11/1.11 % Current number of unprocessed clauses: 16082
% 4.11/1.11 % ...number of literals in the above : 57243
% 4.11/1.11 % Current number of archived formulas : 0
% 4.11/1.11 % Current number of archived clauses : 139
% 4.11/1.11 % Clause-clause subsumption calls (NU) : 186600
% 4.11/1.11 % Rec. Clause-clause subsumption calls : 111152
% 4.11/1.11 % Non-unit clause-clause subsumptions : 794
% 4.11/1.11 % Unit Clause-clause subsumption calls : 17891
% 4.11/1.11 % Rewrite failures with RHS unbound : 0
% 4.11/1.11 % BW rewrite match attempts : 559
% 4.11/1.11 % BW rewrite match successes : 34
% 4.11/1.11 % Condensation attempts : 0
% 4.11/1.11 % Condensation successes : 0
% 4.11/1.11 % Termbank termtop insertions : 531111
% 4.11/1.11 % Search garbage collected termcells : 1947
% 4.11/1.11
% 4.11/1.11 % -------------------------------------------------
% 4.11/1.11 % User time : 0.475 s
% 4.11/1.11 % System time : 0.036 s
% 4.11/1.11 % Total time : 0.511 s
% 4.11/1.11 % Maximum resident set size: 4252 pages
% 4.11/1.11
% 4.11/1.11 % -------------------------------------------------
% 4.11/1.11 % User time : 2.251 s
% 4.11/1.11 % System time : 0.102 s
% 4.11/1.11 % Total time : 2.353 s
% 4.11/1.11 % Maximum resident set size: 4608 pages
% 4.11/1.11 % E exiting
%------------------------------------------------------------------------------