%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU349+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 : n014.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 02:24:48 PM UTC 2026
% Result : Theorem 6.00s 1.48s
% Output : CNFRefutation 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 15
% Syntax : Number of formulae : 121 ( 25 unt; 0 def)
% Number of atoms : 575 ( 29 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 700 ( 246 ~; 285 |; 109 &)
% ( 13 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 178 ( 2 sgn 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t30_lattice3,conjecture,
! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_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_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(d17_lattice3,axiom,
! [X1] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X4,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_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(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(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(t7_lattice3,axiom,
! [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(d9_lattice3,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( relstr_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X2)
=> related(X1,X4,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice3) ).
fof(fc4_lattice3,axiom,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(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))
& ~ empty_carrier(poset_of_lattice(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice3) ).
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(cc1_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( ( lattice(X1)
& ~ empty_carrier(X1) )
=> ( join_absorbing(X1)
& meet_absorbing(X1)
& meet_associative(X1)
& meet_commutative(X1)
& join_associative(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
fof(redefinition_r3_lattices,axiom,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& latt_str(X1)
& join_absorbing(X1)
& meet_absorbing(X1)
& meet_commutative(X1)
& ~ empty_carrier(X1) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(assume_negation,[status(cth)],[t30_lattice3]) ).
fof(c_0_16,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_17,negated_conjecture,
~ ! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X32] :
( ( ~ latt_str(X32)
| ~ lattice(X32)
| empty_carrier(X32)
| rel_str(poset_of_lattice(X32)) )
& ( ~ latt_str(X32)
| ~ lattice(X32)
| empty_carrier(X32)
| antisymmetric_relstr(poset_of_lattice(X32)) )
& ( ~ latt_str(X32)
| ~ lattice(X32)
| empty_carrier(X32)
| transitive_relstr(poset_of_lattice(X32)) )
& ( ~ latt_str(X32)
| ~ lattice(X32)
| empty_carrier(X32)
| reflexive_relstr(poset_of_lattice(X32)) )
& ( ~ latt_str(X32)
| ~ lattice(X32)
| empty_carrier(X32)
| strict_rel_str(poset_of_lattice(X32)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_19,negated_conjecture,
( ( relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0))
| latt_element_smaller(esk20_0,esk21_0,esk19_0) )
& ( ~ relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0))
| ~ latt_element_smaller(esk20_0,esk21_0,esk19_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_17])])])]) ).
fof(c_0_20,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_21,plain,
! [X45] :
( relation_of2_as_subset(the_InternalRel(X45),the_carrier(X45),the_carrier(X45))
| ~ rel_str(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])])]) ).
cnf(c_0_22,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| rel_str(poset_of_lattice(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
lattice(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
latt_str(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
~ empty_carrier(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_26,plain,
! [X1] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X4,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d17_lattice3]) ).
fof(c_0_27,plain,
! [X20,X21] :
( cast_to_el_of_LattPOSet(X20,X21) = X21
| ~ element(X21,the_carrier(X20))
| ~ latt_str(X20)
| ~ lattice(X20)
| empty_carrier(X20) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
fof(c_0_28,plain,
! [X85,X86,X87] :
( ( relation_of2_as_subset(X87,X85,X86)
| ~ relation_of2(X87,X85,X86) )
& ( relation_of2(X87,X85,X86)
| ~ relation_of2_as_subset(X87,X85,X86) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
cnf(c_0_29,plain,
( ~ rel_str(X1)
| relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,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_22,c_0_23]),c_0_24])]),c_0_25]) ).
fof(c_0_31,plain,
! [X5] :
( X5 = rel_str_of(the_carrier(X5),the_InternalRel(X5))
| ~ strict_rel_str(X5)
| ~ rel_str(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])])]) ).
cnf(c_0_32,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| strict_rel_str(poset_of_lattice(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_33,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_34,plain,
! [X13,X14,X15,X16,X17] :
( ( ~ latt_str(X13)
| empty_carrier(X13)
| ~ element(X14,the_carrier(X13))
| latt_element_smaller(X13,X14,X17)
| ~ below(X13,esk1_3(X13,X14,X17),X14) )
& ( ~ latt_str(X13)
| empty_carrier(X13)
| ~ element(X14,the_carrier(X13))
| latt_element_smaller(X13,X14,X17)
| in(esk1_3(X13,X14,X17),X17) )
& ( ~ latt_str(X13)
| empty_carrier(X13)
| ~ element(X14,the_carrier(X13))
| latt_element_smaller(X13,X14,X17)
| element(esk1_3(X13,X14,X17),the_carrier(X13)) )
& ( ~ latt_str(X13)
| empty_carrier(X13)
| ~ element(X14,the_carrier(X13))
| below(X13,X16,X14)
| ~ in(X16,X15)
| ~ element(X16,the_carrier(X13))
| ~ latt_element_smaller(X13,X14,X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])])])])]) ).
cnf(c_0_35,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_27]) ).
fof(c_0_36,plain,
! [X69,X70,X71,X72] :
( ( ~ relation_of2(X70,X69,X69)
| rel_str_of(X69,X70) != rel_str_of(X71,X72)
| X70 = X72 )
& ( ~ relation_of2(X70,X69,X69)
| rel_str_of(X69,X70) != rel_str_of(X71,X72)
| X69 = X71 ) ),
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_37,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,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_29,c_0_30]) ).
cnf(c_0_39,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_31]) ).
cnf(c_0_40,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_32,c_0_23]),c_0_24])]),c_0_25]) ).
fof(c_0_41,plain,
! [X19] :
( poset_of_lattice(X19) = rel_str_of(the_carrier(X19),k2_lattice3(X19))
| ~ latt_str(X19)
| ~ lattice(X19)
| empty_carrier(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
cnf(c_0_42,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| element(esk1_3(X1,X2,X3),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,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_35,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_44,negated_conjecture,
element(esk21_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_45,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_36]) ).
cnf(c_0_46,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_37,c_0_38]) ).
cnf(c_0_47,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_39,c_0_40]),c_0_30])]) ).
cnf(c_0_48,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_41]) ).
fof(c_0_49,plain,
! [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)],[t7_lattice3]) ).
cnf(c_0_50,negated_conjecture,
( ~ element(X1,the_carrier(esk20_0))
| element(esk1_3(esk20_0,X1,X2),the_carrier(esk20_0))
| latt_element_smaller(esk20_0,X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_24]),c_0_25]) ).
fof(c_0_51,plain,
! [X24,X25,X26,X27] :
( ( ~ rel_str(X24)
| ~ element(X26,the_carrier(X24))
| relstr_set_smaller(X24,X25,X26)
| ~ related(X24,esk2_3(X24,X25,X26),X26) )
& ( ~ rel_str(X24)
| ~ element(X26,the_carrier(X24))
| relstr_set_smaller(X24,X25,X26)
| in(esk2_3(X24,X25,X26),X25) )
& ( ~ rel_str(X24)
| ~ element(X26,the_carrier(X24))
| relstr_set_smaller(X24,X25,X26)
| element(esk2_3(X24,X25,X26),the_carrier(X24)) )
& ( ~ rel_str(X24)
| ~ element(X26,the_carrier(X24))
| related(X24,X27,X26)
| ~ in(X27,X25)
| ~ element(X27,the_carrier(X24))
| ~ relstr_set_smaller(X24,X25,X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_lattice3])])])])])]) ).
cnf(c_0_52,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0))
| latt_element_smaller(esk20_0,esk21_0,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_53,negated_conjecture,
cast_to_el_of_LattPOSet(esk20_0,esk21_0) = esk21_0,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,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_45,c_0_46]),c_0_47]) ).
cnf(c_0_55,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_48,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_56,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| in(esk1_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_57,plain,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(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))
& ~ empty_carrier(poset_of_lattice(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc4_lattice3]) ).
fof(c_0_58,plain,
! [X119,X120,X121] :
( ( ~ latt_str(X119)
| ~ lattice(X119)
| empty_carrier(X119)
| ~ element(X120,the_carrier(X119))
| ~ element(X121,the_carrier(X119))
| below_refl(X119,X120,X121)
| ~ related_reflexive(poset_of_lattice(X119),cast_to_el_of_LattPOSet(X119,X120),cast_to_el_of_LattPOSet(X119,X121)) )
& ( ~ latt_str(X119)
| ~ lattice(X119)
| empty_carrier(X119)
| ~ element(X120,the_carrier(X119))
| ~ element(X121,the_carrier(X119))
| related_reflexive(poset_of_lattice(X119),cast_to_el_of_LattPOSet(X119,X120),cast_to_el_of_LattPOSet(X119,X121))
| ~ below_refl(X119,X120,X121) ) ),
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_49])])])])]) ).
cnf(c_0_59,negated_conjecture,
( element(esk1_3(esk20_0,esk21_0,X1),the_carrier(esk20_0))
| latt_element_smaller(esk20_0,esk21_0,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_44]) ).
fof(c_0_60,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_61,plain,
( ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X1))
| ~ relstr_set_smaller(X1,X2,X3)
| related(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_62,negated_conjecture,
( latt_element_smaller(esk20_0,esk21_0,esk19_0)
| relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0) ),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_63,negated_conjecture,
the_carrier(poset_of_lattice(esk20_0)) = the_carrier(esk20_0),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_64,negated_conjecture,
( ~ element(X1,the_carrier(esk20_0))
| in(esk1_3(esk20_0,X1,X2),X2)
| latt_element_smaller(esk20_0,X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_24]),c_0_25]) ).
fof(c_0_65,plain,
! [X66] :
( ( ~ latt_str(X66)
| ~ lattice(X66)
| empty_carrier(X66)
| antisymmetric_relstr(poset_of_lattice(X66)) )
& ( ~ latt_str(X66)
| ~ lattice(X66)
| empty_carrier(X66)
| transitive_relstr(poset_of_lattice(X66)) )
& ( ~ latt_str(X66)
| ~ lattice(X66)
| empty_carrier(X66)
| reflexive_relstr(poset_of_lattice(X66)) )
& ( ~ latt_str(X66)
| ~ lattice(X66)
| empty_carrier(X66)
| strict_rel_str(poset_of_lattice(X66)) )
& ( ~ latt_str(X66)
| ~ lattice(X66)
| empty_carrier(X66)
| ~ empty_carrier(poset_of_lattice(X66)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
cnf(c_0_66,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
| empty_carrier(X1)
| below_refl(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,negated_conjecture,
( latt_element_smaller(esk20_0,esk21_0,X1)
| cast_to_el_of_LattPOSet(esk20_0,esk1_3(esk20_0,esk21_0,X1)) = esk1_3(esk20_0,esk21_0,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_59]) ).
fof(c_0_68,plain,
! [X91,X92,X93] :
( ( ~ element(X93,the_carrier(X91))
| ~ element(X92,the_carrier(X91))
| ~ rel_str(X91)
| ~ reflexive_relstr(X91)
| empty_carrier(X91)
| related_reflexive(X91,X92,X93)
| ~ related(X91,X92,X93) )
& ( ~ element(X93,the_carrier(X91))
| ~ element(X92,the_carrier(X91))
| ~ rel_str(X91)
| ~ reflexive_relstr(X91)
| empty_carrier(X91)
| related(X91,X92,X93)
| ~ related_reflexive(X91,X92,X93) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])])]) ).
cnf(c_0_69,negated_conjecture,
( ~ in(X1,esk19_0)
| ~ element(X1,the_carrier(esk20_0))
| latt_element_smaller(esk20_0,esk21_0,esk19_0)
| related(poset_of_lattice(esk20_0),X1,esk21_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_61,c_0_62]),c_0_63]),c_0_63]),c_0_44]),c_0_30])]) ).
cnf(c_0_70,negated_conjecture,
( in(esk1_3(esk20_0,esk21_0,X1),X1)
| latt_element_smaller(esk20_0,esk21_0,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_44]) ).
cnf(c_0_71,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| reflexive_relstr(poset_of_lattice(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_72,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ empty_carrier(poset_of_lattice(X1))
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
fof(c_0_73,plain,
! [X1] :
( latt_str(X1)
=> ( ( lattice(X1)
& ~ empty_carrier(X1) )
=> ( join_absorbing(X1)
& meet_absorbing(X1)
& meet_associative(X1)
& meet_commutative(X1)
& join_associative(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
fof(c_0_74,plain,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& latt_str(X1)
& join_absorbing(X1)
& meet_absorbing(X1)
& meet_commutative(X1)
& ~ empty_carrier(X1) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_lattices]) ).
cnf(c_0_75,negated_conjecture,
( ~ element(X2,the_carrier(esk20_0))
| ~ related_reflexive(poset_of_lattice(esk20_0),esk1_3(esk20_0,esk21_0,X1),cast_to_el_of_LattPOSet(esk20_0,X2))
| latt_element_smaller(esk20_0,esk21_0,X1)
| below_refl(esk20_0,esk1_3(esk20_0,esk21_0,X1),X2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_23]),c_0_24])]),c_0_25]),c_0_59]) ).
cnf(c_0_76,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_68]) ).
cnf(c_0_77,negated_conjecture,
( latt_element_smaller(esk20_0,esk21_0,esk19_0)
| related(poset_of_lattice(esk20_0),esk1_3(esk20_0,esk21_0,esk19_0),esk21_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_59]) ).
cnf(c_0_78,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_71,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_79,negated_conjecture,
~ empty_carrier(poset_of_lattice(esk20_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_23]),c_0_24])]),c_0_25]) ).
fof(c_0_80,plain,
! [X8] :
( ( ~ latt_str(X8)
| ~ lattice(X8)
| empty_carrier(X8)
| join_absorbing(X8) )
& ( ~ latt_str(X8)
| ~ lattice(X8)
| empty_carrier(X8)
| meet_absorbing(X8) )
& ( ~ latt_str(X8)
| ~ lattice(X8)
| empty_carrier(X8)
| meet_associative(X8) )
& ( ~ latt_str(X8)
| ~ lattice(X8)
| empty_carrier(X8)
| meet_commutative(X8) )
& ( ~ latt_str(X8)
| ~ lattice(X8)
| empty_carrier(X8)
| join_associative(X8) )
& ( ~ latt_str(X8)
| ~ lattice(X8)
| empty_carrier(X8)
| join_commutative(X8) )
& ( ~ latt_str(X8)
| ~ lattice(X8)
| empty_carrier(X8)
| ~ empty_carrier(X8) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])])])]) ).
fof(c_0_81,plain,
! [X88,X89,X90] :
( ( ~ element(X90,the_carrier(X88))
| ~ element(X89,the_carrier(X88))
| ~ latt_str(X88)
| ~ join_absorbing(X88)
| ~ meet_absorbing(X88)
| ~ meet_commutative(X88)
| empty_carrier(X88)
| below_refl(X88,X89,X90)
| ~ below(X88,X89,X90) )
& ( ~ element(X90,the_carrier(X88))
| ~ element(X89,the_carrier(X88))
| ~ latt_str(X88)
| ~ join_absorbing(X88)
| ~ meet_absorbing(X88)
| ~ meet_commutative(X88)
| empty_carrier(X88)
| below(X88,X89,X90)
| ~ below_refl(X88,X89,X90) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])])]) ).
cnf(c_0_82,negated_conjecture,
( ~ related_reflexive(poset_of_lattice(esk20_0),esk1_3(esk20_0,esk21_0,X1),esk21_0)
| latt_element_smaller(esk20_0,esk21_0,X1)
| below_refl(esk20_0,esk1_3(esk20_0,esk21_0,X1),esk21_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_53]),c_0_44])]) ).
cnf(c_0_83,negated_conjecture,
( latt_element_smaller(esk20_0,esk21_0,esk19_0)
| related_reflexive(poset_of_lattice(esk20_0),esk1_3(esk20_0,esk21_0,esk19_0),esk21_0) ),
inference(csr,[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(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_63]),c_0_44]),c_0_63]),c_0_30])]),c_0_79]),c_0_59]) ).
cnf(c_0_84,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| join_absorbing(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_85,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| meet_absorbing(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_86,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| meet_commutative(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_87,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ below_refl(X1,X2,X3)
| empty_carrier(X1)
| below(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( latt_element_smaller(esk20_0,esk21_0,esk19_0)
| below_refl(esk20_0,esk1_3(esk20_0,esk21_0,esk19_0),esk21_0) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_89,negated_conjecture,
join_absorbing(esk20_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_90,negated_conjecture,
meet_absorbing(esk20_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_91,negated_conjecture,
meet_commutative(esk20_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_92,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ below(X1,esk1_3(X1,X2,X3),X2)
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_93,negated_conjecture,
( latt_element_smaller(esk20_0,esk21_0,esk19_0)
| below(esk20_0,esk1_3(esk20_0,esk21_0,esk19_0),esk21_0) ),
inference(csr,[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(spm,[status(thm)],[c_0_87,c_0_88]),c_0_44]),c_0_89]),c_0_90]),c_0_91]),c_0_24])]),c_0_25]),c_0_59]) ).
cnf(c_0_94,plain,
( ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| relstr_set_smaller(X1,X2,X3)
| in(esk2_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_95,negated_conjecture,
( ~ relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0))
| ~ latt_element_smaller(esk20_0,esk21_0,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_96,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ in(X4,X3)
| ~ element(X4,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| below(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_97,negated_conjecture,
latt_element_smaller(esk20_0,esk21_0,esk19_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_44]),c_0_24])]),c_0_25]) ).
cnf(c_0_98,negated_conjecture,
( ~ element(X2,the_carrier(esk20_0))
| in(esk2_3(poset_of_lattice(esk20_0),X1,X2),X1)
| relstr_set_smaller(poset_of_lattice(esk20_0),X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_30]),c_0_63]) ).
cnf(c_0_99,negated_conjecture,
( ~ latt_element_smaller(esk20_0,esk21_0,esk19_0)
| ~ relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0) ),
inference(rw,[status(thm)],[c_0_95,c_0_53]) ).
cnf(c_0_100,plain,
( ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| relstr_set_smaller(X1,X2,X3)
| element(esk2_3(X1,X2,X3),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_101,negated_conjecture,
( ~ in(X1,esk19_0)
| ~ element(X1,the_carrier(esk20_0))
| below(esk20_0,X1,esk21_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_44]),c_0_24])]),c_0_25]) ).
cnf(c_0_102,negated_conjecture,
( in(esk2_3(poset_of_lattice(esk20_0),X1,esk21_0),X1)
| relstr_set_smaller(poset_of_lattice(esk20_0),X1,esk21_0) ),
inference(spm,[status(thm)],[c_0_98,c_0_44]) ).
cnf(c_0_103,negated_conjecture,
~ relstr_set_smaller(poset_of_lattice(esk20_0),esk19_0,esk21_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_97])]) ).
cnf(c_0_104,negated_conjecture,
( ~ element(X2,the_carrier(esk20_0))
| element(esk2_3(poset_of_lattice(esk20_0),X1,X2),the_carrier(esk20_0))
| relstr_set_smaller(poset_of_lattice(esk20_0),X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_30]),c_0_63]),c_0_63]) ).
cnf(c_0_105,negated_conjecture,
( ~ element(esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0),the_carrier(esk20_0))
| below(esk20_0,esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0),esk21_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]) ).
cnf(c_0_106,negated_conjecture,
( element(esk2_3(poset_of_lattice(esk20_0),X1,esk21_0),the_carrier(esk20_0))
| relstr_set_smaller(poset_of_lattice(esk20_0),X1,esk21_0) ),
inference(spm,[status(thm)],[c_0_104,c_0_44]) ).
cnf(c_0_107,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ below(X1,X2,X3)
| empty_carrier(X1)
| below_refl(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_108,negated_conjecture,
below(esk20_0,esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0),esk21_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_103]) ).
cnf(c_0_109,negated_conjecture,
( ~ element(esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0),the_carrier(esk20_0))
| below_refl(esk20_0,esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0),esk21_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_107,c_0_108]),c_0_44]),c_0_89]),c_0_90]),c_0_91]),c_0_24])]),c_0_25]) ).
cnf(c_0_110,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below_refl(X1,X2,X3)
| empty_carrier(X1)
| related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_111,negated_conjecture,
below_refl(esk20_0,esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0),esk21_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_106]),c_0_103]) ).
cnf(c_0_112,negated_conjecture,
( ~ element(esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0),the_carrier(esk20_0))
| related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0)),esk21_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_110,c_0_111]),c_0_53]),c_0_44]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_113,negated_conjecture,
related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0)),esk21_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_106]),c_0_103]) ).
cnf(c_0_114,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk20_0),X1,esk21_0)
| cast_to_el_of_LattPOSet(esk20_0,esk2_3(poset_of_lattice(esk20_0),X1,esk21_0)) = esk2_3(poset_of_lattice(esk20_0),X1,esk21_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_106]) ).
cnf(c_0_115,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_68]) ).
cnf(c_0_116,negated_conjecture,
related_reflexive(poset_of_lattice(esk20_0),esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0),esk21_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_103]) ).
cnf(c_0_117,negated_conjecture,
( ~ element(esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0),the_carrier(esk20_0))
| related(poset_of_lattice(esk20_0),esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0),esk21_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_115,c_0_116]),c_0_78]),c_0_63]),c_0_44]),c_0_63]),c_0_30])]),c_0_79]) ).
cnf(c_0_118,plain,
( ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ related(X1,esk2_3(X1,X2,X3),X3)
| relstr_set_smaller(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_119,negated_conjecture,
related(poset_of_lattice(esk20_0),esk2_3(poset_of_lattice(esk20_0),esk19_0,esk21_0),esk21_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_106]),c_0_103]) ).
cnf(c_0_120,negated_conjecture,
$false,
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_118,c_0_119]),c_0_63]),c_0_44]),c_0_30])]),c_0_103]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU349+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 06:14:35 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.46 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
% 6.00/1.48 % Version: 3.5.1
% 6.00/1.48 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.00/1.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.00/1.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.00/1.48 % Starting new_bool_3 with 300s (1) cores
% 6.00/1.48 % Starting new_bool_1 with 300s (1) cores
% 6.00/1.48 % Starting sh5l with 300s (1) cores
% 6.00/1.48 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3313496 completed with status 0
% 6.00/1.48 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 6.00/1.48 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.00/1.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.00/1.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.00/1.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.00/1.48 % No SInE strategy applied
% 6.00/1.48 % Search class: FGHSM-FFMM31-SFFFFFNN
% 6.00/1.48 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 6.00/1.48 % Starting SubtermCWHack with 136s (1) cores
% 6.00/1.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.00/1.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 6.00/1.48 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 6.00/1.48 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 6.00/1.48 % G-E--_208_C18_F1_SE_CS_SP_PS_S4b with pid 3313502 completed with status 0
% 6.00/1.48 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4b
% 6.00/1.48 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.00/1.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.00/1.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.00/1.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.00/1.48 % No SInE strategy applied
% 6.00/1.48 % Search class: FGHSM-FFMM31-SFFFFFNN
% 6.00/1.48 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 6.00/1.48 % Starting SubtermCWHack with 136s (1) cores
% 6.00/1.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.00/1.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 6.00/1.48 % Preprocessing time : 0.004 s
% 6.00/1.48 % Presaturation interreduction done
% 6.00/1.48
% 6.00/1.48 % Proof found!
% 6.00/1.48 % SZS status Theorem
% 6.00/1.48 % SZS output start CNFRefutation
% See solution above
% 6.00/1.48 % Parsed axioms : 71
% 6.00/1.48 % Removed by relevancy pruning/SinE : 0
% 6.00/1.48 % Initial clauses : 127
% 6.00/1.48 % Removed in clause preprocessing : 9
% 6.00/1.48 % Initial clauses in saturation : 118
% 6.00/1.48 % Processed clauses : 3572
% 6.00/1.48 % ...of these trivial : 92
% 6.00/1.48 % ...subsumed : 1663
% 6.00/1.48 % ...remaining for further processing : 1817
% 6.00/1.48 % Other redundant clauses eliminated : 0
% 6.00/1.48 % Clauses deleted for lack of memory : 0
% 6.00/1.48 % Backward-subsumed : 33
% 6.00/1.48 % Backward-rewritten : 80
% 6.00/1.48 % Generated clauses : 14193
% 6.00/1.48 % ...of the previous two non-redundant : 13736
% 6.00/1.48 % ...aggressively subsumed : 0
% 6.00/1.48 % Contextual simplify-reflections : 31
% 6.00/1.48 % Paramodulations : 14187
% 6.00/1.48 % Factorizations : 0
% 6.00/1.48 % NegExts : 0
% 6.00/1.48 % Equation resolutions : 6
% 6.00/1.48 % Disequality decompositions : 0
% 6.00/1.48 % Total rewrite steps : 2538
% 6.00/1.48 % ...of those cached : 2359
% 6.00/1.48 % Propositional unsat checks : 0
% 6.00/1.48 % Propositional check models : 0
% 6.00/1.48 % Propositional check unsatisfiable : 0
% 6.00/1.48 % Propositional clauses : 0
% 6.00/1.48 % Propositional clauses after purity: 0
% 6.00/1.48 % Propositional unsat core size : 0
% 6.00/1.48 % Propositional preprocessing time : 0.000
% 6.00/1.48 % Propositional encoding time : 0.000
% 6.00/1.48 % Propositional solver time : 0.000
% 6.00/1.48 % Success case prop preproc time : 0.000
% 6.00/1.48 % Success case prop encoding time : 0.000
% 6.00/1.48 % Success case prop solver time : 0.000
% 6.00/1.48 % Current number of processed clauses : 1592
% 6.00/1.48 % Positive orientable unit clauses : 253
% 6.00/1.48 % Positive unorientable unit clauses: 0
% 6.00/1.48 % Negative unit clauses : 55
% 6.00/1.48 % Non-unit-clauses : 1284
% 6.00/1.48 % Current number of unprocessed clauses: 10252
% 6.00/1.48 % ...number of literals in the above : 36338
% 6.00/1.48 % Current number of archived formulas : 0
% 6.00/1.48 % Current number of archived clauses : 225
% 6.00/1.48 % Clause-clause subsumption calls (NU) : 211512
% 6.00/1.48 % Rec. Clause-clause subsumption calls : 163331
% 6.00/1.48 % Non-unit clause-clause subsumptions : 1550
% 6.00/1.48 % Unit Clause-clause subsumption calls : 17649
% 6.00/1.48 % Rewrite failures with RHS unbound : 0
% 6.00/1.48 % BW rewrite match attempts : 775
% 6.00/1.48 % BW rewrite match successes : 29
% 6.00/1.48 % Condensation attempts : 0
% 6.00/1.48 % Condensation successes : 0
% 6.00/1.48 % Termbank termtop insertions : 459289
% 6.00/1.48 % Search garbage collected termcells : 1550
% 6.00/1.48
% 6.00/1.48 % -------------------------------------------------
% 6.00/1.48 % User time : 0.887 s
% 6.00/1.48 % System time : 0.036 s
% 6.00/1.48 % Total time : 0.923 s
% 6.00/1.48 % Maximum resident set size: 3968 pages
% 6.00/1.48
% 6.00/1.48 % -------------------------------------------------
% 6.00/1.48 % User time : 4.224 s
% 6.00/1.48 % System time : 0.134 s
% 6.00/1.48 % Total time : 4.358 s
% 6.00/1.48 % Maximum resident set size: 4608 pages
% 6.00/1.48 % E exiting
%------------------------------------------------------------------------------