%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU369+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 02:24:52 PM UTC 2026
% Result : Theorem 7.56s 1.55s
% Output : CNFRefutation 7.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 84 ( 22 unt; 0 def)
% Number of atoms : 361 ( 27 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 414 ( 137 ~; 143 |; 99 &)
% ( 8 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 115 ( 7 sgn 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_u1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(t2_yellow_1,conjecture,
! [X1,X2] :
( element(X2,the_carrier(boole_POSet(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_POSet(X1)))
=> ( related_reflexive(boole_POSet(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_yellow_1) ).
fof(free_g1_orders_2,axiom,
! [X1,X2] :
( relation_of2(X2,X1,X1)
=> ! [X3,X4] :
( rel_str_of(X1,X2) = rel_str_of(X3,X4)
=> ( X2 = X4
& X1 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(abstractness_v1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( strict_rel_str(X1)
=> X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(d2_lattice3,axiom,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice3) ).
fof(dt_k3_lattice3,axiom,
! [X1] :
( ( 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/sandbox/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(d2_yellow_1,axiom,
! [X1] : boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_yellow_1) ).
fof(fc1_knaster,axiom,
! [X1] :
( complete_latt_str(boole_lattice(X1))
& boolean_lattstr(boole_lattice(X1))
& complemented_lattstr(boole_lattice(X1))
& bounded_lattstr(boole_lattice(X1))
& upper_bounded_semilattstr(boole_lattice(X1))
& lower_bounded_semilattstr(boole_lattice(X1))
& modular_lattstr(boole_lattice(X1))
& distributive_lattstr(boole_lattice(X1))
& lattice(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& ~ empty_carrier(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_knaster) ).
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/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( latt_str(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
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/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
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/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(t2_lattice3,axiom,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( below(boole_lattice(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).
fof(c_0_14,plain,
! [X139,X140,X141] :
( ( relation_of2_as_subset(X141,X139,X140)
| ~ relation_of2(X141,X139,X140) )
& ( relation_of2(X141,X139,X140)
| ~ relation_of2_as_subset(X141,X139,X140) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
fof(c_0_15,plain,
! [X60] :
( relation_of2_as_subset(the_InternalRel(X60),the_carrier(X60),the_carrier(X60))
| ~ rel_str(X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])])]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X2] :
( element(X2,the_carrier(boole_POSet(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_POSet(X1)))
=> ( related_reflexive(boole_POSet(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
inference(assume_negation,[status(cth)],[t2_yellow_1]) ).
fof(c_0_17,plain,
! [X103,X104,X105,X106] :
( ( ~ relation_of2(X104,X103,X103)
| rel_str_of(X103,X104) != rel_str_of(X105,X106)
| X104 = X106 )
& ( ~ relation_of2(X104,X103,X103)
| rel_str_of(X103,X104) != rel_str_of(X105,X106)
| X103 = X105 ) ),
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])])])])]) ).
fof(c_0_18,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_19,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ rel_str(X1)
| relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,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_22,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_23,negated_conjecture,
( ( subset(esk30_0,esk31_0)
| related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0) )
& ( ~ subset(esk30_0,esk31_0)
| ~ related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0) )
& element(esk31_0,the_carrier(boole_POSet(esk29_0)))
& element(esk30_0,the_carrier(boole_POSet(esk29_0))) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_24,plain,
! [X32] : boole_POSet(X32) = poset_of_lattice(boole_lattice(X32)),
inference(variable_rename,[status(thm)],[d2_yellow_1]) ).
cnf(c_0_25,plain,
( ~ relation_of2(X3,X1,X1)
| rel_str_of(X1,X3) != rel_str_of(X2,X4)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,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_18]) ).
cnf(c_0_27,plain,
( ~ rel_str(X1)
| relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_28,plain,
! [X31] :
( poset_of_lattice(X31) = rel_str_of(the_carrier(X31),k2_lattice3(X31))
| ~ latt_str(X31)
| ~ lattice(X31)
| empty_carrier(X31) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_29,plain,
! [X47] :
( ( ~ latt_str(X47)
| ~ lattice(X47)
| empty_carrier(X47)
| rel_str(poset_of_lattice(X47)) )
& ( ~ latt_str(X47)
| ~ lattice(X47)
| empty_carrier(X47)
| antisymmetric_relstr(poset_of_lattice(X47)) )
& ( ~ latt_str(X47)
| ~ lattice(X47)
| empty_carrier(X47)
| transitive_relstr(poset_of_lattice(X47)) )
& ( ~ latt_str(X47)
| ~ lattice(X47)
| empty_carrier(X47)
| reflexive_relstr(poset_of_lattice(X47)) )
& ( ~ latt_str(X47)
| ~ lattice(X47)
| empty_carrier(X47)
| strict_rel_str(poset_of_lattice(X47)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
fof(c_0_30,plain,
! [X1] :
( complete_latt_str(boole_lattice(X1))
& boolean_lattstr(boole_lattice(X1))
& complemented_lattstr(boole_lattice(X1))
& bounded_lattstr(boole_lattice(X1))
& upper_bounded_semilattstr(boole_lattice(X1))
& lower_bounded_semilattstr(boole_lattice(X1))
& modular_lattstr(boole_lattice(X1))
& distributive_lattstr(boole_lattice(X1))
& lattice(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& ~ empty_carrier(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_knaster]) ).
fof(c_0_31,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]) ).
cnf(c_0_32,negated_conjecture,
element(esk31_0,the_carrier(boole_POSet(esk29_0))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
( ~ rel_str(rel_str_of(X1,X2))
| ~ strict_rel_str(rel_str_of(X1,X2))
| the_carrier(rel_str_of(X1,X2)) = X1 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26])]),c_0_27]) ).
cnf(c_0_35,plain,
( ~ 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_28]) ).
cnf(c_0_36,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| rel_str(poset_of_lattice(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| strict_rel_str(poset_of_lattice(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_38,plain,
! [X75] :
( complete_latt_str(boole_lattice(X75))
& boolean_lattstr(boole_lattice(X75))
& complemented_lattstr(boole_lattice(X75))
& bounded_lattstr(boole_lattice(X75))
& upper_bounded_semilattstr(boole_lattice(X75))
& lower_bounded_semilattstr(boole_lattice(X75))
& modular_lattstr(boole_lattice(X75))
& distributive_lattstr(boole_lattice(X75))
& lattice(boole_lattice(X75))
& join_absorbing(boole_lattice(X75))
& meet_absorbing(boole_lattice(X75))
& meet_associative(boole_lattice(X75))
& meet_commutative(boole_lattice(X75))
& join_associative(boole_lattice(X75))
& join_commutative(boole_lattice(X75))
& strict_latt_str(boole_lattice(X75))
& ~ empty_carrier(boole_lattice(X75)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
fof(c_0_39,plain,
! [X45] :
( latt_str(boole_lattice(X45))
& strict_latt_str(boole_lattice(X45)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
fof(c_0_40,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]) ).
fof(c_0_41,plain,
! [X33,X34] :
( cast_to_el_of_LattPOSet(X33,X34) = X34
| ~ element(X34,the_carrier(X33))
| ~ latt_str(X33)
| ~ lattice(X33)
| empty_carrier(X33) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
cnf(c_0_42,negated_conjecture,
element(esk31_0,the_carrier(poset_of_lattice(boole_lattice(esk29_0)))),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_43,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| the_carrier(poset_of_lattice(X1)) = the_carrier(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37]) ).
cnf(c_0_44,plain,
lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,negated_conjecture,
element(esk30_0,the_carrier(boole_POSet(esk29_0))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_48,plain,
! [X176,X177,X178] :
( ( ~ latt_str(X176)
| ~ lattice(X176)
| empty_carrier(X176)
| ~ element(X177,the_carrier(X176))
| ~ element(X178,the_carrier(X176))
| below_refl(X176,X177,X178)
| ~ related_reflexive(poset_of_lattice(X176),cast_to_el_of_LattPOSet(X176,X177),cast_to_el_of_LattPOSet(X176,X178)) )
& ( ~ latt_str(X176)
| ~ lattice(X176)
| empty_carrier(X176)
| ~ element(X177,the_carrier(X176))
| ~ element(X178,the_carrier(X176))
| related_reflexive(poset_of_lattice(X176),cast_to_el_of_LattPOSet(X176,X177),cast_to_el_of_LattPOSet(X176,X178))
| ~ below_refl(X176,X177,X178) ) ),
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_40])])])])]) ).
cnf(c_0_49,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_41]) ).
cnf(c_0_50,negated_conjecture,
element(esk31_0,the_carrier(boole_lattice(esk29_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]),c_0_46]) ).
cnf(c_0_51,negated_conjecture,
element(esk30_0,the_carrier(poset_of_lattice(boole_lattice(esk29_0)))),
inference(rw,[status(thm)],[c_0_47,c_0_33]) ).
fof(c_0_52,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_53,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_48]) ).
cnf(c_0_54,negated_conjecture,
cast_to_el_of_LattPOSet(boole_lattice(esk29_0),esk31_0) = esk31_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_44]),c_0_45])]),c_0_46]) ).
cnf(c_0_55,negated_conjecture,
element(esk30_0,the_carrier(boole_lattice(esk29_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_43]),c_0_44]),c_0_45])]),c_0_46]) ).
fof(c_0_56,plain,
! [X142,X143,X144] :
( ( ~ element(X144,the_carrier(X142))
| ~ element(X143,the_carrier(X142))
| ~ latt_str(X142)
| ~ join_absorbing(X142)
| ~ meet_absorbing(X142)
| ~ meet_commutative(X142)
| empty_carrier(X142)
| below_refl(X142,X143,X144)
| ~ below(X142,X143,X144) )
& ( ~ element(X144,the_carrier(X142))
| ~ element(X143,the_carrier(X142))
| ~ latt_str(X142)
| ~ join_absorbing(X142)
| ~ meet_absorbing(X142)
| ~ meet_commutative(X142)
| empty_carrier(X142)
| below(X142,X143,X144)
| ~ below_refl(X142,X143,X144) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
cnf(c_0_57,negated_conjecture,
( ~ element(X1,the_carrier(boole_lattice(esk29_0)))
| ~ related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),cast_to_el_of_LattPOSet(boole_lattice(esk29_0),X1),esk31_0)
| below_refl(boole_lattice(esk29_0),X1,esk31_0) ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_50]),c_0_44]),c_0_45])]),c_0_46]),c_0_54]) ).
cnf(c_0_58,negated_conjecture,
cast_to_el_of_LattPOSet(boole_lattice(esk29_0),esk30_0) = esk30_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_55]),c_0_44]),c_0_45])]),c_0_46]) ).
cnf(c_0_59,negated_conjecture,
( subset(esk30_0,esk31_0)
| related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_60,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_56]) ).
cnf(c_0_61,plain,
join_absorbing(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_62,plain,
meet_absorbing(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_63,plain,
meet_commutative(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_64,negated_conjecture,
( ~ related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0)
| below_refl(boole_lattice(esk29_0),esk30_0,esk31_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_55]),c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0)
| subset(esk30_0,esk31_0) ),
inference(rw,[status(thm)],[c_0_59,c_0_33]) ).
fof(c_0_66,plain,
! [X157,X158,X159] :
( ( ~ element(X158,the_carrier(boole_lattice(X157)))
| ~ element(X159,the_carrier(boole_lattice(X157)))
| below(boole_lattice(X157),X158,X159)
| ~ subset(X158,X159) )
& ( ~ element(X158,the_carrier(boole_lattice(X157)))
| ~ element(X159,the_carrier(boole_lattice(X157)))
| subset(X158,X159)
| ~ below(boole_lattice(X157),X158,X159) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_lattice3])])])])]) ).
cnf(c_0_67,negated_conjecture,
( ~ element(X1,the_carrier(boole_lattice(esk29_0)))
| ~ below_refl(boole_lattice(esk29_0),X1,esk31_0)
| below(boole_lattice(esk29_0),X1,esk31_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_50]),c_0_61]),c_0_62]),c_0_63]),c_0_45])]),c_0_46]) ).
cnf(c_0_68,negated_conjecture,
( below_refl(boole_lattice(esk29_0),esk30_0,esk31_0)
| subset(esk30_0,esk31_0) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,plain,
( ~ element(X1,the_carrier(boole_lattice(X3)))
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ subset(X1,X2)
| below(boole_lattice(X3),X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_70,plain,
( ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ below(boole_lattice(X1),X2,X3)
| subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_71,negated_conjecture,
( below(boole_lattice(esk29_0),esk30_0,esk31_0)
| subset(esk30_0,esk31_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_55])]) ).
cnf(c_0_72,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_56]) ).
cnf(c_0_73,negated_conjecture,
( ~ element(X1,the_carrier(boole_lattice(esk29_0)))
| ~ subset(X1,esk31_0)
| below(boole_lattice(esk29_0),X1,esk31_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_50]) ).
cnf(c_0_74,negated_conjecture,
subset(esk30_0,esk31_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_50]),c_0_55])]) ).
cnf(c_0_75,negated_conjecture,
( ~ subset(esk30_0,esk31_0)
| ~ related_reflexive(boole_POSet(esk29_0),esk30_0,esk31_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_76,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_48]) ).
cnf(c_0_77,negated_conjecture,
( ~ element(X1,the_carrier(boole_lattice(esk29_0)))
| ~ below(boole_lattice(esk29_0),X1,esk31_0)
| below_refl(boole_lattice(esk29_0),X1,esk31_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_50]),c_0_61]),c_0_62]),c_0_63]),c_0_45])]),c_0_46]) ).
cnf(c_0_78,negated_conjecture,
below(boole_lattice(esk29_0),esk30_0,esk31_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_55])]) ).
cnf(c_0_79,negated_conjecture,
( ~ related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0)
| ~ subset(esk30_0,esk31_0) ),
inference(rw,[status(thm)],[c_0_75,c_0_33]) ).
cnf(c_0_80,negated_conjecture,
( ~ element(X1,the_carrier(boole_lattice(esk29_0)))
| ~ below_refl(boole_lattice(esk29_0),X1,esk31_0)
| related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),cast_to_el_of_LattPOSet(boole_lattice(esk29_0),X1),esk31_0) ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_50]),c_0_44]),c_0_45])]),c_0_46]),c_0_54]) ).
cnf(c_0_81,negated_conjecture,
below_refl(boole_lattice(esk29_0),esk30_0,esk31_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_55])]) ).
cnf(c_0_82,negated_conjecture,
~ related_reflexive(poset_of_lattice(boole_lattice(esk29_0)),esk30_0,esk31_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_74])]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_58]),c_0_55])]),c_0_82]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU369+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 % Computer : n020.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Mon Sep 21 06:17:17 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.50 Running first-order theorem proving
% 0.15/0.50 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 7.56/1.55 % Version: 3.5.1
% 7.56/1.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.56/1.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.56/1.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.56/1.55 % Starting new_bool_3 with 300s (1) cores
% 7.56/1.55 % Starting new_bool_1 with 300s (1) cores
% 7.56/1.55 % Starting sh5l with 300s (1) cores
% 7.56/1.55 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2183692 completed with status 0
% 7.56/1.55 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 7.56/1.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.56/1.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.56/1.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.56/1.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.56/1.55 % No SInE strategy applied
% 7.56/1.55 % Search class: FGHSM-FSLM31-MFFFFFNN
% 7.56/1.55 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 7.56/1.55 % Starting SubtermCWHack with 136s (1) cores
% 7.56/1.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 7.56/1.55 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 7.56/1.55 % Starting G-E--_207_B07_F1_AE_CS_SP_PI_PS_S0Y with 136s (1) cores
% 7.56/1.55 % Starting U----_116Y_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 7.56/1.55 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2183698 completed with status 0
% 7.56/1.55 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 7.56/1.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.56/1.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.56/1.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.56/1.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.56/1.55 % No SInE strategy applied
% 7.56/1.55 % Search class: FGHSM-FSLM31-MFFFFFNN
% 7.56/1.55 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 7.56/1.55 % Starting SubtermCWHack with 136s (1) cores
% 7.56/1.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 7.56/1.55 % Preprocessing time : 0.008 s
% 7.56/1.55 % Presaturation interreduction done
% 7.56/1.55
% 7.56/1.55 % Proof found!
% 7.56/1.55 % SZS status Theorem
% 7.56/1.55 % SZS output start CNFRefutation
% See solution above
% 7.56/1.55 % Parsed axioms : 121
% 7.56/1.55 % Removed by relevancy pruning/SinE : 0
% 7.56/1.55 % Initial clauses : 402
% 7.56/1.55 % Removed in clause preprocessing : 26
% 7.56/1.55 % Initial clauses in saturation : 376
% 7.56/1.55 % Processed clauses : 4537
% 7.56/1.55 % ...of these trivial : 35
% 7.56/1.55 % ...subsumed : 2682
% 7.56/1.55 % ...remaining for further processing : 1820
% 7.56/1.55 % Other redundant clauses eliminated : 32
% 7.56/1.55 % Clauses deleted for lack of memory : 0
% 7.56/1.55 % Backward-subsumed : 28
% 7.56/1.55 % Backward-rewritten : 19
% 7.56/1.55 % Generated clauses : 14471
% 7.56/1.55 % ...of the previous two non-redundant : 14094
% 7.56/1.55 % ...aggressively subsumed : 0
% 7.56/1.55 % Contextual simplify-reflections : 55
% 7.56/1.55 % Paramodulations : 14437
% 7.56/1.55 % Factorizations : 0
% 7.56/1.55 % NegExts : 0
% 7.56/1.55 % Equation resolutions : 34
% 7.56/1.55 % Disequality decompositions : 0
% 7.56/1.55 % Total rewrite steps : 1682
% 7.56/1.55 % ...of those cached : 1474
% 7.56/1.55 % Propositional unsat checks : 0
% 7.56/1.55 % Propositional check models : 0
% 7.56/1.55 % Propositional check unsatisfiable : 0
% 7.56/1.55 % Propositional clauses : 0
% 7.56/1.55 % Propositional clauses after purity: 0
% 7.56/1.55 % Propositional unsat core size : 0
% 7.56/1.55 % Propositional preprocessing time : 0.000
% 7.56/1.55 % Propositional encoding time : 0.000
% 7.56/1.55 % Propositional solver time : 0.000
% 7.56/1.55 % Success case prop preproc time : 0.000
% 7.56/1.55 % Success case prop encoding time : 0.000
% 7.56/1.55 % Success case prop solver time : 0.000
% 7.56/1.55 % Current number of processed clauses : 1477
% 7.56/1.55 % Positive orientable unit clauses : 232
% 7.56/1.55 % Positive unorientable unit clauses: 1
% 7.56/1.55 % Negative unit clauses : 36
% 7.56/1.55 % Non-unit-clauses : 1208
% 7.56/1.55 % Current number of unprocessed clauses: 10215
% 7.56/1.55 % ...number of literals in the above : 62163
% 7.56/1.55 % Current number of archived formulas : 0
% 7.56/1.55 % Current number of archived clauses : 345
% 7.56/1.55 % Clause-clause subsumption calls (NU) : 444400
% 7.56/1.55 % Rec. Clause-clause subsumption calls : 101526
% 7.56/1.55 % Non-unit clause-clause subsumptions : 2066
% 7.56/1.55 % Unit Clause-clause subsumption calls : 9832
% 7.56/1.55 % Rewrite failures with RHS unbound : 0
% 7.56/1.55 % BW rewrite match attempts : 59
% 7.56/1.55 % BW rewrite match successes : 7
% 7.56/1.55 % Condensation attempts : 0
% 7.56/1.55 % Condensation successes : 0
% 7.56/1.55 % Termbank termtop insertions : 262833
% 7.56/1.55 % Search garbage collected termcells : 2855
% 7.56/1.55
% 7.56/1.55 % -------------------------------------------------
% 7.56/1.55 % User time : 0.951 s
% 7.56/1.55 % System time : 0.034 s
% 7.56/1.55 % Total time : 0.985 s
% 7.56/1.55 % Maximum resident set size: 4244 pages
% 7.56/1.55
% 7.56/1.55 % -------------------------------------------------
% 7.56/1.55 % User time : 4.725 s
% 7.56/1.55 % System time : 0.136 s
% 7.56/1.55 % Total time : 4.860 s
% 7.56/1.55 % Maximum resident set size: 4608 pages
% 7.56/1.55 % E exiting
%------------------------------------------------------------------------------