%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU347+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:11:33 PM UTC 2026
% Result : Theorem 5.60s 4.34s
% Output : CNFRefutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 114 ( 7 unt; 0 def)
% Number of atoms : 712 ( 8 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 961 ( 363 ~; 422 |; 117 &)
% ( 11 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 204 ( 1 sgn 99 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t28_lattice3,conjecture,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_set_smaller(X2,X3,X1)
<=> relstr_element_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lattice3) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(d8_lattice3,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( relstr_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X2)
=> related(X1,X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
fof(redefinition_r3_orders_2,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& rel_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( related_reflexive(X1,X2,X3)
<=> related(X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
fof(dt_k4_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(X1)) )
=> element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
fof(d16_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattice3) ).
fof(t7_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
fof(dt_k3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(d3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
fof(redefinition_r3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(fc4_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(poset_of_lattice(X1))
& strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice3) ).
fof(dt_k5_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(poset_of_lattice(X1))) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattice3) ).
fof(d4_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice3) ).
fof(cc1_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_set_smaller(X2,X3,X1)
<=> relstr_element_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t28_lattice3])]) ).
fof(c_0_17,plain,
! [X234,X235] :
( ~ in(X234,X235)
| ~ empty(X235) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_18,plain,
! [X141,X142,X143,X144] :
( ( ~ relstr_element_smaller(X141,X142,X143)
| ~ element(X144,the_carrier(X141))
| ~ in(X144,X142)
| related(X141,X143,X144)
| ~ element(X143,the_carrier(X141))
| ~ rel_str(X141) )
& ( element(esk2_3(X141,X142,X143),the_carrier(X141))
| relstr_element_smaller(X141,X142,X143)
| ~ element(X143,the_carrier(X141))
| ~ rel_str(X141) )
& ( in(esk2_3(X141,X142,X143),X142)
| relstr_element_smaller(X141,X142,X143)
| ~ element(X143,the_carrier(X141))
| ~ rel_str(X141) )
& ( ~ related(X141,X143,esk2_3(X141,X142,X143))
| relstr_element_smaller(X141,X142,X143)
| ~ element(X143,the_carrier(X141))
| ~ rel_str(X141) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_lattice3])])])])]) ).
fof(c_0_19,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& rel_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( related_reflexive(X1,X2,X3)
<=> related(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_orders_2]) ).
fof(c_0_20,negated_conjecture,
( ~ empty_carrier(esk20_0)
& lattice(esk20_0)
& latt_str(esk20_0)
& element(esk21_0,the_carrier(esk20_0))
& ( ~ latt_set_smaller(esk20_0,esk21_0,esk19_0)
| ~ relstr_element_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0)) )
& ( latt_set_smaller(esk20_0,esk21_0,esk19_0)
| relstr_element_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_21,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( in(esk2_3(X1,X2,X3),X2)
| relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(X1)) )
=> element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k4_lattice3]) ).
fof(c_0_24,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X2,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d16_lattice3]) ).
fof(c_0_25,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t7_lattice3]) ).
fof(c_0_26,plain,
! [X208,X209,X210] :
( ( ~ related_reflexive(X208,X209,X210)
| related(X208,X209,X210)
| empty_carrier(X208)
| ~ reflexive_relstr(X208)
| ~ rel_str(X208)
| ~ element(X209,the_carrier(X208))
| ~ element(X210,the_carrier(X208)) )
& ( ~ related(X208,X209,X210)
| related_reflexive(X208,X209,X210)
| empty_carrier(X208)
| ~ reflexive_relstr(X208)
| ~ rel_str(X208)
| ~ element(X209,the_carrier(X208))
| ~ element(X210,the_carrier(X208)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_27,plain,
( related(X1,X3,X4)
| ~ relstr_element_smaller(X1,X2,X3)
| ~ element(X4,the_carrier(X1))
| ~ in(X4,X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
( latt_set_smaller(esk20_0,esk21_0,esk19_0)
| relstr_element_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( ~ latt_set_smaller(esk20_0,esk21_0,esk19_0)
| ~ relstr_element_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
( relstr_element_smaller(X1,X2,X3)
| ~ empty(X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_31,plain,
! [X150,X151] :
( empty_carrier(X150)
| ~ lattice(X150)
| ~ latt_str(X150)
| ~ element(X151,the_carrier(X150))
| element(cast_to_el_of_LattPOSet(X150,X151),the_carrier(poset_of_lattice(X150))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
fof(c_0_32,plain,
! [X130,X131,X132,X133,X134] :
( ( ~ latt_set_smaller(X130,X131,X132)
| ~ element(X133,the_carrier(X130))
| ~ in(X133,X132)
| below(X130,X131,X133)
| ~ element(X131,the_carrier(X130))
| empty_carrier(X130)
| ~ latt_str(X130) )
& ( element(esk1_3(X130,X131,X134),the_carrier(X130))
| latt_set_smaller(X130,X131,X134)
| ~ element(X131,the_carrier(X130))
| empty_carrier(X130)
| ~ latt_str(X130) )
& ( in(esk1_3(X130,X131,X134),X134)
| latt_set_smaller(X130,X131,X134)
| ~ element(X131,the_carrier(X130))
| empty_carrier(X130)
| ~ latt_str(X130) )
& ( ~ below(X130,X131,esk1_3(X130,X131,X134))
| latt_set_smaller(X130,X131,X134)
| ~ element(X131,the_carrier(X130))
| empty_carrier(X130)
| ~ latt_str(X130) ) ),
inference(distribute,[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_24])])])])])]) ).
fof(c_0_33,plain,
! [X236,X237,X238] :
( ( ~ below_refl(X236,X237,X238)
| related_reflexive(poset_of_lattice(X236),cast_to_el_of_LattPOSet(X236,X237),cast_to_el_of_LattPOSet(X236,X238))
| ~ element(X238,the_carrier(X236))
| ~ element(X237,the_carrier(X236))
| empty_carrier(X236)
| ~ lattice(X236)
| ~ latt_str(X236) )
& ( ~ related_reflexive(poset_of_lattice(X236),cast_to_el_of_LattPOSet(X236,X237),cast_to_el_of_LattPOSet(X236,X238))
| below_refl(X236,X237,X238)
| ~ element(X238,the_carrier(X236))
| ~ element(X237,the_carrier(X236))
| empty_carrier(X236)
| ~ lattice(X236)
| ~ latt_str(X236) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
cnf(c_0_34,plain,
( related_reflexive(X1,X2,X3)
| empty_carrier(X1)
| ~ related(X1,X2,X3)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
( related(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),X1)
| latt_set_smaller(esk20_0,esk21_0,esk19_0)
| ~ element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))
| ~ element(X1,the_carrier(poset_of_lattice(esk20_0)))
| ~ in(X1,esk19_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,negated_conjecture,
( ~ empty(esk19_0)
| ~ latt_set_smaller(esk20_0,esk21_0,esk19_0)
| ~ element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
( empty_carrier(X1)
| element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,negated_conjecture,
element(esk21_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_39,negated_conjecture,
lattice(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_40,negated_conjecture,
latt_str(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_41,negated_conjecture,
~ empty_carrier(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_42,plain,
( in(esk1_3(X1,X2,X3),X3)
| latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_43,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_lattice3]) ).
cnf(c_0_44,plain,
( 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))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,negated_conjecture,
( related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),X1)
| latt_set_smaller(esk20_0,esk21_0,esk19_0)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ reflexive_relstr(poset_of_lattice(esk20_0))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))
| ~ element(X1,the_carrier(poset_of_lattice(esk20_0)))
| ~ in(X1,esk19_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_46,negated_conjecture,
( ~ empty(esk19_0)
| ~ latt_set_smaller(esk20_0,esk21_0,esk19_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_47,plain,
( latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ empty(X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_42]) ).
fof(c_0_48,plain,
! [X149] :
( ( strict_rel_str(poset_of_lattice(X149))
| empty_carrier(X149)
| ~ lattice(X149)
| ~ latt_str(X149) )
& ( reflexive_relstr(poset_of_lattice(X149))
| empty_carrier(X149)
| ~ lattice(X149)
| ~ latt_str(X149) )
& ( transitive_relstr(poset_of_lattice(X149))
| empty_carrier(X149)
| ~ lattice(X149)
| ~ latt_str(X149) )
& ( antisymmetric_relstr(poset_of_lattice(X149))
| empty_carrier(X149)
| ~ lattice(X149)
| ~ latt_str(X149) )
& ( rel_str(poset_of_lattice(X149))
| empty_carrier(X149)
| ~ lattice(X149)
| ~ latt_str(X149) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])]) ).
cnf(c_0_49,negated_conjecture,
( below_refl(esk20_0,esk21_0,X1)
| latt_set_smaller(esk20_0,esk21_0,esk19_0)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ reflexive_relstr(poset_of_lattice(esk20_0))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))
| ~ element(X1,the_carrier(esk20_0))
| ~ in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_38]),c_0_39]),c_0_40])]),c_0_41]) ).
fof(c_0_50,plain,
! [X223,X224] :
( ~ element(X223,X224)
| empty(X224)
| in(X223,X224) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_51,negated_conjecture,
( ~ empty(esk19_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_38]),c_0_40])]),c_0_41]) ).
cnf(c_0_52,plain,
( rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( below_refl(esk20_0,esk21_0,X1)
| latt_set_smaller(esk20_0,esk21_0,esk19_0)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ reflexive_relstr(poset_of_lattice(esk20_0))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))
| ~ element(X1,the_carrier(esk20_0))
| ~ in(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_37]),c_0_38]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_54,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,negated_conjecture,
~ empty(esk19_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_52]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_56,negated_conjecture,
( below_refl(esk20_0,esk21_0,X1)
| latt_set_smaller(esk20_0,esk21_0,esk19_0)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ reflexive_relstr(poset_of_lattice(esk20_0))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,X1),the_carrier(poset_of_lattice(esk20_0)))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)
| ~ element(X1,the_carrier(esk20_0))
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_57,negated_conjecture,
( below_refl(esk20_0,esk21_0,X1)
| latt_set_smaller(esk20_0,esk21_0,esk19_0)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ reflexive_relstr(poset_of_lattice(esk20_0))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)
| ~ element(X1,the_carrier(esk20_0))
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_37]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_58,plain,
( reflexive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_59,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d3_lattice3]) ).
fof(c_0_60,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_lattices]) ).
cnf(c_0_61,negated_conjecture,
( below_refl(esk20_0,esk21_0,X1)
| latt_set_smaller(esk20_0,esk21_0,esk19_0)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)
| ~ element(X1,the_carrier(esk20_0))
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_39]),c_0_40])]),c_0_41]) ).
fof(c_0_62,plain,
! [X137,X138] :
( empty_carrier(X137)
| ~ lattice(X137)
| ~ latt_str(X137)
| ~ element(X138,the_carrier(X137))
| cast_to_el_of_LattPOSet(X137,X138) = X138 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])]) ).
fof(c_0_63,plain,
! [X205,X206,X207] :
( ( ~ below_refl(X205,X206,X207)
| below(X205,X206,X207)
| empty_carrier(X205)
| ~ meet_commutative(X205)
| ~ meet_absorbing(X205)
| ~ join_absorbing(X205)
| ~ latt_str(X205)
| ~ element(X206,the_carrier(X205))
| ~ element(X207,the_carrier(X205)) )
& ( ~ below(X205,X206,X207)
| below_refl(X205,X206,X207)
| empty_carrier(X205)
| ~ meet_commutative(X205)
| ~ meet_absorbing(X205)
| ~ join_absorbing(X205)
| ~ latt_str(X205)
| ~ element(X206,the_carrier(X205))
| ~ element(X207,the_carrier(X205)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).
cnf(c_0_64,negated_conjecture,
( below_refl(esk20_0,esk21_0,X1)
| latt_set_smaller(esk20_0,esk21_0,esk19_0)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,X1),esk19_0)
| ~ element(X1,the_carrier(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_52]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_65,plain,
( empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X2) = X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_66,plain,
( latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ below(X1,X2,esk1_3(X1,X2,X3))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_67,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_68,plain,
( element(esk1_3(X1,X2,X3),the_carrier(X1))
| latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_69,negated_conjecture,
( below_refl(esk20_0,esk21_0,X1)
| latt_set_smaller(esk20_0,esk21_0,esk19_0)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ element(X1,the_carrier(esk20_0))
| ~ element(X1,esk19_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_39]),c_0_40])]),c_0_41]) ).
fof(c_0_70,plain,
! [X218,X219] :
( ~ in(X218,X219)
| element(X218,X219) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_71,plain,
( latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ below_refl(X1,X2,esk1_3(X1,X2,X3))
| ~ element(X2,the_carrier(X1))
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_72,negated_conjecture,
( below_refl(esk20_0,esk21_0,esk1_3(esk20_0,X1,X2))
| latt_set_smaller(esk20_0,esk21_0,esk19_0)
| latt_set_smaller(esk20_0,X1,X2)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ element(esk1_3(esk20_0,X1,X2),esk19_0)
| ~ element(X1,the_carrier(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_68]),c_0_40])]),c_0_41]) ).
cnf(c_0_73,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
fof(c_0_74,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(poset_of_lattice(X1))
& strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc4_lattice3]) ).
cnf(c_0_75,negated_conjecture,
( latt_set_smaller(esk20_0,esk21_0,esk19_0)
| latt_set_smaller(esk20_0,esk21_0,X1)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ element(esk1_3(esk20_0,esk21_0,X1),esk19_0)
| ~ join_absorbing(esk20_0)
| ~ meet_absorbing(esk20_0)
| ~ meet_commutative(esk20_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_38]),c_0_40])]),c_0_41]) ).
cnf(c_0_76,plain,
( latt_set_smaller(X1,X2,X3)
| element(esk1_3(X1,X2,X3),X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_42]) ).
cnf(c_0_77,plain,
( relstr_element_smaller(X1,X3,X2)
| ~ related(X1,X2,esk2_3(X1,X3,X2))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_78,plain,
( related(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(X1,X2,X3)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_79,plain,
( element(esk2_3(X1,X2,X3),the_carrier(X1))
| relstr_element_smaller(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_80,plain,
( 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)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_81,plain,
! [X183] :
( ( ~ empty_carrier(poset_of_lattice(X183))
| empty_carrier(X183)
| ~ lattice(X183)
| ~ latt_str(X183) )
& ( strict_rel_str(poset_of_lattice(X183))
| empty_carrier(X183)
| ~ lattice(X183)
| ~ latt_str(X183) )
& ( reflexive_relstr(poset_of_lattice(X183))
| empty_carrier(X183)
| ~ lattice(X183)
| ~ latt_str(X183) )
& ( transitive_relstr(poset_of_lattice(X183))
| empty_carrier(X183)
| ~ lattice(X183)
| ~ latt_str(X183) )
& ( antisymmetric_relstr(poset_of_lattice(X183))
| empty_carrier(X183)
| ~ lattice(X183)
| ~ latt_str(X183) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])]) ).
cnf(c_0_82,plain,
( below(X1,X2,X4)
| empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X4,the_carrier(X1))
| ~ in(X4,X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_83,negated_conjecture,
( latt_set_smaller(esk20_0,esk21_0,esk19_0)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ join_absorbing(esk20_0)
| ~ meet_absorbing(esk20_0)
| ~ meet_commutative(esk20_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_38]),c_0_40])]),c_0_41]) ).
fof(c_0_84,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(poset_of_lattice(X1))) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattice3]) ).
fof(c_0_85,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d4_lattice3]) ).
cnf(c_0_86,plain,
( relstr_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(X1,X3,esk2_3(X1,X2,X3))
| ~ reflexive_relstr(X1)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_87,plain,
( related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),X3)
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_65]) ).
cnf(c_0_88,plain,
( empty_carrier(X1)
| ~ empty_carrier(poset_of_lattice(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_89,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ below(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_90,negated_conjecture,
( below(esk20_0,esk21_0,X1)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ element(X1,the_carrier(esk20_0))
| ~ join_absorbing(esk20_0)
| ~ meet_absorbing(esk20_0)
| ~ meet_commutative(esk20_0)
| ~ in(X1,esk19_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_38]),c_0_40])]),c_0_41]) ).
fof(c_0_91,plain,
! [X152,X153] :
( empty_carrier(X152)
| ~ lattice(X152)
| ~ latt_str(X152)
| ~ element(X153,the_carrier(poset_of_lattice(X152)))
| element(cast_to_el_of_lattice(X152,X153),the_carrier(X152)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])]) ).
fof(c_0_92,plain,
! [X139,X140] :
( empty_carrier(X139)
| ~ lattice(X139)
| ~ latt_str(X139)
| ~ element(X140,the_carrier(poset_of_lattice(X139)))
| cast_to_el_of_lattice(X139,X140) = X140 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])]) ).
cnf(c_0_93,plain,
( relstr_element_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))
| empty_carrier(X1)
| ~ below_refl(X1,X3,esk2_3(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3)))
| ~ element(esk2_3(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3)),the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_52]),c_0_37]),c_0_58]),c_0_88]) ).
cnf(c_0_94,negated_conjecture,
( below_refl(esk20_0,esk21_0,X1)
| empty_carrier(poset_of_lattice(esk20_0))
| ~ element(X1,the_carrier(esk20_0))
| ~ join_absorbing(esk20_0)
| ~ meet_absorbing(esk20_0)
| ~ meet_commutative(esk20_0)
| ~ in(X1,esk19_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_38]),c_0_40])]),c_0_41]) ).
cnf(c_0_95,plain,
( empty_carrier(X1)
| element(cast_to_el_of_lattice(X1,X2),the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(poset_of_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_96,plain,
( empty_carrier(X1)
| cast_to_el_of_lattice(X1,X2) = X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(poset_of_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0))
| empty_carrier(poset_of_lattice(esk20_0))
| ~ element(esk2_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),the_carrier(esk20_0))
| ~ join_absorbing(esk20_0)
| ~ meet_absorbing(esk20_0)
| ~ meet_commutative(esk20_0)
| ~ in(esk2_3(poset_of_lattice(esk20_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),esk19_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_38]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_98,plain,
( element(X1,the_carrier(X2))
| empty_carrier(X2)
| ~ element(X1,the_carrier(poset_of_lattice(X2)))
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_99,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0))
| empty_carrier(poset_of_lattice(esk20_0))
| ~ element(esk2_3(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0)),the_carrier(esk20_0))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))
| ~ join_absorbing(esk20_0)
| ~ meet_absorbing(esk20_0)
| ~ meet_commutative(esk20_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(spm,[status(thm)],[c_0_97,c_0_22]) ).
cnf(c_0_100,plain,
( relstr_element_smaller(poset_of_lattice(X1),X2,X3)
| element(esk2_3(poset_of_lattice(X1),X2,X3),the_carrier(X1))
| empty_carrier(X1)
| ~ element(X3,the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_79]),c_0_52]) ).
cnf(c_0_101,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(esk20_0),esk19_0,cast_to_el_of_LattPOSet(esk20_0,esk21_0))
| empty_carrier(poset_of_lattice(esk20_0))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))
| ~ join_absorbing(esk20_0)
| ~ meet_absorbing(esk20_0)
| ~ meet_commutative(esk20_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_39]),c_0_40])]),c_0_41]) ).
fof(c_0_102,plain,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
cnf(c_0_103,negated_conjecture,
( empty_carrier(poset_of_lattice(esk20_0))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0)))
| ~ join_absorbing(esk20_0)
| ~ meet_absorbing(esk20_0)
| ~ meet_commutative(esk20_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_101]),c_0_83]) ).
fof(c_0_104,plain,
! [X125] :
( ( ~ empty_carrier(X125)
| empty_carrier(X125)
| ~ lattice(X125)
| ~ latt_str(X125) )
& ( join_commutative(X125)
| empty_carrier(X125)
| ~ lattice(X125)
| ~ latt_str(X125) )
& ( join_associative(X125)
| empty_carrier(X125)
| ~ lattice(X125)
| ~ latt_str(X125) )
& ( meet_commutative(X125)
| empty_carrier(X125)
| ~ lattice(X125)
| ~ latt_str(X125) )
& ( meet_associative(X125)
| empty_carrier(X125)
| ~ lattice(X125)
| ~ latt_str(X125) )
& ( meet_absorbing(X125)
| empty_carrier(X125)
| ~ lattice(X125)
| ~ latt_str(X125) )
& ( join_absorbing(X125)
| empty_carrier(X125)
| ~ lattice(X125)
| ~ latt_str(X125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_102])])]) ).
cnf(c_0_105,negated_conjecture,
( empty_carrier(poset_of_lattice(esk20_0))
| ~ join_absorbing(esk20_0)
| ~ meet_absorbing(esk20_0)
| ~ meet_commutative(esk20_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_37]),c_0_38]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_106,plain,
( join_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_107,negated_conjecture,
( empty_carrier(poset_of_lattice(esk20_0))
| ~ meet_absorbing(esk20_0)
| ~ meet_commutative(esk20_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_108,plain,
( meet_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( empty_carrier(poset_of_lattice(esk20_0))
| ~ meet_commutative(esk20_0)
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_110,plain,
( meet_commutative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_111,negated_conjecture,
( empty_carrier(poset_of_lattice(esk20_0))
| ~ rel_str(poset_of_lattice(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_112,negated_conjecture,
empty_carrier(poset_of_lattice(esk20_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_52]),c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_113,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_88,c_0_112]),c_0_39]),c_0_40])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU347+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n008.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:59:13 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 5.60/4.34 % Version : CSE_E---1.7
% 5.60/4.34 % Problem : theBenchmark.p
% 5.60/4.34 % SZS status Theorem for theBenchmark.p
% 5.60/4.34 % SZS output start CNFRefutation
% See solution above
% 5.60/4.36 % Total time : 3.372s
%------------------------------------------------------------------------------