%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU352+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 : n015.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 05:11:34 PM UTC 2026
% Result : Theorem 1.72s 1.89s
% Output : CNFRefutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 19
% Syntax : Number of formulae : 124 ( 14 unt; 0 def)
% Number of atoms : 734 ( 76 equ)
% Maximal formula atoms : 50 ( 5 avg)
% Number of connectives : 998 ( 388 ~; 419 |; 121 &)
% ( 8 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-3 aty)
% Number of variables : 234 ( 11 sgn 116 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(d21_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( X3 = join_of_latt_set(X1,X2)
<=> ( latt_element_smaller(X1,X3,X2)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_element_smaller(X1,X4,X2)
=> below(X1,X3,X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_lattice3) ).
fof(dt_k15_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_lattice3) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(d17_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(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/sandbox/benchmark/theBenchmark.p',d17_lattice3) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(t50_lattice3,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1)
& lower_bounded_semilattstr(X1)
& latt_str(X1)
& bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattice3) ).
fof(t23_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> below(X1,meet_commut(X1,X2,X3),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattices) ).
fof(redefinition_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
fof(d16_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( X2 = bottom_of_semilattstr(X1)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattices) ).
fof(dt_k5_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> element(bottom_of_semilattstr(X1),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).
fof(t26_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X2,X3)
& below(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
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(commutativity_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(dt_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(meet_commut(X1,X2,X3),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattices) ).
fof(d13_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
<=> ? [X2] :
( element(X2,the_carrier(X1))
& ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_lattices) ).
fof(c_0_19,plain,
! [X267] :
( ~ empty(X267)
| X267 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_20,plain,
! [X223] :
( element(esk15_1(X223),powerset(X223))
& empty(esk15_1(X223)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_21,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( X3 = join_of_latt_set(X1,X2)
<=> ( latt_element_smaller(X1,X3,X2)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_element_smaller(X1,X4,X2)
=> below(X1,X3,X4) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d21_lattice3]) ).
cnf(c_0_22,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
empty(esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X167,X168,X169,X170] :
( ( latt_element_smaller(X167,X169,X168)
| X169 != join_of_latt_set(X167,X168)
| ~ element(X169,the_carrier(X167))
| empty_carrier(X167)
| ~ lattice(X167)
| ~ complete_latt_str(X167)
| ~ latt_str(X167)
| empty_carrier(X167)
| ~ latt_str(X167) )
& ( ~ element(X170,the_carrier(X167))
| ~ latt_element_smaller(X167,X170,X168)
| below(X167,X169,X170)
| X169 != join_of_latt_set(X167,X168)
| ~ element(X169,the_carrier(X167))
| empty_carrier(X167)
| ~ lattice(X167)
| ~ complete_latt_str(X167)
| ~ latt_str(X167)
| empty_carrier(X167)
| ~ latt_str(X167) )
& ( element(esk5_3(X167,X168,X169),the_carrier(X167))
| ~ latt_element_smaller(X167,X169,X168)
| X169 = join_of_latt_set(X167,X168)
| ~ element(X169,the_carrier(X167))
| empty_carrier(X167)
| ~ lattice(X167)
| ~ complete_latt_str(X167)
| ~ latt_str(X167)
| empty_carrier(X167)
| ~ latt_str(X167) )
& ( latt_element_smaller(X167,esk5_3(X167,X168,X169),X168)
| ~ latt_element_smaller(X167,X169,X168)
| X169 = join_of_latt_set(X167,X168)
| ~ element(X169,the_carrier(X167))
| empty_carrier(X167)
| ~ lattice(X167)
| ~ complete_latt_str(X167)
| ~ latt_str(X167)
| empty_carrier(X167)
| ~ latt_str(X167) )
& ( ~ below(X167,X169,esk5_3(X167,X168,X169))
| ~ latt_element_smaller(X167,X169,X168)
| X169 = join_of_latt_set(X167,X168)
| ~ element(X169,the_carrier(X167))
| empty_carrier(X167)
| ~ lattice(X167)
| ~ complete_latt_str(X167)
| ~ latt_str(X167)
| empty_carrier(X167)
| ~ latt_str(X167) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).
fof(c_0_25,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k15_lattice3]) ).
fof(c_0_26,plain,
! [X264,X265,X266] :
( ~ in(X264,X265)
| ~ element(X265,powerset(X266))
| ~ empty(X266) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_27,plain,
element(esk15_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
esk15_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_29,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(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]) ).
cnf(c_0_30,plain,
( below(X2,X4,X1)
| empty_carrier(X2)
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| ~ latt_element_smaller(X2,X1,X3)
| X4 != join_of_latt_set(X2,X3)
| ~ element(X4,the_carrier(X2))
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X177,X178] :
( empty_carrier(X177)
| ~ latt_str(X177)
| element(join_of_latt_set(X177,X178),the_carrier(X177)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
cnf(c_0_32,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_34,plain,
! [X158,X159,X160,X161,X162] :
( ( ~ latt_element_smaller(X158,X159,X160)
| ~ element(X161,the_carrier(X158))
| ~ in(X161,X160)
| below(X158,X161,X159)
| ~ element(X159,the_carrier(X158))
| empty_carrier(X158)
| ~ latt_str(X158) )
& ( element(esk4_3(X158,X159,X162),the_carrier(X158))
| latt_element_smaller(X158,X159,X162)
| ~ element(X159,the_carrier(X158))
| empty_carrier(X158)
| ~ latt_str(X158) )
& ( in(esk4_3(X158,X159,X162),X162)
| latt_element_smaller(X158,X159,X162)
| ~ element(X159,the_carrier(X158))
| empty_carrier(X158)
| ~ latt_str(X158) )
& ( ~ below(X158,esk4_3(X158,X159,X162),X159)
| latt_element_smaller(X158,X159,X162)
| ~ element(X159,the_carrier(X158))
| empty_carrier(X158)
| ~ latt_str(X158) ) ),
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_29])])])])])]) ).
cnf(c_0_35,plain,
( X2 = join_of_latt_set(X1,X3)
| empty_carrier(X1)
| empty_carrier(X1)
| ~ below(X1,X2,esk5_3(X1,X3,X2))
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_36,plain,
( empty_carrier(X2)
| below(X2,X4,X1)
| X4 != join_of_latt_set(X2,X3)
| ~ latt_str(X2)
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_element_smaller(X2,X1,X3)
| ~ element(X4,the_carrier(X2))
| ~ element(X1,the_carrier(X2)) ),
inference(cn,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
( empty_carrier(X1)
| element(join_of_latt_set(X1,X2),the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
( ~ empty(X1)
| ~ in(X2,empty_set) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( in(esk4_3(X1,X2,X3),X3)
| latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
( X2 = join_of_latt_set(X1,X3)
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ below(X1,X2,esk5_3(X1,X3,X2)) ),
inference(cn,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
( below(X1,join_of_latt_set(X1,X2),X3)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_36]),c_0_37]) ).
cnf(c_0_42,plain,
( latt_element_smaller(X1,X2,empty_set)
| empty_carrier(X1)
| ~ empty(X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_44,plain,
( join_of_latt_set(X1,X2) = join_of_latt_set(X1,X3)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,esk5_3(X1,X3,join_of_latt_set(X1,X2)),X2)
| ~ latt_element_smaller(X1,join_of_latt_set(X1,X2),X3)
| ~ element(esk5_3(X1,X3,join_of_latt_set(X1,X2)),the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_37]) ).
cnf(c_0_45,plain,
( latt_element_smaller(X1,X2,empty_set)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,plain,
( element(esk5_3(X1,X2,X3),the_carrier(X1))
| X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_47,plain,
! [X268,X269] :
( ~ in(X268,X269)
| ~ empty(X269) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_48,plain,
( join_of_latt_set(X1,empty_set) = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,join_of_latt_set(X1,empty_set),X2)
| ~ element(esk5_3(X1,X2,join_of_latt_set(X1,empty_set)),the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
( X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| element(esk5_3(X1,X2,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1)) ),
inference(cn,[status(thm)],[c_0_46]) ).
cnf(c_0_50,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_51,plain,
( join_of_latt_set(X1,empty_set) = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,join_of_latt_set(X1,empty_set),X2)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_37]) ).
cnf(c_0_52,plain,
( latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ empty(X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_39]) ).
fof(c_0_53,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1)
& lower_bounded_semilattstr(X1)
& latt_str(X1)
& bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t50_lattice3])]) ).
cnf(c_0_54,plain,
( join_of_latt_set(X1,empty_set) = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| ~ empty(X2)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_37]) ).
fof(c_0_55,negated_conjecture,
( ~ empty_carrier(esk19_0)
& lattice(esk19_0)
& complete_latt_str(esk19_0)
& latt_str(esk19_0)
& ( empty_carrier(esk19_0)
| ~ lattice(esk19_0)
| ~ lower_bounded_semilattstr(esk19_0)
| ~ latt_str(esk19_0)
| bottom_of_semilattstr(esk19_0) != join_of_latt_set(esk19_0,empty_set) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])]) ).
cnf(c_0_56,plain,
( join_of_latt_set(X1,X2) = join_of_latt_set(X1,X3)
| empty_carrier(X1)
| ~ empty(X3)
| ~ empty(X2)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
complete_latt_str(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_58,negated_conjecture,
lattice(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_59,negated_conjecture,
latt_str(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,negated_conjecture,
~ empty_carrier(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,negated_conjecture,
( join_of_latt_set(esk19_0,X1) = join_of_latt_set(esk19_0,X2)
| ~ empty(X2)
| ~ empty(X1) ),
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_57]),c_0_58]),c_0_59])]),c_0_60]) ).
cnf(c_0_62,negated_conjecture,
( join_of_latt_set(esk19_0,empty_set) = join_of_latt_set(esk19_0,X1)
| ~ empty(X2)
| ~ empty(X1) ),
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_54,c_0_61]),c_0_57]),c_0_58]),c_0_59])]),c_0_60]) ).
fof(c_0_63,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> below(X1,meet_commut(X1,X2,X3),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t23_lattices]) ).
fof(c_0_64,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k4_lattices]) ).
fof(c_0_65,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( X2 = bottom_of_semilattstr(X1)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d16_lattices]) ).
fof(c_0_66,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> element(bottom_of_semilattstr(X1),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattices]) ).
fof(c_0_67,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X2,X3)
& below(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[t26_lattices]) ).
cnf(c_0_68,negated_conjecture,
( join_of_latt_set(esk19_0,empty_set) = join_of_latt_set(esk19_0,X1)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_43]) ).
fof(c_0_69,plain,
! [X250,X251,X252] :
( empty_carrier(X250)
| ~ meet_commutative(X250)
| ~ meet_absorbing(X250)
| ~ latt_str(X250)
| ~ element(X251,the_carrier(X250))
| ~ element(X252,the_carrier(X250))
| below(X250,meet_commut(X250,X251,X252),X251) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])]) ).
fof(c_0_70,plain,
! [X235,X236,X237] :
( empty_carrier(X235)
| ~ meet_commutative(X235)
| ~ meet_semilatt_str(X235)
| ~ element(X236,the_carrier(X235))
| ~ element(X237,the_carrier(X235))
| meet_commut(X235,X236,X237) = meet(X235,X236,X237) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])]) ).
fof(c_0_71,plain,
! [X194] :
( ( meet_semilatt_str(X194)
| ~ latt_str(X194) )
& ( join_semilatt_str(X194)
| ~ latt_str(X194) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_72,plain,
! [X154,X155,X156] :
( ( meet(X154,X155,X156) = X155
| ~ element(X156,the_carrier(X154))
| X155 != bottom_of_semilattstr(X154)
| ~ element(X155,the_carrier(X154))
| ~ lower_bounded_semilattstr(X154)
| empty_carrier(X154)
| ~ meet_semilatt_str(X154) )
& ( meet(X154,X156,X155) = X155
| ~ element(X156,the_carrier(X154))
| X155 != bottom_of_semilattstr(X154)
| ~ element(X155,the_carrier(X154))
| ~ lower_bounded_semilattstr(X154)
| empty_carrier(X154)
| ~ meet_semilatt_str(X154) )
& ( element(esk3_2(X154,X155),the_carrier(X154))
| X155 = bottom_of_semilattstr(X154)
| ~ element(X155,the_carrier(X154))
| ~ lower_bounded_semilattstr(X154)
| empty_carrier(X154)
| ~ meet_semilatt_str(X154) )
& ( meet(X154,X155,esk3_2(X154,X155)) != X155
| meet(X154,esk3_2(X154,X155),X155) != X155
| X155 = bottom_of_semilattstr(X154)
| ~ element(X155,the_carrier(X154))
| ~ lower_bounded_semilattstr(X154)
| empty_carrier(X154)
| ~ meet_semilatt_str(X154) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])])]) ).
fof(c_0_73,plain,
! [X191] :
( empty_carrier(X191)
| ~ meet_semilatt_str(X191)
| element(bottom_of_semilattstr(X191),the_carrier(X191)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])]) ).
fof(c_0_74,plain,
! [X253,X254,X255] :
( empty_carrier(X253)
| ~ join_commutative(X253)
| ~ join_semilatt_str(X253)
| ~ element(X254,the_carrier(X253))
| ~ element(X255,the_carrier(X253))
| ~ below(X253,X254,X255)
| ~ below(X253,X255,X254)
| X254 = X255 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])]) ).
cnf(c_0_75,negated_conjecture,
( below(esk19_0,join_of_latt_set(esk19_0,empty_set),X1)
| ~ empty(X2)
| ~ latt_element_smaller(esk19_0,X1,X2)
| ~ element(X1,the_carrier(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_41,c_0_68]),c_0_57]),c_0_58]),c_0_59])]),c_0_60]) ).
cnf(c_0_76,negated_conjecture,
( element(join_of_latt_set(esk19_0,empty_set),the_carrier(esk19_0))
| ~ empty(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_68]),c_0_59])]),c_0_60]) ).
cnf(c_0_77,plain,
( empty_carrier(X1)
| below(X1,meet_commut(X1,X2,X3),X2)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_78,plain,
( empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_79,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_80,plain,
( meet(X1,X2,X3) = X3
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| X3 != bottom_of_semilattstr(X1)
| ~ element(X3,the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_81,plain,
( empty_carrier(X1)
| element(bottom_of_semilattstr(X1),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_82,plain,
( empty_carrier(X1)
| X2 = X3
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below(X1,X2,X3)
| ~ below(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_83,negated_conjecture,
( below(esk19_0,join_of_latt_set(esk19_0,empty_set),X1)
| ~ element(X1,the_carrier(esk19_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_45]),c_0_43]),c_0_59])]),c_0_60]) ).
cnf(c_0_84,negated_conjecture,
element(join_of_latt_set(esk19_0,empty_set),the_carrier(esk19_0)),
inference(spm,[status(thm)],[c_0_76,c_0_43]) ).
cnf(c_0_85,plain,
( below(X1,meet(X1,X2,X3),X2)
| empty_carrier(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_86,plain,
( meet(X1,X2,bottom_of_semilattstr(X1)) = bottom_of_semilattstr(X1)
| empty_carrier(X1)
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_80]),c_0_81]) ).
cnf(c_0_87,negated_conjecture,
( empty_carrier(esk19_0)
| ~ lattice(esk19_0)
| ~ lower_bounded_semilattstr(esk19_0)
| ~ latt_str(esk19_0)
| bottom_of_semilattstr(esk19_0) != join_of_latt_set(esk19_0,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_88,negated_conjecture,
( X1 = join_of_latt_set(esk19_0,empty_set)
| ~ join_semilatt_str(esk19_0)
| ~ below(esk19_0,X1,join_of_latt_set(esk19_0,empty_set))
| ~ element(X1,the_carrier(esk19_0))
| ~ join_commutative(esk19_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]),c_0_60]) ).
cnf(c_0_89,plain,
( below(X1,bottom_of_semilattstr(X1),X2)
| empty_carrier(X1)
| ~ lower_bounded_semilattstr(X1)
| ~ element(X2,the_carrier(X1))
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_81]),c_0_79]) ).
cnf(c_0_90,negated_conjecture,
( join_of_latt_set(esk19_0,empty_set) != bottom_of_semilattstr(esk19_0)
| ~ lower_bounded_semilattstr(esk19_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_59]),c_0_58])]),c_0_60]) ).
fof(c_0_91,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]) ).
fof(c_0_92,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k4_lattices]) ).
cnf(c_0_93,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_94,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(meet_commut(X1,X2,X3),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k4_lattices]) ).
cnf(c_0_95,negated_conjecture,
( ~ join_semilatt_str(esk19_0)
| ~ lower_bounded_semilattstr(esk19_0)
| ~ element(bottom_of_semilattstr(esk19_0),the_carrier(esk19_0))
| ~ meet_absorbing(esk19_0)
| ~ meet_commutative(esk19_0)
| ~ join_commutative(esk19_0) ),
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_88,c_0_89]),c_0_84]),c_0_59])]),c_0_60]),c_0_90]) ).
cnf(c_0_96,negated_conjecture,
meet_semilatt_str(esk19_0),
inference(spm,[status(thm)],[c_0_79,c_0_59]) ).
fof(c_0_97,plain,
! [X139] :
( ( ~ empty_carrier(X139)
| empty_carrier(X139)
| ~ lattice(X139)
| ~ latt_str(X139) )
& ( join_commutative(X139)
| empty_carrier(X139)
| ~ lattice(X139)
| ~ latt_str(X139) )
& ( join_associative(X139)
| empty_carrier(X139)
| ~ lattice(X139)
| ~ latt_str(X139) )
& ( meet_commutative(X139)
| empty_carrier(X139)
| ~ lattice(X139)
| ~ latt_str(X139) )
& ( meet_associative(X139)
| empty_carrier(X139)
| ~ lattice(X139)
| ~ latt_str(X139) )
& ( meet_absorbing(X139)
| empty_carrier(X139)
| ~ lattice(X139)
| ~ latt_str(X139) )
& ( join_absorbing(X139)
| empty_carrier(X139)
| ~ lattice(X139)
| ~ latt_str(X139) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])])]) ).
fof(c_0_98,plain,
! [X146,X147,X148] :
( empty_carrier(X146)
| ~ meet_commutative(X146)
| ~ meet_semilatt_str(X146)
| ~ element(X147,the_carrier(X146))
| ~ element(X148,the_carrier(X146))
| meet_commut(X146,X147,X148) = meet_commut(X146,X148,X147) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])]) ).
cnf(c_0_99,plain,
( meet_commut(X1,X2,X3) = X2
| empty_carrier(X1)
| ~ below(X1,X2,meet_commut(X1,X2,X3))
| ~ element(meet_commut(X1,X2,X3),the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ join_commutative(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_77]),c_0_93]) ).
fof(c_0_100,plain,
! [X188,X189,X190] :
( empty_carrier(X188)
| ~ meet_commutative(X188)
| ~ meet_semilatt_str(X188)
| ~ element(X189,the_carrier(X188))
| ~ element(X190,the_carrier(X188))
| element(meet_commut(X188,X189,X190),the_carrier(X188)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])]) ).
cnf(c_0_101,negated_conjecture,
( ~ join_semilatt_str(esk19_0)
| ~ lower_bounded_semilattstr(esk19_0)
| ~ meet_absorbing(esk19_0)
| ~ meet_commutative(esk19_0)
| ~ join_commutative(esk19_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_81]),c_0_96])]),c_0_60]) ).
cnf(c_0_102,plain,
( join_commutative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
fof(c_0_103,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
<=> ? [X2] :
( element(X2,the_carrier(X1))
& ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d13_lattices]) ).
cnf(c_0_104,plain,
( empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_105,negated_conjecture,
( meet_commut(esk19_0,join_of_latt_set(esk19_0,empty_set),X1) = join_of_latt_set(esk19_0,empty_set)
| ~ element(meet_commut(esk19_0,join_of_latt_set(esk19_0,empty_set),X1),the_carrier(esk19_0))
| ~ element(X1,the_carrier(esk19_0))
| ~ meet_absorbing(esk19_0)
| ~ meet_commutative(esk19_0)
| ~ join_commutative(esk19_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_83]),c_0_84]),c_0_59])]),c_0_60]) ).
cnf(c_0_106,plain,
( empty_carrier(X1)
| element(meet_commut(X1,X2,X3),the_carrier(X1))
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_107,negated_conjecture,
( ~ join_semilatt_str(esk19_0)
| ~ lower_bounded_semilattstr(esk19_0)
| ~ meet_absorbing(esk19_0)
| ~ meet_commutative(esk19_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_58]),c_0_59])]),c_0_60]) ).
fof(c_0_108,plain,
! [X149,X151,X152] :
( ( element(esk1_1(X149),the_carrier(X149))
| ~ lower_bounded_semilattstr(X149)
| empty_carrier(X149)
| ~ meet_semilatt_str(X149) )
& ( meet(X149,esk1_1(X149),X151) = esk1_1(X149)
| ~ element(X151,the_carrier(X149))
| ~ lower_bounded_semilattstr(X149)
| empty_carrier(X149)
| ~ meet_semilatt_str(X149) )
& ( meet(X149,X151,esk1_1(X149)) = esk1_1(X149)
| ~ element(X151,the_carrier(X149))
| ~ lower_bounded_semilattstr(X149)
| empty_carrier(X149)
| ~ meet_semilatt_str(X149) )
& ( element(esk2_2(X149,X152),the_carrier(X149))
| ~ element(X152,the_carrier(X149))
| lower_bounded_semilattstr(X149)
| empty_carrier(X149)
| ~ meet_semilatt_str(X149) )
& ( meet(X149,X152,esk2_2(X149,X152)) != X152
| meet(X149,esk2_2(X149,X152),X152) != X152
| ~ element(X152,the_carrier(X149))
| lower_bounded_semilattstr(X149)
| empty_carrier(X149)
| ~ meet_semilatt_str(X149) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_103])])])])]) ).
cnf(c_0_109,plain,
( meet_commut(X1,X2,X3) = meet(X1,X3,X2)
| empty_carrier(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ meet_commutative(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_104]) ).
cnf(c_0_110,negated_conjecture,
( meet_commut(esk19_0,join_of_latt_set(esk19_0,empty_set),X1) = join_of_latt_set(esk19_0,empty_set)
| ~ element(X1,the_carrier(esk19_0))
| ~ meet_absorbing(esk19_0)
| ~ meet_commutative(esk19_0)
| ~ join_commutative(esk19_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_96]),c_0_84])]),c_0_60]) ).
cnf(c_0_111,negated_conjecture,
( ~ lower_bounded_semilattstr(esk19_0)
| ~ meet_absorbing(esk19_0)
| ~ meet_commutative(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_93]),c_0_59])]) ).
cnf(c_0_112,plain,
( meet_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_113,plain,
( lower_bounded_semilattstr(X1)
| empty_carrier(X1)
| meet(X1,X2,esk2_2(X1,X2)) != X2
| meet(X1,esk2_2(X1,X2),X2) != X2
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_114,negated_conjecture,
( meet(esk19_0,X1,join_of_latt_set(esk19_0,empty_set)) = join_of_latt_set(esk19_0,empty_set)
| ~ element(X1,the_carrier(esk19_0))
| ~ meet_absorbing(esk19_0)
| ~ meet_commutative(esk19_0)
| ~ join_commutative(esk19_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_96]),c_0_84])]),c_0_60]) ).
cnf(c_0_115,negated_conjecture,
( meet(esk19_0,join_of_latt_set(esk19_0,empty_set),X1) = join_of_latt_set(esk19_0,empty_set)
| ~ element(X1,the_carrier(esk19_0))
| ~ meet_absorbing(esk19_0)
| ~ meet_commutative(esk19_0)
| ~ join_commutative(esk19_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_110]),c_0_96]),c_0_84])]),c_0_60]) ).
cnf(c_0_116,negated_conjecture,
( ~ lower_bounded_semilattstr(esk19_0)
| ~ meet_commutative(esk19_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_112]),c_0_58]),c_0_59])]),c_0_60]) ).
cnf(c_0_117,negated_conjecture,
( ~ element(esk2_2(esk19_0,join_of_latt_set(esk19_0,empty_set)),the_carrier(esk19_0))
| ~ meet_absorbing(esk19_0)
| ~ meet_commutative(esk19_0)
| ~ join_commutative(esk19_0) ),
inference(csr,[status(thm)],[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_113,c_0_114]),c_0_96]),c_0_84])]),c_0_60]),c_0_115]),c_0_116]) ).
cnf(c_0_118,plain,
( element(esk2_2(X1,X2),the_carrier(X1))
| lower_bounded_semilattstr(X1)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_119,negated_conjecture,
( ~ meet_absorbing(esk19_0)
| ~ meet_commutative(esk19_0)
| ~ join_commutative(esk19_0) ),
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_117,c_0_118]),c_0_96]),c_0_84])]),c_0_60]),c_0_116]) ).
cnf(c_0_120,negated_conjecture,
( ~ meet_absorbing(esk19_0)
| ~ meet_commutative(esk19_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_102]),c_0_58]),c_0_59])]),c_0_60]) ).
cnf(c_0_121,negated_conjecture,
~ meet_commutative(esk19_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_112]),c_0_58]),c_0_59])]),c_0_60]) ).
cnf(c_0_122,plain,
( meet_commutative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_123,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_121,c_0_122]),c_0_58]),c_0_59])]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU352+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 03:00:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.72/1.89 % Version : CSE_E---1.7
% 1.72/1.89 % Problem : theBenchmark.p
% 1.72/1.89 % SZS status Theorem for theBenchmark.p
% 1.72/1.89 % SZS output start CNFRefutation
% See solution above
% 1.72/1.89 % Total time : 1.372s
%------------------------------------------------------------------------------