%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU352+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 02:24:49 PM UTC 2026
% Result : Theorem 6.44s 1.35s
% Output : CNFRefutation 6.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 122 ( 18 unt; 0 def)
% Number of atoms : 716 ( 76 equ)
% Maximal formula atoms : 50 ( 5 avg)
% Number of connectives : 957 ( 363 ~; 395 |; 126 &)
% ( 10 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 3 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-3 aty)
% Number of variables : 233 ( 9 sgn 119 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( empty(X2)
& element(X2,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( empty(X3)
& element(X2,powerset(X3))
& in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(d21_lattice3,axiom,
! [X1] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> ( ( latt_str(X1)
& complete_latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( X3 = join_of_latt_set(X1,X2)
<=> ( ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_element_smaller(X1,X4,X2)
=> below(X1,X3,X4) ) )
& latt_element_smaller(X1,X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattice3) ).
fof(d17_lattice3,axiom,
! [X1] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X4,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice3) ).
fof(dt_k15_lattice3,axiom,
! [X1,X2] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_lattice3) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t26_lattices,axiom,
! [X1] :
( ( join_semilatt_str(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X3,X2)
& below(X1,X2,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).
fof(cc1_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( ( lattice(X1)
& ~ empty_carrier(X1) )
=> ( join_absorbing(X1)
& meet_absorbing(X1)
& meet_associative(X1)
& meet_commutative(X1)
& join_associative(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
fof(t23_lattices,axiom,
! [X1] :
( ( latt_str(X1)
& meet_absorbing(X1)
& meet_commutative(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> below(X1,meet_commut(X1,X2,X3),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).
fof(redefinition_k4_lattices,axiom,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& meet_semilatt_str(X1)
& meet_commutative(X1)
& ~ empty_carrier(X1) )
=> meet_commut(X1,X2,X3) = meet(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
fof(d16_lattices,axiom,
! [X1] :
( ( meet_semilatt_str(X1)
& ~ empty_carrier(X1) )
=> ( lower_bounded_semilattstr(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( X2 = bottom_of_semilattstr(X1)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X3,X2) = X2
& meet(X1,X2,X3) = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattices) ).
fof(dt_k5_lattices,axiom,
! [X1] :
( ( meet_semilatt_str(X1)
& ~ empty_carrier(X1) )
=> element(bottom_of_semilattstr(X1),the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( join_semilatt_str(X1)
& meet_semilatt_str(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(t50_lattice3,conjecture,
! [X1] :
( ( latt_str(X1)
& complete_latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ( bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set)
& latt_str(X1)
& lower_bounded_semilattstr(X1)
& lattice(X1)
& ~ empty_carrier(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice3) ).
fof(commutativity_k4_lattices,axiom,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& meet_semilatt_str(X1)
& meet_commutative(X1)
& ~ empty_carrier(X1) )
=> meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(d13_lattices,axiom,
! [X1] :
( ( meet_semilatt_str(X1)
& ~ empty_carrier(X1) )
=> ( lower_bounded_semilattstr(X1)
<=> ? [X2] :
( ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X3,X2) = X2
& meet(X1,X2,X3) = X2 ) )
& element(X2,the_carrier(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattices) ).
fof(dt_k2_lattices,axiom,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& meet_semilatt_str(X1)
& ~ empty_carrier(X1) )
=> element(meet(X1,X2,X3),the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
fof(c_0_19,plain,
! [X137] :
( X137 = empty_set
| ~ empty(X137) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
fof(c_0_20,plain,
! [X93] :
( empty(esk15_1(X93))
& element(esk15_1(X93),powerset(X93)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_21,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
empty(esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X134,X135,X136] :
( ~ empty(X136)
| ~ element(X135,powerset(X136))
| ~ in(X134,X135) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
cnf(c_0_24,plain,
element(esk15_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
esk15_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_26,plain,
( ~ epred1_0
<=> ! [X1] : ~ empty(X1) ),
introduced(definition) ).
fof(c_0_27,plain,
( ~ epred2_0
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(definition) ).
cnf(c_0_28,plain,
( ~ empty(X3)
| ~ element(X2,powerset(X3))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( ~ empty(X1)
| epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
fof(c_0_32,plain,
! [X1] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> ( ( latt_str(X1)
& complete_latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( X3 = join_of_latt_set(X1,X2)
<=> ( ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_element_smaller(X1,X4,X2)
=> below(X1,X3,X4) ) )
& latt_element_smaller(X1,X3,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d21_lattice3]) ).
cnf(c_0_33,plain,
( ~ epred1_0
| ~ epred2_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]),c_0_27]) ).
cnf(c_0_34,plain,
epred1_0,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_35,plain,
! [X1] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X4,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d17_lattice3]) ).
fof(c_0_36,plain,
! [X37,X38,X39,X40] :
( ( ~ latt_str(X37)
| empty_carrier(X37)
| ~ latt_str(X37)
| ~ complete_latt_str(X37)
| ~ lattice(X37)
| empty_carrier(X37)
| ~ element(X39,the_carrier(X37))
| X39 = join_of_latt_set(X37,X38)
| ~ latt_element_smaller(X37,X39,X38)
| ~ below(X37,X39,esk5_3(X37,X38,X39)) )
& ( ~ latt_str(X37)
| empty_carrier(X37)
| ~ latt_str(X37)
| ~ complete_latt_str(X37)
| ~ lattice(X37)
| empty_carrier(X37)
| ~ element(X39,the_carrier(X37))
| X39 = join_of_latt_set(X37,X38)
| ~ latt_element_smaller(X37,X39,X38)
| latt_element_smaller(X37,esk5_3(X37,X38,X39),X38) )
& ( ~ latt_str(X37)
| empty_carrier(X37)
| ~ latt_str(X37)
| ~ complete_latt_str(X37)
| ~ lattice(X37)
| empty_carrier(X37)
| ~ element(X39,the_carrier(X37))
| X39 = join_of_latt_set(X37,X38)
| ~ latt_element_smaller(X37,X39,X38)
| element(esk5_3(X37,X38,X39),the_carrier(X37)) )
& ( ~ latt_str(X37)
| empty_carrier(X37)
| ~ latt_str(X37)
| ~ complete_latt_str(X37)
| ~ lattice(X37)
| empty_carrier(X37)
| ~ element(X39,the_carrier(X37))
| X39 != join_of_latt_set(X37,X38)
| below(X37,X39,X40)
| ~ latt_element_smaller(X37,X40,X38)
| ~ element(X40,the_carrier(X37)) )
& ( ~ latt_str(X37)
| empty_carrier(X37)
| ~ latt_str(X37)
| ~ complete_latt_str(X37)
| ~ lattice(X37)
| empty_carrier(X37)
| ~ element(X39,the_carrier(X37))
| X39 != join_of_latt_set(X37,X38)
| latt_element_smaller(X37,X39,X38) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])])])]) ).
cnf(c_0_37,plain,
~ epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
fof(c_0_38,plain,
! [X28,X29,X30,X31,X32] :
( ( ~ latt_str(X28)
| empty_carrier(X28)
| ~ element(X29,the_carrier(X28))
| latt_element_smaller(X28,X29,X32)
| ~ below(X28,esk4_3(X28,X29,X32),X29) )
& ( ~ latt_str(X28)
| empty_carrier(X28)
| ~ element(X29,the_carrier(X28))
| latt_element_smaller(X28,X29,X32)
| in(esk4_3(X28,X29,X32),X32) )
& ( ~ latt_str(X28)
| empty_carrier(X28)
| ~ element(X29,the_carrier(X28))
| latt_element_smaller(X28,X29,X32)
| element(esk4_3(X28,X29,X32),the_carrier(X28)) )
& ( ~ latt_str(X28)
| empty_carrier(X28)
| ~ element(X29,the_carrier(X28))
| below(X28,X31,X29)
| ~ in(X31,X30)
| ~ element(X31,the_carrier(X28))
| ~ latt_element_smaller(X28,X29,X30) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])])])])]) ).
cnf(c_0_39,plain,
( ~ latt_str(X2)
| ~ latt_str(X2)
| ~ complete_latt_str(X2)
| ~ lattice(X2)
| ~ element(X4,the_carrier(X2))
| X4 != join_of_latt_set(X2,X3)
| ~ latt_element_smaller(X2,X1,X3)
| ~ element(X1,the_carrier(X2))
| empty_carrier(X2)
| empty_carrier(X2)
| below(X2,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_27]),c_0_37]) ).
cnf(c_0_41,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| in(esk4_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_42,plain,
! [X1,X2] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k15_lattice3]) ).
fof(c_0_43,plain,
! [X138,X139] :
( ~ empty(X139)
| ~ in(X138,X139) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
fof(c_0_44,plain,
! [X1] :
( ( join_semilatt_str(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X3,X2)
& below(X1,X2,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[t26_lattices]) ).
cnf(c_0_45,plain,
( ~ element(X1,the_carrier(X2))
| ~ element(X4,the_carrier(X2))
| ~ latt_element_smaller(X2,X1,X3)
| ~ complete_latt_str(X2)
| ~ lattice(X2)
| ~ latt_str(X2)
| X4 != join_of_latt_set(X2,X3)
| below(X2,X4,X1)
| empty_carrier(X2) ),
inference(cn,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| latt_element_smaller(X1,X2,empty_set) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_47,plain,
! [X47,X48] :
( element(join_of_latt_set(X47,X48),the_carrier(X47))
| ~ latt_str(X47)
| empty_carrier(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
fof(c_0_48,plain,
! [X1] :
( latt_str(X1)
=> ( ( lattice(X1)
& ~ empty_carrier(X1) )
=> ( join_absorbing(X1)
& meet_absorbing(X1)
& meet_associative(X1)
& meet_commutative(X1)
& join_associative(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
cnf(c_0_49,plain,
( ~ empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_50,plain,
! [X1] :
( ( latt_str(X1)
& meet_absorbing(X1)
& meet_commutative(X1)
& ~ empty_carrier(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_51,plain,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& meet_semilatt_str(X1)
& meet_commutative(X1)
& ~ empty_carrier(X1) )
=> meet_commut(X1,X2,X3) = meet(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k4_lattices]) ).
fof(c_0_52,plain,
! [X1] :
( ( meet_semilatt_str(X1)
& ~ empty_carrier(X1) )
=> ( lower_bounded_semilattstr(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( X2 = bottom_of_semilattstr(X1)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X3,X2) = X2
& meet(X1,X2,X3) = X2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d16_lattices]) ).
fof(c_0_53,plain,
! [X1] :
( ( meet_semilatt_str(X1)
& ~ empty_carrier(X1) )
=> element(bottom_of_semilattstr(X1),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattices]) ).
fof(c_0_54,plain,
! [X123,X124,X125] :
( X124 = X125
| ~ below(X123,X125,X124)
| ~ below(X123,X124,X125)
| ~ element(X125,the_carrier(X123))
| ~ element(X124,the_carrier(X123))
| ~ join_semilatt_str(X123)
| ~ join_commutative(X123)
| empty_carrier(X123) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
cnf(c_0_55,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ complete_latt_str(X1)
| X2 != join_of_latt_set(X1,empty_set)
| empty_carrier(X1)
| below(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,plain,
( ~ latt_str(X1)
| element(join_of_latt_set(X1,X2),the_carrier(X1))
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_57,plain,
! [X9] :
( ( ~ latt_str(X9)
| ~ lattice(X9)
| empty_carrier(X9)
| join_absorbing(X9) )
& ( ~ latt_str(X9)
| ~ lattice(X9)
| empty_carrier(X9)
| meet_absorbing(X9) )
& ( ~ latt_str(X9)
| ~ lattice(X9)
| empty_carrier(X9)
| meet_associative(X9) )
& ( ~ latt_str(X9)
| ~ lattice(X9)
| empty_carrier(X9)
| meet_commutative(X9) )
& ( ~ latt_str(X9)
| ~ lattice(X9)
| empty_carrier(X9)
| join_associative(X9) )
& ( ~ latt_str(X9)
| ~ lattice(X9)
| empty_carrier(X9)
| join_commutative(X9) )
& ( ~ latt_str(X9)
| ~ lattice(X9)
| empty_carrier(X9)
| ~ empty_carrier(X9) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])]) ).
fof(c_0_58,plain,
! [X64] :
( ( ~ latt_str(X64)
| join_semilatt_str(X64) )
& ( ~ latt_str(X64)
| meet_semilatt_str(X64) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])])]) ).
cnf(c_0_59,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ empty(X3)
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_41]) ).
fof(c_0_60,negated_conjecture,
~ ! [X1] :
( ( latt_str(X1)
& complete_latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ( bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set)
& latt_str(X1)
& lower_bounded_semilattstr(X1)
& lattice(X1)
& ~ empty_carrier(X1) ) ),
inference(assume_negation,[status(cth)],[t50_lattice3]) ).
fof(c_0_61,plain,
! [X120,X121,X122] :
( below(X120,meet_commut(X120,X121,X122),X121)
| ~ element(X122,the_carrier(X120))
| ~ element(X121,the_carrier(X120))
| ~ latt_str(X120)
| ~ meet_absorbing(X120)
| ~ meet_commutative(X120)
| empty_carrier(X120) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])]) ).
fof(c_0_62,plain,
! [X105,X106,X107] :
( meet_commut(X105,X106,X107) = meet(X105,X106,X107)
| ~ element(X107,the_carrier(X105))
| ~ element(X106,the_carrier(X105))
| ~ meet_semilatt_str(X105)
| ~ meet_commutative(X105)
| empty_carrier(X105) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])]) ).
fof(c_0_63,plain,
! [X24,X25,X26] :
( ( ~ meet_semilatt_str(X24)
| empty_carrier(X24)
| ~ lower_bounded_semilattstr(X24)
| ~ element(X25,the_carrier(X24))
| X25 = bottom_of_semilattstr(X24)
| meet(X24,esk3_2(X24,X25),X25) != X25
| meet(X24,X25,esk3_2(X24,X25)) != X25 )
& ( ~ meet_semilatt_str(X24)
| empty_carrier(X24)
| ~ lower_bounded_semilattstr(X24)
| ~ element(X25,the_carrier(X24))
| X25 = bottom_of_semilattstr(X24)
| element(esk3_2(X24,X25),the_carrier(X24)) )
& ( ~ meet_semilatt_str(X24)
| empty_carrier(X24)
| ~ lower_bounded_semilattstr(X24)
| ~ element(X25,the_carrier(X24))
| X25 != bottom_of_semilattstr(X24)
| ~ element(X26,the_carrier(X24))
| meet(X24,X26,X25) = X25 )
& ( ~ meet_semilatt_str(X24)
| empty_carrier(X24)
| ~ lower_bounded_semilattstr(X24)
| ~ element(X25,the_carrier(X24))
| X25 != bottom_of_semilattstr(X24)
| ~ element(X26,the_carrier(X24))
| meet(X24,X25,X26) = X25 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])])])]) ).
fof(c_0_64,plain,
! [X61] :
( element(bottom_of_semilattstr(X61),the_carrier(X61))
| ~ meet_semilatt_str(X61)
| empty_carrier(X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])]) ).
cnf(c_0_65,plain,
( ~ below(X1,X3,X2)
| ~ below(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1)
| X2 = X3
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| below(X1,join_of_latt_set(X1,empty_set),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_55]),c_0_56]) ).
cnf(c_0_67,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| join_commutative(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_68,plain,
( ~ latt_str(X1)
| join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_69,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ complete_latt_str(X1)
| ~ empty(X4)
| X2 != join_of_latt_set(X1,X4)
| empty_carrier(X1)
| below(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_59]) ).
fof(c_0_70,negated_conjecture,
~ ! [X1] :
( ( latt_str(X1)
& complete_latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ( bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set)
& latt_str(X1)
& lower_bounded_semilattstr(X1)
& lattice(X1)
& ~ empty_carrier(X1) ) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
cnf(c_0_71,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| below(X1,meet_commut(X1,X2,X3),X2)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_72,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1)
| meet_commut(X1,X2,X3) = meet(X1,X2,X3)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_73,plain,
( ~ latt_str(X1)
| meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_74,plain,
( ~ meet_semilatt_str(X1)
| ~ lower_bounded_semilattstr(X1)
| ~ element(X3,the_carrier(X1))
| X3 != bottom_of_semilattstr(X1)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| meet(X1,X2,X3) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_75,plain,
( ~ meet_semilatt_str(X1)
| element(bottom_of_semilattstr(X1),the_carrier(X1))
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_76,plain,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& meet_semilatt_str(X1)
& meet_commutative(X1)
& ~ empty_carrier(X1) )
=> meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k4_lattices]) ).
cnf(c_0_77,plain,
( ~ latt_str(X2)
| ~ lattice(X2)
| ~ element(X1,the_carrier(X2))
| ~ below(X2,X1,join_of_latt_set(X2,empty_set))
| ~ complete_latt_str(X2)
| empty_carrier(X2)
| X1 = join_of_latt_set(X2,empty_set) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_56]),c_0_68]) ).
cnf(c_0_78,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X3,the_carrier(X1))
| ~ complete_latt_str(X1)
| ~ empty(X2)
| empty_carrier(X1)
| below(X1,join_of_latt_set(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_69]),c_0_56]) ).
fof(c_0_79,negated_conjecture,
( ( bottom_of_semilattstr(esk19_0) != join_of_latt_set(esk19_0,empty_set)
| ~ latt_str(esk19_0)
| ~ lower_bounded_semilattstr(esk19_0)
| ~ lattice(esk19_0)
| empty_carrier(esk19_0) )
& latt_str(esk19_0)
& complete_latt_str(esk19_0)
& lattice(esk19_0)
& ~ empty_carrier(esk19_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])])]) ).
cnf(c_0_80,plain,
( ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X3)
| ~ below(X1,X2,esk5_3(X1,X3,X2))
| empty_carrier(X1)
| empty_carrier(X1)
| X2 = join_of_latt_set(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_81,plain,
( ~ latt_str(X1)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| empty_carrier(X1)
| below(X1,meet(X1,X2,X3),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_82,plain,
( ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ lower_bounded_semilattstr(X1)
| empty_carrier(X1)
| meet(X1,X2,bottom_of_semilattstr(X1)) = bottom_of_semilattstr(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_74]),c_0_75]) ).
cnf(c_0_83,plain,
( ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X3,the_carrier(X1))
| ~ latt_element_smaller(X1,X3,X2)
| empty_carrier(X1)
| empty_carrier(X1)
| X3 = join_of_latt_set(X1,X2)
| element(esk5_3(X1,X2,X3),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_84,plain,
! [X16,X17,X18] :
( meet_commut(X16,X17,X18) = meet_commut(X16,X18,X17)
| ~ element(X18,the_carrier(X16))
| ~ element(X17,the_carrier(X16))
| ~ meet_semilatt_str(X16)
| ~ meet_commutative(X16)
| empty_carrier(X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])]) ).
cnf(c_0_85,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ empty(X2)
| empty_carrier(X1)
| join_of_latt_set(X1,X2) = join_of_latt_set(X1,empty_set) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_56]),c_0_56]) ).
cnf(c_0_86,negated_conjecture,
complete_latt_str(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_87,negated_conjecture,
lattice(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_88,negated_conjecture,
latt_str(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,negated_conjecture,
~ empty_carrier(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_90,plain,
( ~ below(X1,X2,esk5_3(X1,X3,X2))
| ~ element(X2,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X3)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| empty_carrier(X1)
| X2 = join_of_latt_set(X1,X3) ),
inference(cn,[status(thm)],[c_0_80]) ).
cnf(c_0_91,plain,
( ~ latt_str(X1)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ element(X2,the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| empty_carrier(X1)
| below(X1,bottom_of_semilattstr(X1),X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_75]),c_0_73]) ).
cnf(c_0_92,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| meet_commutative(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_93,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| meet_absorbing(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_94,plain,
( ~ element(X3,the_carrier(X1))
| ~ latt_element_smaller(X1,X3,X2)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| element(esk5_3(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| X3 = join_of_latt_set(X1,X2) ),
inference(cn,[status(thm)],[c_0_83]) ).
fof(c_0_95,plain,
! [X1] :
( ( meet_semilatt_str(X1)
& ~ empty_carrier(X1) )
=> ( lower_bounded_semilattstr(X1)
<=> ? [X2] :
( ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X3,X2) = X2
& meet(X1,X2,X3) = X2 ) )
& element(X2,the_carrier(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[d13_lattices]) ).
cnf(c_0_96,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1)
| meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
fof(c_0_97,plain,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& meet_semilatt_str(X1)
& ~ empty_carrier(X1) )
=> element(meet(X1,X2,X3),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k2_lattices]) ).
cnf(c_0_98,negated_conjecture,
( ~ empty(X1)
| join_of_latt_set(esk19_0,X1) = join_of_latt_set(esk19_0,empty_set) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_88])]),c_0_89]) ).
cnf(c_0_99,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(bottom_of_semilattstr(X1),the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ latt_element_smaller(X1,bottom_of_semilattstr(X1),X2)
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| bottom_of_semilattstr(X1) = join_of_latt_set(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_93]),c_0_94]) ).
fof(c_0_100,plain,
! [X19,X21,X22] :
( ( ~ meet_semilatt_str(X19)
| empty_carrier(X19)
| lower_bounded_semilattstr(X19)
| ~ element(X22,the_carrier(X19))
| meet(X19,esk2_2(X19,X22),X22) != X22
| meet(X19,X22,esk2_2(X19,X22)) != X22 )
& ( ~ meet_semilatt_str(X19)
| empty_carrier(X19)
| lower_bounded_semilattstr(X19)
| ~ element(X22,the_carrier(X19))
| element(esk2_2(X19,X22),the_carrier(X19)) )
& ( ~ meet_semilatt_str(X19)
| empty_carrier(X19)
| ~ lower_bounded_semilattstr(X19)
| ~ element(X21,the_carrier(X19))
| meet(X19,X21,esk1_1(X19)) = esk1_1(X19) )
& ( ~ meet_semilatt_str(X19)
| empty_carrier(X19)
| ~ lower_bounded_semilattstr(X19)
| ~ element(X21,the_carrier(X19))
| meet(X19,esk1_1(X19),X21) = esk1_1(X19) )
& ( ~ meet_semilatt_str(X19)
| empty_carrier(X19)
| ~ lower_bounded_semilattstr(X19)
| element(esk1_1(X19),the_carrier(X19)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])])])])]) ).
cnf(c_0_101,plain,
( ~ meet_commutative(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_96]) ).
cnf(c_0_102,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(meet(X1,join_of_latt_set(X1,empty_set),X2),the_carrier(X1))
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| meet(X1,join_of_latt_set(X1,empty_set),X2) = join_of_latt_set(X1,empty_set) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_81]),c_0_92]),c_0_93]),c_0_56]) ).
fof(c_0_103,plain,
! [X55,X56,X57] :
( element(meet(X55,X56,X57),the_carrier(X55))
| ~ element(X57,the_carrier(X55))
| ~ element(X56,the_carrier(X55))
| ~ meet_semilatt_str(X55)
| empty_carrier(X55) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])])]) ).
cnf(c_0_104,negated_conjecture,
( ~ empty(X1)
| element(join_of_latt_set(esk19_0,empty_set),the_carrier(esk19_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_98]),c_0_88])]),c_0_89]) ).
cnf(c_0_105,negated_conjecture,
( bottom_of_semilattstr(esk19_0) != join_of_latt_set(esk19_0,empty_set)
| ~ latt_str(esk19_0)
| ~ lower_bounded_semilattstr(esk19_0)
| ~ lattice(esk19_0)
| empty_carrier(esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_106,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(bottom_of_semilattstr(X1),the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_99,c_0_46]) ).
cnf(c_0_107,plain,
( ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| meet(X1,esk2_2(X1,X2),X2) != X2
| meet(X1,X2,esk2_2(X1,X2)) != X2
| empty_carrier(X1)
| lower_bounded_semilattstr(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_108,plain,
( ~ meet_commutative(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| empty_carrier(X1)
| meet(X1,X2,X3) = meet(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_101]) ).
cnf(c_0_109,plain,
( ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| lower_bounded_semilattstr(X1)
| element(esk2_2(X1,X2),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_110,negated_conjecture,
( ~ element(X1,the_carrier(esk19_0))
| ~ element(meet(esk19_0,join_of_latt_set(esk19_0,empty_set),X1),the_carrier(esk19_0))
| meet(esk19_0,join_of_latt_set(esk19_0,empty_set),X1) = join_of_latt_set(esk19_0,empty_set) ),
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_102,c_0_98]),c_0_86]),c_0_87]),c_0_88]),c_0_31])]),c_0_89]) ).
cnf(c_0_111,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| element(meet(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_112,negated_conjecture,
meet_semilatt_str(esk19_0),
inference(spm,[status(thm)],[c_0_73,c_0_88]) ).
cnf(c_0_113,negated_conjecture,
element(join_of_latt_set(esk19_0,empty_set),the_carrier(esk19_0)),
inference(spm,[status(thm)],[c_0_104,c_0_31]) ).
cnf(c_0_114,negated_conjecture,
( ~ lower_bounded_semilattstr(esk19_0)
| bottom_of_semilattstr(esk19_0) != join_of_latt_set(esk19_0,empty_set) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_88]),c_0_87])]),c_0_89]) ).
cnf(c_0_115,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ lower_bounded_semilattstr(X1)
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_75]),c_0_73]) ).
cnf(c_0_116,plain,
( ~ meet_commutative(X1)
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| meet(X1,X2,esk2_2(X1,X2)) != X2
| empty_carrier(X1)
| lower_bounded_semilattstr(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_117,negated_conjecture,
( ~ element(X1,the_carrier(esk19_0))
| meet(esk19_0,join_of_latt_set(esk19_0,empty_set),X1) = join_of_latt_set(esk19_0,empty_set) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_113])]),c_0_89]) ).
cnf(c_0_118,negated_conjecture,
~ lower_bounded_semilattstr(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_114,c_0_115]),c_0_86]),c_0_87]),c_0_88])]),c_0_89]) ).
cnf(c_0_119,negated_conjecture,
( ~ meet_commutative(esk19_0)
| ~ element(esk2_2(esk19_0,join_of_latt_set(esk19_0,empty_set)),the_carrier(esk19_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_112]),c_0_113])]),c_0_118]),c_0_89]) ).
cnf(c_0_120,negated_conjecture,
~ meet_commutative(esk19_0),
inference(sr,[status(thm)],[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_109]),c_0_112]),c_0_113])]),c_0_118]),c_0_89]) ).
cnf(c_0_121,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_120,c_0_92]),c_0_87]),c_0_88])]),c_0_89]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU352+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 06:15:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.44/1.35 % Version: 3.5.1
% 6.44/1.35 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.44/1.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.44/1.35 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.44/1.35 % Starting new_bool_3 with 300s (1) cores
% 6.44/1.35 % Starting new_bool_1 with 300s (1) cores
% 6.44/1.35 % Starting sh5l with 300s (1) cores
% 6.44/1.35 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 189946 completed with status 0
% 6.44/1.35 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 6.44/1.35 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.44/1.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.44/1.35 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.44/1.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.44/1.35 % No SInE strategy applied
% 6.44/1.35 % Search class: FGHSM-FFMM31-MFFFFFNN
% 6.44/1.35 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 6.44/1.35 % Starting SubtermCWHack with 136s (1) cores
% 6.44/1.35 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.44/1.35 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 6.44/1.35 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 6.44/1.35 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 6.44/1.35 % G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with pid 189957 completed with status 0
% 6.44/1.35 % Result found by G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y
% 6.44/1.35 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.44/1.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.44/1.35 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.44/1.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.44/1.35 % No SInE strategy applied
% 6.44/1.35 % Search class: FGHSM-FFMM31-MFFFFFNN
% 6.44/1.35 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 6.44/1.35 % Starting SubtermCWHack with 136s (1) cores
% 6.44/1.35 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.44/1.35 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 6.44/1.35 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 6.44/1.35 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 6.44/1.35 % Preprocessing time : 0.003 s
% 6.44/1.35
% 6.44/1.35 % Proof found!
% 6.44/1.35 % SZS status Theorem
% 6.44/1.35 % SZS output start CNFRefutation
% See solution above
% 6.44/1.35 % Parsed axioms : 73
% 6.44/1.35 % Removed by relevancy pruning/SinE : 0
% 6.44/1.35 % Initial clauses : 116
% 6.44/1.35 % Removed in clause preprocessing : 15
% 6.44/1.35 % Initial clauses in saturation : 101
% 6.44/1.35 % Processed clauses : 6723
% 6.44/1.35 % ...of these trivial : 133
% 6.44/1.35 % ...subsumed : 5558
% 6.44/1.35 % ...remaining for further processing : 1032
% 6.44/1.35 % Other redundant clauses eliminated : 0
% 6.44/1.35 % Clauses deleted for lack of memory : 0
% 6.44/1.35 % Backward-subsumed : 162
% 6.44/1.35 % Backward-rewritten : 8
% 6.44/1.35 % Generated clauses : 20626
% 6.44/1.35 % ...of the previous two non-redundant : 19806
% 6.44/1.35 % ...aggressively subsumed : 0
% 6.44/1.35 % Contextual simplify-reflections : 275
% 6.44/1.35 % Paramodulations : 20580
% 6.44/1.35 % Factorizations : 0
% 6.44/1.35 % NegExts : 0
% 6.44/1.35 % Equation resolutions : 34
% 6.44/1.35 % Disequality decompositions : 0
% 6.44/1.35 % Total rewrite steps : 13737
% 6.44/1.35 % ...of those cached : 13718
% 6.44/1.35 % Propositional unsat checks : 0
% 6.44/1.35 % Propositional check models : 0
% 6.44/1.35 % Propositional check unsatisfiable : 0
% 6.44/1.35 % Propositional clauses : 0
% 6.44/1.35 % Propositional clauses after purity: 0
% 6.44/1.35 % Propositional unsat core size : 0
% 6.44/1.35 % Propositional preprocessing time : 0.000
% 6.44/1.35 % Propositional encoding time : 0.000
% 6.44/1.35 % Propositional solver time : 0.000
% 6.44/1.35 % Success case prop preproc time : 0.000
% 6.44/1.35 % Success case prop encoding time : 0.000
% 6.44/1.35 % Success case prop solver time : 0.000
% 6.44/1.35 % Current number of processed clauses : 855
% 6.44/1.35 % Positive orientable unit clauses : 32
% 6.44/1.35 % Positive unorientable unit clauses: 1
% 6.44/1.35 % Negative unit clauses : 13
% 6.44/1.35 % Non-unit-clauses : 809
% 6.44/1.35 % Current number of unprocessed clauses: 12560
% 6.44/1.35 % ...number of literals in the above : 77730
% 6.44/1.35 % Current number of archived formulas : 0
% 6.44/1.35 % Current number of archived clauses : 171
% 6.44/1.35 % Clause-clause subsumption calls (NU) : 407493
% 6.44/1.35 % Rec. Clause-clause subsumption calls : 125564
% 6.44/1.35 % Non-unit clause-clause subsumptions : 5266
% 6.44/1.35 % Unit Clause-clause subsumption calls : 1921
% 6.44/1.35 % Rewrite failures with RHS unbound : 0
% 6.44/1.35 % BW rewrite match attempts : 17
% 6.44/1.35 % BW rewrite match successes : 8
% 6.44/1.35 % Condensation attempts : 0
% 6.44/1.35 % Condensation successes : 0
% 6.44/1.35 % Termbank termtop insertions : 450267
% 6.44/1.35 % Search garbage collected termcells : 1752
% 6.44/1.35
% 6.44/1.35 % -------------------------------------------------
% 6.44/1.35 % User time : 0.656 s
% 6.44/1.35 % System time : 0.026 s
% 6.44/1.35 % Total time : 0.683 s
% 6.44/1.35 % Maximum resident set size: 3964 pages
% 6.44/1.35
% 6.44/1.35 % -------------------------------------------------
% 6.44/1.35 % User time : 3.745 s
% 6.44/1.35 % System time : 0.125 s
% 6.44/1.35 % Total time : 3.870 s
% 6.44/1.35 % Maximum resident set size: 4864 pages
% 6.44/1.35 % E exiting
%------------------------------------------------------------------------------