%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU351+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:29:05 PM UTC 2026
% Result : Theorem 3.88s 1.06s
% Output : CNFRefutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 109 ( 8 unt; 0 def)
% Number of atoms : 722 ( 59 equ)
% Maximal formula atoms : 50 ( 6 avg)
% Number of connectives : 990 ( 377 ~; 455 |; 93 &)
% ( 13 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 236 ( 2 sgn 92 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t34_lattice3,conjecture,
! [X1] :
( ( latt_str(X1)
& complete_latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( X2 = meet_of_latt_set(X1,X3)
<=> ( ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_set_smaller(X1,X4,X3)
=> below_refl(X1,X4,X2) ) )
& latt_set_smaller(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice3) ).
fof(redefinition_r3_lattices,axiom,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& latt_str(X1)
& join_absorbing(X1)
& meet_absorbing(X1)
& meet_commutative(X1)
& ~ empty_carrier(X1) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(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/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(fraenkel_a_2_2_lattice3,axiom,
! [X1,X2,X3] :
( ( latt_str(X2)
& ~ empty_carrier(X2) )
=> ( in(X1,a_2_2_lattice3(X2,X3))
<=> ? [X4] :
( latt_set_smaller(X2,X4,X3)
& X1 = X4
& element(X4,the_carrier(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_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/sandbox/benchmark/theBenchmark.p',d17_lattice3) ).
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/sandbox/benchmark/theBenchmark.p',d21_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/sandbox/benchmark/theBenchmark.p',dt_k15_lattice3) ).
fof(d22_lattice3,axiom,
! [X1] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] : meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d22_lattice3) ).
fof(d16_lattice3,axiom,
! [X1] :
( ( latt_str(X1)
& ~ empty_carrier(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(dt_k16_lattice3,axiom,
! [X1,X2] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> element(meet_of_latt_set(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_lattice3) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ( latt_str(X1)
& complete_latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( X2 = meet_of_latt_set(X1,X3)
<=> ( ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_set_smaller(X1,X4,X3)
=> below_refl(X1,X4,X2) ) )
& latt_set_smaller(X1,X2,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t34_lattice3]) ).
fof(c_0_11,plain,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& latt_str(X1)
& join_absorbing(X1)
& meet_absorbing(X1)
& meet_commutative(X1)
& ~ empty_carrier(X1) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_lattices]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( latt_str(X1)
& complete_latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( X2 = meet_of_latt_set(X1,X3)
<=> ( ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_set_smaller(X1,X4,X3)
=> below_refl(X1,X4,X2) ) )
& latt_set_smaller(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X10,X11,X12] :
( ( ~ element(X12,the_carrier(X10))
| ~ element(X11,the_carrier(X10))
| ~ latt_str(X10)
| ~ join_absorbing(X10)
| ~ meet_absorbing(X10)
| ~ meet_commutative(X10)
| empty_carrier(X10)
| below_refl(X10,X11,X12)
| ~ below(X10,X11,X12) )
& ( ~ element(X12,the_carrier(X10))
| ~ element(X11,the_carrier(X10))
| ~ latt_str(X10)
| ~ join_absorbing(X10)
| ~ meet_absorbing(X10)
| ~ meet_commutative(X10)
| empty_carrier(X10)
| below(X10,X11,X12)
| ~ below_refl(X10,X11,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_14,negated_conjecture,
! [X9] :
( ( esk2_0 = meet_of_latt_set(esk1_0,esk3_0)
| below_refl(esk1_0,X9,esk2_0)
| ~ latt_set_smaller(esk1_0,X9,esk3_0)
| ~ element(X9,the_carrier(esk1_0)) )
& ( esk2_0 = meet_of_latt_set(esk1_0,esk3_0)
| latt_set_smaller(esk1_0,esk2_0,esk3_0) )
& ( esk2_0 != meet_of_latt_set(esk1_0,esk3_0)
| ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| ~ below_refl(esk1_0,esk4_0,esk2_0) )
& ( esk2_0 != meet_of_latt_set(esk1_0,esk3_0)
| ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| latt_set_smaller(esk1_0,esk4_0,esk3_0) )
& ( esk2_0 != meet_of_latt_set(esk1_0,esk3_0)
| ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| element(esk4_0,the_carrier(esk1_0)) )
& element(esk2_0,the_carrier(esk1_0))
& latt_str(esk1_0)
& complete_latt_str(esk1_0)
& lattice(esk1_0)
& ~ empty_carrier(esk1_0) ),
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_12])])])])])]) ).
fof(c_0_15,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_16,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ below_refl(X1,X2,X3)
| empty_carrier(X1)
| below(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( ~ latt_set_smaller(esk1_0,X1,esk3_0)
| ~ element(X1,the_carrier(esk1_0))
| esk2_0 = meet_of_latt_set(esk1_0,esk3_0)
| below_refl(esk1_0,X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
element(esk2_0,the_carrier(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
latt_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
~ empty_carrier(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X54] :
( ( ~ latt_str(X54)
| ~ lattice(X54)
| empty_carrier(X54)
| join_absorbing(X54) )
& ( ~ latt_str(X54)
| ~ lattice(X54)
| empty_carrier(X54)
| meet_absorbing(X54) )
& ( ~ latt_str(X54)
| ~ lattice(X54)
| empty_carrier(X54)
| meet_associative(X54) )
& ( ~ latt_str(X54)
| ~ lattice(X54)
| empty_carrier(X54)
| meet_commutative(X54) )
& ( ~ latt_str(X54)
| ~ lattice(X54)
| empty_carrier(X54)
| join_associative(X54) )
& ( ~ latt_str(X54)
| ~ lattice(X54)
| empty_carrier(X54)
| join_commutative(X54) )
& ( ~ latt_str(X54)
| ~ lattice(X54)
| empty_carrier(X54)
| ~ empty_carrier(X54) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_22,negated_conjecture,
( ~ meet_commutative(esk1_0)
| ~ meet_absorbing(esk1_0)
| ~ join_absorbing(esk1_0)
| ~ element(X1,the_carrier(esk1_0))
| ~ latt_set_smaller(esk1_0,X1,esk3_0)
| below(esk1_0,X1,esk2_0)
| meet_of_latt_set(esk1_0,esk3_0) = esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_23,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| join_absorbing(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
lattice(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,negated_conjecture,
( ~ meet_commutative(esk1_0)
| ~ meet_absorbing(esk1_0)
| ~ element(X1,the_carrier(esk1_0))
| ~ latt_set_smaller(esk1_0,X1,esk3_0)
| below(esk1_0,X1,esk2_0)
| meet_of_latt_set(esk1_0,esk3_0) = esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_19])]),c_0_20]) ).
cnf(c_0_26,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| meet_absorbing(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X1,X2,X3] :
( ( latt_str(X2)
& ~ empty_carrier(X2) )
=> ( in(X1,a_2_2_lattice3(X2,X3))
<=> ? [X4] :
( latt_set_smaller(X2,X4,X3)
& X1 = X4
& element(X4,the_carrier(X2)) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_2_lattice3]) ).
fof(c_0_28,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_29,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_30,negated_conjecture,
( ~ meet_commutative(esk1_0)
| ~ element(X1,the_carrier(esk1_0))
| ~ latt_set_smaller(esk1_0,X1,esk3_0)
| below(esk1_0,X1,esk2_0)
| meet_of_latt_set(esk1_0,esk3_0) = esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24]),c_0_19])]),c_0_20]) ).
cnf(c_0_31,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| meet_commutative(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_32,plain,
! [X22,X23,X24,X26,X27] :
( ( ~ latt_str(X23)
| empty_carrier(X23)
| in(X22,a_2_2_lattice3(X23,X26))
| ~ latt_set_smaller(X23,X27,X26)
| X22 != X27
| ~ element(X27,the_carrier(X23)) )
& ( ~ latt_str(X23)
| empty_carrier(X23)
| ~ in(X22,a_2_2_lattice3(X23,X24))
| latt_set_smaller(X23,esk6_3(X22,X23,X24),X24) )
& ( ~ latt_str(X23)
| empty_carrier(X23)
| ~ in(X22,a_2_2_lattice3(X23,X24))
| X22 = esk6_3(X22,X23,X24) )
& ( ~ latt_str(X23)
| empty_carrier(X23)
| ~ in(X22,a_2_2_lattice3(X23,X24))
| element(esk6_3(X22,X23,X24),the_carrier(X23)) ) ),
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_27])])])])])])]) ).
fof(c_0_33,plain,
! [X57,X58,X59,X60,X61] :
( ( ~ latt_str(X57)
| empty_carrier(X57)
| ~ element(X58,the_carrier(X57))
| latt_element_smaller(X57,X58,X61)
| ~ below(X57,esk12_3(X57,X58,X61),X58) )
& ( ~ latt_str(X57)
| empty_carrier(X57)
| ~ element(X58,the_carrier(X57))
| latt_element_smaller(X57,X58,X61)
| in(esk12_3(X57,X58,X61),X61) )
& ( ~ latt_str(X57)
| empty_carrier(X57)
| ~ element(X58,the_carrier(X57))
| latt_element_smaller(X57,X58,X61)
| element(esk12_3(X57,X58,X61),the_carrier(X57)) )
& ( ~ latt_str(X57)
| empty_carrier(X57)
| ~ element(X58,the_carrier(X57))
| below(X57,X60,X58)
| ~ in(X60,X59)
| ~ element(X60,the_carrier(X57))
| ~ latt_element_smaller(X57,X58,X59) ) ),
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_28])])])])])])]) ).
fof(c_0_34,plain,
! [X49,X50,X51,X52] :
( ( ~ latt_str(X49)
| empty_carrier(X49)
| ~ latt_str(X49)
| ~ complete_latt_str(X49)
| ~ lattice(X49)
| empty_carrier(X49)
| ~ element(X51,the_carrier(X49))
| X51 = join_of_latt_set(X49,X50)
| ~ latt_element_smaller(X49,X51,X50)
| ~ below(X49,X51,esk10_3(X49,X50,X51)) )
& ( ~ latt_str(X49)
| empty_carrier(X49)
| ~ latt_str(X49)
| ~ complete_latt_str(X49)
| ~ lattice(X49)
| empty_carrier(X49)
| ~ element(X51,the_carrier(X49))
| X51 = join_of_latt_set(X49,X50)
| ~ latt_element_smaller(X49,X51,X50)
| latt_element_smaller(X49,esk10_3(X49,X50,X51),X50) )
& ( ~ latt_str(X49)
| empty_carrier(X49)
| ~ latt_str(X49)
| ~ complete_latt_str(X49)
| ~ lattice(X49)
| empty_carrier(X49)
| ~ element(X51,the_carrier(X49))
| X51 = join_of_latt_set(X49,X50)
| ~ latt_element_smaller(X49,X51,X50)
| element(esk10_3(X49,X50,X51),the_carrier(X49)) )
& ( ~ latt_str(X49)
| empty_carrier(X49)
| ~ latt_str(X49)
| ~ complete_latt_str(X49)
| ~ lattice(X49)
| empty_carrier(X49)
| ~ element(X51,the_carrier(X49))
| X51 != join_of_latt_set(X49,X50)
| below(X49,X51,X52)
| ~ latt_element_smaller(X49,X52,X50)
| ~ element(X52,the_carrier(X49)) )
& ( ~ latt_str(X49)
| empty_carrier(X49)
| ~ latt_str(X49)
| ~ complete_latt_str(X49)
| ~ lattice(X49)
| empty_carrier(X49)
| ~ element(X51,the_carrier(X49))
| X51 != join_of_latt_set(X49,X50)
| latt_element_smaller(X49,X51,X50) ) ),
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_29])])])])])]) ).
cnf(c_0_35,negated_conjecture,
( ~ element(X1,the_carrier(esk1_0))
| ~ latt_set_smaller(esk1_0,X1,esk3_0)
| below(esk1_0,X1,esk2_0)
| meet_of_latt_set(esk1_0,esk3_0) = esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24]),c_0_19])]),c_0_20]) ).
cnf(c_0_36,plain,
( ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3))
| empty_carrier(X1)
| latt_set_smaller(X1,esk6_3(X2,X1,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
( ~ latt_str(X2)
| ~ in(X1,a_2_2_lattice3(X2,X3))
| empty_carrier(X2)
| X1 = esk6_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| in(esk12_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,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)
| latt_element_smaller(X1,esk10_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,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(esk10_3(X1,X2,X3),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( ~ in(X1,a_2_2_lattice3(esk1_0,esk3_0))
| ~ element(esk6_3(X1,esk1_0,esk3_0),the_carrier(esk1_0))
| below(esk1_0,esk6_3(X1,esk1_0,esk3_0),esk2_0)
| meet_of_latt_set(esk1_0,esk3_0) = esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_19])]),c_0_20]) ).
cnf(c_0_42,plain,
( ~ latt_str(X1)
| ~ latt_str(X3)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X3)
| empty_carrier(X1)
| latt_element_smaller(X1,X2,a_2_2_lattice3(X3,X4))
| esk6_3(esk12_3(X1,X2,a_2_2_lattice3(X3,X4)),X3,X4) = esk12_3(X1,X2,a_2_2_lattice3(X3,X4)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_43,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]) ).
cnf(c_0_44,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,esk10_3(X1,X3,X2))
| empty_carrier(X1)
| empty_carrier(X1)
| X2 = join_of_latt_set(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ in(X4,X3)
| ~ element(X4,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| below(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_46,plain,
( ~ element(X3,the_carrier(X1))
| ~ latt_element_smaller(X1,X3,X2)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| latt_element_smaller(X1,esk10_3(X1,X2,X3),X2)
| empty_carrier(X1)
| X3 = join_of_latt_set(X1,X2) ),
inference(cn,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
( ~ element(X3,the_carrier(X1))
| ~ latt_element_smaller(X1,X3,X2)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| element(esk10_3(X1,X2,X3),the_carrier(X1))
| empty_carrier(X1)
| X3 = join_of_latt_set(X1,X2) ),
inference(cn,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ below(X1,esk12_3(X1,X2,X3),X2)
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_49,negated_conjecture,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(esk12_3(X1,X2,a_2_2_lattice3(esk1_0,esk3_0)),the_carrier(esk1_0))
| empty_carrier(X1)
| below(esk1_0,esk12_3(X1,X2,a_2_2_lattice3(esk1_0,esk3_0)),esk2_0)
| latt_element_smaller(X1,X2,a_2_2_lattice3(esk1_0,esk3_0))
| meet_of_latt_set(esk1_0,esk3_0) = esk2_0 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_19])]),c_0_20]),c_0_38]) ).
cnf(c_0_50,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_34]) ).
fof(c_0_51,plain,
! [X34,X35] :
( element(join_of_latt_set(X34,X35),the_carrier(X34))
| ~ latt_str(X34)
| empty_carrier(X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])]) ).
fof(c_0_52,plain,
! [X1] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] : meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2)) ),
inference(fof_simplification,[status(thm)],[d22_lattice3]) ).
cnf(c_0_53,plain,
( ~ below(X1,X2,esk10_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_44]) ).
cnf(c_0_54,plain,
( ~ in(X4,X3)
| ~ latt_str(X2)
| ~ lattice(X2)
| ~ element(X1,the_carrier(X2))
| ~ element(X4,the_carrier(X2))
| ~ latt_element_smaller(X2,X1,X3)
| ~ complete_latt_str(X2)
| empty_carrier(X2)
| below(X2,X4,esk10_3(X2,X3,X1))
| X1 = join_of_latt_set(X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_55,negated_conjecture,
( ~ element(esk12_3(esk1_0,esk2_0,a_2_2_lattice3(esk1_0,esk3_0)),the_carrier(esk1_0))
| latt_element_smaller(esk1_0,esk2_0,a_2_2_lattice3(esk1_0,esk3_0))
| meet_of_latt_set(esk1_0,esk3_0) = esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_56,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| element(esk12_3(X1,X2,X3),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_57,plain,
! [X1] :
( ( latt_str(X1)
& ~ empty_carrier(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]) ).
cnf(c_0_58,plain,
( ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| X2 != join_of_latt_set(X1,X3)
| empty_carrier(X1)
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_59,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_50]) ).
cnf(c_0_60,plain,
( ~ latt_str(X1)
| element(join_of_latt_set(X1,X2),the_carrier(X1))
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_61,plain,
! [X45,X46] :
( meet_of_latt_set(X45,X46) = join_of_latt_set(X45,a_2_2_lattice3(X45,X46))
| ~ latt_str(X45)
| empty_carrier(X45) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
fof(c_0_62,plain,
! [X1,X2] :
( ( latt_str(X1)
& ~ empty_carrier(X1) )
=> element(meet_of_latt_set(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k16_lattice3]) ).
cnf(c_0_63,plain,
( ~ in(X1,X3)
| ~ latt_str(X2)
| ~ lattice(X2)
| ~ element(X1,the_carrier(X2))
| ~ latt_element_smaller(X2,X1,X3)
| ~ complete_latt_str(X2)
| empty_carrier(X2)
| X1 = join_of_latt_set(X2,X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_64,negated_conjecture,
( latt_element_smaller(esk1_0,esk2_0,a_2_2_lattice3(esk1_0,esk3_0))
| meet_of_latt_set(esk1_0,esk3_0) = esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_65,negated_conjecture,
complete_latt_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_66,plain,
! [X16,X17,X18,X19,X20] :
( ( ~ latt_str(X16)
| empty_carrier(X16)
| ~ element(X17,the_carrier(X16))
| latt_set_smaller(X16,X17,X20)
| ~ below(X16,X17,esk5_3(X16,X17,X20)) )
& ( ~ latt_str(X16)
| empty_carrier(X16)
| ~ element(X17,the_carrier(X16))
| latt_set_smaller(X16,X17,X20)
| in(esk5_3(X16,X17,X20),X20) )
& ( ~ latt_str(X16)
| empty_carrier(X16)
| ~ element(X17,the_carrier(X16))
| latt_set_smaller(X16,X17,X20)
| element(esk5_3(X16,X17,X20),the_carrier(X16)) )
& ( ~ latt_str(X16)
| empty_carrier(X16)
| ~ element(X17,the_carrier(X16))
| below(X16,X17,X19)
| ~ in(X19,X18)
| ~ element(X19,the_carrier(X16))
| ~ latt_set_smaller(X16,X17,X18) ) ),
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_57])])])])])])]) ).
cnf(c_0_67,negated_conjecture,
( esk2_0 != meet_of_latt_set(esk1_0,esk3_0)
| ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| ~ below_refl(esk1_0,esk4_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_68,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ below(X1,X2,X3)
| empty_carrier(X1)
| below_refl(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_69,negated_conjecture,
( esk2_0 != meet_of_latt_set(esk1_0,esk3_0)
| ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| element(esk4_0,the_carrier(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_70,plain,
( ~ element(X2,the_carrier(X1))
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| X2 != join_of_latt_set(X1,X3)
| latt_element_smaller(X1,X2,X3)
| empty_carrier(X1) ),
inference(cn,[status(thm)],[c_0_58]) ).
cnf(c_0_71,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X3,the_carrier(X1))
| ~ latt_element_smaller(X1,X3,X2)
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| below(X1,join_of_latt_set(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_60]) ).
cnf(c_0_72,plain,
( ~ latt_str(X1)
| meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2))
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_73,plain,
! [X36,X37] :
( element(meet_of_latt_set(X36,X37),the_carrier(X36))
| ~ latt_str(X36)
| empty_carrier(X36) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])]) ).
cnf(c_0_74,negated_conjecture,
( ~ in(esk2_0,a_2_2_lattice3(esk1_0,esk3_0))
| meet_of_latt_set(esk1_0,esk3_0) = esk2_0
| join_of_latt_set(esk1_0,a_2_2_lattice3(esk1_0,esk3_0)) = esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_18]),c_0_24]),c_0_19])]),c_0_20]) ).
cnf(c_0_75,plain,
( ~ latt_str(X2)
| ~ latt_set_smaller(X2,X1,X4)
| X3 != X1
| ~ element(X1,the_carrier(X2))
| empty_carrier(X2)
| in(X3,a_2_2_lattice3(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_76,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ in(X4,X3)
| ~ element(X4,the_carrier(X1))
| ~ latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| below(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,plain,
( ~ latt_str(X2)
| ~ in(X1,a_2_2_lattice3(X2,X3))
| empty_carrier(X2)
| element(esk6_3(X1,X2,X3),the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_78,negated_conjecture,
( ~ meet_commutative(esk1_0)
| ~ meet_absorbing(esk1_0)
| ~ join_absorbing(esk1_0)
| ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| ~ below(esk1_0,esk4_0,esk2_0)
| meet_of_latt_set(esk1_0,esk3_0) != esk2_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_67,c_0_68]),c_0_18]),c_0_19])]),c_0_20]),c_0_69]) ).
cnf(c_0_79,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| latt_element_smaller(X1,join_of_latt_set(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_70]),c_0_60]) ).
cnf(c_0_80,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ below(X1,X2,esk5_3(X1,X2,X3))
| empty_carrier(X1)
| latt_set_smaller(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_81,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X3,the_carrier(X1))
| ~ latt_element_smaller(X1,X3,a_2_2_lattice3(X1,X2))
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| below(X1,meet_of_latt_set(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_82,plain,
( ~ latt_str(X1)
| element(meet_of_latt_set(X1,X2),the_carrier(X1))
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_83,negated_conjecture,
( ~ in(esk2_0,a_2_2_lattice3(esk1_0,esk3_0))
| meet_of_latt_set(esk1_0,esk3_0) = esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_74]),c_0_19])]),c_0_20]) ).
cnf(c_0_84,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_set_smaller(X1,X2,X3)
| in(X2,a_2_2_lattice3(X1,X3))
| empty_carrier(X1) ),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_85,negated_conjecture,
( esk2_0 = meet_of_latt_set(esk1_0,esk3_0)
| latt_set_smaller(esk1_0,esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_86,plain,
( ~ in(X4,X3)
| ~ in(X2,a_2_2_lattice3(X1,X3))
| ~ latt_str(X1)
| ~ element(X4,the_carrier(X1))
| empty_carrier(X1)
| below(X1,esk6_3(X2,X1,X3),X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_36]),c_0_77]) ).
cnf(c_0_87,negated_conjecture,
( ~ meet_commutative(esk1_0)
| ~ meet_absorbing(esk1_0)
| ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| ~ below(esk1_0,esk4_0,esk2_0)
| meet_of_latt_set(esk1_0,esk3_0) != esk2_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_23]),c_0_24]),c_0_19])]),c_0_20]) ).
cnf(c_0_88,plain,
( ~ in(X2,X3)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| below(X1,X2,join_of_latt_set(X1,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_79]),c_0_60]) ).
cnf(c_0_89,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(esk5_3(X1,meet_of_latt_set(X1,X2),X3),the_carrier(X1))
| ~ latt_element_smaller(X1,esk5_3(X1,meet_of_latt_set(X1,X2),X3),a_2_2_lattice3(X1,X2))
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| latt_set_smaller(X1,meet_of_latt_set(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_90,negated_conjecture,
meet_of_latt_set(esk1_0,esk3_0) = esk2_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_83,c_0_84]),c_0_18]),c_0_19])]),c_0_20]),c_0_85]) ).
cnf(c_0_91,plain,
( ~ in(X5,X4)
| ~ latt_str(X1)
| ~ latt_str(X3)
| ~ element(X2,the_carrier(X1))
| ~ element(X5,the_carrier(X3))
| empty_carrier(X3)
| empty_carrier(X1)
| below(X3,esk12_3(X1,X2,a_2_2_lattice3(X3,X4)),X5)
| latt_element_smaller(X1,X2,a_2_2_lattice3(X3,X4)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_42]),c_0_38]) ).
cnf(c_0_92,negated_conjecture,
( ~ meet_commutative(esk1_0)
| ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| ~ below(esk1_0,esk4_0,esk2_0)
| meet_of_latt_set(esk1_0,esk3_0) != esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_26]),c_0_24]),c_0_19])]),c_0_20]) ).
cnf(c_0_93,plain,
( ~ in(X2,a_2_2_lattice3(X1,X3))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ complete_latt_str(X1)
| empty_carrier(X1)
| below(X1,X2,meet_of_latt_set(X1,X3)) ),
inference(spm,[status(thm)],[c_0_88,c_0_72]) ).
cnf(c_0_94,negated_conjecture,
( ~ element(esk5_3(esk1_0,esk2_0,X1),the_carrier(esk1_0))
| ~ latt_element_smaller(esk1_0,esk5_3(esk1_0,esk2_0,X1),a_2_2_lattice3(esk1_0,esk3_0))
| latt_set_smaller(esk1_0,esk2_0,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_89,c_0_90]),c_0_65]),c_0_24]),c_0_19])]),c_0_20]) ).
cnf(c_0_95,plain,
( ~ in(X2,X3)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| latt_element_smaller(X1,X2,a_2_2_lattice3(X1,X3)) ),
inference(spm,[status(thm)],[c_0_48,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| ~ below(esk1_0,esk4_0,esk2_0)
| meet_of_latt_set(esk1_0,esk3_0) != esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_31]),c_0_24]),c_0_19])]),c_0_20]) ).
cnf(c_0_97,negated_conjecture,
( ~ in(X1,a_2_2_lattice3(esk1_0,esk3_0))
| ~ element(X1,the_carrier(esk1_0))
| below(esk1_0,X1,esk2_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_90]),c_0_65]),c_0_24]),c_0_19])]),c_0_20]) ).
cnf(c_0_98,negated_conjecture,
( esk2_0 != meet_of_latt_set(esk1_0,esk3_0)
| ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| latt_set_smaller(esk1_0,esk4_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_99,negated_conjecture,
( ~ in(esk5_3(esk1_0,esk2_0,X1),esk3_0)
| ~ element(esk5_3(esk1_0,esk2_0,X1),the_carrier(esk1_0))
| latt_set_smaller(esk1_0,esk2_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_19])]),c_0_20]) ).
cnf(c_0_100,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| latt_set_smaller(X1,X2,X3)
| element(esk5_3(X1,X2,X3),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_101,negated_conjecture,
( ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| ~ below(esk1_0,esk4_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_90])]) ).
cnf(c_0_102,negated_conjecture,
( ~ element(X1,the_carrier(esk1_0))
| ~ latt_set_smaller(esk1_0,X1,esk3_0)
| below(esk1_0,X1,esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_84]),c_0_19])]),c_0_20]) ).
cnf(c_0_103,negated_conjecture,
( ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| element(esk4_0,the_carrier(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_90])]) ).
cnf(c_0_104,negated_conjecture,
( ~ latt_set_smaller(esk1_0,esk2_0,esk3_0)
| latt_set_smaller(esk1_0,esk4_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_90])]) ).
cnf(c_0_105,negated_conjecture,
( ~ in(esk5_3(esk1_0,esk2_0,X1),esk3_0)
| latt_set_smaller(esk1_0,esk2_0,X1) ),
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_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_106,plain,
( ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| latt_set_smaller(X1,X2,X3)
| in(esk5_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_107,negated_conjecture,
~ latt_set_smaller(esk1_0,esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_104]) ).
cnf(c_0_108,negated_conjecture,
$false,
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_105,c_0_106]),c_0_18]),c_0_19])]),c_0_107]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU351+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n014.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 06:14:20 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.51 Running first-order theorem proving
% 0.25/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.88/1.06 % Version: 3.5.1
% 3.88/1.06 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.88/1.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.88/1.06 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.88/1.06 % Starting new_bool_3 with 300s (1) cores
% 3.88/1.06 % Starting new_bool_1 with 300s (1) cores
% 3.88/1.06 % Starting sh5l with 300s (1) cores
% 3.88/1.06 % sh5l with pid 3312691 completed with status 0
% 3.88/1.06 % Result found by sh5l
% 3.88/1.06 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.88/1.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.88/1.06 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.88/1.06 % Starting new_bool_3 with 300s (1) cores
% 3.88/1.06 % Starting new_bool_1 with 300s (1) cores
% 3.88/1.06 % Starting sh5l with 300s (1) cores
% 3.88/1.06 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 3.88/1.06 % SinE strategy is gf500_gu_R04_F100_L20000
% 3.88/1.06 % Search class: FGHSF-FFMM32-SFFFFFNN
% 3.88/1.06 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.88/1.06 % Starting SubtermCWHack with 28s (1) cores
% 3.88/1.06 % SubtermCWHack with pid 3312692 completed with status 0
% 3.88/1.06 % Result found by SubtermCWHack
% 3.88/1.06 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.88/1.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.88/1.06 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.88/1.06 % Starting new_bool_3 with 300s (1) cores
% 3.88/1.06 % Starting new_bool_1 with 300s (1) cores
% 3.88/1.06 % Starting sh5l with 300s (1) cores
% 3.88/1.06 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 3.88/1.06 % SinE strategy is gf500_gu_R04_F100_L20000
% 3.88/1.06 % Search class: FGHSF-FFMM32-SFFFFFNN
% 3.88/1.06 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.88/1.06 % Starting SubtermCWHack with 28s (1) cores
% 3.88/1.06 % Preprocessing time : 0.003 s
% 3.88/1.06
% 3.88/1.06 % Proof found!
% 3.88/1.06 % SZS status Theorem
% 3.88/1.06 % SZS output start CNFRefutation
% See solution above
% 3.88/1.06 % Parsed axioms : 37
% 3.88/1.06 % Removed by relevancy pruning/SinE : 4
% 3.88/1.06 % Initial clauses : 69
% 3.88/1.06 % Removed in clause preprocessing : 2
% 3.88/1.06 % Initial clauses in saturation : 67
% 3.88/1.06 % Processed clauses : 2811
% 3.88/1.06 % ...of these trivial : 9
% 3.88/1.06 % ...subsumed : 1664
% 3.88/1.06 % ...remaining for further processing : 1138
% 3.88/1.06 % Other redundant clauses eliminated : 4
% 3.88/1.06 % Clauses deleted for lack of memory : 0
% 3.88/1.06 % Backward-subsumed : 125
% 3.88/1.06 % Backward-rewritten : 58
% 3.88/1.06 % Generated clauses : 6797
% 3.88/1.06 % ...of the previous two non-redundant : 6392
% 3.88/1.06 % ...aggressively subsumed : 0
% 3.88/1.06 % Contextual simplify-reflections : 194
% 3.88/1.06 % Paramodulations : 6741
% 3.88/1.06 % Factorizations : 44
% 3.88/1.06 % NegExts : 0
% 3.88/1.06 % Equation resolutions : 4
% 3.88/1.06 % Disequality decompositions : 0
% 3.88/1.06 % Total rewrite steps : 5913
% 3.88/1.06 % ...of those cached : 5879
% 3.88/1.06 % Propositional unsat checks : 0
% 3.88/1.06 % Propositional check models : 0
% 3.88/1.06 % Propositional check unsatisfiable : 0
% 3.88/1.06 % Propositional clauses : 0
% 3.88/1.06 % Propositional clauses after purity: 0
% 3.88/1.06 % Propositional unsat core size : 0
% 3.88/1.06 % Propositional preprocessing time : 0.000
% 3.88/1.06 % Propositional encoding time : 0.000
% 3.88/1.06 % Propositional solver time : 0.000
% 3.88/1.06 % Success case prop preproc time : 0.000
% 3.88/1.06 % Success case prop encoding time : 0.000
% 3.88/1.06 % Success case prop solver time : 0.000
% 3.88/1.06 % Current number of processed clauses : 943
% 3.88/1.06 % Positive orientable unit clauses : 35
% 3.88/1.06 % Positive unorientable unit clauses: 0
% 3.88/1.06 % Negative unit clauses : 11
% 3.88/1.06 % Non-unit-clauses : 897
% 3.88/1.06 % Current number of unprocessed clauses: 3463
% 3.88/1.06 % ...number of literals in the above : 20081
% 3.88/1.06 % Current number of archived formulas : 0
% 3.88/1.06 % Current number of archived clauses : 191
% 3.88/1.06 % Clause-clause subsumption calls (NU) : 94363
% 3.88/1.06 % Rec. Clause-clause subsumption calls : 20221
% 3.88/1.06 % Non-unit clause-clause subsumptions : 1823
% 3.88/1.06 % Unit Clause-clause subsumption calls : 1635
% 3.88/1.06 % Rewrite failures with RHS unbound : 0
% 3.88/1.06 % BW rewrite match attempts : 29
% 3.88/1.06 % BW rewrite match successes : 11
% 3.88/1.06 % Condensation attempts : 0
% 3.88/1.06 % Condensation successes : 0
% 3.88/1.06 % Termbank termtop insertions : 204045
% 3.88/1.06 % Search garbage collected termcells : 1343
% 3.88/1.06
% 3.88/1.06 % -------------------------------------------------
% 3.88/1.06 % User time : 0.498 s
% 3.88/1.06 % System time : 0.019 s
% 3.88/1.06 % Total time : 0.517 s
% 3.88/1.06 % Maximum resident set size: 3928 pages
% 3.88/1.06
% 3.88/1.06 % -------------------------------------------------
% 3.88/1.06 % User time : 0.502 s
% 3.88/1.06 % System time : 0.025 s
% 3.88/1.06 % Total time : 0.527 s
% 3.88/1.06 % Maximum resident set size: 4864 pages
% 3.88/1.06 % E exiting
%------------------------------------------------------------------------------