TSTP Solution File: SEU351+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SEU351+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n018.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:31:45 EDT 2023
% Result : Theorem 13.72s 2.24s
% Output : CNFRefutation 13.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 117 ( 9 unt; 0 def)
% Number of atoms : 816 ( 67 equ)
% Maximal formula atoms : 50 ( 6 avg)
% Number of connectives : 1143 ( 444 ~; 537 |; 100 &)
% ( 14 <=>; 48 =>; 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 : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 270 ( 1 sgn; 93 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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/tmp/tmp.bJqMUusQFE/E---3.1_20842.p',d17_lattice3) ).
fof(redefinition_r3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.bJqMUusQFE/E---3.1_20842.p',redefinition_r3_lattices) ).
fof(fraenkel_a_2_2_lattice3,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& latt_str(X2) )
=> ( in(X1,a_2_2_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bJqMUusQFE/E---3.1_20842.p',fraenkel_a_2_2_lattice3) ).
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/tmp/tmp.bJqMUusQFE/E---3.1_20842.p',d21_lattice3) ).
fof(t34_lattice3,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( X2 = meet_of_latt_set(X1,X3)
<=> ( latt_set_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_set_smaller(X1,X4,X3)
=> below_refl(X1,X4,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bJqMUusQFE/E---3.1_20842.p',t34_lattice3) ).
fof(d22_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] : meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.bJqMUusQFE/E---3.1_20842.p',d22_lattice3) ).
fof(cc1_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bJqMUusQFE/E---3.1_20842.p',cc1_lattices) ).
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/tmp/tmp.bJqMUusQFE/E---3.1_20842.p',dt_k15_lattice3) ).
fof(fraenkel_a_2_3_lattice3,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& complete_latt_str(X2)
& latt_str(X2) )
=> ( in(X1,a_2_3_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bJqMUusQFE/E---3.1_20842.p',fraenkel_a_2_3_lattice3) ).
fof(d16_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bJqMUusQFE/E---3.1_20842.p',d16_lattice3) ).
fof(c_0_10,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]) ).
fof(c_0_11,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_lattices]) ).
fof(c_0_12,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& latt_str(X2) )
=> ( in(X1,a_2_2_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_2_lattice3]) ).
fof(c_0_13,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]) ).
fof(c_0_14,plain,
! [X15,X16,X17,X18,X19] :
( ( ~ latt_element_smaller(X15,X16,X17)
| ~ element(X18,the_carrier(X15))
| ~ in(X18,X17)
| below(X15,X18,X16)
| ~ element(X16,the_carrier(X15))
| empty_carrier(X15)
| ~ latt_str(X15) )
& ( element(esk2_3(X15,X16,X19),the_carrier(X15))
| latt_element_smaller(X15,X16,X19)
| ~ element(X16,the_carrier(X15))
| empty_carrier(X15)
| ~ latt_str(X15) )
& ( in(esk2_3(X15,X16,X19),X19)
| latt_element_smaller(X15,X16,X19)
| ~ element(X16,the_carrier(X15))
| empty_carrier(X15)
| ~ latt_str(X15) )
& ( ~ below(X15,esk2_3(X15,X16,X19),X16)
| latt_element_smaller(X15,X16,X19)
| ~ element(X16,the_carrier(X15))
| empty_carrier(X15)
| ~ latt_str(X15) ) ),
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_10])])])])])]) ).
fof(c_0_15,plain,
! [X57,X58,X59] :
( ( ~ below_refl(X57,X58,X59)
| below(X57,X58,X59)
| empty_carrier(X57)
| ~ meet_commutative(X57)
| ~ meet_absorbing(X57)
| ~ join_absorbing(X57)
| ~ latt_str(X57)
| ~ element(X58,the_carrier(X57))
| ~ element(X59,the_carrier(X57)) )
& ( ~ below(X57,X58,X59)
| below_refl(X57,X58,X59)
| empty_carrier(X57)
| ~ meet_commutative(X57)
| ~ meet_absorbing(X57)
| ~ join_absorbing(X57)
| ~ latt_str(X57)
| ~ element(X58,the_carrier(X57))
| ~ element(X59,the_carrier(X57)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( X2 = meet_of_latt_set(X1,X3)
<=> ( latt_set_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_set_smaller(X1,X4,X3)
=> below_refl(X1,X4,X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t34_lattice3])]) ).
fof(c_0_17,plain,
! [X42,X43,X44,X46,X47] :
( ( element(esk9_3(X42,X43,X44),the_carrier(X43))
| ~ in(X42,a_2_2_lattice3(X43,X44))
| empty_carrier(X43)
| ~ latt_str(X43) )
& ( X42 = esk9_3(X42,X43,X44)
| ~ in(X42,a_2_2_lattice3(X43,X44))
| empty_carrier(X43)
| ~ latt_str(X43) )
& ( latt_set_smaller(X43,esk9_3(X42,X43,X44),X44)
| ~ in(X42,a_2_2_lattice3(X43,X44))
| empty_carrier(X43)
| ~ latt_str(X43) )
& ( ~ element(X47,the_carrier(X43))
| X42 != X47
| ~ latt_set_smaller(X43,X47,X46)
| in(X42,a_2_2_lattice3(X43,X46))
| empty_carrier(X43)
| ~ latt_str(X43) ) ),
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_12])])])])])]) ).
fof(c_0_18,plain,
! [X21,X22,X23,X24] :
( ( latt_element_smaller(X21,X23,X22)
| X23 != join_of_latt_set(X21,X22)
| ~ element(X23,the_carrier(X21))
| empty_carrier(X21)
| ~ lattice(X21)
| ~ complete_latt_str(X21)
| ~ latt_str(X21)
| empty_carrier(X21)
| ~ latt_str(X21) )
& ( ~ element(X24,the_carrier(X21))
| ~ latt_element_smaller(X21,X24,X22)
| below(X21,X23,X24)
| X23 != join_of_latt_set(X21,X22)
| ~ element(X23,the_carrier(X21))
| empty_carrier(X21)
| ~ lattice(X21)
| ~ complete_latt_str(X21)
| ~ latt_str(X21)
| empty_carrier(X21)
| ~ latt_str(X21) )
& ( element(esk3_3(X21,X22,X23),the_carrier(X21))
| ~ latt_element_smaller(X21,X23,X22)
| X23 = join_of_latt_set(X21,X22)
| ~ element(X23,the_carrier(X21))
| empty_carrier(X21)
| ~ lattice(X21)
| ~ complete_latt_str(X21)
| ~ latt_str(X21)
| empty_carrier(X21)
| ~ latt_str(X21) )
& ( latt_element_smaller(X21,esk3_3(X21,X22,X23),X22)
| ~ latt_element_smaller(X21,X23,X22)
| X23 = join_of_latt_set(X21,X22)
| ~ element(X23,the_carrier(X21))
| empty_carrier(X21)
| ~ lattice(X21)
| ~ complete_latt_str(X21)
| ~ latt_str(X21)
| empty_carrier(X21)
| ~ latt_str(X21) )
& ( ~ below(X21,X23,esk3_3(X21,X22,X23))
| ~ latt_element_smaller(X21,X23,X22)
| X23 = join_of_latt_set(X21,X22)
| ~ element(X23,the_carrier(X21))
| empty_carrier(X21)
| ~ lattice(X21)
| ~ complete_latt_str(X21)
| ~ latt_str(X21)
| empty_carrier(X21)
| ~ latt_str(X21) ) ),
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_13])])])])]) ).
cnf(c_0_19,plain,
( latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ below(X1,esk2_3(X1,X2,X3),X2)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( element(esk2_3(X1,X2,X3),the_carrier(X1))
| latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_22,negated_conjecture,
! [X74] :
( ~ empty_carrier(esk15_0)
& lattice(esk15_0)
& complete_latt_str(esk15_0)
& latt_str(esk15_0)
& element(esk16_0,the_carrier(esk15_0))
& ( element(esk18_0,the_carrier(esk15_0))
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0)
| esk16_0 != meet_of_latt_set(esk15_0,esk17_0) )
& ( latt_set_smaller(esk15_0,esk18_0,esk17_0)
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0)
| esk16_0 != meet_of_latt_set(esk15_0,esk17_0) )
& ( ~ below_refl(esk15_0,esk18_0,esk16_0)
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0)
| esk16_0 != meet_of_latt_set(esk15_0,esk17_0) )
& ( latt_set_smaller(esk15_0,esk16_0,esk17_0)
| esk16_0 = meet_of_latt_set(esk15_0,esk17_0) )
& ( ~ element(X74,the_carrier(esk15_0))
| ~ latt_set_smaller(esk15_0,X74,esk17_0)
| below_refl(esk15_0,X74,esk16_0)
| esk16_0 = meet_of_latt_set(esk15_0,esk17_0) ) ),
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_16])])])])]) ).
cnf(c_0_23,plain,
( X1 = esk9_3(X1,X2,X3)
| empty_carrier(X2)
| ~ in(X1,a_2_2_lattice3(X2,X3))
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( in(esk2_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_14]) ).
cnf(c_0_25,plain,
( latt_element_smaller(X1,esk3_3(X1,X2,X3),X2)
| 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_18]) ).
cnf(c_0_26,plain,
( element(esk3_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_18]) ).
cnf(c_0_27,plain,
( latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ below_refl(X1,esk2_3(X1,X2,X3),X2)
| ~ element(X2,the_carrier(X1))
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( below_refl(esk15_0,X1,esk16_0)
| esk16_0 = meet_of_latt_set(esk15_0,esk17_0)
| ~ element(X1,the_carrier(esk15_0))
| ~ latt_set_smaller(esk15_0,X1,esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
element(esk16_0,the_carrier(esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
latt_str(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,negated_conjecture,
~ empty_carrier(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
( latt_set_smaller(X1,esk9_3(X2,X1,X3),X3)
| empty_carrier(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,plain,
( esk9_3(esk2_3(X1,X2,a_2_2_lattice3(X3,X4)),X3,X4) = esk2_3(X1,X2,a_2_2_lattice3(X3,X4))
| latt_element_smaller(X1,X2,a_2_2_lattice3(X3,X4))
| empty_carrier(X1)
| empty_carrier(X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X3)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_34,plain,
( X2 = join_of_latt_set(X1,X3)
| empty_carrier(X1)
| empty_carrier(X1)
| ~ below(X1,X2,esk3_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_18]) ).
cnf(c_0_35,plain,
( below(X1,X4,X2)
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X4,the_carrier(X1))
| ~ in(X4,X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_36,plain,
( X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| latt_element_smaller(X1,esk3_3(X1,X2,X3),X2)
| ~ 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_25]) ).
cnf(c_0_37,plain,
( X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| element(esk3_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_26]) ).
cnf(c_0_38,negated_conjecture,
( meet_of_latt_set(esk15_0,esk17_0) = esk16_0
| latt_element_smaller(esk15_0,esk16_0,X1)
| ~ latt_set_smaller(esk15_0,esk2_3(esk15_0,esk16_0,X1),esk17_0)
| ~ element(esk2_3(esk15_0,esk16_0,X1),the_carrier(esk15_0))
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(esk15_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_39,plain,
( latt_element_smaller(X1,X2,a_2_2_lattice3(X3,X4))
| latt_set_smaller(X3,esk2_3(X1,X2,a_2_2_lattice3(X3,X4)),X4)
| empty_carrier(X1)
| empty_carrier(X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X3)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_24]) ).
fof(c_0_40,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(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_41,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,esk3_3(X1,X3,X2)) ),
inference(cn,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( X1 = join_of_latt_set(X2,X3)
| below(X2,X4,esk3_3(X2,X3,X1))
| empty_carrier(X2)
| ~ complete_latt_str(X2)
| ~ latt_element_smaller(X2,X1,X3)
| ~ element(X4,the_carrier(X2))
| ~ element(X1,the_carrier(X2))
| ~ lattice(X2)
| ~ latt_str(X2)
| ~ in(X4,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( meet_of_latt_set(esk15_0,esk17_0) = esk16_0
| latt_element_smaller(esk15_0,esk16_0,a_2_2_lattice3(esk15_0,esk17_0))
| ~ element(esk2_3(esk15_0,esk16_0,a_2_2_lattice3(esk15_0,esk17_0)),the_carrier(esk15_0))
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(esk15_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_29]),c_0_30])]),c_0_31]) ).
fof(c_0_44,plain,
! [X26,X27] :
( empty_carrier(X26)
| ~ latt_str(X26)
| meet_of_latt_set(X26,X27) = join_of_latt_set(X26,a_2_2_lattice3(X26,X27)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
cnf(c_0_45,plain,
( X1 = join_of_latt_set(X2,X3)
| empty_carrier(X2)
| ~ complete_latt_str(X2)
| ~ latt_element_smaller(X2,X1,X3)
| ~ element(X1,the_carrier(X2))
| ~ lattice(X2)
| ~ latt_str(X2)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( meet_of_latt_set(esk15_0,esk17_0) = esk16_0
| latt_element_smaller(esk15_0,esk16_0,a_2_2_lattice3(esk15_0,esk17_0))
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(esk15_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_21]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_47,negated_conjecture,
complete_latt_str(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_48,negated_conjecture,
lattice(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_49,plain,
( empty_carrier(X1)
| meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( join_of_latt_set(esk15_0,a_2_2_lattice3(esk15_0,esk17_0)) = esk16_0
| meet_of_latt_set(esk15_0,esk17_0) = esk16_0
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(esk15_0)
| ~ in(esk16_0,a_2_2_lattice3(esk15_0,esk17_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_45,c_0_46]),c_0_47]),c_0_29]),c_0_48]),c_0_30])]),c_0_31]) ).
cnf(c_0_51,plain,
( in(X3,a_2_2_lattice3(X2,X4))
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| X3 != X1
| ~ latt_set_smaller(X2,X1,X4)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_52,plain,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
cnf(c_0_53,plain,
( latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| empty_carrier(X1)
| X2 != join_of_latt_set(X1,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_18]) ).
fof(c_0_54,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]) ).
cnf(c_0_55,negated_conjecture,
( meet_of_latt_set(esk15_0,esk17_0) = esk16_0
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(esk15_0)
| ~ in(esk16_0,a_2_2_lattice3(esk15_0,esk17_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_30])]),c_0_31]) ).
cnf(c_0_56,plain,
( empty_carrier(X1)
| in(X2,a_2_2_lattice3(X1,X3))
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( latt_set_smaller(esk15_0,esk16_0,esk17_0)
| esk16_0 = meet_of_latt_set(esk15_0,esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_58,plain,
! [X7] :
( ( ~ empty_carrier(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( join_commutative(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( join_associative(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( meet_commutative(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( meet_associative(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( meet_absorbing(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( join_absorbing(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
cnf(c_0_59,plain,
( empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| X2 != join_of_latt_set(X1,X3)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(cn,[status(thm)],[c_0_53]) ).
fof(c_0_60,plain,
! [X28,X29] :
( empty_carrier(X28)
| ~ latt_str(X28)
| element(join_of_latt_set(X28,X29),the_carrier(X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])]) ).
cnf(c_0_61,negated_conjecture,
( meet_of_latt_set(esk15_0,esk17_0) = esk16_0
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(esk15_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_55,c_0_56]),c_0_29]),c_0_30])]),c_0_31]),c_0_57]) ).
cnf(c_0_62,plain,
( join_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| X3 != join_of_latt_set(X1,X4)
| ~ complete_latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_59]) ).
cnf(c_0_64,plain,
( empty_carrier(X1)
| element(join_of_latt_set(X1,X2),the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( meet_of_latt_set(esk15_0,esk17_0) = esk16_0
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(esk15_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_48]),c_0_30])]),c_0_31]) ).
cnf(c_0_66,plain,
( meet_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,plain,
( below(X1,X2,join_of_latt_set(X1,X3))
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_63]),c_0_64]) ).
cnf(c_0_68,negated_conjecture,
( meet_of_latt_set(esk15_0,esk17_0) = esk16_0
| ~ meet_commutative(esk15_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_48]),c_0_30])]),c_0_31]) ).
cnf(c_0_69,plain,
( meet_commutative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_70,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& complete_latt_str(X2)
& latt_str(X2) )
=> ( in(X1,a_2_3_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_3_lattice3]) ).
fof(c_0_71,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X2,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d16_lattice3]) ).
cnf(c_0_72,plain,
( below(X1,X2,meet_of_latt_set(X1,X3))
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3)) ),
inference(spm,[status(thm)],[c_0_67,c_0_49]) ).
cnf(c_0_73,negated_conjecture,
meet_of_latt_set(esk15_0,esk17_0) = esk16_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_48]),c_0_30])]),c_0_31]) ).
fof(c_0_74,plain,
! [X48,X49,X50,X52,X53] :
( ( element(esk10_3(X48,X49,X50),the_carrier(X49))
| ~ in(X48,a_2_3_lattice3(X49,X50))
| empty_carrier(X49)
| ~ lattice(X49)
| ~ complete_latt_str(X49)
| ~ latt_str(X49) )
& ( X48 = esk10_3(X48,X49,X50)
| ~ in(X48,a_2_3_lattice3(X49,X50))
| empty_carrier(X49)
| ~ lattice(X49)
| ~ complete_latt_str(X49)
| ~ latt_str(X49) )
& ( latt_set_smaller(X49,esk10_3(X48,X49,X50),X50)
| ~ in(X48,a_2_3_lattice3(X49,X50))
| empty_carrier(X49)
| ~ lattice(X49)
| ~ complete_latt_str(X49)
| ~ latt_str(X49) )
& ( ~ element(X53,the_carrier(X49))
| X48 != X53
| ~ latt_set_smaller(X49,X53,X52)
| in(X48,a_2_3_lattice3(X49,X52))
| empty_carrier(X49)
| ~ lattice(X49)
| ~ complete_latt_str(X49)
| ~ latt_str(X49) ) ),
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_70])])])])])]) ).
fof(c_0_75,plain,
! [X9,X10,X11,X12,X13] :
( ( ~ latt_set_smaller(X9,X10,X11)
| ~ element(X12,the_carrier(X9))
| ~ in(X12,X11)
| below(X9,X10,X12)
| ~ element(X10,the_carrier(X9))
| empty_carrier(X9)
| ~ latt_str(X9) )
& ( element(esk1_3(X9,X10,X13),the_carrier(X9))
| latt_set_smaller(X9,X10,X13)
| ~ element(X10,the_carrier(X9))
| empty_carrier(X9)
| ~ latt_str(X9) )
& ( in(esk1_3(X9,X10,X13),X13)
| latt_set_smaller(X9,X10,X13)
| ~ element(X10,the_carrier(X9))
| empty_carrier(X9)
| ~ latt_str(X9) )
& ( ~ below(X9,X10,esk1_3(X9,X10,X13))
| latt_set_smaller(X9,X10,X13)
| ~ element(X10,the_carrier(X9))
| empty_carrier(X9)
| ~ latt_str(X9) ) ),
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_71])])])])])]) ).
cnf(c_0_76,negated_conjecture,
( below(esk15_0,X1,esk16_0)
| ~ element(X1,the_carrier(esk15_0))
| ~ in(X1,a_2_2_lattice3(esk15_0,esk17_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_72,c_0_73]),c_0_47]),c_0_48]),c_0_30])]),c_0_31]) ).
cnf(c_0_77,plain,
( X1 = esk10_3(X1,X2,X3)
| empty_carrier(X2)
| ~ in(X1,a_2_3_lattice3(X2,X3))
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_78,plain,
( below(X1,X2,X4)
| empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X4,the_carrier(X1))
| ~ in(X4,X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_79,plain,
( element(esk9_3(X1,X2,X3),the_carrier(X2))
| empty_carrier(X2)
| ~ in(X1,a_2_2_lattice3(X2,X3))
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_80,negated_conjecture,
( below(esk15_0,X1,esk16_0)
| ~ latt_set_smaller(esk15_0,X1,esk17_0)
| ~ element(X1,the_carrier(esk15_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_56]),c_0_30])]),c_0_31]) ).
cnf(c_0_81,plain,
( latt_set_smaller(X1,esk10_3(X2,X1,X3),X3)
| empty_carrier(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_82,plain,
( esk10_3(esk2_3(X1,X2,a_2_3_lattice3(X3,X4)),X3,X4) = esk2_3(X1,X2,a_2_3_lattice3(X3,X4))
| latt_element_smaller(X1,X2,a_2_3_lattice3(X3,X4))
| empty_carrier(X1)
| empty_carrier(X3)
| ~ complete_latt_str(X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X3)
| ~ latt_str(X3)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_24]) ).
cnf(c_0_83,plain,
( below(X1,esk9_3(X2,X1,X3),X4)
| empty_carrier(X1)
| ~ element(X4,the_carrier(X1))
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3))
| ~ in(X4,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_32]),c_0_79]) ).
cnf(c_0_84,negated_conjecture,
( latt_element_smaller(esk15_0,esk16_0,X1)
| ~ latt_set_smaller(esk15_0,esk2_3(esk15_0,esk16_0,X1),esk17_0)
| ~ element(esk2_3(esk15_0,esk16_0,X1),the_carrier(esk15_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_80]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_85,plain,
( latt_element_smaller(X1,X2,a_2_3_lattice3(X3,X4))
| latt_set_smaller(X3,esk2_3(X1,X2,a_2_3_lattice3(X3,X4)),X4)
| empty_carrier(X1)
| empty_carrier(X3)
| ~ complete_latt_str(X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X3)
| ~ latt_str(X3)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_24]) ).
cnf(c_0_86,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_18]) ).
cnf(c_0_87,plain,
( latt_element_smaller(X1,X2,a_2_2_lattice3(X3,X4))
| below(X3,esk2_3(X1,X2,a_2_2_lattice3(X3,X4)),X5)
| empty_carrier(X1)
| empty_carrier(X3)
| ~ element(X5,the_carrier(X3))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X3)
| ~ latt_str(X1)
| ~ in(X5,X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_33]),c_0_24]) ).
cnf(c_0_88,negated_conjecture,
( latt_element_smaller(esk15_0,esk16_0,a_2_3_lattice3(esk15_0,esk17_0))
| ~ element(esk2_3(esk15_0,esk16_0,a_2_3_lattice3(esk15_0,esk17_0)),the_carrier(esk15_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_84,c_0_85]),c_0_47]),c_0_29]),c_0_48]),c_0_30])]),c_0_31]) ).
cnf(c_0_89,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_86]) ).
cnf(c_0_90,plain,
( latt_element_smaller(X1,X2,a_2_2_lattice3(X1,X3))
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ in(X2,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_87]) ).
cnf(c_0_91,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ below(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_92,negated_conjecture,
latt_element_smaller(esk15_0,esk16_0,a_2_3_lattice3(esk15_0,esk17_0)),
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_21]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_93,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| X2 != join_of_latt_set(X1,a_2_2_lattice3(X1,X4))
| ~ complete_latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X3,X4) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_94,plain,
( below_refl(X1,X2,join_of_latt_set(X1,X3))
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_67]),c_0_69]),c_0_66]),c_0_62]),c_0_64]) ).
cnf(c_0_95,negated_conjecture,
( join_of_latt_set(esk15_0,a_2_3_lattice3(esk15_0,esk17_0)) = esk16_0
| ~ in(esk16_0,a_2_3_lattice3(esk15_0,esk17_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_45,c_0_92]),c_0_47]),c_0_29]),c_0_48]),c_0_30])]),c_0_31]) ).
cnf(c_0_96,plain,
( in(X3,a_2_3_lattice3(X2,X4))
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| X3 != X1
| ~ latt_set_smaller(X2,X1,X4)
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_97,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| X2 != meet_of_latt_set(X1,X4)
| ~ complete_latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X3,X4) ),
inference(spm,[status(thm)],[c_0_93,c_0_49]) ).
cnf(c_0_98,negated_conjecture,
( below_refl(esk15_0,X1,esk16_0)
| ~ element(X1,the_carrier(esk15_0))
| ~ in(esk16_0,a_2_3_lattice3(esk15_0,esk17_0))
| ~ in(X1,a_2_3_lattice3(esk15_0,esk17_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_94,c_0_95]),c_0_47]),c_0_48]),c_0_30])]),c_0_31]) ).
cnf(c_0_99,plain,
( empty_carrier(X1)
| in(X2,a_2_3_lattice3(X1,X3))
| ~ complete_latt_str(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(er,[status(thm)],[c_0_96]) ).
cnf(c_0_100,plain,
( latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ below(X1,X2,esk1_3(X1,X2,X3))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_101,negated_conjecture,
( below(esk15_0,X1,X2)
| X1 != esk16_0
| ~ element(X1,the_carrier(esk15_0))
| ~ element(X2,the_carrier(esk15_0))
| ~ in(X2,esk17_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_97,c_0_73]),c_0_47]),c_0_48]),c_0_30])]),c_0_31]) ).
cnf(c_0_102,negated_conjecture,
( ~ below_refl(esk15_0,esk18_0,esk16_0)
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0)
| esk16_0 != meet_of_latt_set(esk15_0,esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_103,negated_conjecture,
( below_refl(esk15_0,X1,esk16_0)
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0)
| ~ element(X1,the_carrier(esk15_0))
| ~ in(X1,a_2_3_lattice3(esk15_0,esk17_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_98,c_0_99]),c_0_47]),c_0_29]),c_0_48]),c_0_30])]),c_0_31]) ).
cnf(c_0_104,negated_conjecture,
( element(esk18_0,the_carrier(esk15_0))
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0)
| esk16_0 != meet_of_latt_set(esk15_0,esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_105,negated_conjecture,
( latt_set_smaller(esk15_0,esk18_0,esk17_0)
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0)
| esk16_0 != meet_of_latt_set(esk15_0,esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_106,negated_conjecture,
( latt_set_smaller(esk15_0,X1,X2)
| X1 != esk16_0
| ~ element(esk1_3(esk15_0,X1,X2),the_carrier(esk15_0))
| ~ element(X1,the_carrier(esk15_0))
| ~ in(esk1_3(esk15_0,X1,X2),esk17_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_30])]),c_0_31]) ).
cnf(c_0_107,plain,
( in(esk1_3(X1,X2,X3),X3)
| latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_108,negated_conjecture,
( ~ below_refl(esk15_0,esk18_0,esk16_0)
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_73])]) ).
cnf(c_0_109,negated_conjecture,
( below_refl(esk15_0,X1,esk16_0)
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0)
| ~ latt_set_smaller(esk15_0,X1,esk17_0)
| ~ element(X1,the_carrier(esk15_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_99]),c_0_47]),c_0_48]),c_0_30])]),c_0_31]) ).
cnf(c_0_110,negated_conjecture,
( element(esk18_0,the_carrier(esk15_0))
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_73])]) ).
cnf(c_0_111,negated_conjecture,
( latt_set_smaller(esk15_0,esk18_0,esk17_0)
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_73])]) ).
cnf(c_0_112,negated_conjecture,
( latt_set_smaller(esk15_0,X1,esk17_0)
| X1 != esk16_0
| ~ element(esk1_3(esk15_0,X1,esk17_0),the_carrier(esk15_0))
| ~ element(X1,the_carrier(esk15_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_30])]),c_0_31]) ).
cnf(c_0_113,plain,
( element(esk1_3(X1,X2,X3),the_carrier(X1))
| latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_114,negated_conjecture,
~ latt_set_smaller(esk15_0,esk16_0,esk17_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]),c_0_111]) ).
cnf(c_0_115,negated_conjecture,
( latt_set_smaller(esk15_0,X1,esk17_0)
| X1 != esk16_0
| ~ element(X1,the_carrier(esk15_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_30])]),c_0_31]) ).
cnf(c_0_116,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU351+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 2400
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Oct 2 09:05:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.48 Running first-order model finding
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.bJqMUusQFE/E---3.1_20842.p
% 13.72/2.24 # Version: 3.1pre001
% 13.72/2.24 # Preprocessing class: FSMSSMSSSSSNFFN.
% 13.72/2.24 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.72/2.24 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.72/2.24 # Starting new_bool_3 with 300s (1) cores
% 13.72/2.24 # Starting new_bool_1 with 300s (1) cores
% 13.72/2.24 # Starting sh5l with 300s (1) cores
% 13.72/2.24 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 21064 completed with status 0
% 13.72/2.24 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 13.72/2.24 # Preprocessing class: FSMSSMSSSSSNFFN.
% 13.72/2.24 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.72/2.24 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.72/2.24 # No SInE strategy applied
% 13.72/2.24 # Search class: FGHSF-FFMM32-SFFFFFNN
% 13.72/2.24 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 13.72/2.24 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SA with 811s (1) cores
% 13.72/2.24 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.72/2.24 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 13.72/2.24 # Starting G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 13.72/2.24 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 13.72/2.24 # G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y with pid 21080 completed with status 0
% 13.72/2.24 # Result found by G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y
% 13.72/2.24 # Preprocessing class: FSMSSMSSSSSNFFN.
% 13.72/2.24 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.72/2.24 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.72/2.24 # No SInE strategy applied
% 13.72/2.24 # Search class: FGHSF-FFMM32-SFFFFFNN
% 13.72/2.24 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 13.72/2.24 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SA with 811s (1) cores
% 13.72/2.24 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.72/2.24 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 13.72/2.24 # Starting G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 13.72/2.24 # Preprocessing time : 0.004 s
% 13.72/2.24 # Presaturation interreduction done
% 13.72/2.24
% 13.72/2.24 # Proof found!
% 13.72/2.24 # SZS status Theorem
% 13.72/2.24 # SZS output start CNFRefutation
% See solution above
% 13.72/2.24 # Parsed axioms : 37
% 13.72/2.24 # Removed by relevancy pruning/SinE : 0
% 13.72/2.24 # Initial clauses : 73
% 13.72/2.24 # Removed in clause preprocessing : 6
% 13.72/2.24 # Initial clauses in saturation : 67
% 13.72/2.24 # Processed clauses : 10011
% 13.72/2.24 # ...of these trivial : 41
% 13.72/2.24 # ...subsumed : 6791
% 13.72/2.24 # ...remaining for further processing : 3179
% 13.72/2.24 # Other redundant clauses eliminated : 2
% 13.72/2.24 # Clauses deleted for lack of memory : 0
% 13.72/2.24 # Backward-subsumed : 519
% 13.72/2.24 # Backward-rewritten : 33
% 13.72/2.24 # Generated clauses : 41545
% 13.72/2.24 # ...of the previous two non-redundant : 38422
% 13.72/2.24 # ...aggressively subsumed : 0
% 13.72/2.24 # Contextual simplify-reflections : 853
% 13.72/2.24 # Paramodulations : 41459
% 13.72/2.24 # Factorizations : 24
% 13.72/2.24 # NegExts : 0
% 13.72/2.24 # Equation resolutions : 62
% 13.72/2.24 # Total rewrite steps : 30883
% 13.72/2.24 # Propositional unsat checks : 0
% 13.72/2.24 # Propositional check models : 0
% 13.72/2.24 # Propositional check unsatisfiable : 0
% 13.72/2.24 # Propositional clauses : 0
% 13.72/2.24 # Propositional clauses after purity: 0
% 13.72/2.24 # Propositional unsat core size : 0
% 13.72/2.24 # Propositional preprocessing time : 0.000
% 13.72/2.24 # Propositional encoding time : 0.000
% 13.72/2.24 # Propositional solver time : 0.000
% 13.72/2.24 # Success case prop preproc time : 0.000
% 13.72/2.24 # Success case prop encoding time : 0.000
% 13.72/2.24 # Success case prop solver time : 0.000
% 13.72/2.24 # Current number of processed clauses : 2558
% 13.72/2.24 # Positive orientable unit clauses : 18
% 13.72/2.24 # Positive unorientable unit clauses: 0
% 13.72/2.24 # Negative unit clauses : 5
% 13.72/2.24 # Non-unit-clauses : 2535
% 13.72/2.24 # Current number of unprocessed clauses: 27076
% 13.72/2.24 # ...number of literals in the above : 219742
% 13.72/2.24 # Current number of archived formulas : 0
% 13.72/2.24 # Current number of archived clauses : 619
% 13.72/2.24 # Clause-clause subsumption calls (NU) : 936579
% 13.72/2.24 # Rec. Clause-clause subsumption calls : 61803
% 13.72/2.24 # Non-unit clause-clause subsumptions : 7733
% 13.72/2.24 # Unit Clause-clause subsumption calls : 288
% 13.72/2.24 # Rewrite failures with RHS unbound : 0
% 13.72/2.24 # BW rewrite match attempts : 9
% 13.72/2.24 # BW rewrite match successes : 5
% 13.72/2.24 # Condensation attempts : 0
% 13.72/2.24 # Condensation successes : 0
% 13.72/2.24 # Termbank termtop insertions : 1334079
% 13.72/2.24
% 13.72/2.24 # -------------------------------------------------
% 13.72/2.24 # User time : 1.653 s
% 13.72/2.24 # System time : 0.029 s
% 13.72/2.24 # Total time : 1.682 s
% 13.72/2.24 # Maximum resident set size: 1984 pages
% 13.72/2.24
% 13.72/2.24 # -------------------------------------------------
% 13.72/2.24 # User time : 8.418 s
% 13.72/2.24 # System time : 0.147 s
% 13.72/2.24 # Total time : 8.565 s
% 13.72/2.24 # Maximum resident set size: 1732 pages
% 13.72/2.24 % E---3.1 exiting
%------------------------------------------------------------------------------