TSTP Solution File: SEU351+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU351+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 09:19:16 EDT 2022
% Result : Theorem 0.21s 1.40s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 126 ( 8 unt; 0 def)
% Number of atoms : 816 ( 67 equ)
% Maximal formula atoms : 50 ( 6 avg)
% Number of connectives : 1160 ( 470 ~; 578 |; 72 &)
% ( 9 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 286 ( 9 sgn 84 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fraenkel_a_2_2_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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fraenkel_a_2_3_lattice3) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_tarski) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t34_lattice3) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t7_boole) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_r3_lattices) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d16_lattice3) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t1_subset) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d21_lattice3) ).
fof(dt_k15_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k15_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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',cc1_lattices) ).
fof(c_0_14,plain,
! [X5,X6,X7,X7,X9] :
( ( element(esk9_3(X5,X6,X7),the_carrier(X6))
| ~ in(X5,a_2_2_lattice3(X6,X7))
| empty_carrier(X6)
| ~ latt_str(X6) )
& ( X5 = esk9_3(X5,X6,X7)
| ~ in(X5,a_2_2_lattice3(X6,X7))
| empty_carrier(X6)
| ~ latt_str(X6) )
& ( latt_set_smaller(X6,esk9_3(X5,X6,X7),X7)
| ~ in(X5,a_2_2_lattice3(X6,X7))
| empty_carrier(X6)
| ~ latt_str(X6) )
& ( ~ element(X9,the_carrier(X6))
| X5 != X9
| ~ latt_set_smaller(X6,X9,X7)
| in(X5,a_2_2_lattice3(X6,X7))
| empty_carrier(X6)
| ~ latt_str(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fraenkel_a_2_2_lattice3])])])])])])])]) ).
fof(c_0_15,plain,
! [X5,X6,X7,X7,X9] :
( ( element(esk10_3(X5,X6,X7),the_carrier(X6))
| ~ in(X5,a_2_3_lattice3(X6,X7))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ complete_latt_str(X6)
| ~ latt_str(X6) )
& ( X5 = esk10_3(X5,X6,X7)
| ~ in(X5,a_2_3_lattice3(X6,X7))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ complete_latt_str(X6)
| ~ latt_str(X6) )
& ( latt_set_smaller(X6,esk10_3(X5,X6,X7),X7)
| ~ in(X5,a_2_3_lattice3(X6,X7))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ complete_latt_str(X6)
| ~ latt_str(X6) )
& ( ~ element(X9,the_carrier(X6))
| X5 != X9
| ~ latt_set_smaller(X6,X9,X7)
| in(X5,a_2_3_lattice3(X6,X7))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ complete_latt_str(X6)
| ~ latt_str(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fraenkel_a_2_3_lattice3])])])])])])])]) ).
cnf(c_0_16,plain,
( empty_carrier(X1)
| in(X2,a_2_2_lattice3(X1,X3))
| ~ latt_str(X1)
| ~ latt_set_smaller(X1,X4,X3)
| X2 != X4
| ~ element(X4,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
( empty_carrier(X1)
| latt_set_smaller(X1,esk10_3(X2,X1,X3),X3)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
( empty_carrier(X1)
| X2 = esk10_3(X2,X1,X3)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( empty_carrier(X1)
| element(esk10_3(X2,X1,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,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_16]) ).
cnf(c_0_21,plain,
( latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( element(X1,the_carrier(X2))
| empty_carrier(X2)
| ~ complete_latt_str(X2)
| ~ lattice(X2)
| ~ latt_str(X2)
| ~ in(X1,a_2_3_lattice3(X2,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
fof(c_0_23,plain,
! [X4,X5] :
( ( ~ in(esk14_2(X4,X5),X4)
| ~ in(esk14_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk14_2(X4,X5),X4)
| in(esk14_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])])]) ).
fof(c_0_24,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(assume_negation,[status(cth)],[t34_lattice3]) ).
cnf(c_0_25,plain,
( empty_carrier(X1)
| in(X2,a_2_3_lattice3(X1,X3))
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_set_smaller(X1,X4,X3)
| X2 != X4
| ~ element(X4,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( empty_carrier(X1)
| in(X2,a_2_2_lattice3(X1,X3))
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_27,plain,
( X1 = X2
| in(esk14_2(X1,X2),X2)
| in(esk14_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_28,negated_conjecture,
! [X9] :
( ~ 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(X9,the_carrier(esk15_0))
| ~ latt_set_smaller(esk15_0,X9,esk17_0)
| below_refl(esk15_0,X9,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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_24])])])])])])])]) ).
fof(c_0_29,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_30,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_25]) ).
cnf(c_0_31,plain,
( empty_carrier(X1)
| latt_set_smaller(X1,esk9_3(X2,X1,X3),X3)
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,plain,
( empty_carrier(X1)
| element(esk9_3(X2,X1,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_33,plain,
( X1 = a_2_3_lattice3(X2,X3)
| empty_carrier(X2)
| in(esk14_2(X1,a_2_3_lattice3(X2,X3)),a_2_2_lattice3(X2,X3))
| in(esk14_2(X1,a_2_3_lattice3(X2,X3)),X1)
| ~ complete_latt_str(X2)
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
complete_latt_str(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
lattice(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,negated_conjecture,
latt_str(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,negated_conjecture,
~ empty_carrier(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_38,plain,
! [X5,X6,X7,X8,X7] :
( ( ~ latt_element_smaller(X5,X6,X7)
| ~ element(X8,the_carrier(X5))
| ~ in(X8,X7)
| below(X5,X8,X6)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( element(esk2_3(X5,X6,X7),the_carrier(X5))
| latt_element_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( in(esk2_3(X5,X6,X7),X7)
| latt_element_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( ~ below(X5,esk2_3(X5,X6,X7),X6)
| latt_element_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d17_lattice3])])])])])])])]) ).
fof(c_0_39,plain,
! [X4,X5,X6] :
( ( ~ below_refl(X4,X5,X6)
| below(X4,X5,X6)
| empty_carrier(X4)
| ~ meet_commutative(X4)
| ~ meet_absorbing(X4)
| ~ join_absorbing(X4)
| ~ latt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4)) )
& ( ~ below(X4,X5,X6)
| below_refl(X4,X5,X6)
| empty_carrier(X4)
| ~ meet_commutative(X4)
| ~ meet_absorbing(X4)
| ~ join_absorbing(X4)
| ~ latt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_r3_lattices])])])]) ).
fof(c_0_40,plain,
! [X5,X6,X7,X8,X7] :
( ( ~ latt_set_smaller(X5,X6,X7)
| ~ element(X8,the_carrier(X5))
| ~ in(X8,X7)
| below(X5,X6,X8)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( element(esk1_3(X5,X6,X7),the_carrier(X5))
| latt_set_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( in(esk1_3(X5,X6,X7),X7)
| latt_set_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( ~ below(X5,X6,esk1_3(X5,X6,X7))
| latt_set_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d16_lattice3])])])])])])])]) ).
cnf(c_0_41,plain,
( empty_carrier(X1)
| X2 = esk9_3(X2,X1,X3)
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_42,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_43,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_44,plain,
( empty_carrier(X1)
| in(esk9_3(X2,X1,X3),a_2_3_lattice3(X1,X3))
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_45,negated_conjecture,
( X1 = a_2_3_lattice3(esk15_0,X2)
| in(esk14_2(X1,a_2_3_lattice3(esk15_0,X2)),a_2_2_lattice3(esk15_0,X2))
| in(esk14_2(X1,a_2_3_lattice3(esk15_0,X2)),X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]),c_0_37]) ).
cnf(c_0_46,plain,
( empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ below(X1,esk2_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
( empty_carrier(X2)
| below(X2,X3,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| ~ latt_str(X2)
| ~ join_absorbing(X2)
| ~ meet_absorbing(X2)
| ~ meet_commutative(X2)
| ~ below_refl(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
( empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| element(esk2_3(X1,X2,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_49,plain,
( empty_carrier(X1)
| below(X1,X2,X3)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ in(X3,X4)
| ~ element(X3,the_carrier(X1))
| ~ latt_set_smaller(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_50,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_51,plain,
( latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3)) ),
inference(spm,[status(thm)],[c_0_31,c_0_41]) ).
cnf(c_0_52,plain,
( element(X1,the_carrier(X2))
| empty_carrier(X2)
| ~ latt_str(X2)
| ~ in(X1,a_2_2_lattice3(X2,X3)) ),
inference(spm,[status(thm)],[c_0_32,c_0_41]) ).
cnf(c_0_53,plain,
( X1 = X2
| ~ in(esk14_2(X1,X2),X2)
| ~ in(esk14_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_54,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_55,plain,
( empty_carrier(X1)
| ~ empty(a_2_3_lattice3(X1,X2))
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X3,a_2_2_lattice3(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_56,negated_conjecture,
( a_2_3_lattice3(esk15_0,X1) = a_2_2_lattice3(esk15_0,X1)
| in(esk14_2(a_2_2_lattice3(esk15_0,X1),a_2_3_lattice3(esk15_0,X1)),a_2_2_lattice3(esk15_0,X1)) ),
inference(ef,[status(thm)],[c_0_45]) ).
fof(c_0_57,plain,
! [X5,X6,X7,X8] :
( ( latt_element_smaller(X5,X7,X6)
| X7 != join_of_latt_set(X5,X6)
| ~ element(X7,the_carrier(X5))
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( ~ element(X8,the_carrier(X5))
| ~ latt_element_smaller(X5,X8,X6)
| below(X5,X7,X8)
| X7 != join_of_latt_set(X5,X6)
| ~ element(X7,the_carrier(X5))
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( element(esk3_3(X5,X6,X7),the_carrier(X5))
| ~ latt_element_smaller(X5,X7,X6)
| X7 = join_of_latt_set(X5,X6)
| ~ element(X7,the_carrier(X5))
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( latt_element_smaller(X5,esk3_3(X5,X6,X7),X6)
| ~ latt_element_smaller(X5,X7,X6)
| X7 = join_of_latt_set(X5,X6)
| ~ element(X7,the_carrier(X5))
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( ~ below(X5,X7,esk3_3(X5,X6,X7))
| ~ latt_element_smaller(X5,X7,X6)
| X7 = join_of_latt_set(X5,X6)
| ~ element(X7,the_carrier(X5))
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ latt_str(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d21_lattice3])])])])])])])]) ).
cnf(c_0_58,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_46,c_0_47]),c_0_48]) ).
cnf(c_0_59,negated_conjecture,
( esk16_0 = meet_of_latt_set(esk15_0,esk17_0)
| below_refl(esk15_0,X1,esk16_0)
| ~ latt_set_smaller(esk15_0,X1,esk17_0)
| ~ element(X1,the_carrier(esk15_0)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_60,negated_conjecture,
element(esk16_0,the_carrier(esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_61,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,a_2_3_lattice3(X1,X4))
| ~ in(X3,X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_21]),c_0_22]) ).
cnf(c_0_62,plain,
( empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| in(esk2_3(X1,X2,X3),X3)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_63,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_64,plain,
( empty_carrier(X1)
| in(X2,a_2_3_lattice3(X1,X3))
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_51]),c_0_52]) ).
cnf(c_0_65,plain,
( X1 = X2
| empty(X2)
| ~ element(esk14_2(X1,X2),X2)
| ~ in(esk14_2(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_66,negated_conjecture,
( a_2_3_lattice3(esk15_0,X1) = a_2_2_lattice3(esk15_0,X1)
| ~ empty(a_2_3_lattice3(esk15_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_55,c_0_56]),c_0_34]),c_0_35]),c_0_36])]),c_0_37]) ).
cnf(c_0_67,plain,
( empty_carrier(X1)
| empty_carrier(X1)
| X2 = join_of_latt_set(X1,X3)
| latt_element_smaller(X1,esk3_3(X1,X3,X2),X3)
| ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_68,plain,
( empty_carrier(X1)
| empty_carrier(X1)
| X2 = join_of_latt_set(X1,X3)
| element(esk3_3(X1,X3,X2),the_carrier(X1))
| ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_69,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_58,c_0_59]),c_0_60]),c_0_36])]),c_0_37]) ).
cnf(c_0_70,plain,
( latt_element_smaller(X1,X2,a_2_3_lattice3(X3,X4))
| below(X3,esk2_3(X1,X2,a_2_3_lattice3(X3,X4)),X5)
| empty_carrier(X1)
| empty_carrier(X3)
| ~ complete_latt_str(X3)
| ~ element(X5,the_carrier(X3))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X3)
| ~ latt_str(X3)
| ~ latt_str(X1)
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,plain,
( element(X1,a_2_3_lattice3(X2,X3))
| empty_carrier(X2)
| ~ complete_latt_str(X2)
| ~ lattice(X2)
| ~ latt_str(X2)
| ~ in(X1,a_2_2_lattice3(X2,X3)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,negated_conjecture,
( a_2_3_lattice3(esk15_0,X1) = a_2_2_lattice3(esk15_0,X1)
| ~ element(esk14_2(a_2_2_lattice3(esk15_0,X1),a_2_3_lattice3(esk15_0,X1)),a_2_3_lattice3(esk15_0,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_56]),c_0_66]) ).
cnf(c_0_73,plain,
( empty_carrier(X1)
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| X2 != join_of_latt_set(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_74,plain,
( empty_carrier(X1)
| empty_carrier(X1)
| X2 = join_of_latt_set(X1,X3)
| ~ 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,esk3_3(X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_75,plain,
( empty_carrier(X1)
| below(X1,X3,X2)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ in(X3,X4)
| ~ element(X3,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_76,plain,
( X2 = join_of_latt_set(X1,X3)
| empty_carrier(X1)
| latt_element_smaller(X1,esk3_3(X1,X3,X2),X3)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1)) ),
inference(cn,[status(thm)],[c_0_67]) ).
cnf(c_0_77,plain,
( X2 = join_of_latt_set(X1,X3)
| empty_carrier(X1)
| element(esk3_3(X1,X3,X2),the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1)) ),
inference(cn,[status(thm)],[c_0_68]) ).
cnf(c_0_78,negated_conjecture,
( meet_of_latt_set(esk15_0,esk17_0) = esk16_0
| latt_element_smaller(esk15_0,esk16_0,X1)
| ~ element(esk2_3(esk15_0,esk16_0,X1),the_carrier(esk15_0))
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(esk15_0)
| ~ in(esk2_3(esk15_0,esk16_0,X1),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_69,c_0_51]),c_0_36])]),c_0_37]) ).
cnf(c_0_79,plain,
( empty_carrier(X1)
| empty_carrier(X1)
| below(X1,X2,X4)
| ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| X2 != join_of_latt_set(X1,X3)
| ~ latt_element_smaller(X1,X4,X3)
| ~ element(X4,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_80,plain,
( latt_element_smaller(X1,X2,a_2_3_lattice3(X1,X3))
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_70]) ).
cnf(c_0_81,negated_conjecture,
a_2_3_lattice3(esk15_0,X1) = a_2_2_lattice3(esk15_0,X1),
inference(csr,[status(thm)],[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_71,c_0_56]),c_0_34]),c_0_35]),c_0_36])]),c_0_37]),c_0_72]) ).
cnf(c_0_82,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_73]) ).
fof(c_0_83,plain,
! [X3,X4] :
( empty_carrier(X3)
| ~ latt_str(X3)
| element(join_of_latt_set(X3,X4),the_carrier(X3)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k15_lattice3])])])])]) ).
cnf(c_0_84,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_74]) ).
cnf(c_0_85,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_75,c_0_76]),c_0_77]) ).
cnf(c_0_86,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_78,c_0_62]),c_0_60]),c_0_36])]),c_0_37]) ).
cnf(c_0_87,negated_conjecture,
( esk16_0 = meet_of_latt_set(esk15_0,esk17_0)
| latt_set_smaller(esk15_0,esk16_0,esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_88,plain,
( empty_carrier(X1)
| below(X1,X2,X4)
| X2 != join_of_latt_set(X1,X3)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X4,X3)
| ~ element(X4,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(cn,[status(thm)],[c_0_79]) ).
cnf(c_0_89,negated_conjecture,
( latt_element_smaller(esk15_0,X1,a_2_2_lattice3(esk15_0,X2))
| ~ element(X1,the_carrier(esk15_0))
| ~ in(X1,X2) ),
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_80,c_0_81]),c_0_34]),c_0_35]),c_0_36])]),c_0_37]) ).
fof(c_0_90,plain,
! [X3,X4] :
( empty_carrier(X3)
| ~ latt_str(X3)
| meet_of_latt_set(X3,X4) = join_of_latt_set(X3,a_2_2_lattice3(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d22_lattice3])])])])])]) ).
cnf(c_0_91,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_75,c_0_82]) ).
cnf(c_0_92,plain,
( element(join_of_latt_set(X1,X2),the_carrier(X1))
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_93,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_84,c_0_85]) ).
cnf(c_0_94,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_86,c_0_48]),c_0_60]),c_0_36])]),c_0_37]) ).
cnf(c_0_95,negated_conjecture,
( meet_of_latt_set(esk15_0,esk17_0) = esk16_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(spm,[status(thm)],[c_0_20,c_0_87]),c_0_60]),c_0_36])]),c_0_37]) ).
cnf(c_0_96,negated_conjecture,
( below(esk15_0,X1,X2)
| X1 != join_of_latt_set(esk15_0,a_2_2_lattice3(esk15_0,X3))
| ~ element(X2,the_carrier(esk15_0))
| ~ element(X1,the_carrier(esk15_0))
| ~ in(X2,X3) ),
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_88,c_0_89]),c_0_34]),c_0_35]),c_0_36])]),c_0_37]) ).
cnf(c_0_97,plain,
( meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2))
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_98,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_91]),c_0_92]) ).
cnf(c_0_99,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) ),
inference(csr,[status(thm)],[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_93,c_0_94]),c_0_34]),c_0_60]),c_0_35]),c_0_36])]),c_0_37]),c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( below(esk15_0,X1,X2)
| X1 != meet_of_latt_set(esk15_0,X3)
| ~ element(X2,the_carrier(esk15_0))
| ~ element(X1,the_carrier(esk15_0))
| ~ in(X2,X3) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_36])]),c_0_37]) ).
cnf(c_0_101,plain,
( below(X1,X2,meet_of_latt_set(X1,X3))
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_97]),c_0_52]) ).
cnf(c_0_102,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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_99]),c_0_36])]),c_0_37]) ).
cnf(c_0_103,negated_conjecture,
( below(esk15_0,meet_of_latt_set(esk15_0,X1),X2)
| ~ element(meet_of_latt_set(esk15_0,X1),the_carrier(esk15_0))
| ~ element(X2,the_carrier(esk15_0))
| ~ in(X2,X1) ),
inference(er,[status(thm)],[c_0_100]) ).
cnf(c_0_104,plain,
( empty_carrier(X2)
| below_refl(X2,X3,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| ~ latt_str(X2)
| ~ join_absorbing(X2)
| ~ meet_absorbing(X2)
| ~ meet_commutative(X2)
| ~ below(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_105,negated_conjecture,
( below(esk15_0,X1,esk16_0)
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(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_101,c_0_102]),c_0_34]),c_0_35]),c_0_36])]),c_0_37]) ).
cnf(c_0_106,negated_conjecture,
( latt_set_smaller(esk15_0,esk18_0,esk17_0)
| esk16_0 != meet_of_latt_set(esk15_0,esk17_0)
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_107,negated_conjecture,
( element(esk18_0,the_carrier(esk15_0))
| esk16_0 != meet_of_latt_set(esk15_0,esk17_0)
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_108,plain,
( empty_carrier(X1)
| latt_set_smaller(X1,X2,X3)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ below(X1,X2,esk1_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_109,negated_conjecture,
( below(esk15_0,esk16_0,X1)
| ~ element(X1,the_carrier(esk15_0))
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(esk15_0)
| ~ in(X1,esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_102]),c_0_60])]) ).
cnf(c_0_110,negated_conjecture,
( esk16_0 != meet_of_latt_set(esk15_0,esk17_0)
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0)
| ~ below_refl(esk15_0,esk18_0,esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_111,negated_conjecture,
( below_refl(esk15_0,X1,esk16_0)
| ~ element(X1,the_carrier(esk15_0))
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(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(spm,[status(thm)],[c_0_104,c_0_105]),c_0_60]),c_0_36])]),c_0_37]) ).
cnf(c_0_112,negated_conjecture,
( in(esk18_0,a_2_2_lattice3(esk15_0,esk17_0))
| meet_of_latt_set(esk15_0,esk17_0) != esk16_0
| ~ latt_set_smaller(esk15_0,esk16_0,esk17_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_106]),c_0_36])]),c_0_37]),c_0_107]) ).
cnf(c_0_113,negated_conjecture,
( latt_set_smaller(esk15_0,esk16_0,X1)
| ~ element(esk1_3(esk15_0,esk16_0,X1),the_carrier(esk15_0))
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(esk15_0)
| ~ in(esk1_3(esk15_0,esk16_0,X1),esk17_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_60]),c_0_36])]),c_0_37]) ).
cnf(c_0_114,plain,
( empty_carrier(X1)
| latt_set_smaller(X1,X2,X3)
| in(esk1_3(X1,X2,X3),X3)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_115,negated_conjecture,
( ~ latt_set_smaller(esk15_0,esk16_0,esk17_0)
| ~ join_absorbing(esk15_0)
| ~ meet_absorbing(esk15_0)
| ~ meet_commutative(esk15_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_107]),c_0_102]) ).
cnf(c_0_116,negated_conjecture,
( ~ element(esk1_3(esk15_0,esk16_0,esk17_0),the_carrier(esk15_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_113,c_0_114]),c_0_60]),c_0_36])]),c_0_37]),c_0_115]) ).
cnf(c_0_117,plain,
( empty_carrier(X1)
| latt_set_smaller(X1,X2,X3)
| element(esk1_3(X1,X2,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_118,plain,
! [X2] :
( ( ~ empty_carrier(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( join_commutative(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( join_associative(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( meet_commutative(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( meet_associative(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( meet_absorbing(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( join_absorbing(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc1_lattices])])])]) ).
cnf(c_0_119,negated_conjecture,
( ~ 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_116,c_0_117]),c_0_60]),c_0_36])]),c_0_37]),c_0_115]) ).
cnf(c_0_120,plain,
( empty_carrier(X1)
| join_absorbing(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_121,negated_conjecture,
( ~ 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_119,c_0_120]),c_0_35]),c_0_36])]),c_0_37]) ).
cnf(c_0_122,plain,
( empty_carrier(X1)
| meet_absorbing(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_123,negated_conjecture,
~ 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_121,c_0_122]),c_0_35]),c_0_36])]),c_0_37]) ).
cnf(c_0_124,plain,
( empty_carrier(X1)
| meet_commutative(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_125,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_123,c_0_124]),c_0_35]),c_0_36])]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU351+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : run_ET %s %d
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jun 19 18:55:38 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.21/1.40 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.21/1.40 # Preprocessing time : 0.019 s
% 0.21/1.40
% 0.21/1.40 # Proof found!
% 0.21/1.40 # SZS status Theorem
% 0.21/1.40 # SZS output start CNFRefutation
% See solution above
% 0.21/1.40 # Proof object total steps : 126
% 0.21/1.40 # Proof object clause steps : 97
% 0.21/1.40 # Proof object formula steps : 29
% 0.21/1.40 # Proof object conjectures : 40
% 0.21/1.40 # Proof object clause conjectures : 37
% 0.21/1.40 # Proof object formula conjectures : 3
% 0.21/1.40 # Proof object initial clauses used : 43
% 0.21/1.40 # Proof object initial formulas used : 14
% 0.21/1.40 # Proof object generating inferences : 47
% 0.21/1.40 # Proof object simplifying inferences : 117
% 0.21/1.40 # Training examples: 0 positive, 0 negative
% 0.21/1.40 # Parsed axioms : 37
% 0.21/1.40 # Removed by relevancy pruning/SinE : 0
% 0.21/1.40 # Initial clauses : 73
% 0.21/1.40 # Removed in clause preprocessing : 6
% 0.21/1.40 # Initial clauses in saturation : 67
% 0.21/1.40 # Processed clauses : 1144
% 0.21/1.40 # ...of these trivial : 0
% 0.21/1.40 # ...subsumed : 509
% 0.21/1.40 # ...remaining for further processing : 635
% 0.21/1.40 # Other redundant clauses eliminated : 2
% 0.21/1.40 # Clauses deleted for lack of memory : 0
% 0.21/1.40 # Backward-subsumed : 94
% 0.21/1.40 # Backward-rewritten : 89
% 0.21/1.40 # Generated clauses : 2239
% 0.21/1.40 # ...of the previous two non-trivial : 2207
% 0.21/1.40 # Contextual simplify-reflections : 560
% 0.21/1.40 # Paramodulations : 2210
% 0.21/1.40 # Factorizations : 22
% 0.21/1.40 # Equation resolutions : 7
% 0.21/1.40 # Current number of processed clauses : 450
% 0.21/1.40 # Positive orientable unit clauses : 14
% 0.21/1.40 # Positive unorientable unit clauses: 0
% 0.21/1.40 # Negative unit clauses : 7
% 0.21/1.40 # Non-unit-clauses : 429
% 0.21/1.40 # Current number of unprocessed clauses: 870
% 0.21/1.40 # ...number of literals in the above : 7474
% 0.21/1.40 # Current number of archived formulas : 0
% 0.21/1.40 # Current number of archived clauses : 183
% 0.21/1.40 # Clause-clause subsumption calls (NU) : 98025
% 0.21/1.40 # Rec. Clause-clause subsumption calls : 11751
% 0.21/1.40 # Non-unit clause-clause subsumptions : 1128
% 0.21/1.40 # Unit Clause-clause subsumption calls : 289
% 0.21/1.40 # Rewrite failures with RHS unbound : 0
% 0.21/1.40 # BW rewrite match attempts : 5
% 0.21/1.40 # BW rewrite match successes : 5
% 0.21/1.40 # Condensation attempts : 0
% 0.21/1.40 # Condensation successes : 0
% 0.21/1.40 # Termbank termtop insertions : 70189
% 0.21/1.40
% 0.21/1.40 # -------------------------------------------------
% 0.21/1.40 # User time : 0.151 s
% 0.21/1.40 # System time : 0.005 s
% 0.21/1.40 # Total time : 0.156 s
% 0.21/1.40 # Maximum resident set size: 5416 pages
% 0.21/23.40 eprover: CPU time limit exceeded, terminating
% 0.21/23.41 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.21/23.41 eprover: No such file or directory
% 0.21/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.21/23.42 eprover: No such file or directory
% 0.21/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.21/23.42 eprover: No such file or directory
% 0.21/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.21/23.43 eprover: No such file or directory
% 0.21/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.21/23.44 eprover: No such file or directory
% 0.21/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.21/23.44 eprover: No such file or directory
% 0.21/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.21/23.45 eprover: No such file or directory
% 0.21/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.21/23.45 eprover: No such file or directory
% 0.21/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.21/23.46 eprover: No such file or directory
% 0.21/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.21/23.46 eprover: No such file or directory
% 0.21/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.21/23.47 eprover: No such file or directory
%------------------------------------------------------------------------------