TSTP Solution File: LAT333+1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : LAT333+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 18:08:42 EDT 2023
% Result : Theorem 443.37s 57.14s
% Output : CNFRefutation 443.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 126 ( 14 unt; 0 def)
% Number of atoms : 844 ( 54 equ)
% Maximal formula atoms : 54 ( 6 avg)
% Number of connectives : 1143 ( 425 ~; 480 |; 162 &)
% ( 2 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 2 con; 0-3 aty)
% Number of variables : 265 ( 4 sgn; 134 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_m2_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',dt_m2_lattice4) ).
fof(dt_m2_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',dt_m2_filter_2) ).
fof(t76_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> v13_lattices(k23_filter_2(X1,X2)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',t76_filter_2) ).
fof(t23_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m2_filter_2(X4,X1)
=> ( r2_hidden(X2,X4)
=> ( r2_hidden(k4_lattices(X1,X2,X3),X4)
& r2_hidden(k4_lattices(X1,X3,X2),X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',t23_filter_2) ).
fof(d13_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_lattices(X1) )
=> ( v13_lattices(X1)
<=> ? [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
& ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( k2_lattices(X1,X2,X3) = X2
& k2_lattices(X1,X3,X2) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',d13_lattices) ).
fof(redefinition_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',redefinition_k4_lattices) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3)) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',t4_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',t1_subset) ).
fof(cc1_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',cc1_lattices) ).
fof(t69_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_nat_lat(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',t69_filter_2) ).
fof(dt_m2_nat_lat,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_nat_lat(X2,X1)
=> ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',dt_m2_nat_lat) ).
fof(dt_k23_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> m2_nat_lat(k23_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',dt_k23_filter_2) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',dt_l3_lattices) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',existence_m1_subset_1) ).
fof(t73_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( u1_struct_0(k23_filter_2(X1,X2)) = X2
& u2_lattices(k23_filter_2(X1,X2)) = k1_realset1(u2_lattices(X1),X2)
& u1_lattices(k23_filter_2(X1,X2)) = k1_realset1(u1_lattices(X1),X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',t73_filter_2) ).
fof(fc5_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( ~ v3_struct_0(k23_filter_2(X1,X2))
& v3_lattices(k23_filter_2(X1,X2))
& v4_lattices(k23_filter_2(X1,X2))
& v5_lattices(k23_filter_2(X1,X2))
& v6_lattices(k23_filter_2(X1,X2))
& v7_lattices(k23_filter_2(X1,X2))
& v8_lattices(k23_filter_2(X1,X2))
& v9_lattices(k23_filter_2(X1,X2))
& v10_lattices(k23_filter_2(X1,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',fc5_filter_2) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3))
& v1_xboole_0(X3) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',t5_subset) ).
fof(rc1_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ? [X2] :
( m2_lattice4(X2,X1)
& ~ v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',rc1_lattice4) ).
fof(commutativity_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',commutativity_k4_lattices) ).
fof(t74_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ! [X5] :
( m1_subset_1(X5,u1_struct_0(k23_filter_2(X1,X2)))
=> ! [X6] :
( m1_subset_1(X6,u1_struct_0(k23_filter_2(X1,X2)))
=> ( ( X3 = X5
& X4 = X6 )
=> ( k3_lattices(X1,X3,X4) = k3_lattices(k23_filter_2(X1,X2),X5,X6)
& k4_lattices(X1,X3,X4) = k4_lattices(k23_filter_2(X1,X2),X5,X6) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p',t74_filter_2) ).
fof(c_0_21,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_lattice4]) ).
fof(c_0_22,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_filter_2]) ).
fof(c_0_23,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> v13_lattices(k23_filter_2(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t76_filter_2])]) ).
fof(c_0_24,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m2_filter_2(X4,X1)
=> ( r2_hidden(X2,X4)
=> ( r2_hidden(k4_lattices(X1,X2,X3),X4)
& r2_hidden(k4_lattices(X1,X3,X2),X4) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t23_filter_2]) ).
fof(c_0_25,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_lattices(X1) )
=> ( v13_lattices(X1)
<=> ? [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
& ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( k2_lattices(X1,X2,X3) = X2
& k2_lattices(X1,X3,X2) = X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d13_lattices]) ).
fof(c_0_26,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k4_lattices]) ).
fof(c_0_27,plain,
! [X102,X103,X104] :
( ~ r2_hidden(X102,X103)
| ~ m1_subset_1(X103,k1_zfmisc_1(X104))
| m1_subset_1(X102,X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_28,plain,
! [X57,X58] :
( v3_struct_0(X57)
| ~ v10_lattices(X57)
| ~ l3_lattices(X57)
| ~ m2_lattice4(X58,X57)
| m1_subset_1(X58,k1_zfmisc_1(u1_struct_0(X57))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_29,plain,
! [X26,X27] :
( ( ~ v1_xboole_0(X27)
| ~ m2_filter_2(X27,X26)
| v3_struct_0(X26)
| ~ v10_lattices(X26)
| ~ l3_lattices(X26) )
& ( m2_lattice4(X27,X26)
| ~ m2_filter_2(X27,X26)
| v3_struct_0(X26)
| ~ v10_lattices(X26)
| ~ l3_lattices(X26) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
fof(c_0_30,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m2_filter_2(esk2_0,esk1_0)
& v13_lattices(esk1_0)
& ~ v13_lattices(k23_filter_2(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
fof(c_0_31,plain,
! [X98,X99] :
( ~ r2_hidden(X98,X99)
| m1_subset_1(X98,X99) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_32,plain,
! [X30,X31,X32,X33] :
( ( r2_hidden(k4_lattices(X30,X31,X32),X33)
| ~ r2_hidden(X31,X33)
| ~ m2_filter_2(X33,X30)
| ~ m1_subset_1(X32,u1_struct_0(X30))
| ~ m1_subset_1(X31,u1_struct_0(X30))
| v3_struct_0(X30)
| ~ v10_lattices(X30)
| ~ l3_lattices(X30) )
& ( r2_hidden(k4_lattices(X30,X32,X31),X33)
| ~ r2_hidden(X31,X33)
| ~ m2_filter_2(X33,X30)
| ~ m1_subset_1(X32,u1_struct_0(X30))
| ~ m1_subset_1(X31,u1_struct_0(X30))
| v3_struct_0(X30)
| ~ v10_lattices(X30)
| ~ l3_lattices(X30) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_33,plain,
! [X9,X11,X12] :
( ( m1_subset_1(esk3_1(X9),u1_struct_0(X9))
| ~ v13_lattices(X9)
| v3_struct_0(X9)
| ~ l1_lattices(X9) )
& ( k2_lattices(X9,esk3_1(X9),X11) = esk3_1(X9)
| ~ m1_subset_1(X11,u1_struct_0(X9))
| ~ v13_lattices(X9)
| v3_struct_0(X9)
| ~ l1_lattices(X9) )
& ( k2_lattices(X9,X11,esk3_1(X9)) = esk3_1(X9)
| ~ m1_subset_1(X11,u1_struct_0(X9))
| ~ v13_lattices(X9)
| v3_struct_0(X9)
| ~ l1_lattices(X9) )
& ( m1_subset_1(esk4_2(X9,X12),u1_struct_0(X9))
| ~ m1_subset_1(X12,u1_struct_0(X9))
| v13_lattices(X9)
| v3_struct_0(X9)
| ~ l1_lattices(X9) )
& ( k2_lattices(X9,X12,esk4_2(X9,X12)) != X12
| k2_lattices(X9,esk4_2(X9,X12),X12) != X12
| ~ m1_subset_1(X12,u1_struct_0(X9))
| v13_lattices(X9)
| v3_struct_0(X9)
| ~ l1_lattices(X9) ) ),
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_25])])])])]) ).
fof(c_0_34,plain,
! [X41,X42,X43] :
( v3_struct_0(X41)
| ~ v6_lattices(X41)
| ~ l1_lattices(X41)
| ~ m1_subset_1(X42,u1_struct_0(X41))
| ~ m1_subset_1(X43,u1_struct_0(X41))
| k4_lattices(X41,X42,X43) = k2_lattices(X41,X42,X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
fof(c_0_35,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
cnf(c_0_36,plain,
( m1_subset_1(X1,X3)
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
( v3_struct_0(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
( m2_lattice4(X1,X2)
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_43,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_nat_lat(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[t69_filter_2]) ).
fof(c_0_44,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_nat_lat(X2,X1)
=> ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_nat_lat]) ).
fof(c_0_45,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> m2_nat_lat(k23_filter_2(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k23_filter_2]) ).
cnf(c_0_46,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_47,plain,
( r2_hidden(k4_lattices(X1,X2,X3),X4)
| v3_struct_0(X1)
| ~ r2_hidden(X3,X4)
| ~ m2_filter_2(X4,X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_48,plain,
( k2_lattices(X1,esk3_1(X1),X2) = esk3_1(X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v13_lattices(X1)
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_49,plain,
( v3_struct_0(X1)
| k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3)
| ~ v6_lattices(X1)
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_50,plain,
( m1_subset_1(esk3_1(X1),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v13_lattices(X1)
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_51,plain,
! [X67] :
( ( ~ v3_struct_0(X67)
| v3_struct_0(X67)
| ~ v10_lattices(X67)
| ~ l3_lattices(X67) )
& ( v4_lattices(X67)
| v3_struct_0(X67)
| ~ v10_lattices(X67)
| ~ l3_lattices(X67) )
& ( v5_lattices(X67)
| v3_struct_0(X67)
| ~ v10_lattices(X67)
| ~ l3_lattices(X67) )
& ( v6_lattices(X67)
| v3_struct_0(X67)
| ~ v10_lattices(X67)
| ~ l3_lattices(X67) )
& ( v7_lattices(X67)
| v3_struct_0(X67)
| ~ v10_lattices(X67)
| ~ l3_lattices(X67) )
& ( v8_lattices(X67)
| v3_struct_0(X67)
| ~ v10_lattices(X67)
| ~ l3_lattices(X67) )
& ( v9_lattices(X67)
| v3_struct_0(X67)
| ~ v10_lattices(X67)
| ~ l3_lattices(X67) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
fof(c_0_52,plain,
! [X46] :
( ( l1_lattices(X46)
| ~ l3_lattices(X46) )
& ( l2_lattices(X46)
| ~ l3_lattices(X46) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_53,plain,
( m1_subset_1(X1,u1_struct_0(X2))
| v3_struct_0(X2)
| ~ m2_lattice4(X3,X2)
| ~ r2_hidden(X1,X3)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_54,negated_conjecture,
m2_lattice4(esk2_0,esk1_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_40]),c_0_41])]),c_0_42]) ).
fof(c_0_55,plain,
! [X100,X101] :
( ~ m1_subset_1(X100,X101)
| v1_xboole_0(X101)
| r2_hidden(X100,X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_56,plain,
( v3_struct_0(X2)
| ~ v1_xboole_0(X1)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_57,plain,
! [X54,X55,X56] :
( v3_struct_0(X54)
| ~ v10_lattices(X54)
| ~ l3_lattices(X54)
| ~ m2_nat_lat(X55,X54)
| ~ m1_subset_1(X56,u1_struct_0(X55))
| m1_subset_1(X56,u1_struct_0(X54)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])]) ).
fof(c_0_58,plain,
! [X44] : m1_subset_1(esk7_1(X44),X44),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_59,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( u1_struct_0(k23_filter_2(X1,X2)) = X2
& u2_lattices(k23_filter_2(X1,X2)) = k1_realset1(u2_lattices(X1),X2)
& u1_lattices(k23_filter_2(X1,X2)) = k1_realset1(u1_lattices(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t73_filter_2]) ).
fof(c_0_60,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( ~ v3_struct_0(k23_filter_2(X1,X2))
& v3_lattices(k23_filter_2(X1,X2))
& v4_lattices(k23_filter_2(X1,X2))
& v5_lattices(k23_filter_2(X1,X2))
& v6_lattices(k23_filter_2(X1,X2))
& v7_lattices(k23_filter_2(X1,X2))
& v8_lattices(k23_filter_2(X1,X2))
& v9_lattices(k23_filter_2(X1,X2))
& v10_lattices(k23_filter_2(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc5_filter_2]) ).
fof(c_0_61,plain,
! [X48,X49] :
( ( ~ v3_struct_0(X49)
| ~ m2_nat_lat(X49,X48)
| v3_struct_0(X48)
| ~ v10_lattices(X48)
| ~ l3_lattices(X48) )
& ( v10_lattices(X49)
| ~ m2_nat_lat(X49,X48)
| v3_struct_0(X48)
| ~ v10_lattices(X48)
| ~ l3_lattices(X48) )
& ( l3_lattices(X49)
| ~ m2_nat_lat(X49,X48)
| v3_struct_0(X48)
| ~ v10_lattices(X48)
| ~ l3_lattices(X48) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
fof(c_0_62,plain,
! [X14,X15] :
( v3_struct_0(X14)
| ~ v10_lattices(X14)
| ~ l3_lattices(X14)
| v1_xboole_0(X15)
| ~ m2_lattice4(X15,X14)
| m2_nat_lat(k23_filter_2(X14,X15),X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])]) ).
fof(c_0_63,plain,
! [X105,X106,X107] :
( ~ r2_hidden(X105,X106)
| ~ m1_subset_1(X106,k1_zfmisc_1(X107))
| ~ v1_xboole_0(X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_64,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ? [X2] :
( m2_lattice4(X2,X1)
& ~ v1_xboole_0(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_lattice4]) ).
cnf(c_0_65,plain,
( m1_subset_1(k4_lattices(X1,X2,X3),X4)
| v3_struct_0(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(X3,X4)
| ~ m2_filter_2(X4,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_66,plain,
( k4_lattices(X1,esk3_1(X1),X2) = esk3_1(X1)
| v3_struct_0(X1)
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v6_lattices(X1)
| ~ v13_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_67,plain,
( v6_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_68,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_69,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_70,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_71,negated_conjecture,
~ v1_xboole_0(esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_72,plain,
( v3_struct_0(X1)
| m1_subset_1(X3,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_nat_lat(X2,X1)
| ~ m1_subset_1(X3,u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_73,plain,
m1_subset_1(esk7_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_74,plain,
! [X18,X19] :
( ( u1_struct_0(k23_filter_2(X18,X19)) = X19
| v1_xboole_0(X19)
| ~ m2_lattice4(X19,X18)
| v3_struct_0(X18)
| ~ v10_lattices(X18)
| ~ l3_lattices(X18) )
& ( u2_lattices(k23_filter_2(X18,X19)) = k1_realset1(u2_lattices(X18),X19)
| v1_xboole_0(X19)
| ~ m2_lattice4(X19,X18)
| v3_struct_0(X18)
| ~ v10_lattices(X18)
| ~ l3_lattices(X18) )
& ( u1_lattices(k23_filter_2(X18,X19)) = k1_realset1(u1_lattices(X18),X19)
| v1_xboole_0(X19)
| ~ m2_lattice4(X19,X18)
| v3_struct_0(X18)
| ~ v10_lattices(X18)
| ~ l3_lattices(X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])]) ).
fof(c_0_75,plain,
! [X16,X17] :
( ( ~ v3_struct_0(k23_filter_2(X16,X17))
| v3_struct_0(X16)
| ~ v10_lattices(X16)
| ~ l3_lattices(X16)
| v1_xboole_0(X17)
| ~ m2_lattice4(X17,X16) )
& ( v3_lattices(k23_filter_2(X16,X17))
| v3_struct_0(X16)
| ~ v10_lattices(X16)
| ~ l3_lattices(X16)
| v1_xboole_0(X17)
| ~ m2_lattice4(X17,X16) )
& ( v4_lattices(k23_filter_2(X16,X17))
| v3_struct_0(X16)
| ~ v10_lattices(X16)
| ~ l3_lattices(X16)
| v1_xboole_0(X17)
| ~ m2_lattice4(X17,X16) )
& ( v5_lattices(k23_filter_2(X16,X17))
| v3_struct_0(X16)
| ~ v10_lattices(X16)
| ~ l3_lattices(X16)
| v1_xboole_0(X17)
| ~ m2_lattice4(X17,X16) )
& ( v6_lattices(k23_filter_2(X16,X17))
| v3_struct_0(X16)
| ~ v10_lattices(X16)
| ~ l3_lattices(X16)
| v1_xboole_0(X17)
| ~ m2_lattice4(X17,X16) )
& ( v7_lattices(k23_filter_2(X16,X17))
| v3_struct_0(X16)
| ~ v10_lattices(X16)
| ~ l3_lattices(X16)
| v1_xboole_0(X17)
| ~ m2_lattice4(X17,X16) )
& ( v8_lattices(k23_filter_2(X16,X17))
| v3_struct_0(X16)
| ~ v10_lattices(X16)
| ~ l3_lattices(X16)
| v1_xboole_0(X17)
| ~ m2_lattice4(X17,X16) )
& ( v9_lattices(k23_filter_2(X16,X17))
| v3_struct_0(X16)
| ~ v10_lattices(X16)
| ~ l3_lattices(X16)
| v1_xboole_0(X17)
| ~ m2_lattice4(X17,X16) )
& ( v10_lattices(k23_filter_2(X16,X17))
| v3_struct_0(X16)
| ~ v10_lattices(X16)
| ~ l3_lattices(X16)
| v1_xboole_0(X17)
| ~ m2_lattice4(X17,X16) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).
cnf(c_0_76,plain,
( l3_lattices(X1)
| v3_struct_0(X2)
| ~ m2_nat_lat(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_77,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| m2_nat_lat(k23_filter_2(X1,X2),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_78,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_79,plain,
! [X61] :
( ( m2_lattice4(esk12_1(X61),X61)
| v3_struct_0(X61)
| ~ v10_lattices(X61)
| ~ l3_lattices(X61) )
& ( ~ v1_xboole_0(esk12_1(X61))
| v3_struct_0(X61)
| ~ v10_lattices(X61)
| ~ l3_lattices(X61) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])]) ).
cnf(c_0_80,plain,
( v13_lattices(X1)
| v3_struct_0(X1)
| k2_lattices(X1,X2,esk4_2(X1,X2)) != X2
| k2_lattices(X1,esk4_2(X1,X2),X2) != X2
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_81,plain,
( m1_subset_1(esk4_2(X1,X2),u1_struct_0(X1))
| v13_lattices(X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_82,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k4_lattices]) ).
fof(c_0_83,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ! [X5] :
( m1_subset_1(X5,u1_struct_0(k23_filter_2(X1,X2)))
=> ! [X6] :
( m1_subset_1(X6,u1_struct_0(k23_filter_2(X1,X2)))
=> ( ( X3 = X5
& X4 = X6 )
=> ( k3_lattices(X1,X3,X4) = k3_lattices(k23_filter_2(X1,X2),X5,X6)
& k4_lattices(X1,X3,X4) = k4_lattices(k23_filter_2(X1,X2),X5,X6) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t74_filter_2]) ).
cnf(c_0_84,plain,
( m1_subset_1(esk3_1(X1),X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ r2_hidden(X3,X2)
| ~ v13_lattices(X1)
| ~ m2_filter_2(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_50]),c_0_68]) ).
cnf(c_0_85,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_86,negated_conjecture,
v13_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_87,plain,
( m1_subset_1(esk7_1(u1_struct_0(X1)),u1_struct_0(X2))
| v3_struct_0(X2)
| ~ m2_nat_lat(X1,X2)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_88,plain,
( u1_struct_0(k23_filter_2(X1,X2)) = X2
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ m2_lattice4(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_89,plain,
( v10_lattices(k23_filter_2(X1,X2))
| v3_struct_0(X1)
| v1_xboole_0(X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_90,plain,
( v1_xboole_0(X1)
| l3_lattices(k23_filter_2(X2,X1))
| v3_struct_0(X2)
| ~ m2_lattice4(X1,X2)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_91,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| ~ v3_struct_0(k23_filter_2(X1,X2))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_92,plain,
( v3_struct_0(X1)
| ~ m2_lattice4(X2,X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ r2_hidden(X3,X2)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_37]) ).
cnf(c_0_93,plain,
( m2_lattice4(esk12_1(X1),X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_94,plain,
( v13_lattices(X1)
| v3_struct_0(X1)
| k2_lattices(X1,X2,esk4_2(X1,X2)) != X2
| k4_lattices(X1,esk4_2(X1,X2),X2) != X2
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v6_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_49]),c_0_81]) ).
fof(c_0_95,plain,
! [X81,X82,X83] :
( v3_struct_0(X81)
| ~ v6_lattices(X81)
| ~ l1_lattices(X81)
| ~ m1_subset_1(X82,u1_struct_0(X81))
| ~ m1_subset_1(X83,u1_struct_0(X81))
| k4_lattices(X81,X82,X83) = k4_lattices(X81,X83,X82) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])]) ).
fof(c_0_96,plain,
! [X20,X21,X22,X23,X24,X25] :
( ( k3_lattices(X20,X22,X23) = k3_lattices(k23_filter_2(X20,X21),X24,X25)
| X22 != X24
| X23 != X25
| ~ m1_subset_1(X25,u1_struct_0(k23_filter_2(X20,X21)))
| ~ m1_subset_1(X24,u1_struct_0(k23_filter_2(X20,X21)))
| ~ m1_subset_1(X23,u1_struct_0(X20))
| ~ m1_subset_1(X22,u1_struct_0(X20))
| v1_xboole_0(X21)
| ~ m2_lattice4(X21,X20)
| v3_struct_0(X20)
| ~ v10_lattices(X20)
| ~ l3_lattices(X20) )
& ( k4_lattices(X20,X22,X23) = k4_lattices(k23_filter_2(X20,X21),X24,X25)
| X22 != X24
| X23 != X25
| ~ m1_subset_1(X25,u1_struct_0(k23_filter_2(X20,X21)))
| ~ m1_subset_1(X24,u1_struct_0(k23_filter_2(X20,X21)))
| ~ m1_subset_1(X23,u1_struct_0(X20))
| ~ m1_subset_1(X22,u1_struct_0(X20))
| v1_xboole_0(X21)
| ~ m2_lattice4(X21,X20)
| v3_struct_0(X20)
| ~ v10_lattices(X20)
| ~ l3_lattices(X20) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])])]) ).
cnf(c_0_97,negated_conjecture,
( m1_subset_1(esk3_1(esk1_0),X1)
| ~ m1_subset_1(X2,esk2_0)
| ~ r2_hidden(X2,X1)
| ~ m2_filter_2(X1,esk1_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_84,c_0_85]),c_0_86]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_98,plain,
( m1_subset_1(esk7_1(u1_struct_0(X1)),X2)
| v1_xboole_0(X2)
| v3_struct_0(X3)
| ~ m2_nat_lat(X1,k23_filter_2(X3,X2))
| ~ m2_lattice4(X2,X3)
| ~ l3_lattices(X3)
| ~ v10_lattices(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_90]),c_0_91]) ).
cnf(c_0_99,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ r2_hidden(X2,esk12_1(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_100,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(esk12_1(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_101,plain,
( v13_lattices(X1)
| v3_struct_0(X1)
| k4_lattices(X1,X2,esk4_2(X1,X2)) != X2
| k4_lattices(X1,esk4_2(X1,X2),X2) != X2
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v6_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_49]),c_0_81]) ).
cnf(c_0_102,plain,
( v3_struct_0(X1)
| k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2)
| ~ v6_lattices(X1)
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_103,plain,
( k4_lattices(X1,X2,X3) = k4_lattices(k23_filter_2(X1,X4),X5,X6)
| v1_xboole_0(X4)
| v3_struct_0(X1)
| X2 != X5
| X3 != X6
| ~ m1_subset_1(X6,u1_struct_0(k23_filter_2(X1,X4)))
| ~ m1_subset_1(X5,u1_struct_0(k23_filter_2(X1,X4)))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m2_lattice4(X4,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_104,negated_conjecture,
( m1_subset_1(esk3_1(esk1_0),X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X2,esk2_0)
| ~ m1_subset_1(X2,X1)
| ~ m2_filter_2(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_97,c_0_70]) ).
cnf(c_0_105,plain,
( m1_subset_1(esk7_1(u1_struct_0(k23_filter_2(k23_filter_2(X1,X2),X3))),X2)
| v1_xboole_0(X3)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ m2_lattice4(X3,k23_filter_2(X1,X2))
| ~ m2_lattice4(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_77]),c_0_89]),c_0_90]),c_0_91]) ).
cnf(c_0_106,plain,
( v3_struct_0(X1)
| ~ m1_subset_1(X2,esk12_1(X1))
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_70]),c_0_100]) ).
cnf(c_0_107,plain,
( v13_lattices(X1)
| v3_struct_0(X1)
| k4_lattices(X1,X2,esk4_2(X1,X2)) != X2
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v6_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_81]) ).
cnf(c_0_108,plain,
( k4_lattices(k23_filter_2(X1,X2),X3,X4) = k4_lattices(X1,X3,X4)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ m2_lattice4(X2,X1)
| ~ m1_subset_1(X4,u1_struct_0(k23_filter_2(X1,X2)))
| ~ m1_subset_1(X3,u1_struct_0(k23_filter_2(X1,X2)))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_103])]) ).
cnf(c_0_109,plain,
( v6_lattices(k23_filter_2(X1,X2))
| v3_struct_0(X1)
| v1_xboole_0(X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_110,negated_conjecture,
( m1_subset_1(esk3_1(esk1_0),X1)
| v1_xboole_0(X2)
| v1_xboole_0(X1)
| v3_struct_0(X3)
| ~ m2_lattice4(X2,k23_filter_2(X3,esk2_0))
| ~ m2_lattice4(esk2_0,X3)
| ~ m1_subset_1(esk7_1(u1_struct_0(k23_filter_2(k23_filter_2(X3,esk2_0),X2))),X1)
| ~ m2_filter_2(X1,esk1_0)
| ~ l3_lattices(X3)
| ~ v10_lattices(X3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_71]) ).
cnf(c_0_111,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_73]) ).
cnf(c_0_112,plain,
( v1_xboole_0(X1)
| v13_lattices(k23_filter_2(X2,X1))
| v3_struct_0(X2)
| k4_lattices(X2,X3,esk4_2(k23_filter_2(X2,X1),X3)) != X3
| ~ m2_lattice4(X1,X2)
| ~ l1_lattices(k23_filter_2(X2,X1))
| ~ m1_subset_1(esk4_2(k23_filter_2(X2,X1),X3),u1_struct_0(X2))
| ~ m1_subset_1(X3,u1_struct_0(k23_filter_2(X2,X1)))
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]),c_0_81]),c_0_91]) ).
cnf(c_0_113,plain,
( v3_struct_0(X2)
| ~ v3_struct_0(X1)
| ~ m2_nat_lat(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_114,negated_conjecture,
( m1_subset_1(esk3_1(esk1_0),u1_struct_0(X1))
| v1_xboole_0(X2)
| v3_struct_0(X1)
| v3_struct_0(X3)
| ~ m2_nat_lat(k23_filter_2(k23_filter_2(X3,esk2_0),X2),X1)
| ~ m2_lattice4(X2,k23_filter_2(X3,esk2_0))
| ~ m2_lattice4(esk2_0,X3)
| ~ m2_filter_2(u1_struct_0(X1),esk1_0)
| ~ l3_lattices(X3)
| ~ l3_lattices(X1)
| ~ v10_lattices(X3)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_87]),c_0_111]) ).
cnf(c_0_115,plain,
( v1_xboole_0(X1)
| v13_lattices(k23_filter_2(X2,X1))
| v3_struct_0(X2)
| ~ m2_lattice4(X1,X2)
| ~ l1_lattices(k23_filter_2(X2,X1))
| ~ m1_subset_1(esk4_2(k23_filter_2(X2,X1),esk3_1(X2)),u1_struct_0(X2))
| ~ m1_subset_1(esk3_1(X2),u1_struct_0(k23_filter_2(X2,X1)))
| ~ v13_lattices(X2)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_66]),c_0_67]),c_0_50]),c_0_68]) ).
cnf(c_0_116,plain,
( m1_subset_1(esk4_2(X1,X2),u1_struct_0(X3))
| v13_lattices(X1)
| v3_struct_0(X3)
| ~ m2_nat_lat(X1,X3)
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X3)
| ~ v10_lattices(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_81]),c_0_113]) ).
cnf(c_0_117,negated_conjecture,
( m1_subset_1(esk3_1(esk1_0),u1_struct_0(k23_filter_2(X1,esk2_0)))
| v1_xboole_0(X2)
| v3_struct_0(k23_filter_2(X1,esk2_0))
| v3_struct_0(X1)
| ~ m2_lattice4(X2,k23_filter_2(X1,esk2_0))
| ~ m2_lattice4(esk2_0,X1)
| ~ m2_filter_2(u1_struct_0(k23_filter_2(X1,esk2_0)),esk1_0)
| ~ l3_lattices(k23_filter_2(X1,esk2_0))
| ~ l3_lattices(X1)
| ~ v10_lattices(k23_filter_2(X1,esk2_0))
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_77]) ).
cnf(c_0_118,plain,
( v1_xboole_0(X1)
| v13_lattices(k23_filter_2(X2,X1))
| v3_struct_0(X2)
| ~ m2_lattice4(X1,X2)
| ~ l1_lattices(k23_filter_2(X2,X1))
| ~ m1_subset_1(esk3_1(X2),u1_struct_0(k23_filter_2(X2,X1)))
| ~ v13_lattices(X2)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_77]) ).
cnf(c_0_119,negated_conjecture,
( m1_subset_1(esk3_1(esk1_0),u1_struct_0(k23_filter_2(X1,esk2_0)))
| v3_struct_0(k23_filter_2(X1,esk2_0))
| v3_struct_0(X1)
| ~ m2_lattice4(esk2_0,X1)
| ~ m2_filter_2(u1_struct_0(k23_filter_2(X1,esk2_0)),esk1_0)
| ~ l3_lattices(k23_filter_2(X1,esk2_0))
| ~ l3_lattices(X1)
| ~ v10_lattices(k23_filter_2(X1,esk2_0))
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_93]),c_0_100]) ).
cnf(c_0_120,negated_conjecture,
~ v13_lattices(k23_filter_2(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_121,negated_conjecture,
~ v3_struct_0(k23_filter_2(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_54]),c_0_40]),c_0_41])]),c_0_71]),c_0_42]) ).
cnf(c_0_122,negated_conjecture,
( ~ m2_filter_2(u1_struct_0(k23_filter_2(esk1_0,esk2_0)),esk1_0)
| ~ l3_lattices(k23_filter_2(esk1_0,esk2_0))
| ~ v10_lattices(k23_filter_2(esk1_0,esk2_0)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[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_118,c_0_119]),c_0_54]),c_0_86]),c_0_40]),c_0_41])]),c_0_71]),c_0_120]),c_0_42]),c_0_121]),c_0_68]) ).
cnf(c_0_123,negated_conjecture,
( ~ l3_lattices(k23_filter_2(esk1_0,esk2_0))
| ~ v10_lattices(k23_filter_2(esk1_0,esk2_0)) ),
inference(sr,[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_122,c_0_88]),c_0_39]),c_0_54]),c_0_40]),c_0_41])]),c_0_71]),c_0_42]) ).
cnf(c_0_124,negated_conjecture,
~ l3_lattices(k23_filter_2(esk1_0,esk2_0)),
inference(sr,[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_123,c_0_89]),c_0_54]),c_0_40]),c_0_41])]),c_0_71]),c_0_42]) ).
cnf(c_0_125,negated_conjecture,
$false,
inference(sr,[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_124,c_0_90]),c_0_54]),c_0_40]),c_0_41])]),c_0_71]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT333+1 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n032.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 2400
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Oct 2 10:01:19 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.oUH7szPgLK/E---3.1_27079.p
% 443.37/57.14 # Version: 3.1pre001
% 443.37/57.14 # Preprocessing class: FSLSSMSSSSSNFFN.
% 443.37/57.14 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 443.37/57.14 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 443.37/57.14 # Starting new_bool_3 with 300s (1) cores
% 443.37/57.14 # Starting new_bool_1 with 300s (1) cores
% 443.37/57.14 # Starting sh5l with 300s (1) cores
% 443.37/57.14 # new_bool_3 with pid 27168 completed with status 0
% 443.37/57.14 # Result found by new_bool_3
% 443.37/57.14 # Preprocessing class: FSLSSMSSSSSNFFN.
% 443.37/57.14 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 443.37/57.14 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 443.37/57.14 # Starting new_bool_3 with 300s (1) cores
% 443.37/57.14 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 443.37/57.14 # Search class: FGHSM-FSLM31-SFFFFFNN
% 443.37/57.14 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 443.37/57.14 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 163s (1) cores
% 443.37/57.14 # G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 27171 completed with status 0
% 443.37/57.14 # Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y
% 443.37/57.14 # Preprocessing class: FSLSSMSSSSSNFFN.
% 443.37/57.14 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 443.37/57.14 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 443.37/57.14 # Starting new_bool_3 with 300s (1) cores
% 443.37/57.14 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 443.37/57.14 # Search class: FGHSM-FSLM31-SFFFFFNN
% 443.37/57.14 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 443.37/57.14 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 163s (1) cores
% 443.37/57.14 # Preprocessing time : 0.003 s
% 443.37/57.14
% 443.37/57.14 # Proof found!
% 443.37/57.14 # SZS status Theorem
% 443.37/57.14 # SZS output start CNFRefutation
% See solution above
% 443.37/57.14 # Parsed axioms : 108
% 443.37/57.14 # Removed by relevancy pruning/SinE : 40
% 443.37/57.14 # Initial clauses : 138
% 443.37/57.14 # Removed in clause preprocessing : 2
% 443.37/57.14 # Initial clauses in saturation : 136
% 443.37/57.14 # Processed clauses : 23994
% 443.37/57.14 # ...of these trivial : 60
% 443.37/57.14 # ...subsumed : 15872
% 443.37/57.14 # ...remaining for further processing : 8062
% 443.37/57.14 # Other redundant clauses eliminated : 7
% 443.37/57.14 # Clauses deleted for lack of memory : 0
% 443.37/57.14 # Backward-subsumed : 955
% 443.37/57.14 # Backward-rewritten : 10
% 443.37/57.14 # Generated clauses : 628743
% 443.37/57.14 # ...of the previous two non-redundant : 591221
% 443.37/57.14 # ...aggressively subsumed : 0
% 443.37/57.14 # Contextual simplify-reflections : 6013
% 443.37/57.14 # Paramodulations : 628010
% 443.37/57.14 # Factorizations : 0
% 443.37/57.14 # NegExts : 0
% 443.37/57.14 # Equation resolutions : 735
% 443.37/57.14 # Total rewrite steps : 26461
% 443.37/57.14 # Propositional unsat checks : 1
% 443.37/57.14 # Propositional check models : 0
% 443.37/57.14 # Propositional check unsatisfiable : 0
% 443.37/57.14 # Propositional clauses : 0
% 443.37/57.14 # Propositional clauses after purity: 0
% 443.37/57.14 # Propositional unsat core size : 0
% 443.37/57.14 # Propositional preprocessing time : 0.000
% 443.37/57.14 # Propositional encoding time : 1.421
% 443.37/57.14 # Propositional solver time : 0.234
% 443.37/57.14 # Success case prop preproc time : 0.000
% 443.37/57.14 # Success case prop encoding time : 0.000
% 443.37/57.14 # Success case prop solver time : 0.000
% 443.37/57.14 # Current number of processed clauses : 7095
% 443.37/57.14 # Positive orientable unit clauses : 41
% 443.37/57.14 # Positive unorientable unit clauses: 0
% 443.37/57.14 # Negative unit clauses : 12
% 443.37/57.14 # Non-unit-clauses : 7042
% 443.37/57.14 # Current number of unprocessed clauses: 562630
% 443.37/57.14 # ...number of literals in the above : 9808015
% 443.37/57.14 # Current number of archived formulas : 0
% 443.37/57.14 # Current number of archived clauses : 965
% 443.37/57.14 # Clause-clause subsumption calls (NU) : 20228864
% 443.37/57.14 # Rec. Clause-clause subsumption calls : 572592
% 443.37/57.14 # Non-unit clause-clause subsumptions : 20768
% 443.37/57.14 # Unit Clause-clause subsumption calls : 4179
% 443.37/57.14 # Rewrite failures with RHS unbound : 0
% 443.37/57.14 # BW rewrite match attempts : 30
% 443.37/57.14 # BW rewrite match successes : 10
% 443.37/57.14 # Condensation attempts : 0
% 443.37/57.14 # Condensation successes : 0
% 443.37/57.14 # Termbank termtop insertions : 49520251
% 443.37/57.14
% 443.37/57.14 # -------------------------------------------------
% 443.37/57.14 # User time : 55.026 s
% 443.37/57.14 # System time : 0.880 s
% 443.37/57.14 # Total time : 55.906 s
% 443.37/57.14 # Maximum resident set size: 2320 pages
% 443.37/57.14
% 443.37/57.14 # -------------------------------------------------
% 443.37/57.14 # User time : 55.029 s
% 443.37/57.14 # System time : 0.884 s
% 443.37/57.14 # Total time : 55.913 s
% 443.37/57.14 # Maximum resident set size: 1792 pages
% 443.37/57.14 % E---3.1 exiting
% 443.37/57.15 % E---3.1 exiting
%------------------------------------------------------------------------------