TSTP Solution File: LAT329+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT329+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 : 300s
% DateTime : Thu Aug 31 06:01:26 EDT 2023
% Result : Theorem 245.05s 245.03s
% Output : CNFRefutation 245.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 73
% Syntax : Number of formulae : 180 ( 29 unt; 52 typ; 0 def)
% Number of atoms : 615 ( 15 equ)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 781 ( 294 ~; 301 |; 107 &)
% ( 10 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 42 >; 22 *; 0 +; 0 <<)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 10 con; 0-3 aty)
% Number of variables : 226 ( 2 sgn; 136 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v3_struct_0: $i > $o ).
tff(decl_23,type,
v10_lattices: $i > $o ).
tff(decl_24,type,
l3_lattices: $i > $o ).
tff(decl_25,type,
u1_struct_0: $i > $i ).
tff(decl_26,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_27,type,
v14_lattices: $i > $o ).
tff(decl_28,type,
k2_filter_2: ( $i * $i ) > $i ).
tff(decl_29,type,
k6_lattices: $i > $i ).
tff(decl_30,type,
k22_filter_2: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
r1_filter_2: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_33,type,
v1_xboole_0: $i > $o ).
tff(decl_34,type,
v1_funct_1: $i > $o ).
tff(decl_35,type,
v4_lattices: $i > $o ).
tff(decl_36,type,
v5_lattices: $i > $o ).
tff(decl_37,type,
v6_lattices: $i > $o ).
tff(decl_38,type,
v7_lattices: $i > $o ).
tff(decl_39,type,
v8_lattices: $i > $o ).
tff(decl_40,type,
v9_lattices: $i > $o ).
tff(decl_41,type,
k1_zfmisc_1: $i > $i ).
tff(decl_42,type,
k2_filter_0: ( $i * $i ) > $i ).
tff(decl_43,type,
a_2_0_filter_0: ( $i * $i ) > $i ).
tff(decl_44,type,
m2_lattice4: ( $i * $i ) > $o ).
tff(decl_45,type,
m1_filter_0: ( $i * $i ) > $o ).
tff(decl_46,type,
m1_filter_2: ( $i * $i ) > $o ).
tff(decl_47,type,
l2_lattices: $i > $o ).
tff(decl_48,type,
l1_lattices: $i > $o ).
tff(decl_49,type,
l1_struct_0: $i > $o ).
tff(decl_50,type,
k1_xboole_0: $i ).
tff(decl_51,type,
r3_lattices: ( $i * $i * $i ) > $o ).
tff(decl_52,type,
r1_lattices: ( $i * $i * $i ) > $o ).
tff(decl_53,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_54,type,
esk1_0: $i ).
tff(decl_55,type,
esk2_0: $i ).
tff(decl_56,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
esk4_0: $i ).
tff(decl_58,type,
esk5_0: $i ).
tff(decl_59,type,
esk6_0: $i ).
tff(decl_60,type,
esk7_0: $i ).
tff(decl_61,type,
esk8_1: $i > $i ).
tff(decl_62,type,
esk9_1: $i > $i ).
tff(decl_63,type,
esk10_1: $i > $i ).
tff(decl_64,type,
esk11_1: $i > $i ).
tff(decl_65,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
esk13_1: $i > $i ).
tff(decl_67,type,
esk14_1: $i > $i ).
tff(decl_68,type,
esk15_0: $i ).
tff(decl_69,type,
esk16_1: $i > $i ).
tff(decl_70,type,
esk17_0: $i ).
tff(decl_71,type,
esk18_0: $i ).
tff(decl_72,type,
esk19_1: $i > $i ).
tff(decl_73,type,
esk20_2: ( $i * $i ) > $i ).
fof(dt_k2_filter_0,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_filter_0(k2_filter_0(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_0) ).
fof(t66_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( v14_lattices(X1)
=> r1_filter_2(u1_struct_0(X1),k2_filter_2(X1,X2),k22_filter_2(X1,X2,k6_lattices(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_filter_2) ).
fof(redefinition_k2_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k2_filter_2(X1,X2) = k2_filter_0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).
fof(dt_m1_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_0) ).
fof(dt_k2_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_filter_2(k2_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_2) ).
fof(dt_m1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_2) ).
fof(dt_k22_filter_2,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> ( ~ v1_xboole_0(k22_filter_2(X1,X2,X3))
& m2_lattice4(k22_filter_2(X1,X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k22_filter_2) ).
fof(dt_k6_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l2_lattices(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lattices) ).
fof(t18_filter_0,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))
=> ( r2_hidden(X2,k2_filter_0(X1,X3))
<=> r3_lattices(X1,X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_0) ).
fof(t45_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r3_lattices(X1,X2,k6_lattices(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattices) ).
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/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(symmetry_r1_filter_2,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,k1_zfmisc_1(X1))
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
=> ( r1_filter_2(X1,X2,X3)
=> r1_filter_2(X1,X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).
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/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
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/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(d1_filter_2,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ( r1_filter_2(X1,X2,X3)
<=> ! [X4] :
( m1_subset_1(X4,X1)
=> ( r2_hidden(X4,X2)
<=> r2_hidden(X4,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_2) ).
fof(t63_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] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( r3_lattices(X1,X2,X3)
=> ( r2_hidden(X4,k22_filter_2(X1,X2,X3))
<=> ( r3_lattices(X1,X2,X4)
& r3_lattices(X1,X4,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_filter_2) ).
fof(fraenkel_a_2_0_filter_0,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2)
& m1_subset_1(X3,u1_struct_0(X2)) )
=> ( r2_hidden(X1,a_2_0_filter_0(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,u1_struct_0(X2))
& X1 = X4
& r3_lattices(X2,X3,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).
fof(d3_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k2_filter_0(X1,X2) = a_2_0_filter_0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_filter_0) ).
fof(c_0_21,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_filter_0(k2_filter_0(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k2_filter_0]) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( v14_lattices(X1)
=> r1_filter_2(u1_struct_0(X1),k2_filter_2(X1,X2),k22_filter_2(X1,X2,k6_lattices(X1))) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t66_filter_2])]) ).
fof(c_0_23,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k2_filter_2(X1,X2) = k2_filter_0(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_filter_2]) ).
fof(c_0_24,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_filter_0]) ).
fof(c_0_25,plain,
! [X22,X23] :
( v3_struct_0(X22)
| ~ v10_lattices(X22)
| ~ l3_lattices(X22)
| ~ m1_subset_1(X23,u1_struct_0(X22))
| m1_filter_0(k2_filter_0(X22,X23),X22) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
fof(c_0_26,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& v14_lattices(esk1_0)
& ~ r1_filter_2(u1_struct_0(esk1_0),k2_filter_2(esk1_0,esk2_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
fof(c_0_27,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_filter_2(k2_filter_2(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k2_filter_2]) ).
fof(c_0_28,plain,
! [X66,X67] :
( v3_struct_0(X66)
| ~ v10_lattices(X66)
| ~ l3_lattices(X66)
| ~ m1_subset_1(X67,u1_struct_0(X66))
| k2_filter_2(X66,X67) = k2_filter_0(X66,X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
fof(c_0_29,plain,
! [X30,X31] :
( ( ~ v1_xboole_0(X31)
| ~ m1_filter_0(X31,X30)
| v3_struct_0(X30)
| ~ v10_lattices(X30)
| ~ l3_lattices(X30) )
& ( m1_subset_1(X31,k1_zfmisc_1(u1_struct_0(X30)))
| ~ m1_filter_0(X31,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])])])]) ).
cnf(c_0_30,plain,
( v3_struct_0(X1)
| m1_filter_0(k2_filter_0(X1,X2),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_35,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_filter_2]) ).
fof(c_0_36,plain,
! [X24,X25] :
( v3_struct_0(X24)
| ~ v10_lattices(X24)
| ~ l3_lattices(X24)
| ~ m1_subset_1(X25,u1_struct_0(X24))
| m1_filter_2(k2_filter_2(X24,X25),X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
cnf(c_0_37,plain,
( v3_struct_0(X1)
| k2_filter_2(X1,X2) = k2_filter_0(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_38,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> ( ~ v1_xboole_0(k22_filter_2(X1,X2,X3))
& m2_lattice4(k22_filter_2(X1,X2,X3),X1) ) ),
inference(fof_simplification,[status(thm)],[dt_k22_filter_2]) ).
fof(c_0_39,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l2_lattices(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k6_lattices]) ).
fof(c_0_40,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))
=> ( r2_hidden(X2,k2_filter_0(X1,X3))
<=> r3_lattices(X1,X3,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[t18_filter_0]) ).
fof(c_0_41,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r3_lattices(X1,X2,k6_lattices(X1)) ) ),
inference(fof_simplification,[status(thm)],[t45_lattices]) ).
fof(c_0_42,plain,
! [X103,X104,X105] :
( ~ r2_hidden(X103,X104)
| ~ m1_subset_1(X104,k1_zfmisc_1(X105))
| ~ v1_xboole_0(X105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_43,plain,
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ m1_filter_0(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_44,negated_conjecture,
m1_filter_0(k2_filter_0(esk1_0,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_30,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
fof(c_0_45,plain,
! [X91,X92] :
( ~ m1_subset_1(X91,X92)
| v1_xboole_0(X92)
| r2_hidden(X91,X92) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_46,plain,
! [X44] : m1_subset_1(esk10_1(X44),X44),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_47,plain,
! [X32,X33] :
( ( ~ v1_xboole_0(X33)
| ~ m1_filter_2(X33,X32)
| v3_struct_0(X32)
| ~ v10_lattices(X32)
| ~ l3_lattices(X32) )
& ( m2_lattice4(X33,X32)
| ~ m1_filter_2(X33,X32)
| v3_struct_0(X32)
| ~ v10_lattices(X32)
| ~ l3_lattices(X32) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])]) ).
cnf(c_0_48,plain,
( v3_struct_0(X1)
| m1_filter_2(k2_filter_2(X1,X2),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,negated_conjecture,
k2_filter_2(esk1_0,esk2_0) = k2_filter_0(esk1_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_37,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
fof(c_0_50,plain,
! [X19,X20,X21] :
( ( ~ v1_xboole_0(k22_filter_2(X19,X20,X21))
| v3_struct_0(X19)
| ~ v10_lattices(X19)
| ~ l3_lattices(X19)
| ~ m1_subset_1(X20,u1_struct_0(X19))
| ~ m1_subset_1(X21,u1_struct_0(X19)) )
& ( m2_lattice4(k22_filter_2(X19,X20,X21),X19)
| v3_struct_0(X19)
| ~ v10_lattices(X19)
| ~ l3_lattices(X19)
| ~ m1_subset_1(X20,u1_struct_0(X19))
| ~ m1_subset_1(X21,u1_struct_0(X19)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
fof(c_0_51,plain,
! [X26] :
( v3_struct_0(X26)
| ~ l2_lattices(X26)
| m1_subset_1(k6_lattices(X26),u1_struct_0(X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])]) ).
fof(c_0_52,plain,
! [X29] :
( ( l1_lattices(X29)
| ~ l3_lattices(X29) )
& ( l2_lattices(X29)
| ~ l3_lattices(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_53,plain,
! [X86,X87,X88] :
( ( ~ r2_hidden(X87,k2_filter_0(X86,X88))
| r3_lattices(X86,X88,X87)
| ~ m1_subset_1(X88,u1_struct_0(X86))
| ~ m1_subset_1(X87,u1_struct_0(X86))
| v3_struct_0(X86)
| ~ v10_lattices(X86)
| ~ l3_lattices(X86) )
& ( ~ r3_lattices(X86,X88,X87)
| r2_hidden(X87,k2_filter_0(X86,X88))
| ~ m1_subset_1(X88,u1_struct_0(X86))
| ~ m1_subset_1(X87,u1_struct_0(X86))
| v3_struct_0(X86)
| ~ v10_lattices(X86)
| ~ l3_lattices(X86) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
fof(c_0_54,plain,
! [X98,X99] :
( v3_struct_0(X98)
| ~ v10_lattices(X98)
| ~ v14_lattices(X98)
| ~ l3_lattices(X98)
| ~ m1_subset_1(X99,u1_struct_0(X98))
| r3_lattices(X98,X99,k6_lattices(X98)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).
fof(c_0_55,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,k1_zfmisc_1(X1))
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
=> ( r1_filter_2(X1,X2,X3)
=> r1_filter_2(X1,X3,X2) ) ),
inference(fof_simplification,[status(thm)],[symmetry_r1_filter_2]) ).
cnf(c_0_56,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_57,negated_conjecture,
m1_subset_1(k2_filter_0(esk1_0,esk2_0),k1_zfmisc_1(u1_struct_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_43,c_0_44]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_58,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_59,plain,
m1_subset_1(esk10_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_60,plain,
( v3_struct_0(X2)
| ~ v1_xboole_0(X1)
| ~ m1_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_61,negated_conjecture,
m1_filter_2(k2_filter_0(esk1_0,esk2_0),esk1_0),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_31]),c_0_32]),c_0_33])]),c_0_34]),c_0_49]) ).
fof(c_0_62,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]) ).
cnf(c_0_63,plain,
( m2_lattice4(k22_filter_2(X1,X2,X3),X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_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_50]) ).
cnf(c_0_64,plain,
( v3_struct_0(X1)
| m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_65,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_66,plain,
! [X100,X101,X102] :
( ~ r2_hidden(X100,X101)
| ~ m1_subset_1(X101,k1_zfmisc_1(X102))
| m1_subset_1(X100,X102) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_67,plain,
( r2_hidden(X3,k2_filter_0(X1,X2))
| v3_struct_0(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ 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_53]) ).
cnf(c_0_68,plain,
( v3_struct_0(X1)
| r3_lattices(X1,X2,k6_lattices(X1))
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_69,negated_conjecture,
v14_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_70,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ( r1_filter_2(X1,X2,X3)
<=> ! [X4] :
( m1_subset_1(X4,X1)
=> ( r2_hidden(X4,X2)
<=> r2_hidden(X4,X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_filter_2]) ).
fof(c_0_71,plain,
! [X83,X84,X85] :
( v1_xboole_0(X83)
| ~ m1_subset_1(X84,k1_zfmisc_1(X83))
| ~ m1_subset_1(X85,k1_zfmisc_1(X83))
| ~ r1_filter_2(X83,X84,X85)
| r1_filter_2(X83,X85,X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])]) ).
cnf(c_0_72,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ r2_hidden(X1,k2_filter_0(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_73,plain,
( v1_xboole_0(X1)
| r2_hidden(esk10_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_74,negated_conjecture,
~ v1_xboole_0(k2_filter_0(esk1_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_60,c_0_61]),c_0_32]),c_0_33])]),c_0_34]) ).
fof(c_0_75,plain,
! [X34,X35] :
( v3_struct_0(X34)
| ~ v10_lattices(X34)
| ~ l3_lattices(X34)
| ~ m2_lattice4(X35,X34)
| m1_subset_1(X35,k1_zfmisc_1(u1_struct_0(X34))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])]) ).
cnf(c_0_76,plain,
( m2_lattice4(k22_filter_2(X1,X2,k6_lattices(X1)),X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
cnf(c_0_77,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_66]) ).
cnf(c_0_78,plain,
( r2_hidden(k6_lattices(X1),k2_filter_0(X1,X2))
| v3_struct_0(X1)
| ~ r3_lattices(X1,X2,k6_lattices(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_64]),c_0_65]) ).
cnf(c_0_79,negated_conjecture,
r3_lattices(esk1_0,esk2_0,k6_lattices(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_68,c_0_31]),c_0_69]),c_0_32]),c_0_33])]),c_0_34]) ).
fof(c_0_80,plain,
! [X12,X13,X14,X15] :
( ( ~ r2_hidden(X15,X13)
| r2_hidden(X15,X14)
| ~ m1_subset_1(X15,X12)
| ~ r1_filter_2(X12,X13,X14)
| ~ m1_subset_1(X14,k1_zfmisc_1(X12))
| ~ m1_subset_1(X13,k1_zfmisc_1(X12))
| v1_xboole_0(X12) )
& ( ~ r2_hidden(X15,X14)
| r2_hidden(X15,X13)
| ~ m1_subset_1(X15,X12)
| ~ r1_filter_2(X12,X13,X14)
| ~ m1_subset_1(X14,k1_zfmisc_1(X12))
| ~ m1_subset_1(X13,k1_zfmisc_1(X12))
| v1_xboole_0(X12) )
& ( m1_subset_1(esk3_3(X12,X13,X14),X12)
| r1_filter_2(X12,X13,X14)
| ~ m1_subset_1(X14,k1_zfmisc_1(X12))
| ~ m1_subset_1(X13,k1_zfmisc_1(X12))
| v1_xboole_0(X12) )
& ( ~ r2_hidden(esk3_3(X12,X13,X14),X13)
| ~ r2_hidden(esk3_3(X12,X13,X14),X14)
| r1_filter_2(X12,X13,X14)
| ~ m1_subset_1(X14,k1_zfmisc_1(X12))
| ~ m1_subset_1(X13,k1_zfmisc_1(X12))
| v1_xboole_0(X12) )
& ( r2_hidden(esk3_3(X12,X13,X14),X13)
| r2_hidden(esk3_3(X12,X13,X14),X14)
| r1_filter_2(X12,X13,X14)
| ~ m1_subset_1(X14,k1_zfmisc_1(X12))
| ~ m1_subset_1(X13,k1_zfmisc_1(X12))
| v1_xboole_0(X12) ) ),
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_70])])])])]) ).
cnf(c_0_81,plain,
( v1_xboole_0(X1)
| r1_filter_2(X1,X3,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ r1_filter_2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_82,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_83,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_75]) ).
cnf(c_0_84,negated_conjecture,
m2_lattice4(k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_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_76,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_85,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),k2_filter_2(esk1_0,esk2_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_86,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X1,k2_filter_0(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_77,c_0_57]) ).
cnf(c_0_87,negated_conjecture,
r2_hidden(k6_lattices(esk1_0),k2_filter_0(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_31]),c_0_79]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_88,plain,
( r1_filter_2(X1,X2,X3)
| v1_xboole_0(X1)
| ~ r2_hidden(esk3_3(X1,X2,X3),X2)
| ~ r2_hidden(esk3_3(X1,X2,X3),X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
fof(c_0_89,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] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( r3_lattices(X1,X2,X3)
=> ( r2_hidden(X4,k22_filter_2(X1,X2,X3))
<=> ( r3_lattices(X1,X2,X4)
& r3_lattices(X1,X4,X3) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t63_filter_2]) ).
cnf(c_0_90,plain,
( m1_subset_1(esk3_3(X1,X2,X3),X1)
| r1_filter_2(X1,X2,X3)
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_91,negated_conjecture,
( r1_filter_2(u1_struct_0(esk1_0),k2_filter_0(esk1_0,esk2_0),X1)
| ~ r1_filter_2(u1_struct_0(esk1_0),X1,k2_filter_0(esk1_0,esk2_0))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_57]),c_0_82]) ).
cnf(c_0_92,negated_conjecture,
m1_subset_1(k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)),k1_zfmisc_1(u1_struct_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_83,c_0_84]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_93,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),k2_filter_0(esk1_0,esk2_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0))),
inference(rw,[status(thm)],[c_0_85,c_0_49]) ).
cnf(c_0_94,negated_conjecture,
m1_subset_1(k6_lattices(esk1_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_95,plain,
( r1_filter_2(X1,X2,X3)
| ~ r2_hidden(esk3_3(X1,X2,X3),X3)
| ~ r2_hidden(esk3_3(X1,X2,X3),X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(csr,[status(thm)],[c_0_88,c_0_56]) ).
fof(c_0_96,plain,
! [X106,X107,X108,X109] :
( ( r3_lattices(X106,X107,X109)
| ~ r2_hidden(X109,k22_filter_2(X106,X107,X108))
| ~ r3_lattices(X106,X107,X108)
| ~ m1_subset_1(X109,u1_struct_0(X106))
| ~ m1_subset_1(X108,u1_struct_0(X106))
| ~ m1_subset_1(X107,u1_struct_0(X106))
| v3_struct_0(X106)
| ~ v10_lattices(X106)
| ~ l3_lattices(X106) )
& ( r3_lattices(X106,X109,X108)
| ~ r2_hidden(X109,k22_filter_2(X106,X107,X108))
| ~ r3_lattices(X106,X107,X108)
| ~ m1_subset_1(X109,u1_struct_0(X106))
| ~ m1_subset_1(X108,u1_struct_0(X106))
| ~ m1_subset_1(X107,u1_struct_0(X106))
| v3_struct_0(X106)
| ~ v10_lattices(X106)
| ~ l3_lattices(X106) )
& ( ~ r3_lattices(X106,X107,X109)
| ~ r3_lattices(X106,X109,X108)
| r2_hidden(X109,k22_filter_2(X106,X107,X108))
| ~ r3_lattices(X106,X107,X108)
| ~ m1_subset_1(X109,u1_struct_0(X106))
| ~ m1_subset_1(X108,u1_struct_0(X106))
| ~ m1_subset_1(X107,u1_struct_0(X106))
| v3_struct_0(X106)
| ~ v10_lattices(X106)
| ~ l3_lattices(X106) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_89])])])]) ).
cnf(c_0_97,negated_conjecture,
( r1_filter_2(u1_struct_0(esk1_0),X1,k2_filter_0(esk1_0,esk2_0))
| m1_subset_1(esk3_3(u1_struct_0(esk1_0),X1,k2_filter_0(esk1_0,esk2_0)),u1_struct_0(esk1_0))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_57]),c_0_82]) ).
cnf(c_0_98,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)),k2_filter_0(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).
fof(c_0_99,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2)
& m1_subset_1(X3,u1_struct_0(X2)) )
=> ( r2_hidden(X1,a_2_0_filter_0(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,u1_struct_0(X2))
& X1 = X4
& r3_lattices(X2,X3,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_filter_0]) ).
fof(c_0_100,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k2_filter_0(X1,X2) = a_2_0_filter_0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d3_filter_0]) ).
cnf(c_0_101,negated_conjecture,
( m2_lattice4(k22_filter_2(esk1_0,X1,k6_lattices(esk1_0)),esk1_0)
| ~ m1_subset_1(X1,u1_struct_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_63,c_0_94]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_102,plain,
( r2_hidden(esk3_3(X1,X2,X3),X2)
| r2_hidden(esk3_3(X1,X2,X3),X3)
| r1_filter_2(X1,X2,X3)
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_103,negated_conjecture,
( r1_filter_2(u1_struct_0(esk1_0),X1,k2_filter_0(esk1_0,esk2_0))
| ~ r2_hidden(esk3_3(u1_struct_0(esk1_0),X1,k2_filter_0(esk1_0,esk2_0)),k2_filter_0(esk1_0,esk2_0))
| ~ r2_hidden(esk3_3(u1_struct_0(esk1_0),X1,k2_filter_0(esk1_0,esk2_0)),X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0))) ),
inference(spm,[status(thm)],[c_0_95,c_0_57]) ).
cnf(c_0_104,plain,
( r2_hidden(X3,k22_filter_2(X1,X2,X4))
| v3_struct_0(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ r3_lattices(X1,X3,X4)
| ~ r3_lattices(X1,X2,X4)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_105,negated_conjecture,
m1_subset_1(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)),k2_filter_0(esk1_0,esk2_0)),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_92]),c_0_98]) ).
cnf(c_0_106,plain,
( r3_lattices(X2,X3,X1)
| v3_struct_0(X2)
| ~ r2_hidden(X1,k2_filter_0(X2,X3))
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_107,plain,
! [X50,X51,X52,X54] :
( ( m1_subset_1(esk12_3(X50,X51,X52),u1_struct_0(X51))
| ~ r2_hidden(X50,a_2_0_filter_0(X51,X52))
| v3_struct_0(X51)
| ~ v10_lattices(X51)
| ~ l3_lattices(X51)
| ~ m1_subset_1(X52,u1_struct_0(X51)) )
& ( X50 = esk12_3(X50,X51,X52)
| ~ r2_hidden(X50,a_2_0_filter_0(X51,X52))
| v3_struct_0(X51)
| ~ v10_lattices(X51)
| ~ l3_lattices(X51)
| ~ m1_subset_1(X52,u1_struct_0(X51)) )
& ( r3_lattices(X51,X52,esk12_3(X50,X51,X52))
| ~ r2_hidden(X50,a_2_0_filter_0(X51,X52))
| v3_struct_0(X51)
| ~ v10_lattices(X51)
| ~ l3_lattices(X51)
| ~ m1_subset_1(X52,u1_struct_0(X51)) )
& ( ~ m1_subset_1(X54,u1_struct_0(X51))
| X50 != X54
| ~ r3_lattices(X51,X52,X54)
| r2_hidden(X50,a_2_0_filter_0(X51,X52))
| v3_struct_0(X51)
| ~ v10_lattices(X51)
| ~ l3_lattices(X51)
| ~ m1_subset_1(X52,u1_struct_0(X51)) ) ),
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_99])])])])]) ).
fof(c_0_108,plain,
! [X17,X18] :
( v3_struct_0(X17)
| ~ v10_lattices(X17)
| ~ l3_lattices(X17)
| ~ m1_subset_1(X18,u1_struct_0(X17))
| k2_filter_0(X17,X18) = a_2_0_filter_0(X17,X18) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])]) ).
cnf(c_0_109,negated_conjecture,
( m1_subset_1(k22_filter_2(esk1_0,X1,k6_lattices(esk1_0)),k1_zfmisc_1(u1_struct_0(esk1_0)))
| ~ m1_subset_1(X1,u1_struct_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_83,c_0_101]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_110,negated_conjecture,
( r2_hidden(esk3_3(u1_struct_0(esk1_0),X1,k2_filter_0(esk1_0,esk2_0)),k2_filter_0(esk1_0,esk2_0))
| r2_hidden(esk3_3(u1_struct_0(esk1_0),X1,k2_filter_0(esk1_0,esk2_0)),X1)
| r1_filter_2(u1_struct_0(esk1_0),X1,k2_filter_0(esk1_0,esk2_0))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_57]),c_0_82]) ).
cnf(c_0_111,negated_conjecture,
( ~ r2_hidden(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)),k2_filter_0(esk1_0,esk2_0)),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)))
| ~ r2_hidden(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)),k2_filter_0(esk1_0,esk2_0)),k2_filter_0(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_92]),c_0_98]) ).
cnf(c_0_112,negated_conjecture,
( r2_hidden(X1,k22_filter_2(esk1_0,X2,k6_lattices(esk1_0)))
| ~ r3_lattices(esk1_0,X1,k6_lattices(esk1_0))
| ~ r3_lattices(esk1_0,X2,k6_lattices(esk1_0))
| ~ r3_lattices(esk1_0,X2,X1)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_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_104,c_0_94]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_113,negated_conjecture,
r3_lattices(esk1_0,esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)),k2_filter_0(esk1_0,esk2_0)),k6_lattices(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_68,c_0_105]),c_0_69]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_114,negated_conjecture,
( r3_lattices(esk1_0,esk2_0,X1)
| ~ r2_hidden(X1,k2_filter_0(esk1_0,esk2_0)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_31]),c_0_32]),c_0_33])]),c_0_34]),c_0_86]) ).
cnf(c_0_115,plain,
( r2_hidden(X3,a_2_0_filter_0(X2,X4))
| v3_struct_0(X2)
| ~ m1_subset_1(X1,u1_struct_0(X2))
| X3 != X1
| ~ r3_lattices(X2,X4,X1)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| ~ m1_subset_1(X4,u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_116,plain,
( v3_struct_0(X1)
| k2_filter_0(X1,X2) = a_2_0_filter_0(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_117,plain,
( r3_lattices(X1,X2,X3)
| v3_struct_0(X1)
| ~ r2_hidden(X3,k22_filter_2(X1,X2,X4))
| ~ r3_lattices(X1,X2,X4)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_118,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X1,k22_filter_2(esk1_0,X2,k6_lattices(esk1_0)))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_77,c_0_109]) ).
cnf(c_0_119,negated_conjecture,
( r2_hidden(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)),k2_filter_0(esk1_0,esk2_0)),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)))
| r2_hidden(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)),k2_filter_0(esk1_0,esk2_0)),k2_filter_0(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_92]),c_0_98]) ).
cnf(c_0_120,negated_conjecture,
~ r2_hidden(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)),k2_filter_0(esk1_0,esk2_0)),k2_filter_0(esk1_0,esk2_0)),
inference(csr,[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_111,c_0_112]),c_0_113]),c_0_79]),c_0_105]),c_0_31])]),c_0_114]) ).
cnf(c_0_121,plain,
( r2_hidden(X1,a_2_0_filter_0(X2,X3))
| v3_struct_0(X2)
| ~ r3_lattices(X2,X3,X1)
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(er,[status(thm)],[c_0_115]) ).
cnf(c_0_122,negated_conjecture,
a_2_0_filter_0(esk1_0,esk2_0) = k2_filter_0(esk1_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_116,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_123,negated_conjecture,
( r3_lattices(esk1_0,X1,X2)
| ~ r3_lattices(esk1_0,X1,k6_lattices(esk1_0))
| ~ r2_hidden(X2,k22_filter_2(esk1_0,X1,k6_lattices(esk1_0)))
| ~ m1_subset_1(X1,u1_struct_0(esk1_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_117,c_0_94]),c_0_32]),c_0_33])]),c_0_34]),c_0_118]) ).
cnf(c_0_124,negated_conjecture,
r2_hidden(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)),k2_filter_0(esk1_0,esk2_0)),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0))),
inference(sr,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_125,negated_conjecture,
( r2_hidden(X1,k2_filter_0(esk1_0,esk2_0))
| ~ r3_lattices(esk1_0,esk2_0,X1)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(rw,[status(thm)],[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_31]),c_0_32]),c_0_33])]),c_0_34]),c_0_122]) ).
cnf(c_0_126,negated_conjecture,
r3_lattices(esk1_0,esk2_0,esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,k6_lattices(esk1_0)),k2_filter_0(esk1_0,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_79]),c_0_31])]) ).
cnf(c_0_127,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_125]),c_0_105])]),c_0_126])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : LAT329+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.09 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.27 % Computer : n022.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Thu Aug 24 07:26:41 EDT 2023
% 0.08/0.27 % CPUTime :
% 0.12/0.45 start to proof: theBenchmark
% 245.05/245.03 % Version : CSE_E---1.5
% 245.05/245.03 % Problem : theBenchmark.p
% 245.05/245.03 % Proof found
% 245.05/245.03 % SZS status Theorem for theBenchmark.p
% 245.05/245.03 % SZS output start Proof
% See solution above
% 245.05/245.04 % Total time : 244.561000 s
% 245.05/245.04 % SZS output end Proof
% 245.05/245.04 % Total time : 244.576000 s
%------------------------------------------------------------------------------