TSTP Solution File: LAT311+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT311+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 : n026.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 06:01:11 EDT 2023
% Result : Theorem 17.34s 17.40s
% Output : CNFRefutation 17.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 101
% Syntax : Number of formulae : 191 ( 19 unt; 81 typ; 0 def)
% Number of atoms : 521 ( 60 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 623 ( 212 ~; 222 |; 129 &)
% ( 0 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 106 ( 64 >; 42 *; 0 +; 0 <<)
% Number of predicates : 34 ( 32 usr; 1 prp; 0-3 aty)
% Number of functors : 49 ( 49 usr; 17 con; 0-3 aty)
% Number of variables : 147 ( 1 sgn; 103 !; 2 ?; 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,
v1_xboole_0: $i > $o ).
tff(decl_28,type,
k1_zfmisc_1: $i > $i ).
tff(decl_29,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_30,type,
k18_filter_2: ( $i * $i ) > $i ).
tff(decl_31,type,
k19_filter_2: ( $i * $i ) > $i ).
tff(decl_32,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_33,type,
v3_lattices: $i > $o ).
tff(decl_34,type,
u2_lattices: $i > $i ).
tff(decl_35,type,
u1_lattices: $i > $i ).
tff(decl_36,type,
g3_lattices: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
v1_funct_1: $i > $o ).
tff(decl_38,type,
v4_lattices: $i > $o ).
tff(decl_39,type,
v5_lattices: $i > $o ).
tff(decl_40,type,
v6_lattices: $i > $o ).
tff(decl_41,type,
v7_lattices: $i > $o ).
tff(decl_42,type,
v8_lattices: $i > $o ).
tff(decl_43,type,
v9_lattices: $i > $o ).
tff(decl_44,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(decl_45,type,
v1_relat_1: $i > $o ).
tff(decl_46,type,
v2_funct_1: $i > $o ).
tff(decl_47,type,
k1_lattice2: $i > $i ).
tff(decl_48,type,
k2_filter_0: ( $i * $i ) > $i ).
tff(decl_49,type,
a_2_0_filter_0: ( $i * $i ) > $i ).
tff(decl_50,type,
k5_filter_2: ( $i * $i ) > $i ).
tff(decl_51,type,
k7_filter_2: ( $i * $i ) > $i ).
tff(decl_52,type,
k8_filter_2: ( $i * $i ) > $i ).
tff(decl_53,type,
a_2_0_filter_2: ( $i * $i ) > $i ).
tff(decl_54,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_55,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_56,type,
m2_filter_2: ( $i * $i ) > $o ).
tff(decl_57,type,
m1_filter_0: ( $i * $i ) > $o ).
tff(decl_58,type,
k2_filter_2: ( $i * $i ) > $i ).
tff(decl_59,type,
m1_filter_2: ( $i * $i ) > $o ).
tff(decl_60,type,
k3_filter_0: ( $i * $i ) > $i ).
tff(decl_61,type,
k3_filter_2: ( $i * $i ) > $i ).
tff(decl_62,type,
l1_lattices: $i > $o ).
tff(decl_63,type,
l1_struct_0: $i > $o ).
tff(decl_64,type,
l2_lattices: $i > $o ).
tff(decl_65,type,
m2_lattice4: ( $i * $i ) > $o ).
tff(decl_66,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_67,type,
k1_xboole_0: $i ).
tff(decl_68,type,
v1_binop_1: ( $i * $i ) > $o ).
tff(decl_69,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_70,type,
v2_binop_1: ( $i * $i ) > $o ).
tff(decl_71,type,
r3_lattices: ( $i * $i * $i ) > $o ).
tff(decl_72,type,
r1_lattices: ( $i * $i * $i ) > $o ).
tff(decl_73,type,
esk1_0: $i ).
tff(decl_74,type,
esk2_0: $i ).
tff(decl_75,type,
esk3_0: $i ).
tff(decl_76,type,
esk4_0: $i ).
tff(decl_77,type,
esk5_0: $i ).
tff(decl_78,type,
esk6_0: $i ).
tff(decl_79,type,
esk7_0: $i ).
tff(decl_80,type,
esk8_1: $i > $i ).
tff(decl_81,type,
esk9_1: $i > $i ).
tff(decl_82,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_83,type,
esk11_1: $i > $i ).
tff(decl_84,type,
esk12_1: $i > $i ).
tff(decl_85,type,
esk13_1: $i > $i ).
tff(decl_86,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_87,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
esk17_0: $i ).
tff(decl_90,type,
esk18_1: $i > $i ).
tff(decl_91,type,
esk19_1: $i > $i ).
tff(decl_92,type,
esk20_0: $i ).
tff(decl_93,type,
esk21_0: $i ).
tff(decl_94,type,
esk22_1: $i > $i ).
tff(decl_95,type,
esk23_0: $i ).
tff(decl_96,type,
esk24_0: $i ).
tff(decl_97,type,
esk25_0: $i ).
tff(decl_98,type,
esk26_0: $i ).
tff(decl_99,type,
esk27_1: $i > $i ).
tff(decl_100,type,
esk28_0: $i ).
tff(decl_101,type,
esk29_0: $i ).
tff(decl_102,type,
esk30_2: ( $i * $i ) > $i ).
fof(d6_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> k7_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_2) ).
fof(t40_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( r2_hidden(X2,X3)
=> r1_tarski(k18_filter_2(X1,X2),k19_filter_2(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_2) ).
fof(dt_k7_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> m1_subset_1(k7_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_2) ).
fof(t29_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( r2_hidden(X2,X3)
=> r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_0) ).
fof(t37_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) )
=> ( k3_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2)) = k19_filter_2(X1,X2)
& k3_filter_2(X1,X2) = k19_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2))
& k3_filter_2(X1,k8_filter_2(X1,X3)) = k19_filter_2(k1_lattice2(X1),X3)
& k3_filter_2(k1_lattice2(X1),X3) = k19_filter_2(X1,k8_filter_2(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_2) ).
fof(rc5_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
fof(d7_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
=> k8_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_2) ).
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(t7_boole,axiom,
! [X1,X2] :
~ ( r2_hidden(X1,X2)
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(redefinition_k3_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> k3_filter_2(X1,X2) = k3_filter_0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).
fof(d4_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k5_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_2) ).
fof(d9_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).
fof(fc6_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(dt_k5_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_subset_1(k5_filter_2(X1,X2),u1_struct_0(k1_lattice2(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_2) ).
fof(t30_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k18_filter_2(X1,X2) = k2_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2))
& k18_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2)) = k2_filter_2(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_2) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
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_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).
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(fc1_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(c_0_20,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> k7_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d6_filter_2]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( r2_hidden(X2,X3)
=> r1_tarski(k18_filter_2(X1,X2),k19_filter_2(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t40_filter_2])]) ).
fof(c_0_22,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> m1_subset_1(k7_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
inference(fof_simplification,[status(thm)],[dt_k7_filter_2]) ).
fof(c_0_23,plain,
! [X25,X26] :
( v3_struct_0(X25)
| ~ v10_lattices(X25)
| ~ l3_lattices(X25)
| ~ m1_subset_1(X26,k1_zfmisc_1(u1_struct_0(X25)))
| k7_filter_2(X25,X26) = X26 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
fof(c_0_24,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))
& ~ v1_xboole_0(esk3_0)
& m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& r2_hidden(esk2_0,esk3_0)
& ~ r1_tarski(k18_filter_2(esk1_0,esk2_0),k19_filter_2(esk1_0,esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_25,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( r2_hidden(X2,X3)
=> r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t29_filter_0]) ).
fof(c_0_26,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ! [X3] :
( ( ~ v1_xboole_0(X3)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) )
=> ( k3_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2)) = k19_filter_2(X1,X2)
& k3_filter_2(X1,X2) = k19_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2))
& k3_filter_2(X1,k8_filter_2(X1,X3)) = k19_filter_2(k1_lattice2(X1),X3)
& k3_filter_2(k1_lattice2(X1),X3) = k19_filter_2(X1,k8_filter_2(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t37_filter_2]) ).
fof(c_0_27,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) ) ),
inference(fof_simplification,[status(thm)],[rc5_struct_0]) ).
fof(c_0_28,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
=> k8_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d7_filter_2]) ).
fof(c_0_29,plain,
! [X49,X50] :
( v3_struct_0(X49)
| ~ v10_lattices(X49)
| ~ l3_lattices(X49)
| ~ m1_subset_1(X50,k1_zfmisc_1(u1_struct_0(X49)))
| m1_subset_1(k7_filter_2(X49,X50),k1_zfmisc_1(u1_struct_0(k1_lattice2(X49)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])]) ).
cnf(c_0_30,plain,
( v3_struct_0(X1)
| k7_filter_2(X1,X2) = X2
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_35,plain,
! [X157,X158,X159] :
( v3_struct_0(X157)
| ~ v10_lattices(X157)
| ~ l3_lattices(X157)
| ~ m1_subset_1(X158,u1_struct_0(X157))
| v1_xboole_0(X159)
| ~ m1_subset_1(X159,k1_zfmisc_1(u1_struct_0(X157)))
| ~ r2_hidden(X158,X159)
| r1_tarski(k2_filter_0(X157,X158),k3_filter_0(X157,X159)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
fof(c_0_36,plain,
! [X172,X173,X174] :
( ~ r2_hidden(X172,X173)
| ~ m1_subset_1(X173,k1_zfmisc_1(X174))
| m1_subset_1(X172,X174) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_37,plain,
! [X179,X180] :
( ~ r2_hidden(X179,X180)
| ~ v1_xboole_0(X180) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_38,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> k3_filter_2(X1,X2) = k3_filter_0(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k3_filter_2]) ).
fof(c_0_39,plain,
! [X167,X168,X169] :
( ( k3_filter_2(k1_lattice2(X167),k7_filter_2(X167,X168)) = k19_filter_2(X167,X168)
| v1_xboole_0(X169)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(k1_lattice2(X167))))
| v1_xboole_0(X168)
| ~ m1_subset_1(X168,k1_zfmisc_1(u1_struct_0(X167)))
| v3_struct_0(X167)
| ~ v10_lattices(X167)
| ~ l3_lattices(X167) )
& ( k3_filter_2(X167,X168) = k19_filter_2(k1_lattice2(X167),k7_filter_2(X167,X168))
| v1_xboole_0(X169)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(k1_lattice2(X167))))
| v1_xboole_0(X168)
| ~ m1_subset_1(X168,k1_zfmisc_1(u1_struct_0(X167)))
| v3_struct_0(X167)
| ~ v10_lattices(X167)
| ~ l3_lattices(X167) )
& ( k3_filter_2(X167,k8_filter_2(X167,X169)) = k19_filter_2(k1_lattice2(X167),X169)
| v1_xboole_0(X169)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(k1_lattice2(X167))))
| v1_xboole_0(X168)
| ~ m1_subset_1(X168,k1_zfmisc_1(u1_struct_0(X167)))
| v3_struct_0(X167)
| ~ v10_lattices(X167)
| ~ l3_lattices(X167) )
& ( k3_filter_2(k1_lattice2(X167),X169) = k19_filter_2(X167,k8_filter_2(X167,X169))
| v1_xboole_0(X169)
| ~ m1_subset_1(X169,k1_zfmisc_1(u1_struct_0(k1_lattice2(X167))))
| v1_xboole_0(X168)
| ~ m1_subset_1(X168,k1_zfmisc_1(u1_struct_0(X167)))
| v3_struct_0(X167)
| ~ v10_lattices(X167)
| ~ l3_lattices(X167) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
fof(c_0_40,plain,
! [X135] :
( ( m1_subset_1(esk27_1(X135),k1_zfmisc_1(u1_struct_0(X135)))
| v3_struct_0(X135)
| ~ l1_struct_0(X135) )
& ( ~ v1_xboole_0(esk27_1(X135))
| v3_struct_0(X135)
| ~ l1_struct_0(X135) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
fof(c_0_41,plain,
! [X27,X28] :
( v3_struct_0(X27)
| ~ v10_lattices(X27)
| ~ l3_lattices(X27)
| ~ m1_subset_1(X28,k1_zfmisc_1(u1_struct_0(k1_lattice2(X27))))
| k8_filter_2(X27,X28) = X28 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
cnf(c_0_42,plain,
( v3_struct_0(X1)
| m1_subset_1(k7_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,negated_conjecture,
k7_filter_2(esk1_0,esk3_0) = esk3_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_44,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k5_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d4_filter_2]) ).
fof(c_0_45,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d9_filter_2]) ).
cnf(c_0_46,plain,
( v3_struct_0(X1)
| v1_xboole_0(X3)
| r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X3))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,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_36]) ).
cnf(c_0_48,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_49,plain,
! [X141,X142] :
( v3_struct_0(X141)
| ~ v10_lattices(X141)
| ~ l3_lattices(X141)
| v1_xboole_0(X142)
| ~ m1_subset_1(X142,k1_zfmisc_1(u1_struct_0(X141)))
| k3_filter_2(X141,X142) = k3_filter_0(X141,X142) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])]) ).
fof(c_0_50,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc6_lattice2]) ).
cnf(c_0_51,plain,
( k3_filter_2(k1_lattice2(X1),X2) = k19_filter_2(X1,k8_filter_2(X1,X2))
| v1_xboole_0(X2)
| v1_xboole_0(X3)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_52,plain,
( m1_subset_1(esk27_1(X1),k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(esk27_1(X1))
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_54,plain,
( v3_struct_0(X1)
| k8_filter_2(X1,X2) = X2
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_55,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(k1_lattice2(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_42,c_0_31]),c_0_43]),c_0_32]),c_0_33])]),c_0_34]) ).
fof(c_0_56,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_subset_1(k5_filter_2(X1,X2),u1_struct_0(k1_lattice2(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k5_filter_2]) ).
fof(c_0_57,plain,
! [X23,X24] :
( v3_struct_0(X23)
| ~ v10_lattices(X23)
| ~ l3_lattices(X23)
| ~ m1_subset_1(X24,u1_struct_0(X23))
| k5_filter_2(X23,X24) = X24 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])]) ).
fof(c_0_58,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k18_filter_2(X1,X2) = k2_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2))
& k18_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2)) = k2_filter_2(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[t30_filter_2]) ).
fof(c_0_59,plain,
! [X29,X30] :
( v3_struct_0(X29)
| ~ v10_lattices(X29)
| ~ l3_lattices(X29)
| ~ m1_subset_1(X30,u1_struct_0(X29))
| k18_filter_2(X29,X30) = a_2_0_filter_2(X29,X30) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
cnf(c_0_60,plain,
( r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X3))
| v3_struct_0(X1)
| ~ r2_hidden(X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_61,negated_conjecture,
r2_hidden(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_62,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| k3_filter_2(X1,X2) = k3_filter_0(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_63,negated_conjecture,
~ v1_xboole_0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_64,plain,
! [X105] :
( ( ~ v3_struct_0(k1_lattice2(X105))
| v3_struct_0(X105)
| ~ v10_lattices(X105)
| ~ l3_lattices(X105) )
& ( v3_lattices(k1_lattice2(X105))
| v3_struct_0(X105)
| ~ v10_lattices(X105)
| ~ l3_lattices(X105) )
& ( v4_lattices(k1_lattice2(X105))
| v3_struct_0(X105)
| ~ v10_lattices(X105)
| ~ l3_lattices(X105) )
& ( v5_lattices(k1_lattice2(X105))
| v3_struct_0(X105)
| ~ v10_lattices(X105)
| ~ l3_lattices(X105) )
& ( v6_lattices(k1_lattice2(X105))
| v3_struct_0(X105)
| ~ v10_lattices(X105)
| ~ l3_lattices(X105) )
& ( v7_lattices(k1_lattice2(X105))
| v3_struct_0(X105)
| ~ v10_lattices(X105)
| ~ l3_lattices(X105) )
& ( v8_lattices(k1_lattice2(X105))
| v3_struct_0(X105)
| ~ v10_lattices(X105)
| ~ l3_lattices(X105) )
& ( v9_lattices(k1_lattice2(X105))
| v3_struct_0(X105)
| ~ v10_lattices(X105)
| ~ l3_lattices(X105) )
& ( v10_lattices(k1_lattice2(X105))
| v3_struct_0(X105)
| ~ v10_lattices(X105)
| ~ l3_lattices(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])]) ).
cnf(c_0_65,plain,
( k19_filter_2(X1,k8_filter_2(X1,X2)) = k3_filter_2(k1_lattice2(X1),X2)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_66,negated_conjecture,
k8_filter_2(esk1_0,esk3_0) = esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_32]),c_0_33])]),c_0_34]) ).
fof(c_0_67,plain,
! [X53] :
( ~ l1_lattices(X53)
| l1_struct_0(X53) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
fof(c_0_68,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_69,plain,
! [X47,X48] :
( v3_struct_0(X47)
| ~ v10_lattices(X47)
| ~ l3_lattices(X47)
| ~ m1_subset_1(X48,u1_struct_0(X47))
| m1_subset_1(k5_filter_2(X47,X48),u1_struct_0(k1_lattice2(X47))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])]) ).
cnf(c_0_70,plain,
( v3_struct_0(X1)
| k5_filter_2(X1,X2) = X2
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_71,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_72,plain,
! [X165,X166] :
( ( k18_filter_2(X165,X166) = k2_filter_2(k1_lattice2(X165),k5_filter_2(X165,X166))
| ~ m1_subset_1(X166,u1_struct_0(X165))
| v3_struct_0(X165)
| ~ v10_lattices(X165)
| ~ l3_lattices(X165) )
& ( k18_filter_2(k1_lattice2(X165),k5_filter_2(X165,X166)) = k2_filter_2(X165,X166)
| ~ m1_subset_1(X166,u1_struct_0(X165))
| v3_struct_0(X165)
| ~ v10_lattices(X165)
| ~ l3_lattices(X165) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])]) ).
cnf(c_0_73,plain,
( v3_struct_0(X1)
| k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_74,negated_conjecture,
( r1_tarski(k2_filter_0(X1,esk2_0),k3_filter_0(X1,esk3_0))
| v3_struct_0(X1)
| ~ m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_75,negated_conjecture,
( k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k3_filter_2(k1_lattice2(esk1_0),esk3_0)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0))
| ~ v10_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_55]),c_0_63]) ).
cnf(c_0_76,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_77,plain,
! [X38] :
( ( v3_lattices(k1_lattice2(X38))
| ~ l3_lattices(X38) )
& ( l3_lattices(k1_lattice2(X38))
| ~ l3_lattices(X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
cnf(c_0_78,negated_conjecture,
( k3_filter_2(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_0)
| ~ l1_struct_0(esk1_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_65,c_0_55]),c_0_66]),c_0_32]),c_0_33])]),c_0_63]),c_0_34]) ).
cnf(c_0_79,plain,
( l1_struct_0(X1)
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
fof(c_0_80,plain,
! [X55] :
( ( l1_lattices(X55)
| ~ l3_lattices(X55) )
& ( l2_lattices(X55)
| ~ l3_lattices(X55) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_81,plain,
! [X139,X140] :
( v3_struct_0(X139)
| ~ v10_lattices(X139)
| ~ l3_lattices(X139)
| ~ m1_subset_1(X140,u1_struct_0(X139))
| k2_filter_2(X139,X140) = k2_filter_0(X139,X140) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])]) ).
cnf(c_0_82,plain,
( v3_struct_0(X1)
| m1_subset_1(k5_filter_2(X1,X2),u1_struct_0(k1_lattice2(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_83,negated_conjecture,
k5_filter_2(esk1_0,esk2_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_70,c_0_71]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_84,plain,
( k18_filter_2(X1,X2) = k2_filter_2(k1_lattice2(X1),k5_filter_2(X1,X2))
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_85,negated_conjecture,
k18_filter_2(esk1_0,esk2_0) = a_2_0_filter_2(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_73,c_0_71]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_86,negated_conjecture,
( r1_tarski(k2_filter_0(k1_lattice2(esk1_0),esk2_0),k3_filter_0(k1_lattice2(esk1_0),esk3_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0))
| ~ v10_lattices(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_74,c_0_55]) ).
cnf(c_0_87,negated_conjecture,
( k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k3_filter_2(k1_lattice2(esk1_0),esk3_0)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_88,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_89,negated_conjecture,
( k3_filter_2(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_0)
| ~ l1_lattices(esk1_0) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_90,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_91,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_81]) ).
cnf(c_0_92,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(k1_lattice2(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_82,c_0_71]),c_0_83]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_93,negated_conjecture,
k2_filter_2(k1_lattice2(esk1_0),esk2_0) = a_2_0_filter_2(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_71]),c_0_83]),c_0_85]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_94,negated_conjecture,
( r1_tarski(k2_filter_0(k1_lattice2(esk1_0),esk2_0),k3_filter_0(k1_lattice2(esk1_0),esk3_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_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_76]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_95,negated_conjecture,
( k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k3_filter_2(k1_lattice2(esk1_0),esk3_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_32])]) ).
cnf(c_0_96,negated_conjecture,
k3_filter_2(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_32])]) ).
cnf(c_0_97,negated_conjecture,
( k2_filter_0(k1_lattice2(esk1_0),esk2_0) = a_2_0_filter_2(esk1_0,esk2_0)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0))
| ~ v10_lattices(k1_lattice2(esk1_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).
fof(c_0_98,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc1_lattice2]) ).
cnf(c_0_99,negated_conjecture,
( r1_tarski(k2_filter_0(k1_lattice2(esk1_0),esk2_0),k3_filter_0(k1_lattice2(esk1_0),esk3_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_88]),c_0_32])]) ).
cnf(c_0_100,negated_conjecture,
( k3_filter_0(k1_lattice2(esk1_0),esk3_0) = k19_filter_2(esk1_0,esk3_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(rw,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( k2_filter_0(k1_lattice2(esk1_0),esk2_0) = a_2_0_filter_2(esk1_0,esk2_0)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_76]),c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_102,negated_conjecture,
~ r1_tarski(k18_filter_2(esk1_0,esk2_0),k19_filter_2(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_103,plain,
! [X91] :
( ( ~ v3_struct_0(k1_lattice2(X91))
| v3_struct_0(X91)
| ~ l3_lattices(X91) )
& ( v3_lattices(k1_lattice2(X91))
| v3_struct_0(X91)
| ~ l3_lattices(X91) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_98])])]) ).
cnf(c_0_104,negated_conjecture,
( r1_tarski(k2_filter_0(k1_lattice2(esk1_0),esk2_0),k19_filter_2(esk1_0,esk3_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_105,negated_conjecture,
( k2_filter_0(k1_lattice2(esk1_0),esk2_0) = a_2_0_filter_2(esk1_0,esk2_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_88]),c_0_32])]) ).
cnf(c_0_106,negated_conjecture,
~ r1_tarski(a_2_0_filter_2(esk1_0,esk2_0),k19_filter_2(esk1_0,esk3_0)),
inference(rw,[status(thm)],[c_0_102,c_0_85]) ).
cnf(c_0_107,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_108,negated_conjecture,
v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).
cnf(c_0_109,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_32])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT311+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 08:26:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.54 start to proof: theBenchmark
% 17.34/17.40 % Version : CSE_E---1.5
% 17.34/17.40 % Problem : theBenchmark.p
% 17.34/17.40 % Proof found
% 17.34/17.40 % SZS status Theorem for theBenchmark.p
% 17.34/17.40 % SZS output start Proof
% See solution above
% 17.34/17.42 % Total time : 16.849000 s
% 17.34/17.42 % SZS output end Proof
% 17.34/17.42 % Total time : 16.855000 s
%------------------------------------------------------------------------------