TSTP Solution File: LAT306+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT306+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 06:01:04 EDT 2023
% Result : Theorem 1.53s 1.56s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 110
% Syntax : Number of formulae : 230 ( 11 unt; 84 typ; 0 def)
% Number of atoms : 655 ( 92 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 834 ( 325 ~; 330 |; 125 &)
% ( 6 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 107 ( 68 >; 39 *; 0 +; 0 <<)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-3 aty)
% Number of functors : 48 ( 48 usr; 16 con; 0-3 aty)
% Number of variables : 223 ( 25 sgn; 101 !; 0 ?; 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,
v14_lattices: $i > $o ).
tff(decl_26,type,
u1_struct_0: $i > $i ).
tff(decl_27,type,
k17_filter_2: $i > $i ).
tff(decl_28,type,
k6_lattices: $i > $i ).
tff(decl_29,type,
k18_filter_2: ( $i * $i ) > $i ).
tff(decl_30,type,
r1_filter_2: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
v3_lattices: $i > $o ).
tff(decl_32,type,
u2_lattices: $i > $i ).
tff(decl_33,type,
u1_lattices: $i > $i ).
tff(decl_34,type,
g3_lattices: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_36,type,
v1_xboole_0: $i > $o ).
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,
k1_zfmisc_1: $i > $i ).
tff(decl_46,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_47,type,
v1_relat_1: $i > $o ).
tff(decl_48,type,
v2_funct_1: $i > $o ).
tff(decl_49,type,
v13_lattices: $i > $o ).
tff(decl_50,type,
v15_lattices: $i > $o ).
tff(decl_51,type,
k1_filter_0: $i > $i ).
tff(decl_52,type,
k1_lattice2: $i > $i ).
tff(decl_53,type,
k2_filter_0: ( $i * $i ) > $i ).
tff(decl_54,type,
a_2_0_filter_0: ( $i * $i ) > $i ).
tff(decl_55,type,
k5_filter_2: ( $i * $i ) > $i ).
tff(decl_56,type,
a_2_0_filter_2: ( $i * $i ) > $i ).
tff(decl_57,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_58,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_59,type,
m2_filter_2: ( $i * $i ) > $o ).
tff(decl_60,type,
m1_filter_0: ( $i * $i ) > $o ).
tff(decl_61,type,
k1_filter_2: $i > $i ).
tff(decl_62,type,
m1_filter_2: ( $i * $i ) > $o ).
tff(decl_63,type,
k2_filter_2: ( $i * $i ) > $i ).
tff(decl_64,type,
l1_lattices: $i > $o ).
tff(decl_65,type,
k5_lattices: $i > $i ).
tff(decl_66,type,
l2_lattices: $i > $o ).
tff(decl_67,type,
l1_struct_0: $i > $o ).
tff(decl_68,type,
m2_lattice4: ( $i * $i ) > $o ).
tff(decl_69,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_70,type,
k1_xboole_0: $i ).
tff(decl_71,type,
v1_binop_1: ( $i * $i ) > $o ).
tff(decl_72,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_73,type,
v2_binop_1: ( $i * $i ) > $o ).
tff(decl_74,type,
r3_lattices: ( $i * $i * $i ) > $o ).
tff(decl_75,type,
r1_lattices: ( $i * $i * $i ) > $o ).
tff(decl_76,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_77,type,
esk1_0: $i ).
tff(decl_78,type,
esk2_0: $i ).
tff(decl_79,type,
esk3_0: $i ).
tff(decl_80,type,
esk4_0: $i ).
tff(decl_81,type,
esk5_0: $i ).
tff(decl_82,type,
esk6_1: $i > $i ).
tff(decl_83,type,
esk7_1: $i > $i ).
tff(decl_84,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_85,type,
esk9_1: $i > $i ).
tff(decl_86,type,
esk10_1: $i > $i ).
tff(decl_87,type,
esk11_1: $i > $i ).
tff(decl_88,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_89,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
esk15_0: $i ).
tff(decl_92,type,
esk16_0: $i ).
tff(decl_93,type,
esk17_1: $i > $i ).
tff(decl_94,type,
esk18_1: $i > $i ).
tff(decl_95,type,
esk19_0: $i ).
tff(decl_96,type,
esk20_0: $i ).
tff(decl_97,type,
esk21_1: $i > $i ).
tff(decl_98,type,
esk22_0: $i ).
tff(decl_99,type,
esk23_0: $i ).
tff(decl_100,type,
esk24_0: $i ).
tff(decl_101,type,
esk25_0: $i ).
tff(decl_102,type,
esk26_1: $i > $i ).
tff(decl_103,type,
esk27_0: $i ).
tff(decl_104,type,
esk28_0: $i ).
tff(decl_105,type,
esk29_2: ( $i * $i ) > $i ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_u2_lattices,axiom,
! [X1] :
( l2_lattices(X1)
=> ( v1_funct_1(u2_lattices(X1))
& v1_funct_2(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& m2_relset_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(free_g3_lattices,axiom,
! [X1,X2,X3] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X3)
& v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)
& m1_relset_1(X3,k2_zfmisc_1(X1,X1),X1) )
=> ! [X4,X5,X6] :
( g3_lattices(X1,X2,X3) = g3_lattices(X4,X5,X6)
=> ( X1 = X4
& X2 = X5
& X3 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
fof(dt_u1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> ( v1_funct_1(u1_lattices(X1))
& v1_funct_2(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
& m2_relset_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
fof(abstractness_v3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(X1)
=> X1 = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(d2_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> k1_lattice2(X1) = g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice2) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(t20_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_0(X1) = k2_filter_0(X1,k5_lattices(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_filter_0) ).
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/sandbox/benchmark/theBenchmark.p',redefinition_k2_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/sandbox/benchmark/theBenchmark.p',t30_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/sandbox/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/sandbox/benchmark/theBenchmark.p',dt_k5_filter_2) ).
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/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(t79_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> k6_lattices(X1) = k5_lattices(k1_lattice2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_lattice2) ).
fof(t64_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v14_lattices(X1)
<=> v13_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_lattice2) ).
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/sandbox/benchmark/theBenchmark.p',d4_filter_2) ).
fof(t32_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v14_lattices(X1)
=> r1_filter_2(u1_struct_0(X1),k17_filter_2(X1),k18_filter_2(X1,k6_lattices(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_2) ).
fof(d2_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_0(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_0) ).
fof(d8_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k17_filter_2(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_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/sandbox/benchmark/theBenchmark.p',dt_k6_lattices) ).
fof(redefinition_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)
<=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : r1_tarski(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(c_0_26,plain,
! [X134,X135,X136] :
( ( ~ m2_relset_1(X136,X134,X135)
| m1_relset_1(X136,X134,X135) )
& ( ~ m1_relset_1(X136,X134,X135)
| m2_relset_1(X136,X134,X135) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_27,plain,
! [X61] :
( ( v1_funct_1(u2_lattices(X61))
| ~ l2_lattices(X61) )
& ( v1_funct_2(u2_lattices(X61),k2_zfmisc_1(u1_struct_0(X61),u1_struct_0(X61)),u1_struct_0(X61))
| ~ l2_lattices(X61) )
& ( m2_relset_1(u2_lattices(X61),k2_zfmisc_1(u1_struct_0(X61),u1_struct_0(X61)),u1_struct_0(X61))
| ~ l2_lattices(X61) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
fof(c_0_28,plain,
! [X105,X106,X107,X108,X109,X110] :
( ( X105 = X108
| g3_lattices(X105,X106,X107) != g3_lattices(X108,X109,X110)
| ~ v1_funct_1(X106)
| ~ v1_funct_2(X106,k2_zfmisc_1(X105,X105),X105)
| ~ m1_relset_1(X106,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_1(X107)
| ~ v1_funct_2(X107,k2_zfmisc_1(X105,X105),X105)
| ~ m1_relset_1(X107,k2_zfmisc_1(X105,X105),X105) )
& ( X106 = X109
| g3_lattices(X105,X106,X107) != g3_lattices(X108,X109,X110)
| ~ v1_funct_1(X106)
| ~ v1_funct_2(X106,k2_zfmisc_1(X105,X105),X105)
| ~ m1_relset_1(X106,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_1(X107)
| ~ v1_funct_2(X107,k2_zfmisc_1(X105,X105),X105)
| ~ m1_relset_1(X107,k2_zfmisc_1(X105,X105),X105) )
& ( X107 = X110
| g3_lattices(X105,X106,X107) != g3_lattices(X108,X109,X110)
| ~ v1_funct_1(X106)
| ~ v1_funct_2(X106,k2_zfmisc_1(X105,X105),X105)
| ~ m1_relset_1(X106,k2_zfmisc_1(X105,X105),X105)
| ~ v1_funct_1(X107)
| ~ v1_funct_2(X107,k2_zfmisc_1(X105,X105),X105)
| ~ m1_relset_1(X107,k2_zfmisc_1(X105,X105),X105) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g3_lattices])])])]) ).
cnf(c_0_29,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
( m2_relset_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_31,plain,
! [X60] :
( ( v1_funct_1(u1_lattices(X60))
| ~ l1_lattices(X60) )
& ( v1_funct_2(u1_lattices(X60),k2_zfmisc_1(u1_struct_0(X60),u1_struct_0(X60)),u1_struct_0(X60))
| ~ l1_lattices(X60) )
& ( m2_relset_1(u1_lattices(X60),k2_zfmisc_1(u1_struct_0(X60),u1_struct_0(X60)),u1_struct_0(X60))
| ~ l1_lattices(X60) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
cnf(c_0_32,plain,
( X1 = X2
| g3_lattices(X3,X4,X1) != g3_lattices(X5,X6,X2)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X1,k2_zfmisc_1(X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
( m1_relset_1(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( v1_funct_1(u2_lattices(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
( v1_funct_2(u2_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
( m2_relset_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
( X1 = X2
| g3_lattices(u1_struct_0(X3),u2_lattices(X3),X1) != g3_lattices(X4,X5,X2)
| ~ l2_lattices(X3)
| ~ m1_relset_1(X1,k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X3)),u1_struct_0(X3))
| ~ v1_funct_2(X1,k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X3)),u1_struct_0(X3))
| ~ v1_funct_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_38,plain,
( m1_relset_1(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_36]) ).
cnf(c_0_39,plain,
( v1_funct_1(u1_lattices(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,plain,
( v1_funct_2(u1_lattices(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_41,plain,
! [X8] :
( ~ l3_lattices(X8)
| ~ v3_lattices(X8)
| X8 = g3_lattices(u1_struct_0(X8),u2_lattices(X8),u1_lattices(X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_lattices])]) ).
fof(c_0_42,plain,
! [X48] :
( ( l1_lattices(X48)
| ~ l3_lattices(X48) )
& ( l2_lattices(X48)
| ~ l3_lattices(X48) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_43,plain,
( u1_lattices(X1) = X2
| g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) != g3_lattices(X3,X4,X2)
| ~ l2_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]) ).
cnf(c_0_44,plain,
( X1 = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
| ~ l3_lattices(X1)
| ~ v3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_47,plain,
! [X21] :
( ~ l3_lattices(X21)
| k1_lattice2(X21) = g3_lattices(u1_struct_0(X21),u1_lattices(X21),u2_lattices(X21)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_lattice2])]) ).
cnf(c_0_48,plain,
( X1 = X2
| g3_lattices(X3,X1,X4) != g3_lattices(X5,X2,X6)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X1,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X3,X3),X3)
| ~ m1_relset_1(X4,k2_zfmisc_1(X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_49,plain,
( u1_lattices(X1) = X2
| X1 != g3_lattices(X3,X4,X2)
| ~ v3_lattices(X1)
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_50,plain,
( k1_lattice2(X1) = g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_51,plain,
! [X37] :
( ( v3_lattices(k1_lattice2(X37))
| ~ l3_lattices(X37) )
& ( l3_lattices(k1_lattice2(X37))
| ~ l3_lattices(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_52,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_0(X1) = k2_filter_0(X1,k5_lattices(X1)) ) ),
inference(fof_simplification,[status(thm)],[t20_filter_0]) ).
fof(c_0_53,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_54,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_55,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]) ).
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,
! [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_58,plain,
( X1 = X2
| g3_lattices(u1_struct_0(X3),X1,u2_lattices(X3)) != g3_lattices(X4,X2,X5)
| ~ l2_lattices(X3)
| ~ m1_relset_1(X1,k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X3)),u1_struct_0(X3))
| ~ v1_funct_2(X1,k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X3)),u1_struct_0(X3))
| ~ v1_funct_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_59,plain,
( u1_lattices(X1) = u2_lattices(X2)
| X1 != k1_lattice2(X2)
| ~ v3_lattices(X1)
| ~ l3_lattices(X1)
| ~ l3_lattices(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_60,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,plain,
( v3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_62,plain,
! [X155] :
( v3_struct_0(X155)
| ~ v10_lattices(X155)
| ~ l3_lattices(X155)
| v3_struct_0(X155)
| ~ v10_lattices(X155)
| ~ v13_lattices(X155)
| ~ l3_lattices(X155)
| k1_filter_0(X155) = k2_filter_0(X155,k5_lattices(X155)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])]) ).
fof(c_0_63,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> k6_lattices(X1) = k5_lattices(k1_lattice2(X1)) ),
inference(fof_simplification,[status(thm)],[t79_lattice2]) ).
fof(c_0_64,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v14_lattices(X1)
<=> v13_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t64_lattice2]) ).
fof(c_0_65,plain,
! [X130,X131] :
( v3_struct_0(X130)
| ~ v10_lattices(X130)
| ~ l3_lattices(X130)
| ~ m1_subset_1(X131,u1_struct_0(X130))
| k2_filter_2(X130,X131) = k2_filter_0(X130,X131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])]) ).
fof(c_0_66,plain,
! [X161,X162] :
( ( k18_filter_2(X161,X162) = k2_filter_2(k1_lattice2(X161),k5_filter_2(X161,X162))
| ~ m1_subset_1(X162,u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v10_lattices(X161)
| ~ l3_lattices(X161) )
& ( k18_filter_2(k1_lattice2(X161),k5_filter_2(X161,X162)) = k2_filter_2(X161,X162)
| ~ m1_subset_1(X162,u1_struct_0(X161))
| v3_struct_0(X161)
| ~ v10_lattices(X161)
| ~ l3_lattices(X161) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])])]) ).
fof(c_0_67,plain,
! [X94] :
( ( ~ v3_struct_0(k1_lattice2(X94))
| v3_struct_0(X94)
| ~ v10_lattices(X94)
| ~ l3_lattices(X94) )
& ( v3_lattices(k1_lattice2(X94))
| v3_struct_0(X94)
| ~ v10_lattices(X94)
| ~ l3_lattices(X94) )
& ( v4_lattices(k1_lattice2(X94))
| v3_struct_0(X94)
| ~ v10_lattices(X94)
| ~ l3_lattices(X94) )
& ( v5_lattices(k1_lattice2(X94))
| v3_struct_0(X94)
| ~ v10_lattices(X94)
| ~ l3_lattices(X94) )
& ( v6_lattices(k1_lattice2(X94))
| v3_struct_0(X94)
| ~ v10_lattices(X94)
| ~ l3_lattices(X94) )
& ( v7_lattices(k1_lattice2(X94))
| v3_struct_0(X94)
| ~ v10_lattices(X94)
| ~ l3_lattices(X94) )
& ( v8_lattices(k1_lattice2(X94))
| v3_struct_0(X94)
| ~ v10_lattices(X94)
| ~ l3_lattices(X94) )
& ( v9_lattices(k1_lattice2(X94))
| v3_struct_0(X94)
| ~ v10_lattices(X94)
| ~ l3_lattices(X94) )
& ( v10_lattices(k1_lattice2(X94))
| v3_struct_0(X94)
| ~ v10_lattices(X94)
| ~ l3_lattices(X94) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
fof(c_0_68,plain,
! [X42,X43] :
( v3_struct_0(X42)
| ~ v10_lattices(X42)
| ~ l3_lattices(X42)
| ~ m1_subset_1(X43,u1_struct_0(X42))
| m1_subset_1(k5_filter_2(X42,X43),u1_struct_0(k1_lattice2(X42))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])]) ).
fof(c_0_69,plain,
! [X82] :
( ( ~ v3_struct_0(k1_lattice2(X82))
| v3_struct_0(X82)
| ~ l3_lattices(X82) )
& ( v3_lattices(k1_lattice2(X82))
| v3_struct_0(X82)
| ~ l3_lattices(X82) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])]) ).
fof(c_0_70,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]) ).
cnf(c_0_71,plain,
( u1_lattices(X1) = X2
| g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1)) != g3_lattices(X3,X2,X4)
| ~ l2_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_38]),c_0_39]),c_0_40]) ).
cnf(c_0_72,plain,
( u1_lattices(k1_lattice2(X1)) = u2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_60]),c_0_61]) ).
cnf(c_0_73,plain,
( v3_struct_0(X1)
| v3_struct_0(X1)
| k1_filter_0(X1) = k2_filter_0(X1,k5_lattices(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v13_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_74,plain,
! [X173] :
( v3_struct_0(X173)
| ~ v10_lattices(X173)
| ~ v14_lattices(X173)
| ~ l3_lattices(X173)
| k6_lattices(X173) = k5_lattices(k1_lattice2(X173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])]) ).
fof(c_0_75,plain,
! [X171] :
( ( ~ v14_lattices(X171)
| v13_lattices(k1_lattice2(X171))
| v3_struct_0(X171)
| ~ v10_lattices(X171)
| ~ l3_lattices(X171) )
& ( ~ v13_lattices(k1_lattice2(X171))
| v14_lattices(X171)
| v3_struct_0(X171)
| ~ v10_lattices(X171)
| ~ l3_lattices(X171) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])]) ).
cnf(c_0_76,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_65]) ).
cnf(c_0_77,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_66]) ).
cnf(c_0_78,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_79,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_68]) ).
cnf(c_0_80,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
fof(c_0_81,plain,
! [X24,X25] :
( v3_struct_0(X24)
| ~ v10_lattices(X24)
| ~ l3_lattices(X24)
| ~ m1_subset_1(X25,u1_struct_0(X24))
| k5_filter_2(X24,X25) = X25 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])]) ).
cnf(c_0_82,plain,
( X1 = X2
| g3_lattices(X1,X3,X4) != g3_lattices(X2,X5,X6)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X3,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
| ~ m1_relset_1(X4,k2_zfmisc_1(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_83,plain,
( u1_lattices(X1) = X2
| k1_lattice2(X1) != g3_lattices(X3,X2,X4)
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_50]),c_0_45]),c_0_46]) ).
cnf(c_0_84,plain,
( g3_lattices(u1_struct_0(k1_lattice2(X1)),u2_lattices(k1_lattice2(X1)),u2_lattices(X1)) = k1_lattice2(X1)
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_72]),c_0_60]),c_0_61]) ).
fof(c_0_85,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v14_lattices(X1)
=> r1_filter_2(u1_struct_0(X1),k17_filter_2(X1),k18_filter_2(X1,k6_lattices(X1))) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t32_filter_2])]) ).
cnf(c_0_86,plain,
( k1_filter_0(X1) = k2_filter_0(X1,k5_lattices(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v13_lattices(X1) ),
inference(cn,[status(thm)],[c_0_73]) ).
cnf(c_0_87,plain,
( v3_struct_0(X1)
| k6_lattices(X1) = k5_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_88,plain,
( v14_lattices(X1)
| v3_struct_0(X1)
| ~ v13_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_89,plain,
( k2_filter_0(k1_lattice2(X1),k5_filter_2(X1,X2)) = k18_filter_2(X1,X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_60]),c_0_79]),c_0_80]) ).
cnf(c_0_90,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_81]) ).
cnf(c_0_91,plain,
( u1_struct_0(X1) = X2
| g3_lattices(u1_struct_0(X1),X3,u2_lattices(X1)) != g3_lattices(X2,X4,X5)
| ~ l2_lattices(X1)
| ~ m1_relset_1(X3,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_2(X3,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))
| ~ v1_funct_1(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_92,plain,
( u1_lattices(X1) = u2_lattices(k1_lattice2(X2))
| k1_lattice2(X1) != k1_lattice2(X2)
| ~ l3_lattices(X1)
| ~ l3_lattices(X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
fof(c_0_93,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& v14_lattices(esk1_0)
& ~ r1_filter_2(u1_struct_0(esk1_0),k17_filter_2(esk1_0),k18_filter_2(esk1_0,k6_lattices(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])]) ).
cnf(c_0_94,plain,
( k2_filter_0(k1_lattice2(X1),k6_lattices(X1)) = k1_filter_0(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v13_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_78]),c_0_60]),c_0_88]),c_0_80]) ).
cnf(c_0_95,plain,
( k2_filter_0(k1_lattice2(X1),X2) = k18_filter_2(X1,X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
fof(c_0_96,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_0(X1) = u1_struct_0(X1) ),
inference(fof_simplification,[status(thm)],[d2_filter_0]) ).
cnf(c_0_97,plain,
( u1_struct_0(X1) = X2
| g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1)) != g3_lattices(X2,X3,X4)
| ~ l2_lattices(X1)
| ~ l1_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_38]),c_0_39]),c_0_40]) ).
cnf(c_0_98,plain,
( u2_lattices(k1_lattice2(X1)) = u1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(er,[status(thm)],[c_0_92]) ).
cnf(c_0_99,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),k17_filter_2(esk1_0),k18_filter_2(esk1_0,k6_lattices(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_100,plain,
( k18_filter_2(X1,k6_lattices(X1)) = k1_filter_0(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v13_lattices(k1_lattice2(X1))
| ~ m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_101,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_102,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_103,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
fof(c_0_104,plain,
! [X20] :
( v3_struct_0(X20)
| ~ v10_lattices(X20)
| ~ l3_lattices(X20)
| k1_filter_0(X20) = u1_struct_0(X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])]) ).
cnf(c_0_105,plain,
( u1_struct_0(X1) = X2
| k1_lattice2(X1) != g3_lattices(X2,X3,X4)
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_50]),c_0_45]),c_0_46]) ).
cnf(c_0_106,plain,
( g3_lattices(u1_struct_0(k1_lattice2(X1)),u1_lattices(X1),u1_lattices(k1_lattice2(X1))) = k1_lattice2(X1)
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_98]),c_0_60]),c_0_61]) ).
cnf(c_0_107,negated_conjecture,
( ~ v13_lattices(k1_lattice2(esk1_0))
| ~ m1_subset_1(k6_lattices(esk1_0),u1_struct_0(esk1_0))
| ~ r1_filter_2(u1_struct_0(esk1_0),k17_filter_2(esk1_0),k1_filter_0(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_99,c_0_100]),c_0_101]),c_0_102])]),c_0_103]) ).
cnf(c_0_108,plain,
( v3_struct_0(X1)
| k1_filter_0(X1) = u1_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_109,plain,
( u1_struct_0(X1) = u1_struct_0(k1_lattice2(X2))
| k1_lattice2(X1) != k1_lattice2(X2)
| ~ l3_lattices(X1)
| ~ l3_lattices(X2) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
fof(c_0_110,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k17_filter_2(X1) = u1_struct_0(X1) ),
inference(fof_simplification,[status(thm)],[d8_filter_2]) ).
cnf(c_0_111,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| ~ v13_lattices(k1_lattice2(esk1_0))
| ~ m1_subset_1(k6_lattices(esk1_0),u1_struct_0(esk1_0))
| ~ r1_filter_2(u1_struct_0(esk1_0),k17_filter_2(esk1_0),u1_struct_0(k1_lattice2(esk1_0)))
| ~ l3_lattices(k1_lattice2(esk1_0))
| ~ v10_lattices(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_112,plain,
( u1_struct_0(k1_lattice2(X1)) = u1_struct_0(X1)
| ~ l3_lattices(X1) ),
inference(er,[status(thm)],[c_0_109]) ).
fof(c_0_113,plain,
! [X26] :
( v3_struct_0(X26)
| ~ v10_lattices(X26)
| ~ l3_lattices(X26)
| k17_filter_2(X26) = u1_struct_0(X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_110])]) ).
fof(c_0_114,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_115,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)
<=> X2 = X3 ) ),
inference(fof_simplification,[status(thm)],[redefinition_r1_filter_2]) ).
cnf(c_0_116,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| ~ v13_lattices(k1_lattice2(esk1_0))
| ~ m1_subset_1(k6_lattices(esk1_0),u1_struct_0(esk1_0))
| ~ r1_filter_2(u1_struct_0(esk1_0),k17_filter_2(esk1_0),u1_struct_0(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0))
| ~ v10_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_101])]) ).
cnf(c_0_117,plain,
( v3_struct_0(X1)
| k17_filter_2(X1) = u1_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
fof(c_0_118,plain,
! [X45] :
( v3_struct_0(X45)
| ~ l2_lattices(X45)
| m1_subset_1(k6_lattices(X45),u1_struct_0(X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_114])]) ).
fof(c_0_119,plain,
! [X137,X138,X139] :
( ( ~ r1_filter_2(X137,X138,X139)
| X138 = X139
| v1_xboole_0(X137)
| ~ m1_subset_1(X138,k1_zfmisc_1(X137))
| ~ m1_subset_1(X139,k1_zfmisc_1(X137)) )
& ( X138 != X139
| r1_filter_2(X137,X138,X139)
| v1_xboole_0(X137)
| ~ m1_subset_1(X138,k1_zfmisc_1(X137))
| ~ m1_subset_1(X139,k1_zfmisc_1(X137)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_115])])]) ).
fof(c_0_120,plain,
! [X163,X164] :
( ( ~ m1_subset_1(X163,k1_zfmisc_1(X164))
| r1_tarski(X163,X164) )
& ( ~ r1_tarski(X163,X164)
| m1_subset_1(X163,k1_zfmisc_1(X164)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_121,plain,
! [X146] : r1_tarski(X146,X146),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_122,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| ~ v13_lattices(k1_lattice2(esk1_0))
| ~ m1_subset_1(k6_lattices(esk1_0),u1_struct_0(esk1_0))
| ~ r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0))
| ~ v10_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_116,c_0_117]),c_0_101]),c_0_102])]),c_0_103]) ).
cnf(c_0_123,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_118]) ).
cnf(c_0_124,plain,
( r1_filter_2(X3,X1,X2)
| v1_xboole_0(X3)
| X1 != X2
| ~ m1_subset_1(X1,k1_zfmisc_1(X3))
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_125,plain,
( m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_126,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_127,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| ~ l2_lattices(esk1_0)
| ~ v13_lattices(k1_lattice2(esk1_0))
| ~ r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0))
| ~ v10_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_103]) ).
cnf(c_0_128,plain,
( v1_xboole_0(X1)
| r1_filter_2(X1,X2,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(er,[status(thm)],[c_0_124]) ).
cnf(c_0_129,plain,
m1_subset_1(X1,k1_zfmisc_1(X1)),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
fof(c_0_130,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_131,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l2_lattices(esk1_0)
| ~ v13_lattices(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0))
| ~ v10_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129])]) ).
cnf(c_0_132,plain,
( v13_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_133,negated_conjecture,
v14_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
fof(c_0_134,plain,
! [X83] :
( v3_struct_0(X83)
| ~ l1_struct_0(X83)
| ~ v1_xboole_0(u1_struct_0(X83)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_130])]) ).
fof(c_0_135,plain,
! [X46] :
( ~ l1_lattices(X46)
| l1_struct_0(X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
cnf(c_0_136,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l2_lattices(esk1_0)
| ~ l3_lattices(k1_lattice2(esk1_0))
| ~ v10_lattices(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_131,c_0_132]),c_0_133]),c_0_101]),c_0_102])]),c_0_103]) ).
cnf(c_0_137,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_138,plain,
( l1_struct_0(X1)
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_139,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l2_lattices(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_136,c_0_78]),c_0_101]),c_0_102])]),c_0_103]) ).
cnf(c_0_140,plain,
( v3_struct_0(X1)
| ~ l1_lattices(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_141,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_46]),c_0_101])]) ).
cnf(c_0_142,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_140,c_0_45]) ).
cnf(c_0_143,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_60]),c_0_101])]) ).
cnf(c_0_144,negated_conjecture,
v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_101])]),c_0_103]) ).
cnf(c_0_145,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_144]),c_0_101])]),c_0_103]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT306+1 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.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 07:21:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.62 start to proof: theBenchmark
% 1.53/1.56 % Version : CSE_E---1.5
% 1.53/1.56 % Problem : theBenchmark.p
% 1.53/1.56 % Proof found
% 1.53/1.56 % SZS status Theorem for theBenchmark.p
% 1.53/1.56 % SZS output start Proof
% See solution above
% 1.53/1.58 % Total time : 0.937000 s
% 1.53/1.58 % SZS output end Proof
% 1.53/1.58 % Total time : 0.943000 s
%------------------------------------------------------------------------------