TSTP Solution File: LAT331+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT331+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 : n023.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 06:01:27 EDT 2023
% Result : Theorem 3.32s 3.40s
% Output : CNFRefutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 77
% Syntax : Number of formulae : 150 ( 19 unt; 68 typ; 0 def)
% Number of atoms : 490 ( 92 equ)
% Maximal formula atoms : 98 ( 5 avg)
% Number of connectives : 672 ( 264 ~; 288 |; 90 &)
% ( 5 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 50 >; 28 *; 0 +; 0 <<)
% Number of predicates : 31 ( 29 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 18 con; 0-3 aty)
% Number of variables : 145 ( 16 sgn; 55 !; 4 ?; 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,
m1_filter_2: ( $i * $i ) > $o ).
tff(decl_26,type,
u1_struct_0: $i > $i ).
tff(decl_27,type,
u2_lattices: $i > $i ).
tff(decl_28,type,
u1_lattices: $i > $i ).
tff(decl_29,type,
g3_lattices: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
k8_filter_0: ( $i * $i ) > $i ).
tff(decl_31,type,
v3_lattices: $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,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(decl_42,type,
k1_zfmisc_1: $i > $i ).
tff(decl_43,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_44,type,
v1_relat_1: $i > $o ).
tff(decl_45,type,
v2_funct_1: $i > $o ).
tff(decl_46,type,
m1_filter_0: ( $i * $i ) > $o ).
tff(decl_47,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_48,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_49,type,
k1_realset1: ( $i * $i ) > $i ).
tff(decl_50,type,
k7_relat_1: ( $i * $i ) > $i ).
tff(decl_51,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_52,type,
l1_lattices: $i > $o ).
tff(decl_53,type,
l1_struct_0: $i > $o ).
tff(decl_54,type,
l2_lattices: $i > $o ).
tff(decl_55,type,
m2_lattice4: ( $i * $i ) > $o ).
tff(decl_56,type,
k1_xboole_0: $i ).
tff(decl_57,type,
v1_binop_1: ( $i * $i ) > $o ).
tff(decl_58,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_59,type,
v2_binop_1: ( $i * $i ) > $o ).
tff(decl_60,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_61,type,
esk1_0: $i ).
tff(decl_62,type,
esk2_0: $i ).
tff(decl_63,type,
esk3_0: $i ).
tff(decl_64,type,
esk4_0: $i ).
tff(decl_65,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
esk7_0: $i ).
tff(decl_68,type,
esk8_0: $i ).
tff(decl_69,type,
esk9_0: $i ).
tff(decl_70,type,
esk10_0: $i ).
tff(decl_71,type,
esk11_1: $i > $i ).
tff(decl_72,type,
esk12_1: $i > $i ).
tff(decl_73,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk14_1: $i > $i ).
tff(decl_75,type,
esk15_1: $i > $i ).
tff(decl_76,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_77,type,
esk17_0: $i ).
tff(decl_78,type,
esk18_1: $i > $i ).
tff(decl_79,type,
esk19_1: $i > $i ).
tff(decl_80,type,
esk20_0: $i ).
tff(decl_81,type,
esk21_0: $i ).
tff(decl_82,type,
esk22_1: $i > $i ).
tff(decl_83,type,
esk23_0: $i ).
tff(decl_84,type,
esk24_0: $i ).
tff(decl_85,type,
esk25_0: $i ).
tff(decl_86,type,
esk26_0: $i ).
tff(decl_87,type,
esk27_1: $i > $i ).
tff(decl_88,type,
esk28_0: $i ).
tff(decl_89,type,
esk29_0: $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(t68_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ! [X3] :
( m1_filter_2(X3,X1)
=> ! [X4] :
( m1_filter_2(X4,X2)
=> ( ( g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) = g3_lattices(u1_struct_0(X2),u2_lattices(X2),u1_lattices(X2))
& X3 = X4 )
=> k8_filter_0(X1,X3) = k8_filter_0(X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_filter_2) ).
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(d10_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v10_lattices(X3)
& l3_lattices(X3) )
=> ( X3 = k8_filter_0(X1,X2)
<=> ? [X4] :
( v1_funct_1(X4)
& v1_funct_2(X4,k2_zfmisc_1(X2,X2),X2)
& m2_relset_1(X4,k2_zfmisc_1(X2,X2),X2)
& ? [X5] :
( v1_funct_1(X5)
& v1_funct_2(X5,k2_zfmisc_1(X2,X2),X2)
& m2_relset_1(X5,k2_zfmisc_1(X2,X2),X2)
& X4 = k1_realset1(u2_lattices(X1),X2)
& X5 = k1_realset1(u1_lattices(X1),X2)
& X3 = g3_lattices(X2,X4,X5) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_filter_0) ).
fof(dt_k8_filter_0,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,X1) )
=> ( ~ v3_struct_0(k8_filter_0(X1,X2))
& v10_lattices(k8_filter_0(X1,X2))
& l3_lattices(k8_filter_0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_0) ).
fof(redefinition_m1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(c_0_9,plain,
! [X113,X114,X115] :
( ( ~ m2_relset_1(X115,X113,X114)
| m1_relset_1(X115,X113,X114) )
& ( ~ m1_relset_1(X115,X113,X114)
| m2_relset_1(X115,X113,X114) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_10,plain,
! [X50] :
( ( v1_funct_1(u2_lattices(X50))
| ~ l2_lattices(X50) )
& ( v1_funct_2(u2_lattices(X50),k2_zfmisc_1(u1_struct_0(X50),u1_struct_0(X50)),u1_struct_0(X50))
| ~ l2_lattices(X50) )
& ( m2_relset_1(u2_lattices(X50),k2_zfmisc_1(u1_struct_0(X50),u1_struct_0(X50)),u1_struct_0(X50))
| ~ l2_lattices(X50) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
fof(c_0_11,plain,
! [X88,X89,X90,X91,X92,X93] :
( ( X88 = X91
| g3_lattices(X88,X89,X90) != g3_lattices(X91,X92,X93)
| ~ v1_funct_1(X89)
| ~ v1_funct_2(X89,k2_zfmisc_1(X88,X88),X88)
| ~ m1_relset_1(X89,k2_zfmisc_1(X88,X88),X88)
| ~ v1_funct_1(X90)
| ~ v1_funct_2(X90,k2_zfmisc_1(X88,X88),X88)
| ~ m1_relset_1(X90,k2_zfmisc_1(X88,X88),X88) )
& ( X89 = X92
| g3_lattices(X88,X89,X90) != g3_lattices(X91,X92,X93)
| ~ v1_funct_1(X89)
| ~ v1_funct_2(X89,k2_zfmisc_1(X88,X88),X88)
| ~ m1_relset_1(X89,k2_zfmisc_1(X88,X88),X88)
| ~ v1_funct_1(X90)
| ~ v1_funct_2(X90,k2_zfmisc_1(X88,X88),X88)
| ~ m1_relset_1(X90,k2_zfmisc_1(X88,X88),X88) )
& ( X90 = X93
| g3_lattices(X88,X89,X90) != g3_lattices(X91,X92,X93)
| ~ v1_funct_1(X89)
| ~ v1_funct_2(X89,k2_zfmisc_1(X88,X88),X88)
| ~ m1_relset_1(X89,k2_zfmisc_1(X88,X88),X88)
| ~ v1_funct_1(X90)
| ~ v1_funct_2(X90,k2_zfmisc_1(X88,X88),X88)
| ~ m1_relset_1(X90,k2_zfmisc_1(X88,X88),X88) ) ),
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_12,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,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_10]) ).
fof(c_0_14,plain,
! [X49] :
( ( v1_funct_1(u1_lattices(X49))
| ~ l1_lattices(X49) )
& ( v1_funct_2(u1_lattices(X49),k2_zfmisc_1(u1_struct_0(X49),u1_struct_0(X49)),u1_struct_0(X49))
| ~ l1_lattices(X49) )
& ( m2_relset_1(u1_lattices(X49),k2_zfmisc_1(u1_struct_0(X49),u1_struct_0(X49)),u1_struct_0(X49))
| ~ l1_lattices(X49) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
cnf(c_0_15,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_11]) ).
cnf(c_0_16,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_12,c_0_13]) ).
cnf(c_0_17,plain,
( v1_funct_1(u2_lattices(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,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_10]) ).
cnf(c_0_19,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_14]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ! [X3] :
( m1_filter_2(X3,X1)
=> ! [X4] :
( m1_filter_2(X4,X2)
=> ( ( g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) = g3_lattices(u1_struct_0(X2),u2_lattices(X2),u1_lattices(X2))
& X3 = X4 )
=> k8_filter_0(X1,X3) = k8_filter_0(X2,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t68_filter_2])]) ).
cnf(c_0_21,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_15,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_22,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_12,c_0_19]) ).
cnf(c_0_23,plain,
( v1_funct_1(u1_lattices(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,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_14]) ).
fof(c_0_25,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& ~ v3_struct_0(esk2_0)
& v10_lattices(esk2_0)
& l3_lattices(esk2_0)
& m1_filter_2(esk3_0,esk1_0)
& m1_filter_2(esk4_0,esk2_0)
& g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) = g3_lattices(u1_struct_0(esk2_0),u2_lattices(esk2_0),u1_lattices(esk2_0))
& esk3_0 = esk4_0
& k8_filter_0(esk1_0,esk3_0) != k8_filter_0(esk2_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_26,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_21,c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_27,negated_conjecture,
g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) = g3_lattices(u1_struct_0(esk2_0),u2_lattices(esk2_0),u1_lattices(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( u1_lattices(esk2_0) = X1
| g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) != g3_lattices(X2,X3,X1)
| ~ l2_lattices(esk2_0)
| ~ l1_lattices(esk2_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_29,plain,
! [X39] :
( ( l1_lattices(X39)
| ~ l3_lattices(X39) )
& ( l2_lattices(X39)
| ~ l3_lattices(X39) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_30,negated_conjecture,
( u1_lattices(esk2_0) = u1_lattices(esk1_0)
| ~ l2_lattices(esk2_0)
| ~ l1_lattices(esk2_0) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_31,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,negated_conjecture,
l3_lattices(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,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_11]) ).
cnf(c_0_34,negated_conjecture,
( u1_lattices(esk2_0) = u1_lattices(esk1_0)
| ~ l1_lattices(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_35,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( X1 = X2
| g3_lattices(u1_struct_0(X3),X1,u1_lattices(X3)) != g3_lattices(X4,X2,X5)
| ~ l1_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_33,c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_37,negated_conjecture,
u1_lattices(esk2_0) = u1_lattices(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_32])]) ).
fof(c_0_38,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v10_lattices(X3)
& l3_lattices(X3) )
=> ( X3 = k8_filter_0(X1,X2)
<=> ? [X4] :
( v1_funct_1(X4)
& v1_funct_2(X4,k2_zfmisc_1(X2,X2),X2)
& m2_relset_1(X4,k2_zfmisc_1(X2,X2),X2)
& ? [X5] :
( v1_funct_1(X5)
& v1_funct_2(X5,k2_zfmisc_1(X2,X2),X2)
& m2_relset_1(X5,k2_zfmisc_1(X2,X2),X2)
& X4 = k1_realset1(u2_lattices(X1),X2)
& X5 = k1_realset1(u1_lattices(X1),X2)
& X3 = g3_lattices(X2,X4,X5) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d10_filter_0]) ).
cnf(c_0_39,plain,
( u2_lattices(X1) = X2
| g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_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_36,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_40,negated_conjecture,
g3_lattices(u1_struct_0(esk2_0),u2_lattices(esk2_0),u1_lattices(esk1_0)) = g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)),
inference(rw,[status(thm)],[c_0_27,c_0_37]) ).
fof(c_0_41,plain,
! [X21,X22,X23,X26,X27] :
( ( v1_funct_1(esk5_3(X21,X22,X23))
| X23 != k8_filter_0(X21,X22)
| v3_struct_0(X23)
| ~ v10_lattices(X23)
| ~ l3_lattices(X23)
| ~ m1_filter_0(X22,X21)
| v3_struct_0(X21)
| ~ v10_lattices(X21)
| ~ l3_lattices(X21) )
& ( v1_funct_2(esk5_3(X21,X22,X23),k2_zfmisc_1(X22,X22),X22)
| X23 != k8_filter_0(X21,X22)
| v3_struct_0(X23)
| ~ v10_lattices(X23)
| ~ l3_lattices(X23)
| ~ m1_filter_0(X22,X21)
| v3_struct_0(X21)
| ~ v10_lattices(X21)
| ~ l3_lattices(X21) )
& ( m2_relset_1(esk5_3(X21,X22,X23),k2_zfmisc_1(X22,X22),X22)
| X23 != k8_filter_0(X21,X22)
| v3_struct_0(X23)
| ~ v10_lattices(X23)
| ~ l3_lattices(X23)
| ~ m1_filter_0(X22,X21)
| v3_struct_0(X21)
| ~ v10_lattices(X21)
| ~ l3_lattices(X21) )
& ( v1_funct_1(esk6_3(X21,X22,X23))
| X23 != k8_filter_0(X21,X22)
| v3_struct_0(X23)
| ~ v10_lattices(X23)
| ~ l3_lattices(X23)
| ~ m1_filter_0(X22,X21)
| v3_struct_0(X21)
| ~ v10_lattices(X21)
| ~ l3_lattices(X21) )
& ( v1_funct_2(esk6_3(X21,X22,X23),k2_zfmisc_1(X22,X22),X22)
| X23 != k8_filter_0(X21,X22)
| v3_struct_0(X23)
| ~ v10_lattices(X23)
| ~ l3_lattices(X23)
| ~ m1_filter_0(X22,X21)
| v3_struct_0(X21)
| ~ v10_lattices(X21)
| ~ l3_lattices(X21) )
& ( m2_relset_1(esk6_3(X21,X22,X23),k2_zfmisc_1(X22,X22),X22)
| X23 != k8_filter_0(X21,X22)
| v3_struct_0(X23)
| ~ v10_lattices(X23)
| ~ l3_lattices(X23)
| ~ m1_filter_0(X22,X21)
| v3_struct_0(X21)
| ~ v10_lattices(X21)
| ~ l3_lattices(X21) )
& ( esk5_3(X21,X22,X23) = k1_realset1(u2_lattices(X21),X22)
| X23 != k8_filter_0(X21,X22)
| v3_struct_0(X23)
| ~ v10_lattices(X23)
| ~ l3_lattices(X23)
| ~ m1_filter_0(X22,X21)
| v3_struct_0(X21)
| ~ v10_lattices(X21)
| ~ l3_lattices(X21) )
& ( esk6_3(X21,X22,X23) = k1_realset1(u1_lattices(X21),X22)
| X23 != k8_filter_0(X21,X22)
| v3_struct_0(X23)
| ~ v10_lattices(X23)
| ~ l3_lattices(X23)
| ~ m1_filter_0(X22,X21)
| v3_struct_0(X21)
| ~ v10_lattices(X21)
| ~ l3_lattices(X21) )
& ( X23 = g3_lattices(X22,esk5_3(X21,X22,X23),esk6_3(X21,X22,X23))
| X23 != k8_filter_0(X21,X22)
| v3_struct_0(X23)
| ~ v10_lattices(X23)
| ~ l3_lattices(X23)
| ~ m1_filter_0(X22,X21)
| v3_struct_0(X21)
| ~ v10_lattices(X21)
| ~ l3_lattices(X21) )
& ( ~ v1_funct_1(X26)
| ~ v1_funct_2(X26,k2_zfmisc_1(X22,X22),X22)
| ~ m2_relset_1(X26,k2_zfmisc_1(X22,X22),X22)
| ~ v1_funct_1(X27)
| ~ v1_funct_2(X27,k2_zfmisc_1(X22,X22),X22)
| ~ m2_relset_1(X27,k2_zfmisc_1(X22,X22),X22)
| X26 != k1_realset1(u2_lattices(X21),X22)
| X27 != k1_realset1(u1_lattices(X21),X22)
| X23 != g3_lattices(X22,X26,X27)
| X23 = k8_filter_0(X21,X22)
| v3_struct_0(X23)
| ~ v10_lattices(X23)
| ~ l3_lattices(X23)
| ~ m1_filter_0(X22,X21)
| v3_struct_0(X21)
| ~ v10_lattices(X21)
| ~ l3_lattices(X21) ) ),
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_38])])])])]) ).
cnf(c_0_42,negated_conjecture,
( u2_lattices(esk2_0) = X1
| g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) != g3_lattices(X2,X1,X3)
| ~ l2_lattices(esk2_0)
| ~ l1_lattices(esk2_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_40]) ).
cnf(c_0_43,plain,
( X1 = g3_lattices(X2,esk5_3(X3,X2,X1),esk6_3(X3,X2,X1))
| v3_struct_0(X1)
| v3_struct_0(X3)
| X1 != k8_filter_0(X3,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_44,plain,
( esk6_3(X1,X2,X3) = k1_realset1(u1_lattices(X1),X2)
| v3_struct_0(X3)
| v3_struct_0(X1)
| X3 != k8_filter_0(X1,X2)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3)
| ~ m1_filter_0(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_45,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,X1) )
=> ( ~ v3_struct_0(k8_filter_0(X1,X2))
& v10_lattices(k8_filter_0(X1,X2))
& l3_lattices(k8_filter_0(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[dt_k8_filter_0]) ).
cnf(c_0_46,plain,
( esk5_3(X1,X2,X3) = k1_realset1(u2_lattices(X1),X2)
| v3_struct_0(X3)
| v3_struct_0(X1)
| X3 != k8_filter_0(X1,X2)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3)
| ~ m1_filter_0(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,negated_conjecture,
v10_lattices(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_48,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_49,negated_conjecture,
( u2_lattices(esk2_0) = u2_lattices(esk1_0)
| ~ l2_lattices(esk2_0)
| ~ l1_lattices(esk2_0) ),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
( g3_lattices(X1,esk5_3(X2,X1,X3),k1_realset1(u1_lattices(X2),X1)) = X3
| v3_struct_0(X2)
| v3_struct_0(X3)
| X3 != k8_filter_0(X2,X1)
| ~ m1_filter_0(X1,X2)
| ~ l3_lattices(X2)
| ~ l3_lattices(X3)
| ~ v10_lattices(X2)
| ~ v10_lattices(X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_51,plain,
! [X35,X36] :
( ( ~ v3_struct_0(k8_filter_0(X35,X36))
| v3_struct_0(X35)
| ~ v10_lattices(X35)
| ~ l3_lattices(X35)
| ~ m1_filter_0(X36,X35) )
& ( v10_lattices(k8_filter_0(X35,X36))
| v3_struct_0(X35)
| ~ v10_lattices(X35)
| ~ l3_lattices(X35)
| ~ m1_filter_0(X36,X35) )
& ( l3_lattices(k8_filter_0(X35,X36))
| v3_struct_0(X35)
| ~ v10_lattices(X35)
| ~ l3_lattices(X35)
| ~ m1_filter_0(X36,X35) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
cnf(c_0_52,plain,
( g3_lattices(X1,k1_realset1(u2_lattices(X2),X1),esk6_3(X2,X1,X3)) = X3
| v3_struct_0(X2)
| v3_struct_0(X3)
| X3 != k8_filter_0(X2,X1)
| ~ m1_filter_0(X1,X2)
| ~ l3_lattices(X2)
| ~ l3_lattices(X3)
| ~ v10_lattices(X2)
| ~ v10_lattices(X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( esk6_3(esk2_0,X1,X2) = k1_realset1(u1_lattices(esk1_0),X1)
| v3_struct_0(X2)
| X2 != k8_filter_0(esk2_0,X1)
| ~ m1_filter_0(X1,esk2_0)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_37]),c_0_32]),c_0_47])]),c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( u2_lattices(esk2_0) = u2_lattices(esk1_0)
| ~ l1_lattices(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_31]),c_0_32])]) ).
cnf(c_0_55,plain,
( g3_lattices(X1,k1_realset1(u2_lattices(X2),X1),k1_realset1(u1_lattices(X2),X1)) = X3
| v3_struct_0(X3)
| v3_struct_0(X2)
| X3 != k8_filter_0(X2,X1)
| ~ m1_filter_0(X1,X2)
| ~ l3_lattices(X2)
| ~ l3_lattices(X3)
| ~ v10_lattices(X2)
| ~ v10_lattices(X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_46]) ).
cnf(c_0_56,plain,
( v10_lattices(k8_filter_0(X1,X2))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,plain,
( l3_lattices(k8_filter_0(X1,X2))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k8_filter_0(X1,X2))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,negated_conjecture,
( g3_lattices(X1,k1_realset1(u2_lattices(esk2_0),X1),k1_realset1(u1_lattices(esk1_0),X1)) = X2
| v3_struct_0(X2)
| X2 != k8_filter_0(esk2_0,X1)
| ~ m1_filter_0(X1,esk2_0)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_32]),c_0_47])]),c_0_48]) ).
cnf(c_0_60,negated_conjecture,
u2_lattices(esk2_0) = u2_lattices(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_35]),c_0_32])]) ).
cnf(c_0_61,plain,
( g3_lattices(X1,k1_realset1(u2_lattices(X2),X1),k1_realset1(u1_lattices(X2),X1)) = k8_filter_0(X2,X1)
| v3_struct_0(X2)
| ~ m1_filter_0(X1,X2)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_55]),c_0_56]),c_0_57]),c_0_58]) ).
cnf(c_0_62,negated_conjecture,
( g3_lattices(X1,k1_realset1(u2_lattices(esk1_0),X1),k1_realset1(u1_lattices(esk1_0),X1)) = k8_filter_0(esk2_0,X1)
| v3_struct_0(k8_filter_0(esk2_0,X1))
| ~ m1_filter_0(X1,esk2_0)
| ~ l3_lattices(k8_filter_0(esk2_0,X1))
| ~ v10_lattices(k8_filter_0(esk2_0,X1)) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_60]) ).
cnf(c_0_63,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_64,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_65,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_66,negated_conjecture,
( k8_filter_0(esk2_0,X1) = k8_filter_0(esk1_0,X1)
| v3_struct_0(k8_filter_0(esk2_0,X1))
| ~ m1_filter_0(X1,esk1_0)
| ~ m1_filter_0(X1,esk2_0)
| ~ l3_lattices(k8_filter_0(esk2_0,X1))
| ~ v10_lattices(k8_filter_0(esk2_0,X1)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_64])]),c_0_65]) ).
fof(c_0_67,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m1_filter_2]) ).
cnf(c_0_68,negated_conjecture,
( k8_filter_0(esk2_0,X1) = k8_filter_0(esk1_0,X1)
| v3_struct_0(k8_filter_0(esk2_0,X1))
| ~ m1_filter_0(X1,esk1_0)
| ~ m1_filter_0(X1,esk2_0)
| ~ l3_lattices(k8_filter_0(esk2_0,X1)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_56]),c_0_32]),c_0_47])]),c_0_48]) ).
fof(c_0_69,plain,
! [X111,X112] :
( ( ~ m1_filter_2(X112,X111)
| m1_filter_0(X112,X111)
| v3_struct_0(X111)
| ~ v10_lattices(X111)
| ~ l3_lattices(X111) )
& ( ~ m1_filter_0(X112,X111)
| m1_filter_2(X112,X111)
| v3_struct_0(X111)
| ~ v10_lattices(X111)
| ~ l3_lattices(X111) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])]) ).
cnf(c_0_70,negated_conjecture,
m1_filter_2(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_71,negated_conjecture,
esk3_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_72,negated_conjecture,
k8_filter_0(esk1_0,esk3_0) != k8_filter_0(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_73,negated_conjecture,
( k8_filter_0(esk2_0,X1) = k8_filter_0(esk1_0,X1)
| v3_struct_0(k8_filter_0(esk2_0,X1))
| ~ m1_filter_0(X1,esk1_0)
| ~ m1_filter_0(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_57]),c_0_32]),c_0_47])]),c_0_48]) ).
cnf(c_0_74,plain,
( m1_filter_0(X1,X2)
| v3_struct_0(X2)
| ~ m1_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_75,negated_conjecture,
m1_filter_2(esk3_0,esk2_0),
inference(rw,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
m1_filter_2(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_77,negated_conjecture,
k8_filter_0(esk2_0,esk3_0) != k8_filter_0(esk1_0,esk3_0),
inference(rw,[status(thm)],[c_0_72,c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( k8_filter_0(esk2_0,X1) = k8_filter_0(esk1_0,X1)
| ~ m1_filter_0(X1,esk2_0)
| ~ m1_filter_0(X1,esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_73]),c_0_32]),c_0_47])]),c_0_48]) ).
cnf(c_0_79,negated_conjecture,
m1_filter_0(esk3_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_74,c_0_75]),c_0_32]),c_0_47])]),c_0_48]) ).
cnf(c_0_80,negated_conjecture,
m1_filter_0(esk3_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_74,c_0_76]),c_0_63]),c_0_64])]),c_0_65]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_80])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT331+1 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 09:45:12 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 3.32/3.40 % Version : CSE_E---1.5
% 3.32/3.40 % Problem : theBenchmark.p
% 3.32/3.40 % Proof found
% 3.32/3.40 % SZS status Theorem for theBenchmark.p
% 3.32/3.40 % SZS output start Proof
% See solution above
% 3.32/3.41 % Total time : 2.833000 s
% 3.32/3.41 % SZS output end Proof
% 3.32/3.41 % Total time : 2.838000 s
%------------------------------------------------------------------------------