TSTP Solution File: LAT297+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT297+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 : n007.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 06:00:50 EDT 2023
% Result : Theorem 0.99s 1.07s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 84
% Syntax : Number of formulae : 150 ( 20 unt; 72 typ; 0 def)
% Number of atoms : 398 ( 18 equ)
% Maximal formula atoms : 51 ( 5 avg)
% Number of connectives : 495 ( 175 ~; 196 |; 78 &)
% ( 6 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 92 ( 55 >; 37 *; 0 +; 0 <<)
% Number of predicates : 32 ( 30 usr; 3 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 15 con; 0-6 aty)
% Number of variables : 131 ( 1 sgn; 81 !; 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,
u1_struct_0: $i > $i ).
tff(decl_26,type,
k1_zfmisc_1: $i > $i ).
tff(decl_27,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_28,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_29,type,
k4_lattices: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
m2_lattice4: ( $i * $i ) > $o ).
tff(decl_31,type,
v1_xboole_0: $i > $o ).
tff(decl_32,type,
v1_funct_1: $i > $o ).
tff(decl_33,type,
v4_lattices: $i > $o ).
tff(decl_34,type,
v5_lattices: $i > $o ).
tff(decl_35,type,
v6_lattices: $i > $o ).
tff(decl_36,type,
v7_lattices: $i > $o ).
tff(decl_37,type,
v8_lattices: $i > $o ).
tff(decl_38,type,
v9_lattices: $i > $o ).
tff(decl_39,type,
v1_realset1: $i > $o ).
tff(decl_40,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(decl_41,type,
v1_relat_1: $i > $o ).
tff(decl_42,type,
v2_funct_1: $i > $o ).
tff(decl_43,type,
k2_tarski: ( $i * $i ) > $i ).
tff(decl_44,type,
l2_lattices: $i > $o ).
tff(decl_45,type,
k3_lattices: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
l1_lattices: $i > $o ).
tff(decl_47,type,
k1_binop_1: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
k4_tarski: ( $i * $i ) > $i ).
tff(decl_49,type,
k1_funct_1: ( $i * $i ) > $i ).
tff(decl_50,type,
k1_lattices: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
u2_lattices: $i > $i ).
tff(decl_52,type,
k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_53,type,
k2_lattices: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
u1_lattices: $i > $i ).
tff(decl_55,type,
k1_tarski: $i > $i ).
tff(decl_56,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_57,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_58,type,
l1_struct_0: $i > $o ).
tff(decl_59,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_60,type,
k1_xboole_0: $i ).
tff(decl_61,type,
v1_binop_1: ( $i * $i ) > $o ).
tff(decl_62,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_63,type,
v2_binop_1: ( $i * $i ) > $o ).
tff(decl_64,type,
v1_finset_1: $i > $o ).
tff(decl_65,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_66,type,
esk1_0: $i ).
tff(decl_67,type,
esk2_0: $i ).
tff(decl_68,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk5_1: $i > $i ).
tff(decl_71,type,
esk6_1: $i > $i ).
tff(decl_72,type,
esk7_0: $i ).
tff(decl_73,type,
esk8_0: $i ).
tff(decl_74,type,
esk9_0: $i ).
tff(decl_75,type,
esk10_0: $i ).
tff(decl_76,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_77,type,
esk12_1: $i > $i ).
tff(decl_78,type,
esk13_1: $i > $i ).
tff(decl_79,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_80,type,
esk15_0: $i ).
tff(decl_81,type,
esk16_1: $i > $i ).
tff(decl_82,type,
esk17_0: $i ).
tff(decl_83,type,
esk18_1: $i > $i ).
tff(decl_84,type,
esk19_0: $i ).
tff(decl_85,type,
esk20_0: $i ).
tff(decl_86,type,
esk21_0: $i ).
tff(decl_87,type,
esk22_1: $i > $i ).
tff(decl_88,type,
esk23_0: $i ).
tff(decl_89,type,
esk24_0: $i ).
tff(decl_90,type,
esk25_0: $i ).
tff(decl_91,type,
esk26_1: $i > $i ).
tff(decl_92,type,
epred1_0: $o ).
tff(decl_93,type,
epred2_0: $o ).
fof(t13_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
<=> r2_hidden(k4_lattices(X1,X3,X4),X2) ) ) )
=> m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_filter_2) ).
fof(d10_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( m2_lattice4(X2,X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
=> ( r2_hidden(k4_lattices(X1,X3,X4),X2)
& r2_hidden(k3_lattices(X1,X3,X4),X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_lattice4) ).
fof(cc1_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(d9_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( v9_lattices(X1)
<=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k2_lattices(X1,X2,k1_lattices(X1,X2,X3)) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattices) ).
fof(redefinition_k3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& l2_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k3_lattices(X1,X2,X3) = k1_lattices(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_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(dt_k1_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& l2_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> m1_subset_1(k1_lattices(X1,X2,X3),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattices) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3)) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(redefinition_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( r2_hidden(X1,X2)
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
<=> r2_hidden(k4_lattices(X1,X3,X4),X2) ) ) )
=> m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t13_filter_2])]) ).
fof(c_0_13,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( m2_lattice4(X2,X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
=> ( r2_hidden(k4_lattices(X1,X3,X4),X2)
& r2_hidden(k3_lattices(X1,X3,X4),X2) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d10_lattice4]) ).
fof(c_0_14,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
fof(c_0_15,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( v9_lattices(X1)
<=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k2_lattices(X1,X2,k1_lattices(X1,X2,X3)) = X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[d9_lattices]) ).
fof(c_0_16,negated_conjecture,
! [X9,X10] :
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& ( ~ r2_hidden(X9,esk2_0)
| ~ r2_hidden(X10,esk2_0)
| r2_hidden(k4_lattices(esk1_0,X9,X10),esk2_0)
| ~ m1_subset_1(X10,u1_struct_0(esk1_0))
| ~ m1_subset_1(X9,u1_struct_0(esk1_0)) )
& ( r2_hidden(X9,esk2_0)
| ~ r2_hidden(k4_lattices(esk1_0,X9,X10),esk2_0)
| ~ m1_subset_1(X10,u1_struct_0(esk1_0))
| ~ m1_subset_1(X9,u1_struct_0(esk1_0)) )
& ( r2_hidden(X10,esk2_0)
| ~ r2_hidden(k4_lattices(esk1_0,X9,X10),esk2_0)
| ~ m1_subset_1(X10,u1_struct_0(esk1_0))
| ~ m1_subset_1(X9,u1_struct_0(esk1_0)) )
& ~ m2_lattice4(esk2_0,esk1_0) ),
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_12])])])])]) ).
fof(c_0_17,plain,
! [X29,X30,X31,X32] :
( ( r2_hidden(k4_lattices(X29,X31,X32),X30)
| ~ r2_hidden(X31,X30)
| ~ r2_hidden(X32,X30)
| ~ m1_subset_1(X32,u1_struct_0(X29))
| ~ m1_subset_1(X31,u1_struct_0(X29))
| ~ m2_lattice4(X30,X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| v3_struct_0(X29)
| ~ v10_lattices(X29)
| ~ l3_lattices(X29) )
& ( r2_hidden(k3_lattices(X29,X31,X32),X30)
| ~ r2_hidden(X31,X30)
| ~ r2_hidden(X32,X30)
| ~ m1_subset_1(X32,u1_struct_0(X29))
| ~ m1_subset_1(X31,u1_struct_0(X29))
| ~ m2_lattice4(X30,X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| v3_struct_0(X29)
| ~ v10_lattices(X29)
| ~ l3_lattices(X29) )
& ( m1_subset_1(esk3_2(X29,X30),u1_struct_0(X29))
| m2_lattice4(X30,X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| v3_struct_0(X29)
| ~ v10_lattices(X29)
| ~ l3_lattices(X29) )
& ( m1_subset_1(esk4_2(X29,X30),u1_struct_0(X29))
| m2_lattice4(X30,X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| v3_struct_0(X29)
| ~ v10_lattices(X29)
| ~ l3_lattices(X29) )
& ( r2_hidden(esk3_2(X29,X30),X30)
| m2_lattice4(X30,X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| v3_struct_0(X29)
| ~ v10_lattices(X29)
| ~ l3_lattices(X29) )
& ( r2_hidden(esk4_2(X29,X30),X30)
| m2_lattice4(X30,X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| v3_struct_0(X29)
| ~ v10_lattices(X29)
| ~ l3_lattices(X29) )
& ( ~ r2_hidden(k4_lattices(X29,esk3_2(X29,X30),esk4_2(X29,X30)),X30)
| ~ r2_hidden(k3_lattices(X29,esk3_2(X29,X30),esk4_2(X29,X30)),X30)
| m2_lattice4(X30,X29)
| ~ m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))
| v3_struct_0(X29)
| ~ v10_lattices(X29)
| ~ l3_lattices(X29) ) ),
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_13])])])])]) ).
fof(c_0_18,plain,
! [X14] :
( ( ~ v3_struct_0(X14)
| v3_struct_0(X14)
| ~ v10_lattices(X14)
| ~ l3_lattices(X14) )
& ( v4_lattices(X14)
| v3_struct_0(X14)
| ~ v10_lattices(X14)
| ~ l3_lattices(X14) )
& ( v5_lattices(X14)
| v3_struct_0(X14)
| ~ v10_lattices(X14)
| ~ l3_lattices(X14) )
& ( v6_lattices(X14)
| v3_struct_0(X14)
| ~ v10_lattices(X14)
| ~ l3_lattices(X14) )
& ( v7_lattices(X14)
| v3_struct_0(X14)
| ~ v10_lattices(X14)
| ~ l3_lattices(X14) )
& ( v8_lattices(X14)
| v3_struct_0(X14)
| ~ v10_lattices(X14)
| ~ l3_lattices(X14) )
& ( v9_lattices(X14)
| v3_struct_0(X14)
| ~ v10_lattices(X14)
| ~ l3_lattices(X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_19,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& l2_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k3_lattices(X1,X2,X3) = k1_lattices(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k3_lattices]) ).
fof(c_0_20,plain,
! [X71] :
( ( l1_lattices(X71)
| ~ l3_lattices(X71) )
& ( l2_lattices(X71)
| ~ l3_lattices(X71) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_21,plain,
! [X46,X47,X48] :
( ( ~ v9_lattices(X46)
| ~ m1_subset_1(X47,u1_struct_0(X46))
| ~ m1_subset_1(X48,u1_struct_0(X46))
| k2_lattices(X46,X47,k1_lattices(X46,X47,X48)) = X47
| v3_struct_0(X46)
| ~ l3_lattices(X46) )
& ( m1_subset_1(esk5_1(X46),u1_struct_0(X46))
| v9_lattices(X46)
| v3_struct_0(X46)
| ~ l3_lattices(X46) )
& ( m1_subset_1(esk6_1(X46),u1_struct_0(X46))
| v9_lattices(X46)
| v3_struct_0(X46)
| ~ l3_lattices(X46) )
& ( k2_lattices(X46,esk5_1(X46),k1_lattices(X46,esk5_1(X46),esk6_1(X46))) != esk5_1(X46)
| v9_lattices(X46)
| v3_struct_0(X46)
| ~ l3_lattices(X46) ) ),
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_15])])])])]) ).
cnf(c_0_22,negated_conjecture,
~ m2_lattice4(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( m1_subset_1(esk4_2(X1,X2),u1_struct_0(X1))
| m2_lattice4(X2,X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,plain,
( v9_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_29,plain,
! [X127,X128,X129] :
( v3_struct_0(X127)
| ~ v4_lattices(X127)
| ~ l2_lattices(X127)
| ~ m1_subset_1(X128,u1_struct_0(X127))
| ~ m1_subset_1(X129,u1_struct_0(X127))
| k3_lattices(X127,X128,X129) = k1_lattices(X127,X128,X129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
cnf(c_0_30,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
( v4_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_32,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& l2_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> m1_subset_1(k1_lattices(X1,X2,X3),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k1_lattices]) ).
fof(c_0_33,plain,
! [X143,X144,X145] :
( ~ r2_hidden(X143,X144)
| ~ m1_subset_1(X144,k1_zfmisc_1(X145))
| m1_subset_1(X143,X145) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_34,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k4_lattices]) ).
cnf(c_0_35,plain,
( k2_lattices(X1,X2,k1_lattices(X1,X2,X3)) = X2
| v3_struct_0(X1)
| ~ v9_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_36,negated_conjecture,
m1_subset_1(esk4_2(esk1_0,esk2_0),u1_struct_0(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_22,c_0_23]),c_0_24]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_37,negated_conjecture,
v9_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_25])]),c_0_27]) ).
cnf(c_0_38,plain,
( m1_subset_1(esk3_2(X1,X2),u1_struct_0(X1))
| m2_lattice4(X2,X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_39,plain,
( v3_struct_0(X1)
| k3_lattices(X1,X2,X3) = k1_lattices(X1,X2,X3)
| ~ v4_lattices(X1)
| ~ l2_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,negated_conjecture,
l2_lattices(esk1_0),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_41,negated_conjecture,
v4_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_25])]),c_0_27]) ).
fof(c_0_42,plain,
! [X51,X52,X53] :
( v3_struct_0(X51)
| ~ l2_lattices(X51)
| ~ m1_subset_1(X52,u1_struct_0(X51))
| ~ m1_subset_1(X53,u1_struct_0(X51))
| m1_subset_1(k1_lattices(X51,X52,X53),u1_struct_0(X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])]) ).
fof(c_0_43,plain,
! [X139,X140] :
( ~ m1_subset_1(X139,X140)
| v1_xboole_0(X140)
| r2_hidden(X139,X140) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_44,plain,
! [X150,X151] :
( ~ r2_hidden(X150,X151)
| ~ v1_xboole_0(X151) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_45,plain,
! [X137,X138] :
( ~ r2_hidden(X137,X138)
| m1_subset_1(X137,X138) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_46,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_33]) ).
fof(c_0_47,plain,
! [X130,X131,X132] :
( v3_struct_0(X130)
| ~ v6_lattices(X130)
| ~ l1_lattices(X130)
| ~ m1_subset_1(X131,u1_struct_0(X130))
| ~ m1_subset_1(X132,u1_struct_0(X130))
| k4_lattices(X130,X131,X132) = k2_lattices(X130,X131,X132) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])]) ).
cnf(c_0_48,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_49,plain,
( v6_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_50,negated_conjecture,
( k2_lattices(esk1_0,X1,k1_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0))) = X1
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_25])]),c_0_27]) ).
cnf(c_0_51,negated_conjecture,
m1_subset_1(esk3_2(esk1_0,esk2_0),u1_struct_0(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_22,c_0_38]),c_0_24]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_52,negated_conjecture,
( k1_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0)) = k3_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0))
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_36]),c_0_40]),c_0_41])]),c_0_27]) ).
cnf(c_0_53,plain,
( v3_struct_0(X1)
| m1_subset_1(k1_lattices(X1,X2,X3),u1_struct_0(X1))
| ~ l2_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,plain,
( m2_lattice4(X2,X1)
| v3_struct_0(X1)
| ~ r2_hidden(k4_lattices(X1,esk3_2(X1,X2),esk4_2(X1,X2)),X2)
| ~ r2_hidden(k3_lattices(X1,esk3_2(X1,X2),esk4_2(X1,X2)),X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_55,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_56,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_58,negated_conjecture,
( r2_hidden(k4_lattices(esk1_0,X1,X2),esk2_0)
| ~ r2_hidden(X1,esk2_0)
| ~ r2_hidden(X2,esk2_0)
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_59,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_24]) ).
cnf(c_0_60,plain,
( r2_hidden(esk4_2(X1,X2),X2)
| m2_lattice4(X2,X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_61,plain,
( r2_hidden(esk3_2(X1,X2),X2)
| m2_lattice4(X2,X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_62,negated_conjecture,
( r2_hidden(X1,esk2_0)
| ~ r2_hidden(k4_lattices(esk1_0,X2,X1),esk2_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_63,plain,
( v3_struct_0(X1)
| k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3)
| ~ v6_lattices(X1)
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_64,negated_conjecture,
l1_lattices(esk1_0),
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
cnf(c_0_65,negated_conjecture,
v6_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_26]),c_0_25])]),c_0_27]) ).
cnf(c_0_66,negated_conjecture,
k2_lattices(esk1_0,esk3_2(esk1_0,esk2_0),k1_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0))) = esk3_2(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_67,negated_conjecture,
k1_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0)) = k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_68,negated_conjecture,
( m1_subset_1(k1_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0)),u1_struct_0(esk1_0))
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_36]),c_0_40])]),c_0_27]) ).
cnf(c_0_69,plain,
( m2_lattice4(X1,X2)
| v3_struct_0(X2)
| ~ r2_hidden(k3_lattices(X2,esk3_2(X2,X1),esk4_2(X2,X1)),X1)
| ~ m1_subset_1(k4_lattices(X2,esk3_2(X2,X1),esk4_2(X2,X1)),X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_70,negated_conjecture,
( m1_subset_1(k4_lattices(esk1_0,X1,X2),esk2_0)
| ~ r2_hidden(X2,esk2_0)
| ~ r2_hidden(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_59]) ).
cnf(c_0_71,negated_conjecture,
r2_hidden(esk4_2(esk1_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_60]),c_0_24]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_72,negated_conjecture,
r2_hidden(esk3_2(esk1_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_61]),c_0_24]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_73,negated_conjecture,
( r2_hidden(X1,esk2_0)
| ~ r2_hidden(k2_lattices(esk1_0,X2,X1),esk2_0)
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_27]),c_0_64]),c_0_65])]) ).
cnf(c_0_74,negated_conjecture,
k2_lattices(esk1_0,esk3_2(esk1_0,esk2_0),k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0))) = esk3_2(esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,negated_conjecture,
m1_subset_1(k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0)),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_67]),c_0_51])]) ).
cnf(c_0_76,negated_conjecture,
~ r2_hidden(k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0)),esk2_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_24]),c_0_25]),c_0_26]),c_0_71]),c_0_72])]),c_0_22]),c_0_27]) ).
cnf(c_0_77,negated_conjecture,
$false,
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_73,c_0_74]),c_0_72]),c_0_51]),c_0_75])]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT297+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n007.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 05:59:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.99/1.07 % Version : CSE_E---1.5
% 0.99/1.07 % Problem : theBenchmark.p
% 0.99/1.07 % Proof found
% 0.99/1.07 % SZS status Theorem for theBenchmark.p
% 0.99/1.07 % SZS output start Proof
% See solution above
% 0.99/1.09 % Total time : 0.481000 s
% 0.99/1.09 % SZS output end Proof
% 0.99/1.09 % Total time : 0.486000 s
%------------------------------------------------------------------------------