TSTP Solution File: LAT305+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT305+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 06:01:02 EDT 2023
% Result : Theorem 3.31s 3.43s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 83
% Syntax : Number of formulae : 151 ( 17 unt; 72 typ; 0 def)
% Number of atoms : 412 ( 18 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 531 ( 198 ~; 199 |; 99 &)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 97 ( 56 >; 41 *; 0 +; 0 <<)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 16 con; 0-6 aty)
% Number of variables : 122 ( 1 sgn; 74 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v3_struct_0: $i > $o ).
tff(decl_23,type,
v10_lattices: $i > $o ).
tff(decl_24,type,
l3_lattices: $i > $o ).
tff(decl_25,type,
u1_struct_0: $i > $i ).
tff(decl_26,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_27,type,
k18_filter_2: ( $i * $i ) > $i ).
tff(decl_28,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_29,type,
k4_lattices: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
v1_xboole_0: $i > $o ).
tff(decl_31,type,
v1_funct_1: $i > $o ).
tff(decl_32,type,
v4_lattices: $i > $o ).
tff(decl_33,type,
v5_lattices: $i > $o ).
tff(decl_34,type,
v6_lattices: $i > $o ).
tff(decl_35,type,
v7_lattices: $i > $o ).
tff(decl_36,type,
v8_lattices: $i > $o ).
tff(decl_37,type,
v9_lattices: $i > $o ).
tff(decl_38,type,
v1_realset1: $i > $o ).
tff(decl_39,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(decl_40,type,
k1_zfmisc_1: $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,
l1_lattices: $i > $o ).
tff(decl_45,type,
k1_binop_1: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
k4_tarski: ( $i * $i ) > $i ).
tff(decl_47,type,
k1_funct_1: ( $i * $i ) > $i ).
tff(decl_48,type,
k2_lattices: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
u1_lattices: $i > $i ).
tff(decl_50,type,
k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_51,type,
k1_tarski: $i > $i ).
tff(decl_52,type,
a_2_0_filter_2: ( $i * $i ) > $i ).
tff(decl_53,type,
m2_filter_2: ( $i * $i ) > $o ).
tff(decl_54,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_55,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_56,type,
l1_struct_0: $i > $o ).
tff(decl_57,type,
l2_lattices: $i > $o ).
tff(decl_58,type,
m2_lattice4: ( $i * $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_finset_1: $i > $o ).
tff(decl_62,type,
v1_binop_1: ( $i * $i ) > $o ).
tff(decl_63,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_64,type,
v2_binop_1: ( $i * $i ) > $o ).
tff(decl_65,type,
r3_lattices: ( $i * $i * $i ) > $o ).
tff(decl_66,type,
r1_lattices: ( $i * $i * $i ) > $o ).
tff(decl_67,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_68,type,
esk1_0: $i ).
tff(decl_69,type,
esk2_0: $i ).
tff(decl_70,type,
esk3_0: $i ).
tff(decl_71,type,
esk4_0: $i ).
tff(decl_72,type,
esk5_0: $i ).
tff(decl_73,type,
esk6_0: $i ).
tff(decl_74,type,
esk7_0: $i ).
tff(decl_75,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_76,type,
esk9_1: $i > $i ).
tff(decl_77,type,
esk10_1: $i > $i ).
tff(decl_78,type,
esk11_1: $i > $i ).
tff(decl_79,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_80,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
esk14_0: $i ).
tff(decl_82,type,
esk15_1: $i > $i ).
tff(decl_83,type,
esk16_0: $i ).
tff(decl_84,type,
esk17_1: $i > $i ).
tff(decl_85,type,
esk18_0: $i ).
tff(decl_86,type,
esk19_0: $i ).
tff(decl_87,type,
esk20_0: $i ).
tff(decl_88,type,
esk21_1: $i > $i ).
tff(decl_89,type,
esk22_0: $i ).
tff(decl_90,type,
esk23_0: $i ).
tff(decl_91,type,
esk24_0: $i ).
tff(decl_92,type,
esk25_1: $i > $i ).
tff(decl_93,type,
esk26_2: ( $i * $i ) > $i ).
fof(reflexivity_r3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> r3_lattices(X1,X2,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
fof(commutativity_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) = k4_lattices(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(t31_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X2,k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_2) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(redefinition_r3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> ( r3_lattices(X1,X2,X3)
<=> r1_lattices(X1,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(t23_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> r1_lattices(X1,k4_lattices(X1,X2,X3),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).
fof(dt_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)) )
=> m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).
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/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
fof(d9_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(fraenkel_a_2_0_filter_2,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2)
& m1_subset_1(X3,u1_struct_0(X2)) )
=> ( r2_hidden(X1,a_2_0_filter_2(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,u1_struct_0(X2))
& X1 = X4
& r3_lattices(X2,X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_2) ).
fof(c_0_11,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> r3_lattices(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[reflexivity_r3_lattices]) ).
fof(c_0_12,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) = k4_lattices(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k4_lattices]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X2,k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t31_filter_2])]) ).
fof(c_0_14,plain,
! [X123,X124,X125] :
( v3_struct_0(X123)
| ~ v6_lattices(X123)
| ~ v8_lattices(X123)
| ~ v9_lattices(X123)
| ~ l3_lattices(X123)
| ~ m1_subset_1(X124,u1_struct_0(X123))
| ~ m1_subset_1(X125,u1_struct_0(X123))
| r3_lattices(X123,X124,X124) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_15,plain,
! [X67] : m1_subset_1(esk9_1(X67),X67),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_16,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> ( r3_lattices(X1,X2,X3)
<=> r1_lattices(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_lattices]) ).
fof(c_0_17,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> r1_lattices(X1,k4_lattices(X1,X2,X3),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t23_lattices]) ).
fof(c_0_18,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)) )
=> m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k4_lattices]) ).
fof(c_0_19,plain,
! [X22,X23,X24] :
( v3_struct_0(X22)
| ~ v6_lattices(X22)
| ~ l1_lattices(X22)
| ~ m1_subset_1(X23,u1_struct_0(X22))
| ~ m1_subset_1(X24,u1_struct_0(X22))
| k4_lattices(X22,X23,X24) = k4_lattices(X22,X24,X23) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_20,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& m1_subset_1(esk3_0,u1_struct_0(esk1_0))
& ( ~ r2_hidden(esk2_0,k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_21,plain,
( v3_struct_0(X1)
| r3_lattices(X1,X2,X2)
| ~ v6_lattices(X1)
| ~ v8_lattices(X1)
| ~ v9_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
m1_subset_1(esk9_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,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_24,plain,
! [X119,X120,X121] :
( ( ~ r3_lattices(X119,X120,X121)
| r1_lattices(X119,X120,X121)
| v3_struct_0(X119)
| ~ v6_lattices(X119)
| ~ v8_lattices(X119)
| ~ v9_lattices(X119)
| ~ l3_lattices(X119)
| ~ m1_subset_1(X120,u1_struct_0(X119))
| ~ m1_subset_1(X121,u1_struct_0(X119)) )
& ( ~ r1_lattices(X119,X120,X121)
| r3_lattices(X119,X120,X121)
| v3_struct_0(X119)
| ~ v6_lattices(X119)
| ~ v8_lattices(X119)
| ~ v9_lattices(X119)
| ~ l3_lattices(X119)
| ~ m1_subset_1(X120,u1_struct_0(X119))
| ~ m1_subset_1(X121,u1_struct_0(X119)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_25,plain,
! [X128,X129,X130] :
( v3_struct_0(X128)
| ~ v6_lattices(X128)
| ~ v8_lattices(X128)
| ~ l3_lattices(X128)
| ~ m1_subset_1(X129,u1_struct_0(X128))
| ~ m1_subset_1(X130,u1_struct_0(X128))
| r1_lattices(X128,k4_lattices(X128,X129,X130),X129) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_26,plain,
! [X46,X47,X48] :
( v3_struct_0(X46)
| ~ v6_lattices(X46)
| ~ l1_lattices(X46)
| ~ m1_subset_1(X47,u1_struct_0(X46))
| ~ m1_subset_1(X48,u1_struct_0(X46))
| m1_subset_1(k4_lattices(X46,X47,X48),u1_struct_0(X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
fof(c_0_27,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d9_filter_2]) ).
cnf(c_0_28,plain,
( v3_struct_0(X1)
| k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2)
| ~ 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_19]) ).
cnf(c_0_29,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_31,plain,
! [X51] :
( ( l1_lattices(X51)
| ~ l3_lattices(X51) )
& ( l2_lattices(X51)
| ~ l3_lattices(X51) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_32,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2)
& m1_subset_1(X3,u1_struct_0(X2)) )
=> ( r2_hidden(X1,a_2_0_filter_2(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,u1_struct_0(X2))
& X1 = X4
& r3_lattices(X2,X4,X3) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_filter_2]) ).
cnf(c_0_33,plain,
( r3_lattices(X1,X2,X2)
| v3_struct_0(X1)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ v6_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_35,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_36,plain,
! [X13] :
( ( ~ v3_struct_0(X13)
| v3_struct_0(X13)
| ~ v10_lattices(X13)
| ~ l3_lattices(X13) )
& ( v4_lattices(X13)
| v3_struct_0(X13)
| ~ v10_lattices(X13)
| ~ l3_lattices(X13) )
& ( v5_lattices(X13)
| v3_struct_0(X13)
| ~ v10_lattices(X13)
| ~ l3_lattices(X13) )
& ( v6_lattices(X13)
| v3_struct_0(X13)
| ~ v10_lattices(X13)
| ~ l3_lattices(X13) )
& ( v7_lattices(X13)
| v3_struct_0(X13)
| ~ v10_lattices(X13)
| ~ l3_lattices(X13) )
& ( v8_lattices(X13)
| v3_struct_0(X13)
| ~ v10_lattices(X13)
| ~ l3_lattices(X13) )
& ( v9_lattices(X13)
| v3_struct_0(X13)
| ~ v10_lattices(X13)
| ~ l3_lattices(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
cnf(c_0_37,plain,
( r3_lattices(X1,X2,X3)
| v3_struct_0(X1)
| ~ r1_lattices(X1,X2,X3)
| ~ v6_lattices(X1)
| ~ v8_lattices(X1)
| ~ v9_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_38,plain,
( v3_struct_0(X1)
| r1_lattices(X1,k4_lattices(X1,X2,X3),X2)
| ~ v6_lattices(X1)
| ~ v8_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_39,plain,
( v3_struct_0(X1)
| m1_subset_1(k4_lattices(X1,X2,X3),u1_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)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_40,plain,
! [X33,X34] :
( v3_struct_0(X33)
| ~ v10_lattices(X33)
| ~ l3_lattices(X33)
| ~ m1_subset_1(X34,u1_struct_0(X33))
| k18_filter_2(X33,X34) = a_2_0_filter_2(X33,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_41,negated_conjecture,
( k4_lattices(esk1_0,X1,esk3_0) = k4_lattices(esk1_0,esk3_0,X1)
| ~ l1_lattices(esk1_0)
| ~ v6_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_42,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_43,plain,
! [X86,X87,X88,X90] :
( ( m1_subset_1(esk13_3(X86,X87,X88),u1_struct_0(X87))
| ~ r2_hidden(X86,a_2_0_filter_2(X87,X88))
| v3_struct_0(X87)
| ~ v10_lattices(X87)
| ~ l3_lattices(X87)
| ~ m1_subset_1(X88,u1_struct_0(X87)) )
& ( X86 = esk13_3(X86,X87,X88)
| ~ r2_hidden(X86,a_2_0_filter_2(X87,X88))
| v3_struct_0(X87)
| ~ v10_lattices(X87)
| ~ l3_lattices(X87)
| ~ m1_subset_1(X88,u1_struct_0(X87)) )
& ( r3_lattices(X87,esk13_3(X86,X87,X88),X88)
| ~ r2_hidden(X86,a_2_0_filter_2(X87,X88))
| v3_struct_0(X87)
| ~ v10_lattices(X87)
| ~ l3_lattices(X87)
| ~ m1_subset_1(X88,u1_struct_0(X87)) )
& ( ~ m1_subset_1(X90,u1_struct_0(X87))
| X86 != X90
| ~ r3_lattices(X87,X90,X88)
| r2_hidden(X86,a_2_0_filter_2(X87,X88))
| v3_struct_0(X87)
| ~ v10_lattices(X87)
| ~ l3_lattices(X87)
| ~ m1_subset_1(X88,u1_struct_0(X87)) ) ),
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_32])])])])]) ).
cnf(c_0_44,negated_conjecture,
( r3_lattices(esk1_0,esk2_0,esk2_0)
| ~ v9_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v6_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),c_0_30]) ).
cnf(c_0_45,plain,
( v9_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_47,negated_conjecture,
( r3_lattices(esk1_0,X1,esk2_0)
| ~ r1_lattices(esk1_0,X1,esk2_0)
| ~ v9_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v6_lattices(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_37,c_0_34]),c_0_35])]),c_0_30]) ).
cnf(c_0_48,negated_conjecture,
( r1_lattices(esk1_0,k4_lattices(esk1_0,X1,esk3_0),X1)
| ~ v8_lattices(esk1_0)
| ~ v6_lattices(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_38,c_0_29]),c_0_35])]),c_0_30]) ).
cnf(c_0_49,plain,
( v8_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_50,negated_conjecture,
( m1_subset_1(k4_lattices(esk1_0,X1,esk3_0),u1_struct_0(esk1_0))
| ~ l1_lattices(esk1_0)
| ~ v6_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_29]),c_0_30]) ).
cnf(c_0_51,plain,
( v3_struct_0(X1)
| k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_52,negated_conjecture,
( k4_lattices(esk1_0,X1,esk3_0) = k4_lattices(esk1_0,esk3_0,X1)
| ~ v6_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_35])]) ).
cnf(c_0_53,plain,
( v6_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_54,plain,
( r2_hidden(X3,a_2_0_filter_2(X2,X4))
| v3_struct_0(X2)
| ~ m1_subset_1(X1,u1_struct_0(X2))
| X3 != X1
| ~ r3_lattices(X2,X1,X4)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| ~ m1_subset_1(X4,u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,negated_conjecture,
( r3_lattices(esk1_0,esk2_0,esk2_0)
| ~ v8_lattices(esk1_0)
| ~ v6_lattices(esk1_0) ),
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_45]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_56,negated_conjecture,
( r3_lattices(esk1_0,X1,esk2_0)
| ~ r1_lattices(esk1_0,X1,esk2_0)
| ~ v8_lattices(esk1_0)
| ~ v6_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_45]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_57,negated_conjecture,
( r1_lattices(esk1_0,k4_lattices(esk1_0,X1,esk3_0),X1)
| ~ v6_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_58,negated_conjecture,
( m1_subset_1(k4_lattices(esk1_0,X1,esk3_0),u1_struct_0(esk1_0))
| ~ v6_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_42]),c_0_35])]) ).
cnf(c_0_59,negated_conjecture,
( ~ r2_hidden(esk2_0,k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_60,negated_conjecture,
k18_filter_2(esk1_0,esk2_0) = a_2_0_filter_2(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_34]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_61,negated_conjecture,
( k4_lattices(esk1_0,X1,esk3_0) = k4_lattices(esk1_0,esk3_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_52,c_0_53]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_62,plain,
( r2_hidden(X1,a_2_0_filter_2(X2,X3))
| v3_struct_0(X2)
| ~ r3_lattices(X2,X1,X3)
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_63,negated_conjecture,
( r3_lattices(esk1_0,esk2_0,esk2_0)
| ~ v6_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_49]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_64,negated_conjecture,
( r3_lattices(esk1_0,X1,esk2_0)
| ~ r1_lattices(esk1_0,X1,esk2_0)
| ~ v6_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_65,negated_conjecture,
( r1_lattices(esk1_0,k4_lattices(esk1_0,X1,esk3_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_57,c_0_53]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_66,negated_conjecture,
( m1_subset_1(k4_lattices(esk1_0,X1,esk3_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_53]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_67,negated_conjecture,
( ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),a_2_0_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),a_2_0_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_60]),c_0_60]) ).
cnf(c_0_68,negated_conjecture,
k4_lattices(esk1_0,esk3_0,esk2_0) = k4_lattices(esk1_0,esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_61,c_0_34]) ).
cnf(c_0_69,negated_conjecture,
( r2_hidden(X1,a_2_0_filter_2(esk1_0,esk2_0))
| ~ r3_lattices(esk1_0,X1,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_62,c_0_34]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_70,negated_conjecture,
r3_lattices(esk1_0,esk2_0,esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_53]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_71,negated_conjecture,
( r3_lattices(esk1_0,X1,esk2_0)
| ~ r1_lattices(esk1_0,X1,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_64,c_0_53]),c_0_35]),c_0_46])]),c_0_30]) ).
cnf(c_0_72,negated_conjecture,
r1_lattices(esk1_0,k4_lattices(esk1_0,esk2_0,esk3_0),esk2_0),
inference(spm,[status(thm)],[c_0_65,c_0_34]) ).
cnf(c_0_73,negated_conjecture,
m1_subset_1(k4_lattices(esk1_0,esk2_0,esk3_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_66,c_0_34]) ).
cnf(c_0_74,negated_conjecture,
( ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),a_2_0_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_75,negated_conjecture,
r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_34])]) ).
cnf(c_0_76,negated_conjecture,
r3_lattices(esk1_0,k4_lattices(esk1_0,esk2_0,esk3_0),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_77,negated_conjecture,
~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),a_2_0_filter_2(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_76]),c_0_73])]),c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT305+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n011.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 07:12:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 3.31/3.43 % Version : CSE_E---1.5
% 3.31/3.43 % Problem : theBenchmark.p
% 3.31/3.43 % Proof found
% 3.31/3.43 % SZS status Theorem for theBenchmark.p
% 3.31/3.43 % SZS output start Proof
% See solution above
% 3.31/3.44 % Total time : 2.837000 s
% 3.31/3.44 % SZS output end Proof
% 3.31/3.44 % Total time : 2.842000 s
%------------------------------------------------------------------------------