TSTP Solution File: LAT291+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT291+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 : n012.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 06:00:40 EDT 2023
% Result : Theorem 0.20s 0.78s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 89
% Syntax : Number of formulae : 118 ( 13 unt; 82 typ; 0 def)
% Number of atoms : 126 ( 21 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 142 ( 52 ~; 38 |; 39 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 96 ( 70 >; 26 *; 0 +; 0 <<)
% Number of predicates : 50 ( 48 usr; 3 prp; 0-3 aty)
% Number of functors : 34 ( 34 usr; 10 con; 0-4 aty)
% Number of variables : 28 ( 0 sgn; 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v3_struct_0: $i > $o ).
tff(decl_23,type,
v10_lattices: $i > $o ).
tff(decl_24,type,
v17_lattices: $i > $o ).
tff(decl_25,type,
v3_realset2: $i > $o ).
tff(decl_26,type,
l3_lattices: $i > $o ).
tff(decl_27,type,
u1_struct_0: $i > $i ).
tff(decl_28,type,
k7_lopclset: $i > $i ).
tff(decl_29,type,
k1_zfmisc_1: $i > $i ).
tff(decl_30,type,
k9_lopclset: $i > $i ).
tff(decl_31,type,
k6_lattices: $i > $i ).
tff(decl_32,type,
k8_funct_2: ( $i * $i * $i * $i ) > $i ).
tff(decl_33,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_34,type,
v1_membered: $i > $o ).
tff(decl_35,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_36,type,
v1_xcmplx_0: $i > $o ).
tff(decl_37,type,
v2_membered: $i > $o ).
tff(decl_38,type,
v1_xreal_0: $i > $o ).
tff(decl_39,type,
v3_membered: $i > $o ).
tff(decl_40,type,
v1_rat_1: $i > $o ).
tff(decl_41,type,
v4_membered: $i > $o ).
tff(decl_42,type,
v1_int_1: $i > $o ).
tff(decl_43,type,
v5_membered: $i > $o ).
tff(decl_44,type,
v4_ordinal2: $i > $o ).
tff(decl_45,type,
v1_xboole_0: $i > $o ).
tff(decl_46,type,
v1_finset_1: $i > $o ).
tff(decl_47,type,
v4_finsub_1: $i > $o ).
tff(decl_48,type,
v1_finsub_1: $i > $o ).
tff(decl_49,type,
v3_finsub_1: $i > $o ).
tff(decl_50,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_51,type,
v1_funct_1: $i > $o ).
tff(decl_52,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_53,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(decl_54,type,
v4_lattices: $i > $o ).
tff(decl_55,type,
v5_lattices: $i > $o ).
tff(decl_56,type,
v6_lattices: $i > $o ).
tff(decl_57,type,
v7_lattices: $i > $o ).
tff(decl_58,type,
v8_lattices: $i > $o ).
tff(decl_59,type,
v9_lattices: $i > $o ).
tff(decl_60,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(decl_61,type,
v1_relat_1: $i > $o ).
tff(decl_62,type,
v13_lattices: $i > $o ).
tff(decl_63,type,
v14_lattices: $i > $o ).
tff(decl_64,type,
v15_lattices: $i > $o ).
tff(decl_65,type,
v11_lattices: $i > $o ).
tff(decl_66,type,
v16_lattices: $i > $o ).
tff(decl_67,type,
v12_lattices: $i > $o ).
tff(decl_68,type,
a_1_1_lopclset: $i > $i ).
tff(decl_69,type,
l1_lattices: $i > $o ).
tff(decl_70,type,
k5_lattices: $i > $i ).
tff(decl_71,type,
l2_lattices: $i > $o ).
tff(decl_72,type,
k7_lattices: ( $i * $i ) > $i ).
tff(decl_73,type,
k8_lopclset: $i > $i ).
tff(decl_74,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff(decl_75,type,
l1_struct_0: $i > $o ).
tff(decl_76,type,
m1_filter_0: ( $i * $i ) > $o ).
tff(decl_77,type,
k4_xboole_0: ( $i * $i ) > $i ).
tff(decl_78,type,
k1_xboole_0: $i ).
tff(decl_79,type,
v1_filter_0: ( $i * $i ) > $o ).
tff(decl_80,type,
k1_funct_1: ( $i * $i ) > $i ).
tff(decl_81,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_82,type,
esk1_0: $i ).
tff(decl_83,type,
esk2_0: $i ).
tff(decl_84,type,
esk3_0: $i ).
tff(decl_85,type,
esk4_0: $i ).
tff(decl_86,type,
esk5_0: $i ).
tff(decl_87,type,
esk6_1: $i > $i ).
tff(decl_88,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_89,type,
esk8_1: $i > $i ).
tff(decl_90,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_91,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_92,type,
esk11_0: $i ).
tff(decl_93,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_94,type,
esk13_0: $i ).
tff(decl_95,type,
esk14_0: $i ).
tff(decl_96,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_97,type,
esk16_1: $i > $i ).
tff(decl_98,type,
esk17_0: $i ).
tff(decl_99,type,
esk18_1: $i > $i ).
tff(decl_100,type,
esk19_1: $i > $i ).
tff(decl_101,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_102,type,
epred1_0: $o ).
tff(decl_103,type,
epred2_0: $o ).
fof(t37_lopclset,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k6_lattices(X1)) = k7_lopclset(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lopclset) ).
fof(t37_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
=> k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lattice4) ).
fof(t28_lopclset,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lopclset) ).
fof(t36_lopclset,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_lopclset) ).
fof(t3_boole,axiom,
! [X1] : k4_xboole_0(X1,k1_xboole_0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(dt_k5_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_lattices(X1) )
=> m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_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(c_0_7,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k6_lattices(X1)) = k7_lopclset(X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t37_lopclset])]) ).
fof(c_0_8,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
=> k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1) ),
inference(fof_simplification,[status(thm)],[t37_lattice4]) ).
fof(c_0_9,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& v17_lattices(esk1_0)
& ~ v3_realset2(esk1_0)
& l3_lattices(esk1_0)
& k8_funct_2(u1_struct_0(esk1_0),k1_zfmisc_1(k7_lopclset(esk1_0)),k9_lopclset(esk1_0),k6_lattices(esk1_0)) != k7_lopclset(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X147] :
( v3_struct_0(X147)
| ~ v10_lattices(X147)
| ~ v17_lattices(X147)
| ~ l3_lattices(X147)
| k7_lattices(X147,k5_lattices(X147)) = k6_lattices(X147) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[t28_lopclset]) ).
cnf(c_0_12,negated_conjecture,
k8_funct_2(u1_struct_0(esk1_0),k1_zfmisc_1(k7_lopclset(esk1_0)),k9_lopclset(esk1_0),k6_lattices(esk1_0)) != k7_lopclset(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( v3_struct_0(X1)
| k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1)
| ~ v10_lattices(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
v17_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_18,plain,
! [X139,X140] :
( v3_struct_0(X139)
| ~ v10_lattices(X139)
| ~ v17_lattices(X139)
| v3_realset2(X139)
| ~ l3_lattices(X139)
| ~ m1_subset_1(X140,u1_struct_0(X139))
| k4_xboole_0(k7_lopclset(X139),k8_funct_2(u1_struct_0(X139),k1_zfmisc_1(k7_lopclset(X139)),k9_lopclset(X139),X140)) = k8_funct_2(u1_struct_0(X139),k1_zfmisc_1(k7_lopclset(X139)),k9_lopclset(X139),k7_lattices(X139,X140)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_19,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0 ),
inference(fof_simplification,[status(thm)],[t36_lopclset]) ).
cnf(c_0_20,negated_conjecture,
k8_funct_2(u1_struct_0(esk1_0),k1_zfmisc_1(k7_lopclset(esk1_0)),k9_lopclset(esk1_0),k7_lattices(esk1_0,k5_lattices(esk1_0))) != k7_lopclset(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_12,c_0_13]),c_0_14]),c_0_15]),c_0_16])]),c_0_17]) ).
cnf(c_0_21,plain,
( v3_struct_0(X1)
| v3_realset2(X1)
| k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2))
| ~ v10_lattices(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
~ v3_realset2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_23,plain,
! [X146] :
( v3_struct_0(X146)
| ~ v10_lattices(X146)
| ~ v17_lattices(X146)
| v3_realset2(X146)
| ~ l3_lattices(X146)
| k8_funct_2(u1_struct_0(X146),k1_zfmisc_1(k7_lopclset(X146)),k9_lopclset(X146),k5_lattices(X146)) = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
fof(c_0_24,plain,
! [X148] : k4_xboole_0(X148,k1_xboole_0) = X148,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(c_0_25,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_lattices(X1) )
=> m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattices]) ).
fof(c_0_26,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])])]) ).
cnf(c_0_27,negated_conjecture,
( k4_xboole_0(k7_lopclset(esk1_0),k8_funct_2(u1_struct_0(esk1_0),k1_zfmisc_1(k7_lopclset(esk1_0)),k9_lopclset(esk1_0),k5_lattices(esk1_0))) != k7_lopclset(esk1_0)
| ~ m1_subset_1(k5_lattices(esk1_0),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14]),c_0_15]),c_0_16])]),c_0_22]),c_0_17]) ).
cnf(c_0_28,plain,
( v3_struct_0(X1)
| v3_realset2(X1)
| k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0
| ~ v10_lattices(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
k4_xboole_0(X1,k1_xboole_0) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X58] :
( v3_struct_0(X58)
| ~ l1_lattices(X58)
| m1_subset_1(k5_lattices(X58),u1_struct_0(X58)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
cnf(c_0_31,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
~ m1_subset_1(k5_lattices(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_14]),c_0_15]),c_0_16])]),c_0_22]),c_0_17]) ).
cnf(c_0_33,plain,
( v3_struct_0(X1)
| m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
l1_lattices(esk1_0),
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT291+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 : n012.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 09:38:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.78 % Version : CSE_E---1.5
% 0.20/0.78 % Problem : theBenchmark.p
% 0.20/0.78 % Proof found
% 0.20/0.78 % SZS status Theorem for theBenchmark.p
% 0.20/0.78 % SZS output start Proof
% See solution above
% 0.59/0.78 % Total time : 0.183000 s
% 0.59/0.78 % SZS output end Proof
% 0.59/0.78 % Total time : 0.188000 s
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