TSTP Solution File: SEU250+2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU250+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n008.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 16:23:48 EDT 2023
% Result : Theorem 1.29s 1.39s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 187
% Syntax : Number of formulae : 203 ( 3 unt; 184 typ; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 57 ( 22 ~; 22 |; 7 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 333 ( 169 >; 164 *; 0 +; 0 <<)
% Number of predicates : 29 ( 28 usr; 1 prp; 0-2 aty)
% Number of functors : 156 ( 156 usr; 15 con; 0-5 aty)
% Number of variables : 38 ( 2 sgn; 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
empty: $i > $o ).
tff(decl_25,type,
function: $i > $o ).
tff(decl_26,type,
ordinal: $i > $o ).
tff(decl_27,type,
epsilon_transitive: $i > $o ).
tff(decl_28,type,
epsilon_connected: $i > $o ).
tff(decl_29,type,
relation: $i > $o ).
tff(decl_30,type,
one_to_one: $i > $o ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_33,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_34,type,
ordinal_subset: ( $i * $i ) > $o ).
tff(decl_35,type,
identity_relation: $i > $i ).
tff(decl_36,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_37,type,
subset: ( $i * $i ) > $o ).
tff(decl_38,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff(decl_39,type,
relation_image: ( $i * $i ) > $i ).
tff(decl_40,type,
relation_dom: $i > $i ).
tff(decl_41,type,
apply: ( $i * $i ) > $i ).
tff(decl_42,type,
relation_rng_restriction: ( $i * $i ) > $i ).
tff(decl_43,type,
antisymmetric: $i > $o ).
tff(decl_44,type,
relation_field: $i > $i ).
tff(decl_45,type,
is_antisymmetric_in: ( $i * $i ) > $o ).
tff(decl_46,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_47,type,
connected: $i > $o ).
tff(decl_48,type,
is_connected_in: ( $i * $i ) > $o ).
tff(decl_49,type,
transitive: $i > $o ).
tff(decl_50,type,
is_transitive_in: ( $i * $i ) > $o ).
tff(decl_51,type,
unordered_triple: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
succ: $i > $i ).
tff(decl_53,type,
singleton: $i > $i ).
tff(decl_54,type,
is_reflexive_in: ( $i * $i ) > $o ).
tff(decl_55,type,
empty_set: $i ).
tff(decl_56,type,
set_meet: $i > $i ).
tff(decl_57,type,
powerset: $i > $i ).
tff(decl_58,type,
element: ( $i * $i ) > $o ).
tff(decl_59,type,
well_founded_relation: $i > $o ).
tff(decl_60,type,
fiber: ( $i * $i ) > $i ).
tff(decl_61,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_62,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_63,type,
is_well_founded_in: ( $i * $i ) > $o ).
tff(decl_64,type,
cast_to_subset: $i > $i ).
tff(decl_65,type,
union: $i > $i ).
tff(decl_66,type,
well_ordering: $i > $o ).
tff(decl_67,type,
reflexive: $i > $o ).
tff(decl_68,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_69,type,
relation_rng: $i > $i ).
tff(decl_70,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_71,type,
well_orders: ( $i * $i ) > $o ).
tff(decl_72,type,
being_limit_ordinal: $i > $o ).
tff(decl_73,type,
relation_restriction: ( $i * $i ) > $i ).
tff(decl_74,type,
relation_inverse: $i > $i ).
tff(decl_75,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_76,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_77,type,
function_inverse: $i > $i ).
tff(decl_78,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_79,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_80,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
relation_empty_yielding: $i > $o ).
tff(decl_82,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_83,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_84,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_85,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
esk5_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_92,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_93,type,
esk11_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_95,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_97,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_99,type,
esk17_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_100,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_101,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_102,type,
esk20_1: $i > $i ).
tff(decl_103,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_104,type,
esk22_3: ( $i * $i * $i ) > $i ).
tff(decl_105,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_106,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_107,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_108,type,
esk26_1: $i > $i ).
tff(decl_109,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_110,type,
esk28_1: $i > $i ).
tff(decl_111,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_112,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_113,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_114,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_115,type,
esk33_1: $i > $i ).
tff(decl_116,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_117,type,
esk35_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_118,type,
esk36_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
esk37_3: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
esk38_3: ( $i * $i * $i ) > $i ).
tff(decl_121,type,
esk39_3: ( $i * $i * $i ) > $i ).
tff(decl_122,type,
esk40_1: $i > $i ).
tff(decl_123,type,
esk41_1: $i > $i ).
tff(decl_124,type,
esk42_2: ( $i * $i ) > $i ).
tff(decl_125,type,
esk43_2: ( $i * $i ) > $i ).
tff(decl_126,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_127,type,
esk45_3: ( $i * $i * $i ) > $i ).
tff(decl_128,type,
esk46_2: ( $i * $i ) > $i ).
tff(decl_129,type,
esk47_3: ( $i * $i * $i ) > $i ).
tff(decl_130,type,
esk48_3: ( $i * $i * $i ) > $i ).
tff(decl_131,type,
esk49_2: ( $i * $i ) > $i ).
tff(decl_132,type,
esk50_2: ( $i * $i ) > $i ).
tff(decl_133,type,
esk51_2: ( $i * $i ) > $i ).
tff(decl_134,type,
esk52_2: ( $i * $i ) > $i ).
tff(decl_135,type,
esk53_3: ( $i * $i * $i ) > $i ).
tff(decl_136,type,
esk54_2: ( $i * $i ) > $i ).
tff(decl_137,type,
esk55_2: ( $i * $i ) > $i ).
tff(decl_138,type,
esk56_3: ( $i * $i * $i ) > $i ).
tff(decl_139,type,
esk57_3: ( $i * $i * $i ) > $i ).
tff(decl_140,type,
esk58_2: ( $i * $i ) > $i ).
tff(decl_141,type,
esk59_2: ( $i * $i ) > $i ).
tff(decl_142,type,
esk60_3: ( $i * $i * $i ) > $i ).
tff(decl_143,type,
esk61_2: ( $i * $i ) > $i ).
tff(decl_144,type,
esk62_2: ( $i * $i ) > $i ).
tff(decl_145,type,
esk63_2: ( $i * $i ) > $i ).
tff(decl_146,type,
esk64_2: ( $i * $i ) > $i ).
tff(decl_147,type,
esk65_2: ( $i * $i ) > $i ).
tff(decl_148,type,
esk66_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk67_1: $i > $i ).
tff(decl_150,type,
esk68_1: $i > $i ).
tff(decl_151,type,
esk69_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_152,type,
esk70_3: ( $i * $i * $i ) > $i ).
tff(decl_153,type,
esk71_3: ( $i * $i * $i ) > $i ).
tff(decl_154,type,
esk72_3: ( $i * $i * $i ) > $i ).
tff(decl_155,type,
esk73_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk74_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk75_2: ( $i * $i ) > $i ).
tff(decl_158,type,
esk76_3: ( $i * $i * $i ) > $i ).
tff(decl_159,type,
esk77_1: $i > $i ).
tff(decl_160,type,
esk78_1: $i > $i ).
tff(decl_161,type,
esk79_1: $i > $i ).
tff(decl_162,type,
esk80_1: $i > $i ).
tff(decl_163,type,
esk81_1: $i > $i ).
tff(decl_164,type,
esk82_1: $i > $i ).
tff(decl_165,type,
esk83_1: $i > $i ).
tff(decl_166,type,
esk84_1: $i > $i ).
tff(decl_167,type,
esk85_1: $i > $i ).
tff(decl_168,type,
esk86_2: ( $i * $i ) > $i ).
tff(decl_169,type,
esk87_0: $i ).
tff(decl_170,type,
esk88_0: $i ).
tff(decl_171,type,
esk89_0: $i ).
tff(decl_172,type,
esk90_1: $i > $i ).
tff(decl_173,type,
esk91_0: $i ).
tff(decl_174,type,
esk92_0: $i ).
tff(decl_175,type,
esk93_0: $i ).
tff(decl_176,type,
esk94_0: $i ).
tff(decl_177,type,
esk95_1: $i > $i ).
tff(decl_178,type,
esk96_0: $i ).
tff(decl_179,type,
esk97_0: $i ).
tff(decl_180,type,
esk98_0: $i ).
tff(decl_181,type,
esk99_0: $i ).
tff(decl_182,type,
esk100_0: $i ).
tff(decl_183,type,
esk101_1: $i > $i ).
tff(decl_184,type,
esk102_3: ( $i * $i * $i ) > $i ).
tff(decl_185,type,
esk103_3: ( $i * $i * $i ) > $i ).
tff(decl_186,type,
esk104_0: $i ).
tff(decl_187,type,
esk105_0: $i ).
tff(decl_188,type,
esk106_2: ( $i * $i ) > $i ).
tff(decl_189,type,
esk107_1: $i > $i ).
tff(decl_190,type,
esk108_2: ( $i * $i ) > $i ).
tff(decl_191,type,
esk109_2: ( $i * $i ) > $i ).
tff(decl_192,type,
esk110_2: ( $i * $i ) > $i ).
tff(decl_193,type,
esk111_1: $i > $i ).
tff(decl_194,type,
esk112_1: $i > $i ).
tff(decl_195,type,
esk113_2: ( $i * $i ) > $i ).
tff(decl_196,type,
esk114_2: ( $i * $i ) > $i ).
tff(decl_197,type,
esk115_2: ( $i * $i ) > $i ).
tff(decl_198,type,
esk116_2: ( $i * $i ) > $i ).
tff(decl_199,type,
esk117_2: ( $i * $i ) > $i ).
tff(decl_200,type,
esk118_1: $i > $i ).
tff(decl_201,type,
esk119_1: $i > $i ).
tff(decl_202,type,
esk120_3: ( $i * $i * $i ) > $i ).
tff(decl_203,type,
esk121_2: ( $i * $i ) > $i ).
tff(decl_204,type,
esk122_1: $i > $i ).
tff(decl_205,type,
esk123_2: ( $i * $i ) > $i ).
fof(t19_wellord1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_field(relation_restriction(X3,X2)))
=> ( in(X1,relation_field(X3))
& in(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t20_wellord1,conjecture,
! [X1,X2] :
( relation(X2)
=> ( subset(relation_field(relation_restriction(X2,X1)),relation_field(X2))
& subset(relation_field(relation_restriction(X2,X1)),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_wellord1) ).
fof(c_0_3,lemma,
! [X603,X604,X605] :
( ( in(X603,relation_field(X605))
| ~ in(X603,relation_field(relation_restriction(X605,X604)))
| ~ relation(X605) )
& ( in(X603,X604)
| ~ in(X603,relation_field(relation_restriction(X605,X604)))
| ~ relation(X605) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_wellord1])])]) ).
fof(c_0_4,plain,
! [X222,X223,X224,X225,X226] :
( ( ~ subset(X222,X223)
| ~ in(X224,X222)
| in(X224,X223) )
& ( in(esk44_2(X225,X226),X225)
| subset(X225,X226) )
& ( ~ in(esk44_2(X225,X226),X226)
| subset(X225,X226) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( subset(relation_field(relation_restriction(X2,X1)),relation_field(X2))
& subset(relation_field(relation_restriction(X2,X1)),X1) ) ),
inference(assume_negation,[status(cth)],[t20_wellord1]) ).
cnf(c_0_6,lemma,
( in(X1,relation_field(X2))
| ~ in(X1,relation_field(relation_restriction(X2,X3)))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,plain,
( in(esk44_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
( relation(esk105_0)
& ( ~ subset(relation_field(relation_restriction(esk105_0,esk104_0)),relation_field(esk105_0))
| ~ subset(relation_field(relation_restriction(esk105_0,esk104_0)),esk104_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| ~ in(esk44_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,lemma,
( subset(relation_field(relation_restriction(X1,X2)),X3)
| in(esk44_2(relation_field(relation_restriction(X1,X2)),X3),relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,lemma,
( in(X1,X2)
| ~ in(X1,relation_field(relation_restriction(X3,X2)))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_12,negated_conjecture,
( ~ subset(relation_field(relation_restriction(esk105_0,esk104_0)),relation_field(esk105_0))
| ~ subset(relation_field(relation_restriction(esk105_0,esk104_0)),esk104_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,lemma,
( subset(relation_field(relation_restriction(X1,X2)),relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk105_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,lemma,
( subset(relation_field(relation_restriction(X1,X2)),X3)
| in(esk44_2(relation_field(relation_restriction(X1,X2)),X3),X2)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_16,negated_conjecture,
~ subset(relation_field(relation_restriction(esk105_0,esk104_0)),esk104_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_17,lemma,
( subset(relation_field(relation_restriction(X1,X2)),X2)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_18,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU250+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n008.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 01:32:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 1.29/1.39 % Version : CSE_E---1.5
% 1.29/1.39 % Problem : theBenchmark.p
% 1.29/1.39 % Proof found
% 1.29/1.39 % SZS status Theorem for theBenchmark.p
% 1.29/1.39 % SZS output start Proof
% See solution above
% 1.29/1.40 % Total time : 0.815000 s
% 1.29/1.40 % SZS output end Proof
% 1.29/1.40 % Total time : 0.821000 s
%------------------------------------------------------------------------------