TSTP Solution File: SEU284+2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU284+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 : n020.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 16:24:06 EDT 2023
% Result : Theorem 234.20s 234.23s
% Output : CNFRefutation 234.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 277
% Syntax : Number of formulae : 330 ( 11 unt; 274 typ; 0 def)
% Number of atoms : 263 ( 160 equ)
% Maximal formula atoms : 104 ( 4 avg)
% Number of connectives : 307 ( 100 ~; 157 |; 45 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 521 ( 257 >; 264 *; 0 +; 0 <<)
% Number of predicates : 35 ( 33 usr; 1 prp; 0-3 aty)
% Number of functors : 241 ( 241 usr; 17 con; 0-5 aty)
% Number of variables : 97 ( 26 sgn; 17 !; 3 ?; 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,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_31,type,
powerset: $i > $i ).
tff(decl_32,type,
element: ( $i * $i ) > $o ).
tff(decl_33,type,
one_to_one: $i > $o ).
tff(decl_34,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_35,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_36,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_37,type,
ordinal_subset: ( $i * $i ) > $o ).
tff(decl_38,type,
identity_relation: $i > $i ).
tff(decl_39,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_40,type,
subset: ( $i * $i ) > $o ).
tff(decl_41,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff(decl_42,type,
relation_image: ( $i * $i ) > $i ).
tff(decl_43,type,
relation_dom: $i > $i ).
tff(decl_44,type,
apply: ( $i * $i ) > $i ).
tff(decl_45,type,
relation_rng_restriction: ( $i * $i ) > $i ).
tff(decl_46,type,
antisymmetric: $i > $o ).
tff(decl_47,type,
relation_field: $i > $i ).
tff(decl_48,type,
is_antisymmetric_in: ( $i * $i ) > $o ).
tff(decl_49,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_50,type,
connected: $i > $o ).
tff(decl_51,type,
is_connected_in: ( $i * $i ) > $o ).
tff(decl_52,type,
transitive: $i > $o ).
tff(decl_53,type,
is_transitive_in: ( $i * $i ) > $o ).
tff(decl_54,type,
unordered_triple: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
pair_first: $i > $i ).
tff(decl_56,type,
succ: $i > $i ).
tff(decl_57,type,
singleton: $i > $i ).
tff(decl_58,type,
is_reflexive_in: ( $i * $i ) > $o ).
tff(decl_59,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_60,type,
empty_set: $i ).
tff(decl_61,type,
set_meet: $i > $i ).
tff(decl_62,type,
fiber: ( $i * $i ) > $i ).
tff(decl_63,type,
inclusion_relation: $i > $i ).
tff(decl_64,type,
pair_second: $i > $i ).
tff(decl_65,type,
well_founded_relation: $i > $o ).
tff(decl_66,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_67,type,
is_well_founded_in: ( $i * $i ) > $o ).
tff(decl_68,type,
cast_to_subset: $i > $i ).
tff(decl_69,type,
union: $i > $i ).
tff(decl_70,type,
well_ordering: $i > $o ).
tff(decl_71,type,
reflexive: $i > $o ).
tff(decl_72,type,
equipotent: ( $i * $i ) > $o ).
tff(decl_73,type,
relation_rng: $i > $i ).
tff(decl_74,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_75,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_76,type,
well_orders: ( $i * $i ) > $o ).
tff(decl_77,type,
being_limit_ordinal: $i > $o ).
tff(decl_78,type,
relation_restriction: ( $i * $i ) > $i ).
tff(decl_79,type,
relation_inverse: $i > $i ).
tff(decl_80,type,
relation_isomorphism: ( $i * $i * $i ) > $o ).
tff(decl_81,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_82,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_83,type,
function_inverse: $i > $i ).
tff(decl_84,type,
relation_dom_as_subset: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
relation_rng_as_subset: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_87,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_88,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_90,type,
relation_empty_yielding: $i > $o ).
tff(decl_91,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_92,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_93,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_94,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_95,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_97,type,
esk5_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_98,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_99,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_101,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_102,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_103,type,
esk11_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_104,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_105,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_106,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_107,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_108,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_109,type,
esk17_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_110,type,
esk18_1: $i > $i ).
tff(decl_111,type,
esk19_1: $i > $i ).
tff(decl_112,type,
esk20_1: $i > $i ).
tff(decl_113,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_114,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_115,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_116,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_117,type,
esk25_1: $i > $i ).
tff(decl_118,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_119,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_121,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_122,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_123,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_124,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_125,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_126,type,
esk34_1: $i > $i ).
tff(decl_127,type,
esk35_2: ( $i * $i ) > $i ).
tff(decl_128,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_129,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_130,type,
esk38_1: $i > $i ).
tff(decl_131,type,
esk39_2: ( $i * $i ) > $i ).
tff(decl_132,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_133,type,
esk41_3: ( $i * $i * $i ) > $i ).
tff(decl_134,type,
esk42_2: ( $i * $i ) > $i ).
tff(decl_135,type,
esk43_1: $i > $i ).
tff(decl_136,type,
esk44_3: ( $i * $i * $i ) > $i ).
tff(decl_137,type,
esk45_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_138,type,
esk46_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_139,type,
esk47_3: ( $i * $i * $i ) > $i ).
tff(decl_140,type,
esk48_3: ( $i * $i * $i ) > $i ).
tff(decl_141,type,
esk49_3: ( $i * $i * $i ) > $i ).
tff(decl_142,type,
esk50_1: $i > $i ).
tff(decl_143,type,
esk51_1: $i > $i ).
tff(decl_144,type,
esk52_2: ( $i * $i ) > $i ).
tff(decl_145,type,
esk53_2: ( $i * $i ) > $i ).
tff(decl_146,type,
esk54_2: ( $i * $i ) > $i ).
tff(decl_147,type,
esk55_3: ( $i * $i * $i ) > $i ).
tff(decl_148,type,
esk56_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk57_3: ( $i * $i * $i ) > $i ).
tff(decl_150,type,
esk58_3: ( $i * $i * $i ) > $i ).
tff(decl_151,type,
esk59_2: ( $i * $i ) > $i ).
tff(decl_152,type,
esk60_2: ( $i * $i ) > $i ).
tff(decl_153,type,
esk61_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk62_2: ( $i * $i ) > $i ).
tff(decl_155,type,
esk63_3: ( $i * $i * $i ) > $i ).
tff(decl_156,type,
esk64_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk65_2: ( $i * $i ) > $i ).
tff(decl_158,type,
esk66_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk67_3: ( $i * $i * $i ) > $i ).
tff(decl_160,type,
esk68_3: ( $i * $i * $i ) > $i ).
tff(decl_161,type,
esk69_2: ( $i * $i ) > $i ).
tff(decl_162,type,
esk70_2: ( $i * $i ) > $i ).
tff(decl_163,type,
esk71_3: ( $i * $i * $i ) > $i ).
tff(decl_164,type,
esk72_2: ( $i * $i ) > $i ).
tff(decl_165,type,
esk73_2: ( $i * $i ) > $i ).
tff(decl_166,type,
esk74_2: ( $i * $i ) > $i ).
tff(decl_167,type,
esk75_2: ( $i * $i ) > $i ).
tff(decl_168,type,
esk76_2: ( $i * $i ) > $i ).
tff(decl_169,type,
esk77_2: ( $i * $i ) > $i ).
tff(decl_170,type,
esk78_3: ( $i * $i * $i ) > $i ).
tff(decl_171,type,
esk79_3: ( $i * $i * $i ) > $i ).
tff(decl_172,type,
esk80_1: $i > $i ).
tff(decl_173,type,
esk81_1: $i > $i ).
tff(decl_174,type,
esk82_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_175,type,
esk83_3: ( $i * $i * $i ) > $i ).
tff(decl_176,type,
esk84_3: ( $i * $i * $i ) > $i ).
tff(decl_177,type,
esk85_3: ( $i * $i * $i ) > $i ).
tff(decl_178,type,
esk86_2: ( $i * $i ) > $i ).
tff(decl_179,type,
esk87_2: ( $i * $i ) > $i ).
tff(decl_180,type,
esk88_2: ( $i * $i ) > $i ).
tff(decl_181,type,
esk89_3: ( $i * $i * $i ) > $i ).
tff(decl_182,type,
esk90_2: ( $i * $i ) > $i ).
tff(decl_183,type,
esk91_1: $i > $i ).
tff(decl_184,type,
esk92_2: ( $i * $i ) > $i ).
tff(decl_185,type,
esk93_1: $i > $i ).
tff(decl_186,type,
esk94_1: $i > $i ).
tff(decl_187,type,
esk95_1: $i > $i ).
tff(decl_188,type,
esk96_1: $i > $i ).
tff(decl_189,type,
esk97_2: ( $i * $i ) > $i ).
tff(decl_190,type,
esk98_1: $i > $i ).
tff(decl_191,type,
esk99_1: $i > $i ).
tff(decl_192,type,
esk100_1: $i > $i ).
tff(decl_193,type,
esk101_1: $i > $i ).
tff(decl_194,type,
esk102_2: ( $i * $i ) > $i ).
tff(decl_195,type,
esk103_0: $i ).
tff(decl_196,type,
esk104_0: $i ).
tff(decl_197,type,
esk105_0: $i ).
tff(decl_198,type,
esk106_1: $i > $i ).
tff(decl_199,type,
esk107_0: $i ).
tff(decl_200,type,
esk108_0: $i ).
tff(decl_201,type,
esk109_0: $i ).
tff(decl_202,type,
esk110_0: $i ).
tff(decl_203,type,
esk111_1: $i > $i ).
tff(decl_204,type,
esk112_0: $i ).
tff(decl_205,type,
esk113_0: $i ).
tff(decl_206,type,
esk114_0: $i ).
tff(decl_207,type,
esk115_0: $i ).
tff(decl_208,type,
esk116_0: $i ).
tff(decl_209,type,
esk117_1: $i > $i ).
tff(decl_210,type,
esk118_1: $i > $i ).
tff(decl_211,type,
esk119_1: $i > $i ).
tff(decl_212,type,
esk120_1: $i > $i ).
tff(decl_213,type,
esk121_1: $i > $i ).
tff(decl_214,type,
esk122_3: ( $i * $i * $i ) > $i ).
tff(decl_215,type,
esk123_1: $i > $i ).
tff(decl_216,type,
esk124_1: $i > $i ).
tff(decl_217,type,
esk125_1: $i > $i ).
tff(decl_218,type,
esk126_1: $i > $i ).
tff(decl_219,type,
esk127_2: ( $i * $i ) > $i ).
tff(decl_220,type,
esk128_1: $i > $i ).
tff(decl_221,type,
esk129_1: $i > $i ).
tff(decl_222,type,
esk130_1: $i > $i ).
tff(decl_223,type,
esk131_1: $i > $i ).
tff(decl_224,type,
esk132_1: $i > $i ).
tff(decl_225,type,
esk133_1: $i > $i ).
tff(decl_226,type,
esk134_1: $i > $i ).
tff(decl_227,type,
esk135_2: ( $i * $i ) > $i ).
tff(decl_228,type,
esk136_3: ( $i * $i * $i ) > $i ).
tff(decl_229,type,
esk137_3: ( $i * $i * $i ) > $i ).
tff(decl_230,type,
esk138_3: ( $i * $i * $i ) > $i ).
tff(decl_231,type,
esk139_3: ( $i * $i * $i ) > $i ).
tff(decl_232,type,
esk140_3: ( $i * $i * $i ) > $i ).
tff(decl_233,type,
esk141_3: ( $i * $i * $i ) > $i ).
tff(decl_234,type,
esk142_3: ( $i * $i * $i ) > $i ).
tff(decl_235,type,
esk143_3: ( $i * $i * $i ) > $i ).
tff(decl_236,type,
esk144_3: ( $i * $i * $i ) > $i ).
tff(decl_237,type,
esk145_3: ( $i * $i * $i ) > $i ).
tff(decl_238,type,
esk146_3: ( $i * $i * $i ) > $i ).
tff(decl_239,type,
esk147_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_240,type,
esk148_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_241,type,
esk149_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_242,type,
esk150_0: $i ).
tff(decl_243,type,
esk151_0: $i ).
tff(decl_244,type,
esk152_0: $i ).
tff(decl_245,type,
esk153_1: $i > $i ).
tff(decl_246,type,
esk154_2: ( $i * $i ) > $i ).
tff(decl_247,type,
esk155_2: ( $i * $i ) > $i ).
tff(decl_248,type,
esk156_2: ( $i * $i ) > $i ).
tff(decl_249,type,
esk157_2: ( $i * $i ) > $i ).
tff(decl_250,type,
esk158_2: ( $i * $i ) > $i ).
tff(decl_251,type,
esk159_2: ( $i * $i ) > $i ).
tff(decl_252,type,
esk160_2: ( $i * $i ) > $i ).
tff(decl_253,type,
esk161_3: ( $i * $i * $i ) > $i ).
tff(decl_254,type,
esk162_3: ( $i * $i * $i ) > $i ).
tff(decl_255,type,
esk163_2: ( $i * $i ) > $i ).
tff(decl_256,type,
esk164_3: ( $i * $i * $i ) > $i ).
tff(decl_257,type,
esk165_3: ( $i * $i * $i ) > $i ).
tff(decl_258,type,
esk166_3: ( $i * $i * $i ) > $i ).
tff(decl_259,type,
esk167_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_260,type,
esk168_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_261,type,
esk169_1: $i > $i ).
tff(decl_262,type,
esk170_2: ( $i * $i ) > $i ).
tff(decl_263,type,
esk171_3: ( $i * $i * $i ) > $i ).
tff(decl_264,type,
esk172_1: $i > $i ).
tff(decl_265,type,
esk173_1: $i > $i ).
tff(decl_266,type,
esk174_1: $i > $i ).
tff(decl_267,type,
esk175_1: $i > $i ).
tff(decl_268,type,
esk176_1: $i > $i ).
tff(decl_269,type,
esk177_0: $i ).
tff(decl_270,type,
esk178_1: $i > $i ).
tff(decl_271,type,
esk179_1: $i > $i ).
tff(decl_272,type,
esk180_3: ( $i * $i * $i ) > $i ).
tff(decl_273,type,
esk181_3: ( $i * $i * $i ) > $i ).
tff(decl_274,type,
esk182_3: ( $i * $i * $i ) > $i ).
tff(decl_275,type,
esk183_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_276,type,
esk184_3: ( $i * $i * $i ) > $i ).
tff(decl_277,type,
esk185_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_278,type,
esk186_2: ( $i * $i ) > $i ).
tff(decl_279,type,
esk187_1: $i > $i ).
tff(decl_280,type,
esk188_2: ( $i * $i ) > $i ).
tff(decl_281,type,
esk189_2: ( $i * $i ) > $i ).
tff(decl_282,type,
esk190_2: ( $i * $i ) > $i ).
tff(decl_283,type,
esk191_1: $i > $i ).
tff(decl_284,type,
esk192_1: $i > $i ).
tff(decl_285,type,
esk193_2: ( $i * $i ) > $i ).
tff(decl_286,type,
esk194_2: ( $i * $i ) > $i ).
tff(decl_287,type,
esk195_2: ( $i * $i ) > $i ).
tff(decl_288,type,
esk196_2: ( $i * $i ) > $i ).
tff(decl_289,type,
esk197_2: ( $i * $i ) > $i ).
tff(decl_290,type,
esk198_1: $i > $i ).
tff(decl_291,type,
esk199_1: $i > $i ).
tff(decl_292,type,
esk200_3: ( $i * $i * $i ) > $i ).
tff(decl_293,type,
esk201_2: ( $i * $i ) > $i ).
tff(decl_294,type,
esk202_1: $i > $i ).
tff(decl_295,type,
esk203_2: ( $i * $i ) > $i ).
fof(s2_funct_1__e16_22__wellord2__1,lemma,
! [X1] :
( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& X4 = singleton(X2) )
=> X3 = X4 )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] : X3 != singleton(X2) ) )
=> ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(s3_funct_1__e16_22__wellord2,conjecture,
! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
fof(c_0_3,lemma,
! [X742,X747,X749] :
( ( relation(esk176_1(X742))
| in(esk175_1(X742),X742)
| in(esk172_1(X742),X742) )
& ( function(esk176_1(X742))
| in(esk175_1(X742),X742)
| in(esk172_1(X742),X742) )
& ( relation_dom(esk176_1(X742)) = X742
| in(esk175_1(X742),X742)
| in(esk172_1(X742),X742) )
& ( ~ in(X749,X742)
| apply(esk176_1(X742),X749) = singleton(X749)
| in(esk175_1(X742),X742)
| in(esk172_1(X742),X742) )
& ( relation(esk176_1(X742))
| X747 != singleton(esk175_1(X742))
| in(esk172_1(X742),X742) )
& ( function(esk176_1(X742))
| X747 != singleton(esk175_1(X742))
| in(esk172_1(X742),X742) )
& ( relation_dom(esk176_1(X742)) = X742
| X747 != singleton(esk175_1(X742))
| in(esk172_1(X742),X742) )
& ( ~ in(X749,X742)
| apply(esk176_1(X742),X749) = singleton(X749)
| X747 != singleton(esk175_1(X742))
| in(esk172_1(X742),X742) )
& ( relation(esk176_1(X742))
| in(esk175_1(X742),X742)
| esk173_1(X742) = singleton(esk172_1(X742)) )
& ( function(esk176_1(X742))
| in(esk175_1(X742),X742)
| esk173_1(X742) = singleton(esk172_1(X742)) )
& ( relation_dom(esk176_1(X742)) = X742
| in(esk175_1(X742),X742)
| esk173_1(X742) = singleton(esk172_1(X742)) )
& ( ~ in(X749,X742)
| apply(esk176_1(X742),X749) = singleton(X749)
| in(esk175_1(X742),X742)
| esk173_1(X742) = singleton(esk172_1(X742)) )
& ( relation(esk176_1(X742))
| X747 != singleton(esk175_1(X742))
| esk173_1(X742) = singleton(esk172_1(X742)) )
& ( function(esk176_1(X742))
| X747 != singleton(esk175_1(X742))
| esk173_1(X742) = singleton(esk172_1(X742)) )
& ( relation_dom(esk176_1(X742)) = X742
| X747 != singleton(esk175_1(X742))
| esk173_1(X742) = singleton(esk172_1(X742)) )
& ( ~ in(X749,X742)
| apply(esk176_1(X742),X749) = singleton(X749)
| X747 != singleton(esk175_1(X742))
| esk173_1(X742) = singleton(esk172_1(X742)) )
& ( relation(esk176_1(X742))
| in(esk175_1(X742),X742)
| esk174_1(X742) = singleton(esk172_1(X742)) )
& ( function(esk176_1(X742))
| in(esk175_1(X742),X742)
| esk174_1(X742) = singleton(esk172_1(X742)) )
& ( relation_dom(esk176_1(X742)) = X742
| in(esk175_1(X742),X742)
| esk174_1(X742) = singleton(esk172_1(X742)) )
& ( ~ in(X749,X742)
| apply(esk176_1(X742),X749) = singleton(X749)
| in(esk175_1(X742),X742)
| esk174_1(X742) = singleton(esk172_1(X742)) )
& ( relation(esk176_1(X742))
| X747 != singleton(esk175_1(X742))
| esk174_1(X742) = singleton(esk172_1(X742)) )
& ( function(esk176_1(X742))
| X747 != singleton(esk175_1(X742))
| esk174_1(X742) = singleton(esk172_1(X742)) )
& ( relation_dom(esk176_1(X742)) = X742
| X747 != singleton(esk175_1(X742))
| esk174_1(X742) = singleton(esk172_1(X742)) )
& ( ~ in(X749,X742)
| apply(esk176_1(X742),X749) = singleton(X749)
| X747 != singleton(esk175_1(X742))
| esk174_1(X742) = singleton(esk172_1(X742)) )
& ( relation(esk176_1(X742))
| in(esk175_1(X742),X742)
| esk173_1(X742) != esk174_1(X742) )
& ( function(esk176_1(X742))
| in(esk175_1(X742),X742)
| esk173_1(X742) != esk174_1(X742) )
& ( relation_dom(esk176_1(X742)) = X742
| in(esk175_1(X742),X742)
| esk173_1(X742) != esk174_1(X742) )
& ( ~ in(X749,X742)
| apply(esk176_1(X742),X749) = singleton(X749)
| in(esk175_1(X742),X742)
| esk173_1(X742) != esk174_1(X742) )
& ( relation(esk176_1(X742))
| X747 != singleton(esk175_1(X742))
| esk173_1(X742) != esk174_1(X742) )
& ( function(esk176_1(X742))
| X747 != singleton(esk175_1(X742))
| esk173_1(X742) != esk174_1(X742) )
& ( relation_dom(esk176_1(X742)) = X742
| X747 != singleton(esk175_1(X742))
| esk173_1(X742) != esk174_1(X742) )
& ( ~ in(X749,X742)
| apply(esk176_1(X742),X749) = singleton(X749)
| X747 != singleton(esk175_1(X742))
| esk173_1(X742) != esk174_1(X742) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s2_funct_1__e16_22__wellord2__1])])])])]) ).
fof(c_0_4,lemma,
! [X1071] : unordered_pair(X1071,X1071) = singleton(X1071),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
cnf(c_0_5,lemma,
( relation_dom(esk176_1(X1)) = X1
| esk173_1(X1) = singleton(esk172_1(X1))
| X2 != singleton(esk175_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,lemma,
( relation_dom(esk176_1(X1)) = X1
| esk174_1(X1) = singleton(esk172_1(X1))
| X2 != singleton(esk175_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,lemma,
( relation_dom(esk176_1(X1)) = X1
| X2 != singleton(esk175_1(X1))
| esk173_1(X1) != esk174_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,lemma,
( relation(esk176_1(X1))
| esk173_1(X1) = singleton(esk172_1(X1))
| X2 != singleton(esk175_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_10,lemma,
( relation(esk176_1(X1))
| esk174_1(X1) = singleton(esk172_1(X1))
| X2 != singleton(esk175_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_11,lemma,
( relation(esk176_1(X1))
| X2 != singleton(esk175_1(X1))
| esk173_1(X1) != esk174_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_12,lemma,
( function(esk176_1(X1))
| esk173_1(X1) = singleton(esk172_1(X1))
| X2 != singleton(esk175_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_13,lemma,
( function(esk176_1(X1))
| esk174_1(X1) = singleton(esk172_1(X1))
| X2 != singleton(esk175_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_14,lemma,
( function(esk176_1(X1))
| X2 != singleton(esk175_1(X1))
| esk173_1(X1) != esk174_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ),
inference(assume_negation,[status(cth)],[s3_funct_1__e16_22__wellord2]) ).
cnf(c_0_16,lemma,
( relation_dom(esk176_1(X1)) = X1
| esk173_1(X1) = unordered_pair(esk172_1(X1),esk172_1(X1))
| X2 != unordered_pair(esk175_1(X1),esk175_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_6]),c_0_6]) ).
cnf(c_0_17,lemma,
( relation_dom(esk176_1(X1)) = X1
| esk174_1(X1) = unordered_pair(esk172_1(X1),esk172_1(X1))
| X2 != unordered_pair(esk175_1(X1),esk175_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_6]),c_0_6]) ).
cnf(c_0_18,lemma,
( relation_dom(esk176_1(X1)) = X1
| esk174_1(X1) != esk173_1(X1)
| X2 != unordered_pair(esk175_1(X1),esk175_1(X1)) ),
inference(rw,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_19,lemma,
( esk173_1(X1) = unordered_pair(esk172_1(X1),esk172_1(X1))
| relation(esk176_1(X1))
| X2 != unordered_pair(esk175_1(X1),esk175_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_6]),c_0_6]) ).
cnf(c_0_20,lemma,
( esk174_1(X1) = unordered_pair(esk172_1(X1),esk172_1(X1))
| relation(esk176_1(X1))
| X2 != unordered_pair(esk175_1(X1),esk175_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_6]),c_0_6]) ).
cnf(c_0_21,lemma,
( relation(esk176_1(X1))
| esk174_1(X1) != esk173_1(X1)
| X2 != unordered_pair(esk175_1(X1),esk175_1(X1)) ),
inference(rw,[status(thm)],[c_0_11,c_0_6]) ).
cnf(c_0_22,lemma,
( esk173_1(X1) = unordered_pair(esk172_1(X1),esk172_1(X1))
| function(esk176_1(X1))
| X2 != unordered_pair(esk175_1(X1),esk175_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_6]),c_0_6]) ).
cnf(c_0_23,lemma,
( esk174_1(X1) = unordered_pair(esk172_1(X1),esk172_1(X1))
| function(esk176_1(X1))
| X2 != unordered_pair(esk175_1(X1),esk175_1(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_6]),c_0_6]) ).
cnf(c_0_24,lemma,
( function(esk176_1(X1))
| esk174_1(X1) != esk173_1(X1)
| X2 != unordered_pair(esk175_1(X1),esk175_1(X1)) ),
inference(rw,[status(thm)],[c_0_14,c_0_6]) ).
fof(c_0_25,negated_conjecture,
! [X751] :
( ( in(esk178_1(X751),esk177_0)
| ~ relation(X751)
| ~ function(X751)
| relation_dom(X751) != esk177_0 )
& ( apply(X751,esk178_1(X751)) != singleton(esk178_1(X751))
| ~ relation(X751)
| ~ function(X751)
| relation_dom(X751) != esk177_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_26,lemma,
( apply(esk176_1(X2),X1) = singleton(X1)
| esk173_1(X2) = singleton(esk172_1(X2))
| ~ in(X1,X2)
| X3 != singleton(esk175_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_27,lemma,
( unordered_pair(esk172_1(X1),esk172_1(X1)) = esk173_1(X1)
| relation_dom(esk176_1(X1)) = X1 ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_28,lemma,
( unordered_pair(esk172_1(X1),esk172_1(X1)) = esk174_1(X1)
| relation_dom(esk176_1(X1)) = X1 ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_29,lemma,
( relation_dom(esk176_1(X1)) = X1
| esk174_1(X1) != esk173_1(X1) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_30,lemma,
( unordered_pair(esk172_1(X1),esk172_1(X1)) = esk173_1(X1)
| relation(esk176_1(X1)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_31,lemma,
( unordered_pair(esk172_1(X1),esk172_1(X1)) = esk174_1(X1)
| relation(esk176_1(X1)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_32,lemma,
( relation(esk176_1(X1))
| esk174_1(X1) != esk173_1(X1) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_33,lemma,
( unordered_pair(esk172_1(X1),esk172_1(X1)) = esk173_1(X1)
| function(esk176_1(X1)) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_34,lemma,
( unordered_pair(esk172_1(X1),esk172_1(X1)) = esk174_1(X1)
| function(esk176_1(X1)) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_35,lemma,
( function(esk176_1(X1))
| esk174_1(X1) != esk173_1(X1) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_36,negated_conjecture,
( apply(X1,esk178_1(X1)) != singleton(esk178_1(X1))
| ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != esk177_0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,lemma,
( apply(esk176_1(X2),X1) = singleton(X1)
| esk174_1(X2) = singleton(esk172_1(X2))
| ~ in(X1,X2)
| X3 != singleton(esk175_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_38,lemma,
( apply(esk176_1(X2),X1) = unordered_pair(X1,X1)
| esk173_1(X2) = unordered_pair(esk172_1(X2),esk172_1(X2))
| X3 != unordered_pair(esk175_1(X2),esk175_1(X2))
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_6]),c_0_6]),c_0_6]) ).
cnf(c_0_39,negated_conjecture,
( in(esk178_1(X1),esk177_0)
| ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != esk177_0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_40,lemma,
relation_dom(esk176_1(X1)) = X1,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_41,lemma,
relation(esk176_1(X1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_42,lemma,
function(esk176_1(X1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_43,negated_conjecture,
( relation_dom(X1) != esk177_0
| apply(X1,esk178_1(X1)) != unordered_pair(esk178_1(X1),esk178_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_36,c_0_6]) ).
cnf(c_0_44,lemma,
( apply(esk176_1(X2),X1) = singleton(X1)
| ~ in(X1,X2)
| X3 != singleton(esk175_1(X2))
| esk173_1(X2) != esk174_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_45,lemma,
( apply(esk176_1(X2),X1) = unordered_pair(X1,X1)
| esk174_1(X2) = unordered_pair(esk172_1(X2),esk172_1(X2))
| X3 != unordered_pair(esk175_1(X2),esk175_1(X2))
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_6]),c_0_6]),c_0_6]) ).
cnf(c_0_46,lemma,
( unordered_pair(esk172_1(X1),esk172_1(X1)) = esk173_1(X1)
| apply(esk176_1(X1),X2) = unordered_pair(X2,X2)
| ~ in(X2,X1) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_47,negated_conjecture,
in(esk178_1(esk176_1(esk177_0)),esk177_0),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42])])]) ).
cnf(c_0_48,negated_conjecture,
unordered_pair(esk178_1(esk176_1(esk177_0)),esk178_1(esk176_1(esk177_0))) != apply(esk176_1(esk177_0),esk178_1(esk176_1(esk177_0))),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_40]),c_0_41]),c_0_42])])]) ).
cnf(c_0_49,lemma,
( apply(esk176_1(X2),X1) = unordered_pair(X1,X1)
| esk174_1(X2) != esk173_1(X2)
| X3 != unordered_pair(esk175_1(X2),esk175_1(X2))
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_6]),c_0_6]) ).
cnf(c_0_50,lemma,
( unordered_pair(esk172_1(X1),esk172_1(X1)) = esk174_1(X1)
| apply(esk176_1(X1),X2) = unordered_pair(X2,X2)
| ~ in(X2,X1) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_51,negated_conjecture,
unordered_pair(esk172_1(esk177_0),esk172_1(esk177_0)) = esk173_1(esk177_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_52,lemma,
( apply(esk176_1(X1),X2) = unordered_pair(X2,X2)
| esk174_1(X1) != esk173_1(X1)
| ~ in(X2,X1) ),
inference(er,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
esk174_1(esk177_0) = esk173_1(esk177_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_47]),c_0_51]),c_0_48]) ).
cnf(c_0_54,lemma,
( apply(esk176_1(esk177_0),X1) = unordered_pair(X1,X1)
| ~ in(X1,esk177_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_47]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU284+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Wed Aug 23 15:35:00 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 234.20/234.23 % Version : CSE_E---1.5
% 234.20/234.23 % Problem : theBenchmark.p
% 234.20/234.23 % Proof found
% 234.20/234.23 % SZS status Theorem for theBenchmark.p
% 234.20/234.23 % SZS output start Proof
% See solution above
% 234.20/234.25 % Total time : 233.686000 s
% 234.20/234.25 % SZS output end Proof
% 234.20/234.25 % Total time : 233.708000 s
%------------------------------------------------------------------------------