TSTP Solution File: SEU265+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU265+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 16:23:57 EDT 2023
% Result : Theorem 73.09s 73.30s
% Output : CNFRefutation 73.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 210
% Syntax : Number of formulae : 267 ( 17 unt; 197 typ; 0 def)
% Number of atoms : 186 ( 50 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 197 ( 81 ~; 81 |; 18 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 361 ( 180 >; 181 *; 0 +; 0 <<)
% Number of predicates : 34 ( 32 usr; 1 prp; 0-3 aty)
% Number of functors : 165 ( 165 usr; 17 con; 0-5 aty)
% Number of variables : 138 ( 11 sgn; 80 !; 1 ?; 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,
succ: $i > $i ).
tff(decl_56,type,
singleton: $i > $i ).
tff(decl_57,type,
is_reflexive_in: ( $i * $i ) > $o ).
tff(decl_58,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_59,type,
empty_set: $i ).
tff(decl_60,type,
set_meet: $i > $i ).
tff(decl_61,type,
fiber: ( $i * $i ) > $i ).
tff(decl_62,type,
well_founded_relation: $i > $o ).
tff(decl_63,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_64,type,
is_well_founded_in: ( $i * $i ) > $o ).
tff(decl_65,type,
cast_to_subset: $i > $i ).
tff(decl_66,type,
union: $i > $i ).
tff(decl_67,type,
well_ordering: $i > $o ).
tff(decl_68,type,
reflexive: $i > $o ).
tff(decl_69,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_70,type,
relation_rng: $i > $i ).
tff(decl_71,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_72,type,
well_orders: ( $i * $i ) > $o ).
tff(decl_73,type,
being_limit_ordinal: $i > $o ).
tff(decl_74,type,
relation_restriction: ( $i * $i ) > $i ).
tff(decl_75,type,
relation_inverse: $i > $i ).
tff(decl_76,type,
relation_isomorphism: ( $i * $i * $i ) > $o ).
tff(decl_77,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_78,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_79,type,
function_inverse: $i > $i ).
tff(decl_80,type,
relation_dom_as_subset: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_82,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_83,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_85,type,
relation_empty_yielding: $i > $o ).
tff(decl_86,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_87,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_88,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_89,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_90,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_92,type,
esk5_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_95,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_97,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
esk11_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_101,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_102,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_103,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_104,type,
esk17_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_105,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_106,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_107,type,
esk20_1: $i > $i ).
tff(decl_108,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_109,type,
esk22_3: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_111,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_112,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_113,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_114,type,
esk27_1: $i > $i ).
tff(decl_115,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_116,type,
esk29_1: $i > $i ).
tff(decl_117,type,
esk30_2: ( $i * $i ) > $i ).
tff(decl_118,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_119,type,
esk32_3: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_121,type,
esk34_1: $i > $i ).
tff(decl_122,type,
esk35_3: ( $i * $i * $i ) > $i ).
tff(decl_123,type,
esk36_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_124,type,
esk37_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_125,type,
esk38_3: ( $i * $i * $i ) > $i ).
tff(decl_126,type,
esk39_3: ( $i * $i * $i ) > $i ).
tff(decl_127,type,
esk40_3: ( $i * $i * $i ) > $i ).
tff(decl_128,type,
esk41_1: $i > $i ).
tff(decl_129,type,
esk42_1: $i > $i ).
tff(decl_130,type,
esk43_2: ( $i * $i ) > $i ).
tff(decl_131,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_132,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_133,type,
esk46_3: ( $i * $i * $i ) > $i ).
tff(decl_134,type,
esk47_2: ( $i * $i ) > $i ).
tff(decl_135,type,
esk48_3: ( $i * $i * $i ) > $i ).
tff(decl_136,type,
esk49_3: ( $i * $i * $i ) > $i ).
tff(decl_137,type,
esk50_2: ( $i * $i ) > $i ).
tff(decl_138,type,
esk51_2: ( $i * $i ) > $i ).
tff(decl_139,type,
esk52_2: ( $i * $i ) > $i ).
tff(decl_140,type,
esk53_2: ( $i * $i ) > $i ).
tff(decl_141,type,
esk54_3: ( $i * $i * $i ) > $i ).
tff(decl_142,type,
esk55_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk56_2: ( $i * $i ) > $i ).
tff(decl_144,type,
esk57_3: ( $i * $i * $i ) > $i ).
tff(decl_145,type,
esk58_3: ( $i * $i * $i ) > $i ).
tff(decl_146,type,
esk59_2: ( $i * $i ) > $i ).
tff(decl_147,type,
esk60_2: ( $i * $i ) > $i ).
tff(decl_148,type,
esk61_3: ( $i * $i * $i ) > $i ).
tff(decl_149,type,
esk62_2: ( $i * $i ) > $i ).
tff(decl_150,type,
esk63_2: ( $i * $i ) > $i ).
tff(decl_151,type,
esk64_2: ( $i * $i ) > $i ).
tff(decl_152,type,
esk65_2: ( $i * $i ) > $i ).
tff(decl_153,type,
esk66_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk67_2: ( $i * $i ) > $i ).
tff(decl_155,type,
esk68_3: ( $i * $i * $i ) > $i ).
tff(decl_156,type,
esk69_3: ( $i * $i * $i ) > $i ).
tff(decl_157,type,
esk70_1: $i > $i ).
tff(decl_158,type,
esk71_1: $i > $i ).
tff(decl_159,type,
esk72_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_160,type,
esk73_3: ( $i * $i * $i ) > $i ).
tff(decl_161,type,
esk74_3: ( $i * $i * $i ) > $i ).
tff(decl_162,type,
esk75_3: ( $i * $i * $i ) > $i ).
tff(decl_163,type,
esk76_2: ( $i * $i ) > $i ).
tff(decl_164,type,
esk77_2: ( $i * $i ) > $i ).
tff(decl_165,type,
esk78_2: ( $i * $i ) > $i ).
tff(decl_166,type,
esk79_3: ( $i * $i * $i ) > $i ).
tff(decl_167,type,
esk80_2: ( $i * $i ) > $i ).
tff(decl_168,type,
esk81_1: $i > $i ).
tff(decl_169,type,
esk82_2: ( $i * $i ) > $i ).
tff(decl_170,type,
esk83_1: $i > $i ).
tff(decl_171,type,
esk84_1: $i > $i ).
tff(decl_172,type,
esk85_1: $i > $i ).
tff(decl_173,type,
esk86_1: $i > $i ).
tff(decl_174,type,
esk87_1: $i > $i ).
tff(decl_175,type,
esk88_1: $i > $i ).
tff(decl_176,type,
esk89_1: $i > $i ).
tff(decl_177,type,
esk90_1: $i > $i ).
tff(decl_178,type,
esk91_2: ( $i * $i ) > $i ).
tff(decl_179,type,
esk92_0: $i ).
tff(decl_180,type,
esk93_0: $i ).
tff(decl_181,type,
esk94_0: $i ).
tff(decl_182,type,
esk95_1: $i > $i ).
tff(decl_183,type,
esk96_0: $i ).
tff(decl_184,type,
esk97_0: $i ).
tff(decl_185,type,
esk98_0: $i ).
tff(decl_186,type,
esk99_0: $i ).
tff(decl_187,type,
esk100_1: $i > $i ).
tff(decl_188,type,
esk101_0: $i ).
tff(decl_189,type,
esk102_0: $i ).
tff(decl_190,type,
esk103_0: $i ).
tff(decl_191,type,
esk104_0: $i ).
tff(decl_192,type,
esk105_0: $i ).
tff(decl_193,type,
esk106_1: $i > $i ).
tff(decl_194,type,
esk107_3: ( $i * $i * $i ) > $i ).
tff(decl_195,type,
esk108_3: ( $i * $i * $i ) > $i ).
tff(decl_196,type,
esk109_0: $i ).
tff(decl_197,type,
esk110_0: $i ).
tff(decl_198,type,
esk111_0: $i ).
tff(decl_199,type,
esk112_0: $i ).
tff(decl_200,type,
esk113_1: $i > $i ).
tff(decl_201,type,
esk114_2: ( $i * $i ) > $i ).
tff(decl_202,type,
esk115_1: $i > $i ).
tff(decl_203,type,
esk116_2: ( $i * $i ) > $i ).
tff(decl_204,type,
esk117_2: ( $i * $i ) > $i ).
tff(decl_205,type,
esk118_2: ( $i * $i ) > $i ).
tff(decl_206,type,
esk119_1: $i > $i ).
tff(decl_207,type,
esk120_1: $i > $i ).
tff(decl_208,type,
esk121_2: ( $i * $i ) > $i ).
tff(decl_209,type,
esk122_2: ( $i * $i ) > $i ).
tff(decl_210,type,
esk123_2: ( $i * $i ) > $i ).
tff(decl_211,type,
esk124_2: ( $i * $i ) > $i ).
tff(decl_212,type,
esk125_2: ( $i * $i ) > $i ).
tff(decl_213,type,
esk126_1: $i > $i ).
tff(decl_214,type,
esk127_1: $i > $i ).
tff(decl_215,type,
esk128_3: ( $i * $i * $i ) > $i ).
tff(decl_216,type,
esk129_2: ( $i * $i ) > $i ).
tff(decl_217,type,
esk130_1: $i > $i ).
tff(decl_218,type,
esk131_2: ( $i * $i ) > $i ).
fof(t22_relset_1,conjecture,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X4,X5),X3) )
<=> relation_dom_as_subset(X2,X1,X3) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(t12_relset_1,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(redefinition_k4_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(t20_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X4,X5),X3) )
<=> relation_dom_as_subset(X2,X1,X3) = X2 ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t22_relset_1])]) ).
fof(c_0_14,plain,
! [X323,X324] : ordered_pair(X323,X324) = unordered_pair(unordered_pair(X323,X324),singleton(X323)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_15,lemma,
! [X868] : unordered_pair(X868,X868) = singleton(X868),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_16,lemma,
! [X594,X595,X596] :
( ( subset(relation_dom(X596),X594)
| ~ relation_of2_as_subset(X596,X594,X595) )
& ( subset(relation_rng(X596),X595)
| ~ relation_of2_as_subset(X596,X594,X595) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_relset_1])])]) ).
fof(c_0_17,negated_conjecture,
! [X688,X689] :
( relation_of2_as_subset(esk111_0,esk110_0,esk109_0)
& ( in(esk112_0,esk110_0)
| relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0 )
& ( ~ in(ordered_pair(esk112_0,X688),esk111_0)
| relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0 )
& ( ~ in(X689,esk110_0)
| in(ordered_pair(X689,esk113_1(X689)),esk111_0)
| relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_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_13])])])])]) ).
cnf(c_0_18,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X36,X37] :
( ( subset(X36,X37)
| X36 != X37 )
& ( subset(X37,X36)
| X36 != X37 )
& ( ~ subset(X36,X37)
| ~ subset(X37,X36)
| X36 = X37 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_21,lemma,
( subset(relation_dom(X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
relation_of2_as_subset(esk111_0,esk110_0,esk109_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X262,X263,X264,X266,X267,X268,X270] :
( ( ~ in(X264,X263)
| in(ordered_pair(X264,esk49_3(X262,X263,X264)),X262)
| X263 != relation_dom(X262)
| ~ relation(X262) )
& ( ~ in(ordered_pair(X266,X267),X262)
| in(X266,X263)
| X263 != relation_dom(X262)
| ~ relation(X262) )
& ( ~ in(esk50_2(X262,X268),X268)
| ~ in(ordered_pair(esk50_2(X262,X268),X270),X262)
| X268 = relation_dom(X262)
| ~ relation(X262) )
& ( in(esk50_2(X262,X268),X268)
| in(ordered_pair(esk50_2(X262,X268),esk51_2(X262,X268)),X262)
| X268 = relation_dom(X262)
| ~ relation(X262) ) ),
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)],[d4_relat_1])])])])])]) ).
cnf(c_0_24,negated_conjecture,
( in(ordered_pair(X1,esk113_1(X1)),esk111_0)
| relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
| ~ in(X1,esk110_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_26,plain,
! [X20,X21] : unordered_pair(X20,X21) = unordered_pair(X21,X20),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_27,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
subset(relation_dom(esk111_0),esk110_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_29,plain,
! [X236,X237,X238,X239,X240] :
( ( ~ subset(X236,X237)
| ~ in(X238,X236)
| in(X238,X237) )
& ( in(esk45_2(X239,X240),X239)
| subset(X239,X240) )
& ( ~ in(esk45_2(X239,X240),X240)
| subset(X239,X240) ) ),
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_30,plain,
! [X547,X548,X549] :
( ~ relation_of2(X549,X547,X548)
| relation_dom_as_subset(X547,X548,X549) = relation_dom(X549) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
fof(c_0_31,plain,
! [X557,X558,X559] :
( ( ~ relation_of2_as_subset(X559,X557,X558)
| relation_of2(X559,X557,X558) )
& ( ~ relation_of2(X559,X557,X558)
| relation_of2_as_subset(X559,X557,X558) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(ordered_pair(esk112_0,X1),esk111_0)
| relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,plain,
( in(ordered_pair(X1,esk49_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_34,plain,
! [X14,X15,X16] :
( ~ element(X16,powerset(cartesian_product2(X14,X15)))
| relation(X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_35,plain,
! [X419,X420,X421] :
( ~ relation_of2_as_subset(X421,X419,X420)
| element(X421,powerset(cartesian_product2(X419,X420))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_36,lemma,
! [X667,X668,X669] :
( ( in(X667,relation_dom(X669))
| ~ in(ordered_pair(X667,X668),X669)
| ~ relation(X669) )
& ( in(X668,relation_rng(X669))
| ~ in(ordered_pair(X667,X668),X669)
| ~ relation(X669) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).
cnf(c_0_37,negated_conjecture,
( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
| in(unordered_pair(unordered_pair(X1,esk113_1(X1)),unordered_pair(X1,X1)),esk111_0)
| ~ in(X1,esk110_0) ),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_38,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39,negated_conjecture,
( relation_dom(esk111_0) = esk110_0
| ~ subset(esk110_0,relation_dom(esk111_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_40,plain,
( in(esk45_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,plain,
( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,negated_conjecture,
( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0
| ~ in(unordered_pair(unordered_pair(esk112_0,X1),unordered_pair(esk112_0,esk112_0)),esk111_0) ),
inference(rw,[status(thm)],[c_0_32,c_0_25]) ).
cnf(c_0_44,plain,
( in(unordered_pair(unordered_pair(X1,esk49_3(X3,X2,X1)),unordered_pair(X1,X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_45,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,lemma,
( in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,negated_conjecture,
( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
| in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk113_1(X1))),esk111_0)
| ~ in(X1,esk110_0) ),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_49,negated_conjecture,
( relation_dom(esk111_0) = esk110_0
| in(esk45_2(esk110_0,relation_dom(esk111_0)),esk110_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_50,plain,
( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_51,negated_conjecture,
( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0
| ~ in(unordered_pair(unordered_pair(esk112_0,esk112_0),unordered_pair(esk112_0,X1)),esk111_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_38]) ).
cnf(c_0_52,plain,
( in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk49_3(X2,relation_dom(X2),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_38])]) ).
cnf(c_0_53,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_54,lemma,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[c_0_47,c_0_25]) ).
cnf(c_0_55,negated_conjecture,
( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
| relation_dom(esk111_0) = esk110_0
| in(unordered_pair(unordered_pair(esk45_2(esk110_0,relation_dom(esk111_0)),esk45_2(esk110_0,relation_dom(esk111_0))),unordered_pair(esk45_2(esk110_0,relation_dom(esk111_0)),esk113_1(esk45_2(esk110_0,relation_dom(esk111_0))))),esk111_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
relation_dom(esk111_0) = relation_dom_as_subset(esk110_0,esk109_0,esk111_0),
inference(spm,[status(thm)],[c_0_50,c_0_22]) ).
cnf(c_0_57,negated_conjecture,
( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0
| ~ relation(esk111_0)
| ~ in(esk112_0,relation_dom(esk111_0)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
relation(esk111_0),
inference(spm,[status(thm)],[c_0_53,c_0_22]) ).
cnf(c_0_59,lemma,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_38]) ).
cnf(c_0_60,negated_conjecture,
( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
| in(unordered_pair(unordered_pair(esk45_2(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0)),esk45_2(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0))),unordered_pair(esk45_2(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0)),esk113_1(esk45_2(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0))))),esk111_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_56]),c_0_56]),c_0_56]),c_0_56])]) ).
cnf(c_0_61,negated_conjecture,
( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0
| ~ in(esk112_0,relation_dom(esk111_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_62,plain,
( subset(X1,X2)
| ~ in(esk45_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_63,negated_conjecture,
( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
| in(esk45_2(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0)),relation_dom_as_subset(esk110_0,esk109_0,esk111_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_56]),c_0_58])]) ).
cnf(c_0_64,negated_conjecture,
( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0
| ~ subset(esk110_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_56]),c_0_56]) ).
cnf(c_0_65,negated_conjecture,
( relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0
| ~ in(esk112_0,relation_dom_as_subset(esk110_0,esk109_0,esk111_0)) ),
inference(rw,[status(thm)],[c_0_61,c_0_56]) ).
cnf(c_0_66,negated_conjecture,
relation_dom_as_subset(esk110_0,esk109_0,esk111_0) = esk110_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_67,negated_conjecture,
( in(esk112_0,esk110_0)
| relation_dom_as_subset(esk110_0,esk109_0,esk111_0) != esk110_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_68,negated_conjecture,
~ in(esk112_0,esk110_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_66])]) ).
cnf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_66])]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU265+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/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 : Wed Aug 23 13:14:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 73.09/73.30 % Version : CSE_E---1.5
% 73.09/73.30 % Problem : theBenchmark.p
% 73.09/73.30 % Proof found
% 73.09/73.30 % SZS status Theorem for theBenchmark.p
% 73.09/73.30 % SZS output start Proof
% See solution above
% 73.09/73.31 % Total time : 72.728000 s
% 73.09/73.31 % SZS output end Proof
% 73.09/73.31 % Total time : 72.738000 s
%------------------------------------------------------------------------------