TSTP Solution File: SEU230+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU230+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 : n014.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 16:23:36 EDT 2023
% Result : Theorem 0.67s 0.80s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 140
% Syntax : Number of formulae : 158 ( 17 unt; 134 typ; 0 def)
% Number of atoms : 58 ( 15 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 56 ( 22 ~; 23 |; 8 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 265 ( 123 >; 142 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 123 ( 123 usr; 11 con; 0-5 aty)
% Number of variables : 43 ( 5 sgn; 27 !; 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,
relation: $i > $o ).
tff(decl_27,type,
one_to_one: $i > $o ).
tff(decl_28,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_29,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_30,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_31,type,
identity_relation: $i > $i ).
tff(decl_32,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_33,type,
subset: ( $i * $i ) > $o ).
tff(decl_34,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff(decl_35,type,
relation_image: ( $i * $i ) > $i ).
tff(decl_36,type,
relation_dom: $i > $i ).
tff(decl_37,type,
apply: ( $i * $i ) > $i ).
tff(decl_38,type,
relation_rng_restriction: ( $i * $i ) > $i ).
tff(decl_39,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_40,type,
unordered_triple: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
succ: $i > $i ).
tff(decl_42,type,
singleton: $i > $i ).
tff(decl_43,type,
empty_set: $i ).
tff(decl_44,type,
set_meet: $i > $i ).
tff(decl_45,type,
powerset: $i > $i ).
tff(decl_46,type,
element: ( $i * $i ) > $o ).
tff(decl_47,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_48,type,
cast_to_subset: $i > $i ).
tff(decl_49,type,
union: $i > $i ).
tff(decl_50,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_51,type,
relation_rng: $i > $i ).
tff(decl_52,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_53,type,
relation_field: $i > $i ).
tff(decl_54,type,
relation_inverse: $i > $i ).
tff(decl_55,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_56,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_57,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_58,type,
function_inverse: $i > $i ).
tff(decl_59,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_60,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_61,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
relation_empty_yielding: $i > $o ).
tff(decl_63,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_64,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_66,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
esk5_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_69,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
esk11_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_75,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_78,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
esk17_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_81,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_82,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_83,type,
esk20_1: $i > $i ).
tff(decl_84,type,
esk21_3: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_86,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_87,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_88,type,
esk25_1: $i > $i ).
tff(decl_89,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_90,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_91,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_92,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_93,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
esk31_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
esk32_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
esk33_3: ( $i * $i * $i ) > $i ).
tff(decl_97,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
esk35_3: ( $i * $i * $i ) > $i ).
tff(decl_99,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_100,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_101,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_102,type,
esk39_3: ( $i * $i * $i ) > $i ).
tff(decl_103,type,
esk40_3: ( $i * $i * $i ) > $i ).
tff(decl_104,type,
esk41_2: ( $i * $i ) > $i ).
tff(decl_105,type,
esk42_2: ( $i * $i ) > $i ).
tff(decl_106,type,
esk43_3: ( $i * $i * $i ) > $i ).
tff(decl_107,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_108,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_109,type,
esk46_3: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
esk47_3: ( $i * $i * $i ) > $i ).
tff(decl_111,type,
esk48_2: ( $i * $i ) > $i ).
tff(decl_112,type,
esk49_2: ( $i * $i ) > $i ).
tff(decl_113,type,
esk50_3: ( $i * $i * $i ) > $i ).
tff(decl_114,type,
esk51_2: ( $i * $i ) > $i ).
tff(decl_115,type,
esk52_2: ( $i * $i ) > $i ).
tff(decl_116,type,
esk53_2: ( $i * $i ) > $i ).
tff(decl_117,type,
esk54_2: ( $i * $i ) > $i ).
tff(decl_118,type,
esk55_1: $i > $i ).
tff(decl_119,type,
esk56_1: $i > $i ).
tff(decl_120,type,
esk57_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_121,type,
esk58_3: ( $i * $i * $i ) > $i ).
tff(decl_122,type,
esk59_3: ( $i * $i * $i ) > $i ).
tff(decl_123,type,
esk60_3: ( $i * $i * $i ) > $i ).
tff(decl_124,type,
esk61_3: ( $i * $i * $i ) > $i ).
tff(decl_125,type,
esk62_1: $i > $i ).
tff(decl_126,type,
esk63_2: ( $i * $i ) > $i ).
tff(decl_127,type,
esk64_0: $i ).
tff(decl_128,type,
esk65_0: $i ).
tff(decl_129,type,
esk66_1: $i > $i ).
tff(decl_130,type,
esk67_0: $i ).
tff(decl_131,type,
esk68_0: $i ).
tff(decl_132,type,
esk69_0: $i ).
tff(decl_133,type,
esk70_1: $i > $i ).
tff(decl_134,type,
esk71_0: $i ).
tff(decl_135,type,
esk72_0: $i ).
tff(decl_136,type,
esk73_0: $i ).
tff(decl_137,type,
esk74_0: $i ).
tff(decl_138,type,
esk75_0: $i ).
tff(decl_139,type,
esk76_1: $i > $i ).
tff(decl_140,type,
esk77_3: ( $i * $i * $i ) > $i ).
tff(decl_141,type,
esk78_3: ( $i * $i * $i ) > $i ).
tff(decl_142,type,
esk79_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk80_2: ( $i * $i ) > $i ).
tff(decl_144,type,
esk81_2: ( $i * $i ) > $i ).
tff(decl_145,type,
esk82_2: ( $i * $i ) > $i ).
tff(decl_146,type,
esk83_2: ( $i * $i ) > $i ).
tff(decl_147,type,
esk84_2: ( $i * $i ) > $i ).
tff(decl_148,type,
esk85_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk86_2: ( $i * $i ) > $i ).
tff(decl_150,type,
esk87_1: $i > $i ).
tff(decl_151,type,
esk88_1: $i > $i ).
tff(decl_152,type,
esk89_3: ( $i * $i * $i ) > $i ).
tff(decl_153,type,
esk90_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk91_1: $i > $i ).
tff(decl_155,type,
esk92_2: ( $i * $i ) > $i ).
fof(t10_ordinal1,conjecture,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t38_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] : in(X1,succ(X1)),
inference(assume_negation,[status(cth)],[t10_ordinal1]) ).
fof(c_0_7,plain,
! [X103] : succ(X103) = set_union2(X103,singleton(X103)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_8,lemma,
! [X647] : unordered_pair(X647,X647) = singleton(X647),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_9,negated_conjecture,
~ in(esk75_0,succ(esk75_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_10,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X162,X163,X164,X165,X166,X167,X168,X169] :
( ( ~ in(X165,X164)
| in(X165,X162)
| in(X165,X163)
| X164 != set_union2(X162,X163) )
& ( ~ in(X166,X162)
| in(X166,X164)
| X164 != set_union2(X162,X163) )
& ( ~ in(X166,X163)
| in(X166,X164)
| X164 != set_union2(X162,X163) )
& ( ~ in(esk30_3(X167,X168,X169),X167)
| ~ in(esk30_3(X167,X168,X169),X169)
| X169 = set_union2(X167,X168) )
& ( ~ in(esk30_3(X167,X168,X169),X168)
| ~ in(esk30_3(X167,X168,X169),X169)
| X169 = set_union2(X167,X168) )
& ( in(esk30_3(X167,X168,X169),X169)
| in(esk30_3(X167,X168,X169),X167)
| in(esk30_3(X167,X168,X169),X168)
| X169 = set_union2(X167,X168) ) ),
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)],[d2_xboole_0])])])])])]) ).
fof(c_0_13,lemma,
! [X552,X553,X554] :
( ( in(X552,X554)
| ~ subset(unordered_pair(X552,X553),X554) )
& ( in(X553,X554)
| ~ subset(unordered_pair(X552,X553),X554) )
& ( ~ in(X552,X554)
| ~ in(X553,X554)
| subset(unordered_pair(X552,X553),X554) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
fof(c_0_14,plain,
! [X420] : subset(X420,X420),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_15,negated_conjecture,
~ in(esk75_0,succ(esk75_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
succ(X1) = set_union2(X1,unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,lemma,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
~ in(esk75_0,set_union2(esk75_0,unordered_pair(esk75_0,esk75_0))),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_22,lemma,
in(X1,unordered_pair(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU230+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
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 01:04:04 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.54 start to proof: theBenchmark
% 0.67/0.80 % Version : CSE_E---1.5
% 0.67/0.80 % Problem : theBenchmark.p
% 0.67/0.80 % Proof found
% 0.67/0.80 % SZS status Theorem for theBenchmark.p
% 0.67/0.80 % SZS output start Proof
% See solution above
% 0.67/0.81 % Total time : 0.246000 s
% 0.67/0.81 % SZS output end Proof
% 0.67/0.81 % Total time : 0.255000 s
%------------------------------------------------------------------------------