TSTP Solution File: SEU234+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU234+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 : n010.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 16:23:38 EDT 2023
% Result : Theorem 29.08s 29.17s
% Output : CNFRefutation 29.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 148
% Syntax : Number of formulae : 176 ( 6 unt; 143 typ; 0 def)
% Number of atoms : 111 ( 9 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 125 ( 47 ~; 41 |; 24 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 271 ( 129 >; 142 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 129 ( 129 usr; 14 con; 0-5 aty)
% Number of variables : 41 ( 0 sgn; 28 !; 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,
identity_relation: $i > $i ).
tff(decl_35,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_36,type,
subset: ( $i * $i ) > $o ).
tff(decl_37,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff(decl_38,type,
relation_image: ( $i * $i ) > $i ).
tff(decl_39,type,
relation_dom: $i > $i ).
tff(decl_40,type,
apply: ( $i * $i ) > $i ).
tff(decl_41,type,
relation_rng_restriction: ( $i * $i ) > $i ).
tff(decl_42,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_43,type,
unordered_triple: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
succ: $i > $i ).
tff(decl_45,type,
singleton: $i > $i ).
tff(decl_46,type,
empty_set: $i ).
tff(decl_47,type,
set_meet: $i > $i ).
tff(decl_48,type,
powerset: $i > $i ).
tff(decl_49,type,
element: ( $i * $i ) > $o ).
tff(decl_50,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_51,type,
cast_to_subset: $i > $i ).
tff(decl_52,type,
union: $i > $i ).
tff(decl_53,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_54,type,
relation_rng: $i > $i ).
tff(decl_55,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_56,type,
relation_field: $i > $i ).
tff(decl_57,type,
relation_inverse: $i > $i ).
tff(decl_58,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_59,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_60,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_61,type,
function_inverse: $i > $i ).
tff(decl_62,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_63,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_64,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
relation_empty_yielding: $i > $o ).
tff(decl_66,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_67,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk5_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_72,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk11_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_78,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_81,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
esk17_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_84,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_85,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_86,type,
esk20_1: $i > $i ).
tff(decl_87,type,
esk21_3: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_89,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_90,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_91,type,
esk25_1: $i > $i ).
tff(decl_92,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_93,type,
esk27_1: $i > $i ).
tff(decl_94,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_95,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_96,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_97,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
esk32_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
esk33_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_100,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_101,type,
esk35_3: ( $i * $i * $i ) > $i ).
tff(decl_102,type,
esk36_3: ( $i * $i * $i ) > $i ).
tff(decl_103,type,
esk37_1: $i > $i ).
tff(decl_104,type,
esk38_1: $i > $i ).
tff(decl_105,type,
esk39_2: ( $i * $i ) > $i ).
tff(decl_106,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_107,type,
esk41_2: ( $i * $i ) > $i ).
tff(decl_108,type,
esk42_3: ( $i * $i * $i ) > $i ).
tff(decl_109,type,
esk43_3: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_111,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_112,type,
esk46_3: ( $i * $i * $i ) > $i ).
tff(decl_113,type,
esk47_2: ( $i * $i ) > $i ).
tff(decl_114,type,
esk48_2: ( $i * $i ) > $i ).
tff(decl_115,type,
esk49_3: ( $i * $i * $i ) > $i ).
tff(decl_116,type,
esk50_3: ( $i * $i * $i ) > $i ).
tff(decl_117,type,
esk51_2: ( $i * $i ) > $i ).
tff(decl_118,type,
esk52_2: ( $i * $i ) > $i ).
tff(decl_119,type,
esk53_3: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
esk54_2: ( $i * $i ) > $i ).
tff(decl_121,type,
esk55_2: ( $i * $i ) > $i ).
tff(decl_122,type,
esk56_2: ( $i * $i ) > $i ).
tff(decl_123,type,
esk57_2: ( $i * $i ) > $i ).
tff(decl_124,type,
esk58_1: $i > $i ).
tff(decl_125,type,
esk59_1: $i > $i ).
tff(decl_126,type,
esk60_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_127,type,
esk61_3: ( $i * $i * $i ) > $i ).
tff(decl_128,type,
esk62_3: ( $i * $i * $i ) > $i ).
tff(decl_129,type,
esk63_3: ( $i * $i * $i ) > $i ).
tff(decl_130,type,
esk64_3: ( $i * $i * $i ) > $i ).
tff(decl_131,type,
esk65_1: $i > $i ).
tff(decl_132,type,
esk66_2: ( $i * $i ) > $i ).
tff(decl_133,type,
esk67_0: $i ).
tff(decl_134,type,
esk68_0: $i ).
tff(decl_135,type,
esk69_0: $i ).
tff(decl_136,type,
esk70_1: $i > $i ).
tff(decl_137,type,
esk71_0: $i ).
tff(decl_138,type,
esk72_0: $i ).
tff(decl_139,type,
esk73_0: $i ).
tff(decl_140,type,
esk74_0: $i ).
tff(decl_141,type,
esk75_1: $i > $i ).
tff(decl_142,type,
esk76_0: $i ).
tff(decl_143,type,
esk77_0: $i ).
tff(decl_144,type,
esk78_0: $i ).
tff(decl_145,type,
esk79_0: $i ).
tff(decl_146,type,
esk80_0: $i ).
tff(decl_147,type,
esk81_1: $i > $i ).
tff(decl_148,type,
esk82_3: ( $i * $i * $i ) > $i ).
tff(decl_149,type,
esk83_3: ( $i * $i * $i ) > $i ).
tff(decl_150,type,
esk84_2: ( $i * $i ) > $i ).
tff(decl_151,type,
esk85_0: $i ).
tff(decl_152,type,
esk86_2: ( $i * $i ) > $i ).
tff(decl_153,type,
esk87_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk88_2: ( $i * $i ) > $i ).
tff(decl_155,type,
esk89_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk90_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk91_2: ( $i * $i ) > $i ).
tff(decl_158,type,
esk92_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk93_1: $i > $i ).
tff(decl_160,type,
esk94_1: $i > $i ).
tff(decl_161,type,
esk95_3: ( $i * $i * $i ) > $i ).
tff(decl_162,type,
esk96_2: ( $i * $i ) > $i ).
tff(decl_163,type,
esk97_1: $i > $i ).
tff(decl_164,type,
esk98_2: ( $i * $i ) > $i ).
fof(t31_ordinal1,conjecture,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(d3_ordinal1,axiom,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(t24_ordinal1,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(cc2_ordinal1,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
inference(assume_negation,[status(cth)],[t31_ordinal1]) ).
fof(c_0_6,plain,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[d3_ordinal1]) ).
fof(c_0_7,negated_conjecture,
! [X558] :
( ( ordinal(X558)
| ~ in(X558,esk85_0) )
& ( subset(X558,esk85_0)
| ~ in(X558,esk85_0) )
& ~ ordinal(esk85_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_5])])])])]) ).
fof(c_0_8,plain,
! [X146,X147,X148] :
( ( ~ epsilon_transitive(X146)
| ~ in(X147,X146)
| subset(X147,X146) )
& ( in(esk27_1(X148),X148)
| epsilon_transitive(X148) )
& ( ~ subset(esk27_1(X148),X148)
| epsilon_transitive(X148) ) ),
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_ordinal1])])])])])]) ).
fof(c_0_9,lemma,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[t24_ordinal1]) ).
fof(c_0_10,plain,
! [X195,X196,X197,X198] :
( ( ~ epsilon_connected(X195)
| ~ in(X196,X195)
| ~ in(X197,X195)
| in(X196,X197)
| X196 = X197
| in(X197,X196) )
& ( in(esk37_1(X198),X198)
| epsilon_connected(X198) )
& ( in(esk38_1(X198),X198)
| epsilon_connected(X198) )
& ( ~ in(esk37_1(X198),esk38_1(X198))
| epsilon_connected(X198) )
& ( esk37_1(X198) != esk38_1(X198)
| epsilon_connected(X198) )
& ( ~ in(esk38_1(X198),esk37_1(X198))
| epsilon_connected(X198) ) ),
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)],[c_0_6])])])])])]) ).
fof(c_0_11,plain,
! [X15] :
( ~ epsilon_transitive(X15)
| ~ epsilon_connected(X15)
| ordinal(X15) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
cnf(c_0_12,negated_conjecture,
( subset(X1,esk85_0)
| ~ in(X1,esk85_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( in(esk27_1(X1),X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( epsilon_transitive(X1)
| ~ subset(esk27_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_15,lemma,
! [X538,X539] :
( ~ ordinal(X538)
| ~ ordinal(X539)
| in(X538,X539)
| X538 = X539
| in(X539,X538) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_16,negated_conjecture,
( ordinal(X1)
| ~ in(X1,esk85_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,plain,
( in(esk37_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
epsilon_transitive(esk85_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_20,negated_conjecture,
~ ordinal(esk85_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,plain,
( in(esk38_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,plain,
( epsilon_connected(X1)
| ~ in(esk38_1(X1),esk37_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,lemma,
( in(X1,X2)
| X1 = X2
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( epsilon_connected(X1)
| ~ in(esk37_1(X1),esk38_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,plain,
( epsilon_connected(X1)
| esk37_1(X1) != esk38_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
( epsilon_connected(esk85_0)
| ordinal(esk37_1(esk85_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_27,negated_conjecture,
~ epsilon_connected(esk85_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( epsilon_connected(esk85_0)
| ordinal(esk38_1(esk85_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_29,lemma,
( epsilon_connected(X1)
| ~ ordinal(esk37_1(X1))
| ~ ordinal(esk38_1(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_30,negated_conjecture,
ordinal(esk37_1(esk85_0)),
inference(sr,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
ordinal(esk38_1(esk85_0)),
inference(sr,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU234+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
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 18:15:51 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.60 start to proof: theBenchmark
% 29.08/29.17 % Version : CSE_E---1.5
% 29.08/29.17 % Problem : theBenchmark.p
% 29.08/29.17 % Proof found
% 29.08/29.17 % SZS status Theorem for theBenchmark.p
% 29.08/29.17 % SZS output start Proof
% See solution above
% 29.16/29.19 % Total time : 28.512000 s
% 29.16/29.19 % SZS output end Proof
% 29.16/29.19 % Total time : 28.521000 s
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