TSTP Solution File: SEU236+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU236+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 16:23:40 EDT 2023
% Result : Theorem 26.05s 26.12s
% Output : CNFRefutation 26.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 165
% Syntax : Number of formulae : 239 ( 28 unt; 147 typ; 0 def)
% Number of atoms : 291 ( 56 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 316 ( 117 ~; 130 |; 39 &)
% ( 10 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 276 ( 132 >; 144 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 132 ( 132 usr; 15 con; 0-5 aty)
% Number of variables : 133 ( 2 sgn; 86 !; 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,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_44,type,
unordered_triple: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
succ: $i > $i ).
tff(decl_46,type,
singleton: $i > $i ).
tff(decl_47,type,
empty_set: $i ).
tff(decl_48,type,
set_meet: $i > $i ).
tff(decl_49,type,
powerset: $i > $i ).
tff(decl_50,type,
element: ( $i * $i ) > $o ).
tff(decl_51,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_52,type,
cast_to_subset: $i > $i ).
tff(decl_53,type,
union: $i > $i ).
tff(decl_54,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_55,type,
relation_rng: $i > $i ).
tff(decl_56,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_57,type,
relation_field: $i > $i ).
tff(decl_58,type,
relation_inverse: $i > $i ).
tff(decl_59,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_60,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_61,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_62,type,
function_inverse: $i > $i ).
tff(decl_63,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_64,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_65,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
relation_empty_yielding: $i > $o ).
tff(decl_67,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_68,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk5_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_73,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
esk11_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_79,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_82,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
esk17_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_85,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_86,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_87,type,
esk20_1: $i > $i ).
tff(decl_88,type,
esk21_3: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_90,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_91,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_92,type,
esk25_1: $i > $i ).
tff(decl_93,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_94,type,
esk27_1: $i > $i ).
tff(decl_95,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_96,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_97,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_99,type,
esk32_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_100,type,
esk33_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_101,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_102,type,
esk35_3: ( $i * $i * $i ) > $i ).
tff(decl_103,type,
esk36_3: ( $i * $i * $i ) > $i ).
tff(decl_104,type,
esk37_1: $i > $i ).
tff(decl_105,type,
esk38_1: $i > $i ).
tff(decl_106,type,
esk39_2: ( $i * $i ) > $i ).
tff(decl_107,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_108,type,
esk41_2: ( $i * $i ) > $i ).
tff(decl_109,type,
esk42_3: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
esk43_3: ( $i * $i * $i ) > $i ).
tff(decl_111,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_112,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_113,type,
esk46_3: ( $i * $i * $i ) > $i ).
tff(decl_114,type,
esk47_2: ( $i * $i ) > $i ).
tff(decl_115,type,
esk48_2: ( $i * $i ) > $i ).
tff(decl_116,type,
esk49_3: ( $i * $i * $i ) > $i ).
tff(decl_117,type,
esk50_3: ( $i * $i * $i ) > $i ).
tff(decl_118,type,
esk51_2: ( $i * $i ) > $i ).
tff(decl_119,type,
esk52_2: ( $i * $i ) > $i ).
tff(decl_120,type,
esk53_3: ( $i * $i * $i ) > $i ).
tff(decl_121,type,
esk54_2: ( $i * $i ) > $i ).
tff(decl_122,type,
esk55_2: ( $i * $i ) > $i ).
tff(decl_123,type,
esk56_2: ( $i * $i ) > $i ).
tff(decl_124,type,
esk57_2: ( $i * $i ) > $i ).
tff(decl_125,type,
esk58_1: $i > $i ).
tff(decl_126,type,
esk59_1: $i > $i ).
tff(decl_127,type,
esk60_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_128,type,
esk61_3: ( $i * $i * $i ) > $i ).
tff(decl_129,type,
esk62_3: ( $i * $i * $i ) > $i ).
tff(decl_130,type,
esk63_3: ( $i * $i * $i ) > $i ).
tff(decl_131,type,
esk64_3: ( $i * $i * $i ) > $i ).
tff(decl_132,type,
esk65_1: $i > $i ).
tff(decl_133,type,
esk66_2: ( $i * $i ) > $i ).
tff(decl_134,type,
esk67_0: $i ).
tff(decl_135,type,
esk68_0: $i ).
tff(decl_136,type,
esk69_0: $i ).
tff(decl_137,type,
esk70_1: $i > $i ).
tff(decl_138,type,
esk71_0: $i ).
tff(decl_139,type,
esk72_0: $i ).
tff(decl_140,type,
esk73_0: $i ).
tff(decl_141,type,
esk74_0: $i ).
tff(decl_142,type,
esk75_1: $i > $i ).
tff(decl_143,type,
esk76_0: $i ).
tff(decl_144,type,
esk77_0: $i ).
tff(decl_145,type,
esk78_0: $i ).
tff(decl_146,type,
esk79_0: $i ).
tff(decl_147,type,
esk80_0: $i ).
tff(decl_148,type,
esk81_1: $i > $i ).
tff(decl_149,type,
esk82_3: ( $i * $i * $i ) > $i ).
tff(decl_150,type,
esk83_3: ( $i * $i * $i ) > $i ).
tff(decl_151,type,
esk84_2: ( $i * $i ) > $i ).
tff(decl_152,type,
esk85_1: $i > $i ).
tff(decl_153,type,
esk86_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk87_0: $i ).
tff(decl_155,type,
esk88_0: $i ).
tff(decl_156,type,
esk89_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk90_2: ( $i * $i ) > $i ).
tff(decl_158,type,
esk91_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk92_2: ( $i * $i ) > $i ).
tff(decl_160,type,
esk93_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk94_2: ( $i * $i ) > $i ).
tff(decl_162,type,
esk95_2: ( $i * $i ) > $i ).
tff(decl_163,type,
esk96_1: $i > $i ).
tff(decl_164,type,
esk97_1: $i > $i ).
tff(decl_165,type,
esk98_3: ( $i * $i * $i ) > $i ).
tff(decl_166,type,
esk99_2: ( $i * $i ) > $i ).
tff(decl_167,type,
esk100_1: $i > $i ).
tff(decl_168,type,
esk101_2: ( $i * $i ) > $i ).
fof(t33_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_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(fc3_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
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(t10_ordinal1,lemma,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(connectedness_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(t21_ordinal1,lemma,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
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(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(t32_ordinal1,lemma,
! [X1,X2] :
( ordinal(X2)
=> ~ ( subset(X1,X2)
& X1 != empty_set
& ! [X3] :
( ordinal(X3)
=> ~ ( in(X3,X1)
& ! [X4] :
( ordinal(X4)
=> ( in(X4,X1)
=> ordinal_subset(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
fof(reflexivity_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ordinal_subset(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(c_0_18,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
inference(assume_negation,[status(cth)],[t33_ordinal1]) ).
fof(c_0_19,plain,
! [X108] : succ(X108) = set_union2(X108,singleton(X108)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_20,lemma,
! [X687] : unordered_pair(X687,X687) = singleton(X687),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_21,negated_conjecture,
( ordinal(esk87_0)
& ordinal(esk88_0)
& ( ~ in(esk87_0,esk88_0)
| ~ ordinal_subset(succ(esk87_0),esk88_0) )
& ( in(esk87_0,esk88_0)
| ordinal_subset(succ(esk87_0),esk88_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_22,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc3_ordinal1]) ).
fof(c_0_25,plain,
! [X442,X443] :
( ( ~ ordinal_subset(X442,X443)
| subset(X442,X443)
| ~ ordinal(X442)
| ~ ordinal(X443) )
& ( ~ subset(X442,X443)
| ordinal_subset(X442,X443)
| ~ ordinal(X442)
| ~ ordinal(X443) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(c_0_26,negated_conjecture,
( in(esk87_0,esk88_0)
| ordinal_subset(succ(esk87_0),esk88_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
succ(X1) = set_union2(X1,unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_28,plain,
! [X363] :
( ( ~ empty(succ(X363))
| ~ ordinal(X363) )
& ( epsilon_transitive(succ(X363))
| ~ ordinal(X363) )
& ( epsilon_connected(succ(X363))
| ~ ordinal(X363) )
& ( ordinal(succ(X363))
| ~ ordinal(X363) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
cnf(c_0_29,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( in(esk87_0,esk88_0)
| ordinal_subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0) ),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
ordinal(esk88_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_33,plain,
! [X209,X210,X211,X212,X213] :
( ( ~ subset(X209,X210)
| ~ in(X211,X209)
| in(X211,X210) )
& ( in(esk41_2(X212,X213),X212)
| subset(X212,X213) )
& ( ~ in(esk41_2(X212,X213),X213)
| subset(X212,X213) ) ),
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])])])])])]) ).
cnf(c_0_34,negated_conjecture,
( subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0)
| in(esk87_0,esk88_0)
| ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,plain,
( ordinal(set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_36,negated_conjecture,
ordinal(esk87_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_37,lemma,
! [X453] : in(X453,succ(X453)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
cnf(c_0_38,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0)
| in(esk87_0,esk88_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_40,lemma,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( ~ in(esk87_0,esk88_0)
| ~ ordinal_subset(succ(esk87_0),esk88_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_42,negated_conjecture,
( in(esk87_0,esk88_0)
| in(X1,esk88_0)
| ~ in(X1,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,lemma,
in(X1,set_union2(X1,unordered_pair(X1,X1))),
inference(rw,[status(thm)],[c_0_40,c_0_27]) ).
cnf(c_0_44,negated_conjecture,
( ~ in(esk87_0,esk88_0)
| ~ ordinal_subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0) ),
inference(rw,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_45,lemma,
in(esk87_0,esk88_0),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_46,plain,
! [X23,X24] :
( ~ ordinal(X23)
| ~ ordinal(X24)
| ordinal_subset(X23,X24)
| ordinal_subset(X24,X23) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
cnf(c_0_47,negated_conjecture,
~ ordinal_subset(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)),esk88_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
cnf(c_0_48,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( ordinal_subset(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)))
| ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_31])]) ).
cnf(c_0_50,negated_conjecture,
ordinal_subset(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_35]),c_0_36])]) ).
fof(c_0_51,plain,
! [X317,X318] :
( ( subset(X317,X318)
| ~ proper_subset(X317,X318) )
& ( X317 != X318
| ~ proper_subset(X317,X318) )
& ( ~ subset(X317,X318)
| X317 = X318
| proper_subset(X317,X318) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
cnf(c_0_52,negated_conjecture,
( subset(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)))
| ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_50]),c_0_31])]) ).
fof(c_0_53,lemma,
! [X534,X535] :
( ~ epsilon_transitive(X534)
| ~ ordinal(X535)
| ~ proper_subset(X534,X535)
| in(X534,X535) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_ordinal1])])]) ).
cnf(c_0_54,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_55,negated_conjecture,
subset(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_35]),c_0_36])]) ).
cnf(c_0_56,lemma,
( in(X1,X2)
| ~ epsilon_transitive(X1)
| ~ ordinal(X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,negated_conjecture,
( set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)) = esk88_0
| proper_subset(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_58,plain,
! [X12] :
( ( epsilon_transitive(X12)
| ~ ordinal(X12) )
& ( epsilon_connected(X12)
| ~ ordinal(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(c_0_59,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(c_0_60,lemma,
! [X395,X396] :
( ( ~ subset(singleton(X395),X396)
| in(X395,X396) )
& ( ~ in(X395,X396)
| subset(singleton(X395),X396) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
fof(c_0_61,plain,
! [X171,X172,X173,X174,X175,X176,X177,X178] :
( ( ~ in(X174,X173)
| in(X174,X171)
| in(X174,X172)
| X173 != set_union2(X171,X172) )
& ( ~ in(X175,X171)
| in(X175,X173)
| X173 != set_union2(X171,X172) )
& ( ~ in(X175,X172)
| in(X175,X173)
| X173 != set_union2(X171,X172) )
& ( ~ in(esk31_3(X176,X177,X178),X176)
| ~ in(esk31_3(X176,X177,X178),X178)
| X178 = set_union2(X176,X177) )
& ( ~ in(esk31_3(X176,X177,X178),X177)
| ~ in(esk31_3(X176,X177,X178),X178)
| X178 = set_union2(X176,X177) )
& ( in(esk31_3(X176,X177,X178),X178)
| in(esk31_3(X176,X177,X178),X176)
| in(esk31_3(X176,X177,X178),X177)
| X178 = set_union2(X176,X177) ) ),
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])])])])])]) ).
cnf(c_0_62,lemma,
( set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)) = esk88_0
| in(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)))
| ~ epsilon_transitive(esk88_0)
| ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_64,plain,
! [X7,X8] :
( ~ in(X7,X8)
| ~ in(X8,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])]) ).
cnf(c_0_65,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_66,lemma,
! [X388] : singleton(X388) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_0_67,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_68,lemma,
( set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)) = esk88_0
| in(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)))
| ~ ordinal(set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_31])]) ).
cnf(c_0_69,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_70,lemma,
! [X566,X567,X569] :
( ( ordinal(esk86_2(X566,X567))
| ~ subset(X566,X567)
| X566 = empty_set
| ~ ordinal(X567) )
& ( in(esk86_2(X566,X567),X566)
| ~ subset(X566,X567)
| X566 = empty_set
| ~ ordinal(X567) )
& ( ~ ordinal(X569)
| ~ in(X569,X566)
| ordinal_subset(esk86_2(X566,X567),X569)
| ~ subset(X566,X567)
| X566 = empty_set
| ~ ordinal(X567) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t32_ordinal1])])])])]) ).
cnf(c_0_71,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_65,c_0_23]) ).
cnf(c_0_72,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_73,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_67]) ).
cnf(c_0_74,lemma,
( set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)) = esk88_0
| in(esk88_0,set_union2(esk87_0,unordered_pair(esk87_0,esk87_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_35]),c_0_36])]) ).
cnf(c_0_75,lemma,
~ in(esk88_0,esk87_0),
inference(spm,[status(thm)],[c_0_69,c_0_45]) ).
fof(c_0_76,plain,
! [X444,X445] :
( ~ ordinal(X444)
| ~ ordinal(X445)
| ordinal_subset(X444,X444) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1])]) ).
cnf(c_0_77,lemma,
( ordinal(esk86_2(X1,X2))
| X1 = empty_set
| ~ subset(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_78,lemma,
subset(unordered_pair(esk87_0,esk87_0),esk88_0),
inference(spm,[status(thm)],[c_0_71,c_0_45]) ).
cnf(c_0_79,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[c_0_72,c_0_23]) ).
fof(c_0_80,plain,
! [X162,X163,X164,X165,X166,X167,X168,X169] :
( ( ~ in(X165,X164)
| X165 = X162
| X165 = X163
| X164 != unordered_pair(X162,X163) )
& ( X166 != X162
| in(X166,X164)
| X164 != unordered_pair(X162,X163) )
& ( X166 != X163
| in(X166,X164)
| X164 != unordered_pair(X162,X163) )
& ( esk30_3(X167,X168,X169) != X167
| ~ in(esk30_3(X167,X168,X169),X169)
| X169 = unordered_pair(X167,X168) )
& ( esk30_3(X167,X168,X169) != X168
| ~ in(esk30_3(X167,X168,X169),X169)
| X169 = unordered_pair(X167,X168) )
& ( in(esk30_3(X167,X168,X169),X169)
| esk30_3(X167,X168,X169) = X167
| esk30_3(X167,X168,X169) = X168
| X169 = unordered_pair(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_tarski])])])])])]) ).
cnf(c_0_81,lemma,
( set_union2(esk87_0,unordered_pair(esk87_0,esk87_0)) = esk88_0
| in(esk88_0,unordered_pair(esk87_0,esk87_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_82,plain,
( ordinal_subset(X1,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_83,lemma,
ordinal(esk86_2(unordered_pair(esk87_0,esk87_0),esk88_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_31])]),c_0_79]) ).
cnf(c_0_84,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_85,negated_conjecture,
( in(esk88_0,unordered_pair(esk87_0,esk87_0))
| ~ ordinal_subset(esk88_0,esk88_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_81]) ).
cnf(c_0_86,lemma,
( ordinal_subset(X1,X1)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_84]) ).
cnf(c_0_88,lemma,
in(esk88_0,unordered_pair(esk87_0,esk87_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_31])]) ).
cnf(c_0_89,lemma,
esk88_0 = esk87_0,
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_90,lemma,
in(esk87_0,esk87_0),
inference(rw,[status(thm)],[c_0_45,c_0_89]) ).
cnf(c_0_91,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_90]),c_0_90])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU236+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
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 20:39:18 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 26.05/26.12 % Version : CSE_E---1.5
% 26.05/26.12 % Problem : theBenchmark.p
% 26.05/26.12 % Proof found
% 26.05/26.12 % SZS status Theorem for theBenchmark.p
% 26.05/26.12 % SZS output start Proof
% See solution above
% 26.05/26.13 % Total time : 25.545000 s
% 26.05/26.13 % SZS output end Proof
% 26.05/26.14 % Total time : 25.554000 s
%------------------------------------------------------------------------------