TSTP Solution File: SEU225+2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU225+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 : n024.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 16:23:32 EDT 2023
% Result : Theorem 0.77s 0.85s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 130
% Syntax : Number of formulae : 154 ( 8 unt; 124 typ; 0 def)
% Number of atoms : 119 ( 25 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 145 ( 56 ~; 50 |; 19 &)
% ( 5 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 235 ( 112 >; 123 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 113 ( 113 usr; 12 con; 0-5 aty)
% Number of variables : 50 ( 2 sgn; 35 !; 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_rng_restriction: ( $i * $i ) > $i ).
tff(decl_36,type,
relation_image: ( $i * $i ) > $i ).
tff(decl_37,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_38,type,
empty_set: $i ).
tff(decl_39,type,
set_meet: $i > $i ).
tff(decl_40,type,
singleton: $i > $i ).
tff(decl_41,type,
powerset: $i > $i ).
tff(decl_42,type,
element: ( $i * $i ) > $o ).
tff(decl_43,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_44,type,
relation_dom: $i > $i ).
tff(decl_45,type,
apply: ( $i * $i ) > $i ).
tff(decl_46,type,
cast_to_subset: $i > $i ).
tff(decl_47,type,
union: $i > $i ).
tff(decl_48,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_49,type,
relation_rng: $i > $i ).
tff(decl_50,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_51,type,
relation_field: $i > $i ).
tff(decl_52,type,
relation_inverse: $i > $i ).
tff(decl_53,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_54,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_55,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_56,type,
function_inverse: $i > $i ).
tff(decl_57,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_58,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_59,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_60,type,
relation_empty_yielding: $i > $o ).
tff(decl_61,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_62,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
esk7_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_69,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk10_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_72,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_76,type,
esk15_1: $i > $i ).
tff(decl_77,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_79,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_80,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_81,type,
esk20_1: $i > $i ).
tff(decl_82,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_83,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_84,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_85,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
esk26_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
esk27_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_89,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_92,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_93,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_94,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_95,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
esk35_3: ( $i * $i * $i ) > $i ).
tff(decl_97,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_98,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_99,type,
esk38_3: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
esk39_2: ( $i * $i ) > $i ).
tff(decl_101,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_102,type,
esk41_3: ( $i * $i * $i ) > $i ).
tff(decl_103,type,
esk42_3: ( $i * $i * $i ) > $i ).
tff(decl_104,type,
esk43_2: ( $i * $i ) > $i ).
tff(decl_105,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_106,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_107,type,
esk46_2: ( $i * $i ) > $i ).
tff(decl_108,type,
esk47_1: $i > $i ).
tff(decl_109,type,
esk48_1: $i > $i ).
tff(decl_110,type,
esk49_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_111,type,
esk50_3: ( $i * $i * $i ) > $i ).
tff(decl_112,type,
esk51_3: ( $i * $i * $i ) > $i ).
tff(decl_113,type,
esk52_3: ( $i * $i * $i ) > $i ).
tff(decl_114,type,
esk53_3: ( $i * $i * $i ) > $i ).
tff(decl_115,type,
esk54_1: $i > $i ).
tff(decl_116,type,
esk55_2: ( $i * $i ) > $i ).
tff(decl_117,type,
esk56_0: $i ).
tff(decl_118,type,
esk57_0: $i ).
tff(decl_119,type,
esk58_1: $i > $i ).
tff(decl_120,type,
esk59_0: $i ).
tff(decl_121,type,
esk60_0: $i ).
tff(decl_122,type,
esk61_0: $i ).
tff(decl_123,type,
esk62_1: $i > $i ).
tff(decl_124,type,
esk63_0: $i ).
tff(decl_125,type,
esk64_0: $i ).
tff(decl_126,type,
esk65_0: $i ).
tff(decl_127,type,
esk66_1: $i > $i ).
tff(decl_128,type,
esk67_3: ( $i * $i * $i ) > $i ).
tff(decl_129,type,
esk68_3: ( $i * $i * $i ) > $i ).
tff(decl_130,type,
esk69_2: ( $i * $i ) > $i ).
tff(decl_131,type,
esk70_2: ( $i * $i ) > $i ).
tff(decl_132,type,
esk71_2: ( $i * $i ) > $i ).
tff(decl_133,type,
esk72_2: ( $i * $i ) > $i ).
tff(decl_134,type,
esk73_2: ( $i * $i ) > $i ).
tff(decl_135,type,
esk74_2: ( $i * $i ) > $i ).
tff(decl_136,type,
esk75_2: ( $i * $i ) > $i ).
tff(decl_137,type,
esk76_2: ( $i * $i ) > $i ).
tff(decl_138,type,
esk77_1: $i > $i ).
tff(decl_139,type,
esk78_1: $i > $i ).
tff(decl_140,type,
esk79_3: ( $i * $i * $i ) > $i ).
tff(decl_141,type,
esk80_0: $i ).
tff(decl_142,type,
esk81_0: $i ).
tff(decl_143,type,
esk82_0: $i ).
tff(decl_144,type,
esk83_1: $i > $i ).
tff(decl_145,type,
esk84_2: ( $i * $i ) > $i ).
fof(d4_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(t72_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
fof(t70_funct_1,lemma,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
fof(fc4_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(t86_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,X2)
& in(X1,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
fof(c_0_6,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
inference(assume_negation,[status(cth)],[t72_funct_1]) ).
fof(c_0_8,plain,
! [X177,X178,X179] :
( ( X179 != apply(X177,X178)
| in(ordered_pair(X178,X179),X177)
| ~ in(X178,relation_dom(X177))
| ~ relation(X177)
| ~ function(X177) )
& ( ~ in(ordered_pair(X178,X179),X177)
| X179 = apply(X177,X178)
| ~ in(X178,relation_dom(X177))
| ~ relation(X177)
| ~ function(X177) )
& ( X179 != apply(X177,X178)
| X179 = empty_set
| in(X178,relation_dom(X177))
| ~ relation(X177)
| ~ function(X177) )
& ( X179 != empty_set
| X179 = apply(X177,X178)
| in(X178,relation_dom(X177))
| ~ relation(X177)
| ~ function(X177) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,negated_conjecture,
( relation(esk82_0)
& function(esk82_0)
& in(esk81_0,esk80_0)
& apply(relation_dom_restriction(esk82_0,esk80_0),esk81_0) != apply(esk82_0,esk81_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,lemma,
! [X597,X598,X599] :
( ~ relation(X599)
| ~ function(X599)
| ~ in(X598,relation_dom(relation_dom_restriction(X599,X597)))
| apply(relation_dom_restriction(X599,X597),X598) = apply(X599,X598) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t70_funct_1])]) ).
cnf(c_0_11,plain,
( X1 = empty_set
| in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
apply(relation_dom_restriction(esk82_0,esk80_0),esk81_0) != apply(esk82_0,esk81_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,lemma,
( apply(relation_dom_restriction(X1,X3),X2) = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_dom_restriction(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
function(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( apply(X1,X2) = empty_set
| in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
~ in(esk81_0,relation_dom(relation_dom_restriction(esk82_0,esk80_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
fof(c_0_18,plain,
! [X308,X309] :
( ( relation(relation_dom_restriction(X308,X309))
| ~ relation(X308)
| ~ function(X308) )
& ( function(relation_dom_restriction(X308,X309))
| ~ relation(X308)
| ~ function(X308) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
cnf(c_0_19,negated_conjecture,
( apply(esk82_0,esk81_0) != empty_set
| ~ relation(relation_dom_restriction(esk82_0,esk80_0))
| ~ function(relation_dom_restriction(esk82_0,esk80_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_17]) ).
cnf(c_0_20,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X277,X278] :
( ~ relation(X277)
| relation(relation_dom_restriction(X277,X278)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
fof(c_0_22,lemma,
! [X614,X615,X616] :
( ( in(X614,X615)
| ~ in(X614,relation_dom(relation_dom_restriction(X616,X615)))
| ~ relation(X616) )
& ( in(X614,relation_dom(X616))
| ~ in(X614,relation_dom(relation_dom_restriction(X616,X615)))
| ~ relation(X616) )
& ( ~ in(X614,X615)
| ~ in(X614,relation_dom(X616))
| in(X614,relation_dom(relation_dom_restriction(X616,X615)))
| ~ relation(X616) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t86_relat_1])])]) ).
cnf(c_0_23,negated_conjecture,
( apply(esk82_0,esk81_0) != empty_set
| ~ relation(relation_dom_restriction(esk82_0,esk80_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_14]),c_0_15])]) ).
cnf(c_0_24,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,lemma,
( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
| ~ in(X1,X2)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
in(esk81_0,esk80_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
apply(esk82_0,esk81_0) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_14])]) ).
cnf(c_0_28,lemma,
~ in(esk81_0,relation_dom(esk82_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_25]),c_0_14]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_16]),c_0_14]),c_0_15])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.15 % Problem : SEU225+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.16 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.36 % Computer : n024.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Wed Aug 23 17:20:55 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.22/0.56 start to proof: theBenchmark
% 0.77/0.85 % Version : CSE_E---1.5
% 0.77/0.85 % Problem : theBenchmark.p
% 0.77/0.85 % Proof found
% 0.77/0.85 % SZS status Theorem for theBenchmark.p
% 0.77/0.85 % SZS output start Proof
% See solution above
% 0.77/0.86 % Total time : 0.278000 s
% 0.77/0.86 % SZS output end Proof
% 0.77/0.86 % Total time : 0.286000 s
%------------------------------------------------------------------------------