TSTP Solution File: SEU223+2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU223+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 : n006.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 16:23:30 EDT 2023
% Result : Theorem 0.74s 0.92s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 128
% Syntax : Number of formulae : 142 ( 5 unt; 124 typ; 0 def)
% Number of atoms : 82 ( 19 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 106 ( 42 ~; 40 |; 14 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 33 ( 3 sgn; 22 !; 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(t70_funct_1,conjecture,
! [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(t68_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_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(c_0_4,negated_conjecture,
~ ! [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) ) ),
inference(assume_negation,[status(cth)],[t70_funct_1]) ).
fof(c_0_5,lemma,
! [X585,X586,X587,X588] :
( ( relation_dom(X586) = set_intersection2(relation_dom(X587),X585)
| X586 != relation_dom_restriction(X587,X585)
| ~ relation(X587)
| ~ function(X587)
| ~ relation(X586)
| ~ function(X586) )
& ( ~ in(X588,relation_dom(X586))
| apply(X586,X588) = apply(X587,X588)
| X586 != relation_dom_restriction(X587,X585)
| ~ relation(X587)
| ~ function(X587)
| ~ relation(X586)
| ~ function(X586) )
& ( in(esk79_3(X585,X586,X587),relation_dom(X586))
| relation_dom(X586) != set_intersection2(relation_dom(X587),X585)
| X586 = relation_dom_restriction(X587,X585)
| ~ relation(X587)
| ~ function(X587)
| ~ relation(X586)
| ~ function(X586) )
& ( apply(X586,esk79_3(X585,X586,X587)) != apply(X587,esk79_3(X585,X586,X587))
| relation_dom(X586) != set_intersection2(relation_dom(X587),X585)
| X586 = relation_dom_restriction(X587,X585)
| ~ relation(X587)
| ~ function(X587)
| ~ relation(X586)
| ~ function(X586) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_funct_1])])])])]) ).
fof(c_0_6,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])])]) ).
fof(c_0_7,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_8,negated_conjecture,
( relation(esk82_0)
& function(esk82_0)
& in(esk81_0,relation_dom(relation_dom_restriction(esk82_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_4])])]) ).
cnf(c_0_9,lemma,
( apply(X2,X1) = apply(X3,X1)
| ~ in(X1,relation_dom(X2))
| X2 != relation_dom_restriction(X3,X4)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
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_8]) ).
cnf(c_0_13,lemma,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_9]),c_0_10]),c_0_11]) ).
cnf(c_0_14,negated_conjecture,
relation(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
function(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
in(esk81_0,relation_dom(relation_dom_restriction(esk82_0,esk80_0))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[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]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU223+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.35 % Computer : n006.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Wed Aug 23 15:15:23 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.17/0.58 start to proof: theBenchmark
% 0.74/0.92 % Version : CSE_E---1.5
% 0.74/0.92 % Problem : theBenchmark.p
% 0.74/0.92 % Proof found
% 0.74/0.92 % SZS status Theorem for theBenchmark.p
% 0.74/0.92 % SZS output start Proof
% See solution above
% 0.74/0.92 % Total time : 0.320000 s
% 0.74/0.92 % SZS output end Proof
% 0.74/0.92 % Total time : 0.325000 s
%------------------------------------------------------------------------------