TSTP Solution File: SEU215+2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU215+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 : n031.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 16:23:25 EDT 2023
% Result : Theorem 0.93s 1.00s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 118
% Syntax : Number of formulae : 144 ( 9 unt; 112 typ; 0 def)
% Number of atoms : 160 ( 23 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 207 ( 79 ~; 75 |; 29 &)
% ( 5 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 218 ( 102 >; 116 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 102 ( 102 usr; 10 con; 0-5 aty)
% Number of variables : 50 ( 0 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,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_29,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_30,type,
identity_relation: $i > $i ).
tff(decl_31,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
subset: ( $i * $i ) > $o ).
tff(decl_33,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff(decl_34,type,
relation_rng_restriction: ( $i * $i ) > $i ).
tff(decl_35,type,
relation_image: ( $i * $i ) > $i ).
tff(decl_36,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_37,type,
empty_set: $i ).
tff(decl_38,type,
set_meet: $i > $i ).
tff(decl_39,type,
singleton: $i > $i ).
tff(decl_40,type,
powerset: $i > $i ).
tff(decl_41,type,
element: ( $i * $i ) > $o ).
tff(decl_42,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_43,type,
relation_dom: $i > $i ).
tff(decl_44,type,
apply: ( $i * $i ) > $i ).
tff(decl_45,type,
cast_to_subset: $i > $i ).
tff(decl_46,type,
union: $i > $i ).
tff(decl_47,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_48,type,
relation_rng: $i > $i ).
tff(decl_49,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_50,type,
relation_field: $i > $i ).
tff(decl_51,type,
relation_inverse: $i > $i ).
tff(decl_52,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_53,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_54,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff(decl_55,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(decl_56,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(decl_57,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
relation_empty_yielding: $i > $o ).
tff(decl_59,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_60,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
esk7_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_67,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
esk10_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_70,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_73,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk15_1: $i > $i ).
tff(decl_75,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_77,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_78,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_79,type,
esk20_1: $i > $i ).
tff(decl_80,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_81,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_82,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_83,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
esk26_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_86,type,
esk27_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_91,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_92,type,
esk33_2: ( $i * $i ) > $i ).
tff(decl_93,type,
esk34_3: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
esk35_3: ( $i * $i * $i ) > $i ).
tff(decl_95,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_96,type,
esk37_2: ( $i * $i ) > $i ).
tff(decl_97,type,
esk38_3: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
esk39_2: ( $i * $i ) > $i ).
tff(decl_99,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_100,type,
esk41_3: ( $i * $i * $i ) > $i ).
tff(decl_101,type,
esk42_3: ( $i * $i * $i ) > $i ).
tff(decl_102,type,
esk43_2: ( $i * $i ) > $i ).
tff(decl_103,type,
esk44_2: ( $i * $i ) > $i ).
tff(decl_104,type,
esk45_2: ( $i * $i ) > $i ).
tff(decl_105,type,
esk46_2: ( $i * $i ) > $i ).
tff(decl_106,type,
esk47_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_107,type,
esk48_3: ( $i * $i * $i ) > $i ).
tff(decl_108,type,
esk49_3: ( $i * $i * $i ) > $i ).
tff(decl_109,type,
esk50_3: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
esk51_3: ( $i * $i * $i ) > $i ).
tff(decl_111,type,
esk52_1: $i > $i ).
tff(decl_112,type,
esk53_2: ( $i * $i ) > $i ).
tff(decl_113,type,
esk54_0: $i ).
tff(decl_114,type,
esk55_0: $i ).
tff(decl_115,type,
esk56_1: $i > $i ).
tff(decl_116,type,
esk57_0: $i ).
tff(decl_117,type,
esk58_0: $i ).
tff(decl_118,type,
esk59_1: $i > $i ).
tff(decl_119,type,
esk60_0: $i ).
tff(decl_120,type,
esk61_0: $i ).
tff(decl_121,type,
esk62_1: $i > $i ).
tff(decl_122,type,
esk63_3: ( $i * $i * $i ) > $i ).
tff(decl_123,type,
esk64_3: ( $i * $i * $i ) > $i ).
tff(decl_124,type,
esk65_0: $i ).
tff(decl_125,type,
esk66_0: $i ).
tff(decl_126,type,
esk67_0: $i ).
tff(decl_127,type,
esk68_2: ( $i * $i ) > $i ).
tff(decl_128,type,
esk69_2: ( $i * $i ) > $i ).
tff(decl_129,type,
esk70_2: ( $i * $i ) > $i ).
tff(decl_130,type,
esk71_1: $i > $i ).
tff(decl_131,type,
esk72_1: $i > $i ).
tff(decl_132,type,
esk73_1: $i > $i ).
tff(decl_133,type,
esk74_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(t23_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(t22_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
fof(t21_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(fc1_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_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] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
inference(assume_negation,[status(cth)],[t23_funct_1]) ).
fof(c_0_8,plain,
! [X176,X177,X178] :
( ( X178 != apply(X176,X177)
| in(ordered_pair(X177,X178),X176)
| ~ in(X177,relation_dom(X176))
| ~ relation(X176)
| ~ function(X176) )
& ( ~ in(ordered_pair(X177,X178),X176)
| X178 = apply(X176,X177)
| ~ in(X177,relation_dom(X176))
| ~ relation(X176)
| ~ function(X176) )
& ( X178 != apply(X176,X177)
| X178 = empty_set
| in(X177,relation_dom(X176))
| ~ relation(X176)
| ~ function(X176) )
& ( X178 != empty_set
| X178 = apply(X176,X177)
| in(X177,relation_dom(X176))
| ~ relation(X176)
| ~ function(X176) ) ),
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(esk66_0)
& function(esk66_0)
& relation(esk67_0)
& function(esk67_0)
& in(esk65_0,relation_dom(esk66_0))
& apply(relation_composition(esk66_0,esk67_0),esk65_0) != apply(esk67_0,apply(esk66_0,esk65_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_10,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]) ).
fof(c_0_11,lemma,
! [X438,X439,X440] :
( ~ relation(X439)
| ~ function(X439)
| ~ relation(X440)
| ~ function(X440)
| ~ in(X438,relation_dom(relation_composition(X440,X439)))
| apply(relation_composition(X440,X439),X438) = apply(X439,apply(X440,X438)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_funct_1])])]) ).
cnf(c_0_12,negated_conjecture,
apply(relation_composition(esk66_0,esk67_0),esk65_0) != apply(esk67_0,apply(esk66_0,esk65_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( apply(X1,X2) = empty_set
| in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk67_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
function(esk67_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,lemma,
( apply(relation_composition(X2,X1),X3) = apply(X1,apply(X2,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
relation(esk66_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
function(esk66_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_19,lemma,
! [X434,X435,X436] :
( ( in(X434,relation_dom(X436))
| ~ in(X434,relation_dom(relation_composition(X436,X435)))
| ~ relation(X436)
| ~ function(X436)
| ~ relation(X435)
| ~ function(X435) )
& ( in(apply(X436,X434),relation_dom(X435))
| ~ in(X434,relation_dom(relation_composition(X436,X435)))
| ~ relation(X436)
| ~ function(X436)
| ~ relation(X435)
| ~ function(X435) )
& ( ~ in(X434,relation_dom(X436))
| ~ in(apply(X436,X434),relation_dom(X435))
| in(X434,relation_dom(relation_composition(X436,X435)))
| ~ relation(X436)
| ~ function(X436)
| ~ relation(X435)
| ~ function(X435) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])]) ).
cnf(c_0_20,negated_conjecture,
( in(apply(esk66_0,esk65_0),relation_dom(esk67_0))
| apply(relation_composition(esk66_0,esk67_0),esk65_0) != empty_set ),
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])]) ).
cnf(c_0_21,negated_conjecture,
~ in(esk65_0,relation_dom(relation_composition(esk66_0,esk67_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_17]),c_0_14]),c_0_18]),c_0_15])]) ).
cnf(c_0_22,lemma,
( in(X1,relation_dom(relation_composition(X2,X3)))
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),relation_dom(X3))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( in(apply(esk66_0,esk65_0),relation_dom(esk67_0))
| ~ relation(relation_composition(esk66_0,esk67_0))
| ~ function(relation_composition(esk66_0,esk67_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_13]),c_0_21]) ).
cnf(c_0_24,negated_conjecture,
in(esk65_0,relation_dom(esk66_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_25,plain,
! [X279,X280] :
( ( relation(relation_composition(X279,X280))
| ~ relation(X279)
| ~ function(X279)
| ~ relation(X280)
| ~ function(X280) )
& ( function(relation_composition(X279,X280))
| ~ relation(X279)
| ~ function(X279)
| ~ relation(X280)
| ~ function(X280) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
cnf(c_0_26,lemma,
( ~ relation(relation_composition(esk66_0,esk67_0))
| ~ function(relation_composition(esk66_0,esk67_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]),c_0_17]),c_0_15]),c_0_18]),c_0_24])]),c_0_21]) ).
cnf(c_0_27,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_28,plain,
! [X259,X260] :
( ~ relation(X259)
| ~ relation(X260)
| relation(relation_composition(X259,X260)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
cnf(c_0_29,lemma,
~ relation(relation_composition(esk66_0,esk67_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_14]),c_0_17]),c_0_15]),c_0_18])]) ).
cnf(c_0_30,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_14]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.16/0.19 % Problem : SEU215+2 : TPTP v8.1.2. Released v3.3.0.
% 0.16/0.20 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.19/0.43 % Computer : n031.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8042.1875MB
% 0.19/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Wed Aug 23 18:05:20 EDT 2023
% 0.27/0.44 % CPUTime :
% 0.29/0.72 start to proof: theBenchmark
% 0.93/1.00 % Version : CSE_E---1.5
% 0.93/1.00 % Problem : theBenchmark.p
% 0.93/1.00 % Proof found
% 0.93/1.00 % SZS status Theorem for theBenchmark.p
% 0.93/1.00 % SZS output start Proof
% See solution above
% 0.93/1.01 % Total time : 0.269000 s
% 0.93/1.01 % SZS output end Proof
% 0.93/1.01 % Total time : 0.276000 s
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