TSTP Solution File: SEU217+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU217+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 16:23:26 EDT 2023
% Result : Theorem 0.19s 0.76s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 116
% Syntax : Number of formulae : 128 ( 7 unt; 112 typ; 0 def)
% Number of atoms : 51 ( 20 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 59 ( 24 ~; 22 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 220 ( 103 >; 117 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 102 ( 102 usr; 9 con; 0-5 aty)
% Number of variables : 20 ( 2 sgn; 14 !; 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_2: ( $i * $i ) > $i ).
tff(decl_125,type,
esk66_2: ( $i * $i ) > $i ).
tff(decl_126,type,
esk67_0: $i ).
tff(decl_127,type,
esk68_0: $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(t35_funct_1,conjecture,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
fof(t34_funct_1,lemma,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
inference(assume_negation,[status(cth)],[t35_funct_1]) ).
fof(c_0_5,lemma,
! [X469,X470,X471] :
( ( relation_dom(X470) = X469
| X470 != identity_relation(X469)
| ~ relation(X470)
| ~ function(X470) )
& ( ~ in(X471,X469)
| apply(X470,X471) = X471
| X470 != identity_relation(X469)
| ~ relation(X470)
| ~ function(X470) )
& ( in(esk66_2(X469,X470),X469)
| relation_dom(X470) != X469
| X470 = identity_relation(X469)
| ~ relation(X470)
| ~ function(X470) )
& ( apply(X470,esk66_2(X469,X470)) != esk66_2(X469,X470)
| relation_dom(X470) != X469
| X470 = identity_relation(X469)
| ~ relation(X470)
| ~ function(X470) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
fof(c_0_6,negated_conjecture,
( in(esk68_0,esk67_0)
& apply(identity_relation(esk67_0),esk68_0) != esk68_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,lemma,
( apply(X3,X1) = X1
| ~ in(X1,X2)
| X3 != identity_relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
in(esk68_0,esk67_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X263] : relation(identity_relation(X263)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_10,plain,
! [X286] :
( relation(identity_relation(X286))
& function(identity_relation(X286)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
cnf(c_0_11,negated_conjecture,
apply(identity_relation(esk67_0),esk68_0) != esk68_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( apply(X1,esk68_0) = esk68_0
| X1 != identity_relation(esk67_0)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU217+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 13:32:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.19/0.76 % Version : CSE_E---1.5
% 0.19/0.76 % Problem : theBenchmark.p
% 0.19/0.76 % Proof found
% 0.19/0.76 % SZS status Theorem for theBenchmark.p
% 0.19/0.76 % SZS output start Proof
% See solution above
% 0.19/0.77 % Total time : 0.170000 s
% 0.19/0.77 % SZS output end Proof
% 0.19/0.77 % Total time : 0.177000 s
%------------------------------------------------------------------------------