TSTP Solution File: SEU098+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU098+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 16:22:25 EDT 2023
% Result : Theorem 0.68s 0.80s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 74
% Syntax : Number of formulae : 117 ( 16 unt; 62 typ; 0 def)
% Number of atoms : 140 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 53 ~; 52 |; 20 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 56 ( 38 >; 18 *; 0 +; 0 <<)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 24 con; 0-4 aty)
% Number of variables : 86 ( 4 sgn; 46 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
ordinal: $i > $o ).
tff(decl_24,type,
element: ( $i * $i ) > $o ).
tff(decl_25,type,
epsilon_transitive: $i > $o ).
tff(decl_26,type,
epsilon_connected: $i > $o ).
tff(decl_27,type,
empty: $i > $o ).
tff(decl_28,type,
finite: $i > $o ).
tff(decl_29,type,
function: $i > $o ).
tff(decl_30,type,
relation: $i > $o ).
tff(decl_31,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_32,type,
powerset: $i > $i ).
tff(decl_33,type,
natural: $i > $o ).
tff(decl_34,type,
one_to_one: $i > $o ).
tff(decl_35,type,
positive_rationals: $i ).
tff(decl_36,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_37,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
function_image: ( $i * $i * $i * $i ) > $i ).
tff(decl_39,type,
first_projection: ( $i * $i ) > $i ).
tff(decl_40,type,
first_projection_as_func_of: ( $i * $i ) > $i ).
tff(decl_41,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_42,type,
empty_set: $i ).
tff(decl_43,type,
relation_empty_yielding: $i > $o ).
tff(decl_44,type,
relation_image: ( $i * $i ) > $i ).
tff(decl_45,type,
transfinite_sequence: $i > $o ).
tff(decl_46,type,
relation_dom: $i > $i ).
tff(decl_47,type,
relation_non_empty: $i > $o ).
tff(decl_48,type,
relation_rng: $i > $i ).
tff(decl_49,type,
with_non_empty_elements: $i > $o ).
tff(decl_50,type,
function_yielding: $i > $o ).
tff(decl_51,type,
being_limit_ordinal: $i > $o ).
tff(decl_52,type,
ordinal_yielding: $i > $o ).
tff(decl_53,type,
subset: ( $i * $i ) > $o ).
tff(decl_54,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk2_1: $i > $i ).
tff(decl_56,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk4_0: $i ).
tff(decl_58,type,
esk5_0: $i ).
tff(decl_59,type,
esk6_0: $i ).
tff(decl_60,type,
esk7_0: $i ).
tff(decl_61,type,
esk8_0: $i ).
tff(decl_62,type,
esk9_0: $i ).
tff(decl_63,type,
esk10_0: $i ).
tff(decl_64,type,
esk11_1: $i > $i ).
tff(decl_65,type,
esk12_0: $i ).
tff(decl_66,type,
esk13_0: $i ).
tff(decl_67,type,
esk14_1: $i > $i ).
tff(decl_68,type,
esk15_0: $i ).
tff(decl_69,type,
esk16_0: $i ).
tff(decl_70,type,
esk17_0: $i ).
tff(decl_71,type,
esk18_0: $i ).
tff(decl_72,type,
esk19_1: $i > $i ).
tff(decl_73,type,
esk20_0: $i ).
tff(decl_74,type,
esk21_0: $i ).
tff(decl_75,type,
esk22_1: $i > $i ).
tff(decl_76,type,
esk23_0: $i ).
tff(decl_77,type,
esk24_0: $i ).
tff(decl_78,type,
esk25_0: $i ).
tff(decl_79,type,
esk26_1: $i > $i ).
tff(decl_80,type,
esk27_0: $i ).
tff(decl_81,type,
esk28_0: $i ).
tff(decl_82,type,
esk29_0: $i ).
tff(decl_83,type,
esk30_0: $i ).
fof(dt_k9_funct_3,axiom,
! [X1,X2] :
( function(first_projection_as_func_of(X1,X2))
& quasi_total(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1)
& relation_of2_as_subset(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funct_3) ).
fof(redefinition_k9_funct_3,axiom,
! [X1,X2] : first_projection_as_func_of(X1,X2) = first_projection(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_funct_3) ).
fof(t13_finset_1,axiom,
! [X1,X2] :
( ( subset(X1,X2)
& finite(X2) )
=> finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
fof(t21_relat_1,axiom,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(t29_finset_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
<=> finite(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(fc14_finset_1,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
fof(t26_finset_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
=> finite(relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
fof(t100_funct_3,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> function_image(cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1),first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_funct_3) ).
fof(redefinition_k2_funct_2,axiom,
! [X1,X2,X3,X4] :
( ( function(X3)
& quasi_total(X3,X1,X2)
& relation_of2(X3,X1,X2) )
=> function_image(X1,X2,X3,X4) = relation_image(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
fof(dt_k7_funct_3,axiom,
! [X1,X2] :
( relation(first_projection(X1,X2))
& function(first_projection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_3) ).
fof(fc13_finset_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& finite(X2) )
=> finite(relation_image(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
fof(c_0_12,plain,
! [X29,X30] :
( function(first_projection_as_func_of(X29,X30))
& quasi_total(first_projection_as_func_of(X29,X30),cartesian_product2(X29,X30),X29)
& relation_of2_as_subset(first_projection_as_func_of(X29,X30),cartesian_product2(X29,X30),X29) ),
inference(variable_rename,[status(thm)],[dt_k9_funct_3]) ).
fof(c_0_13,plain,
! [X90,X91] : first_projection_as_func_of(X90,X91) = first_projection(X90,X91),
inference(variable_rename,[status(thm)],[redefinition_k9_funct_3]) ).
fof(c_0_14,plain,
! [X97,X98] :
( ~ subset(X97,X98)
| ~ finite(X98)
| finite(X97) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_finset_1])]) ).
fof(c_0_15,plain,
! [X105] :
( ~ relation(X105)
| subset(X105,cartesian_product2(relation_dom(X105),relation_rng(X105))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_relat_1])]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
<=> finite(X1) ) ),
inference(assume_negation,[status(cth)],[t29_finset_1]) ).
fof(c_0_17,plain,
! [X92,X93,X94] :
( ( ~ relation_of2_as_subset(X94,X92,X93)
| relation_of2(X94,X92,X93) )
& ( ~ relation_of2(X94,X92,X93)
| relation_of2_as_subset(X94,X92,X93) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_18,plain,
relation_of2_as_subset(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
first_projection_as_func_of(X1,X2) = first_projection(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( finite(X1)
| ~ subset(X1,X2)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X44,X45] :
( ~ finite(X44)
| ~ finite(X45)
| finite(cartesian_product2(X44,X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc14_finset_1])]) ).
fof(c_0_23,plain,
! [X106] :
( ~ relation(X106)
| ~ function(X106)
| ~ finite(relation_dom(X106))
| finite(relation_rng(X106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_finset_1])]) ).
fof(c_0_24,negated_conjecture,
( relation(esk30_0)
& function(esk30_0)
& ( ~ finite(relation_dom(esk30_0))
| ~ finite(esk30_0) )
& ( finite(relation_dom(esk30_0))
| finite(esk30_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_25,plain,
! [X96] :
( ~ relation(X96)
| ~ function(X96)
| function_image(cartesian_product2(relation_dom(X96),relation_rng(X96)),relation_dom(X96),first_projection_as_func_of(relation_dom(X96),relation_rng(X96)),X96) = relation_dom(X96) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t100_funct_3])]) ).
fof(c_0_26,plain,
! [X86,X87,X88,X89] :
( ~ function(X88)
| ~ quasi_total(X88,X86,X87)
| ~ relation_of2(X88,X86,X87)
| function_image(X86,X87,X88,X89) = relation_image(X88,X89) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_funct_2])]) ).
cnf(c_0_27,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,plain,
relation_of2_as_subset(first_projection(X1,X2),cartesian_product2(X1,X2),X1),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_29,plain,
quasi_total(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_30,plain,
! [X27,X28] :
( relation(first_projection(X27,X28))
& function(first_projection(X27,X28)) ),
inference(variable_rename,[status(thm)],[dt_k7_funct_3]) ).
cnf(c_0_31,plain,
( finite(X1)
| ~ relation(X1)
| ~ finite(cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_32,plain,
( finite(cartesian_product2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
( finite(relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,negated_conjecture,
( finite(relation_dom(esk30_0))
| finite(esk30_0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,negated_conjecture,
relation(esk30_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_36,negated_conjecture,
function(esk30_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_37,plain,
( function_image(cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1),first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,plain,
( function_image(X2,X3,X1,X4) = relation_image(X1,X4)
| ~ function(X1)
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39,plain,
relation_of2(first_projection(X1,X2),cartesian_product2(X1,X2),X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_40,plain,
quasi_total(first_projection(X1,X2),cartesian_product2(X1,X2),X1),
inference(rw,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_41,plain,
function(first_projection(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,plain,
( finite(X1)
| ~ relation(X1)
| ~ finite(relation_rng(X1))
| ~ finite(relation_dom(X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_43,negated_conjecture,
( finite(relation_rng(esk30_0))
| finite(esk30_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]) ).
fof(c_0_44,plain,
! [X42,X43] :
( ~ relation(X42)
| ~ function(X42)
| ~ finite(X43)
| finite(relation_image(X42,X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc13_finset_1])]) ).
cnf(c_0_45,plain,
( function_image(cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1),first_projection(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_37,c_0_19]) ).
cnf(c_0_46,plain,
function_image(cartesian_product2(X1,X2),X1,first_projection(X1,X2),X3) = relation_image(first_projection(X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_47,negated_conjecture,
( ~ finite(relation_dom(esk30_0))
| ~ finite(esk30_0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_48,negated_conjecture,
finite(esk30_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_35])]),c_0_34]) ).
cnf(c_0_49,plain,
( finite(relation_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
( relation_image(first_projection(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
relation(first_projection(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_52,negated_conjecture,
~ finite(relation_dom(esk30_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_53,plain,
( finite(relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_41])]) ).
cnf(c_0_54,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_52,c_0_53]),c_0_35]),c_0_36]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU098+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 13:19:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.68/0.80 % Version : CSE_E---1.5
% 0.68/0.80 % Problem : theBenchmark.p
% 0.68/0.80 % Proof found
% 0.68/0.80 % SZS status Theorem for theBenchmark.p
% 0.68/0.80 % SZS output start Proof
% See solution above
% 0.68/0.81 % Total time : 0.220000 s
% 0.68/0.81 % SZS output end Proof
% 0.68/0.81 % Total time : 0.224000 s
%------------------------------------------------------------------------------