TSTP Solution File: SEU262+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU262+1 : 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 : n012.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 16:23:53 EDT 2023
% Result : Theorem 136.47s 136.52s
% Output : CNFRefutation 136.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 40
% Syntax : Number of formulae : 87 ( 11 unt; 30 typ; 0 def)
% Number of atoms : 164 ( 20 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 181 ( 74 ~; 78 |; 15 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 24 >; 21 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 6 con; 0-3 aty)
% Number of variables : 146 ( 15 sgn; 66 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_24,type,
powerset: $i > $i ).
tff(decl_25,type,
element: ( $i * $i ) > $o ).
tff(decl_26,type,
relation: $i > $o ).
tff(decl_27,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
subset: ( $i * $i ) > $o ).
tff(decl_29,type,
relation_dom: $i > $i ).
tff(decl_30,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_31,type,
relation_rng: $i > $i ).
tff(decl_32,type,
singleton: $i > $i ).
tff(decl_33,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_34,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
empty_set: $i ).
tff(decl_36,type,
empty: $i > $o ).
tff(decl_37,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk9_1: $i > $i ).
tff(decl_46,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk11_0: $i ).
tff(decl_48,type,
esk12_0: $i ).
tff(decl_49,type,
esk13_0: $i ).
tff(decl_50,type,
esk14_0: $i ).
tff(decl_51,type,
esk15_0: $i ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(t106_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t12_relset_1,conjecture,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(c_0_10,plain,
! [X70,X71] :
( ( ~ element(X70,powerset(X71))
| subset(X70,X71) )
& ( ~ subset(X70,X71)
| element(X70,powerset(X71)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_11,plain,
! [X40,X41,X42] :
( ~ relation_of2_as_subset(X42,X40,X41)
| element(X42,powerset(cartesian_product2(X40,X41))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_12,plain,
! [X59,X60,X61,X62] :
( ( in(X59,X61)
| ~ in(ordered_pair(X59,X60),cartesian_product2(X61,X62)) )
& ( in(X60,X62)
| ~ in(ordered_pair(X59,X60),cartesian_product2(X61,X62)) )
& ( ~ in(X59,X61)
| ~ in(X60,X62)
| in(ordered_pair(X59,X60),cartesian_product2(X61,X62)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
fof(c_0_13,plain,
! [X38,X39] : ordered_pair(X38,X39) = unordered_pair(unordered_pair(X38,X39),singleton(X38)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_14,plain,
! [X12,X13,X14,X15,X16] :
( ( ~ subset(X12,X13)
| ~ in(X14,X12)
| in(X14,X13) )
& ( in(esk1_2(X15,X16),X15)
| subset(X15,X16) )
& ( ~ in(esk1_2(X15,X16),X16)
| subset(X15,X16) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
inference(assume_negation,[status(cth)],[t12_relset_1]) ).
cnf(c_0_18,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X10,X11] : unordered_pair(X10,X11) = unordered_pair(X11,X10),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_21,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_23,negated_conjecture,
( relation_of2_as_subset(esk15_0,esk13_0,esk14_0)
& ( ~ subset(relation_dom(esk15_0),esk13_0)
| ~ subset(relation_rng(esk15_0),esk14_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_24,plain,
! [X18,X19,X20,X22,X23,X24,X26] :
( ( ~ in(X20,X19)
| in(ordered_pair(X20,esk2_3(X18,X19,X20)),X18)
| X19 != relation_dom(X18)
| ~ relation(X18) )
& ( ~ in(ordered_pair(X22,X23),X18)
| in(X22,X19)
| X19 != relation_dom(X18)
| ~ relation(X18) )
& ( ~ in(esk3_2(X18,X24),X24)
| ~ in(ordered_pair(esk3_2(X18,X24),X26),X18)
| X24 = relation_dom(X18)
| ~ relation(X18) )
& ( in(esk3_2(X18,X24),X24)
| in(ordered_pair(esk3_2(X18,X24),esk4_2(X18,X24)),X18)
| X24 = relation_dom(X18)
| ~ relation(X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_relat_1])])])])])]) ).
fof(c_0_25,plain,
! [X7,X8,X9] :
( ~ element(X9,powerset(cartesian_product2(X7,X8)))
| relation(X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
cnf(c_0_26,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( in(X1,cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(X4,X2,X3)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
relation_of2_as_subset(esk15_0,esk13_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( in(ordered_pair(X1,esk2_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_33,plain,
! [X28,X29,X30,X32,X33,X34,X36] :
( ( ~ in(X30,X29)
| in(ordered_pair(esk5_3(X28,X29,X30),X30),X28)
| X29 != relation_rng(X28)
| ~ relation(X28) )
& ( ~ in(ordered_pair(X33,X32),X28)
| in(X32,X29)
| X29 != relation_rng(X28)
| ~ relation(X28) )
& ( ~ in(esk6_2(X28,X34),X34)
| ~ in(ordered_pair(X36,esk6_2(X28,X34)),X28)
| X34 = relation_rng(X28)
| ~ relation(X28) )
& ( in(esk6_2(X28,X34),X34)
| in(ordered_pair(esk7_2(X28,X34),esk6_2(X28,X34)),X28)
| X34 = relation_rng(X28)
| ~ relation(X28) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_relat_1])])])])])]) ).
cnf(c_0_34,plain,
( in(X1,X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(X2,X4)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( in(X1,cartesian_product2(esk13_0,esk14_0))
| ~ in(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( in(unordered_pair(unordered_pair(X1,esk2_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_37,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_38,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_39,plain,
( in(ordered_pair(esk5_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( in(X1,esk13_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk15_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk2_3(X2,relation_dom(X2),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_27])]) ).
cnf(c_0_42,negated_conjecture,
relation(esk15_0),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_43,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_27]) ).
cnf(c_0_44,plain,
( in(unordered_pair(unordered_pair(esk5_3(X3,X2,X1),X1),singleton(esk5_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_39,c_0_19]) ).
cnf(c_0_45,negated_conjecture,
( in(X1,esk13_0)
| ~ in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_46,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_47,negated_conjecture,
( in(X1,esk14_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),esk15_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_35]) ).
cnf(c_0_48,plain,
( in(unordered_pair(unordered_pair(X1,esk5_3(X2,relation_rng(X2),X1)),singleton(esk5_3(X2,relation_rng(X2),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_rng(X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_27])]) ).
cnf(c_0_49,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_50,negated_conjecture,
( subset(relation_dom(esk15_0),X1)
| in(esk1_2(relation_dom(esk15_0),X1),esk13_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( in(X1,esk14_0)
| ~ in(X1,relation_rng(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_42])]) ).
cnf(c_0_52,negated_conjecture,
( ~ subset(relation_dom(esk15_0),esk13_0)
| ~ subset(relation_rng(esk15_0),esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_53,negated_conjecture,
subset(relation_dom(esk15_0),esk13_0),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( subset(relation_rng(esk15_0),X1)
| in(esk1_2(relation_rng(esk15_0),X1),esk14_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_46]) ).
cnf(c_0_55,negated_conjecture,
~ subset(relation_rng(esk15_0),esk14_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_54]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU262+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.31 % Computer : n012.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Aug 24 01:23:12 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.54 start to proof: theBenchmark
% 136.47/136.52 % Version : CSE_E---1.5
% 136.47/136.52 % Problem : theBenchmark.p
% 136.47/136.52 % Proof found
% 136.47/136.52 % SZS status Theorem for theBenchmark.p
% 136.47/136.52 % SZS output start Proof
% See solution above
% 136.47/136.53 % Total time : 135.952000 s
% 136.47/136.53 % SZS output end Proof
% 136.47/136.53 % Total time : 135.961000 s
%------------------------------------------------------------------------------