TSTP Solution File: SEU170+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU170+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 : 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 16:23:02 EDT 2023
% Result : Theorem 36.85s 36.92s
% Output : CNFRefutation 36.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 60
% Syntax : Number of formulae : 110 ( 19 unt; 48 typ; 0 def)
% Number of atoms : 174 ( 24 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 179 ( 67 ~; 59 |; 29 &)
% ( 11 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 86 ( 42 >; 44 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 41 ( 41 usr; 6 con; 0-4 aty)
% Number of variables : 114 ( 5 sgn; 72 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_25,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_26,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_27,type,
subset: ( $i * $i ) > $o ).
tff(decl_28,type,
singleton: $i > $i ).
tff(decl_29,type,
empty_set: $i ).
tff(decl_30,type,
powerset: $i > $i ).
tff(decl_31,type,
empty: $i > $o ).
tff(decl_32,type,
element: ( $i * $i ) > $o ).
tff(decl_33,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_34,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_35,type,
union: $i > $i ).
tff(decl_36,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_37,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_38,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_39,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_40,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk2_1: $i > $i ).
tff(decl_42,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk6_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_46,type,
esk7_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_47,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
esk17_1: $i > $i ).
tff(decl_57,type,
esk18_1: $i > $i ).
tff(decl_58,type,
esk19_0: $i ).
tff(decl_59,type,
esk20_1: $i > $i ).
tff(decl_60,type,
esk21_0: $i ).
tff(decl_61,type,
esk22_1: $i > $i ).
tff(decl_62,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk25_0: $i ).
tff(decl_65,type,
esk26_0: $i ).
tff(decl_66,type,
esk27_0: $i ).
tff(decl_67,type,
esk28_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk29_1: $i > $i ).
tff(decl_69,type,
esk30_2: ( $i * $i ) > $i ).
fof(t43_subset_1,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(t3_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(t83_xboole_1,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(t63_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(l50_zfmisc_1,lemma,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(t99_zfmisc_1,lemma,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(t33_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
inference(assume_negation,[status(cth)],[t43_subset_1]) ).
fof(c_0_13,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_14,plain,
! [X109,X110] :
( ~ element(X110,powerset(X109))
| subset_complement(X109,X110) = set_difference(X109,X110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(c_0_15,negated_conjecture,
( element(esk26_0,powerset(esk25_0))
& element(esk27_0,powerset(esk25_0))
& ( ~ disjoint(esk26_0,esk27_0)
| ~ subset(esk26_0,subset_complement(esk25_0,esk27_0)) )
& ( disjoint(esk26_0,esk27_0)
| subset(esk26_0,subset_complement(esk25_0,esk27_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_16,plain,
! [X100,X101,X102,X103,X104,X105,X106,X107] :
( ( in(X103,X100)
| ~ in(X103,X102)
| X102 != set_difference(X100,X101) )
& ( ~ in(X103,X101)
| ~ in(X103,X102)
| X102 != set_difference(X100,X101) )
& ( ~ in(X104,X100)
| in(X104,X101)
| in(X104,X102)
| X102 != set_difference(X100,X101) )
& ( ~ in(esk16_3(X105,X106,X107),X107)
| ~ in(esk16_3(X105,X106,X107),X105)
| in(esk16_3(X105,X106,X107),X106)
| X107 = set_difference(X105,X106) )
& ( in(esk16_3(X105,X106,X107),X105)
| in(esk16_3(X105,X106,X107),X107)
| X107 = set_difference(X105,X106) )
& ( ~ in(esk16_3(X105,X106,X107),X106)
| in(esk16_3(X105,X106,X107),X107)
| X107 = set_difference(X105,X106) ) ),
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)],[c_0_13])])])])])]) ).
fof(c_0_17,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).
cnf(c_0_18,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
element(esk27_0,powerset(esk25_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,lemma,
! [X230,X231,X233,X234,X235] :
( ( in(esk24_2(X230,X231),X230)
| disjoint(X230,X231) )
& ( in(esk24_2(X230,X231),X231)
| disjoint(X230,X231) )
& ( ~ in(X235,X233)
| ~ in(X235,X234)
| ~ disjoint(X233,X234) ) ),
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)],[c_0_17])])])])])]) ).
fof(c_0_22,lemma,
! [X270,X271] :
( ( ~ disjoint(X270,X271)
| set_difference(X270,X271) = X270 )
& ( set_difference(X270,X271) != X270
| disjoint(X270,X271) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
cnf(c_0_23,negated_conjecture,
( disjoint(esk26_0,esk27_0)
| subset(esk26_0,subset_complement(esk25_0,esk27_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
subset_complement(esk25_0,esk27_0) = set_difference(esk25_0,esk27_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_26,lemma,
( in(esk24_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_28,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_29,lemma,
! [X257,X258,X259] :
( ~ subset(X257,X258)
| ~ disjoint(X258,X259)
| disjoint(X257,X259) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
cnf(c_0_30,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,negated_conjecture,
( disjoint(esk26_0,esk27_0)
| subset(esk26_0,set_difference(esk25_0,esk27_0)) ),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_32,plain,
! [X165,X166] :
( ~ disjoint(X165,X166)
| disjoint(X166,X165) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
cnf(c_0_33,lemma,
( disjoint(X1,set_difference(X2,X3))
| ~ in(esk24_2(X1,set_difference(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,lemma,
( in(esk24_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_35,plain,
! [X37,X38] :
( ( ~ element(X38,X37)
| in(X38,X37)
| empty(X37) )
& ( ~ in(X38,X37)
| element(X38,X37)
| empty(X37) )
& ( ~ element(X38,X37)
| empty(X38)
| ~ empty(X37) )
& ( ~ empty(X38)
| element(X38,X37)
| ~ empty(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
fof(c_0_36,plain,
! [X121] : ~ empty(powerset(X121)),
inference(variable_rename,[status(thm)],[c_0_28]) ).
cnf(c_0_37,lemma,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,lemma,
( set_difference(esk26_0,esk27_0) = esk26_0
| subset(esk26_0,set_difference(esk25_0,esk27_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,lemma,
disjoint(X1,set_difference(X2,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_41,lemma,
! [X152,X153] :
( ~ in(X152,X153)
| subset(X152,union(X153)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l50_zfmisc_1])]) ).
cnf(c_0_42,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,negated_conjecture,
element(esk26_0,powerset(esk25_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_44,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_45,lemma,
! [X282] : union(powerset(X282)) = X282,
inference(variable_rename,[status(thm)],[t99_zfmisc_1]) ).
cnf(c_0_46,lemma,
( set_difference(esk26_0,esk27_0) = esk26_0
| disjoint(esk26_0,X1)
| ~ disjoint(set_difference(esk25_0,esk27_0),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,lemma,
disjoint(set_difference(X1,X2),X2),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_48,lemma,
! [X209,X210,X211] :
( ~ subset(X209,X210)
| subset(set_difference(X209,X211),set_difference(X210,X211)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])]) ).
cnf(c_0_49,lemma,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,negated_conjecture,
in(esk26_0,powerset(esk25_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_51,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,negated_conjecture,
( ~ disjoint(esk26_0,esk27_0)
| ~ subset(esk26_0,subset_complement(esk25_0,esk27_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_53,lemma,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_54,lemma,
set_difference(esk26_0,esk27_0) = esk26_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_30]) ).
cnf(c_0_55,lemma,
( subset(set_difference(X1,X3),set_difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_56,lemma,
subset(esk26_0,esk25_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( ~ disjoint(esk26_0,esk27_0)
| ~ subset(esk26_0,set_difference(esk25_0,esk27_0)) ),
inference(rw,[status(thm)],[c_0_52,c_0_24]) ).
cnf(c_0_58,lemma,
disjoint(esk26_0,esk27_0),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,lemma,
subset(set_difference(esk26_0,X1),set_difference(esk25_0,X1)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
~ subset(esk26_0,set_difference(esk25_0,esk27_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_61,lemma,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_54]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU170+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 12:47:52 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.60 start to proof: theBenchmark
% 36.85/36.92 % Version : CSE_E---1.5
% 36.85/36.92 % Problem : theBenchmark.p
% 36.85/36.92 % Proof found
% 36.85/36.92 % SZS status Theorem for theBenchmark.p
% 36.85/36.92 % SZS output start Proof
% See solution above
% 36.85/36.93 % Total time : 36.313000 s
% 36.85/36.93 % SZS output end Proof
% 36.85/36.93 % Total time : 36.319000 s
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