TSTP Solution File: SET611+3 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET611+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 14:34:49 EDT 2023
% Result : Theorem 0.55s 0.79s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of formulae : 93 ( 21 unt; 12 typ; 0 def)
% Number of atoms : 186 ( 38 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 175 ( 70 ~; 78 |; 15 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 142 ( 12 sgn; 50 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
member: ( $i * $i ) > $o ).
tff(decl_23,type,
intersection: ( $i * $i ) > $i ).
tff(decl_24,type,
difference: ( $i * $i ) > $i ).
tff(decl_25,type,
empty_set: $i ).
tff(decl_26,type,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
empty: $i > $o ).
tff(decl_28,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk4_1: $i > $i ).
tff(decl_32,type,
esk5_0: $i ).
tff(decl_33,type,
esk6_0: $i ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(prove_th84,conjecture,
! [X1,X2] :
( intersection(X1,X2) = empty_set
<=> difference(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th84) ).
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(member_equal,axiom,
! [X1,X2] :
( ! [X3] :
( member(X3,X1)
<=> member(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
fof(c_0_9,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2] :
( intersection(X1,X2) = empty_set
<=> difference(X1,X2) = X1 ),
inference(assume_negation,[status(cth)],[prove_th84]) ).
fof(c_0_11,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_12,plain,
! [X10,X11,X12] :
( ( member(X12,X10)
| ~ member(X12,difference(X10,X11)) )
& ( ~ member(X12,X11)
| ~ member(X12,difference(X10,X11)) )
& ( ~ member(X12,X10)
| member(X12,X11)
| member(X12,difference(X10,X11)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,negated_conjecture,
( ( intersection(esk5_0,esk6_0) != empty_set
| difference(esk5_0,esk6_0) != esk5_0 )
& ( intersection(esk5_0,esk6_0) = empty_set
| difference(esk5_0,esk6_0) = esk5_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_14,plain,
! [X7,X8,X9] :
( ( member(X9,X7)
| ~ member(X9,intersection(X7,X8)) )
& ( member(X9,X8)
| ~ member(X9,intersection(X7,X8)) )
& ( ~ member(X9,X7)
| ~ member(X9,X8)
| member(X9,intersection(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_15,plain,
! [X32,X33,X34] :
( ( ~ empty(X32)
| ~ member(X33,X32) )
& ( member(esk4_1(X34),X34)
| empty(X34) ) ),
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_11])])])])]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| difference(esk5_0,esk6_0) = esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( member(esk4_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
cnf(c_0_21,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| ~ member(X1,esk5_0)
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( empty(intersection(X1,X2))
| member(esk4_1(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_23,plain,
! [X16,X17] : intersection(X16,X17) = intersection(X17,X16),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_24,plain,
! [X13] : ~ member(X13,empty_set),
inference(variable_rename,[status(thm)],[c_0_20]) ).
fof(c_0_25,plain,
! [X25,X26,X27,X28,X29] :
( ( ~ subset(X25,X26)
| ~ member(X27,X25)
| member(X27,X26) )
& ( member(esk3_2(X28,X29),X28)
| subset(X28,X29) )
& ( ~ member(esk3_2(X28,X29),X29)
| subset(X28,X29) ) ),
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)],[subset_defn])])])])])]) ).
cnf(c_0_26,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| empty(intersection(X1,esk6_0))
| ~ member(esk4_1(intersection(X1,esk6_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_28,plain,
! [X14,X15] :
( ( subset(X14,X15)
| X14 != X15 )
& ( subset(X15,X14)
| X14 != X15 )
& ( ~ subset(X14,X15)
| ~ subset(X15,X14)
| X14 = X15 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_29,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( member(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| empty(intersection(esk6_0,X1))
| ~ member(esk4_1(intersection(esk6_0,X1)),esk5_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( subset(X1,X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| empty(intersection(esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_22]),c_0_27]) ).
cnf(c_0_37,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_38,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| subset(intersection(esk5_0,esk6_0),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( ~ empty(intersection(X1,X2))
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
intersection(esk5_0,esk6_0) = empty_set,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
empty(empty_set),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_43,negated_conjecture,
( ~ member(X1,esk6_0)
| ~ member(X1,esk5_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_44,negated_conjecture,
( empty(intersection(X1,esk6_0))
| ~ member(esk4_1(intersection(X1,esk6_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_22]) ).
cnf(c_0_45,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_46,negated_conjecture,
( empty(intersection(esk6_0,X1))
| ~ member(esk4_1(intersection(esk6_0,X1)),esk5_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_27]) ).
cnf(c_0_47,plain,
( empty(intersection(X1,difference(X2,X3)))
| member(esk4_1(intersection(X1,difference(X2,X3))),X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_22]) ).
fof(c_0_48,plain,
! [X4,X5] :
( ( ~ member(esk1_2(X4,X5),X4)
| ~ member(esk1_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk1_2(X4,X5),X4)
| member(esk1_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_equal])])])]) ).
cnf(c_0_49,negated_conjecture,
empty(intersection(esk6_0,difference(esk5_0,X1))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,plain,
( empty(difference(X1,X2))
| ~ member(esk4_1(difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_51,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_52,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk3_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_30]) ).
cnf(c_0_53,plain,
( member(esk1_2(X1,X2),X1)
| member(esk1_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( ~ member(X1,difference(esk5_0,X2))
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_49]) ).
cnf(c_0_55,plain,
( empty(difference(X1,difference(X2,X3)))
| member(esk4_1(difference(X1,difference(X2,X3))),X3)
| ~ member(esk4_1(difference(X1,difference(X2,X3))),X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,plain,
( empty(difference(X1,X2))
| member(esk4_1(difference(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_19]) ).
cnf(c_0_57,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk3_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk3_2(difference(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_58,plain,
( subset(difference(X1,X2),X3)
| member(esk3_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_30]) ).
cnf(c_0_59,plain,
( empty_set = X1
| member(esk1_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( empty(difference(esk5_0,X1))
| ~ member(esk4_1(difference(esk5_0,X1)),esk6_0) ),
inference(spm,[status(thm)],[c_0_54,c_0_19]) ).
cnf(c_0_61,plain,
( empty(difference(X1,difference(X1,X2)))
| member(esk4_1(difference(X1,difference(X1,X2))),X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
( subset(X1,X2)
| ~ member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_63,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk3_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
empty(difference(esk5_0,difference(esk5_0,esk6_0))),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,negated_conjecture,
difference(esk5_0,difference(esk5_0,esk6_0)) = empty_set,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,plain,
( subset(X1,difference(X2,X3))
| member(esk3_2(X1,difference(X2,X3)),X3)
| ~ member(esk3_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_51]) ).
cnf(c_0_69,negated_conjecture,
subset(difference(esk5_0,empty_set),difference(esk5_0,esk6_0)),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,plain,
( subset(difference(X1,X2),difference(X1,X3))
| member(esk3_2(difference(X1,X2),difference(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_68,c_0_58]) ).
cnf(c_0_71,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_62,c_0_58]) ).
cnf(c_0_72,negated_conjecture,
( difference(esk5_0,empty_set) = difference(esk5_0,esk6_0)
| ~ subset(difference(esk5_0,esk6_0),difference(esk5_0,empty_set)) ),
inference(spm,[status(thm)],[c_0_33,c_0_69]) ).
cnf(c_0_73,plain,
subset(difference(X1,X2),difference(X1,empty_set)),
inference(spm,[status(thm)],[c_0_29,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( intersection(esk5_0,esk6_0) != empty_set
| difference(esk5_0,esk6_0) != esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_75,plain,
( difference(X1,X2) = X1
| ~ subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
difference(esk5_0,empty_set) = difference(esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).
cnf(c_0_77,negated_conjecture,
difference(esk5_0,esk6_0) != esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_41])]) ).
cnf(c_0_78,plain,
( subset(X1,difference(X1,X2))
| member(esk3_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_30]) ).
cnf(c_0_79,negated_conjecture,
~ subset(esk5_0,difference(esk5_0,esk6_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_80,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_76]),c_0_79]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET611+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 12:34:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 0.55/0.79 % Version : CSE_E---1.5
% 0.55/0.79 % Problem : theBenchmark.p
% 0.55/0.79 % Proof found
% 0.55/0.79 % SZS status Theorem for theBenchmark.p
% 0.55/0.79 % SZS output start Proof
% See solution above
% 0.55/0.79 % Total time : 0.186000 s
% 0.55/0.79 % SZS output end Proof
% 0.55/0.79 % Total time : 0.189000 s
%------------------------------------------------------------------------------