TSTP Solution File: SET609+3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET609+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 : n026.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 14:34:48 EDT 2023
% Result : Theorem 16.56s 16.64s
% Output : CNFRefutation 16.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 19
% Syntax : Number of formulae : 236 ( 154 unt; 10 typ; 0 def)
% Number of atoms : 353 ( 107 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 202 ( 75 ~; 101 |; 17 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 7 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 648 ( 134 sgn; 56 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
union: ( $i * $i ) > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
intersection: ( $i * $i ) > $i ).
tff(decl_25,type,
difference: ( $i * $i ) > $i ).
tff(decl_26,type,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk3_0: $i ).
tff(decl_30,type,
esk4_0: $i ).
tff(decl_31,type,
esk5_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(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(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(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_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(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(prove_th81,conjecture,
! [X1,X2,X3] : difference(X1,difference(X2,X3)) = union(difference(X1,X2),intersection(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th81) ).
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,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_11,plain,
! [X19,X20,X21,X22,X23] :
( ( ~ subset(X19,X20)
| ~ member(X21,X19)
| member(X21,X20) )
& ( member(esk1_2(X22,X23),X22)
| subset(X22,X23) )
& ( ~ member(esk1_2(X22,X23),X23)
| subset(X22,X23) ) ),
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])])])])])]) ).
fof(c_0_12,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])])]) ).
cnf(c_0_13,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X13,X14] :
( ( subset(X13,X14)
| X13 != X14 )
& ( subset(X14,X13)
| X13 != X14 )
& ( ~ subset(X13,X14)
| ~ subset(X14,X13)
| X13 = X14 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( subset(difference(X1,X2),X3)
| member(esk1_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_22,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_23,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_27,plain,
( subset(intersection(X1,difference(X2,X3)),X4)
| ~ member(esk1_2(intersection(X1,difference(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_28,plain,
( subset(intersection(intersection(X1,X2),X3),X4)
| member(esk1_2(intersection(intersection(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_29,plain,
( difference(X1,X2) = X1
| ~ subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,plain,
( X1 = difference(X2,X2)
| ~ subset(X1,difference(X2,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_32,plain,
subset(intersection(intersection(X1,X2),difference(X3,X2)),X4),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_34,plain,
( member(X1,X2)
| ~ member(X1,difference(X3,X3)) ),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
fof(c_0_35,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
cnf(c_0_36,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_37,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_38,plain,
intersection(intersection(X1,X2),difference(X3,X2)) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_33]),c_0_34]) ).
cnf(c_0_40,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
( subset(X1,difference(X2,X3))
| member(esk1_2(X1,difference(X2,X3)),X3)
| ~ member(esk1_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
cnf(c_0_42,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,intersection(X4,X3)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_43,plain,
( subset(difference(difference(X1,X2),X3),X4)
| member(esk1_2(difference(difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_44,plain,
( subset(difference(X1,union(X2,X3)),X4)
| ~ member(esk1_2(difference(X1,union(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_45,plain,
( subset(X1,difference(X1,X2))
| member(esk1_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_14]) ).
fof(c_0_46,plain,
! [X17,X18] : intersection(X17,X18) = intersection(X18,X17),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_47,plain,
( subset(difference(X1,intersection(X2,X3)),X4)
| ~ member(esk1_2(difference(X1,intersection(X2,X3)),X4),X3)
| ~ member(esk1_2(difference(X1,intersection(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_37]) ).
cnf(c_0_48,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),intersection(X4,X2)) ),
inference(spm,[status(thm)],[c_0_42,c_0_14]) ).
cnf(c_0_49,plain,
( subset(difference(X1,X2),difference(X1,X3))
| member(esk1_2(difference(X1,X2),difference(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_20]) ).
cnf(c_0_50,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_37]) ).
cnf(c_0_51,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk1_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk1_2(difference(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_52,plain,
subset(difference(difference(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_21,c_0_43]) ).
cnf(c_0_53,plain,
subset(difference(X1,union(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_44,c_0_20]) ).
cnf(c_0_54,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[c_0_39,c_0_45]) ).
cnf(c_0_55,plain,
( subset(intersection(difference(X1,X2),X3),X4)
| ~ member(esk1_2(intersection(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_56,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_57,plain,
( subset(difference(X1,intersection(X2,X1)),X3)
| ~ member(esk1_2(difference(X1,intersection(X2,X1)),X3),X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_20]) ).
cnf(c_0_58,plain,
subset(difference(X1,X2),difference(X1,intersection(X3,X2))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_59,plain,
( subset(difference(X1,X2),intersection(X3,X1))
| ~ member(esk1_2(difference(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_20]) ).
cnf(c_0_60,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk1_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_20]) ).
cnf(c_0_61,plain,
difference(difference(difference(X1,X2),X1),X3) = difference(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_29,c_0_52]) ).
cnf(c_0_62,plain,
difference(X1,union(X2,X1)) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_31,c_0_53]) ).
cnf(c_0_63,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_54]),c_0_25])]) ).
cnf(c_0_64,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_65,plain,
subset(intersection(X1,difference(X2,X1)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_22]),c_0_56]) ).
cnf(c_0_66,plain,
subset(difference(X1,intersection(X2,X1)),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_57,c_0_49]) ).
cnf(c_0_67,plain,
subset(difference(X1,X2),difference(X1,intersection(X2,X3))),
inference(spm,[status(thm)],[c_0_58,c_0_56]) ).
cnf(c_0_68,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,plain,
difference(X1,union(X2,X1)) = difference(difference(X3,X4),X3),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_70,plain,
difference(X1,difference(difference(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_63,c_0_61]) ).
cnf(c_0_71,plain,
( subset(intersection(difference(X1,X2),X3),X4)
| member(esk1_2(intersection(difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_72,plain,
( subset(intersection(X1,union(X2,X3)),X4)
| member(esk1_2(intersection(X1,union(X2,X3)),X4),X2)
| member(esk1_2(intersection(X1,union(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_64,c_0_22]) ).
cnf(c_0_73,plain,
difference(intersection(X1,difference(X2,X1)),X3) = intersection(X1,difference(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_65]) ).
cnf(c_0_74,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_66]),c_0_67])]) ).
cnf(c_0_75,plain,
subset(X1,intersection(X1,union(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_56]) ).
cnf(c_0_76,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
fof(c_0_77,plain,
! [X15,X16] : union(X15,X16) = union(X16,X15),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_78,plain,
( subset(intersection(difference(X1,X2),X3),intersection(X4,X1))
| ~ member(esk1_2(intersection(difference(X1,X2),X3),intersection(X4,X1)),X4) ),
inference(spm,[status(thm)],[c_0_50,c_0_71]) ).
cnf(c_0_79,plain,
( subset(intersection(difference(X1,X2),union(X3,X2)),X4)
| member(esk1_2(intersection(difference(X1,X2),union(X3,X2)),X4),X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_72]) ).
cnf(c_0_80,plain,
difference(X1,intersection(X2,difference(X3,X2))) = X1,
inference(spm,[status(thm)],[c_0_63,c_0_73]) ).
cnf(c_0_81,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_74,c_0_56]) ).
cnf(c_0_82,plain,
( subset(intersection(intersection(X1,X2),X3),intersection(X4,X2))
| ~ member(esk1_2(intersection(intersection(X1,X2),X3),intersection(X4,X2)),X4) ),
inference(spm,[status(thm)],[c_0_50,c_0_28]) ).
cnf(c_0_83,plain,
intersection(X1,union(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_75]),c_0_76])]) ).
cnf(c_0_84,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_85,plain,
subset(intersection(difference(X1,X2),union(X3,X2)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_86,plain,
difference(X1,difference(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_87,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_82,c_0_22]) ).
cnf(c_0_88,plain,
intersection(X1,union(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,plain,
subset(intersection(X1,union(X2,difference(X3,X1))),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,plain,
subset(intersection(X1,X2),intersection(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_91,plain,
intersection(X1,union(X2,difference(X3,X1))) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_89]),c_0_90])]) ).
cnf(c_0_92,plain,
subset(difference(X1,X2),intersection(X1,difference(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_14]),c_0_56]) ).
cnf(c_0_93,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_94,plain,
intersection(difference(X1,X2),union(X3,X2)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_91,c_0_86]) ).
cnf(c_0_95,plain,
( subset(difference(intersection(X1,X2),X3),X4)
| member(esk1_2(difference(intersection(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_96,plain,
( subset(difference(union(X1,X2),X3),X4)
| member(esk1_2(difference(union(X1,X2),X3),X4),X1)
| member(esk1_2(difference(union(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_20]) ).
cnf(c_0_97,plain,
( subset(intersection(X1,X2),difference(X1,X3))
| member(esk1_2(intersection(X1,X2),difference(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_23]) ).
cnf(c_0_98,plain,
intersection(X1,difference(X1,X2)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_92]),c_0_93])]) ).
cnf(c_0_99,plain,
intersection(union(X1,X2),difference(X3,X2)) = intersection(X1,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_56,c_0_94]) ).
cnf(c_0_100,plain,
( subset(difference(intersection(X1,X2),X3),difference(X2,X4))
| member(esk1_2(difference(intersection(X1,X2),X3),difference(X2,X4)),X4) ),
inference(spm,[status(thm)],[c_0_41,c_0_95]) ).
cnf(c_0_101,plain,
( subset(difference(union(X1,X2),X2),X3)
| member(esk1_2(difference(union(X1,X2),X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_96]) ).
cnf(c_0_102,plain,
subset(intersection(X1,difference(X2,X3)),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_27,c_0_97]) ).
cnf(c_0_103,plain,
intersection(X1,difference(union(X1,X2),X2)) = difference(union(X1,X2),X2),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_104,plain,
subset(difference(intersection(X1,X2),X3),difference(X2,X3)),
inference(spm,[status(thm)],[c_0_21,c_0_100]) ).
cnf(c_0_105,plain,
subset(difference(union(X1,intersection(X2,X1)),X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_101]),c_0_84]) ).
cnf(c_0_106,plain,
subset(difference(union(X1,X2),X2),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_107,plain,
subset(difference(X1,X2),difference(union(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_104,c_0_88]) ).
cnf(c_0_108,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_40]) ).
cnf(c_0_109,plain,
( subset(difference(difference(X1,X2),X3),X4)
| ~ member(esk1_2(difference(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_110,plain,
subset(difference(X1,X2),difference(difference(X1,X2),intersection(X3,X2))),
inference(spm,[status(thm)],[c_0_48,c_0_45]) ).
cnf(c_0_111,plain,
subset(difference(union(X1,intersection(X1,X2)),X1),X3),
inference(spm,[status(thm)],[c_0_105,c_0_56]) ).
cnf(c_0_112,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_113,plain,
difference(union(X1,X2),X2) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_106]),c_0_107])]) ).
cnf(c_0_114,plain,
subset(difference(X1,X2),difference(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_104,c_0_83]) ).
cnf(c_0_115,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_19,c_0_60]) ).
cnf(c_0_116,plain,
difference(union(X1,intersection(X2,X1)),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_31,c_0_105]) ).
cnf(c_0_117,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_108,c_0_14]) ).
cnf(c_0_118,plain,
( subset(difference(difference(X1,union(X2,X3)),X4),X5)
| ~ member(esk1_2(difference(difference(X1,union(X2,X3)),X4),X5),X3) ),
inference(spm,[status(thm)],[c_0_109,c_0_40]) ).
cnf(c_0_119,plain,
( subset(difference(difference(X1,X2),difference(X1,X3)),X4)
| member(esk1_2(difference(difference(X1,X2),difference(X1,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_43]) ).
cnf(c_0_120,plain,
difference(difference(X1,X2),intersection(X3,X2)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_110]),c_0_25])]) ).
cnf(c_0_121,plain,
difference(union(X1,intersection(X1,X2)),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_31,c_0_111]) ).
cnf(c_0_122,plain,
subset(difference(X1,union(X2,X3)),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_44,c_0_49]) ).
fof(c_0_123,plain,
! [X26,X27,X28,X29,X30,X31] :
( ( ~ member(X28,X26)
| member(X28,X27)
| X26 != X27 )
& ( ~ member(X29,X27)
| member(X29,X26)
| X26 != X27 )
& ( ~ member(esk2_2(X30,X31),X30)
| ~ member(esk2_2(X30,X31),X31)
| X30 = X31 )
& ( member(esk2_2(X30,X31),X30)
| member(esk2_2(X30,X31),X31)
| X30 = X31 ) ),
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)],[equal_member_defn])])])])])]) ).
cnf(c_0_124,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_112]) ).
cnf(c_0_125,plain,
( subset(union(X1,X2),X3)
| member(esk1_2(union(X1,X2),X3),X1)
| member(esk1_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_14]) ).
cnf(c_0_126,plain,
subset(difference(union(X1,X2),difference(X1,X2)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_113]),c_0_83]) ).
cnf(c_0_127,plain,
subset(X1,difference(union(X2,X1),difference(X3,X1))),
inference(spm,[status(thm)],[c_0_114,c_0_86]) ).
cnf(c_0_128,plain,
subset(union(X1,intersection(X2,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_63]) ).
cnf(c_0_129,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_117,c_0_84]) ).
cnf(c_0_130,plain,
subset(difference(difference(X1,union(X2,X3)),difference(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_131,plain,
difference(difference(X1,union(X2,X3)),X2) = difference(X1,union(X2,X3)),
inference(spm,[status(thm)],[c_0_120,c_0_88]) ).
cnf(c_0_132,plain,
difference(X1,difference(union(X2,intersection(X2,X3)),X2)) = X1,
inference(spm,[status(thm)],[c_0_63,c_0_121]) ).
cnf(c_0_133,plain,
subset(difference(X1,union(X2,union(X3,X1))),difference(X4,X4)),
inference(spm,[status(thm)],[c_0_122,c_0_62]) ).
cnf(c_0_134,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_135,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_112]) ).
cnf(c_0_136,plain,
( subset(union(X1,X2),union(X3,X2))
| member(esk1_2(union(X1,X2),union(X3,X2)),X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_125]) ).
cnf(c_0_137,plain,
difference(union(X1,X2),difference(X1,X2)) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_126]),c_0_127])]) ).
cnf(c_0_138,plain,
union(X1,intersection(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_128]),c_0_129])]) ).
cnf(c_0_139,plain,
subset(difference(X1,union(X2,difference(X1,X2))),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_84]) ).
cnf(c_0_140,plain,
difference(X1,difference(union(X2,difference(X2,X3)),X2)) = X1,
inference(spm,[status(thm)],[c_0_132,c_0_98]) ).
cnf(c_0_141,plain,
~ member(X1,difference(X2,union(X3,union(X4,X2)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_133]),c_0_39]) ).
cnf(c_0_142,plain,
( difference(X1,X1) = X2
| member(esk2_2(difference(X1,X1),X2),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_134]) ).
cnf(c_0_143,plain,
subset(union(X1,X2),union(union(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_144,plain,
difference(X1,difference(X1,X2)) = intersection(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_74]),c_0_138]) ).
cnf(c_0_145,plain,
difference(X1,union(X2,difference(X1,X2))) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_31,c_0_139]) ).
cnf(c_0_146,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4) ),
inference(spm,[status(thm)],[c_0_108,c_0_40]) ).
cnf(c_0_147,plain,
( subset(union(X1,X2),union(X1,X3))
| member(esk1_2(union(X1,X2),union(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_148,plain,
subset(union(X1,difference(X1,X2)),X1),
inference(spm,[status(thm)],[c_0_115,c_0_140]) ).
cnf(c_0_149,plain,
difference(X1,X1) = difference(X2,union(X3,union(X4,X2))),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_150,plain,
subset(union(X1,intersection(X2,union(X1,X3))),union(X1,X3)),
inference(spm,[status(thm)],[c_0_143,c_0_138]) ).
cnf(c_0_151,plain,
intersection(X1,union(X2,difference(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_63]),c_0_56]) ).
cnf(c_0_152,plain,
subset(union(X1,X2),union(X1,union(X3,X2))),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_153,plain,
union(X1,difference(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_148]),c_0_129])]) ).
cnf(c_0_154,plain,
intersection(X1,union(difference(X2,X1),X3)) = intersection(X3,X1),
inference(spm,[status(thm)],[c_0_91,c_0_84]) ).
cnf(c_0_155,plain,
subset(X1,intersection(X1,union(X2,union(X3,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_149]),c_0_63]),c_0_56]) ).
cnf(c_0_156,plain,
subset(union(X1,X2),union(X1,difference(X2,X1))),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_157,plain,
subset(union(X1,difference(X2,X3)),union(X1,X2)),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_158,plain,
intersection(difference(X1,X2),union(X2,X3)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_154,c_0_86]) ).
cnf(c_0_159,plain,
intersection(X1,union(X2,union(X3,X1))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_155]),c_0_76])]) ).
cnf(c_0_160,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_156]),c_0_157])]) ).
cnf(c_0_161,plain,
intersection(union(X1,X2),difference(X3,X1)) = intersection(X2,difference(X3,X1)),
inference(spm,[status(thm)],[c_0_56,c_0_158]) ).
cnf(c_0_162,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
inference(spm,[status(thm)],[c_0_124,c_0_40]) ).
cnf(c_0_163,plain,
subset(union(X1,intersection(X1,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_121]),c_0_63]) ).
cnf(c_0_164,plain,
intersection(difference(X1,X2),union(X3,X1)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_159,c_0_153]) ).
cnf(c_0_165,plain,
intersection(X1,difference(X2,difference(X3,X1))) = intersection(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_160]),c_0_154]),c_0_56]) ).
cnf(c_0_166,plain,
intersection(difference(X1,X2),difference(X3,X2)) = intersection(X1,difference(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_160]),c_0_161]) ).
cnf(c_0_167,plain,
subset(union(X1,X2),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_162,c_0_136]) ).
cnf(c_0_168,plain,
union(X1,intersection(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_163]),c_0_129])]) ).
cnf(c_0_169,plain,
intersection(union(X1,X2),difference(X2,X3)) = difference(X2,X3),
inference(spm,[status(thm)],[c_0_56,c_0_164]) ).
cnf(c_0_170,plain,
intersection(X1,difference(X2,X3)) = intersection(X2,difference(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_137]),c_0_166]) ).
cnf(c_0_171,plain,
subset(X1,union(X2,difference(X1,X2))),
inference(spm,[status(thm)],[c_0_93,c_0_151]) ).
cnf(c_0_172,plain,
subset(union(intersection(X1,X2),X3),union(X1,X3)),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_173,plain,
subset(difference(X1,union(X2,union(X3,X1))),X4),
inference(spm,[status(thm)],[c_0_141,c_0_14]) ).
cnf(c_0_174,plain,
subset(union(X1,difference(difference(X1,X2),X3)),X1),
inference(spm,[status(thm)],[c_0_157,c_0_153]) ).
cnf(c_0_175,plain,
intersection(X1,difference(union(X2,X1),X3)) = difference(X1,X3),
inference(rw,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_176,plain,
subset(X1,union(intersection(X1,X2),difference(X1,X2))),
inference(spm,[status(thm)],[c_0_171,c_0_81]) ).
cnf(c_0_177,plain,
subset(union(intersection(X1,X2),difference(X1,X3)),X1),
inference(spm,[status(thm)],[c_0_172,c_0_153]) ).
cnf(c_0_178,plain,
subset(difference(X1,union(union(X2,X1),X3)),X4),
inference(spm,[status(thm)],[c_0_173,c_0_84]) ).
cnf(c_0_179,plain,
union(X1,difference(difference(X1,X2),X3)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_174]),c_0_129])]) ).
cnf(c_0_180,plain,
difference(X1,intersection(X2,union(X3,X1))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_74]),c_0_175]) ).
cnf(c_0_181,plain,
union(intersection(X1,X2),difference(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_176]),c_0_177])]) ).
cnf(c_0_182,plain,
difference(X1,union(X2,difference(X3,X1))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_91]),c_0_74]) ).
cnf(c_0_183,plain,
difference(X1,union(union(X2,X1),X3)) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_31,c_0_178]) ).
cnf(c_0_184,plain,
intersection(X1,difference(difference(X1,X2),X3)) = difference(difference(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_179]),c_0_56]) ).
cnf(c_0_185,plain,
intersection(X1,difference(X2,intersection(X3,X1))) = intersection(X2,difference(X1,X3)),
inference(spm,[status(thm)],[c_0_170,c_0_74]) ).
cnf(c_0_186,plain,
intersection(difference(X1,X2),X3) = intersection(X1,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_56,c_0_170]) ).
cnf(c_0_187,plain,
difference(difference(X1,X2),intersection(X3,X1)) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_180,c_0_181]) ).
cnf(c_0_188,plain,
difference(X1,union(difference(X2,X1),X3)) = difference(X1,X3),
inference(spm,[status(thm)],[c_0_182,c_0_84]) ).
cnf(c_0_189,plain,
subset(X1,intersection(X1,union(union(X2,X1),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_183]),c_0_63]),c_0_56]) ).
cnf(c_0_190,plain,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_186]),c_0_184]),c_0_187]) ).
cnf(c_0_191,plain,
difference(difference(X1,X2),union(X2,X3)) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_188,c_0_86]) ).
cnf(c_0_192,plain,
subset(union(intersection(X1,X2),X3),union(X2,X3)),
inference(spm,[status(thm)],[c_0_167,c_0_138]) ).
cnf(c_0_193,plain,
intersection(X1,union(union(X2,X1),X3)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_189]),c_0_76])]) ).
cnf(c_0_194,plain,
difference(difference(X1,X2),X3) = difference(X1,union(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_190]),c_0_191]) ).
cnf(c_0_195,plain,
subset(X1,union(intersection(X2,X1),difference(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_144]),c_0_84]) ).
cnf(c_0_196,plain,
subset(union(intersection(X1,X2),difference(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_192,c_0_153]) ).
cnf(c_0_197,plain,
intersection(difference(X1,X2),union(X1,X3)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_193,c_0_153]) ).
cnf(c_0_198,plain,
subset(union(X1,difference(intersection(X2,X1),X3)),X1),
inference(spm,[status(thm)],[c_0_157,c_0_138]) ).
cnf(c_0_199,plain,
difference(union(X1,X2),union(X2,X3)) = difference(X1,union(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_113]),c_0_194]) ).
cnf(c_0_200,plain,
union(intersection(X1,X2),difference(X2,X1)) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_195]),c_0_196])]) ).
cnf(c_0_201,plain,
intersection(union(X1,X2),difference(X1,X3)) = difference(X1,X3),
inference(spm,[status(thm)],[c_0_56,c_0_197]) ).
cnf(c_0_202,plain,
difference(X1,difference(union(X2,X1),X3)) = intersection(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_175]),c_0_144]) ).
cnf(c_0_203,plain,
union(X1,difference(intersection(X2,X1),X3)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_198]),c_0_129])]) ).
cnf(c_0_204,plain,
difference(union(X1,intersection(X2,X3)),X3) = difference(X1,X3),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_205,plain,
intersection(X1,difference(union(X1,X2),X3)) = difference(X1,X3),
inference(rw,[status(thm)],[c_0_201,c_0_170]) ).
cnf(c_0_206,plain,
intersection(X1,intersection(X2,union(X3,X1))) = intersection(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_74]),c_0_202]),c_0_56]) ).
cnf(c_0_207,plain,
intersection(X1,difference(intersection(X2,X1),X3)) = difference(intersection(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_203]),c_0_56]) ).
cnf(c_0_208,plain,
union(X1,union(X2,intersection(X3,X1))) = union(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_204]),c_0_160]) ).
cnf(c_0_209,plain,
difference(X1,difference(union(X1,X2),X3)) = intersection(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_205]),c_0_144]) ).
cnf(c_0_210,plain,
difference(intersection(X1,X2),X3) = intersection(X1,difference(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_181]),c_0_186]),c_0_207]) ).
cnf(c_0_211,plain,
intersection(X1,difference(X2,difference(X1,X3))) = intersection(X2,intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_170,c_0_144]) ).
cnf(c_0_212,plain,
union(X1,union(intersection(X2,X1),X3)) = union(X1,X3),
inference(spm,[status(thm)],[c_0_208,c_0_84]) ).
cnf(c_0_213,plain,
intersection(X1,intersection(X2,X3)) = intersection(X2,intersection(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_181]),c_0_210]),c_0_211]) ).
cnf(c_0_214,plain,
union(X1,difference(X2,intersection(X3,X1))) = union(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_160]),c_0_212]) ).
cnf(c_0_215,plain,
difference(X1,intersection(X2,intersection(X3,X1))) = difference(X1,intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_81,c_0_213]) ).
fof(c_0_216,negated_conjecture,
~ ! [X1,X2,X3] : difference(X1,difference(X2,X3)) = union(difference(X1,X2),intersection(X1,X3)),
inference(assume_negation,[status(cth)],[prove_th81]) ).
cnf(c_0_217,plain,
union(intersection(X1,X2),difference(X2,intersection(X3,X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_84]),c_0_138]) ).
fof(c_0_218,negated_conjecture,
difference(esk3_0,difference(esk4_0,esk5_0)) != union(difference(esk3_0,esk4_0),intersection(esk3_0,esk5_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_216])])]) ).
cnf(c_0_219,plain,
union(difference(X1,X2),intersection(union(X2,X3),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_88]),c_0_84]) ).
cnf(c_0_220,plain,
intersection(union(X1,X2),difference(X3,difference(X1,X2))) = intersection(X3,X2),
inference(spm,[status(thm)],[c_0_170,c_0_137]) ).
cnf(c_0_221,negated_conjecture,
difference(esk3_0,difference(esk4_0,esk5_0)) != union(difference(esk3_0,esk4_0),intersection(esk3_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_218]) ).
cnf(c_0_222,plain,
union(difference(X1,X2),intersection(X1,X3)) = difference(X1,difference(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_194]),c_0_84]),c_0_153]) ).
cnf(c_0_223,negated_conjecture,
union(intersection(esk3_0,esk5_0),difference(esk3_0,esk4_0)) != difference(esk3_0,difference(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_221,c_0_84]) ).
cnf(c_0_224,plain,
union(intersection(X1,X2),difference(X1,X3)) = difference(X1,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_84,c_0_222]) ).
cnf(c_0_225,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_223,c_0_224])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET609+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n026.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 : Sat Aug 26 11:47:33 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 16.56/16.64 % Version : CSE_E---1.5
% 16.56/16.64 % Problem : theBenchmark.p
% 16.56/16.64 % Proof found
% 16.56/16.64 % SZS status Theorem for theBenchmark.p
% 16.56/16.64 % SZS output start Proof
% See solution above
% 16.56/16.66 % Total time : 16.065000 s
% 16.56/16.66 % SZS output end Proof
% 16.56/16.66 % Total time : 16.068000 s
%------------------------------------------------------------------------------