TSTP Solution File: SET171+3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET171+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 : n020.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 14:33:27 EDT 2023
% Result : Theorem 138.33s 138.45s
% Output : CNFRefutation 138.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 17
% Syntax : Number of formulae : 221 ( 154 unt; 9 typ; 0 def)
% Number of atoms : 317 ( 87 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 164 ( 59 ~; 85 |; 13 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 631 ( 98 sgn; 47 !; 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,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk3_0: $i ).
tff(decl_29,type,
esk4_0: $i ).
tff(decl_30,type,
esk5_0: $i ).
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(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_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(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_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(prove_union_distributes_over_intersection,conjecture,
! [X1,X2,X3] : union(X1,intersection(X2,X3)) = intersection(union(X1,X2),union(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_distributes_over_intersection) ).
fof(c_0_8,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])])]) ).
fof(c_0_9,plain,
! [X16,X17,X18,X19,X20] :
( ( ~ subset(X16,X17)
| ~ member(X18,X16)
| member(X18,X17) )
& ( member(esk1_2(X19,X20),X19)
| subset(X19,X20) )
& ( ~ member(esk1_2(X19,X20),X20)
| subset(X19,X20) ) ),
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_10,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_11,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X23,X24,X25,X26,X27,X28] :
( ( ~ member(X25,X23)
| member(X25,X24)
| X23 != X24 )
& ( ~ member(X26,X24)
| member(X26,X23)
| X23 != X24 )
& ( ~ member(esk2_2(X27,X28),X27)
| ~ member(esk2_2(X27,X28),X28)
| X27 = X28 )
& ( member(esk2_2(X27,X28),X27)
| member(esk2_2(X27,X28),X28)
| X27 = 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)],[equal_member_defn])])])])])]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,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_11,c_0_12]) ).
cnf(c_0_18,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,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_14,c_0_15]) ).
cnf(c_0_22,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_23,plain,
( subset(union(X1,X2),X2)
| member(esk1_2(union(X1,X2),X2),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
fof(c_0_24,plain,
! [X12,X13] : union(X12,X13) = union(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_25,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,plain,
( intersection(X1,X2) = X3
| member(esk2_2(intersection(X1,X2),X3),X3)
| member(esk2_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_27,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_28,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_29,plain,
( subset(intersection(X1,X2),intersection(X3,X1))
| ~ member(esk1_2(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_30,plain,
! [X10,X11] :
( ( subset(X10,X11)
| X10 != X11 )
& ( subset(X11,X10)
| X10 != X11 )
& ( ~ subset(X10,X11)
| ~ subset(X11,X10)
| X10 = X11 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_31,plain,
( subset(union(intersection(X1,X2),X3),X3)
| member(esk1_2(union(intersection(X1,X2),X3),X3),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_32,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_34,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_25]) ).
cnf(c_0_35,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_36,plain,
( intersection(X1,X2) = X1
| member(esk2_2(intersection(X1,X2),X1),X1) ),
inference(ef,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_38,plain,
subset(intersection(X1,X2),union(X2,X3)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_39,plain,
subset(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
fof(c_0_40,plain,
! [X14,X15] : intersection(X14,X15) = intersection(X15,X14),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_41,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,plain,
subset(union(X1,intersection(X1,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_31]),c_0_32]) ).
cnf(c_0_43,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_12]) ).
cnf(c_0_44,plain,
subset(intersection(X1,X2),intersection(X2,intersection(X1,X2))),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_45,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_14,c_0_28]) ).
cnf(c_0_46,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4) ),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_47,plain,
( subset(union(X1,X2),union(X2,X3))
| member(esk1_2(union(X1,X2),union(X2,X3)),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_48,plain,
( intersection(X1,X2) = X1
| ~ member(esk2_2(intersection(X1,X2),X1),intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_49,plain,
( member(X1,union(X2,X3))
| ~ member(X1,intersection(X4,X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_50,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,intersection(X3,X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_39]) ).
cnf(c_0_51,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_52,plain,
union(X1,intersection(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_53,plain,
intersection(X1,intersection(X2,X1)) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_44]),c_0_45])]) ).
cnf(c_0_54,plain,
subset(union(X1,X2),union(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_55,plain,
( intersection(X1,X2) = X1
| ~ member(esk2_2(intersection(X1,X2),X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_15]),c_0_36]) ).
cnf(c_0_56,plain,
( intersection(intersection(X1,X2),X3) = intersection(X1,X2)
| member(esk2_2(intersection(intersection(X1,X2),X3),intersection(X1,X2)),union(X2,X4)) ),
inference(spm,[status(thm)],[c_0_49,c_0_36]) ).
cnf(c_0_57,plain,
( intersection(intersection(X1,X2),X3) = intersection(X1,X2)
| member(esk2_2(intersection(intersection(X1,X2),X3),intersection(X1,X2)),intersection(X2,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_58,plain,
subset(X1,intersection(X1,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_12]) ).
cnf(c_0_59,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_45,c_0_51]) ).
cnf(c_0_60,plain,
( subset(intersection(X1,intersection(X2,X3)),X4)
| member(esk1_2(intersection(X1,intersection(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_61,plain,
union(X1,intersection(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
subset(union(X1,X2),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_54,c_0_32]) ).
cnf(c_0_63,plain,
intersection(intersection(X1,X2),union(X2,X3)) = intersection(X1,X2),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_64,plain,
intersection(intersection(X1,X2),intersection(X2,X1)) = intersection(X1,X2),
inference(spm,[status(thm)],[c_0_55,c_0_57]) ).
cnf(c_0_65,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_11,c_0_28]) ).
cnf(c_0_66,plain,
intersection(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_58]),c_0_59])]) ).
cnf(c_0_67,plain,
subset(union(X1,union(X2,X1)),union(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_23]) ).
cnf(c_0_68,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_12]) ).
cnf(c_0_69,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_60]) ).
cnf(c_0_70,plain,
( subset(X1,union(X2,intersection(X3,X4)))
| ~ member(esk1_2(X1,union(X2,intersection(X3,X4))),X4)
| ~ member(esk1_2(X1,union(X2,intersection(X3,X4))),X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_15]) ).
cnf(c_0_71,plain,
subset(union(intersection(X1,X2),X3),union(X3,X2)),
inference(spm,[status(thm)],[c_0_54,c_0_61]) ).
cnf(c_0_72,plain,
subset(union(X1,intersection(X2,union(X3,X1))),union(X3,X1)),
inference(spm,[status(thm)],[c_0_62,c_0_61]) ).
cnf(c_0_73,plain,
intersection(intersection(X1,X2),union(intersection(X2,X1),X3)) = intersection(X1,X2),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_74,plain,
( subset(intersection(X1,X2),intersection(union(X3,X4),X1))
| ~ member(esk1_2(intersection(X1,X2),intersection(union(X3,X4),X1)),X4) ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_75,plain,
( subset(intersection(X1,union(X2,X3)),X3)
| member(esk1_2(intersection(X1,union(X2,X3)),X3),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_65]) ).
cnf(c_0_76,plain,
intersection(X1,union(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_63,c_0_66]) ).
cnf(c_0_77,plain,
union(X1,union(X2,X1)) = union(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_67]),c_0_68])]) ).
cnf(c_0_78,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_69,c_0_51]) ).
cnf(c_0_79,plain,
( subset(intersection(X1,X2),union(X3,intersection(X4,X1)))
| ~ member(esk1_2(intersection(X1,X2),union(X3,intersection(X4,X1))),X4) ),
inference(spm,[status(thm)],[c_0_70,c_0_22]) ).
cnf(c_0_80,plain,
( subset(intersection(X1,union(X2,X3)),union(X3,X4))
| member(esk1_2(intersection(X1,union(X2,X3)),union(X3,X4)),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_65]) ).
cnf(c_0_81,plain,
subset(union(intersection(X1,X2),X3),union(X3,intersection(X2,X1))),
inference(spm,[status(thm)],[c_0_71,c_0_64]) ).
cnf(c_0_82,plain,
subset(union(X1,intersection(X2,X3)),union(intersection(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,plain,
subset(intersection(X1,union(X2,intersection(union(X3,X2),X1))),intersection(union(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_84,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_69,c_0_51]) ).
cnf(c_0_85,plain,
intersection(X1,union(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_86,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_78,c_0_51]) ).
cnf(c_0_87,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X3,intersection(X1,intersection(X2,X3)))),
inference(spm,[status(thm)],[c_0_33,c_0_60]) ).
cnf(c_0_88,plain,
subset(intersection(X1,union(X2,X3)),union(X3,intersection(X2,X1))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_89,plain,
union(X1,intersection(X2,X3)) = union(intersection(X3,X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_81]),c_0_82])]) ).
cnf(c_0_90,plain,
subset(intersection(X1,union(intersection(X2,X3),intersection(X3,X1))),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_83,c_0_61]) ).
cnf(c_0_91,plain,
subset(intersection(X1,X2),intersection(X2,union(X3,intersection(X1,X2)))),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_92,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(intersection(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_69,c_0_64]) ).
cnf(c_0_93,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,intersection(X2,X1))),
inference(spm,[status(thm)],[c_0_86,c_0_64]) ).
cnf(c_0_94,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X2,intersection(intersection(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_87,c_0_51]) ).
cnf(c_0_95,plain,
( subset(intersection(X1,intersection(X2,X3)),X4)
| member(esk1_2(intersection(X1,intersection(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_28]) ).
cnf(c_0_96,plain,
subset(intersection(X1,union(X2,X3)),union(intersection(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,plain,
intersection(X1,union(intersection(X2,X3),intersection(X3,X1))) = intersection(X3,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_90]),c_0_91])]) ).
cnf(c_0_98,plain,
intersection(intersection(X1,X2),X3) = intersection(X3,intersection(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_92]),c_0_93])]) ).
cnf(c_0_99,plain,
intersection(X1,intersection(intersection(X2,X1),X3)) = intersection(intersection(X2,X1),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_94]),c_0_45])]) ).
cnf(c_0_100,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_95]) ).
cnf(c_0_101,plain,
subset(intersection(X1,union(union(intersection(X2,X3),intersection(X3,X1)),X4)),union(intersection(X3,X1),X4)),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_102,plain,
union(intersection(X1,X2),intersection(intersection(X2,X1),X3)) = intersection(X1,X2),
inference(spm,[status(thm)],[c_0_61,c_0_98]) ).
cnf(c_0_103,plain,
intersection(union(X1,X2),intersection(X2,X3)) = intersection(X2,X3),
inference(spm,[status(thm)],[c_0_99,c_0_85]) ).
cnf(c_0_104,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X1,X2)),
inference(spm,[status(thm)],[c_0_100,c_0_51]) ).
cnf(c_0_105,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X2,intersection(X1,intersection(X2,X3)))),
inference(spm,[status(thm)],[c_0_33,c_0_95]) ).
cnf(c_0_106,plain,
subset(intersection(X1,union(union(intersection(X2,X3),intersection(X3,X1)),intersection(intersection(X1,X3),X4))),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,plain,
intersection(X1,union(X2,intersection(union(X3,X2),X1))) = intersection(union(X3,X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_83]),c_0_91])]) ).
cnf(c_0_108,plain,
union(union(X1,X2),intersection(X2,X3)) = union(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_103]) ).
cnf(c_0_109,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_104,c_0_51]) ).
cnf(c_0_110,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X1,intersection(intersection(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_105,c_0_51]) ).
cnf(c_0_111,plain,
( subset(X1,union(intersection(X2,X3),X4))
| ~ member(esk1_2(X1,union(intersection(X2,X3),X4)),X3)
| ~ member(esk1_2(X1,union(intersection(X2,X3),X4)),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_112,plain,
subset(intersection(union(X1,intersection(union(X2,X1),X3)),union(intersection(X4,X3),intersection(union(X2,X1),X3))),intersection(union(X2,X1),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_51]),c_0_107]),c_0_108]) ).
cnf(c_0_113,plain,
subset(intersection(intersection(intersection(X1,X2),X3),X4),intersection(X4,X2)),
inference(spm,[status(thm)],[c_0_109,c_0_99]) ).
cnf(c_0_114,plain,
intersection(intersection(X1,X2),union(X3,X2)) = intersection(X1,X2),
inference(spm,[status(thm)],[c_0_63,c_0_77]) ).
cnf(c_0_115,plain,
intersection(X1,intersection(intersection(X1,X2),X3)) = intersection(intersection(X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_110]),c_0_45])]) ).
cnf(c_0_116,plain,
( subset(intersection(X1,X2),union(intersection(X3,X1),X4))
| ~ member(esk1_2(intersection(X1,X2),union(intersection(X3,X1),X4)),X3) ),
inference(spm,[status(thm)],[c_0_111,c_0_22]) ).
cnf(c_0_117,plain,
( subset(intersection(X1,union(X2,X3)),union(X4,union(X5,X3)))
| member(esk1_2(intersection(X1,union(X2,X3)),union(X4,union(X5,X3))),X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_65]) ).
cnf(c_0_118,plain,
subset(union(X1,union(X2,union(X3,X1))),union(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_119,plain,
subset(union(intersection(X1,X2),intersection(X2,union(X3,intersection(X1,X2)))),intersection(X2,union(X3,intersection(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_66]),c_0_51]),c_0_51]) ).
cnf(c_0_120,plain,
intersection(X1,intersection(X2,intersection(X1,X3))) = intersection(X2,intersection(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_105]),c_0_45])]) ).
cnf(c_0_121,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X2,union(intersection(X3,intersection(X1,X2)),X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_73]),c_0_51]) ).
cnf(c_0_122,plain,
intersection(intersection(X1,X2),union(X3,intersection(X2,X1))) = intersection(X1,X2),
inference(spm,[status(thm)],[c_0_114,c_0_64]) ).
cnf(c_0_123,plain,
union(X1,intersection(intersection(X1,X2),X3)) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_115]) ).
cnf(c_0_124,plain,
subset(intersection(X1,union(X2,X3)),union(intersection(X2,X1),union(X4,X3))),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_125,plain,
subset(union(X1,union(union(X2,X1),X3)),union(union(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_118,c_0_32]) ).
cnf(c_0_126,plain,
subset(union(intersection(X1,X2),intersection(X1,union(X3,intersection(X1,X2)))),intersection(X1,union(X3,intersection(X1,X2)))),
inference(spm,[status(thm)],[c_0_119,c_0_51]) ).
cnf(c_0_127,plain,
union(X1,intersection(X2,intersection(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_120]) ).
cnf(c_0_128,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X2,union(intersection(X1,intersection(X3,X2)),X4))),
inference(spm,[status(thm)],[c_0_121,c_0_98]) ).
cnf(c_0_129,plain,
union(intersection(X1,X2),union(X3,intersection(X2,X1))) = union(X3,intersection(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_122]),c_0_32]) ).
cnf(c_0_130,plain,
subset(union(intersection(X1,X2),intersection(intersection(X2,X3),X1)),intersection(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_123]),c_0_32]) ).
cnf(c_0_131,plain,
subset(intersection(X1,union(X2,X3)),union(intersection(X1,X2),union(X4,X3))),
inference(spm,[status(thm)],[c_0_124,c_0_51]) ).
cnf(c_0_132,plain,
union(X1,union(union(X2,X1),X3)) = union(union(X2,X1),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_125]),c_0_68])]) ).
cnf(c_0_133,plain,
subset(union(intersection(X1,X2),intersection(X1,intersection(X2,X3))),intersection(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_32]) ).
cnf(c_0_134,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X2,union(X4,intersection(intersection(X3,X2),X1)))),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_135,plain,
union(intersection(X1,X2),intersection(intersection(X2,X3),X1)) = intersection(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_130]),c_0_43])]) ).
cnf(c_0_136,plain,
subset(intersection(X1,union(X2,X3)),union(union(X4,intersection(X1,X2)),X3)),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_137,plain,
union(intersection(X1,X2),intersection(X1,intersection(X2,X3))) = intersection(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_133]),c_0_43])]) ).
cnf(c_0_138,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X2,intersection(X1,X3))),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_139,plain,
subset(intersection(X1,union(intersection(X2,X3),X4)),union(intersection(X1,X2),X4)),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_140,plain,
intersection(X1,intersection(X2,X3)) = intersection(X2,intersection(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_138]),c_0_138])]) ).
cnf(c_0_141,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_142,plain,
subset(union(intersection(X1,X2),X3),union(X3,intersection(X1,union(intersection(X1,X2),X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_66]),c_0_51]),c_0_32]) ).
cnf(c_0_143,plain,
intersection(X1,intersection(X2,union(X1,X3))) = intersection(X2,X1),
inference(spm,[status(thm)],[c_0_140,c_0_76]) ).
cnf(c_0_144,plain,
subset(union(X1,union(X2,union(X1,X3))),union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_141,c_0_23]) ).
cnf(c_0_145,plain,
( subset(intersection(X1,X2),intersection(union(X3,X4),X1))
| ~ member(esk1_2(intersection(X1,X2),intersection(union(X3,X4),X1)),X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_146,plain,
subset(union(intersection(X1,X2),X3),union(X3,intersection(X2,union(intersection(X1,X2),X3)))),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_147,plain,
subset(union(X1,union(union(X1,X2),X3)),union(union(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_144,c_0_32]) ).
cnf(c_0_148,plain,
subset(union(X1,X2),union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_141,c_0_47]) ).
cnf(c_0_149,plain,
subset(intersection(X1,union(X2,intersection(union(X2,X3),X1))),intersection(union(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_145,c_0_75]) ).
cnf(c_0_150,plain,
union(X1,union(X2,union(X3,X1))) = union(X2,union(X3,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_118]),c_0_68])]) ).
cnf(c_0_151,plain,
subset(union(X1,X2),union(X2,intersection(union(X1,X3),union(X1,X2)))),
inference(spm,[status(thm)],[c_0_146,c_0_76]) ).
cnf(c_0_152,plain,
union(X1,union(union(X1,X2),X3)) = union(union(X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_147]),c_0_68])]) ).
cnf(c_0_153,plain,
subset(union(X1,X2),union(X2,intersection(union(X3,X1),union(X1,X2)))),
inference(spm,[status(thm)],[c_0_146,c_0_85]) ).
cnf(c_0_154,plain,
subset(union(X1,X2),union(union(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_148,c_0_32]) ).
cnf(c_0_155,plain,
subset(intersection(X1,union(X2,intersection(union(X3,union(X4,X2)),X1))),intersection(union(X3,union(X4,X2)),X1)),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_156,plain,
union(X1,intersection(union(X2,X3),union(X2,X1))) = union(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_151]),c_0_72])]) ).
cnf(c_0_157,plain,
subset(intersection(X1,union(X2,intersection(union(union(X2,X3),X4),X1))),intersection(union(union(X2,X3),X4),X1)),
inference(spm,[status(thm)],[c_0_149,c_0_152]) ).
cnf(c_0_158,plain,
union(X1,intersection(union(X2,X3),union(X3,X1))) = union(X3,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_153]),c_0_72])]) ).
cnf(c_0_159,plain,
intersection(union(X1,X2),intersection(X3,X1)) = intersection(X3,X1),
inference(spm,[status(thm)],[c_0_51,c_0_63]) ).
cnf(c_0_160,plain,
subset(union(X1,intersection(X2,union(X1,X3))),union(X1,X3)),
inference(spm,[status(thm)],[c_0_154,c_0_61]) ).
cnf(c_0_161,plain,
union(X1,union(X2,union(X1,X3))) = union(X2,union(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_144]),c_0_68])]) ).
cnf(c_0_162,plain,
subset(union(X1,X2),intersection(union(X1,X2),union(X1,union(X3,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_66]),c_0_51]) ).
cnf(c_0_163,plain,
subset(union(X1,X2),intersection(union(X1,X2),union(union(X2,X3),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_66]),c_0_51]) ).
cnf(c_0_164,plain,
union(union(X1,X2),intersection(X3,X1)) = union(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_159]) ).
cnf(c_0_165,plain,
subset(union(X1,intersection(X2,union(X3,union(X1,X4)))),union(X3,union(X1,X4))),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_166,plain,
intersection(union(X1,X2),union(X1,union(X3,X2))) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_162]),c_0_59])]) ).
cnf(c_0_167,plain,
subset(union(X1,intersection(X2,union(union(X3,X1),X4))),union(union(X3,X1),X4)),
inference(spm,[status(thm)],[c_0_160,c_0_132]) ).
cnf(c_0_168,plain,
intersection(union(X1,X2),union(union(X2,X3),X1)) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_163]),c_0_59])]) ).
cnf(c_0_169,plain,
subset(union(intersection(X1,X2),intersection(X1,union(X2,X3))),intersection(X1,union(X2,X3))),
inference(spm,[status(thm)],[c_0_126,c_0_164]) ).
cnf(c_0_170,plain,
subset(union(X1,union(X2,X3)),union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_171,plain,
subset(union(X1,union(X2,X3)),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_172,plain,
intersection(X1,intersection(union(X2,X1),X3)) = intersection(X1,X3),
inference(rw,[status(thm)],[c_0_103,c_0_140]) ).
cnf(c_0_173,plain,
subset(union(intersection(X1,X2),intersection(union(X2,X3),X1)),intersection(union(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_169,c_0_51]) ).
cnf(c_0_174,plain,
union(intersection(X1,X2),union(X2,X3)) = union(X2,X3),
inference(spm,[status(thm)],[c_0_132,c_0_61]) ).
cnf(c_0_175,plain,
union(X1,union(X2,X3)) = union(X2,union(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_170]),c_0_170])]) ).
cnf(c_0_176,plain,
subset(union(X1,union(X2,intersection(X3,union(X2,X1)))),union(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_61]),c_0_32]) ).
cnf(c_0_177,plain,
subset(union(intersection(X1,X2),X3),union(X3,intersection(union(X4,X1),X2))),
inference(spm,[status(thm)],[c_0_71,c_0_172]) ).
cnf(c_0_178,plain,
union(intersection(X1,X2),intersection(union(X2,X3),X1)) = intersection(union(X2,X3),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_173]),c_0_68])]) ).
cnf(c_0_179,plain,
intersection(X1,union(union(X2,X1),X3)) = X1,
inference(spm,[status(thm)],[c_0_76,c_0_132]) ).
cnf(c_0_180,plain,
( subset(union(intersection(X1,X2),X3),X3)
| member(esk1_2(union(intersection(X1,X2),X3),X3),intersection(X2,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_23]) ).
cnf(c_0_181,plain,
union(X1,union(intersection(X2,X1),X3)) = union(X1,X3),
inference(rw,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_182,plain,
union(X1,union(X2,intersection(X3,union(X2,X1)))) = union(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_176]),c_0_148])]) ).
cnf(c_0_183,plain,
union(X1,union(X2,intersection(X3,X1))) = union(X2,X1),
inference(spm,[status(thm)],[c_0_175,c_0_61]) ).
cnf(c_0_184,plain,
subset(union(intersection(X1,X2),intersection(X2,X3)),intersection(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_185,plain,
intersection(X1,intersection(X2,union(union(X3,X1),X4))) = intersection(X2,X1),
inference(spm,[status(thm)],[c_0_140,c_0_179]) ).
cnf(c_0_186,plain,
union(union(X1,X2),X3) = union(X1,union(X3,X2)),
inference(spm,[status(thm)],[c_0_32,c_0_175]) ).
cnf(c_0_187,plain,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_51,c_0_140]) ).
fof(c_0_188,negated_conjecture,
~ ! [X1,X2,X3] : union(X1,intersection(X2,X3)) = intersection(union(X1,X2),union(X1,X3)),
inference(assume_negation,[status(cth)],[prove_union_distributes_over_intersection]) ).
cnf(c_0_189,plain,
subset(intersection(X1,union(X2,X3)),union(X2,intersection(X3,X1))),
inference(spm,[status(thm)],[c_0_88,c_0_32]) ).
cnf(c_0_190,plain,
subset(union(intersection(X1,X2),union(X3,union(X4,intersection(X2,X1)))),union(X3,union(X4,intersection(X2,X1)))),
inference(spm,[status(thm)],[c_0_46,c_0_180]) ).
cnf(c_0_191,plain,
union(X1,union(X2,intersection(X3,union(X2,intersection(X4,X1))))) = union(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_183]) ).
cnf(c_0_192,plain,
( subset(X1,union(intersection(X2,X1),X3))
| ~ member(esk1_2(X1,union(intersection(X2,X1),X3)),X2) ),
inference(spm,[status(thm)],[c_0_111,c_0_12]) ).
cnf(c_0_193,plain,
( subset(intersection(X1,union(X2,X3)),union(X4,intersection(X3,X1)))
| member(esk1_2(intersection(X1,union(X2,X3)),union(X4,intersection(X3,X1))),X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_65]) ).
cnf(c_0_194,plain,
subset(union(intersection(X1,X2),intersection(X1,X3)),intersection(X1,union(X3,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_143]),c_0_185]),c_0_186]),c_0_187]),c_0_76]) ).
cnf(c_0_195,plain,
intersection(X1,intersection(X2,intersection(X3,X1))) = intersection(X2,intersection(X3,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_87]),c_0_45])]) ).
fof(c_0_196,negated_conjecture,
union(esk3_0,intersection(esk4_0,esk5_0)) != intersection(union(esk3_0,esk4_0),union(esk3_0,esk5_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_188])])]) ).
cnf(c_0_197,plain,
subset(union(X1,intersection(X2,union(X1,X3))),intersection(union(X1,X2),union(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_156]),c_0_186]),c_0_52]) ).
cnf(c_0_198,plain,
subset(intersection(union(X1,X2),X3),union(X1,intersection(X2,X3))),
inference(spm,[status(thm)],[c_0_189,c_0_51]) ).
cnf(c_0_199,plain,
subset(union(X1,union(X2,intersection(union(X1,intersection(X3,X2)),X4))),union(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_32]),c_0_186]),c_0_32]) ).
cnf(c_0_200,plain,
subset(union(X1,X2),union(X1,union(X2,X3))),
inference(spm,[status(thm)],[c_0_148,c_0_161]) ).
cnf(c_0_201,plain,
subset(intersection(X1,union(X2,X3)),union(intersection(X1,X2),intersection(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_143]) ).
cnf(c_0_202,plain,
subset(union(intersection(X1,X2),intersection(X3,X1)),intersection(X1,union(X2,X3))),
inference(spm,[status(thm)],[c_0_194,c_0_89]) ).
cnf(c_0_203,plain,
union(X1,intersection(X2,intersection(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_195]) ).
cnf(c_0_204,negated_conjecture,
union(esk3_0,intersection(esk4_0,esk5_0)) != intersection(union(esk3_0,esk4_0),union(esk3_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_196]) ).
cnf(c_0_205,plain,
intersection(union(X1,X2),union(X1,X3)) = union(X1,intersection(X2,union(X1,X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_197]),c_0_198])]) ).
cnf(c_0_206,plain,
union(X1,union(X2,intersection(union(X1,intersection(X3,X2)),X4))) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_199]),c_0_200])]) ).
cnf(c_0_207,plain,
union(intersection(X1,X2),intersection(X3,X1)) = intersection(X1,union(X2,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_201]),c_0_202])]) ).
cnf(c_0_208,plain,
union(X1,union(X2,intersection(X3,intersection(X4,X1)))) = union(X2,X1),
inference(spm,[status(thm)],[c_0_175,c_0_203]) ).
cnf(c_0_209,negated_conjecture,
union(esk3_0,intersection(esk4_0,union(esk3_0,esk5_0))) != union(esk3_0,intersection(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_204,c_0_205]) ).
cnf(c_0_210,plain,
union(X1,intersection(X2,union(X1,X3))) = union(X1,intersection(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_208]) ).
cnf(c_0_211,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_210])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET171+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
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sat Aug 26 14:08:59 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 138.33/138.45 % Version : CSE_E---1.5
% 138.33/138.45 % Problem : theBenchmark.p
% 138.33/138.45 % Proof found
% 138.33/138.45 % SZS status Theorem for theBenchmark.p
% 138.33/138.45 % SZS output start Proof
% See solution above
% 138.37/138.46 % Total time : 137.744000 s
% 138.37/138.46 % SZS output end Proof
% 138.37/138.46 % Total time : 137.753000 s
%------------------------------------------------------------------------------