%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET609+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:17:40 PM UTC 2026
% Result : Theorem 104.74s 13.80s
% Output : CNFRefutation 104.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 8
% Syntax : Number of formulae : 235 ( 166 unt; 0 def)
% Number of atoms : 346 ( 118 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 180 ( 69 ~; 90 |; 14 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% 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 : 671 ( 118 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
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,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X2)
| member(X3,X1) ) ),
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(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_8,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_9,plain,
! [X10,X11,X12] :
( ( member(X12,difference(X10,X11))
| member(X12,X11)
| ~ member(X12,X10) )
& ( ~ member(X12,difference(X10,X11))
| ~ member(X12,X11) )
& ( ~ member(X12,difference(X10,X11))
| member(X12,X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_10,plain,
! [X19,X20,X21,X22,X23] :
( ( subset(X22,X23)
| ~ member(esk1_2(X22,X23),X23) )
& ( subset(X22,X23)
| member(esk1_2(X22,X23),X22) )
& ( member(X21,X20)
| ~ member(X21,X19)
| ~ subset(X19,X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_11,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X7,X8,X9] :
( ( member(X9,intersection(X7,X8))
| ~ member(X9,X8)
| ~ member(X9,X7) )
& ( ~ member(X9,intersection(X7,X8))
| member(X9,X8) )
& ( ~ member(X9,intersection(X7,X8))
| member(X9,X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
fof(c_0_14,plain,
! [X13,X14] :
( ( X13 = X14
| ~ subset(X14,X13)
| ~ subset(X13,X14) )
& ( X13 != X14
| subset(X14,X13) )
& ( X13 != X14
| subset(X13,X14) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_15,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( ~ member(esk1_2(difference(X1,X2),X3),X2)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_23,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_24,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_25,plain,
( ~ subset(X1,difference(X1,X2))
| difference(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_27,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_28,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_29,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,plain,
( ~ subset(X1,intersection(X1,X2))
| intersection(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_27]) ).
cnf(c_0_32,plain,
( ~ subset(X2,intersection(X1,X2))
| intersection(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_33,plain,
( member(esk1_2(difference(difference(X1,X2),X3),X4),X1)
| subset(difference(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
fof(c_0_34,plain,
! [X4,X5,X6] :
( ( member(X6,union(X4,X5))
| ~ member(X6,X5) )
& ( member(X6,union(X4,X5))
| ~ member(X6,X4) )
& ( member(X6,X5)
| member(X6,X4)
| ~ member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
cnf(c_0_35,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_36,plain,
( ~ member(esk1_2(intersection(X1,difference(X2,X3)),X4),X3)
| subset(intersection(X1,difference(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_37,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_38,plain,
( ~ member(X1,X3)
| ~ member(X1,difference(X2,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_39,plain,
( ~ member(esk1_2(X1,difference(X2,X3)),X2)
| member(esk1_2(X1,difference(X2,X3)),X3)
| subset(X1,difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_30]) ).
cnf(c_0_40,plain,
intersection(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_41,plain,
intersection(X1,difference(X2,X2)) = difference(X2,X2),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_42,plain,
subset(difference(difference(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_43,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
( ~ member(esk1_2(difference(X1,intersection(X2,X3)),X4),X2)
| ~ member(esk1_2(difference(X1,intersection(X2,X3)),X4),X3)
| subset(difference(X1,intersection(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_45,plain,
subset(intersection(X1,difference(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_36,c_0_23]) ).
cnf(c_0_46,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_26]),c_0_38]) ).
cnf(c_0_47,plain,
( member(esk1_2(X1,difference(X1,X2)),X2)
| subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_12]) ).
cnf(c_0_48,plain,
difference(X1,X1) = difference(X2,X2),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
difference(difference(difference(X1,X2),X1),X3) = difference(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_42]) ).
cnf(c_0_50,plain,
( ~ member(esk1_2(difference(X1,union(X2,X3)),X4),X3)
| subset(difference(X1,union(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_43]) ).
cnf(c_0_51,plain,
( ~ member(esk1_2(difference(X1,intersection(X2,X1)),X3),X2)
| subset(difference(X1,intersection(X2,X1)),X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_16]) ).
cnf(c_0_52,plain,
( member(esk1_2(difference(X1,X2),difference(X1,X3)),X3)
| subset(difference(X1,X2),difference(X1,X3)) ),
inference(spm,[status(thm)],[c_0_39,c_0_16]) ).
fof(c_0_53,plain,
! [X17,X18] : intersection(X17,X18) = intersection(X18,X17),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_54,plain,
difference(intersection(X1,difference(X2,X1)),X3) = intersection(X1,difference(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_55,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_56,plain,
( ~ member(esk1_2(X1,intersection(X2,X3)),X2)
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| subset(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_35]) ).
cnf(c_0_57,plain,
( ~ member(esk1_2(difference(X1,difference(X2,X3)),X4),X2)
| member(esk1_2(difference(X1,difference(X2,X3)),X4),X3)
| subset(difference(X1,difference(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_58,plain,
difference(difference(X1,X2),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_59,plain,
subset(difference(X1,union(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_50,c_0_16]) ).
cnf(c_0_60,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_61,plain,
subset(difference(X1,intersection(X2,X1)),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_62,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
intersection(X1,difference(X2,X1)) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_48,c_0_54]) ).
cnf(c_0_64,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_55]),c_0_21])]) ).
cnf(c_0_65,plain,
( ~ member(esk1_2(difference(X1,X2),intersection(X3,X1)),X3)
| subset(difference(X1,X2),intersection(X3,X1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_16]) ).
cnf(c_0_66,plain,
( member(esk1_2(difference(X1,difference(X1,X2)),X3),X2)
| subset(difference(X1,difference(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_16]) ).
cnf(c_0_67,plain,
difference(difference(X1,X2),X1) = difference(difference(X3,X4),X3),
inference(spm,[status(thm)],[c_0_49,c_0_58]) ).
cnf(c_0_68,plain,
difference(difference(X1,union(X2,X1)),X3) = difference(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_59]) ).
cnf(c_0_69,plain,
( member(esk1_2(intersection(difference(X1,X2),X3),X4),X1)
| subset(intersection(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_11,c_0_23]) ).
cnf(c_0_70,plain,
( ~ member(esk1_2(intersection(difference(X1,X2),X3),X4),X2)
| subset(intersection(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_71,plain,
( member(esk1_2(intersection(X1,union(X2,X3)),X4),X2)
| member(esk1_2(intersection(X1,union(X2,X3)),X4),X3)
| subset(intersection(X1,union(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_60,c_0_24]) ).
cnf(c_0_72,plain,
subset(difference(X1,intersection(X1,X2)),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_73,plain,
intersection(X1,difference(X2,X1)) = intersection(X3,difference(X4,X3)),
inference(spm,[status(thm)],[c_0_54,c_0_63]) ).
cnf(c_0_74,plain,
difference(X1,intersection(X2,difference(X3,X2))) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_54]) ).
cnf(c_0_75,plain,
( member(esk1_2(intersection(intersection(X1,X2),X3),X4),X2)
| subset(intersection(intersection(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_76,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_77,plain,
difference(X1,union(X2,X1)) = difference(difference(X3,X4),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_68]) ).
cnf(c_0_78,plain,
difference(X1,difference(difference(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_49]) ).
cnf(c_0_79,plain,
( ~ member(esk1_2(intersection(difference(X1,X2),X3),intersection(X4,X1)),X4)
| subset(intersection(difference(X1,X2),X3),intersection(X4,X1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_69]) ).
cnf(c_0_80,plain,
( member(esk1_2(intersection(difference(X1,X2),union(X2,X3)),X4),X3)
| subset(intersection(difference(X1,X2),union(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_81,plain,
subset(X1,difference(X1,difference(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_82,plain,
( ~ member(esk1_2(intersection(intersection(X1,X2),X3),intersection(X4,X2)),X4)
| subset(intersection(intersection(X1,X2),X3),intersection(X4,X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_75]) ).
cnf(c_0_83,plain,
subset(X1,intersection(X1,union(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_62]) ).
cnf(c_0_84,plain,
subset(intersection(difference(X1,X2),union(X2,X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
difference(X1,difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_81]),c_0_21])]) ).
cnf(c_0_86,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_82,c_0_24]) ).
cnf(c_0_87,plain,
intersection(X1,union(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_83]),c_0_27])]) ).
cnf(c_0_88,plain,
subset(intersection(X1,union(difference(X2,X1),X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,plain,
subset(intersection(X1,X2),intersection(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_90,plain,
intersection(X1,union(difference(X2,X1),X3)) = intersection(X3,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_88]),c_0_89])]) ).
cnf(c_0_91,plain,
subset(difference(X1,X2),intersection(X1,difference(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_12]),c_0_62]) ).
cnf(c_0_92,plain,
intersection(difference(X1,X2),union(X2,X3)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_90,c_0_85]) ).
cnf(c_0_93,plain,
( member(esk1_2(difference(intersection(X1,X2),X3),X4),X2)
| subset(difference(intersection(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_94,plain,
~ member(X1,difference(difference(X2,X3),X2)),
inference(spm,[status(thm)],[c_0_46,c_0_49]) ).
cnf(c_0_95,plain,
( member(esk1_2(difference(union(X1,X2),X3),X4),X1)
| member(esk1_2(difference(union(X1,X2),X3),X4),X2)
| subset(difference(union(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_60,c_0_16]) ).
cnf(c_0_96,plain,
( member(esk1_2(intersection(X1,X2),difference(X1,X3)),X3)
| subset(intersection(X1,X2),difference(X1,X3)) ),
inference(spm,[status(thm)],[c_0_39,c_0_23]) ).
cnf(c_0_97,plain,
intersection(X1,difference(X1,X2)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_91]),c_0_28])]) ).
cnf(c_0_98,plain,
intersection(union(X1,X2),difference(X3,X1)) = intersection(X2,difference(X3,X1)),
inference(spm,[status(thm)],[c_0_62,c_0_92]) ).
cnf(c_0_99,plain,
( member(esk1_2(difference(intersection(X1,X2),X3),difference(X2,X4)),X4)
| subset(difference(intersection(X1,X2),X3),difference(X2,X4)) ),
inference(spm,[status(thm)],[c_0_39,c_0_93]) ).
fof(c_0_100,plain,
! [X15,X16] : union(X15,X16) = union(X16,X15),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_101,plain,
( member(esk1_2(difference(union(difference(difference(X1,X2),X1),X3),X4),X5),X3)
| subset(difference(union(difference(difference(X1,X2),X1),X3),X4),X5) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_102,plain,
subset(intersection(X1,difference(X2,X3)),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_36,c_0_96]) ).
cnf(c_0_103,plain,
intersection(X1,difference(union(X2,X1),X2)) = difference(union(X2,X1),X2),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_104,plain,
subset(difference(intersection(X1,X2),X3),difference(X2,X3)),
inference(spm,[status(thm)],[c_0_22,c_0_99]) ).
cnf(c_0_105,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_106,plain,
( ~ member(esk1_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_43]) ).
cnf(c_0_107,plain,
( member(esk1_2(difference(intersection(X1,X2),X3),X4),X1)
| subset(difference(intersection(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_108,plain,
subset(difference(union(difference(difference(X1,X2),X1),X3),X4),X3),
inference(spm,[status(thm)],[c_0_15,c_0_101]) ).
cnf(c_0_109,plain,
subset(difference(union(X1,X2),X1),difference(X2,X1)),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_110,plain,
subset(difference(X1,X2),difference(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_104,c_0_87]) ).
cnf(c_0_111,plain,
intersection(X1,union(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_87,c_0_105]) ).
cnf(c_0_112,plain,
( member(esk1_2(difference(union(X1,X2),X3),union(X4,X1)),X2)
| subset(difference(union(X1,X2),X3),union(X4,X1)) ),
inference(spm,[status(thm)],[c_0_106,c_0_95]) ).
cnf(c_0_113,plain,
( ~ member(esk1_2(difference(intersection(X1,X2),X3),intersection(X4,X1)),X4)
| subset(difference(intersection(X1,X2),X3),intersection(X4,X1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_107]) ).
cnf(c_0_114,plain,
( member(esk1_2(difference(intersection(X1,X2),difference(X2,X3)),X4),X3)
| subset(difference(intersection(X1,X2),difference(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_57,c_0_93]) ).
cnf(c_0_115,plain,
( member(esk1_2(intersection(X1,X2),difference(X2,X3)),X3)
| subset(intersection(X1,X2),difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_39,c_0_24]) ).
cnf(c_0_116,plain,
subset(difference(union(difference(X1,X1),X2),X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_29]),c_0_29]) ).
cnf(c_0_117,plain,
( ~ member(esk1_2(intersection(X1,difference(X2,union(X3,X4))),X5),X4)
| subset(intersection(X1,difference(X2,union(X3,X4))),X5) ),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_118,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_15,c_0_66]) ).
cnf(c_0_119,plain,
difference(union(X1,X2),X1) = difference(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_109]),c_0_110])]) ).
cnf(c_0_120,plain,
subset(difference(X1,X2),difference(union(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_104,c_0_111]) ).
cnf(c_0_121,plain,
subset(difference(union(X1,union(X2,X1)),X3),union(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_112]) ).
cnf(c_0_122,plain,
subset(difference(intersection(X1,X2),difference(X2,X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_123,plain,
subset(intersection(difference(X1,X2),X3),difference(X3,X2)),
inference(spm,[status(thm)],[c_0_70,c_0_115]) ).
cnf(c_0_124,plain,
subset(union(difference(X1,X1),X2),X2),
inference(spm,[status(thm)],[c_0_116,c_0_78]) ).
cnf(c_0_125,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_106,c_0_12]) ).
cnf(c_0_126,plain,
( ~ subset(X1,difference(X2,X2))
| X1 = difference(X2,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_127,plain,
subset(intersection(X1,difference(X2,union(X3,X1))),X4),
inference(spm,[status(thm)],[c_0_117,c_0_23]) ).
cnf(c_0_128,plain,
subset(difference(union(X1,X2),difference(X2,X1)),X1),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_129,plain,
subset(X1,difference(union(X1,X2),difference(X3,X1))),
inference(spm,[status(thm)],[c_0_120,c_0_85]) ).
cnf(c_0_130,plain,
subset(union(X1,union(X2,X1)),union(X2,X1)),
inference(spm,[status(thm)],[c_0_121,c_0_78]) ).
cnf(c_0_131,plain,
subset(difference(X1,difference(union(X2,X1),X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_122,c_0_87]) ).
cnf(c_0_132,plain,
subset(intersection(X1,X2),difference(X2,difference(X3,X1))),
inference(spm,[status(thm)],[c_0_123,c_0_85]) ).
cnf(c_0_133,plain,
union(difference(X1,X1),X2) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_124]),c_0_125])]) ).
cnf(c_0_134,plain,
intersection(X1,difference(X2,union(X3,X1))) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_135,plain,
difference(union(X1,X2),difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_128]),c_0_129])]) ).
cnf(c_0_136,plain,
difference(union(X1,X2),X2) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_119,c_0_105]) ).
cnf(c_0_137,plain,
union(X1,union(X2,X1)) = union(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_130]),c_0_125])]) ).
cnf(c_0_138,plain,
difference(X1,difference(union(X2,X1),X3)) = intersection(X3,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_131]),c_0_132])]) ).
cnf(c_0_139,plain,
union(difference(difference(X1,X2),X1),X3) = X3,
inference(spm,[status(thm)],[c_0_133,c_0_49]) ).
cnf(c_0_140,plain,
( ~ member(esk1_2(difference(difference(X1,X2),X3),X4),X2)
| subset(difference(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_141,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_142,plain,
subset(X1,difference(X1,difference(X2,union(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_134]),c_0_64]) ).
cnf(c_0_143,plain,
subset(difference(X1,difference(union(X1,X2),X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_122,c_0_111]) ).
cnf(c_0_144,plain,
difference(union(X1,X2),difference(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]) ).
cnf(c_0_145,plain,
difference(X1,difference(X1,X2)) = intersection(X2,X1),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_146,plain,
union(X1,difference(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_78,c_0_135]) ).
cnf(c_0_147,plain,
( ~ member(esk1_2(difference(difference(X1,union(X2,X3)),X4),X5),X2)
| subset(difference(difference(X1,union(X2,X3)),X4),X5) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_148,plain,
( member(esk1_2(difference(difference(X1,X2),difference(X1,X3)),X4),X3)
| subset(difference(difference(X1,X2),difference(X1,X3)),X4) ),
inference(spm,[status(thm)],[c_0_57,c_0_33]) ).
cnf(c_0_149,plain,
difference(X1,difference(X2,union(X3,X1))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_142]),c_0_21])]) ).
cnf(c_0_150,plain,
subset(intersection(X1,difference(X2,union(X1,X3))),X4),
inference(spm,[status(thm)],[c_0_127,c_0_105]) ).
cnf(c_0_151,plain,
difference(X1,difference(union(X1,X2),X3)) = intersection(X3,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_143]),c_0_132])]) ).
cnf(c_0_152,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_146]) ).
cnf(c_0_153,plain,
subset(difference(difference(X1,union(X2,X3)),difference(X1,X2)),X4),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_154,plain,
difference(difference(X1,union(X2,X3)),X3) = difference(X1,union(X2,X3)),
inference(spm,[status(thm)],[c_0_85,c_0_149]) ).
cnf(c_0_155,plain,
( ~ member(esk1_2(X1,union(X2,X3)),X2)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_141]) ).
cnf(c_0_156,plain,
subset(difference(intersection(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_22,c_0_107]) ).
cnf(c_0_157,plain,
intersection(X1,difference(X2,union(X1,X3))) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_126,c_0_150]) ).
cnf(c_0_158,plain,
intersection(X1,difference(union(X1,X2),X3)) = difference(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_151]),c_0_152]),c_0_62]) ).
cnf(c_0_159,plain,
subset(difference(X1,union(X2,difference(X1,X2))),X3),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_160,plain,
( ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3)
| subset(X1,union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_155,c_0_43]) ).
cnf(c_0_161,plain,
subset(difference(intersection(X1,X2),X2),X3),
inference(spm,[status(thm)],[c_0_156,c_0_62]) ).
cnf(c_0_162,plain,
subset(X1,difference(X1,difference(X2,union(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_157]),c_0_64]) ).
cnf(c_0_163,plain,
intersection(X1,difference(union(X2,X1),X3)) = difference(X1,X3),
inference(spm,[status(thm)],[c_0_158,c_0_137]) ).
cnf(c_0_164,plain,
difference(X1,union(X2,difference(X1,X2))) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_126,c_0_159]) ).
cnf(c_0_165,plain,
subset(difference(union(X1,X2),X3),union(union(X4,X2),X1)),
inference(spm,[status(thm)],[c_0_160,c_0_112]) ).
cnf(c_0_166,plain,
difference(difference(intersection(X1,X2),X2),X3) = difference(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_25,c_0_161]) ).
cnf(c_0_167,plain,
difference(X1,difference(X2,union(X1,X3))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_162]),c_0_21])]) ).
cnf(c_0_168,plain,
difference(difference(X1,X2),difference(X1,X3)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_138,c_0_146]) ).
cnf(c_0_169,plain,
intersection(difference(X1,X2),difference(X1,X3)) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_163,c_0_146]) ).
cnf(c_0_170,plain,
intersection(X1,union(X2,difference(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_164]),c_0_64]),c_0_62]) ).
cnf(c_0_171,plain,
subset(union(X1,X2),union(union(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_165,c_0_78]) ).
cnf(c_0_172,plain,
difference(X1,difference(intersection(X2,X3),X3)) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_166]) ).
cnf(c_0_173,plain,
difference(difference(X1,union(X2,X3)),X2) = difference(X1,union(X2,X3)),
inference(spm,[status(thm)],[c_0_85,c_0_167]) ).
cnf(c_0_174,plain,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_168]),c_0_152]),c_0_169]) ).
cnf(c_0_175,plain,
difference(difference(X1,X2),union(X2,X3)) = difference(difference(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_98]),c_0_152]) ).
cnf(c_0_176,plain,
subset(X1,union(X2,difference(X1,X2))),
inference(spm,[status(thm)],[c_0_28,c_0_170]) ).
cnf(c_0_177,plain,
subset(union(X1,difference(X2,X3)),union(X2,X1)),
inference(spm,[status(thm)],[c_0_171,c_0_146]) ).
cnf(c_0_178,plain,
union(X1,intersection(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_172,c_0_135]) ).
cnf(c_0_179,plain,
subset(union(X1,X2),union(X1,union(X3,X2))),
inference(spm,[status(thm)],[c_0_171,c_0_105]) ).
cnf(c_0_180,plain,
difference(difference(X1,X2),X3) = difference(X1,union(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_174]),c_0_175]) ).
cnf(c_0_181,plain,
subset(X1,union(intersection(X2,X1),difference(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_145]),c_0_105]) ).
cnf(c_0_182,plain,
subset(union(intersection(X1,X2),difference(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_183,plain,
subset(union(X1,X2),union(X1,difference(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_135]),c_0_105]) ).
cnf(c_0_184,plain,
subset(union(X1,difference(X2,X3)),union(X1,X2)),
inference(spm,[status(thm)],[c_0_179,c_0_146]) ).
cnf(c_0_185,plain,
difference(union(X1,X2),union(X1,X3)) = difference(X2,union(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_119]),c_0_180]) ).
cnf(c_0_186,plain,
union(intersection(X1,X2),difference(X2,X1)) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_181]),c_0_182])]) ).
cnf(c_0_187,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_183]),c_0_184])]) ).
cnf(c_0_188,plain,
difference(union(intersection(X1,X2),X3),X2) = difference(X3,X2),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_189,plain,
union(X1,union(intersection(X2,X1),X3)) = union(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_187]) ).
cnf(c_0_190,plain,
difference(difference(intersection(X1,X2),X1),X3) = difference(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_156]) ).
cnf(c_0_191,plain,
union(X1,union(X2,intersection(X3,X1))) = union(X1,X2),
inference(spm,[status(thm)],[c_0_189,c_0_105]) ).
cnf(c_0_192,plain,
difference(X1,difference(intersection(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_190]) ).
cnf(c_0_193,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_152,c_0_62]) ).
cnf(c_0_194,plain,
union(union(X1,X2),union(X2,X3)) = union(union(X1,X2),X3),
inference(spm,[status(thm)],[c_0_189,c_0_87]) ).
cnf(c_0_195,plain,
union(union(X1,X2),union(X3,X1)) = union(union(X1,X2),X3),
inference(spm,[status(thm)],[c_0_191,c_0_111]) ).
cnf(c_0_196,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_138,c_0_152]),c_0_138]),c_0_62]) ).
cnf(c_0_197,plain,
union(X1,intersection(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_192,c_0_135]) ).
cnf(c_0_198,plain,
intersection(X1,intersection(union(X2,X1),X3)) = intersection(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_193]),c_0_138]),c_0_62]) ).
cnf(c_0_199,plain,
union(union(X1,X2),X3) = union(union(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_194]),c_0_195]) ).
cnf(c_0_200,plain,
intersection(intersection(X1,X2),intersection(X3,X1)) = intersection(X3,intersection(X1,X2)),
inference(spm,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_201,plain,
intersection(intersection(X1,X2),intersection(X2,X3)) = intersection(X3,intersection(X1,X2)),
inference(spm,[status(thm)],[c_0_198,c_0_178]) ).
cnf(c_0_202,plain,
union(union(X1,X2),X3) = union(X2,union(X3,X1)),
inference(spm,[status(thm)],[c_0_105,c_0_199]) ).
cnf(c_0_203,plain,
intersection(X1,intersection(X2,X3)) = intersection(X2,intersection(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_200]),c_0_201]) ).
cnf(c_0_204,plain,
difference(union(X1,union(X2,X3)),X2) = difference(union(X3,X1),X2),
inference(spm,[status(thm)],[c_0_136,c_0_202]) ).
cnf(c_0_205,plain,
intersection(intersection(X1,X2),difference(X2,X3)) = difference(intersection(X1,X2),X3),
inference(spm,[status(thm)],[c_0_163,c_0_178]) ).
cnf(c_0_206,plain,
intersection(difference(X1,X2),intersection(X3,X1)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_196,c_0_146]) ).
cnf(c_0_207,plain,
intersection(X1,union(X2,difference(X3,X1))) = intersection(X2,X1),
inference(spm,[status(thm)],[c_0_90,c_0_105]) ).
cnf(c_0_208,plain,
union(X1,difference(X2,intersection(X3,X1))) = union(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_187]),c_0_189]) ).
cnf(c_0_209,plain,
difference(X1,intersection(X2,intersection(X1,X3))) = difference(X1,intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_193,c_0_203]) ).
cnf(c_0_210,plain,
difference(union(X1,union(X2,X3)),X3) = difference(union(X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_137]),c_0_202]),c_0_119]) ).
cnf(c_0_211,plain,
difference(intersection(X1,X2),X3) = intersection(X1,difference(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_205]),c_0_206]) ).
cnf(c_0_212,plain,
intersection(difference(X1,X2),union(X3,X2)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_207,c_0_85]) ).
cnf(c_0_213,plain,
difference(X1,intersection(X2,intersection(X3,X1))) = difference(X1,intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_193,c_0_203]) ).
fof(c_0_214,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_215,plain,
union(intersection(X1,X2),difference(X1,intersection(X2,X3))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_105]),c_0_197]) ).
cnf(c_0_216,plain,
difference(union(X1,X2),difference(union(X3,X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_210]),c_0_87]) ).
cnf(c_0_217,plain,
difference(X1,union(intersection(X1,X2),X3)) = difference(X1,union(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_193]),c_0_180]) ).
cnf(c_0_218,plain,
union(X1,intersection(X2,difference(X3,X1))) = union(X1,intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_187,c_0_211]) ).
cnf(c_0_219,plain,
intersection(union(X1,X2),difference(X3,X2)) = intersection(X1,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_62,c_0_212]) ).
cnf(c_0_220,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_208,c_0_213]),c_0_105]),c_0_178]) ).
cnf(c_0_221,plain,
intersection(difference(X1,X2),X3) = intersection(X1,difference(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_198]),c_0_211]),c_0_211]),c_0_198]) ).
fof(c_0_222,negated_conjecture,
difference(esk3_0,difference(esk4_0,esk5_0)) != union(difference(esk3_0,esk4_0),intersection(esk3_0,esk5_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_214])])])]) ).
cnf(c_0_223,plain,
union(intersection(X1,X2),difference(X1,difference(X2,X3))) = X1,
inference(spm,[status(thm)],[c_0_215,c_0_163]) ).
cnf(c_0_224,plain,
difference(union(intersection(X1,X2),X3),difference(X1,X3)) = X3,
inference(spm,[status(thm)],[c_0_216,c_0_197]) ).
cnf(c_0_225,plain,
intersection(X1,union(intersection(X1,X2),X3)) = intersection(union(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_217]),c_0_145]),c_0_62]) ).
cnf(c_0_226,plain,
union(X1,intersection(union(X2,X1),X3)) = union(X1,intersection(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_218]) ).
cnf(c_0_227,plain,
union(difference(X1,X2),intersection(union(X3,X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_87]),c_0_105]) ).
cnf(c_0_228,plain,
intersection(union(X1,X2),difference(X3,difference(X2,X1))) = intersection(X1,X3),
inference(spm,[status(thm)],[c_0_221,c_0_135]) ).
cnf(c_0_229,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_222]) ).
cnf(c_0_230,plain,
union(X1,intersection(X2,X3)) = union(intersection(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_62]),c_0_225]),c_0_105]),c_0_226]) ).
cnf(c_0_231,plain,
union(difference(X1,X2),intersection(X3,X1)) = difference(X1,difference(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_180]),c_0_105]),c_0_146]) ).
cnf(c_0_232,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_229,c_0_105]) ).
cnf(c_0_233,plain,
union(intersection(X1,X2),difference(X1,X3)) = difference(X1,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_234,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_232,c_0_233])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET609+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:29:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 104.74/13.80 % Version: 3.5.1
% 104.74/13.80 % Preprocessing class: FSMSSMSSSSSNFFN.
% 104.74/13.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 104.74/13.80 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 104.74/13.80 % Starting new_bool_3 with 300s (1) cores
% 104.74/13.80 % Starting new_bool_1 with 300s (1) cores
% 104.74/13.80 % Starting sh5l with 300s (1) cores
% 104.74/13.80 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2337465 completed with status 0
% 104.74/13.80 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 104.74/13.80 % Preprocessing class: FSMSSMSSSSSNFFN.
% 104.74/13.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 104.74/13.80 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 104.74/13.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 104.74/13.80 % No SInE strategy applied
% 104.74/13.80 % Search class: FGHSS-FFSF22-SFFFFFNN
% 104.74/13.80 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 104.74/13.80 % Starting SubtermCWHack with 136s (1) cores
% 104.74/13.80 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 104.74/13.80 % Starting G----_0010_evo with 136s (1) cores
% 104.74/13.80 % Starting new_bool_3 with 136s (1) cores
% 104.74/13.80 % Starting new_bool_1 with 136s (1) cores
% 104.74/13.80 % G----_0010_evo with pid 2337474 completed with status 0
% 104.74/13.80 % Result found by G----_0010_evo
% 104.74/13.80 % Preprocessing class: FSMSSMSSSSSNFFN.
% 104.74/13.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 104.74/13.80 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 104.74/13.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 104.74/13.80 % No SInE strategy applied
% 104.74/13.80 % Search class: FGHSS-FFSF22-SFFFFFNN
% 104.74/13.80 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 104.74/13.80 % Starting SubtermCWHack with 136s (1) cores
% 104.74/13.80 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 104.74/13.80 % Starting G----_0010_evo with 136s (1) cores
% 104.74/13.80 % Preprocessing time : 0.001 s
% 104.74/13.80
% 104.74/13.80 % Proof found!
% 104.74/13.80 % SZS status Theorem
% 104.74/13.80 % SZS output start CNFRefutation
% See solution above
% 104.74/13.80 % Parsed axioms : 10
% 104.74/13.80 % Removed by relevancy pruning/SinE : 0
% 104.74/13.80 % Initial clauses : 23
% 104.74/13.80 % Removed in clause preprocessing : 2
% 104.74/13.80 % Initial clauses in saturation : 21
% 104.74/13.80 % Processed clauses : 56415
% 104.74/13.80 % ...of these trivial : 9405
% 104.74/13.80 % ...subsumed : 43453
% 104.74/13.80 % ...remaining for further processing : 3557
% 104.74/13.80 % Other redundant clauses eliminated : 2
% 104.74/13.80 % Clauses deleted for lack of memory : 0
% 104.74/13.80 % Backward-subsumed : 8
% 104.74/13.80 % Backward-rewritten : 1775
% 104.74/13.80 % Generated clauses : 1659325
% 104.74/13.80 % ...of the previous two non-redundant : 954661
% 104.74/13.80 % ...aggressively subsumed : 0
% 104.74/13.80 % Contextual simplify-reflections : 1
% 104.74/13.80 % Paramodulations : 1658231
% 104.74/13.80 % Factorizations : 1092
% 104.74/13.80 % NegExts : 0
% 104.74/13.80 % Equation resolutions : 2
% 104.74/13.80 % Disequality decompositions : 0
% 104.74/13.80 % Total rewrite steps : 2305664
% 104.74/13.80 % ...of those cached : 2105695
% 104.74/13.80 % Propositional unsat checks : 0
% 104.74/13.80 % Propositional check models : 0
% 104.74/13.80 % Propositional check unsatisfiable : 0
% 104.74/13.80 % Propositional clauses : 0
% 104.74/13.80 % Propositional clauses after purity: 0
% 104.74/13.80 % Propositional unsat core size : 0
% 104.74/13.80 % Propositional preprocessing time : 0.000
% 104.74/13.80 % Propositional encoding time : 0.000
% 104.74/13.80 % Propositional solver time : 0.000
% 104.74/13.80 % Success case prop preproc time : 0.000
% 104.74/13.80 % Success case prop encoding time : 0.000
% 104.74/13.80 % Success case prop solver time : 0.000
% 104.74/13.80 % Current number of processed clauses : 1772
% 104.74/13.80 % Positive orientable unit clauses : 954
% 104.74/13.80 % Positive unorientable unit clauses: 21
% 104.74/13.80 % Negative unit clauses : 11
% 104.74/13.80 % Non-unit-clauses : 786
% 104.74/13.80 % Current number of unprocessed clauses: 882995
% 104.74/13.80 % ...number of literals in the above : 1977591
% 104.74/13.80 % Current number of archived formulas : 0
% 104.74/13.80 % Current number of archived clauses : 1783
% 104.74/13.80 % Clause-clause subsumption calls (NU) : 351355
% 104.74/13.80 % Rec. Clause-clause subsumption calls : 187999
% 104.74/13.80 % Non-unit clause-clause subsumptions : 7017
% 104.74/13.80 % Unit Clause-clause subsumption calls : 340758
% 104.74/13.80 % Rewrite failures with RHS unbound : 6113
% 104.74/13.80 % BW rewrite match attempts : 50332
% 104.74/13.80 % BW rewrite match successes : 3211
% 104.74/13.80 % Condensation attempts : 0
% 104.74/13.80 % Condensation successes : 0
% 104.74/13.80 % Termbank termtop insertions : 20282177
% 104.74/13.80 % Search garbage collected termcells : 339
% 104.74/13.80
% 104.74/13.80 % -------------------------------------------------
% 104.74/13.80 % User time : 12.331 s
% 104.74/13.80 % System time : 0.625 s
% 104.74/13.80 % Total time : 12.957 s
% 104.74/13.80 % Maximum resident set size: 3636 pages
% 104.74/13.80
% 104.74/13.80 % -------------------------------------------------
% 104.74/13.80 % User time : 62.469 s
% 104.74/13.80 % System time : 2.825 s
% 104.74/13.80 % Total time : 65.294 s
% 104.74/13.80 % Maximum resident set size: 4864 pages
% 104.74/13.80 % E exiting
%------------------------------------------------------------------------------