%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET615+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 : n019.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 02:17:42 PM UTC 2026
% Result : Theorem 255.46s 32.81s
% Output : CNFRefutation 255.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 6
% Syntax : Number of formulae : 240 ( 184 unt; 0 def)
% Number of atoms : 330 ( 115 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 141 ( 51 ~; 73 |; 11 &)
% ( 5 <=>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 703 ( 106 sgn 37 !; 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(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(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_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(prove_difference_distributes_over_union,conjecture,
! [X1,X2,X3] : difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_distributes_over_union) ).
fof(c_0_6,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_7,plain,
! [X7,X8,X9] :
( ( member(X9,difference(X7,X8))
| member(X9,X8)
| ~ member(X9,X7) )
& ( ~ member(X9,difference(X7,X8))
| ~ member(X9,X8) )
& ( ~ member(X9,difference(X7,X8))
| member(X9,X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_8,plain,
! [X14,X15,X16,X17,X18] :
( ( subset(X17,X18)
| ~ member(esk1_2(X17,X18),X18) )
& ( subset(X17,X18)
| member(esk1_2(X17,X18),X17) )
& ( member(X16,X15)
| ~ member(X16,X14)
| ~ subset(X14,X15) ) ),
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_9,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,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_13,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_15,plain,
! [X10,X11] :
( ( X10 = X11
| ~ subset(X11,X10)
| ~ subset(X10,X11) )
& ( X10 != X11
| subset(X11,X10) )
& ( X10 != X11
| subset(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_16,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,plain,
( ~ member(esk1_2(difference(X1,X2),X3),X2)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_18,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,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_13,c_0_14]) ).
cnf(c_0_20,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_22,plain,
( ~ member(esk1_2(difference(difference(X1,X2),X3),X4),X2)
| subset(difference(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_23,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,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_17,c_0_14]) ).
cnf(c_0_25,plain,
( member(esk1_2(difference(difference(X1,X2),X3),X4),X1)
| subset(difference(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_26,plain,
( ~ member(esk1_2(difference(X1,union(X2,X3)),X4),X2)
| subset(difference(X1,union(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_27,plain,
( member(esk1_2(X1,difference(X1,X2)),X2)
| subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_28,plain,
( ~ subset(X1,difference(X1,X2))
| difference(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_30,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_31,plain,
( ~ member(esk1_2(difference(difference(X1,union(X2,X3)),X4),X5),X3)
| subset(difference(difference(X1,union(X2,X3)),X4),X5) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,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_24,c_0_25]) ).
cnf(c_0_33,plain,
subset(difference(X1,union(X2,X3)),difference(difference(X1,union(X2,X3)),X2)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_34,plain,
! [X12,X13] : union(X12,X13) = union(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_35,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( ~ member(X1,difference(X3,X3))
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_37,plain,
subset(difference(difference(X1,union(X2,X3)),difference(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
difference(difference(X1,union(X2,X3)),X2) = difference(X1,union(X2,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_33]),c_0_21])]) ).
cnf(c_0_39,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_35]),c_0_36]) ).
cnf(c_0_41,plain,
( ~ subset(X1,difference(X2,X2))
| X1 = difference(X2,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_42,plain,
subset(difference(X1,union(X2,difference(X1,X2))),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_43,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[c_0_40,c_0_27]) ).
cnf(c_0_44,plain,
( ~ member(esk1_2(X1,difference(X1,difference(X2,X3))),X3)
| subset(X1,difference(X1,difference(X2,X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_27]) ).
cnf(c_0_45,plain,
( member(esk1_2(difference(X1,difference(X1,X2)),X3),X2)
| subset(difference(X1,difference(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_46,plain,
difference(X1,union(X2,difference(X1,X2))) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_43]),c_0_21])]) ).
cnf(c_0_48,plain,
( member(esk1_2(difference(difference(difference(X1,X2),X3),X4),X5),X1)
| subset(difference(difference(difference(X1,X2),X3),X4),X5) ),
inference(spm,[status(thm)],[c_0_9,c_0_25]) ).
cnf(c_0_49,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_50,plain,
( member(esk1_2(difference(difference(X1,X2),X3),difference(X1,X4)),X4)
| subset(difference(difference(X1,X2),X3),difference(X1,X4)) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_51,plain,
subset(X1,difference(X1,difference(X2,X1))),
inference(spm,[status(thm)],[c_0_44,c_0_10]) ).
cnf(c_0_52,plain,
( member(esk1_2(X1,X2),union(X3,difference(X1,X3)))
| subset(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_47]) ).
cnf(c_0_53,plain,
( member(esk1_2(difference(difference(difference(X1,X2),X3),difference(X1,X4)),X5),X4)
| subset(difference(difference(difference(X1,X2),X3),difference(X1,X4)),X5) ),
inference(spm,[status(thm)],[c_0_24,c_0_48]) ).
cnf(c_0_54,plain,
subset(difference(difference(X1,X2),X3),difference(difference(difference(X1,X2),X3),X2)),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_55,plain,
( member(esk1_2(union(X1,X2),X3),X1)
| member(esk1_2(union(X1,X2),X3),X2)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_10]) ).
cnf(c_0_56,plain,
( ~ member(esk1_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_57,plain,
subset(difference(difference(X1,X2),X3),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_17,c_0_50]) ).
cnf(c_0_58,plain,
difference(X1,difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_51]),c_0_21])]) ).
cnf(c_0_59,plain,
subset(X1,difference(X1,difference(X2,union(X3,difference(X1,X3))))),
inference(spm,[status(thm)],[c_0_44,c_0_52]) ).
cnf(c_0_60,plain,
subset(difference(difference(difference(X1,X2),X3),difference(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_22,c_0_53]) ).
cnf(c_0_61,plain,
difference(difference(difference(X1,X2),X3),X2) = difference(difference(X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_54]),c_0_21])]) ).
cnf(c_0_62,plain,
( member(esk1_2(union(X1,X2),X1),X2)
| subset(union(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_55]) ).
cnf(c_0_63,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_56,c_0_10]) ).
cnf(c_0_64,plain,
subset(difference(X1,X2),difference(X1,difference(X3,difference(X1,X2)))),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,plain,
difference(X1,difference(X2,union(X3,difference(X1,X3)))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_59]),c_0_21])]) ).
cnf(c_0_66,plain,
subset(difference(difference(X1,difference(X1,X2)),X2),X3),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,plain,
subset(union(X1,difference(X2,X2)),X1),
inference(spm,[status(thm)],[c_0_40,c_0_62]) ).
cnf(c_0_68,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_63,c_0_39]) ).
cnf(c_0_69,plain,
( member(esk1_2(difference(difference(union(X1,X2),X3),X4),X5),X1)
| member(esk1_2(difference(difference(union(X1,X2),X3),X4),X5),X2)
| subset(difference(difference(union(X1,X2),X3),X4),X5) ),
inference(spm,[status(thm)],[c_0_49,c_0_25]) ).
cnf(c_0_70,plain,
subset(difference(X1,union(X2,difference(X3,X2))),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,plain,
difference(difference(X1,difference(X1,X2)),X2) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_41,c_0_66]) ).
cnf(c_0_72,plain,
union(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_67]),c_0_68])]) ).
cnf(c_0_73,plain,
( ~ member(esk1_2(X1,union(X2,X3)),X2)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_74,plain,
( ~ member(esk1_2(X1,union(X2,difference(X3,X4))),X3)
| member(esk1_2(X1,union(X2,difference(X3,X4))),X4)
| subset(X1,union(X2,difference(X3,X4))) ),
inference(spm,[status(thm)],[c_0_56,c_0_14]) ).
cnf(c_0_75,plain,
subset(difference(difference(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_76,plain,
( member(esk1_2(difference(difference(union(X1,X2),X3),X1),X4),X2)
| subset(difference(difference(union(X1,X2),X3),X1),X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_69]) ).
cnf(c_0_77,plain,
subset(difference(X1,X2),difference(X1,difference(X3,difference(X3,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_78,plain,
( ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3)
| subset(X1,union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_73,c_0_23]) ).
cnf(c_0_79,plain,
( member(esk1_2(difference(X1,X2),union(X3,difference(X1,X4))),X4)
| subset(difference(X1,X2),union(X3,difference(X1,X4))) ),
inference(spm,[status(thm)],[c_0_74,c_0_16]) ).
cnf(c_0_80,plain,
difference(difference(difference(X1,X2),X1),X3) = difference(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_28,c_0_75]) ).
cnf(c_0_81,plain,
subset(difference(difference(union(X1,X2),X2),X1),X3),
inference(spm,[status(thm)],[c_0_22,c_0_76]) ).
cnf(c_0_82,plain,
subset(X1,difference(X1,difference(X2,difference(X2,difference(X3,X1))))),
inference(spm,[status(thm)],[c_0_77,c_0_58]) ).
cnf(c_0_83,plain,
subset(difference(X1,X2),union(union(X3,X4),difference(X1,X4))),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,plain,
difference(X1,difference(difference(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_80]) ).
cnf(c_0_85,plain,
union(difference(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_39,c_0_72]) ).
cnf(c_0_86,plain,
difference(difference(union(X1,X2),X2),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_41,c_0_81]) ).
cnf(c_0_87,plain,
difference(X1,difference(X2,difference(X2,difference(X3,X1)))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_82]),c_0_21])]) ).
cnf(c_0_88,plain,
( ~ member(esk1_2(difference(X1,union(X2,X3)),X4),X3)
| subset(difference(X1,union(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_89,plain,
subset(X1,union(union(X2,X3),difference(X1,X3))),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_90,plain,
union(difference(difference(union(X1,X2),X2),X1),X3) = X3,
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_91,plain,
difference(difference(X1,X2),difference(X3,difference(X3,X2))) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_87,c_0_58]) ).
cnf(c_0_92,plain,
subset(difference(X1,union(X2,X3)),difference(difference(X1,union(X2,X3)),X3)),
inference(spm,[status(thm)],[c_0_88,c_0_27]) ).
cnf(c_0_93,plain,
subset(X1,union(difference(X1,X2),union(X3,X2))),
inference(spm,[status(thm)],[c_0_89,c_0_39]) ).
cnf(c_0_94,plain,
union(difference(union(X1,difference(X2,difference(X2,X1))),X1),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_39]) ).
cnf(c_0_95,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_22,c_0_18]) ).
cnf(c_0_96,plain,
( ~ member(esk1_2(X1,union(X2,union(X3,X4))),X3)
| subset(X1,union(X2,union(X3,X4))) ),
inference(spm,[status(thm)],[c_0_56,c_0_18]) ).
cnf(c_0_97,plain,
( ~ member(esk1_2(X1,union(union(X2,X3),X4)),X2)
| subset(X1,union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_73,c_0_18]) ).
cnf(c_0_98,plain,
difference(difference(X1,union(X2,X3)),X3) = difference(X1,union(X2,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_92]),c_0_21])]) ).
cnf(c_0_99,plain,
subset(union(X1,difference(X2,difference(X2,X1))),union(X3,X1)),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_100,plain,
union(difference(difference(X1,X2),X1),X3) = X3,
inference(spm,[status(thm)],[c_0_85,c_0_80]) ).
cnf(c_0_101,plain,
subset(difference(difference(union(X1,X2),union(X2,X3)),X1),X4),
inference(spm,[status(thm)],[c_0_95,c_0_76]) ).
cnf(c_0_102,plain,
subset(union(X1,union(X2,union(X1,X3))),union(X2,union(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_62]),c_0_39]) ).
cnf(c_0_103,plain,
subset(union(X1,union(union(X1,X2),X3)),union(union(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_62]),c_0_39]) ).
cnf(c_0_104,plain,
subset(difference(difference(union(X1,X2),union(X3,X2)),X1),X4),
inference(spm,[status(thm)],[c_0_31,c_0_76]) ).
cnf(c_0_105,plain,
difference(difference(X1,union(union(X2,X3),X4)),X3) = difference(X1,union(union(X2,X3),X4)),
inference(spm,[status(thm)],[c_0_98,c_0_38]) ).
cnf(c_0_106,plain,
subset(union(X1,difference(X2,difference(X2,X1))),X1),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_107,plain,
subset(difference(union(X1,X2),union(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_101,c_0_98]) ).
cnf(c_0_108,plain,
( member(esk1_2(union(X1,X2),union(X1,X3)),X2)
| subset(union(X1,X2),union(X1,X3)) ),
inference(spm,[status(thm)],[c_0_73,c_0_55]) ).
cnf(c_0_109,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_20,c_0_102]),c_0_63])]) ).
cnf(c_0_110,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_20,c_0_103]),c_0_63])]) ).
cnf(c_0_111,plain,
subset(difference(union(X1,X2),union(union(X3,X1),X2)),X4),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,plain,
( ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4)
| subset(X1,union(X2,union(X3,X4))) ),
inference(spm,[status(thm)],[c_0_56,c_0_23]) ).
cnf(c_0_113,plain,
( member(esk1_2(union(X1,X2),union(X2,X3)),X1)
| subset(union(X1,X2),union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_73,c_0_55]) ).
cnf(c_0_114,plain,
union(X1,difference(X2,difference(X2,X1))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_106]),c_0_68])]) ).
cnf(c_0_115,plain,
difference(union(X1,X2),union(X2,X1)) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_41,c_0_107]) ).
cnf(c_0_116,plain,
( member(esk1_2(union(X1,X2),union(X3,X1)),X2)
| subset(union(X1,X2),union(X3,X1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_55]) ).
cnf(c_0_117,plain,
subset(union(X1,X2),union(X1,union(X2,X3))),
inference(spm,[status(thm)],[c_0_96,c_0_108]) ).
cnf(c_0_118,plain,
union(X1,union(X2,union(union(X1,X3),X4))) = union(X2,union(union(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_119,plain,
difference(union(X1,X2),union(union(X3,X1),X2)) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_41,c_0_111]) ).
cnf(c_0_120,plain,
subset(union(X1,X2),union(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_121,plain,
union(union(X1,X2),union(X2,X1)) = union(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_47]) ).
cnf(c_0_122,plain,
subset(union(X1,X2),union(union(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_78,c_0_116]) ).
cnf(c_0_123,plain,
difference(X1,difference(difference(X2,X1),X3)) = X1,
inference(spm,[status(thm)],[c_0_58,c_0_61]) ).
cnf(c_0_124,plain,
subset(union(X1,X2),union(X2,union(union(X1,X3),X4))),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_125,plain,
union(union(X1,X2),union(union(X3,X1),X2)) = union(union(X3,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_119]),c_0_47]),c_0_39]) ).
cnf(c_0_126,plain,
subset(union(union(X1,X2),X3),union(X3,union(X2,X1))),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_127,plain,
subset(union(X1,union(X2,X3)),union(union(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_122,c_0_121]) ).
cnf(c_0_128,plain,
difference(difference(X1,X2),difference(X2,X3)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_123,c_0_58]) ).
cnf(c_0_129,plain,
subset(union(X1,union(X2,X3)),union(union(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_130,plain,
union(X1,union(X2,X3)) = union(union(X3,X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_126]),c_0_127])]) ).
cnf(c_0_131,plain,
subset(difference(difference(X1,X2),difference(X1,X3)),X3),
inference(spm,[status(thm)],[c_0_13,c_0_32]) ).
cnf(c_0_132,plain,
subset(difference(union(X1,difference(X1,X2)),X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_128]),c_0_39]) ).
cnf(c_0_133,plain,
subset(union(X1,union(X2,X3)),union(X3,union(X2,X1))),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_134,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_131,c_0_84]) ).
cnf(c_0_135,plain,
difference(union(X1,difference(X1,X2)),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_41,c_0_132]) ).
cnf(c_0_136,plain,
subset(union(X1,union(union(X2,X1),X3)),union(union(X2,X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_62]),c_0_39]) ).
cnf(c_0_137,plain,
subset(union(X1,union(X2,union(X3,X1))),union(X2,union(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_62]),c_0_39]) ).
cnf(c_0_138,plain,
union(X1,union(X2,X3)) = union(X3,union(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_133]),c_0_133])]) ).
cnf(c_0_139,plain,
subset(union(X1,difference(X1,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_47]) ).
cnf(c_0_140,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_20,c_0_136]),c_0_63])]) ).
cnf(c_0_141,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_20,c_0_137]),c_0_63])]) ).
cnf(c_0_142,plain,
union(union(X1,X2),X3) = union(X2,union(X1,X3)),
inference(spm,[status(thm)],[c_0_39,c_0_138]) ).
cnf(c_0_143,plain,
union(X1,union(X2,difference(X1,X2))) = union(X2,difference(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_46]),c_0_47]),c_0_39]) ).
cnf(c_0_144,plain,
union(X1,difference(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_139]),c_0_68])]) ).
cnf(c_0_145,plain,
union(difference(X1,difference(X1,X2)),union(X2,X3)) = union(X2,X3),
inference(spm,[status(thm)],[c_0_140,c_0_114]) ).
cnf(c_0_146,plain,
union(X1,union(X2,X3)) = union(X2,union(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_138]),c_0_141]),c_0_142]),c_0_109]),c_0_142]) ).
cnf(c_0_147,plain,
subset(union(X1,X2),union(X2,difference(X1,X2))),
inference(spm,[status(thm)],[c_0_117,c_0_143]) ).
cnf(c_0_148,plain,
subset(union(X1,difference(X2,X3)),union(X2,X1)),
inference(spm,[status(thm)],[c_0_122,c_0_144]) ).
cnf(c_0_149,plain,
union(difference(X1,difference(X1,X2)),union(X3,X2)) = union(X3,X2),
inference(spm,[status(thm)],[c_0_141,c_0_114]) ).
cnf(c_0_150,plain,
subset(union(X1,X2),union(X1,union(X3,X2))),
inference(spm,[status(thm)],[c_0_112,c_0_108]) ).
cnf(c_0_151,plain,
union(X1,union(difference(X2,difference(X2,X1)),X3)) = union(X1,X3),
inference(rw,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_152,plain,
union(X1,difference(X2,X1)) = union(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_147]),c_0_148])]) ).
cnf(c_0_153,plain,
union(X1,union(X2,difference(X3,difference(X3,X1)))) = union(X2,X1),
inference(rw,[status(thm)],[c_0_149,c_0_138]) ).
cnf(c_0_154,plain,
subset(union(X1,difference(X2,difference(X2,X3))),union(X1,X3)),
inference(spm,[status(thm)],[c_0_150,c_0_114]) ).
cnf(c_0_155,plain,
union(X1,difference(X2,difference(X3,difference(X3,X1)))) = union(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]) ).
cnf(c_0_156,plain,
difference(difference(difference(X1,X2),X3),difference(X1,X3)) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_41,c_0_60]) ).
cnf(c_0_157,plain,
subset(difference(X1,X2),difference(X1,difference(union(X2,X3),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_86]),c_0_72]) ).
cnf(c_0_158,plain,
difference(difference(X1,union(X2,X3)),difference(X1,X3)) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_41,c_0_37]) ).
cnf(c_0_159,plain,
subset(union(X1,difference(X2,difference(X2,difference(X1,X3)))),X1),
inference(spm,[status(thm)],[c_0_154,c_0_144]) ).
cnf(c_0_160,plain,
union(X1,difference(difference(X2,X3),difference(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_72]),c_0_39]) ).
cnf(c_0_161,plain,
difference(difference(X1,difference(X1,difference(X2,X3))),X3) = difference(X1,difference(X1,difference(X2,X3))),
inference(spm,[status(thm)],[c_0_58,c_0_87]) ).
cnf(c_0_162,plain,
subset(X1,difference(X1,difference(union(difference(X2,X1),X3),X3))),
inference(spm,[status(thm)],[c_0_157,c_0_58]) ).
cnf(c_0_163,plain,
union(X1,difference(X2,union(X3,difference(X2,X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_158]),c_0_72]),c_0_39]) ).
cnf(c_0_164,plain,
union(X1,difference(X2,difference(X2,difference(X1,X3)))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_159]),c_0_68])]) ).
cnf(c_0_165,plain,
union(X1,union(X2,difference(X3,X1))) = union(X2,union(X3,X1)),
inference(spm,[status(thm)],[c_0_146,c_0_152]) ).
cnf(c_0_166,plain,
union(X1,difference(X2,difference(X2,difference(X3,difference(X2,X1))))) = X1,
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_167,plain,
difference(X1,difference(union(difference(X2,X1),X3),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,
subset(difference(X1,union(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_88,c_0_16]) ).
cnf(c_0_169,plain,
union(difference(X1,X2),difference(X1,difference(X2,X3))) = difference(X1,difference(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_39]) ).
cnf(c_0_170,plain,
union(X1,difference(X2,difference(X3,difference(X2,X1)))) = union(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_144]),c_0_39]) ).
cnf(c_0_171,plain,
difference(difference(X1,X2),difference(union(X2,X3),X3)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_167,c_0_58]) ).
cnf(c_0_172,plain,
difference(difference(X1,union(X2,X1)),X3) = difference(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_168]) ).
cnf(c_0_173,plain,
difference(X1,difference(X2,difference(X1,difference(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_39]),c_0_144]) ).
cnf(c_0_174,plain,
union(difference(union(X1,difference(union(X1,X2),X2)),X1),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_171]),c_0_39]) ).
cnf(c_0_175,plain,
union(difference(X1,union(X2,X1)),X3) = X3,
inference(spm,[status(thm)],[c_0_85,c_0_172]) ).
cnf(c_0_176,plain,
union(difference(X1,X2),difference(X2,difference(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_173]),c_0_39]),c_0_114]),c_0_39]) ).
cnf(c_0_177,plain,
subset(union(X1,difference(union(X1,X2),X2)),union(X3,X1)),
inference(spm,[status(thm)],[c_0_93,c_0_174]) ).
cnf(c_0_178,plain,
difference(union(X1,X2),difference(union(X1,X2),X2)) = X2,
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_179,plain,
subset(difference(X1,X2),difference(difference(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_180,plain,
difference(difference(union(X1,X2),union(X3,X2)),X1) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_41,c_0_104]) ).
cnf(c_0_181,plain,
subset(union(X1,difference(union(X1,X2),X2)),X1),
inference(spm,[status(thm)],[c_0_177,c_0_100]) ).
cnf(c_0_182,plain,
subset(difference(X1,X2),difference(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_57,c_0_178]) ).
cnf(c_0_183,plain,
difference(difference(X1,X2),X2) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_179]),c_0_21])]) ).
cnf(c_0_184,plain,
union(X1,difference(union(X1,X2),union(X3,X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_180]),c_0_47]) ).
cnf(c_0_185,plain,
union(X1,difference(union(X1,X2),X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_181]),c_0_68])]) ).
cnf(c_0_186,plain,
( member(esk1_2(difference(difference(union(X1,X2),X3),X4),X1),X2)
| subset(difference(difference(union(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_69]) ).
cnf(c_0_187,plain,
subset(difference(X1,X2),difference(union(X3,difference(X1,X2)),X2)),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_188,plain,
union(X1,difference(union(X1,difference(X2,X3)),X2)) = X1,
inference(spm,[status(thm)],[c_0_184,c_0_144]) ).
cnf(c_0_189,plain,
union(difference(union(X1,X2),X2),union(X1,X3)) = union(X1,X3),
inference(spm,[status(thm)],[c_0_140,c_0_185]) ).
cnf(c_0_190,plain,
union(difference(union(X1,X2),X2),union(X3,X1)) = union(X3,X1),
inference(spm,[status(thm)],[c_0_141,c_0_185]) ).
cnf(c_0_191,plain,
subset(difference(difference(union(X1,X2),X3),X2),X1),
inference(spm,[status(thm)],[c_0_17,c_0_186]) ).
cnf(c_0_192,plain,
subset(union(X1,X2),union(X2,union(X3,difference(X1,X2)))),
inference(spm,[status(thm)],[c_0_150,c_0_152]) ).
cnf(c_0_193,plain,
subset(difference(union(X1,difference(X2,X3)),X2),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_194,plain,
subset(difference(X1,X2),difference(union(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_182,c_0_39]) ).
cnf(c_0_195,plain,
union(X1,union(difference(union(X1,X2),X2),X3)) = union(X1,X3),
inference(rw,[status(thm)],[c_0_189,c_0_146]) ).
cnf(c_0_196,plain,
union(X1,union(X2,difference(union(X1,X3),X3))) = union(X2,X1),
inference(rw,[status(thm)],[c_0_190,c_0_138]) ).
cnf(c_0_197,plain,
subset(difference(union(X1,X2),union(X3,X2)),X1),
inference(spm,[status(thm)],[c_0_191,c_0_98]) ).
cnf(c_0_198,plain,
subset(union(X1,union(X2,difference(X1,X3))),union(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_188]),c_0_39]) ).
cnf(c_0_199,plain,
difference(union(X1,difference(X2,X3)),X2) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_193]),c_0_194])]) ).
cnf(c_0_200,plain,
union(X1,difference(X2,difference(union(X1,X3),X3))) = union(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_152]),c_0_196]) ).
cnf(c_0_201,plain,
subset(difference(union(X1,X2),union(X3,difference(X1,X2))),X2),
inference(spm,[status(thm)],[c_0_197,c_0_152]) ).
cnf(c_0_202,plain,
union(X1,union(X2,difference(X1,X3))) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_198]),c_0_117])]) ).
cnf(c_0_203,plain,
union(difference(union(X1,X2),union(X2,X1)),X3) = X3,
inference(spm,[status(thm)],[c_0_85,c_0_115]) ).
cnf(c_0_204,plain,
difference(union(X1,X2),X1) = difference(X2,X1),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_205,plain,
difference(union(X1,X2),X2) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_199,c_0_84]) ).
cnf(c_0_206,plain,
subset(difference(union(X1,X2),X3),union(X2,difference(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_163]),c_0_202]) ).
cnf(c_0_207,plain,
difference(X1,difference(X2,difference(X2,X1))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_176]),c_0_169]) ).
cnf(c_0_208,plain,
union(difference(difference(X1,difference(X1,X2)),X2),X3) = X3,
inference(spm,[status(thm)],[c_0_203,c_0_71]) ).
cnf(c_0_209,plain,
subset(union(X1,union(X2,X1)),union(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_62]),c_0_39]) ).
cnf(c_0_210,plain,
difference(union(X1,union(X2,X3)),X2) = difference(union(X1,X3),X2),
inference(spm,[status(thm)],[c_0_204,c_0_146]) ).
cnf(c_0_211,plain,
difference(union(X1,union(X2,X3)),X3) = difference(union(X2,X1),X3),
inference(spm,[status(thm)],[c_0_205,c_0_142]) ).
cnf(c_0_212,plain,
subset(difference(union(X1,X2),X3),union(X1,difference(X2,X3))),
inference(spm,[status(thm)],[c_0_206,c_0_39]) ).
cnf(c_0_213,plain,
difference(X1,difference(X1,X2)) = difference(X2,difference(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_207]),c_0_208]) ).
cnf(c_0_214,plain,
difference(X1,difference(X2,union(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_58,c_0_98]) ).
cnf(c_0_215,plain,
union(difference(X1,X2),union(X3,X1)) = union(X3,X1),
inference(spm,[status(thm)],[c_0_141,c_0_144]) ).
cnf(c_0_216,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_209]),c_0_63])]) ).
cnf(c_0_217,plain,
difference(union(X1,difference(X2,X3)),X3) = difference(union(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_152]),c_0_211]) ).
cnf(c_0_218,plain,
subset(difference(union(X1,difference(X2,X3)),difference(X2,X1)),X1),
inference(spm,[status(thm)],[c_0_212,c_0_160]) ).
cnf(c_0_219,plain,
difference(union(X1,X2),difference(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_205]),c_0_214]) ).
cnf(c_0_220,plain,
subset(X1,difference(union(X2,X1),difference(X3,X1))),
inference(spm,[status(thm)],[c_0_64,c_0_178]) ).
cnf(c_0_221,plain,
union(union(X1,X2),difference(X2,X3)) = union(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_215]) ).
cnf(c_0_222,plain,
union(difference(X1,X2),difference(difference(X1,X3),X2)) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_156]),c_0_47]) ).
cnf(c_0_223,plain,
union(X1,difference(union(X2,X1),difference(X3,X2))) = union(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_216]) ).
cnf(c_0_224,plain,
difference(union(difference(X1,X2),X3),difference(X1,X3)) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_160]),c_0_58]) ).
cnf(c_0_225,plain,
difference(union(difference(X1,X2),X3),X2) = difference(union(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_183]),c_0_217]) ).
cnf(c_0_226,plain,
subset(difference(union(X1,X2),difference(union(X3,X2),X1)),X1),
inference(spm,[status(thm)],[c_0_218,c_0_219]) ).
cnf(c_0_227,plain,
subset(X1,difference(union(X1,X2),difference(X3,X1))),
inference(spm,[status(thm)],[c_0_220,c_0_39]) ).
cnf(c_0_228,plain,
union(X1,difference(difference(union(X1,X2),X2),X3)) = X1,
inference(spm,[status(thm)],[c_0_221,c_0_185]) ).
fof(c_0_229,negated_conjecture,
~ ! [X1,X2,X3] : difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
inference(assume_negation,[status(cth)],[prove_difference_distributes_over_union]) ).
cnf(c_0_230,plain,
union(difference(X1,X2),difference(union(X3,X1),X2)) = difference(union(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_219]),c_0_39]) ).
cnf(c_0_231,plain,
union(X1,difference(union(X2,X1),X3)) = union(difference(X2,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_225]) ).
cnf(c_0_232,plain,
difference(union(X1,X2),difference(union(X3,X2),X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_226]),c_0_227])]) ).
cnf(c_0_233,plain,
union(X1,difference(difference(union(X2,X1),difference(X2,X1)),X3)) = X1,
inference(spm,[status(thm)],[c_0_228,c_0_152]) ).
fof(c_0_234,negated_conjecture,
difference(union(esk3_0,esk4_0),esk5_0) != union(difference(esk3_0,esk5_0),difference(esk4_0,esk5_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_229])])])]) ).
cnf(c_0_235,plain,
difference(union(X1,X2),difference(X3,X2)) = union(X2,difference(X1,difference(X3,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_58]),c_0_231]),c_0_39]) ).
cnf(c_0_236,plain,
difference(union(X1,difference(X2,X3)),difference(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_233]),c_0_219]) ).
cnf(c_0_237,negated_conjecture,
difference(union(esk3_0,esk4_0),esk5_0) != union(difference(esk3_0,esk5_0),difference(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_238,plain,
union(difference(X1,X2),difference(X3,X2)) = difference(union(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_217]) ).
cnf(c_0_239,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_237,c_0_238])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET615+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:29:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 255.46/32.81 % Version: 3.5.1
% 255.46/32.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 255.46/32.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 255.46/32.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 255.46/32.81 % Starting new_bool_3 with 300s (1) cores
% 255.46/32.81 % Starting new_bool_1 with 300s (1) cores
% 255.46/32.81 % Starting sh5l with 300s (1) cores
% 255.46/32.81 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1774659 completed with status 0
% 255.46/32.81 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 255.46/32.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 255.46/32.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 255.46/32.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 255.46/32.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 255.46/32.81 % No SInE strategy applied
% 255.46/32.81 % Search class: FGHSS-FFSF22-SFFFFFNN
% 255.46/32.81 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 255.46/32.81 % Starting SubtermCWHack with 136s (1) cores
% 255.46/32.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 255.46/32.81 % Starting G----_0010_evo with 136s (1) cores
% 255.46/32.81 % Starting new_bool_3 with 136s (1) cores
% 255.46/32.81 % Starting new_bool_1 with 136s (1) cores
% 255.46/32.81 % G----_0010_evo with pid 1774665 completed with status 0
% 255.46/32.81 % Result found by G----_0010_evo
% 255.46/32.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 255.46/32.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 255.46/32.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 255.46/32.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 255.46/32.81 % No SInE strategy applied
% 255.46/32.81 % Search class: FGHSS-FFSF22-SFFFFFNN
% 255.46/32.81 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 255.46/32.81 % Starting SubtermCWHack with 136s (1) cores
% 255.46/32.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 255.46/32.81 % Starting G----_0010_evo with 136s (1) cores
% 255.46/32.81 % Preprocessing time : 0.001 s
% 255.46/32.81
% 255.46/32.81 % Proof found!
% 255.46/32.81 % SZS status Theorem
% 255.46/32.81 % SZS output start CNFRefutation
% See solution above
% 255.46/32.81 % Parsed axioms : 8
% 255.46/32.81 % Removed by relevancy pruning/SinE : 0
% 255.46/32.81 % Initial clauses : 19
% 255.46/32.81 % Removed in clause preprocessing : 2
% 255.46/32.81 % Initial clauses in saturation : 17
% 255.46/32.81 % Processed clauses : 89010
% 255.46/32.81 % ...of these trivial : 8426
% 255.46/32.81 % ...subsumed : 77645
% 255.46/32.81 % ...remaining for further processing : 2939
% 255.46/32.81 % Other redundant clauses eliminated : 2
% 255.46/32.81 % Clauses deleted for lack of memory : 0
% 255.46/32.81 % Backward-subsumed : 11
% 255.46/32.81 % Backward-rewritten : 1001
% 255.46/32.81 % Generated clauses : 2510530
% 255.46/32.81 % ...of the previous two non-redundant : 1447909
% 255.46/32.81 % ...aggressively subsumed : 0
% 255.46/32.81 % Contextual simplify-reflections : 18
% 255.46/32.81 % Paramodulations : 2509130
% 255.46/32.81 % Factorizations : 1398
% 255.46/32.81 % NegExts : 0
% 255.46/32.81 % Equation resolutions : 2
% 255.46/32.81 % Disequality decompositions : 0
% 255.46/32.81 % Total rewrite steps : 2875768
% 255.46/32.81 % ...of those cached : 2582096
% 255.46/32.81 % Propositional unsat checks : 0
% 255.46/32.81 % Propositional check models : 0
% 255.46/32.81 % Propositional check unsatisfiable : 0
% 255.46/32.81 % Propositional clauses : 0
% 255.46/32.81 % Propositional clauses after purity: 0
% 255.46/32.81 % Propositional unsat core size : 0
% 255.46/32.81 % Propositional preprocessing time : 0.000
% 255.46/32.81 % Propositional encoding time : 0.000
% 255.46/32.81 % Propositional solver time : 0.000
% 255.46/32.81 % Success case prop preproc time : 0.000
% 255.46/32.81 % Success case prop encoding time : 0.000
% 255.46/32.81 % Success case prop solver time : 0.000
% 255.46/32.81 % Current number of processed clauses : 1925
% 255.46/32.81 % Positive orientable unit clauses : 1036
% 255.46/32.81 % Positive unorientable unit clauses: 31
% 255.46/32.81 % Negative unit clauses : 7
% 255.46/32.81 % Non-unit-clauses : 851
% 255.46/32.81 % Current number of unprocessed clauses: 1347118
% 255.46/32.81 % ...number of literals in the above : 3393129
% 255.46/32.81 % Current number of archived formulas : 0
% 255.46/32.81 % Current number of archived clauses : 1012
% 255.46/32.81 % Clause-clause subsumption calls (NU) : 352005
% 255.46/32.81 % Rec. Clause-clause subsumption calls : 167310
% 255.46/32.81 % Non-unit clause-clause subsumptions : 24423
% 255.46/32.81 % Unit Clause-clause subsumption calls : 217656
% 255.46/32.81 % Rewrite failures with RHS unbound : 9177
% 255.46/32.81 % BW rewrite match attempts : 111669
% 255.46/32.81 % BW rewrite match successes : 3607
% 255.46/32.81 % Condensation attempts : 0
% 255.46/32.81 % Condensation successes : 0
% 255.46/32.81 % Termbank termtop insertions : 32713024
% 255.46/32.81 % Search garbage collected termcells : 304
% 255.46/32.81
% 255.46/32.81 % -------------------------------------------------
% 255.46/32.81 % User time : 30.685 s
% 255.46/32.81 % System time : 1.090 s
% 255.46/32.81 % Total time : 31.774 s
% 255.46/32.81 % Maximum resident set size: 3380 pages
% 255.46/32.81
% 255.46/32.81 % -------------------------------------------------
% 255.46/32.81 % User time : 153.477 s
% 255.46/32.81 % System time : 5.975 s
% 255.46/32.81 % Total time : 159.452 s
% 255.46/32.81 % Maximum resident set size: 4608 pages
% 255.46/32.81 % E exiting
%------------------------------------------------------------------------------