TSTP Solution File: SET612+3 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET612+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 : Sat May 4 09:19:34 EDT 2024
% Result : Theorem 212.36s 27.31s
% Output : CNFRefutation 212.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 12
% Syntax : Number of formulae : 246 ( 156 unt; 0 def)
% Number of atoms : 386 ( 103 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 229 ( 89 ~; 116 |; 15 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 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 : 669 ( 116 sgn 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',difference_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',subset_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',equal_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',commutativity_of_intersection) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',union_defn) ).
fof(subset_difference,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X3,X2),difference(X3,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',subset_difference) ).
fof(intersection_of_subsets,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',intersection_of_subsets) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',reflexivity_of_subset) ).
fof(subset_of_union,axiom,
! [X1,X2] : subset(X1,union(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',subset_of_union) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',commutativity_of_union) ).
fof(prove_th85,conjecture,
! [X1,X2,X3] : difference(X1,union(X2,X3)) = intersection(difference(X1,X2),difference(X1,X3)),
file('/export/starexec/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p',prove_th85) ).
fof(c_0_12,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_13,plain,
! [X10,X11,X12] :
( ( member(X12,X10)
| ~ member(X12,difference(X10,X11)) )
& ( ~ member(X12,X11)
| ~ member(X12,difference(X10,X11)) )
& ( ~ member(X12,X10)
| member(X12,X11)
| member(X12,difference(X10,X11)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_14,plain,
! [X27,X28,X29,X30,X31] :
( ( ~ subset(X27,X28)
| ~ member(X29,X27)
| member(X29,X28) )
& ( member(esk1_2(X30,X31),X30)
| subset(X30,X31) )
& ( ~ member(esk1_2(X30,X31),X31)
| subset(X30,X31) ) ),
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_15,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X21,X22] :
( ( subset(X21,X22)
| X21 != X22 )
& ( subset(X22,X21)
| X21 != X22 )
& ( ~ subset(X21,X22)
| ~ subset(X22,X21)
| X21 = X22 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( subset(difference(X1,X2),X3)
| member(esk1_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
fof(c_0_24,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_25,plain,
( difference(X1,X2) = X1
| ~ subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_27,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_30,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
fof(c_0_31,plain,
! [X25,X26] : intersection(X25,X26) = intersection(X26,X25),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_32,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
cnf(c_0_33,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,plain,
( ~ member(X1,difference(X2,X2))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_35,plain,
( subset(X1,difference(X2,X3))
| member(esk1_2(X1,difference(X2,X3)),X3)
| ~ member(esk1_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_36,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_37,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_34]) ).
cnf(c_0_40,plain,
( subset(X1,difference(X1,X2))
| member(esk1_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_16]) ).
cnf(c_0_41,plain,
( subset(difference(difference(X1,X2),X3),X4)
| member(esk1_2(difference(difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_42,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
( subset(difference(union(X1,X2),X3),X4)
| member(esk1_2(difference(union(X1,X2),X3),X4),X1)
| member(esk1_2(difference(union(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_19]) ).
cnf(c_0_44,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
subset(difference(difference(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_23,c_0_41]) ).
fof(c_0_46,plain,
! [X18,X19,X20] :
( ~ subset(X18,X19)
| subset(difference(X20,X19),difference(X20,X18)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_difference])])]) ).
cnf(c_0_47,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_48,plain,
( intersection(X1,X2) = X2
| ~ subset(X2,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_42]) ).
cnf(c_0_49,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_50,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_51,plain,
( subset(difference(union(X1,X1),X2),X3)
| member(esk1_2(difference(union(X1,X1),X2),X3),X1) ),
inference(ef,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_44]),c_0_22])]) ).
cnf(c_0_53,plain,
difference(difference(difference(X1,X2),X1),X3) = difference(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_54,plain,
( subset(difference(X3,X2),difference(X3,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,plain,
intersection(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_47,c_0_26]) ).
cnf(c_0_56,plain,
intersection(X1,difference(X2,X2)) = difference(X2,X2),
inference(spm,[status(thm)],[c_0_48,c_0_26]) ).
cnf(c_0_57,plain,
( subset(intersection(difference(X1,X2),X3),X4)
| ~ member(esk1_2(intersection(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_30]) ).
cnf(c_0_58,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_16]) ).
fof(c_0_59,plain,
! [X15,X16,X17] :
( ~ subset(X15,X16)
| ~ subset(X15,X17)
| subset(X15,intersection(X16,X17)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_of_subsets])])]) ).
fof(c_0_60,plain,
! [X33] : subset(X33,X33),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
cnf(c_0_61,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_50]) ).
cnf(c_0_62,plain,
subset(difference(union(X1,X1),X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_51]) ).
cnf(c_0_63,plain,
difference(X1,difference(difference(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_64,plain,
! [X13,X14] : subset(X13,union(X13,X14)),
inference(variable_rename,[status(thm)],[subset_of_union]) ).
cnf(c_0_65,plain,
( difference(X1,X2) = difference(X1,X3)
| ~ subset(difference(X1,X2),difference(X1,X3))
| ~ subset(X2,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_54]) ).
cnf(c_0_66,plain,
difference(X1,X1) = difference(X2,X2),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_67,plain,
subset(intersection(X1,difference(X2,X1)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_37]) ).
cnf(c_0_68,plain,
( subset(intersection(intersection(X1,X2),X3),X4)
| member(esk1_2(intersection(intersection(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_30]) ).
cnf(c_0_69,plain,
( subset(X1,intersection(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_70,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_71,plain,
( subset(difference(union(X1,X2),X3),union(X4,X2))
| member(esk1_2(difference(union(X1,X2),X3),union(X4,X2)),X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_43]) ).
cnf(c_0_72,plain,
subset(union(X1,X1),X1),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_73,plain,
subset(X1,union(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_74,plain,
( subset(intersection(difference(X1,X2),X3),X4)
| member(esk1_2(intersection(difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_30]) ).
cnf(c_0_75,plain,
( difference(X1,X1) = difference(X2,X3)
| ~ subset(X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_26])]) ).
cnf(c_0_76,plain,
difference(intersection(X1,difference(X2,X1)),X3) = intersection(X1,difference(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_67]) ).
cnf(c_0_77,plain,
subset(intersection(intersection(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_18,c_0_68]) ).
cnf(c_0_78,plain,
( intersection(X1,X2) = X2
| ~ subset(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_69]),c_0_70])]) ).
cnf(c_0_79,plain,
subset(difference(union(X1,X2),X1),union(X3,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_71]) ).
cnf(c_0_80,plain,
union(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_72]),c_0_73])]) ).
cnf(c_0_81,plain,
subset(intersection(difference(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_18,c_0_74]) ).
cnf(c_0_82,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk1_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk1_2(difference(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_83,plain,
difference(X1,X1) = intersection(X2,difference(X3,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_67])]) ).
cnf(c_0_84,plain,
( subset(X1,X2)
| ~ subset(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_85,plain,
subset(difference(union(X1,X2),X1),X2),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_86,plain,
subset(intersection(X1,difference(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_81,c_0_37]) ).
cnf(c_0_87,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_69]),c_0_70])]) ).
cnf(c_0_88,plain,
( subset(difference(intersection(X1,X2),X3),X4)
| member(esk1_2(difference(intersection(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_89,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk1_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_82,c_0_19]) ).
cnf(c_0_90,plain,
( difference(X1,X1) = difference(X2,X3)
| ~ subset(difference(X2,X3),X3) ),
inference(spm,[status(thm)],[c_0_78,c_0_83]) ).
cnf(c_0_91,plain,
subset(difference(union(X1,intersection(X2,X3)),X1),X2),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_92,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_93,plain,
( subset(X1,X2)
| ~ subset(X1,difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_94,plain,
subset(intersection(intersection(X1,X2),X3),X2),
inference(spm,[status(thm)],[c_0_77,c_0_37]) ).
fof(c_0_95,plain,
! [X23,X24] : union(X23,X24) = union(X24,X23),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_96,plain,
subset(difference(intersection(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_18,c_0_88]) ).
cnf(c_0_97,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_98,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_18,c_0_89]) ).
cnf(c_0_99,plain,
difference(X1,X1) = difference(union(X2,intersection(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_100,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_92]) ).
cnf(c_0_101,plain,
subset(difference(union(X1,difference(X2,X3)),X1),X2),
inference(spm,[status(thm)],[c_0_93,c_0_85]) ).
cnf(c_0_102,plain,
( subset(X1,X2)
| ~ subset(X1,intersection(X3,X2)) ),
inference(spm,[status(thm)],[c_0_94,c_0_78]) ).
cnf(c_0_103,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_104,plain,
subset(difference(intersection(difference(X1,X2),X3),X4),X1),
inference(spm,[status(thm)],[c_0_93,c_0_96]) ).
cnf(c_0_105,plain,
( subset(X1,union(X2,difference(X3,X4)))
| member(esk1_2(X1,union(X2,difference(X3,X4))),X4)
| ~ member(esk1_2(X1,union(X2,difference(X3,X4))),X3) ),
inference(spm,[status(thm)],[c_0_61,c_0_29]) ).
cnf(c_0_106,plain,
( subset(difference(X1,intersection(X2,X3)),X4)
| ~ member(esk1_2(difference(X1,intersection(X2,X3)),X4),X3)
| ~ member(esk1_2(difference(X1,intersection(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_97]) ).
cnf(c_0_107,plain,
( subset(difference(X1,union(X2,X3)),X4)
| ~ member(esk1_2(difference(X1,union(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_50]) ).
cnf(c_0_108,plain,
( subset(difference(X1,X2),difference(X1,X3))
| member(esk1_2(difference(X1,X2),difference(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_19]) ).
cnf(c_0_109,plain,
subset(union(X1,intersection(X1,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_52]) ).
cnf(c_0_110,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
inference(spm,[status(thm)],[c_0_100,c_0_50]) ).
cnf(c_0_111,plain,
difference(X1,X1) = difference(union(X2,difference(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_90,c_0_101]) ).
cnf(c_0_112,plain,
subset(difference(union(X1,intersection(X2,X3)),X1),X3),
inference(spm,[status(thm)],[c_0_102,c_0_85]) ).
cnf(c_0_113,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_18,c_0_97]) ).
cnf(c_0_114,plain,
( subset(intersection(union(X1,X2),X3),X4)
| member(esk1_2(intersection(union(X1,X2),X3),X4),X1)
| member(esk1_2(intersection(union(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_115,plain,
subset(union(difference(X1,X1),X2),X2),
inference(spm,[status(thm)],[c_0_85,c_0_52]) ).
cnf(c_0_116,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_73,c_0_103]) ).
cnf(c_0_117,plain,
( subset(difference(union(X1,X2),X3),union(X2,X4))
| member(esk1_2(difference(union(X1,X2),X3),union(X2,X4)),X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_43]) ).
cnf(c_0_118,plain,
( subset(difference(X1,X2),X3)
| ~ subset(X1,difference(X3,X4)) ),
inference(spm,[status(thm)],[c_0_104,c_0_78]) ).
cnf(c_0_119,plain,
( subset(difference(X1,X2),union(X3,difference(X1,X4)))
| member(esk1_2(difference(X1,X2),union(X3,difference(X1,X4))),X4) ),
inference(spm,[status(thm)],[c_0_105,c_0_19]) ).
cnf(c_0_120,plain,
( subset(difference(X1,intersection(X2,X1)),X3)
| ~ member(esk1_2(difference(X1,intersection(X2,X1)),X3),X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_19]) ).
cnf(c_0_121,plain,
subset(difference(X1,union(X2,X3)),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_122,plain,
union(X1,intersection(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_109]),c_0_73])]) ).
cnf(c_0_123,plain,
subset(difference(union(X1,X2),X3),union(union(X4,X1),X2)),
inference(spm,[status(thm)],[c_0_110,c_0_71]) ).
cnf(c_0_124,plain,
subset(union(X1,difference(X1,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_111]),c_0_52]) ).
cnf(c_0_125,plain,
difference(X1,X1) = difference(union(X2,intersection(X3,X2)),X2),
inference(spm,[status(thm)],[c_0_90,c_0_112]) ).
cnf(c_0_126,plain,
( subset(intersection(X1,X2),intersection(X3,X2))
| ~ member(esk1_2(intersection(X1,X2),intersection(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_113,c_0_58]) ).
cnf(c_0_127,plain,
( subset(intersection(union(X1,X2),X3),X2)
| member(esk1_2(intersection(union(X1,X2),X3),X2),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_114]) ).
cnf(c_0_128,plain,
union(difference(X1,X1),X2) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_115]),c_0_116])]) ).
cnf(c_0_129,plain,
( difference(difference(X1,X2),X3) = difference(X1,X2)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_75]) ).
cnf(c_0_130,plain,
subset(difference(union(X1,X2),X3),union(X2,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_117]) ).
cnf(c_0_131,plain,
subset(difference(difference(union(X1,difference(X2,X3)),X1),X4),X2),
inference(spm,[status(thm)],[c_0_118,c_0_85]) ).
cnf(c_0_132,plain,
subset(difference(X1,X2),union(X3,difference(X1,X3))),
inference(spm,[status(thm)],[c_0_100,c_0_119]) ).
cnf(c_0_133,plain,
subset(difference(X1,intersection(X2,X1)),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_120,c_0_108]) ).
cnf(c_0_134,plain,
subset(difference(X1,X2),difference(X1,intersection(X2,X3))),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_135,plain,
subset(union(X1,X2),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_123,c_0_63]) ).
cnf(c_0_136,plain,
union(X1,difference(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_124]),c_0_73])]) ).
cnf(c_0_137,plain,
subset(union(X1,intersection(X2,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_125]),c_0_52]) ).
cnf(c_0_138,plain,
( intersection(X1,X2) = X3
| ~ subset(intersection(X1,X2),X3)
| ~ subset(X3,X2)
| ~ subset(X3,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_69]) ).
cnf(c_0_139,plain,
subset(intersection(X1,union(X2,intersection(X2,X1))),intersection(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_37]) ).
cnf(c_0_140,plain,
( union(difference(X1,X2),X3) = X3
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_141,plain,
difference(X1,X1) = difference(union(X2,X3),union(X3,X2)),
inference(spm,[status(thm)],[c_0_90,c_0_130]) ).
cnf(c_0_142,plain,
subset(difference(difference(union(X1,X2),X1),X3),X2),
inference(spm,[status(thm)],[c_0_131,c_0_63]) ).
cnf(c_0_143,plain,
subset(X1,union(X2,difference(X1,X2))),
inference(spm,[status(thm)],[c_0_132,c_0_63]) ).
cnf(c_0_144,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_133]),c_0_134])]) ).
cnf(c_0_145,plain,
subset(union(difference(X1,X2),X3),union(X1,X3)),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_146,plain,
union(X1,intersection(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_137]),c_0_73])]) ).
cnf(c_0_147,plain,
intersection(X1,union(X2,intersection(X2,X1))) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_116]),c_0_42])]) ).
cnf(c_0_148,plain,
subset(difference(union(X1,union(X2,X1)),X3),union(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_71]),c_0_103]) ).
cnf(c_0_149,plain,
union(difference(union(X1,X2),union(X2,X1)),X3) = X3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_70])]) ).
cnf(c_0_150,plain,
difference(X1,X1) = difference(difference(union(X2,X3),X2),X3),
inference(spm,[status(thm)],[c_0_90,c_0_142]) ).
cnf(c_0_151,plain,
subset(X1,union(difference(X1,X2),intersection(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_103]) ).
cnf(c_0_152,plain,
subset(union(difference(X1,X2),intersection(X3,X1)),X1),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_153,plain,
( subset(difference(intersection(X1,X2),X3),X4)
| member(esk1_2(difference(intersection(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_19]) ).
cnf(c_0_154,plain,
( intersection(X1,union(X2,X1)) = X1
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_147,c_0_78]) ).
cnf(c_0_155,plain,
subset(union(X1,union(X2,X1)),union(X2,X1)),
inference(spm,[status(thm)],[c_0_148,c_0_63]) ).
cnf(c_0_156,plain,
( subset(intersection(X1,difference(X2,X3)),X4)
| ~ member(esk1_2(intersection(X1,difference(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_58]) ).
cnf(c_0_157,plain,
( subset(intersection(X1,X2),difference(X1,X3))
| member(esk1_2(intersection(X1,X2),difference(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_158,plain,
union(difference(difference(union(X1,X2),X1),X2),X3) = X3,
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_159,plain,
union(difference(X1,X2),intersection(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_151]),c_0_152])]) ).
cnf(c_0_160,plain,
( subset(difference(intersection(X1,X2),X3),difference(X2,X4))
| member(esk1_2(difference(intersection(X1,X2),X3),difference(X2,X4)),X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_153]) ).
cnf(c_0_161,plain,
( intersection(X1,union(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_154,c_0_103]) ).
cnf(c_0_162,plain,
union(X1,union(X2,X1)) = union(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_155]),c_0_116])]) ).
cnf(c_0_163,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_38,c_0_58]) ).
cnf(c_0_164,plain,
( subset(intersection(intersection(X1,X2),X3),X4)
| member(esk1_2(intersection(intersection(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_30]) ).
cnf(c_0_165,plain,
subset(intersection(X1,difference(X2,X3)),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_166,plain,
intersection(X1,difference(union(X2,X1),X2)) = difference(union(X2,X1),X2),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_167,plain,
subset(difference(intersection(X1,X2),X3),difference(X2,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_160]) ).
cnf(c_0_168,plain,
intersection(X1,union(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_116])]) ).
cnf(c_0_169,plain,
( subset(intersection(X1,X2),difference(X2,X3))
| member(esk1_2(intersection(X1,X2),difference(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_58]) ).
cnf(c_0_170,plain,
union(X1,union(X1,X2)) = union(X1,X2),
inference(spm,[status(thm)],[c_0_162,c_0_103]) ).
cnf(c_0_171,plain,
( subset(intersection(difference(X1,X2),X3),intersection(X4,X1))
| ~ member(esk1_2(intersection(difference(X1,X2),X3),intersection(X4,X1)),X4) ),
inference(spm,[status(thm)],[c_0_113,c_0_74]) ).
cnf(c_0_172,plain,
( subset(intersection(difference(X1,X2),union(X2,X3)),X4)
| member(esk1_2(intersection(difference(X1,X2),union(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_163]) ).
cnf(c_0_173,plain,
difference(X1,intersection(X2,difference(X3,X2))) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_76]) ).
cnf(c_0_174,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_144,c_0_37]) ).
cnf(c_0_175,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_126,c_0_164]) ).
cnf(c_0_176,plain,
( subset(difference(X1,X2),intersection(X3,X1))
| ~ member(esk1_2(difference(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_113,c_0_19]) ).
cnf(c_0_177,plain,
subset(difference(union(X1,X2),X1),difference(X2,X1)),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_178,plain,
subset(difference(X1,X2),difference(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_179,plain,
subset(intersection(difference(X1,X2),X3),difference(X3,X2)),
inference(spm,[status(thm)],[c_0_57,c_0_169]) ).
cnf(c_0_180,plain,
intersection(X1,union(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_170]),c_0_73])]) ).
cnf(c_0_181,plain,
subset(intersection(difference(X1,X2),union(X2,X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_182,plain,
difference(X1,difference(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_183,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_175,c_0_37]) ).
cnf(c_0_184,plain,
subset(difference(X1,X2),intersection(X1,difference(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_16]),c_0_37]) ).
cnf(c_0_185,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_176,c_0_89]) ).
cnf(c_0_186,plain,
difference(union(X1,X2),X1) = difference(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_177]),c_0_178])]) ).
cnf(c_0_187,plain,
subset(difference(X1,X2),difference(union(difference(X1,X2),X3),X2)),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_188,plain,
subset(intersection(X1,union(difference(X2,X1),X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_189,plain,
subset(intersection(X1,X2),intersection(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_183,c_0_168]) ).
cnf(c_0_190,plain,
union(X1,difference(union(X1,X2),X1)) = union(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_180]),c_0_103]) ).
cnf(c_0_191,plain,
subset(intersection(X1,X2),intersection(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_175,c_0_168]) ).
cnf(c_0_192,plain,
intersection(X1,difference(X1,X2)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_184]),c_0_42])]) ).
cnf(c_0_193,plain,
subset(difference(union(X1,X2),difference(X2,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_180]) ).
cnf(c_0_194,plain,
subset(X1,difference(union(X1,X2),difference(X3,X1))),
inference(spm,[status(thm)],[c_0_187,c_0_182]) ).
cnf(c_0_195,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_21,c_0_188]),c_0_189])]) ).
cnf(c_0_196,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(rw,[status(thm)],[c_0_190,c_0_186]) ).
cnf(c_0_197,plain,
subset(difference(intersection(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_23,c_0_88]) ).
cnf(c_0_198,plain,
subset(difference(X1,X2),intersection(union(X3,X1),difference(X1,X2))),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_199,plain,
difference(union(X1,X2),difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_193]),c_0_194])]) ).
cnf(c_0_200,plain,
intersection(X1,difference(X2,difference(X3,X1))) = intersection(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_195]),c_0_37]) ).
cnf(c_0_201,plain,
( X1 = difference(intersection(X2,X3),X2)
| ~ subset(X1,difference(intersection(X2,X3),X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_197]) ).
cnf(c_0_202,plain,
difference(difference(intersection(X1,X2),X1),X3) = difference(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_197]) ).
cnf(c_0_203,plain,
intersection(union(X1,X2),difference(X2,X3)) = difference(X2,X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_198]),c_0_42])]) ).
cnf(c_0_204,plain,
intersection(difference(X1,X2),union(X2,X3)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_195,c_0_199]) ).
cnf(c_0_205,plain,
intersection(difference(X1,X2),difference(X3,X2)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_200,c_0_199]) ).
cnf(c_0_206,plain,
intersection(difference(X1,X2),intersection(X2,X3)) = difference(intersection(X2,X3),X2),
inference(spm,[status(thm)],[c_0_201,c_0_179]) ).
cnf(c_0_207,plain,
difference(X1,difference(intersection(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_202]) ).
cnf(c_0_208,plain,
intersection(union(X1,X2),difference(X1,X3)) = difference(X1,X3),
inference(spm,[status(thm)],[c_0_203,c_0_103]) ).
cnf(c_0_209,plain,
intersection(X1,difference(X2,X3)) = intersection(X2,difference(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_196]),c_0_204]),c_0_205]) ).
cnf(c_0_210,plain,
difference(intersection(X1,X2),difference(X3,X1)) = intersection(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_206]),c_0_207]) ).
cnf(c_0_211,plain,
intersection(X1,difference(union(X1,X2),X3)) = difference(X1,X3),
inference(rw,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_212,plain,
difference(X1,difference(X1,X2)) = intersection(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_159]),c_0_210]) ).
cnf(c_0_213,plain,
subset(difference(intersection(X1,X2),X2),X3),
inference(spm,[status(thm)],[c_0_197,c_0_37]) ).
cnf(c_0_214,plain,
subset(difference(X1,union(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_107,c_0_19]) ).
cnf(c_0_215,plain,
difference(X1,difference(union(X1,X2),X3)) = intersection(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_211]),c_0_212]) ).
cnf(c_0_216,plain,
( X1 = difference(intersection(X2,X3),X3)
| ~ subset(X1,difference(intersection(X2,X3),X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_213]) ).
cnf(c_0_217,plain,
subset(difference(X1,union(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_214,c_0_103]) ).
cnf(c_0_218,plain,
intersection(X1,intersection(X2,union(X1,X3))) = intersection(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_144]),c_0_215]),c_0_37]) ).
cnf(c_0_219,plain,
intersection(difference(X1,X2),X3) = intersection(X1,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_209]) ).
cnf(c_0_220,plain,
intersection(X1,difference(intersection(X2,X1),X3)) = difference(intersection(X2,X1),X3),
inference(spm,[status(thm)],[c_0_203,c_0_146]) ).
cnf(c_0_221,plain,
difference(X1,union(difference(X2,X1),X3)) = difference(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_195]),c_0_144]) ).
cnf(c_0_222,plain,
subset(difference(X1,X2),intersection(X1,X1)),
inference(spm,[status(thm)],[c_0_176,c_0_19]) ).
fof(c_0_223,negated_conjecture,
~ ! [X1,X2,X3] : difference(X1,union(X2,X3)) = intersection(difference(X1,X2),difference(X1,X3)),
inference(assume_negation,[status(cth)],[prove_th85]) ).
cnf(c_0_224,plain,
intersection(intersection(X1,X2),difference(X3,X2)) = difference(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_216,c_0_165]) ).
cnf(c_0_225,plain,
difference(difference(X1,union(X1,X2)),X3) = difference(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_217]) ).
cnf(c_0_226,plain,
intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_159]),c_0_219]),c_0_220]) ).
cnf(c_0_227,plain,
difference(X1,difference(X2,difference(X3,X1))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_196]),c_0_221]) ).
cnf(c_0_228,plain,
subset(X1,intersection(X1,X1)),
inference(spm,[status(thm)],[c_0_222,c_0_63]) ).
cnf(c_0_229,plain,
difference(X1,intersection(X2,union(X1,X3))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_144]),c_0_211]) ).
fof(c_0_230,negated_conjecture,
difference(esk3_0,union(esk4_0,esk5_0)) != intersection(difference(esk3_0,esk4_0),difference(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_223])])])]) ).
cnf(c_0_231,plain,
intersection(X1,difference(X2,union(X1,X3))) = difference(X1,union(X1,X3)),
inference(spm,[status(thm)],[c_0_224,c_0_180]) ).
cnf(c_0_232,plain,
difference(X1,difference(X2,union(X2,X3))) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_225]) ).
cnf(c_0_233,plain,
difference(difference(X1,X2),difference(X1,X3)) = difference(intersection(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_159]),c_0_226]) ).
cnf(c_0_234,plain,
difference(difference(X1,X2),difference(X3,X2)) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_227,c_0_199]) ).
cnf(c_0_235,plain,
intersection(difference(X1,X2),X3) = difference(intersection(X1,X3),X2),
inference(rw,[status(thm)],[c_0_219,c_0_226]) ).
cnf(c_0_236,plain,
intersection(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_228]),c_0_36])]) ).
cnf(c_0_237,plain,
difference(difference(X1,X2),intersection(X3,X1)) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_229,c_0_159]) ).
cnf(c_0_238,negated_conjecture,
difference(esk3_0,union(esk4_0,esk5_0)) != intersection(difference(esk3_0,esk4_0),difference(esk3_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_239,plain,
intersection(X1,difference(difference(X1,X2),X3)) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_203,c_0_136]) ).
cnf(c_0_240,plain,
difference(difference(X1,union(X2,X3)),X2) = difference(X1,union(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_231]),c_0_232]) ).
cnf(c_0_241,plain,
difference(difference(X1,X2),X3) = difference(difference(X1,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_233]),c_0_234]),c_0_226]),c_0_235]),c_0_236]),c_0_237]) ).
cnf(c_0_242,plain,
difference(difference(X1,X2),union(X2,X3)) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_221,c_0_199]) ).
cnf(c_0_243,negated_conjecture,
difference(esk3_0,union(esk4_0,esk5_0)) != difference(difference(esk3_0,esk4_0),esk5_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_238,c_0_209]),c_0_239]) ).
cnf(c_0_244,plain,
difference(X1,union(X2,X3)) = difference(difference(X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_240,c_0_241]),c_0_242]) ).
cnf(c_0_245,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_243,c_0_244])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET612+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 10:16:35 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.nOwVd8I7Zv/E---3.1_14846.p
% 212.36/27.31 # Version: 3.1.0
% 212.36/27.31 # Preprocessing class: FSMSSMSSSSSNFFN.
% 212.36/27.31 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 212.36/27.31 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 212.36/27.31 # Starting new_bool_3 with 300s (1) cores
% 212.36/27.31 # Starting new_bool_1 with 300s (1) cores
% 212.36/27.31 # Starting sh5l with 300s (1) cores
% 212.36/27.31 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 14924 completed with status 0
% 212.36/27.31 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 212.36/27.31 # Preprocessing class: FSMSSMSSSSSNFFN.
% 212.36/27.31 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 212.36/27.31 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 212.36/27.31 # No SInE strategy applied
% 212.36/27.31 # Search class: FGHSM-FFMF22-SFFFFFNN
% 212.36/27.31 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 212.36/27.31 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 811s (1) cores
% 212.36/27.31 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 212.36/27.31 # Starting new_bool_3 with 136s (1) cores
% 212.36/27.31 # Starting new_bool_1 with 136s (1) cores
% 212.36/27.31 # Starting sh5l with 136s (1) cores
% 212.36/27.31 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 14931 completed with status 0
% 212.36/27.31 # Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 212.36/27.31 # Preprocessing class: FSMSSMSSSSSNFFN.
% 212.36/27.31 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 212.36/27.31 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 212.36/27.31 # No SInE strategy applied
% 212.36/27.31 # Search class: FGHSM-FFMF22-SFFFFFNN
% 212.36/27.31 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 212.36/27.31 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 811s (1) cores
% 212.36/27.31 # Preprocessing time : 0.001 s
% 212.36/27.31 # Presaturation interreduction done
% 212.36/27.31
% 212.36/27.31 # Proof found!
% 212.36/27.31 # SZS status Theorem
% 212.36/27.31 # SZS output start CNFRefutation
% See solution above
% 212.46/27.31 # Parsed axioms : 13
% 212.46/27.31 # Removed by relevancy pruning/SinE : 0
% 212.46/27.31 # Initial clauses : 26
% 212.46/27.31 # Removed in clause preprocessing : 2
% 212.46/27.31 # Initial clauses in saturation : 24
% 212.46/27.31 # Processed clauses : 66075
% 212.46/27.31 # ...of these trivial : 9285
% 212.46/27.31 # ...subsumed : 52339
% 212.46/27.31 # ...remaining for further processing : 4451
% 212.46/27.31 # Other redundant clauses eliminated : 17
% 212.46/27.31 # Clauses deleted for lack of memory : 0
% 212.46/27.31 # Backward-subsumed : 143
% 212.46/27.31 # Backward-rewritten : 2170
% 212.46/27.31 # Generated clauses : 2786428
% 212.46/27.31 # ...of the previous two non-redundant : 1655148
% 212.46/27.31 # ...aggressively subsumed : 0
% 212.46/27.31 # Contextual simplify-reflections : 8
% 212.46/27.31 # Paramodulations : 2785438
% 212.46/27.31 # Factorizations : 972
% 212.46/27.31 # NegExts : 0
% 212.46/27.31 # Equation resolutions : 18
% 212.46/27.31 # Disequality decompositions : 0
% 212.46/27.31 # Total rewrite steps : 3366246
% 212.46/27.31 # ...of those cached : 3121942
% 212.46/27.31 # Propositional unsat checks : 0
% 212.46/27.31 # Propositional check models : 0
% 212.46/27.31 # Propositional check unsatisfiable : 0
% 212.46/27.31 # Propositional clauses : 0
% 212.46/27.31 # Propositional clauses after purity: 0
% 212.46/27.31 # Propositional unsat core size : 0
% 212.46/27.31 # Propositional preprocessing time : 0.000
% 212.46/27.31 # Propositional encoding time : 0.000
% 212.46/27.31 # Propositional solver time : 0.000
% 212.46/27.31 # Success case prop preproc time : 0.000
% 212.46/27.31 # Success case prop encoding time : 0.000
% 212.46/27.31 # Success case prop solver time : 0.000
% 212.46/27.31 # Current number of processed clauses : 2114
% 212.46/27.31 # Positive orientable unit clauses : 1097
% 212.46/27.31 # Positive unorientable unit clauses: 15
% 212.46/27.31 # Negative unit clauses : 8
% 212.46/27.31 # Non-unit-clauses : 994
% 212.46/27.31 # Current number of unprocessed clauses: 1577019
% 212.46/27.31 # ...number of literals in the above : 3736699
% 212.46/27.31 # Current number of archived formulas : 0
% 212.46/27.31 # Current number of archived clauses : 2335
% 212.46/27.31 # Clause-clause subsumption calls (NU) : 427768
% 212.46/27.31 # Rec. Clause-clause subsumption calls : 270635
% 212.46/27.31 # Non-unit clause-clause subsumptions : 16796
% 212.46/27.31 # Unit Clause-clause subsumption calls : 268495
% 212.46/27.31 # Rewrite failures with RHS unbound : 6676
% 212.46/27.31 # BW rewrite match attempts : 93896
% 212.46/27.31 # BW rewrite match successes : 2636
% 212.46/27.31 # Condensation attempts : 0
% 212.46/27.31 # Condensation successes : 0
% 212.46/27.31 # Termbank termtop insertions : 33825319
% 212.46/27.31 # Search garbage collected termcells : 367
% 212.46/27.31
% 212.46/27.31 # -------------------------------------------------
% 212.46/27.31 # User time : 25.574 s
% 212.46/27.31 # System time : 0.957 s
% 212.46/27.31 # Total time : 26.531 s
% 212.46/27.31 # Maximum resident set size: 1760 pages
% 212.46/27.31
% 212.46/27.31 # -------------------------------------------------
% 212.46/27.31 # User time : 130.976 s
% 212.46/27.31 # System time : 1.945 s
% 212.46/27.31 # Total time : 132.922 s
% 212.46/27.31 # Maximum resident set size: 1752 pages
% 212.46/27.31 % E---3.1 exiting
% 212.46/27.31 % E exiting
%------------------------------------------------------------------------------