TSTP Solution File: SET608+3 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET608+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 : Tue May 21 02:54:53 EDT 2024
% Result : Theorem 212.72s 27.41s
% Output : CNFRefutation 212.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 173 ( 106 unt; 0 def)
% Number of atoms : 283 ( 56 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 175 ( 65 ~; 89 |; 14 &)
% ( 6 <=>; 1 =>; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 485 ( 90 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(prove_union_intersection_difference,conjecture,
! [X1,X2] : union(intersection(X1,X2),difference(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_intersection_difference) ).
fof(c_0_8,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_9,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_8])])])]) ).
fof(c_0_10,plain,
! [X19,X20,X21,X22,X23] :
( ( ~ subset(X19,X20)
| ~ member(X21,X19)
| member(X21,X20) )
& ( member(esk1_2(X22,X23),X22)
| subset(X22,X23) )
& ( ~ member(esk1_2(X22,X23),X23)
| subset(X22,X23) ) ),
inference(distribute,[status(thm)],[inference(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])])])])])])]) ).
fof(c_0_11,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_12,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X13,X14] :
( ( subset(X13,X14)
| X13 != X14 )
& ( subset(X14,X13)
| X13 != X14 )
& ( ~ subset(X13,X14)
| ~ subset(X14,X13)
| X13 = X14 ) ),
inference(distribute,[status(thm)],[inference(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_10]) ).
cnf(c_0_19,plain,
( subset(difference(X1,X2),X3)
| member(esk1_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_21,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_22,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_26,plain,
( subset(intersection(X1,difference(X2,X3)),X4)
| ~ member(esk1_2(intersection(X1,difference(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_27,plain,
( subset(intersection(intersection(X1,X2),X3),X4)
| member(esk1_2(intersection(intersection(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_28,plain,
( difference(X1,X2) = X1
| ~ subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,plain,
( X1 = difference(X2,X2)
| ~ subset(X1,difference(X2,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_32,plain,
subset(intersection(intersection(X1,X2),difference(X3,X1)),X4),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_34,plain,
( member(X1,X2)
| ~ member(X1,difference(X3,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
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_30]) ).
cnf(c_0_36,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_37,plain,
intersection(intersection(X1,X2),difference(X3,X1)) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_33]),c_0_34]) ).
cnf(c_0_39,plain,
( subset(X1,difference(X1,X2))
| member(esk1_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_13]) ).
cnf(c_0_40,plain,
( subset(difference(difference(X1,X2),X3),X4)
| member(esk1_2(difference(difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
fof(c_0_41,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_42,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,intersection(X3,X4)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_43,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
subset(difference(difference(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_20,c_0_40]) ).
cnf(c_0_45,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_46,plain,
! [X17,X18] : intersection(X17,X18) = intersection(X18,X17),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_47,plain,
( subset(difference(X1,intersection(X2,X3)),X4)
| ~ member(esk1_2(difference(X1,intersection(X2,X3)),X4),X3)
| ~ member(esk1_2(difference(X1,intersection(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_36]) ).
cnf(c_0_48,plain,
( subset(difference(difference(X1,X2),X3),X4)
| ~ member(esk1_2(difference(difference(X1,X2),X3),X4),intersection(X2,X5)) ),
inference(spm,[status(thm)],[c_0_42,c_0_19]) ).
cnf(c_0_49,plain,
( subset(difference(difference(X1,X2),X3),difference(X1,X4))
| member(esk1_2(difference(difference(X1,X2),X3),difference(X1,X4)),X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_40]) ).
cnf(c_0_50,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_43]),c_0_24])]) ).
cnf(c_0_51,plain,
difference(difference(difference(X1,X2),X1),X3) = difference(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_28,c_0_44]) ).
cnf(c_0_52,plain,
( subset(difference(X1,union(X2,X3)),X4)
| ~ member(esk1_2(difference(X1,union(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_45]) ).
cnf(c_0_53,plain,
( subset(intersection(difference(X1,X2),X3),X4)
| ~ member(esk1_2(intersection(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_22]) ).
cnf(c_0_54,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,plain,
( subset(difference(X1,intersection(X2,X1)),X3)
| ~ member(esk1_2(difference(X1,intersection(X2,X1)),X3),X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_19]) ).
cnf(c_0_56,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_57,plain,
subset(difference(difference(X1,X2),X3),difference(X1,intersection(X2,X4))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,plain,
difference(X1,difference(difference(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_59,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_36]) ).
cnf(c_0_60,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_20,c_0_30]) ).
cnf(c_0_61,plain,
subset(difference(X1,union(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_52,c_0_19]) ).
cnf(c_0_62,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_63,plain,
subset(intersection(X1,difference(X2,X1)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_21]),c_0_54]) ).
cnf(c_0_64,plain,
subset(difference(X1,intersection(X2,X1)),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,plain,
subset(difference(X1,X2),difference(X1,intersection(X2,X3))),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,plain,
( subset(difference(X1,X2),intersection(X3,X1))
| ~ member(esk1_2(difference(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_19]) ).
cnf(c_0_67,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk1_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_19]) ).
cnf(c_0_68,plain,
difference(X1,union(X2,X1)) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_31,c_0_61]) ).
cnf(c_0_69,plain,
( subset(intersection(difference(X1,X2),X3),X4)
| member(esk1_2(intersection(difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_22]) ).
cnf(c_0_70,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_62,c_0_21]) ).
cnf(c_0_71,plain,
difference(intersection(X1,difference(X2,X1)),X3) = intersection(X1,difference(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_63]) ).
cnf(c_0_72,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_64]),c_0_65])]) ).
cnf(c_0_73,plain,
( subset(intersection(intersection(X1,X2),X3),intersection(X4,X1))
| ~ member(esk1_2(intersection(intersection(X1,X2),X3),intersection(X4,X1)),X4) ),
inference(spm,[status(thm)],[c_0_59,c_0_27]) ).
cnf(c_0_74,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,plain,
difference(X1,union(X2,X1)) = difference(difference(X3,X4),X3),
inference(spm,[status(thm)],[c_0_51,c_0_68]) ).
cnf(c_0_76,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_59,c_0_69]) ).
cnf(c_0_77,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_53,c_0_70]) ).
cnf(c_0_78,plain,
difference(X1,intersection(X2,difference(X3,X2))) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_71]) ).
cnf(c_0_79,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_72,c_0_54]) ).
cnf(c_0_80,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_73,c_0_21]) ).
cnf(c_0_81,plain,
subset(X1,intersection(X1,union(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_58]),c_0_54]) ).
cnf(c_0_82,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_83,plain,
subset(intersection(difference(X1,X2),union(X2,X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_84,plain,
difference(X1,difference(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_80,c_0_54]) ).
cnf(c_0_86,plain,
intersection(X1,union(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_81]),c_0_82])]) ).
cnf(c_0_87,plain,
subset(difference(X1,X2),intersection(X1,X1)),
inference(spm,[status(thm)],[c_0_66,c_0_19]) ).
cnf(c_0_88,plain,
subset(intersection(X1,union(difference(X2,X1),X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,plain,
subset(intersection(X1,X2),intersection(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,plain,
subset(X1,intersection(X1,X1)),
inference(spm,[status(thm)],[c_0_87,c_0_58]) ).
cnf(c_0_91,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_23,c_0_88]),c_0_89])]) ).
cnf(c_0_92,plain,
( subset(difference(intersection(X1,X2),X3),X4)
| member(esk1_2(difference(intersection(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_93,plain,
( subset(difference(difference(X1,X2),X3),X4)
| ~ member(esk1_2(difference(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_94,plain,
( subset(difference(difference(union(X1,X2),X3),X4),X5)
| member(esk1_2(difference(difference(union(X1,X2),X3),X4),X5),X1)
| member(esk1_2(difference(difference(union(X1,X2),X3),X4),X5),X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_40]) ).
fof(c_0_95,plain,
! [X15,X16] : union(X15,X16) = union(X16,X15),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_96,plain,
intersection(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_90]),c_0_82])]) ).
cnf(c_0_97,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_21]) ).
cnf(c_0_98,plain,
subset(difference(X1,X2),intersection(X1,difference(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_13]),c_0_54]) ).
cnf(c_0_99,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_100,plain,
intersection(difference(X1,X2),union(X2,X3)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_91,c_0_84]) ).
cnf(c_0_101,plain,
( subset(difference(intersection(X1,X2),X3),difference(X1,X4))
| member(esk1_2(difference(intersection(X1,X2),X3),difference(X1,X4)),X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_92]) ).
cnf(c_0_102,plain,
( subset(difference(difference(union(X1,X2),X2),X3),X4)
| member(esk1_2(difference(difference(union(X1,X2),X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
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(intersection(X1,X2),intersection(X1,intersection(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_96]),c_0_54]) ).
cnf(c_0_105,plain,
subset(difference(X1,X2),difference(difference(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_20,c_0_39]) ).
cnf(c_0_106,plain,
subset(intersection(difference(X1,X2),X3),difference(X3,X2)),
inference(spm,[status(thm)],[c_0_53,c_0_97]) ).
cnf(c_0_107,plain,
intersection(X1,difference(X1,X2)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_98]),c_0_99])]) ).
cnf(c_0_108,plain,
intersection(union(X1,X2),difference(X3,X1)) = intersection(X2,difference(X3,X1)),
inference(spm,[status(thm)],[c_0_54,c_0_100]) ).
cnf(c_0_109,plain,
subset(difference(intersection(X1,X2),X3),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_20,c_0_101]) ).
cnf(c_0_110,plain,
subset(difference(difference(union(X1,intersection(X1,X2)),X1),X3),X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_102]),c_0_103]) ).
cnf(c_0_111,plain,
intersection(X1,intersection(X1,X2)) = intersection(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_104]),c_0_99])]) ).
cnf(c_0_112,plain,
difference(difference(X1,X2),X2) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_105]),c_0_24])]) ).
cnf(c_0_113,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_114,plain,
( subset(difference(intersection(X1,X2),difference(X1,X3)),X4)
| member(esk1_2(difference(intersection(X1,X2),difference(X1,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_60,c_0_92]) ).
cnf(c_0_115,plain,
subset(intersection(X1,difference(X2,X3)),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_106,c_0_54]) ).
cnf(c_0_116,plain,
intersection(X1,difference(union(X2,X1),X2)) = difference(union(X2,X1),X2),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_117,plain,
subset(difference(intersection(X1,X2),X3),difference(X2,X3)),
inference(spm,[status(thm)],[c_0_109,c_0_54]) ).
cnf(c_0_118,plain,
subset(difference(union(X1,intersection(X1,X2)),X1),X3),
inference(spm,[status(thm)],[c_0_110,c_0_58]) ).
cnf(c_0_119,plain,
intersection(X1,intersection(X2,X1)) = intersection(X2,X1),
inference(spm,[status(thm)],[c_0_111,c_0_54]) ).
cnf(c_0_120,plain,
subset(difference(X1,X2),difference(difference(X1,X2),intersection(X2,X3))),
inference(spm,[status(thm)],[c_0_65,c_0_112]) ).
cnf(c_0_121,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_113]) ).
cnf(c_0_122,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_45]) ).
cnf(c_0_123,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_62,c_0_19]) ).
cnf(c_0_124,plain,
subset(difference(intersection(X1,X2),difference(X1,X3)),X3),
inference(spm,[status(thm)],[c_0_18,c_0_114]) ).
cnf(c_0_125,plain,
subset(difference(union(X1,X2),X1),difference(X2,X1)),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_126,plain,
subset(difference(X1,X2),difference(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_117,c_0_86]) ).
cnf(c_0_127,plain,
intersection(X1,union(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_86,c_0_103]) ).
cnf(c_0_128,plain,
subset(difference(union(X1,intersection(X2,X1)),X1),X3),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_129,plain,
difference(difference(X1,X2),intersection(X2,X3)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_120]),c_0_24])]) ).
cnf(c_0_130,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
inference(spm,[status(thm)],[c_0_121,c_0_45]) ).
cnf(c_0_131,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_122,c_0_123]) ).
cnf(c_0_132,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_124,c_0_96]) ).
cnf(c_0_133,plain,
difference(union(X1,X2),X1) = difference(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_125]),c_0_126])]) ).
cnf(c_0_134,plain,
subset(difference(X1,X2),difference(union(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_117,c_0_127]) ).
cnf(c_0_135,plain,
difference(union(X1,intersection(X2,X1)),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_31,c_0_128]) ).
cnf(c_0_136,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_122,c_0_13]) ).
cnf(c_0_137,plain,
( subset(difference(difference(X1,union(X2,X3)),X4),X5)
| ~ member(esk1_2(difference(difference(X1,union(X2,X3)),X4),X5),X3) ),
inference(spm,[status(thm)],[c_0_93,c_0_45]) ).
cnf(c_0_138,plain,
( subset(difference(difference(X1,X2),difference(X1,X3)),X4)
| member(esk1_2(difference(difference(X1,X2),difference(X1,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_60,c_0_40]) ).
cnf(c_0_139,plain,
difference(difference(X1,X2),intersection(X3,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_129,c_0_119]) ).
cnf(c_0_140,plain,
subset(difference(union(X1,X2),X3),union(union(X4,X1),X2)),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_141,plain,
subset(difference(union(X1,X2),difference(X2,X1)),X1),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_142,plain,
subset(X1,difference(union(X1,X2),difference(X3,X1))),
inference(spm,[status(thm)],[c_0_134,c_0_84]) ).
cnf(c_0_143,plain,
subset(union(X1,intersection(X2,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_135]),c_0_50]) ).
cnf(c_0_144,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_136,c_0_103]) ).
cnf(c_0_145,plain,
subset(difference(difference(X1,union(X2,X3)),difference(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_146,plain,
difference(difference(X1,union(X2,X3)),X2) = difference(X1,union(X2,X3)),
inference(spm,[status(thm)],[c_0_139,c_0_127]) ).
cnf(c_0_147,plain,
subset(difference(union(X1,difference(X1,X2)),X1),X3),
inference(spm,[status(thm)],[c_0_118,c_0_107]) ).
cnf(c_0_148,plain,
subset(union(X1,X2),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_140,c_0_58]) ).
cnf(c_0_149,plain,
difference(union(X1,X2),difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_141]),c_0_142])]) ).
cnf(c_0_150,plain,
union(X1,intersection(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_143]),c_0_144])]) ).
cnf(c_0_151,plain,
subset(difference(X1,union(X2,difference(X1,X2))),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_103]) ).
cnf(c_0_152,plain,
difference(union(X1,difference(X1,X2)),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_31,c_0_147]) ).
cnf(c_0_153,plain,
subset(union(X1,X2),union(union(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_148,c_0_103]) ).
cnf(c_0_154,plain,
difference(X1,difference(X1,X2)) = intersection(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_72]),c_0_103]),c_0_150]) ).
cnf(c_0_155,plain,
difference(X1,union(X2,difference(X1,X2))) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_31,c_0_151]) ).
cnf(c_0_156,plain,
subset(union(X1,X2),union(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_148,c_0_103]) ).
cnf(c_0_157,plain,
subset(union(X1,difference(X1,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_152]),c_0_50]) ).
cnf(c_0_158,plain,
subset(union(X1,intersection(X2,union(X1,X3))),union(X1,X3)),
inference(spm,[status(thm)],[c_0_153,c_0_150]) ).
cnf(c_0_159,plain,
intersection(X1,union(X2,difference(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_50]),c_0_54]) ).
cnf(c_0_160,plain,
subset(union(X1,X2),union(X1,union(X3,X2))),
inference(spm,[status(thm)],[c_0_156,c_0_103]) ).
cnf(c_0_161,plain,
union(X1,difference(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_157]),c_0_144])]) ).
cnf(c_0_162,plain,
difference(union(X1,intersection(X1,X2)),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_31,c_0_118]) ).
fof(c_0_163,negated_conjecture,
~ ! [X1,X2] : union(intersection(X1,X2),difference(X1,X2)) = X1,
inference(assume_negation,[status(cth)],[prove_union_intersection_difference]) ).
cnf(c_0_164,plain,
subset(union(X1,X2),union(X1,difference(X2,X1))),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_165,plain,
subset(union(X1,difference(X2,X3)),union(X1,X2)),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_166,plain,
subset(union(X1,intersection(X1,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_162]),c_0_50]) ).
fof(c_0_167,negated_conjecture,
union(intersection(esk3_0,esk4_0),difference(esk3_0,esk4_0)) != esk3_0,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_163])])])]) ).
cnf(c_0_168,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_164]),c_0_165])]) ).
cnf(c_0_169,plain,
union(X1,intersection(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_166]),c_0_144])]) ).
cnf(c_0_170,negated_conjecture,
union(intersection(esk3_0,esk4_0),difference(esk3_0,esk4_0)) != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_171,plain,
union(intersection(X1,X2),difference(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_79]),c_0_103]),c_0_169]) ).
cnf(c_0_172,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_171])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET608+3 : TPTP v8.2.0. Released v2.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 11:58:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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/benchmark/theBenchmark.p
% 212.72/27.41 # Version: 3.1.0
% 212.72/27.41 # Preprocessing class: FSMSSMSSSSSNFFN.
% 212.72/27.41 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 212.72/27.41 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 212.72/27.41 # Starting new_bool_3 with 300s (1) cores
% 212.72/27.41 # Starting new_bool_1 with 300s (1) cores
% 212.72/27.41 # Starting sh5l with 300s (1) cores
% 212.72/27.41 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 30842 completed with status 0
% 212.72/27.41 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 212.72/27.41 # Preprocessing class: FSMSSMSSSSSNFFN.
% 212.72/27.41 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 212.72/27.41 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 212.72/27.41 # No SInE strategy applied
% 212.72/27.41 # Search class: FGHSS-FFSF22-SFFFFFNN
% 212.72/27.41 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 212.72/27.41 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 811s (1) cores
% 212.72/27.41 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 212.72/27.41 # Starting new_bool_3 with 136s (1) cores
% 212.72/27.41 # Starting new_bool_1 with 136s (1) cores
% 212.72/27.41 # Starting sh5l with 136s (1) cores
% 212.72/27.41 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 30848 completed with status 0
% 212.72/27.41 # Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 212.72/27.41 # Preprocessing class: FSMSSMSSSSSNFFN.
% 212.72/27.41 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 212.72/27.41 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 212.72/27.41 # No SInE strategy applied
% 212.72/27.41 # Search class: FGHSS-FFSF22-SFFFFFNN
% 212.72/27.41 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 212.72/27.41 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 811s (1) cores
% 212.72/27.41 # Preprocessing time : 0.001 s
% 212.72/27.41 # Presaturation interreduction done
% 212.72/27.41
% 212.72/27.41 # Proof found!
% 212.72/27.41 # SZS status Theorem
% 212.72/27.41 # SZS output start CNFRefutation
% See solution above
% 212.72/27.41 # Parsed axioms : 10
% 212.72/27.41 # Removed by relevancy pruning/SinE : 0
% 212.72/27.41 # Initial clauses : 23
% 212.72/27.41 # Removed in clause preprocessing : 2
% 212.72/27.41 # Initial clauses in saturation : 21
% 212.72/27.41 # Processed clauses : 80700
% 212.72/27.41 # ...of these trivial : 8842
% 212.72/27.41 # ...subsumed : 66437
% 212.72/27.41 # ...remaining for further processing : 5421
% 212.72/27.41 # Other redundant clauses eliminated : 2
% 212.72/27.41 # Clauses deleted for lack of memory : 0
% 212.72/27.41 # Backward-subsumed : 6
% 212.72/27.41 # Backward-rewritten : 598
% 212.72/27.41 # Generated clauses : 3529990
% 212.72/27.41 # ...of the previous two non-redundant : 2011795
% 212.72/27.41 # ...aggressively subsumed : 0
% 212.72/27.41 # Contextual simplify-reflections : 5
% 212.72/27.41 # Paramodulations : 3528116
% 212.72/27.41 # Factorizations : 1872
% 212.72/27.41 # NegExts : 0
% 212.72/27.41 # Equation resolutions : 2
% 212.72/27.41 # Disequality decompositions : 0
% 212.72/27.41 # Total rewrite steps : 5278399
% 212.72/27.41 # ...of those cached : 5021689
% 212.72/27.41 # Propositional unsat checks : 0
% 212.72/27.41 # Propositional check models : 0
% 212.72/27.41 # Propositional check unsatisfiable : 0
% 212.72/27.41 # Propositional clauses : 0
% 212.72/27.41 # Propositional clauses after purity: 0
% 212.72/27.41 # Propositional unsat core size : 0
% 212.72/27.41 # Propositional preprocessing time : 0.000
% 212.72/27.41 # Propositional encoding time : 0.000
% 212.72/27.41 # Propositional solver time : 0.000
% 212.72/27.41 # Success case prop preproc time : 0.000
% 212.72/27.41 # Success case prop encoding time : 0.000
% 212.72/27.41 # Success case prop solver time : 0.000
% 212.72/27.41 # Current number of processed clauses : 4796
% 212.72/27.41 # Positive orientable unit clauses : 2383
% 212.72/27.41 # Positive unorientable unit clauses: 40
% 212.72/27.41 # Negative unit clauses : 13
% 212.72/27.41 # Non-unit-clauses : 2360
% 212.72/27.41 # Current number of unprocessed clauses: 1921178
% 212.72/27.41 # ...number of literals in the above : 4594251
% 212.72/27.41 # Current number of archived formulas : 0
% 212.72/27.41 # Current number of archived clauses : 623
% 212.72/27.41 # Clause-clause subsumption calls (NU) : 1298085
% 212.72/27.41 # Rec. Clause-clause subsumption calls : 678601
% 212.72/27.41 # Non-unit clause-clause subsumptions : 13683
% 212.72/27.41 # Unit Clause-clause subsumption calls : 942181
% 212.72/27.41 # Rewrite failures with RHS unbound : 8066
% 212.72/27.41 # BW rewrite match attempts : 141537
% 212.72/27.41 # BW rewrite match successes : 826
% 212.72/27.41 # Condensation attempts : 0
% 212.72/27.41 # Condensation successes : 0
% 212.72/27.41 # Termbank termtop insertions : 50647254
% 212.72/27.41 # Search garbage collected termcells : 333
% 212.72/27.41
% 212.72/27.41 # -------------------------------------------------
% 212.72/27.41 # User time : 25.244 s
% 212.72/27.41 # System time : 0.979 s
% 212.72/27.41 # Total time : 26.224 s
% 212.72/27.41 # Maximum resident set size: 1760 pages
% 212.72/27.41
% 212.72/27.41 # -------------------------------------------------
% 212.72/27.41 # User time : 130.086 s
% 212.72/27.41 # System time : 2.064 s
% 212.72/27.41 # Total time : 132.150 s
% 212.72/27.41 # Maximum resident set size: 1700 pages
% 212.72/27.41 % E---3.1 exiting
% 212.72/27.41 % E exiting
%------------------------------------------------------------------------------