TSTP Solution File: SET634+3 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET634+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n009.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 02:55:05 EDT 2024
% Result : Theorem 95.71s 12.47s
% Output : CNFRefutation 95.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 112 ( 53 unt; 0 def)
% Number of atoms : 213 ( 48 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 164 ( 63 ~; 80 |; 13 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 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 : 314 ( 46 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(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(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(member_equal,axiom,
! [X1,X2] :
( ! [X3] :
( member(X3,X1)
<=> member(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
fof(prove_difference_and_intersection,conjecture,
! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_and_intersection) ).
fof(c_0_7,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_8,plain,
! [X10,X11,X12] :
( ( member(X12,X10)
| ~ member(X12,intersection(X10,X11)) )
& ( member(X12,X11)
| ~ member(X12,intersection(X10,X11)) )
& ( ~ member(X12,X10)
| ~ member(X12,X11)
| member(X12,intersection(X10,X11)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
fof(c_0_9,plain,
! [X25,X26,X27,X28,X29] :
( ( ~ subset(X25,X26)
| ~ member(X27,X25)
| member(X27,X26) )
& ( member(esk6_2(X28,X29),X28)
| subset(X28,X29) )
& ( ~ member(esk6_2(X28,X29),X29)
| subset(X28,X29) ) ),
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_10,plain,
! [X7,X8,X9] :
( ( member(X9,X7)
| ~ member(X9,difference(X7,X8)) )
& ( ~ member(X9,X8)
| ~ member(X9,difference(X7,X8)) )
& ( ~ member(X9,X7)
| member(X9,X8)
| member(X9,difference(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_11,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( member(esk6_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| ~ member(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( subset(intersection(X1,X2),X3)
| member(esk6_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_16,plain,
! [X13,X14] : intersection(X13,X14) = intersection(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_17,plain,
! [X31,X32] :
( ( subset(X31,X32)
| X31 != X32 )
& ( subset(X32,X31)
| X31 != X32 )
& ( ~ subset(X31,X32)
| ~ subset(X32,X31)
| X31 = X32 ) ),
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(difference(X1,X2),X3)
| member(esk6_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_19,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
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_14,c_0_18]) ).
cnf(c_0_25,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk6_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_26,plain,
( subset(intersection(X1,X2),X3)
| member(esk6_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_27,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_21,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,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_30,plain,
( subset(intersection(difference(X1,X2),X3),X4)
| ~ member(esk6_2(intersection(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_31,plain,
( subset(intersection(X1,difference(X2,X3)),X4)
| member(esk6_2(intersection(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_32,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_23,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_29]) ).
cnf(c_0_34,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_35,plain,
( X1 = difference(X2,X2)
| ~ subset(X1,difference(X2,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_36,plain,
subset(intersection(difference(X1,X2),difference(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
intersection(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_38,plain,
( ~ member(X1,difference(X2,X2))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
cnf(c_0_39,plain,
( subset(X1,difference(X2,X3))
| member(esk6_2(X1,difference(X2,X3)),X3)
| ~ member(esk6_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_34]) ).
cnf(c_0_40,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_41,plain,
intersection(difference(X1,X2),difference(X2,X3)) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_37]),c_0_38]) ).
cnf(c_0_43,plain,
( subset(X1,difference(X1,X2))
| member(esk6_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_12]) ).
cnf(c_0_44,plain,
( subset(difference(difference(X1,X2),X3),X4)
| member(esk6_2(difference(difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_45,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,difference(X4,X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_46,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
subset(difference(difference(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_48,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk6_2(difference(X1,X2),X3),difference(X4,X1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_12]) ).
cnf(c_0_49,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_46]),c_0_24])]) ).
cnf(c_0_50,plain,
difference(difference(difference(X1,X2),X1),X3) = difference(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_28,c_0_47]) ).
cnf(c_0_51,plain,
subset(difference(X1,X2),difference(difference(X1,X2),difference(X3,X1))),
inference(spm,[status(thm)],[c_0_48,c_0_43]) ).
cnf(c_0_52,plain,
difference(X1,difference(difference(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk6_2(X1,intersection(X2,X3)),X3)
| ~ member(esk6_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_40]) ).
cnf(c_0_54,plain,
( subset(difference(intersection(X1,X2),X3),X4)
| member(esk6_2(difference(intersection(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_55,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk6_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk6_2(difference(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_34]) ).
cnf(c_0_56,plain,
( subset(difference(intersection(X1,X2),X3),X4)
| member(esk6_2(difference(intersection(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_57,plain,
( subset(intersection(X1,X2),difference(X2,X3))
| member(esk6_2(intersection(X1,X2),difference(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_15]) ).
cnf(c_0_58,plain,
subset(X1,difference(X1,difference(X2,X1))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
( subset(intersection(X1,difference(X2,X3)),X4)
| ~ member(esk6_2(intersection(X1,difference(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_60,plain,
( subset(difference(intersection(X1,X2),X3),intersection(X4,X2))
| ~ member(esk6_2(difference(intersection(X1,X2),X3),intersection(X4,X2)),X4) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,plain,
( subset(difference(intersection(X1,X2),difference(X1,X3)),X4)
| member(esk6_2(difference(intersection(X1,X2),difference(X1,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
( subset(difference(X1,X2),intersection(X3,X1))
| ~ member(esk6_2(difference(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_18]) ).
cnf(c_0_63,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk6_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_18]) ).
cnf(c_0_64,plain,
subset(intersection(difference(X1,X2),X3),difference(X3,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_57]) ).
cnf(c_0_65,plain,
difference(X1,difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_58]),c_0_24])]) ).
cnf(c_0_66,plain,
subset(intersection(X1,difference(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_59,c_0_26]) ).
cnf(c_0_67,plain,
subset(difference(intersection(X1,X2),difference(X1,X3)),intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,plain,
( subset(intersection(X1,X2),intersection(X3,X2))
| ~ member(esk6_2(intersection(X1,X2),intersection(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_15]) ).
cnf(c_0_69,plain,
( subset(intersection(intersection(X1,X2),X3),X4)
| member(esk6_2(intersection(intersection(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_26]) ).
cnf(c_0_70,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,plain,
subset(intersection(X1,X2),difference(X2,difference(X3,X1))),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,plain,
( X1 = intersection(X2,difference(X3,X2))
| ~ subset(X1,intersection(X2,difference(X3,X2))) ),
inference(spm,[status(thm)],[c_0_23,c_0_66]) ).
cnf(c_0_73,plain,
subset(difference(intersection(X1,X2),difference(X1,X3)),intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_67,c_0_22]) ).
cnf(c_0_74,plain,
difference(intersection(X1,difference(X2,X1)),X3) = intersection(X1,difference(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_66]) ).
cnf(c_0_75,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,plain,
difference(X1,difference(X1,X2)) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_70]),c_0_71])]) ).
cnf(c_0_77,plain,
difference(intersection(X1,X2),difference(X1,difference(X3,X2))) = intersection(X2,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,plain,
difference(X1,intersection(X2,difference(X3,X2))) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_74]) ).
fof(c_0_79,plain,
! [X15,X16] :
( ( ~ member(esk4_2(X15,X16),X15)
| ~ member(esk4_2(X15,X16),X16)
| X15 = X16 )
& ( member(esk4_2(X15,X16),X15)
| member(esk4_2(X15,X16),X16)
| X15 = X16 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_equal])])])])]) ).
cnf(c_0_80,plain,
( subset(intersection(X1,intersection(X2,X3)),X4)
| member(esk6_2(intersection(X1,intersection(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_81,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_75,c_0_22]) ).
cnf(c_0_82,plain,
intersection(intersection(X1,X2),difference(X1,difference(X3,X2))) = intersection(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_22]) ).
cnf(c_0_83,plain,
( subset(intersection(X1,X2),intersection(X3,X1))
| ~ member(esk6_2(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_26]) ).
cnf(c_0_84,plain,
( member(esk4_2(X1,X2),X1)
| member(esk4_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_85,plain,
subset(intersection(X1,intersection(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_14,c_0_80]) ).
cnf(c_0_86,plain,
subset(intersection(X1,X2),intersection(X2,difference(X1,difference(X3,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_22]) ).
cnf(c_0_87,plain,
subset(intersection(X1,difference(X2,X3)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_83,c_0_31]) ).
cnf(c_0_88,plain,
( X1 = X2
| ~ member(esk4_2(X1,X2),X1)
| ~ member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,plain,
( X1 = intersection(X2,X3)
| member(esk4_2(X1,intersection(X2,X3)),X1)
| member(esk4_2(X1,intersection(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_84]) ).
cnf(c_0_90,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_91,plain,
subset(intersection(intersection(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_85,c_0_22]) ).
cnf(c_0_92,plain,
intersection(X1,difference(X2,difference(X3,X1))) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_86]),c_0_87])]) ).
cnf(c_0_93,plain,
( X1 = intersection(X2,X3)
| ~ member(esk4_2(X1,intersection(X2,X3)),X1)
| ~ member(esk4_2(X1,intersection(X2,X3)),X3)
| ~ member(esk4_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_40]) ).
cnf(c_0_94,plain,
( intersection(X1,X2) = X2
| member(esk4_2(X2,intersection(X1,X2)),X2) ),
inference(ef,[status(thm)],[c_0_89]) ).
cnf(c_0_95,plain,
( member(X1,X2)
| ~ member(X1,intersection(intersection(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,plain,
intersection(difference(X1,X2),difference(X3,X2)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_92,c_0_65]) ).
cnf(c_0_97,plain,
( intersection(X1,X2) = X2
| ~ member(esk4_2(X2,intersection(X1,X2)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_94]) ).
cnf(c_0_98,plain,
( intersection(X1,intersection(intersection(X2,X3),X4)) = intersection(intersection(X2,X3),X4)
| member(esk4_2(intersection(intersection(X2,X3),X4),intersection(X1,intersection(intersection(X2,X3),X4))),X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_94]) ).
cnf(c_0_99,plain,
subset(difference(X1,X2),intersection(X1,difference(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_12]),c_0_22]) ).
fof(c_0_100,negated_conjecture,
~ ! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
inference(assume_negation,[status(cth)],[prove_difference_and_intersection]) ).
cnf(c_0_101,plain,
intersection(X1,difference(X2,X3)) = intersection(X2,difference(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_96]),c_0_96]) ).
cnf(c_0_102,plain,
intersection(X1,intersection(intersection(X1,X2),X3)) = intersection(intersection(X1,X2),X3),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_103,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_99]),c_0_21])]) ).
fof(c_0_104,negated_conjecture,
intersection(esk1_0,difference(esk2_0,esk3_0)) != difference(intersection(esk1_0,esk2_0),esk3_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])])]) ).
cnf(c_0_105,plain,
intersection(X1,difference(X2,difference(X1,X3))) = intersection(X2,intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_101,c_0_76]) ).
cnf(c_0_106,plain,
difference(difference(X1,X2),difference(X3,X1)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_51]),c_0_24])]) ).
cnf(c_0_107,plain,
intersection(difference(X1,X2),X3) = intersection(X1,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_101]) ).
cnf(c_0_108,plain,
intersection(X1,difference(intersection(X1,X2),X3)) = difference(intersection(X1,X2),X3),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_109,negated_conjecture,
intersection(esk1_0,difference(esk2_0,esk3_0)) != difference(intersection(esk1_0,esk2_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_110,plain,
difference(intersection(X1,X2),X3) = intersection(X2,difference(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_108]) ).
cnf(c_0_111,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_101])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET634+3 : TPTP v8.2.0. Released v2.2.0.
% 0.02/0.09 % Command : run_E %s %d THM
% 0.09/0.29 % Computer : n009.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon May 20 12:59:22 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 95.71/12.47 # Version: 3.1.0
% 95.71/12.47 # Preprocessing class: FSMSSMSSSSSNFFN.
% 95.71/12.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 95.71/12.47 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 95.71/12.47 # Starting new_bool_3 with 300s (1) cores
% 95.71/12.47 # Starting new_bool_1 with 300s (1) cores
% 95.71/12.47 # Starting sh5l with 300s (1) cores
% 95.71/12.47 # sh5l with pid 770 completed with status 0
% 95.71/12.47 # Result found by sh5l
% 95.71/12.47 # Preprocessing class: FSMSSMSSSSSNFFN.
% 95.71/12.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 95.71/12.47 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 95.71/12.47 # Starting new_bool_3 with 300s (1) cores
% 95.71/12.47 # Starting new_bool_1 with 300s (1) cores
% 95.71/12.47 # Starting sh5l with 300s (1) cores
% 95.71/12.47 # SinE strategy is gf500_gu_R04_F100_L20000
% 95.71/12.47 # Search class: FGHSS-FFSF22-SFFFFFNN
% 95.71/12.47 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 95.71/12.47 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 181s (1) cores
% 95.71/12.47 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 777 completed with status 0
% 95.71/12.47 # Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 95.71/12.47 # Preprocessing class: FSMSSMSSSSSNFFN.
% 95.71/12.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 95.71/12.47 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 95.71/12.47 # Starting new_bool_3 with 300s (1) cores
% 95.71/12.47 # Starting new_bool_1 with 300s (1) cores
% 95.71/12.47 # Starting sh5l with 300s (1) cores
% 95.71/12.47 # SinE strategy is gf500_gu_R04_F100_L20000
% 95.71/12.47 # Search class: FGHSS-FFSF22-SFFFFFNN
% 95.71/12.47 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 95.71/12.47 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 181s (1) cores
% 95.71/12.47 # Preprocessing time : 0.001 s
% 95.71/12.47 # Presaturation interreduction done
% 95.71/12.47
% 95.71/12.47 # Proof found!
% 95.71/12.47 # SZS status Theorem
% 95.71/12.47 # SZS output start CNFRefutation
% See solution above
% 95.71/12.47 # Parsed axioms : 9
% 95.71/12.47 # Removed by relevancy pruning/SinE : 0
% 95.71/12.47 # Initial clauses : 21
% 95.71/12.47 # Removed in clause preprocessing : 2
% 95.71/12.47 # Initial clauses in saturation : 19
% 95.71/12.47 # Processed clauses : 75059
% 95.71/12.47 # ...of these trivial : 3584
% 95.71/12.47 # ...subsumed : 68839
% 95.71/12.47 # ...remaining for further processing : 2636
% 95.71/12.47 # Other redundant clauses eliminated : 2
% 95.71/12.47 # Clauses deleted for lack of memory : 0
% 95.71/12.47 # Backward-subsumed : 21
% 95.71/12.47 # Backward-rewritten : 1161
% 95.71/12.47 # Generated clauses : 1394835
% 95.71/12.47 # ...of the previous two non-redundant : 944235
% 95.71/12.47 # ...aggressively subsumed : 0
% 95.71/12.47 # Contextual simplify-reflections : 27
% 95.71/12.47 # Paramodulations : 1394293
% 95.71/12.47 # Factorizations : 540
% 95.71/12.47 # NegExts : 0
% 95.71/12.47 # Equation resolutions : 2
% 95.71/12.47 # Disequality decompositions : 0
% 95.71/12.47 # Total rewrite steps : 2029509
% 95.71/12.47 # ...of those cached : 1961749
% 95.71/12.47 # Propositional unsat checks : 0
% 95.71/12.47 # Propositional check models : 0
% 95.71/12.47 # Propositional check unsatisfiable : 0
% 95.71/12.47 # Propositional clauses : 0
% 95.71/12.47 # Propositional clauses after purity: 0
% 95.71/12.47 # Propositional unsat core size : 0
% 95.71/12.47 # Propositional preprocessing time : 0.000
% 95.71/12.47 # Propositional encoding time : 0.000
% 95.71/12.47 # Propositional solver time : 0.000
% 95.71/12.47 # Success case prop preproc time : 0.000
% 95.71/12.47 # Success case prop encoding time : 0.000
% 95.71/12.47 # Success case prop solver time : 0.000
% 95.71/12.47 # Current number of processed clauses : 1435
% 95.71/12.47 # Positive orientable unit clauses : 367
% 95.71/12.47 # Positive unorientable unit clauses: 13
% 95.71/12.47 # Negative unit clauses : 4
% 95.71/12.47 # Non-unit-clauses : 1051
% 95.71/12.47 # Current number of unprocessed clauses: 867209
% 95.71/12.47 # ...number of literals in the above : 1963586
% 95.71/12.47 # Current number of archived formulas : 0
% 95.71/12.47 # Current number of archived clauses : 1199
% 95.71/12.47 # Clause-clause subsumption calls (NU) : 654256
% 95.71/12.47 # Rec. Clause-clause subsumption calls : 358435
% 95.71/12.47 # Non-unit clause-clause subsumptions : 11826
% 95.71/12.47 # Unit Clause-clause subsumption calls : 434672
% 95.71/12.47 # Rewrite failures with RHS unbound : 9802
% 95.71/12.47 # BW rewrite match attempts : 17682
% 95.71/12.47 # BW rewrite match successes : 1201
% 95.71/12.47 # Condensation attempts : 0
% 95.71/12.47 # Condensation successes : 0
% 95.71/12.47 # Termbank termtop insertions : 18141791
% 95.71/12.47 # Search garbage collected termcells : 353
% 95.71/12.47
% 95.71/12.47 # -------------------------------------------------
% 95.71/12.47 # User time : 11.417 s
% 95.71/12.47 # System time : 0.485 s
% 95.71/12.47 # Total time : 11.902 s
% 95.71/12.47 # Maximum resident set size: 1752 pages
% 95.71/12.47
% 95.71/12.47 # -------------------------------------------------
% 95.71/12.47 # User time : 11.418 s
% 95.71/12.47 # System time : 0.487 s
% 95.71/12.47 # Total time : 11.905 s
% 95.71/12.47 # Maximum resident set size: 1692 pages
% 95.71/12.47 % E---3.1 exiting
% 95.71/12.47 % E exiting
%------------------------------------------------------------------------------