TSTP Solution File: SET634+3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET634+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 : Thu Aug 31 14:34:58 EDT 2023
% Result : Theorem 11.68s 11.78s
% Output : CNFRefutation 11.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 122 ( 53 unt; 10 typ; 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 types : 2 ( 0 usr)
% Number of type conns : 14 ( 7 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 314 ( 46 sgn; 42 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
member: ( $i * $i ) > $o ).
tff(decl_23,type,
intersection: ( $i * $i ) > $i ).
tff(decl_24,type,
difference: ( $i * $i ) > $i ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk4_0: $i ).
tff(decl_30,type,
esk5_0: $i ).
tff(decl_31,type,
esk6_0: $i ).
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,
! [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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_9,plain,
! [X24,X25,X26,X27,X28] :
( ( ~ subset(X24,X25)
| ~ member(X26,X24)
| member(X26,X25) )
& ( member(esk3_2(X27,X28),X27)
| subset(X27,X28) )
& ( ~ member(esk3_2(X27,X28),X28)
| subset(X27,X28) ) ),
inference(distribute,[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,
! [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(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(esk3_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(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( subset(intersection(X1,X2),X3)
| member(esk3_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_16,plain,
! [X15,X16] : intersection(X15,X16) = intersection(X16,X15),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_18,plain,
( subset(difference(X1,X2),X3)
| member(esk3_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(esk3_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(esk3_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(esk3_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(esk3_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(esk3_2(X1,difference(X2,X3)),X3)
| ~ member(esk3_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(esk3_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(esk3_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(esk3_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(esk3_2(X1,intersection(X2,X3)),X3)
| ~ member(esk3_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(esk3_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(esk3_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk3_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(esk3_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(esk3_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(esk3_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(esk3_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(esk3_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(esk3_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(esk3_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(esk3_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(esk3_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,
! [X4,X5] :
( ( ~ member(esk1_2(X4,X5),X4)
| ~ member(esk1_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk1_2(X4,X5),X4)
| member(esk1_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[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(esk3_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(esk3_2(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_26]) ).
cnf(c_0_84,plain,
( member(esk1_2(X1,X2),X1)
| member(esk1_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(esk1_2(X1,X2),X1)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,plain,
( X1 = intersection(X2,X3)
| member(esk1_2(X1,intersection(X2,X3)),X1)
| member(esk1_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(esk1_2(X1,intersection(X2,X3)),X1)
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_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(esk1_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(esk1_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(esk1_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(esk4_0,difference(esk5_0,esk6_0)) != difference(intersection(esk4_0,esk5_0),esk6_0),
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(esk4_0,difference(esk5_0,esk6_0)) != difference(intersection(esk4_0,esk5_0),esk6_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
% 0.03/0.11 % Problem : SET634+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Aug 26 14:50:56 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.61/0.64 start to proof: theBenchmark
% 11.68/11.78 % Version : CSE_E---1.5
% 11.68/11.78 % Problem : theBenchmark.p
% 11.68/11.78 % Proof found
% 11.68/11.78 % SZS status Theorem for theBenchmark.p
% 11.68/11.78 % SZS output start Proof
% See solution above
% 11.68/11.78 % Total time : 11.126000 s
% 11.68/11.78 % SZS output end Proof
% 11.68/11.78 % Total time : 11.129000 s
%------------------------------------------------------------------------------