%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET634+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:14:50 PM UTC 2026
% Result : Theorem 149.44s 22.39s
% Output : CNFRefutation 149.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 148 ( 79 unt; 0 def)
% Number of atoms : 265 ( 76 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 188 ( 71 ~; 94 |; 15 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 433 ( 69 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_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(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,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_8,plain,
! [X10,X11,X12] :
( ( member(X12,difference(X10,X11))
| member(X12,X11)
| ~ member(X12,X10) )
& ( ~ member(X12,difference(X10,X11))
| ~ member(X12,X11) )
& ( ~ member(X12,difference(X10,X11))
| member(X12,X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_9,plain,
! [X24,X25,X26,X27,X28] :
( ( subset(X27,X28)
| ~ member(esk3_2(X27,X28),X28) )
& ( subset(X27,X28)
| member(esk3_2(X27,X28),X27) )
& ( member(X26,X25)
| ~ member(X26,X24)
| ~ subset(X24,X25) ) ),
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_10,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X13,X14] :
( ( X13 = X14
| ~ subset(X14,X13)
| ~ subset(X13,X14) )
& ( X13 != X14
| subset(X14,X13) )
& ( X13 != X14
| subset(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_13,plain,
( ~ member(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( member(esk3_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( ~ member(esk3_2(difference(X1,X2),X3),X2)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
fof(c_0_19,plain,
! [X7,X8,X9] :
( ( member(X9,intersection(X7,X8))
| ~ member(X9,X8)
| ~ member(X9,X7) )
& ( ~ member(X9,intersection(X7,X8))
| member(X9,X8) )
& ( ~ member(X9,intersection(X7,X8))
| member(X9,X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_20,plain,
( ~ subset(X1,difference(X1,X2))
| difference(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
fof(c_0_22,plain,
! [X17,X18,X19,X20,X21,X22] :
( ( X21 = X22
| member(esk2_2(X21,X22),X22)
| member(esk2_2(X21,X22),X21) )
& ( X21 = X22
| ~ member(esk2_2(X21,X22),X22)
| ~ member(esk2_2(X21,X22),X21) )
& ( X17 != X18
| member(X20,X17)
| ~ member(X20,X18) )
& ( X17 != X18
| member(X19,X18)
| ~ member(X19,X17) ) ),
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)],[equal_member_defn])])])])])])]) ).
cnf(c_0_23,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X15,X16] : intersection(X15,X16) = intersection(X16,X15),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_25,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( X1 = X2
| member(esk2_2(X1,X2),X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( member(esk3_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_11]) ).
cnf(c_0_30,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( ~ member(esk3_2(X1,intersection(X2,X3)),X2)
| ~ member(esk3_2(X1,intersection(X2,X3)),X3)
| subset(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_25]) ).
cnf(c_0_32,plain,
( ~ member(esk3_2(difference(X1,difference(X2,X3)),X4),X2)
| member(esk3_2(difference(X1,difference(X2,X3)),X4),X3)
| subset(difference(X1,difference(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_33,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,plain,
( ~ member(X1,X3)
| ~ member(X1,difference(X2,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_35,plain,
( ~ member(esk3_2(X1,difference(X2,X3)),X2)
| member(esk3_2(X1,difference(X2,X3)),X3)
| subset(X1,difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_36,plain,
( member(esk2_2(intersection(X1,X2),X3),X2)
| member(esk2_2(intersection(X1,X2),X3),X3)
| intersection(X1,X2) = X3 ),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_37,plain,
( ~ member(esk3_2(intersection(X1,difference(X2,X3)),X4),X3)
| subset(intersection(X1,difference(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_29]) ).
cnf(c_0_38,plain,
( member(esk3_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,plain,
( ~ member(esk3_2(difference(X1,X2),intersection(X3,X1)),X3)
| subset(difference(X1,X2),intersection(X3,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_40,plain,
( member(esk3_2(difference(X1,difference(X1,X2)),X3),X2)
| subset(difference(X1,difference(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_14]) ).
cnf(c_0_41,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_21]),c_0_34]) ).
cnf(c_0_42,plain,
( member(esk3_2(X1,difference(X1,X2)),X2)
| subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_35,c_0_11]) ).
cnf(c_0_43,plain,
( ~ member(esk2_2(X1,X2),X2)
| ~ member(esk2_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_44,plain,
( member(esk2_2(intersection(X1,X2),X2),X2)
| intersection(X1,X2) = X2 ),
inference(ef,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( ~ member(esk3_2(difference(X1,intersection(X2,X3)),X4),X2)
| ~ member(esk3_2(difference(X1,intersection(X2,X3)),X4),X3)
| subset(difference(X1,intersection(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_46,plain,
( member(esk3_2(intersection(X1,intersection(X2,X3)),X4),X3)
| subset(intersection(X1,intersection(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_47,plain,
subset(intersection(X1,difference(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,plain,
( ~ member(esk2_2(intersection(X1,X2),X2),intersection(X1,X2))
| intersection(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,plain,
( ~ member(esk3_2(difference(X1,intersection(X2,X1)),X3),X2)
| subset(difference(X1,intersection(X2,X1)),X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_14]) ).
cnf(c_0_52,plain,
( member(esk3_2(difference(X1,X2),difference(X1,X3)),X3)
| subset(difference(X1,X2),difference(X1,X3)) ),
inference(spm,[status(thm)],[c_0_35,c_0_14]) ).
cnf(c_0_53,plain,
( ~ member(esk3_2(intersection(X1,intersection(X2,X3)),intersection(X4,X3)),X4)
| subset(intersection(X1,intersection(X2,X3)),intersection(X4,X3)) ),
inference(spm,[status(thm)],[c_0_31,c_0_46]) ).
cnf(c_0_54,plain,
( ~ member(esk3_2(intersection(difference(X1,X2),X3),X4),X2)
| subset(intersection(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_38]) ).
cnf(c_0_55,plain,
subset(intersection(X1,intersection(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_13,c_0_46]) ).
cnf(c_0_56,plain,
( ~ subset(X1,intersection(X2,difference(X3,X2)))
| X1 = intersection(X2,difference(X3,X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_47]) ).
cnf(c_0_57,plain,
subset(difference(X1,difference(X1,X2)),intersection(X1,X2)),
inference(spm,[status(thm)],[c_0_48,c_0_30]) ).
cnf(c_0_58,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_49]),c_0_17])]) ).
cnf(c_0_59,plain,
difference(intersection(X1,difference(X2,X1)),X3) = intersection(X1,difference(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_47]) ).
cnf(c_0_60,plain,
( ~ member(esk2_2(intersection(X1,X2),X2),X1)
| intersection(X1,X2) = X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_25]),c_0_44]) ).
cnf(c_0_61,plain,
( member(esk2_2(intersection(X1,difference(X2,X3)),difference(X2,X3)),X2)
| intersection(X1,difference(X2,X3)) = difference(X2,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_44]) ).
cnf(c_0_62,plain,
subset(difference(X1,intersection(X2,X1)),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_63,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_53,c_0_38]) ).
cnf(c_0_64,plain,
( ~ subset(X1,difference(X2,X2))
| X1 = difference(X2,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_65,plain,
subset(intersection(difference(X1,X2),intersection(X3,X2)),X4),
inference(spm,[status(thm)],[c_0_54,c_0_46]) ).
cnf(c_0_66,plain,
( ~ member(X1,intersection(X3,intersection(X4,X2)))
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_55]) ).
cnf(c_0_67,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_68,plain,
difference(X1,difference(X1,difference(X2,X1))) = intersection(X1,difference(X2,X1)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_69,plain,
difference(X1,intersection(X2,difference(X3,X2))) = X1,
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_70,plain,
intersection(X1,difference(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_71,plain,
subset(difference(X1,intersection(X1,X2)),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_62,c_0_30]) ).
cnf(c_0_72,plain,
intersection(X1,intersection(X2,difference(X3,X1))) = intersection(X1,difference(X3,X1)),
inference(spm,[status(thm)],[c_0_56,c_0_63]) ).
cnf(c_0_73,plain,
( member(esk3_2(intersection(difference(X1,X2),X3),X4),X1)
| subset(intersection(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_10,c_0_38]) ).
cnf(c_0_74,plain,
intersection(difference(X1,X2),intersection(X3,X2)) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_75,plain,
( member(esk2_2(intersection(X1,intersection(X2,intersection(X3,X4))),intersection(X2,intersection(X3,X4))),X4)
| intersection(X1,intersection(X2,intersection(X3,X4))) = intersection(X2,intersection(X3,X4)) ),
inference(spm,[status(thm)],[c_0_66,c_0_44]) ).
cnf(c_0_76,plain,
( member(esk3_2(difference(intersection(X1,X2),X3),X4),X1)
| subset(difference(intersection(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_67,c_0_14]) ).
cnf(c_0_77,plain,
( member(esk3_2(difference(intersection(X1,X2),X3),X4),X2)
| subset(difference(intersection(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_78,plain,
subset(X1,difference(X1,difference(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_68]),c_0_69]),c_0_70]) ).
cnf(c_0_79,plain,
subset(X1,difference(X1,intersection(X2,difference(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_69]) ).
cnf(c_0_80,plain,
subset(intersection(difference(X1,X2),difference(X3,X1)),X4),
inference(spm,[status(thm)],[c_0_37,c_0_73]) ).
cnf(c_0_81,plain,
( ~ member(X1,difference(X4,X3))
| ~ member(X1,intersection(X2,X3)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_74]),c_0_41]) ).
cnf(c_0_82,plain,
( ~ member(esk2_2(intersection(difference(X1,X2),X3),X3),X1)
| member(esk2_2(intersection(difference(X1,X2),X3),X3),X2)
| intersection(difference(X1,X2),X3) = X3 ),
inference(spm,[status(thm)],[c_0_60,c_0_26]) ).
cnf(c_0_83,plain,
( member(esk2_2(intersection(X1,intersection(X2,X3)),intersection(X2,X3)),X2)
| intersection(X1,intersection(X2,X3)) = intersection(X2,X3) ),
inference(spm,[status(thm)],[c_0_67,c_0_44]) ).
cnf(c_0_84,plain,
intersection(X1,intersection(X2,intersection(X3,X1))) = intersection(X2,intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_60,c_0_75]) ).
cnf(c_0_85,plain,
( ~ member(esk3_2(difference(intersection(X1,X2),intersection(X3,X1)),X4),X3)
| subset(difference(intersection(X1,X2),intersection(X3,X1)),X4) ),
inference(spm,[status(thm)],[c_0_45,c_0_76]) ).
cnf(c_0_86,plain,
( member(esk3_2(difference(intersection(X1,difference(X2,X3)),X4),X5),X2)
| subset(difference(intersection(X1,difference(X2,X3)),X4),X5) ),
inference(spm,[status(thm)],[c_0_10,c_0_77]) ).
cnf(c_0_87,plain,
difference(X1,difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_78]),c_0_17])]) ).
cnf(c_0_88,plain,
difference(X1,intersection(X2,difference(X3,X1))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_79]),c_0_17])]) ).
cnf(c_0_89,plain,
intersection(difference(X1,X2),difference(X3,X1)) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_64,c_0_80]) ).
cnf(c_0_90,plain,
( ~ member(esk2_2(intersection(X1,intersection(X2,X3)),intersection(X2,X3)),difference(X4,X3))
| intersection(X1,intersection(X2,X3)) = intersection(X2,X3) ),
inference(spm,[status(thm)],[c_0_81,c_0_44]) ).
cnf(c_0_91,plain,
( member(esk2_2(intersection(difference(X1,X2),intersection(X1,X3)),intersection(X1,X3)),X2)
| intersection(difference(X1,X2),intersection(X1,X3)) = intersection(X1,X3) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_92,plain,
intersection(X1,intersection(X2,intersection(X1,X3))) = intersection(X2,intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_84,c_0_30]) ).
cnf(c_0_93,plain,
subset(difference(intersection(X1,difference(X2,X3)),intersection(X2,X1)),X4),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_94,plain,
difference(intersection(X1,difference(X2,X3)),X3) = intersection(X1,difference(X2,X3)),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_95,plain,
( ~ member(X1,difference(X3,X4))
| ~ member(X1,difference(X2,X3)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_89]),c_0_41]) ).
cnf(c_0_96,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_63,c_0_30]) ).
cnf(c_0_97,plain,
intersection(intersection(X1,X2),difference(X1,difference(X3,X2))) = intersection(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_30]) ).
cnf(c_0_98,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X1,X2)),
inference(spm,[status(thm)],[c_0_63,c_0_30]) ).
cnf(c_0_99,plain,
intersection(X1,intersection(X2,difference(X1,X3))) = intersection(X2,difference(X1,X3)),
inference(spm,[status(thm)],[c_0_92,c_0_70]) ).
cnf(c_0_100,plain,
subset(intersection(X1,difference(X2,intersection(X2,X1))),X3),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_101,plain,
( ~ member(esk3_2(difference(X1,X2),X3),difference(X2,X4))
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_95,c_0_11]) ).
cnf(c_0_102,plain,
subset(intersection(X1,X2),intersection(X2,difference(X1,difference(X3,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_30]) ).
cnf(c_0_103,plain,
subset(intersection(X1,difference(X2,X3)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_104,plain,
intersection(X1,difference(X2,intersection(X2,X1))) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_64,c_0_100]) ).
cnf(c_0_105,plain,
subset(difference(X1,X2),difference(difference(X1,X2),difference(X2,X3))),
inference(spm,[status(thm)],[c_0_101,c_0_42]) ).
cnf(c_0_106,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_16,c_0_102]),c_0_103])]) ).
cnf(c_0_107,plain,
subset(X1,difference(X1,difference(X2,intersection(X2,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_104]),c_0_58]) ).
cnf(c_0_108,plain,
intersection(X1,intersection(difference(X2,X1),X3)) = intersection(X1,difference(X2,X1)),
inference(spm,[status(thm)],[c_0_56,c_0_98]) ).
cnf(c_0_109,plain,
( member(esk3_2(intersection(X1,X2),difference(X2,X3)),X3)
| subset(intersection(X1,X2),difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_35,c_0_29]) ).
cnf(c_0_110,plain,
( ~ member(esk2_2(intersection(X1,difference(X2,X3)),difference(X2,X3)),difference(X3,X4))
| intersection(X1,difference(X2,X3)) = difference(X2,X3) ),
inference(spm,[status(thm)],[c_0_95,c_0_44]) ).
cnf(c_0_111,plain,
( member(esk2_2(intersection(difference(X1,X2),difference(X1,X3)),difference(X1,X3)),X2)
| intersection(difference(X1,X2),difference(X1,X3)) = difference(X1,X3) ),
inference(spm,[status(thm)],[c_0_82,c_0_61]) ).
cnf(c_0_112,plain,
( member(esk3_2(difference(difference(X1,X2),X3),X4),X1)
| subset(difference(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_113,plain,
difference(difference(X1,X2),difference(X2,X3)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_105]),c_0_17])]) ).
cnf(c_0_114,plain,
intersection(difference(X1,X2),difference(X3,X2)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_106,c_0_87]) ).
cnf(c_0_115,plain,
difference(X1,difference(X2,intersection(X2,X1))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_107]),c_0_17])]) ).
cnf(c_0_116,plain,
subset(X1,difference(X1,intersection(difference(X2,X1),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_108]),c_0_69]) ).
cnf(c_0_117,plain,
subset(intersection(difference(X1,X2),X3),difference(X3,X2)),
inference(spm,[status(thm)],[c_0_54,c_0_109]) ).
cnf(c_0_118,plain,
intersection(difference(X1,X2),difference(X1,difference(X2,X3))) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_30]) ).
cnf(c_0_119,plain,
( member(esk3_2(difference(difference(X1,X2),X3),difference(X1,X4)),X4)
| subset(difference(difference(X1,X2),X3),difference(X1,X4)) ),
inference(spm,[status(thm)],[c_0_35,c_0_112]) ).
cnf(c_0_120,plain,
( member(esk3_2(difference(difference(X1,X2),difference(X1,X3)),X4),X3)
| subset(difference(difference(X1,X2),difference(X1,X3)),X4) ),
inference(spm,[status(thm)],[c_0_32,c_0_112]) ).
cnf(c_0_121,plain,
difference(X1,difference(difference(X2,X1),X3)) = X1,
inference(spm,[status(thm)],[c_0_113,c_0_87]) ).
cnf(c_0_122,plain,
intersection(X1,difference(X2,X3)) = intersection(X2,difference(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_114]),c_0_114]) ).
cnf(c_0_123,plain,
difference(X1,difference(X2,intersection(X1,X2))) = X1,
inference(spm,[status(thm)],[c_0_115,c_0_30]) ).
cnf(c_0_124,plain,
difference(X1,intersection(difference(X2,X1),X3)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_116]),c_0_17])]) ).
cnf(c_0_125,plain,
subset(difference(X1,X2),difference(difference(X1,difference(X2,X3)),X2)),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_126,plain,
subset(difference(difference(X1,X2),X3),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_18,c_0_119]) ).
cnf(c_0_127,plain,
subset(difference(difference(X1,X2),difference(X1,X3)),intersection(X3,difference(X1,X2))),
inference(spm,[status(thm)],[c_0_39,c_0_120]) ).
cnf(c_0_128,plain,
subset(intersection(X1,X2),difference(X2,difference(X3,X1))),
inference(spm,[status(thm)],[c_0_117,c_0_87]) ).
cnf(c_0_129,plain,
difference(difference(difference(X1,X2),X3),X2) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_87,c_0_121]) ).
cnf(c_0_130,plain,
intersection(X1,intersection(difference(X1,X2),X3)) = intersection(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_99,c_0_30]) ).
cnf(c_0_131,plain,
intersection(difference(X1,X2),X3) = intersection(X1,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_122]) ).
cnf(c_0_132,plain,
difference(difference(X1,intersection(X2,X1)),X2) = difference(X1,intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_87,c_0_123]) ).
cnf(c_0_133,plain,
difference(difference(X1,X2),intersection(X2,X3)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_124,c_0_87]) ).
fof(c_0_134,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_135,plain,
difference(difference(X1,difference(X2,X3)),X2) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_125]),c_0_126])]) ).
cnf(c_0_136,plain,
difference(difference(X1,X2),difference(X1,X3)) = intersection(X3,difference(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_127]),c_0_128])]) ).
cnf(c_0_137,plain,
intersection(X1,difference(X2,difference(difference(X3,X1),X4))) = intersection(X2,X1),
inference(spm,[status(thm)],[c_0_106,c_0_129]) ).
cnf(c_0_138,plain,
intersection(X1,difference(difference(X1,X2),X3)) = difference(difference(X1,X2),X3),
inference(spm,[status(thm)],[c_0_130,c_0_70]) ).
cnf(c_0_139,plain,
intersection(X1,difference(X2,intersection(X3,X1))) = intersection(X1,difference(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_131]),c_0_131]),c_0_133]) ).
cnf(c_0_140,plain,
intersection(X1,intersection(intersection(X2,X1),X3)) = intersection(intersection(X2,X1),X3),
inference(spm,[status(thm)],[c_0_84,c_0_30]) ).
fof(c_0_141,negated_conjecture,
intersection(esk4_0,difference(esk5_0,esk6_0)) != difference(intersection(esk4_0,esk5_0),esk6_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_134])])])]) ).
cnf(c_0_142,plain,
difference(X1,difference(X1,X2)) = intersection(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]) ).
cnf(c_0_143,plain,
difference(difference(X1,X2),intersection(X3,X1)) = difference(difference(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_138]) ).
cnf(c_0_144,plain,
intersection(X1,difference(intersection(X2,X1),X3)) = difference(intersection(X2,X1),X3),
inference(spm,[status(thm)],[c_0_140,c_0_70]) ).
cnf(c_0_145,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_141]) ).
cnf(c_0_146,plain,
difference(intersection(X1,X2),X3) = intersection(X2,difference(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_142]),c_0_131]),c_0_131]),c_0_144]) ).
cnf(c_0_147,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_146]),c_0_122])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET634+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:30:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 149.44/22.39 % Version: 3.5.1
% 149.44/22.39 % Preprocessing class: FSMSSMSSSSSNFFN.
% 149.44/22.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 149.44/22.39 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 149.44/22.39 % Starting new_bool_3 with 300s (1) cores
% 149.44/22.39 % Starting new_bool_1 with 300s (1) cores
% 149.44/22.39 % Starting sh5l with 300s (1) cores
% 149.44/22.39 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 942452 completed with status 0
% 149.44/22.39 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 149.44/22.39 % Preprocessing class: FSMSSMSSSSSNFFN.
% 149.44/22.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 149.44/22.39 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 149.44/22.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 149.44/22.39 % No SInE strategy applied
% 149.44/22.39 % Search class: FGHSS-FFSF22-SFFFFFNN
% 149.44/22.39 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 149.44/22.39 % Starting SubtermCWHack with 136s (1) cores
% 149.44/22.39 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 149.44/22.39 % Starting G----_0010_evo with 136s (1) cores
% 149.44/22.39 % Starting new_bool_3 with 136s (1) cores
% 149.44/22.39 % Starting new_bool_1 with 136s (1) cores
% 149.44/22.39 % G----_0010_evo with pid 942460 completed with status 0
% 149.44/22.39 % Result found by G----_0010_evo
% 149.44/22.39 % Preprocessing class: FSMSSMSSSSSNFFN.
% 149.44/22.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 149.44/22.39 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 149.44/22.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 149.44/22.39 % No SInE strategy applied
% 149.44/22.39 % Search class: FGHSS-FFSF22-SFFFFFNN
% 149.44/22.39 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 149.44/22.39 % Starting SubtermCWHack with 136s (1) cores
% 149.44/22.39 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 149.44/22.39 % Starting G----_0010_evo with 136s (1) cores
% 149.44/22.39 % Preprocessing time : 0.001 s
% 149.44/22.39
% 149.44/22.39 % Proof found!
% 149.44/22.39 % SZS status Theorem
% 149.44/22.39 % SZS output start CNFRefutation
% See solution above
% 149.44/22.39 % Parsed axioms : 9
% 149.44/22.39 % Removed by relevancy pruning/SinE : 0
% 149.44/22.39 % Initial clauses : 21
% 149.44/22.39 % Removed in clause preprocessing : 2
% 149.44/22.39 % Initial clauses in saturation : 19
% 149.44/22.39 % Processed clauses : 70544
% 149.44/22.39 % ...of these trivial : 7172
% 149.44/22.39 % ...subsumed : 60197
% 149.44/22.39 % ...remaining for further processing : 3175
% 149.44/22.39 % Other redundant clauses eliminated : 2
% 149.44/22.39 % Clauses deleted for lack of memory : 0
% 149.44/22.39 % Backward-subsumed : 22
% 149.44/22.39 % Backward-rewritten : 1361
% 149.44/22.39 % Generated clauses : 1804049
% 149.44/22.39 % ...of the previous two non-redundant : 1062914
% 149.44/22.39 % ...aggressively subsumed : 0
% 149.44/22.39 % Contextual simplify-reflections : 27
% 149.44/22.39 % Paramodulations : 1803501
% 149.44/22.39 % Factorizations : 546
% 149.44/22.39 % NegExts : 0
% 149.44/22.39 % Equation resolutions : 2
% 149.44/22.39 % Disequality decompositions : 0
% 149.44/22.39 % Total rewrite steps : 2439597
% 149.44/22.39 % ...of those cached : 2280039
% 149.44/22.39 % Propositional unsat checks : 0
% 149.44/22.39 % Propositional check models : 0
% 149.44/22.39 % Propositional check unsatisfiable : 0
% 149.44/22.39 % Propositional clauses : 0
% 149.44/22.39 % Propositional clauses after purity: 0
% 149.44/22.39 % Propositional unsat core size : 0
% 149.44/22.39 % Propositional preprocessing time : 0.000
% 149.44/22.39 % Propositional encoding time : 0.000
% 149.44/22.39 % Propositional solver time : 0.000
% 149.44/22.39 % Success case prop preproc time : 0.000
% 149.44/22.39 % Success case prop encoding time : 0.000
% 149.44/22.39 % Success case prop solver time : 0.000
% 149.44/22.39 % Current number of processed clauses : 1790
% 149.44/22.39 % Positive orientable unit clauses : 837
% 149.44/22.39 % Positive unorientable unit clauses: 9
% 149.44/22.39 % Negative unit clauses : 3
% 149.44/22.39 % Non-unit-clauses : 941
% 149.44/22.39 % Current number of unprocessed clauses: 979071
% 149.44/22.39 % ...number of literals in the above : 2171966
% 149.44/22.39 % Current number of archived formulas : 0
% 149.44/22.39 % Current number of archived clauses : 1383
% 149.44/22.39 % Clause-clause subsumption calls (NU) : 628278
% 149.44/22.39 % Rec. Clause-clause subsumption calls : 335680
% 149.44/22.39 % Non-unit clause-clause subsumptions : 11817
% 149.44/22.39 % Unit Clause-clause subsumption calls : 807529
% 149.44/22.39 % Rewrite failures with RHS unbound : 7109
% 149.44/22.39 % BW rewrite match attempts : 66759
% 149.44/22.39 % BW rewrite match successes : 1455
% 149.44/22.40 % Condensation attempts : 0
% 149.44/22.40 % Condensation successes : 0
% 149.44/22.40 % Termbank termtop insertions : 21682345
% 149.44/22.40 % Search garbage collected termcells : 351
% 149.44/22.40
% 149.44/22.40 % -------------------------------------------------
% 149.44/22.40 % User time : 19.483 s
% 149.44/22.40 % System time : 0.766 s
% 149.44/22.40 % Total time : 20.249 s
% 149.44/22.40 % Maximum resident set size: 3584 pages
% 149.44/22.40
% 149.44/22.40 % -------------------------------------------------
% 149.44/22.40 % User time : 101.517 s
% 149.44/22.40 % System time : 4.456 s
% 149.44/22.40 % Total time : 105.974 s
% 149.44/22.40 % Maximum resident set size: 4608 pages
% 149.44/22.40 % E exiting
%------------------------------------------------------------------------------