%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET608+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 02:17:40 PM UTC 2026
% Result : Theorem 114.00s 17.01s
% Output : CNFRefutation 114.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 112 ( 54 unt; 0 def)
% Number of atoms : 213 ( 35 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 161 ( 60 ~; 80 |; 14 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 290 ( 42 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
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(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X2)
| member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_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,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_9,plain,
! [X11,X12,X13] :
( ( member(X13,difference(X11,X12))
| member(X13,X12)
| ~ member(X13,X11) )
& ( ~ member(X13,difference(X11,X12))
| ~ member(X13,X12) )
& ( ~ member(X13,difference(X11,X12))
| member(X13,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(X22,X23)
| ~ member(esk3_2(X22,X23),X23) )
& ( subset(X22,X23)
| member(esk3_2(X22,X23),X22) )
& ( member(X21,X20)
| ~ member(X21,X19)
| ~ subset(X19,X20) ) ),
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_11,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X32,X33] :
( ( X32 = X33
| ~ subset(X33,X32)
| ~ subset(X32,X33) )
& ( X32 != X33
| subset(X33,X32) )
& ( X32 != X33
| subset(X32,X33) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_14,plain,
( ~ member(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( member(esk3_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_17,plain,
! [X6,X7,X8] :
( ( member(X8,union(X6,X7))
| ~ member(X8,X7) )
& ( member(X8,union(X6,X7))
| ~ member(X8,X6) )
& ( member(X8,X7)
| member(X8,X6)
| ~ member(X8,union(X6,X7)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
cnf(c_0_18,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( ~ member(esk3_2(difference(X1,X2),X3),X2)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_21,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( ~ subset(X1,difference(X1,X2))
| difference(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_24,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_26,plain,
! [X14,X15,X16] :
( ( member(X16,intersection(X14,X15))
| ~ member(X16,X15)
| ~ member(X16,X14) )
& ( ~ member(X16,intersection(X14,X15))
| member(X16,X15) )
& ( ~ member(X16,intersection(X14,X15))
| member(X16,X14) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_27,plain,
( ~ member(esk3_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_28,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( ~ member(X1,difference(X3,X3))
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_30,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_14,c_0_25]) ).
cnf(c_0_31,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_32,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
subset(difference(X1,X2),union(X3,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_34,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_28]),c_0_29]) ).
cnf(c_0_35,plain,
( member(esk3_2(X1,difference(X1,X2)),X2)
| subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_12]) ).
cnf(c_0_36,plain,
( member(esk3_2(difference(difference(X1,X2),X3),X4),X1)
| subset(difference(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_37,plain,
( ~ member(esk3_2(X1,union(X2,X3)),X2)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_14,c_0_31]) ).
cnf(c_0_38,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_40,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_14,c_0_32]) ).
cnf(c_0_41,plain,
( ~ member(X1,difference(X3,X4))
| member(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_24,c_0_33]) ).
fof(c_0_42,plain,
! [X17,X18] : intersection(X17,X18) = intersection(X18,X17),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_43,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,plain,
( ~ subset(X1,difference(X2,X2))
| X1 = difference(X2,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_45,plain,
subset(difference(difference(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_20,c_0_36]) ).
cnf(c_0_46,plain,
( ~ member(esk3_2(X1,union(X2,intersection(X3,X4))),X3)
| ~ member(esk3_2(X1,union(X2,intersection(X3,X4))),X4)
| subset(X1,union(X2,intersection(X3,X4))) ),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_47,plain,
( ~ member(esk3_2(X1,union(difference(X2,X3),X4)),X2)
| member(esk3_2(X1,union(difference(X2,X3),X4)),X3)
| subset(X1,union(difference(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
fof(c_0_48,plain,
! [X9,X10] : union(X9,X10) = union(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_49,plain,
( member(esk3_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_12]) ).
cnf(c_0_50,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_51,plain,
( member(esk3_2(union(X1,X2),X3),X1)
| member(esk3_2(union(X1,X2),X3),X2)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_12]) ).
cnf(c_0_52,plain,
( ~ member(esk3_2(difference(X1,X2),intersection(X3,X1)),X3)
| subset(difference(X1,X2),intersection(X3,X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_15]) ).
cnf(c_0_53,plain,
( member(esk3_2(difference(X1,X2),X3),union(X4,X1))
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_12]) ).
cnf(c_0_54,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_55,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_43]),c_0_19])]) ).
cnf(c_0_56,plain,
difference(difference(X1,X2),X1) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_57,plain,
( ~ member(esk3_2(X1,union(X2,intersection(X3,X1))),X3)
| subset(X1,union(X2,intersection(X3,X1))) ),
inference(spm,[status(thm)],[c_0_46,c_0_12]) ).
cnf(c_0_58,plain,
( member(esk3_2(X1,union(difference(X1,X2),X3)),X2)
| subset(X1,union(difference(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_47,c_0_12]) ).
cnf(c_0_59,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_60,plain,
( ~ member(esk3_2(intersection(X1,difference(X2,X3)),X4),X3)
| subset(intersection(X1,difference(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_49]) ).
cnf(c_0_61,plain,
( member(esk3_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_12]) ).
cnf(c_0_62,plain,
( member(esk3_2(union(difference(X1,X1),X2),X3),X2)
| subset(union(difference(X1,X1),X2),X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_51]) ).
cnf(c_0_63,plain,
subset(difference(X1,X2),intersection(X1,union(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_64,plain,
difference(X1,difference(difference(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_14,c_0_49]) ).
cnf(c_0_66,plain,
subset(X1,union(intersection(X2,X1),difference(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_67,plain,
subset(intersection(X1,difference(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,plain,
subset(union(difference(X1,X1),X2),X2),
inference(spm,[status(thm)],[c_0_14,c_0_62]) ).
cnf(c_0_69,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_12]) ).
cnf(c_0_70,plain,
subset(X1,intersection(X1,union(X2,X1))),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_65,c_0_54]) ).
cnf(c_0_72,plain,
subset(X1,union(intersection(X1,X2),difference(X1,X2))),
inference(spm,[status(thm)],[c_0_66,c_0_54]) ).
cnf(c_0_73,plain,
intersection(X1,difference(X2,X1)) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_44,c_0_67]) ).
cnf(c_0_74,plain,
union(difference(X1,X1),X2) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_68]),c_0_69])]) ).
cnf(c_0_75,plain,
( member(esk3_2(union(difference(X1,X2),X3),X4),X1)
| member(esk3_2(union(difference(X1,X2),X3),X4),X3)
| subset(union(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_11,c_0_51]) ).
cnf(c_0_76,plain,
intersection(X1,union(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_70]),c_0_71])]) ).
cnf(c_0_77,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_20,c_0_25]) ).
cnf(c_0_78,plain,
( ~ member(esk3_2(intersection(difference(X1,X2),X3),X4),X2)
| subset(intersection(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_61]) ).
cnf(c_0_79,plain,
( member(esk3_2(intersection(X1,X2),difference(X2,X3)),X3)
| subset(intersection(X1,X2),difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_30,c_0_49]) ).
cnf(c_0_80,plain,
subset(X1,difference(X1,difference(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_81,plain,
( ~ member(esk3_2(X1,intersection(X2,X1)),X2)
| subset(X1,intersection(X2,X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_12]) ).
cnf(c_0_82,plain,
( member(esk3_2(union(X1,difference(X1,X2)),X3),X1)
| subset(union(X1,difference(X1,X2)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(ef,[status(thm)],[c_0_75]),c_0_59]),c_0_59]) ).
cnf(c_0_83,plain,
intersection(X1,union(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_76,c_0_59]) ).
cnf(c_0_84,plain,
( member(esk3_2(difference(X1,difference(X1,X2)),X3),X2)
| subset(difference(X1,difference(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_77,c_0_15]) ).
cnf(c_0_85,plain,
subset(intersection(difference(X1,X2),X3),difference(X3,X2)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_86,plain,
difference(X1,difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_80]),c_0_19])]) ).
cnf(c_0_87,plain,
( member(esk3_2(union(X1,X2),union(X3,X1)),X2)
| subset(union(X1,X2),union(X3,X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_51]) ).
cnf(c_0_88,plain,
( ~ member(esk3_2(X1,union(X2,union(X3,X4))),X4)
| subset(X1,union(X2,union(X3,X4))) ),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_89,plain,
( member(esk3_2(union(X1,X2),union(X1,X3)),X2)
| subset(union(X1,X2),union(X1,X3)) ),
inference(spm,[status(thm)],[c_0_37,c_0_51]) ).
cnf(c_0_90,plain,
subset(union(X1,difference(X1,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_91,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_69,c_0_59]) ).
cnf(c_0_92,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_52,c_0_84]) ).
cnf(c_0_93,plain,
subset(intersection(X1,X2),difference(X2,difference(X3,X1))),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_94,plain,
subset(difference(X1,X2),intersection(X1,difference(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_12]),c_0_54]) ).
cnf(c_0_95,plain,
( member(esk3_2(union(X1,X2),union(difference(X2,X3),X1)),X3)
| subset(union(X1,X2),union(difference(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_47,c_0_87]) ).
cnf(c_0_96,plain,
subset(union(X1,X2),union(X1,union(X3,X2))),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,plain,
union(X1,difference(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_90]),c_0_91])]) ).
cnf(c_0_98,plain,
difference(X1,difference(X1,X2)) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_92]),c_0_93])]) ).
cnf(c_0_99,plain,
intersection(X1,difference(X1,X2)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_94]),c_0_65])]) ).
fof(c_0_100,negated_conjecture,
~ ! [X1,X2] : union(intersection(X1,X2),difference(X1,X2)) = X1,
inference(assume_negation,[status(cth)],[prove_union_intersection_difference]) ).
cnf(c_0_101,plain,
subset(union(X1,X2),union(X1,difference(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_95]),c_0_59]) ).
cnf(c_0_102,plain,
subset(union(X1,difference(X2,X3)),union(X1,X2)),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_103,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_98]),c_0_54]),c_0_99]) ).
cnf(c_0_104,plain,
union(X1,intersection(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
fof(c_0_105,negated_conjecture,
union(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)) != esk1_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_106,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_101]),c_0_102])]) ).
cnf(c_0_107,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_103,c_0_54]) ).
cnf(c_0_108,plain,
union(X1,intersection(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_104,c_0_54]) ).
cnf(c_0_109,negated_conjecture,
union(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_110,plain,
union(intersection(X1,X2),difference(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_59]),c_0_108]) ).
cnf(c_0_111,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET608+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:28:57 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 114.00/17.01 % Version: 3.5.1
% 114.00/17.01 % Preprocessing class: FSMSSMSSSSSNFFN.
% 114.00/17.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 114.00/17.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 114.00/17.01 % Starting new_bool_3 with 300s (1) cores
% 114.00/17.01 % Starting new_bool_1 with 300s (1) cores
% 114.00/17.01 % Starting sh5l with 300s (1) cores
% 114.00/17.01 % sh5l with pid 2089763 completed with status 0
% 114.00/17.01 % Result found by sh5l
% 114.00/17.01 % Preprocessing class: FSMSSMSSSSSNFFN.
% 114.00/17.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 114.00/17.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 114.00/17.01 % Starting new_bool_3 with 300s (1) cores
% 114.00/17.01 % Starting new_bool_1 with 300s (1) cores
% 114.00/17.01 % Starting sh5l with 300s (1) cores
% 114.00/17.01 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 114.00/17.01 % SinE strategy is gf500_gu_R04_F100_L20000
% 114.00/17.01 % Search class: FGHSS-FFSF22-SFFFFFNN
% 114.00/17.01 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 114.00/17.01 % Starting SubtermCWHack with 31s (1) cores
% 114.00/17.01 % SubtermCWHack with pid 2089765 completed with status 0
% 114.00/17.01 % Result found by SubtermCWHack
% 114.00/17.01 % Preprocessing class: FSMSSMSSSSSNFFN.
% 114.00/17.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 114.00/17.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 114.00/17.01 % Starting new_bool_3 with 300s (1) cores
% 114.00/17.01 % Starting new_bool_1 with 300s (1) cores
% 114.00/17.01 % Starting sh5l with 300s (1) cores
% 114.00/17.01 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 114.00/17.01 % SinE strategy is gf500_gu_R04_F100_L20000
% 114.00/17.01 % Search class: FGHSS-FFSF22-SFFFFFNN
% 114.00/17.01 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 114.00/17.01 % Starting SubtermCWHack with 31s (1) cores
% 114.00/17.01 % Preprocessing time : 0.001 s
% 114.00/17.01
% 114.00/17.01 % Proof found!
% 114.00/17.01 % SZS status Theorem
% 114.00/17.01 % SZS output start CNFRefutation
% See solution above
% 114.00/17.01 % Parsed axioms : 10
% 114.00/17.01 % Removed by relevancy pruning/SinE : 0
% 114.00/17.01 % Initial clauses : 23
% 114.00/17.01 % Removed in clause preprocessing : 2
% 114.00/17.01 % Initial clauses in saturation : 21
% 114.00/17.01 % Processed clauses : 37292
% 114.00/17.01 % ...of these trivial : 2553
% 114.00/17.01 % ...subsumed : 31638
% 114.00/17.01 % ...remaining for further processing : 3101
% 114.00/17.01 % Other redundant clauses eliminated : 2
% 114.00/17.01 % Clauses deleted for lack of memory : 0
% 114.00/17.01 % Backward-subsumed : 7
% 114.00/17.01 % Backward-rewritten : 158
% 114.00/17.01 % Generated clauses : 1314327
% 114.00/17.01 % ...of the previous two non-redundant : 1010397
% 114.00/17.01 % ...aggressively subsumed : 0
% 114.00/17.01 % Contextual simplify-reflections : 7
% 114.00/17.01 % Paramodulations : 1311917
% 114.00/17.01 % Factorizations : 2408
% 114.00/17.01 % NegExts : 0
% 114.00/17.01 % Equation resolutions : 2
% 114.00/17.01 % Disequality decompositions : 0
% 114.00/17.01 % Total rewrite steps : 1346045
% 114.00/17.01 % ...of those cached : 1292719
% 114.00/17.01 % Propositional unsat checks : 0
% 114.00/17.01 % Propositional check models : 0
% 114.00/17.01 % Propositional check unsatisfiable : 0
% 114.00/17.01 % Propositional clauses : 0
% 114.00/17.01 % Propositional clauses after purity: 0
% 114.00/17.01 % Propositional unsat core size : 0
% 114.00/17.01 % Propositional preprocessing time : 0.000
% 114.00/17.01 % Propositional encoding time : 0.000
% 114.00/17.01 % Propositional solver time : 0.000
% 114.00/17.01 % Success case prop preproc time : 0.000
% 114.00/17.01 % Success case prop encoding time : 0.000
% 114.00/17.01 % Success case prop solver time : 0.000
% 114.00/17.01 % Current number of processed clauses : 2934
% 114.00/17.01 % Positive orientable unit clauses : 866
% 114.00/17.01 % Positive unorientable unit clauses: 60
% 114.00/17.01 % Negative unit clauses : 64
% 114.00/17.01 % Non-unit-clauses : 1944
% 114.00/17.01 % Current number of unprocessed clauses: 971109
% 114.00/17.01 % ...number of literals in the above : 2658982
% 114.00/17.01 % Current number of archived formulas : 0
% 114.00/17.01 % Current number of archived clauses : 165
% 114.00/17.01 % Clause-clause subsumption calls (NU) : 961863
% 114.00/17.01 % Rec. Clause-clause subsumption calls : 384290
% 114.00/17.01 % Non-unit clause-clause subsumptions : 7811
% 114.00/17.01 % Unit Clause-clause subsumption calls : 328201
% 114.00/17.01 % Rewrite failures with RHS unbound : 4426
% 114.00/17.01 % BW rewrite match attempts : 27776
% 114.00/17.01 % BW rewrite match successes : 537
% 114.00/17.01 % Condensation attempts : 0
% 114.00/17.01 % Condensation successes : 0
% 114.00/17.01 % Termbank termtop insertions : 24256333
% 114.00/17.01 % Search garbage collected termcells : 331
% 114.00/17.01
% 114.00/17.01 % -------------------------------------------------
% 114.00/17.01 % User time : 15.563 s
% 114.00/17.01 % System time : 0.671 s
% 114.00/17.01 % Total time : 16.234 s
% 114.00/17.01 % Maximum resident set size: 3636 pages
% 114.00/17.01
% 114.00/17.01 % -------------------------------------------------
% 114.00/17.01 % User time : 15.565 s
% 114.00/17.01 % System time : 0.676 s
% 114.00/17.01 % Total time : 16.241 s
% 114.00/17.01 % Maximum resident set size: 4608 pages
% 114.00/17.01 % E exiting
%------------------------------------------------------------------------------