%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET634+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 5 05:08:11 PM UTC 2026
% Result : Theorem 61.87s 36.65s
% Output : CNFRefutation 62.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of formulae : 135 ( 68 unt; 0 def)
% Number of atoms : 250 ( 69 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 183 ( 68 ~; 92 |; 15 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 4 ( 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 : 386 ( 55 sgn 46 !; 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(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(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,
! [X30,X31,X32] :
( ( member(X32,X30)
| ~ member(X32,intersection(X30,X31)) )
& ( member(X32,X31)
| ~ member(X32,intersection(X30,X31)) )
& ( ~ member(X32,X30)
| ~ member(X32,X31)
| member(X32,intersection(X30,X31)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_9,plain,
! [X47,X48,X49,X50,X51] :
( ( ~ subset(X47,X48)
| ~ member(X49,X47)
| member(X49,X48) )
& ( member(esk3_2(X50,X51),X50)
| subset(X50,X51) )
& ( ~ member(esk3_2(X50,X51),X51)
| subset(X50,X51) ) ),
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,
! [X33,X34,X35] :
( ( member(X35,X33)
| ~ member(X35,difference(X33,X34)) )
& ( ~ member(X35,X34)
| ~ member(X35,difference(X33,X34)) )
& ( ~ member(X35,X33)
| member(X35,X34)
| member(X35,difference(X33,X34)) ) ),
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,
! [X38,X39] : intersection(X38,X39) = intersection(X39,X38),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_17,plain,
! [X36,X37] :
( ( subset(X36,X37)
| X36 != X37 )
& ( subset(X37,X36)
| X36 != X37 )
& ( ~ subset(X36,X37)
| ~ subset(X37,X36)
| X36 = X37 ) ),
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]) ).
fof(c_0_20,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( ~ member(X42,X40)
| member(X42,X41)
| X40 != X41 )
& ( ~ member(X43,X41)
| member(X43,X40)
| X40 != X41 )
& ( ~ member(esk2_2(X44,X45),X44)
| ~ member(esk2_2(X44,X45),X45)
| X44 = X45 )
& ( member(esk2_2(X44,X45),X44)
| member(esk2_2(X44,X45),X45)
| X44 = X45 ) ),
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)],[equal_member_defn])])])])])]) ).
cnf(c_0_21,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_26,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_27,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( subset(intersection(X1,X2),X3)
| member(esk3_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_29,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( difference(X1,X2) = X1
| ~ subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_32,plain,
( intersection(X1,X2) = X3
| member(esk2_2(intersection(X1,X2),X3),X3)
| member(esk2_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_27]) ).
cnf(c_0_33,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_28]) ).
cnf(c_0_34,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_35,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_36,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_38,plain,
( intersection(X1,X2) = X2
| member(esk2_2(intersection(X1,X2),X2),X2) ),
inference(ef,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_40,plain,
( X1 = difference(X2,X2)
| ~ subset(X1,difference(X2,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_31]) ).
cnf(c_0_41,plain,
subset(intersection(difference(X1,X2),difference(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
intersection(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_43,plain,
( ~ member(X1,difference(X2,X2))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
cnf(c_0_44,plain,
( intersection(X1,X2) = X2
| ~ member(esk2_2(intersection(X1,X2),X2),intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_46,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_39]) ).
cnf(c_0_47,plain,
intersection(difference(X1,X2),difference(X2,X3)) = difference(X4,X4),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_42]),c_0_43]) ).
cnf(c_0_49,plain,
( difference(X1,X2) = X3
| member(esk2_2(difference(X1,X2),X3),X3)
| member(esk2_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_27]) ).
cnf(c_0_50,plain,
( intersection(X1,X2) = X2
| ~ member(esk2_2(intersection(X1,X2),X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_38]) ).
cnf(c_0_51,plain,
( intersection(X1,difference(X2,X3)) = difference(X2,X3)
| member(esk2_2(intersection(X1,difference(X2,X3)),difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_38]) ).
cnf(c_0_52,plain,
( subset(X1,difference(X1,X2))
| member(esk3_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_12]) ).
cnf(c_0_53,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_54,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,difference(X4,X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_47]),c_0_48]) ).
cnf(c_0_55,plain,
( difference(X1,X2) = X1
| member(esk2_2(difference(X1,X2),X1),X1) ),
inference(ef,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
( intersection(difference(X1,X2),X3) = X3
| member(esk2_2(intersection(difference(X1,X2),X3),X3),X2)
| ~ member(esk2_2(intersection(difference(X1,X2),X3),X3),X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_39]) ).
cnf(c_0_57,plain,
intersection(X1,difference(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[c_0_48,c_0_52]) ).
cnf(c_0_59,plain,
subset(difference(difference(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_26,c_0_53]) ).
cnf(c_0_60,plain,
( difference(difference(X1,X2),X3) = difference(X1,X2)
| ~ member(esk2_2(difference(difference(X1,X2),X3),difference(X1,X2)),difference(X4,X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
( difference(X1,X2) = X1
| member(esk2_2(difference(X1,X2),X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_38]),c_0_23]),c_0_57]),c_0_23]),c_0_57]) ).
cnf(c_0_62,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_58]),c_0_25])]) ).
cnf(c_0_63,plain,
difference(difference(difference(X1,X2),X1),X3) = difference(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_30,c_0_59]) ).
cnf(c_0_64,plain,
( subset(intersection(X1,X2),difference(X2,X3))
| member(esk3_2(intersection(X1,X2),difference(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_15]) ).
cnf(c_0_65,plain,
difference(difference(X1,X2),difference(X3,X1)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,plain,
difference(X1,difference(difference(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
subset(intersection(difference(X1,X2),X3),difference(X3,X2)),
inference(spm,[status(thm)],[c_0_33,c_0_64]) ).
cnf(c_0_68,plain,
difference(X1,difference(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,plain,
( intersection(X1,intersection(X2,X3)) = intersection(X2,X3)
| member(esk2_2(intersection(X1,intersection(X2,X3)),intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_38]) ).
cnf(c_0_70,plain,
subset(intersection(X1,X2),difference(X2,difference(X3,X1))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,plain,
intersection(X1,intersection(X1,X2)) = intersection(X1,X2),
inference(spm,[status(thm)],[c_0_50,c_0_69]) ).
cnf(c_0_72,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_45]) ).
cnf(c_0_73,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_26,c_0_39]) ).
cnf(c_0_74,plain,
( subset(difference(X1,intersection(X2,X3)),X4)
| ~ member(esk3_2(difference(X1,intersection(X2,X3)),X4),X3)
| ~ member(esk3_2(difference(X1,intersection(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_45]) ).
cnf(c_0_75,plain,
( subset(difference(intersection(X1,X2),X3),X4)
| member(esk3_2(difference(intersection(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_76,plain,
subset(intersection(X1,X2),difference(intersection(X1,X2),difference(X3,X1))),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,plain,
( subset(difference(X1,X2),intersection(X3,X1))
| ~ member(esk3_2(difference(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_72,c_0_18]) ).
cnf(c_0_78,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk3_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_18]) ).
cnf(c_0_79,plain,
( subset(difference(intersection(X1,X2),intersection(X3,X1)),X4)
| ~ member(esk3_2(difference(intersection(X1,X2),intersection(X3,X1)),X4),X3) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_80,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_81,plain,
difference(intersection(X1,X2),difference(X3,X1)) = intersection(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_76]),c_0_25])]) ).
cnf(c_0_82,plain,
intersection(X1,intersection(X2,X1)) = intersection(X2,X1),
inference(spm,[status(thm)],[c_0_71,c_0_23]) ).
cnf(c_0_83,plain,
( subset(intersection(X1,X2),intersection(X3,X2))
| ~ member(esk3_2(intersection(X1,X2),intersection(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_72,c_0_15]) ).
cnf(c_0_84,plain,
( subset(intersection(intersection(X1,X2),X3),X4)
| member(esk3_2(intersection(intersection(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_85,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_86,plain,
subset(difference(intersection(X1,X2),intersection(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_87,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_88,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_72,c_0_80]) ).
cnf(c_0_89,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_73,c_0_75]) ).
cnf(c_0_90,plain,
difference(difference(X1,X2),intersection(X2,X3)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_81]) ).
cnf(c_0_91,plain,
subset(intersection(X1,X2),difference(intersection(X1,X2),difference(X3,X2))),
inference(spm,[status(thm)],[c_0_70,c_0_82]) ).
cnf(c_0_92,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_93,plain,
difference(X1,difference(X1,X2)) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_85]),c_0_70])]) ).
cnf(c_0_94,plain,
difference(intersection(X1,X2),intersection(X2,X1)) = difference(X3,X3),
inference(spm,[status(thm)],[c_0_40,c_0_86]) ).
cnf(c_0_95,plain,
( subset(difference(intersection(X1,X2),X3),intersection(X4,X1))
| ~ member(esk3_2(difference(intersection(X1,X2),X3),intersection(X4,X1)),X4) ),
inference(spm,[status(thm)],[c_0_72,c_0_75]) ).
cnf(c_0_96,plain,
( subset(difference(intersection(X1,X2),difference(X2,X3)),X4)
| member(esk3_2(difference(intersection(X1,X2),difference(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_73,c_0_80]) ).
cnf(c_0_97,plain,
subset(intersection(X1,difference(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_87,c_0_28]) ).
cnf(c_0_98,plain,
subset(difference(intersection(X1,X2),difference(X1,X3)),intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_99,plain,
difference(X1,intersection(difference(X2,X1),X3)) = X1,
inference(spm,[status(thm)],[c_0_90,c_0_68]) ).
cnf(c_0_100,plain,
difference(intersection(X1,X2),difference(X3,X2)) = intersection(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_91]),c_0_25])]) ).
cnf(c_0_101,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_92,c_0_23]) ).
cnf(c_0_102,plain,
intersection(intersection(X1,X2),intersection(X2,X1)) = intersection(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_62]) ).
cnf(c_0_103,plain,
subset(difference(intersection(X1,X2),difference(X2,X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_104,plain,
( X1 = intersection(X2,difference(X3,X2))
| ~ subset(X1,intersection(X2,difference(X3,X2))) ),
inference(spm,[status(thm)],[c_0_24,c_0_97]) ).
cnf(c_0_105,plain,
subset(difference(intersection(X1,X2),difference(X1,X3)),intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_98,c_0_23]) ).
cnf(c_0_106,plain,
difference(X1,intersection(X2,difference(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_99,c_0_82]) ).
cnf(c_0_107,plain,
difference(difference(X1,X2),intersection(X3,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_100]) ).
cnf(c_0_108,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,intersection(X2,X1))),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_109,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(intersection(X3,X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_94]),c_0_62]) ).
cnf(c_0_110,plain,
difference(intersection(X1,X2),difference(X1,difference(X3,X2))) = intersection(X2,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,plain,
difference(intersection(X1,X2),intersection(X3,difference(X4,X2))) = intersection(X1,X2),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_112,plain,
intersection(X1,intersection(X2,X3)) = intersection(intersection(X3,X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_108]),c_0_109])]) ).
cnf(c_0_113,plain,
intersection(intersection(X1,X2),difference(X2,difference(X3,X1))) = intersection(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_110]),c_0_111]),c_0_112]) ).
cnf(c_0_114,plain,
( subset(intersection(X1,X2),intersection(X3,X1))
| ~ member(esk3_2(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_72,c_0_28]) ).
cnf(c_0_115,plain,
subset(intersection(X1,X2),intersection(X2,difference(X1,difference(X3,X2)))),
inference(spm,[status(thm)],[c_0_92,c_0_113]) ).
cnf(c_0_116,plain,
subset(intersection(X1,difference(X2,X3)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_114,c_0_34]) ).
cnf(c_0_117,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_24,c_0_115]),c_0_116])]) ).
cnf(c_0_118,plain,
subset(difference(intersection(X1,X2),X1),X3),
inference(spm,[status(thm)],[c_0_26,c_0_75]) ).
cnf(c_0_119,plain,
( subset(difference(difference(X1,X2),X3),difference(X1,X4))
| member(esk3_2(difference(difference(X1,X2),X3),difference(X1,X4)),X4) ),
inference(spm,[status(thm)],[c_0_46,c_0_53]) ).
cnf(c_0_120,plain,
intersection(difference(X1,X2),difference(X3,X2)) = intersection(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_117,c_0_68]) ).
cnf(c_0_121,plain,
( X1 = difference(intersection(X2,X3),X2)
| ~ subset(X1,difference(intersection(X2,X3),X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_118]) ).
cnf(c_0_122,plain,
subset(difference(difference(X1,X2),X3),difference(X1,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_119]) ).
cnf(c_0_123,plain,
difference(difference(intersection(X1,X2),X1),X3) = difference(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_30,c_0_118]) ).
fof(c_0_124,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_125,plain,
intersection(X1,difference(X2,X3)) = intersection(X2,difference(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_120]),c_0_120]) ).
cnf(c_0_126,plain,
difference(difference(intersection(X1,X2),X3),X1) = difference(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_127,plain,
difference(X1,difference(intersection(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_123]) ).
fof(c_0_128,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_124])])]) ).
cnf(c_0_129,plain,
intersection(X1,difference(X2,difference(X1,X3))) = intersection(X2,intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_125,c_0_93]) ).
cnf(c_0_130,plain,
intersection(difference(X1,X2),X3) = intersection(X1,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_125]) ).
cnf(c_0_131,plain,
intersection(X1,difference(intersection(X1,X2),X3)) = difference(intersection(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_126]),c_0_127]) ).
cnf(c_0_132,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_128]) ).
cnf(c_0_133,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_129,c_0_65]),c_0_130]),c_0_131]) ).
cnf(c_0_134,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133]),c_0_125])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET634+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:30:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 61.87/36.65 % Version : CSE_E---1.7
% 61.87/36.65 % Problem : theBenchmark.p
% 61.87/36.65 % SZS status Theorem for theBenchmark.p
% 61.87/36.65 % SZS output start CNFRefutation
% See solution above
% 62.17/36.93 % Total time : 26.427s
%------------------------------------------------------------------------------