%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET606+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : Tue May 5 05:08:06 PM UTC 2026
% Result : Theorem 22.92s 14.29s
% Output : CNFRefutation 23.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 82 ( 31 unt; 0 def)
% Number of atoms : 180 ( 44 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 156 ( 58 ~; 75 |; 15 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 214 ( 28 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',intersection_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(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(prove_difference_into_intersection,conjecture,
! [X1,X2] : difference(X1,intersection(X1,X2)) = difference(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_into_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,
! [X29,X30,X31] :
( ( member(X31,X29)
| ~ member(X31,intersection(X29,X30)) )
& ( member(X31,X30)
| ~ member(X31,intersection(X29,X30)) )
& ( ~ member(X31,X29)
| ~ member(X31,X30)
| member(X31,intersection(X29,X30)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_9,plain,
! [X46,X47,X48,X49,X50] :
( ( ~ subset(X46,X47)
| ~ member(X48,X46)
| member(X48,X47) )
& ( member(esk3_2(X49,X50),X49)
| subset(X49,X50) )
& ( ~ member(esk3_2(X49,X50),X50)
| subset(X49,X50) ) ),
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,
! [X32,X33,X34] :
( ( member(X34,X32)
| ~ member(X34,difference(X32,X33)) )
& ( ~ member(X34,X33)
| ~ member(X34,difference(X32,X33)) )
& ( ~ member(X34,X32)
| member(X34,X33)
| member(X34,difference(X32,X33)) ) ),
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,
! [X37,X38] : intersection(X37,X38) = intersection(X38,X37),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_17,plain,
! [X35,X36] :
( ( subset(X35,X36)
| X35 != X36 )
& ( subset(X36,X35)
| X35 != X36 )
& ( ~ subset(X35,X36)
| ~ subset(X36,X35)
| X35 = X36 ) ),
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,
! [X39,X40,X41,X42,X43,X44] :
( ( ~ member(X41,X39)
| member(X41,X40)
| X39 != X40 )
& ( ~ member(X42,X40)
| member(X42,X39)
| X39 != X40 )
& ( ~ member(esk2_2(X43,X44),X43)
| ~ member(esk2_2(X43,X44),X44)
| X43 = X44 )
& ( member(esk2_2(X43,X44),X43)
| member(esk2_2(X43,X44),X44)
| X43 = X44 ) ),
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(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_65,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_66,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_67,plain,
difference(difference(X1,X2),difference(X3,X1)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,plain,
difference(X1,difference(difference(X2,X3),X2)) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,plain,
( subset(difference(X1,X2),intersection(X3,X1))
| ~ member(esk3_2(difference(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_64,c_0_18]) ).
cnf(c_0_70,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk3_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_18]) ).
cnf(c_0_71,plain,
subset(intersection(difference(X1,X2),X3),difference(X3,X2)),
inference(spm,[status(thm)],[c_0_33,c_0_66]) ).
cnf(c_0_72,plain,
difference(X1,difference(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,plain,
subset(intersection(X1,X2),difference(X2,difference(X3,X1))),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
fof(c_0_75,negated_conjecture,
~ ! [X1,X2] : difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(assume_negation,[status(cth)],[prove_difference_into_intersection]) ).
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_24,c_0_73]),c_0_74])]) ).
fof(c_0_77,negated_conjecture,
difference(esk4_0,intersection(esk4_0,esk5_0)) != difference(esk4_0,esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])]) ).
cnf(c_0_78,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_76]),c_0_23]),c_0_57]) ).
cnf(c_0_79,negated_conjecture,
difference(esk4_0,intersection(esk4_0,esk5_0)) != difference(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_80,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_23]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET606+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n023.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:30:23 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 22.92/14.29 % Version : CSE_E---1.7
% 22.92/14.29 % Problem : theBenchmark.p
% 22.92/14.29 % SZS status Theorem for theBenchmark.p
% 22.92/14.29 % SZS output start CNFRefutation
% See solution above
% 23.02/14.40 % Total time : 10.379s
%------------------------------------------------------------------------------