%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET937+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 02:15:49 PM UTC 2026
% Result : Theorem 7.80s 1.49s
% Output : CNFRefutation 7.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 95 ( 39 unt; 0 def)
% Number of atoms : 242 ( 68 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 246 ( 99 ~; 108 |; 23 &)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 209 ( 23 sgn 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(t79_xboole_1,axiom,
! [X1,X2] : disjoint(set_difference(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t28_xboole_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(t36_xboole_1,axiom,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X2,X3)
& subset(X1,X2) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(t84_zfmisc_1,conjecture,
! [X1,X2] : subset(powerset(set_difference(X1,X2)),set_union2(singleton(empty_set),set_difference(powerset(X1),powerset(X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t63_xboole_1,axiom,
! [X1,X2,X3] :
( ( disjoint(X2,X3)
& subset(X1,X2) )
=> disjoint(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(c_0_14,plain,
! [X49,X50] :
( ( disjoint(X49,X50)
| set_intersection2(X49,X50) != empty_set )
& ( set_intersection2(X49,X50) = empty_set
| ~ disjoint(X49,X50) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])]) ).
fof(c_0_15,plain,
! [X72,X73] : disjoint(set_difference(X72,X73),X73),
inference(variable_rename,[status(thm)],[t79_xboole_1]) ).
fof(c_0_16,plain,
! [X9,X10] : set_intersection2(X9,X10) = set_intersection2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_17,plain,
! [X65,X66] :
( set_intersection2(X65,X66) = X65
| ~ subset(X65,X66) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])])]) ).
fof(c_0_18,plain,
! [X67,X68] : subset(set_difference(X67,X68),X67),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_19,plain,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
disjoint(set_difference(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( ~ subset(X1,X2)
| set_intersection2(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_25,plain,
! [X62,X63,X64] :
( subset(X62,X64)
| ~ subset(X63,X64)
| ~ subset(X62,X63) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])]) ).
fof(c_0_26,plain,
! [X18,X19,X20,X21,X22,X23] :
( ( X23 = powerset(X22)
| subset(esk2_2(X22,X23),X22)
| in(esk2_2(X22,X23),X23) )
& ( X23 = powerset(X22)
| ~ subset(esk2_2(X22,X23),X22)
| ~ in(esk2_2(X22,X23),X23) )
& ( X19 != powerset(X18)
| in(X21,X19)
| ~ subset(X21,X18) )
& ( X19 != powerset(X18)
| subset(X20,X18)
| ~ in(X20,X19) ) ),
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)],[d1_zfmisc_1])])])])])])]) ).
cnf(c_0_27,plain,
set_intersection2(X1,set_difference(X2,X1)) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_28,plain,
set_intersection2(X1,set_difference(X1,X2)) = set_difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_21]) ).
fof(c_0_29,plain,
! [X40,X41,X42,X43,X44,X45,X46,X47] :
( ( X47 = set_difference(X45,X46)
| in(esk5_3(X45,X46,X47),X47)
| ~ in(esk5_3(X45,X46,X47),X46) )
& ( X47 = set_difference(X45,X46)
| in(esk5_3(X45,X46,X47),X47)
| in(esk5_3(X45,X46,X47),X45) )
& ( X47 = set_difference(X45,X46)
| in(esk5_3(X45,X46,X47),X46)
| ~ in(esk5_3(X45,X46,X47),X45)
| ~ in(esk5_3(X45,X46,X47),X47) )
& ( X42 != set_difference(X40,X41)
| in(X44,X42)
| in(X44,X41)
| ~ in(X44,X40) )
& ( X42 != set_difference(X40,X41)
| ~ in(X43,X42)
| ~ in(X43,X41) )
& ( X42 != set_difference(X40,X41)
| ~ in(X43,X42)
| in(X43,X40) ) ),
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)],[c_0_24])])])])])])]) ).
cnf(c_0_30,plain,
( ~ subset(X2,X3)
| ~ subset(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( X2 != powerset(X3)
| ~ in(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
set_difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( X3 != set_difference(X4,X2)
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_34,negated_conjecture,
~ ! [X1,X2] : subset(powerset(set_difference(X1,X2)),set_union2(singleton(empty_set),set_difference(powerset(X1),powerset(X2)))),
inference(assume_negation,[status(cth)],[t84_zfmisc_1]) ).
cnf(c_0_35,plain,
( ~ subset(X1,set_difference(X2,X3))
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_36,plain,
( ~ in(X1,powerset(X2))
| subset(X1,X2) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_38,plain,
( X3 != set_difference(X2,X4)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( ~ in(X1,X3)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_33]) ).
fof(c_0_40,negated_conjecture,
~ subset(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
fof(c_0_41,plain,
! [X34,X35,X36,X37,X38] :
( ( subset(X37,X38)
| ~ in(esk4_2(X37,X38),X38) )
& ( subset(X37,X38)
| in(esk4_2(X37,X38),X37) )
& ( in(X36,X35)
| ~ in(X36,X34)
| ~ subset(X34,X35) ) ),
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)],[d3_tarski])])])])])])]) ).
cnf(c_0_42,plain,
( ~ in(X1,powerset(set_difference(X2,X3)))
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
set_intersection2(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_22,c_0_37]) ).
cnf(c_0_44,plain,
( ~ in(X1,set_difference(X2,X3))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
( ~ in(X1,X2)
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_46,negated_conjecture,
~ subset(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,plain,
( subset(X1,X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
( ~ in(X1,powerset(set_difference(X2,X3)))
| set_intersection2(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_22,c_0_42]) ).
cnf(c_0_49,plain,
set_difference(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_28,c_0_43]) ).
cnf(c_0_50,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_51,plain,
~ in(X1,empty_set),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_32]),c_0_45]) ).
cnf(c_0_52,plain,
( X3 = set_difference(X1,X2)
| in(esk5_3(X1,X2,X3),X3)
| in(esk5_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_53,plain,
( ~ in(X3,powerset(X2))
| ~ subset(X1,X3)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_54,negated_conjecture,
in(esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),powerset(set_difference(esk8_0,esk9_0))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_55,plain,
! [X59] : subset(X59,X59),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_56,plain,
( ~ in(X1,powerset(empty_set))
| empty_set = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_57,plain,
( in(esk5_3(X1,X2,empty_set),X1)
| set_difference(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_58,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( X16 = singleton(X15)
| esk1_2(X15,X16) = X15
| in(esk1_2(X15,X16),X16) )
& ( X16 = singleton(X15)
| esk1_2(X15,X16) != X15
| ~ in(esk1_2(X15,X16),X16) )
& ( X12 != singleton(X11)
| in(X14,X12)
| X14 != X11 )
& ( X12 != singleton(X11)
| X13 = X11
| ~ in(X13,X12) ) ),
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)],[d1_tarski])])])])])])]) ).
fof(c_0_59,plain,
! [X25,X26,X27,X28,X29,X30,X31,X32] :
( ( X32 = set_union2(X30,X31)
| in(esk3_3(X30,X31,X32),X31)
| in(esk3_3(X30,X31,X32),X30)
| in(esk3_3(X30,X31,X32),X32) )
& ( X32 = set_union2(X30,X31)
| ~ in(esk3_3(X30,X31,X32),X32)
| ~ in(esk3_3(X30,X31,X32),X31) )
& ( X32 = set_union2(X30,X31)
| ~ in(esk3_3(X30,X31,X32),X32)
| ~ in(esk3_3(X30,X31,X32),X30) )
& ( X27 != set_union2(X25,X26)
| in(X29,X27)
| ~ in(X29,X26) )
& ( X27 != set_union2(X25,X26)
| in(X29,X27)
| ~ in(X29,X25) )
& ( X27 != set_union2(X25,X26)
| in(X28,X26)
| in(X28,X25)
| ~ in(X28,X27) ) ),
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)],[d2_xboole_0])])])])])])]) ).
cnf(c_0_60,negated_conjecture,
( ~ subset(X1,esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))))
| subset(X1,set_difference(esk8_0,esk9_0)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_62,plain,
! [X69,X70,X71] :
( disjoint(X69,X71)
| ~ disjoint(X70,X71)
| ~ subset(X69,X70) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])])]) ).
cnf(c_0_63,plain,
( ~ in(esk5_3(X1,X2,X3),X2)
| X3 = set_difference(X1,X2)
| in(esk5_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_64,plain,
( set_difference(powerset(empty_set),X1) = empty_set
| esk5_3(powerset(empty_set),X1,empty_set) = empty_set ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_65,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_66,plain,
( ~ in(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_67,plain,
( X3 != set_union2(X4,X2)
| ~ in(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,plain,
( X3 != powerset(X2)
| ~ subset(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_69,negated_conjecture,
subset(esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),set_difference(esk8_0,esk9_0)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,plain,
( ~ disjoint(X2,X3)
| ~ subset(X1,X2)
| disjoint(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,plain,
( X3 != set_union2(X2,X4)
| ~ in(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_72,plain,
( X4 != set_difference(X2,X3)
| ~ in(X1,X2)
| in(X1,X4)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_73,plain,
( ~ in(empty_set,X1)
| set_difference(powerset(empty_set),X1) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_51]) ).
cnf(c_0_74,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_65])]) ).
cnf(c_0_75,negated_conjecture,
~ in(esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),
inference(spm,[status(thm)],[c_0_46,c_0_66]) ).
cnf(c_0_76,plain,
( ~ in(X1,X3)
| in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[c_0_67]) ).
cnf(c_0_77,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_68]) ).
cnf(c_0_78,negated_conjecture,
subset(esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),esk8_0),
inference(spm,[status(thm)],[c_0_35,c_0_69]) ).
cnf(c_0_79,plain,
( ~ subset(X1,set_difference(X3,X2))
| disjoint(X1,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_20]) ).
cnf(c_0_80,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[c_0_71]) ).
cnf(c_0_81,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_72]) ).
cnf(c_0_82,plain,
set_difference(powerset(empty_set),singleton(empty_set)) = empty_set,
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_83,negated_conjecture,
~ in(esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),set_difference(powerset(esk8_0),powerset(esk9_0))),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,negated_conjecture,
in(esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),powerset(esk8_0)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_85,plain,
( ~ subset(X1,set_difference(X3,X2))
| set_intersection2(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_19,c_0_79]) ).
cnf(c_0_86,negated_conjecture,
~ in(esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),singleton(empty_set)),
inference(spm,[status(thm)],[c_0_75,c_0_80]) ).
cnf(c_0_87,plain,
( ~ in(X1,powerset(empty_set))
| in(X1,singleton(empty_set)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_51]) ).
cnf(c_0_88,plain,
( ~ in(X1,powerset(X2))
| set_intersection2(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_89,negated_conjecture,
in(esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),powerset(esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_81]),c_0_84])]) ).
cnf(c_0_90,negated_conjecture,
set_intersection2(esk9_0,esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0))))) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_69]),c_0_21]) ).
cnf(c_0_91,negated_conjecture,
~ in(esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),powerset(empty_set)),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,negated_conjecture,
esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))) = empty_set,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_21]),c_0_90]) ).
cnf(c_0_93,plain,
in(X1,powerset(X1)),
inference(spm,[status(thm)],[c_0_77,c_0_61]) ).
cnf(c_0_94,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92]),c_0_93])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET937+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:39:56 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 7.80/1.49 % Version: 3.5.1
% 7.80/1.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.80/1.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.80/1.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.80/1.49 % Starting new_bool_3 with 300s (1) cores
% 7.80/1.49 % Starting new_bool_1 with 300s (1) cores
% 7.80/1.49 % Starting sh5l with 300s (1) cores
% 7.80/1.49 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1551799 completed with status 0
% 7.80/1.49 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 7.80/1.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.80/1.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.80/1.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.80/1.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.80/1.49 % No SInE strategy applied
% 7.80/1.49 % Search class: FGHSM-FFMF32-MFFFFFNN
% 7.80/1.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.80/1.49 % Starting SubtermCWHack with 136s (1) cores
% 7.80/1.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.80/1.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S033I with 136s (1) cores
% 7.80/1.49 % Starting new_bool_3 with 136s (1) cores
% 7.80/1.49 % Starting new_bool_1 with 136s (1) cores
% 7.80/1.49 % G-E--_208_C18_F1_SE_CS_SP_PS_S033I with pid 1551806 completed with status 0
% 7.80/1.49 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S033I
% 7.80/1.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.80/1.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.80/1.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.80/1.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.80/1.49 % No SInE strategy applied
% 7.80/1.49 % Search class: FGHSM-FFMF32-MFFFFFNN
% 7.80/1.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.80/1.49 % Starting SubtermCWHack with 136s (1) cores
% 7.80/1.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.80/1.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S033I with 136s (1) cores
% 7.80/1.49 % Preprocessing time : 0.002 s
% 7.80/1.49 % Presaturation interreduction done
% 7.80/1.49
% 7.80/1.49 % Proof found!
% 7.80/1.49 % SZS status Theorem
% 7.80/1.49 % SZS output start CNFRefutation
% See solution above
% 7.80/1.49 % Parsed axioms : 24
% 7.80/1.49 % Removed by relevancy pruning/SinE : 0
% 7.80/1.49 % Initial clauses : 43
% 7.80/1.49 % Removed in clause preprocessing : 0
% 7.80/1.49 % Initial clauses in saturation : 43
% 7.80/1.49 % Processed clauses : 4780
% 7.80/1.49 % ...of these trivial : 85
% 7.80/1.49 % ...subsumed : 3373
% 7.80/1.49 % ...remaining for further processing : 1322
% 7.80/1.49 % Other redundant clauses eliminated : 14
% 7.80/1.49 % Clauses deleted for lack of memory : 0
% 7.80/1.49 % Backward-subsumed : 43
% 7.80/1.49 % Backward-rewritten : 69
% 7.80/1.49 % Generated clauses : 50114
% 7.80/1.49 % ...of the previous two non-redundant : 43359
% 7.80/1.49 % ...aggressively subsumed : 0
% 7.80/1.49 % Contextual simplify-reflections : 2
% 7.80/1.49 % Paramodulations : 49869
% 7.80/1.49 % Factorizations : 232
% 7.80/1.49 % NegExts : 0
% 7.80/1.49 % Equation resolutions : 14
% 7.80/1.49 % Disequality decompositions : 0
% 7.80/1.49 % Total rewrite steps : 12228
% 7.80/1.49 % ...of those cached : 9731
% 7.80/1.49 % Propositional unsat checks : 0
% 7.80/1.49 % Propositional check models : 0
% 7.80/1.49 % Propositional check unsatisfiable : 0
% 7.80/1.49 % Propositional clauses : 0
% 7.80/1.49 % Propositional clauses after purity: 0
% 7.80/1.49 % Propositional unsat core size : 0
% 7.80/1.49 % Propositional preprocessing time : 0.000
% 7.80/1.49 % Propositional encoding time : 0.000
% 7.80/1.49 % Propositional solver time : 0.000
% 7.80/1.49 % Success case prop preproc time : 0.000
% 7.80/1.49 % Success case prop encoding time : 0.000
% 7.80/1.49 % Success case prop solver time : 0.000
% 7.80/1.49 % Current number of processed clauses : 1157
% 7.80/1.49 % Positive orientable unit clauses : 160
% 7.80/1.49 % Positive unorientable unit clauses: 2
% 7.80/1.49 % Negative unit clauses : 302
% 7.80/1.49 % Non-unit-clauses : 693
% 7.80/1.49 % Current number of unprocessed clauses: 38536
% 7.80/1.49 % ...number of literals in the above : 127036
% 7.80/1.49 % Current number of archived formulas : 0
% 7.80/1.49 % Current number of archived clauses : 155
% 7.80/1.49 % Clause-clause subsumption calls (NU) : 102430
% 7.80/1.49 % Rec. Clause-clause subsumption calls : 69451
% 7.80/1.49 % Non-unit clause-clause subsumptions : 1146
% 7.80/1.49 % Unit Clause-clause subsumption calls : 36253
% 7.80/1.49 % Rewrite failures with RHS unbound : 0
% 7.80/1.49 % BW rewrite match attempts : 243
% 7.80/1.49 % BW rewrite match successes : 44
% 7.80/1.49 % Condensation attempts : 0
% 7.80/1.49 % Condensation successes : 0
% 7.80/1.49 % Termbank termtop insertions : 836183
% 7.80/1.49 % Search garbage collected termcells : 758
% 7.80/1.49
% 7.80/1.49 % -------------------------------------------------
% 7.80/1.49 % User time : 0.988 s
% 7.80/1.49 % System time : 0.049 s
% 7.80/1.49 % Total time : 1.037 s
% 7.80/1.49 % Maximum resident set size: 3652 pages
% 7.80/1.49
% 7.80/1.49 % -------------------------------------------------
% 7.80/1.49 % User time : 4.985 s
% 7.80/1.49 % System time : 0.213 s
% 7.80/1.49 % Total time : 5.198 s
% 7.80/1.49 % Maximum resident set size: 4608 pages
% 7.80/1.49 % E exiting
%------------------------------------------------------------------------------