%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET937+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n006.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 05:09:00 PM UTC 2026
% Result : Theorem 4.39s 3.30s
% Output : CNFRefutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 98 ( 43 unt; 0 def)
% Number of atoms : 241 ( 76 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 235 ( 92 ~; 104 |; 23 &)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 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 : 204 ( 21 sgn 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(t79_xboole_1,axiom,
! [X1,X2] : disjoint(set_difference(X1,X2),X2),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(t36_xboole_1,axiom,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t63_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(c_0_14,plain,
! [X102,X103] :
( ( ~ disjoint(X102,X103)
| set_intersection2(X102,X103) = empty_set )
& ( set_intersection2(X102,X103) != empty_set
| disjoint(X102,X103) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(c_0_15,plain,
! [X125,X126] : disjoint(set_difference(X125,X126),X126),
inference(variable_rename,[status(thm)],[t79_xboole_1]) ).
fof(c_0_16,plain,
! [X62,X63] : set_intersection2(X62,X63) = set_intersection2(X63,X62),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_17,plain,
! [X118,X119] :
( ~ subset(X118,X119)
| set_intersection2(X118,X119) = X118 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(c_0_18,plain,
! [X120,X121] : subset(set_difference(X120,X121),X120),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_19,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
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,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
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]) ).
cnf(c_0_24,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_25,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_26,plain,
! [X122,X123,X124] :
( ~ subset(X122,X123)
| ~ disjoint(X123,X124)
| disjoint(X122,X124) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
cnf(c_0_27,plain,
set_difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_28,plain,
! [X71,X72,X73,X74,X75,X76] :
( ( ~ in(X73,X72)
| subset(X73,X71)
| X72 != powerset(X71) )
& ( ~ subset(X74,X71)
| in(X74,X72)
| X72 != powerset(X71) )
& ( ~ in(esk2_2(X75,X76),X76)
| ~ subset(esk2_2(X75,X76),X75)
| X76 = powerset(X75) )
& ( in(esk2_2(X75,X76),X76)
| subset(esk2_2(X75,X76),X75)
| X76 = powerset(X75) ) ),
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)],[d1_zfmisc_1])])])])])]) ).
fof(c_0_29,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]) ).
fof(c_0_30,plain,
! [X87,X88,X89,X90,X91] :
( ( ~ subset(X87,X88)
| ~ in(X89,X87)
| in(X89,X88) )
& ( in(esk4_2(X90,X91),X90)
| subset(X90,X91) )
& ( ~ in(esk4_2(X90,X91),X91)
| subset(X90,X91) ) ),
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)],[d3_tarski])])])])])]) ).
fof(c_0_31,plain,
! [X78,X79,X80,X81,X82,X83,X84,X85] :
( ( ~ in(X81,X80)
| in(X81,X78)
| in(X81,X79)
| X80 != set_union2(X78,X79) )
& ( ~ in(X82,X78)
| in(X82,X80)
| X80 != set_union2(X78,X79) )
& ( ~ in(X82,X79)
| in(X82,X80)
| X80 != set_union2(X78,X79) )
& ( ~ in(esk3_3(X83,X84,X85),X83)
| ~ in(esk3_3(X83,X84,X85),X85)
| X85 = set_union2(X83,X84) )
& ( ~ in(esk3_3(X83,X84,X85),X84)
| ~ in(esk3_3(X83,X84,X85),X85)
| X85 = set_union2(X83,X84) )
& ( in(esk3_3(X83,X84,X85),X85)
| in(esk3_3(X83,X84,X85),X83)
| in(esk3_3(X83,X84,X85),X84)
| X85 = set_union2(X83,X84) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_32,plain,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
disjoint(empty_set,X1),
inference(spm,[status(thm)],[c_0_20,c_0_27]) ).
fof(c_0_34,plain,
! [X115,X116,X117] :
( ~ subset(X115,X116)
| ~ subset(X116,X117)
| subset(X115,X117) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
cnf(c_0_35,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_36,negated_conjecture,
~ subset(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_37,plain,
( subset(X1,X2)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( disjoint(X1,X2)
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_40,plain,
! [X64,X65,X66,X67,X68,X69] :
( ( ~ in(X66,X65)
| X66 = X64
| X65 != singleton(X64) )
& ( X67 != X64
| in(X67,X65)
| X65 != singleton(X64) )
& ( ~ in(esk1_2(X68,X69),X69)
| esk1_2(X68,X69) != X68
| X69 = singleton(X68) )
& ( in(esk1_2(X68,X69),X69)
| esk1_2(X68,X69) = X68
| X69 = singleton(X68) ) ),
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)],[d1_tarski])])])])])]) ).
cnf(c_0_41,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_43,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_36]) ).
cnf(c_0_44,plain,
( in(esk4_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_45,plain,
( set_intersection2(X1,X2) = X1
| ~ in(esk4_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_37]) ).
cnf(c_0_46,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
( set_intersection2(X1,X2) = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_19,c_0_39]) ).
cnf(c_0_48,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_50,plain,
( subset(X1,X2)
| ~ subset(X1,X3)
| ~ in(X3,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_51,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_43,c_0_44]) ).
fof(c_0_52,plain,
! [X112] : subset(X112,X112),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_53,plain,
( set_intersection2(X1,set_union2(X2,X3)) = X1
| ~ in(esk4_2(X1,set_union2(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_54,plain,
( set_intersection2(X1,X2) = X1
| in(esk4_2(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_44]) ).
cnf(c_0_55,plain,
( set_intersection2(X1,X2) = empty_set
| ~ in(X1,powerset(empty_set)) ),
inference(spm,[status(thm)],[c_0_47,c_0_42]) ).
cnf(c_0_56,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_49]) ).
fof(c_0_58,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
cnf(c_0_59,negated_conjecture,
( subset(X1,set_difference(esk8_0,esk9_0))
| ~ subset(X1,esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(singleton(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0))))) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,plain,
set_intersection2(X1,set_union2(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_62,plain,
( set_intersection2(esk4_2(powerset(empty_set),X1),X2) = empty_set
| set_intersection2(powerset(empty_set),X1) = powerset(empty_set) ),
inference(spm,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_63,plain,
( set_intersection2(singleton(X1),X2) = singleton(X1)
| esk4_2(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_56,c_0_54]) ).
cnf(c_0_64,plain,
in(set_difference(X1,X2),powerset(X1)),
inference(spm,[status(thm)],[c_0_57,c_0_23]) ).
fof(c_0_65,plain,
! [X93,X94,X95,X96,X97,X98,X99,X100] :
( ( in(X96,X93)
| ~ in(X96,X95)
| X95 != set_difference(X93,X94) )
& ( ~ in(X96,X94)
| ~ in(X96,X95)
| X95 != set_difference(X93,X94) )
& ( ~ in(X97,X93)
| in(X97,X94)
| in(X97,X95)
| X95 != set_difference(X93,X94) )
& ( ~ in(esk5_3(X98,X99,X100),X100)
| ~ in(esk5_3(X98,X99,X100),X98)
| in(esk5_3(X98,X99,X100),X99)
| X100 = set_difference(X98,X99) )
& ( in(esk5_3(X98,X99,X100),X98)
| in(esk5_3(X98,X99,X100),X100)
| X100 = set_difference(X98,X99) )
& ( ~ in(esk5_3(X98,X99,X100),X99)
| in(esk5_3(X98,X99,X100),X100)
| X100 = set_difference(X98,X99) ) ),
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)],[c_0_58])])])])])]) ).
cnf(c_0_66,plain,
( subset(X1,X2)
| ~ subset(X1,set_difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_41,c_0_23]) ).
cnf(c_0_67,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_59,c_0_60]) ).
cnf(c_0_68,plain,
( set_intersection2(powerset(empty_set),X1) = powerset(empty_set)
| esk4_2(powerset(empty_set),X1) = empty_set ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_70,plain,
( set_intersection2(singleton(X1),X2) = singleton(X1)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_63]) ).
cnf(c_0_71,plain,
in(empty_set,powerset(X1)),
inference(spm,[status(thm)],[c_0_64,c_0_27]) ).
cnf(c_0_72,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_43,c_0_37]) ).
cnf(c_0_73,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,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_66,c_0_67]) ).
cnf(c_0_75,plain,
( set_intersection2(powerset(empty_set),X1) = powerset(empty_set)
| ~ in(empty_set,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_68]) ).
cnf(c_0_76,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_69])]) ).
cnf(c_0_77,plain,
set_intersection2(singleton(empty_set),powerset(X1)) = singleton(empty_set),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_78,plain,
( disjoint(X1,X2)
| ~ subset(X1,set_difference(X3,X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_79,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_80,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_72,c_0_46]) ).
cnf(c_0_81,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_73]) ).
cnf(c_0_82,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_57,c_0_74]) ).
cnf(c_0_83,plain,
set_intersection2(powerset(empty_set),singleton(empty_set)) = powerset(empty_set),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,plain,
set_intersection2(powerset(X1),singleton(empty_set)) = singleton(empty_set),
inference(spm,[status(thm)],[c_0_21,c_0_77]) ).
cnf(c_0_85,plain,
( set_intersection2(X1,X2) = empty_set
| ~ subset(X1,set_difference(X3,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_78]) ).
cnf(c_0_86,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_79]) ).
cnf(c_0_87,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_80,c_0_81]),c_0_82])]) ).
cnf(c_0_88,plain,
singleton(empty_set) = powerset(empty_set),
inference(rw,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,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_67]),c_0_21]) ).
cnf(c_0_90,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_72,c_0_86]) ).
cnf(c_0_91,plain,
( set_intersection2(X1,X2) = X1
| ~ in(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_42]) ).
cnf(c_0_92,negated_conjecture,
in(esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(powerset(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),powerset(esk9_0)),
inference(rw,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_93,negated_conjecture,
set_intersection2(esk9_0,esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(powerset(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0))))) = empty_set,
inference(rw,[status(thm)],[c_0_89,c_0_88]) ).
cnf(c_0_94,negated_conjecture,
~ in(esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(powerset(empty_set),set_difference(powerset(esk8_0),powerset(esk9_0)))),powerset(empty_set)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_88]),c_0_88]) ).
cnf(c_0_95,negated_conjecture,
esk4_2(powerset(set_difference(esk8_0,esk9_0)),set_union2(powerset(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_91,c_0_92]),c_0_21]),c_0_93]) ).
cnf(c_0_96,plain,
in(X1,powerset(X1)),
inference(spm,[status(thm)],[c_0_57,c_0_60]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET937+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.14/0.32 % Computer : n006.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:40:01 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 4.39/3.30 % Version : CSE_E---1.7
% 4.39/3.30 % Problem : theBenchmark.p
% 4.39/3.30 % SZS status Theorem for theBenchmark.p
% 4.39/3.30 % SZS output start CNFRefutation
% See solution above
% 4.39/3.31 % Total time : 2.373s
%------------------------------------------------------------------------------