%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU142+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n014.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 05:10:45 PM UTC 2026
% Result : Theorem 209.46s 153.00s
% Output : CNFRefutation 210.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 24
% Syntax : Number of formulae : 137 ( 61 unt; 0 def)
% Number of atoms : 311 ( 138 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 287 ( 113 ~; 115 |; 41 &)
% ( 14 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-3 aty)
% Number of variables : 311 ( 34 sgn 136 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
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/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(t3_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
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(t40_xboole_1,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_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(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t4_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(t39_xboole_1,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_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(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(t83_xboole_1,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
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(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t69_enumset1,conjecture,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(c_0_24,plain,
! [X227] : set_intersection2(X227,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(c_0_25,lemma,
! [X253,X254] : set_difference(X253,set_difference(X253,X254)) = set_intersection2(X253,X254),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_26,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]) ).
fof(c_0_27,lemma,
! [X211,X212] :
( ~ subset(X211,X212)
| set_union2(X211,X212) = X212 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(c_0_28,lemma,
! [X271,X272] : subset(X271,set_union2(X271,X272)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_29,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
! [X241] : set_difference(X241,empty_set) = X241,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(c_0_32,plain,
! [X184,X185,X186,X187,X188,X189,X190,X191] :
( ( in(X187,X184)
| ~ in(X187,X186)
| X186 != set_difference(X184,X185) )
& ( ~ in(X187,X185)
| ~ in(X187,X186)
| X186 != set_difference(X184,X185) )
& ( ~ in(X188,X184)
| in(X188,X185)
| in(X188,X186)
| X186 != set_difference(X184,X185) )
& ( ~ in(esk7_3(X189,X190,X191),X191)
| ~ in(esk7_3(X189,X190,X191),X189)
| in(esk7_3(X189,X190,X191),X190)
| X191 = set_difference(X189,X190) )
& ( in(esk7_3(X189,X190,X191),X189)
| in(esk7_3(X189,X190,X191),X191)
| X191 = set_difference(X189,X190) )
& ( ~ in(esk7_3(X189,X190,X191),X190)
| in(esk7_3(X189,X190,X191),X191)
| X191 = set_difference(X189,X190) ) ),
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_26])])])])])]) ).
fof(c_0_33,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).
fof(c_0_34,plain,
! [X140,X141,X142,X143,X144,X145] :
( ( ~ in(X142,X141)
| X142 = X140
| X141 != singleton(X140) )
& ( X143 != X140
| in(X143,X141)
| X141 != singleton(X140) )
& ( ~ in(esk1_2(X144,X145),X145)
| esk1_2(X144,X145) != X144
| X145 = singleton(X144) )
& ( in(esk1_2(X144,X145),X145)
| esk1_2(X144,X145) = X144
| X145 = singleton(X144) ) ),
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])])])])])]) ).
fof(c_0_35,lemma,
! [X249,X250] : set_difference(set_union2(X249,X250),X250) = set_difference(X249,X250),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
cnf(c_0_36,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_41,lemma,
! [X242,X243,X245,X246,X247] :
( ( in(esk11_2(X242,X243),X242)
| disjoint(X242,X243) )
& ( in(esk11_2(X242,X243),X243)
| disjoint(X242,X243) )
& ( ~ in(X247,X245)
| ~ in(X247,X246)
| ~ disjoint(X245,X246) ) ),
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_33])])])])])]) ).
cnf(c_0_42,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_43,plain,
! [X136,X137] : set_intersection2(X136,X137) = set_intersection2(X137,X136),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_44,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,lemma,
set_union2(X1,set_union2(X1,X2)) = set_union2(X1,X2),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_46,plain,
set_difference(X1,X1) = empty_set,
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_47,plain,
! [X134,X135] : set_union2(X134,X135) = set_union2(X135,X134),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_48,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(c_0_49,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_50,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_51,lemma,
( in(esk11_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_52,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_53,lemma,
( in(esk11_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,lemma,
set_difference(X1,set_union2(X1,X2)) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_56,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_57,lemma,
! [X256,X257,X259,X260,X261] :
( ( disjoint(X256,X257)
| in(esk12_2(X256,X257),set_intersection2(X256,X257)) )
& ( ~ in(X261,set_intersection2(X259,X260))
| ~ disjoint(X259,X260) ) ),
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_48])])])])]) ).
fof(c_0_58,lemma,
! [X225,X226] :
( ~ subset(X225,X226)
| set_intersection2(X225,X226) = X225 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(c_0_59,plain,
! [X147,X148,X149] :
( ( X147 != empty_set
| ~ in(X148,X147) )
& ( in(esk2_1(X149),X149)
| X149 = empty_set ) ),
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_49])])])])]) ).
fof(c_0_60,lemma,
! [X239,X240] : set_union2(X239,set_difference(X240,X239)) = set_union2(X239,X240),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
cnf(c_0_61,lemma,
( disjoint(X1,set_difference(X2,X3))
| in(esk11_2(X1,set_difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_62,lemma,
( esk11_2(singleton(X1),X2) = X1
| disjoint(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_63,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_30]),c_0_30]) ).
cnf(c_0_64,lemma,
set_difference(X1,set_union2(X2,X1)) = empty_set,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
fof(c_0_65,plain,
! [X151,X152,X153,X154,X155,X156,X157,X158] :
( ( ~ in(X154,X153)
| X154 = X151
| X154 = X152
| X153 != unordered_pair(X151,X152) )
& ( X155 != X151
| in(X155,X153)
| X153 != unordered_pair(X151,X152) )
& ( X155 != X152
| in(X155,X153)
| X153 != unordered_pair(X151,X152) )
& ( esk3_3(X156,X157,X158) != X156
| ~ in(esk3_3(X156,X157,X158),X158)
| X158 = unordered_pair(X156,X157) )
& ( esk3_3(X156,X157,X158) != X157
| ~ in(esk3_3(X156,X157,X158),X158)
| X158 = unordered_pair(X156,X157) )
& ( in(esk3_3(X156,X157,X158),X158)
| esk3_3(X156,X157,X158) = X156
| esk3_3(X156,X157,X158) = X157
| X158 = unordered_pair(X156,X157) ) ),
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_tarski])])])])])]) ).
cnf(c_0_66,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_67,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_68,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_69,lemma,
! [X204,X205] :
( ( set_difference(X204,X205) != empty_set
| subset(X204,X205) )
& ( ~ subset(X204,X205)
| set_difference(X204,X205) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
cnf(c_0_70,lemma,
set_difference(set_union2(X1,X2),X1) = set_difference(X2,X1),
inference(spm,[status(thm)],[c_0_44,c_0_56]) ).
cnf(c_0_71,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_72,lemma,
! [X235,X236] : subset(set_difference(X235,X236),X235),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(c_0_73,plain,
! [X169,X170,X171,X172,X173] :
( ( ~ subset(X169,X170)
| ~ in(X171,X169)
| in(X171,X170) )
& ( in(esk5_2(X172,X173),X172)
| subset(X172,X173) )
& ( ~ in(esk5_2(X172,X173),X173)
| subset(X172,X173) ) ),
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])])])])])]) ).
cnf(c_0_74,lemma,
( disjoint(singleton(X1),set_difference(X2,X3))
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_75,lemma,
set_difference(set_union2(X1,X2),set_difference(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_44]),c_0_64]),c_0_39]) ).
fof(c_0_76,plain,
! [X218] : set_union2(X218,empty_set) = X218,
inference(variable_rename,[status(thm)],[t1_boole]) ).
cnf(c_0_77,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_78,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[c_0_66,c_0_30]) ).
cnf(c_0_79,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[c_0_67,c_0_30]) ).
cnf(c_0_80,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_68]) ).
cnf(c_0_81,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_82,lemma,
set_difference(set_difference(X1,X2),X2) = set_difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_70]) ).
cnf(c_0_83,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_84,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_85,lemma,
( disjoint(singleton(X1),X2)
| in(X1,set_union2(X3,X2)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_86,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_87,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_77]) ).
cnf(c_0_88,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_89,lemma,
( ~ disjoint(X1,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_90,lemma,
disjoint(X1,empty_set),
inference(spm,[status(thm)],[c_0_80,c_0_51]) ).
cnf(c_0_91,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
fof(c_0_92,lemma,
! [X273,X274] :
( ( ~ disjoint(X273,X274)
| set_difference(X273,X274) = X273 )
& ( set_difference(X273,X274) != X273
| disjoint(X273,X274) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
cnf(c_0_93,lemma,
( esk11_2(X1,singleton(X2)) = X2
| disjoint(X1,singleton(X2)) ),
inference(spm,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_94,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_95,plain,
! [X193,X194] :
( ( ~ disjoint(X193,X194)
| set_intersection2(X193,X194) = empty_set )
& ( set_intersection2(X193,X194) != empty_set
| disjoint(X193,X194) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
cnf(c_0_96,lemma,
( set_union2(X1,X2) = X2
| set_difference(X1,X2) != empty_set ),
inference(spm,[status(thm)],[c_0_36,c_0_81]) ).
cnf(c_0_97,lemma,
set_difference(X1,set_difference(X1,set_difference(X2,X1))) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_82]),c_0_46]) ).
cnf(c_0_98,lemma,
set_union2(X1,set_difference(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_83]),c_0_56]) ).
cnf(c_0_99,lemma,
( disjoint(singleton(esk5_2(X1,set_union2(X2,X3))),X3)
| subset(X1,set_union2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_100,plain,
set_union2(empty_set,X1) = X1,
inference(spm,[status(thm)],[c_0_86,c_0_56]) ).
cnf(c_0_101,plain,
( esk5_2(unordered_pair(X1,X2),X3) = X1
| esk5_2(unordered_pair(X1,X2),X3) = X2
| subset(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_102,lemma,
( ~ subset(X1,empty_set)
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_103,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_91])]) ).
cnf(c_0_104,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_105,lemma,
( X1 = X2
| disjoint(singleton(X1),singleton(X2)) ),
inference(spm,[status(thm)],[c_0_93,c_0_62]) ).
cnf(c_0_106,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_94])]) ).
fof(c_0_107,lemma,
! [X219,X220,X221] :
( ~ subset(X219,X220)
| ~ subset(X220,X221)
| subset(X219,X221) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
cnf(c_0_108,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_109,lemma,
set_difference(X1,set_difference(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]) ).
cnf(c_0_110,lemma,
( disjoint(singleton(esk5_2(X1,X2)),X2)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_111,plain,
( esk5_2(unordered_pair(X1,X1),X2) = X1
| subset(unordered_pair(X1,X1),X2) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_101])]) ).
cnf(c_0_112,lemma,
~ subset(unordered_pair(X1,X2),empty_set),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_113,lemma,
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_114,lemma,
~ subset(singleton(X1),empty_set),
inference(spm,[status(thm)],[c_0_102,c_0_106]) ).
cnf(c_0_115,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_116,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[c_0_108,c_0_30]) ).
cnf(c_0_117,lemma,
set_difference(X1,set_difference(X2,set_difference(X2,X1))) = set_difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_63]),c_0_98]) ).
cnf(c_0_118,lemma,
( empty_set = X1
| ~ subset(X1,set_difference(X2,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_109]),c_0_46]) ).
cnf(c_0_119,lemma,
( disjoint(singleton(X1),X2)
| subset(unordered_pair(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_120,lemma,
unordered_pair(X1,X2) != empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_81]),c_0_39]) ).
cnf(c_0_121,lemma,
( set_difference(singleton(X1),set_difference(singleton(X1),singleton(X2))) = empty_set
| X2 = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_113]),c_0_46]) ).
cnf(c_0_122,lemma,
singleton(X1) != empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_81]),c_0_39]) ).
cnf(c_0_123,lemma,
( subset(X1,X2)
| ~ subset(X1,set_difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_115,c_0_83]) ).
cnf(c_0_124,plain,
( set_difference(X1,X2) = empty_set
| ~ disjoint(X1,set_difference(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_63]),c_0_117]) ).
cnf(c_0_125,lemma,
disjoint(singleton(X1),set_difference(X2,unordered_pair(X1,X1))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]) ).
fof(c_0_126,negated_conjecture,
~ ! [X1] : unordered_pair(X1,X1) = singleton(X1),
inference(assume_negation,[status(cth)],[t69_enumset1]) ).
cnf(c_0_127,lemma,
( X1 = X2
| ~ disjoint(singleton(X2),set_difference(singleton(X2),singleton(X1))) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_121]),c_0_39]),c_0_122]) ).
cnf(c_0_128,lemma,
( disjoint(singleton(X1),set_difference(X2,X3))
| subset(unordered_pair(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_123,c_0_119]) ).
cnf(c_0_129,lemma,
set_difference(singleton(X1),unordered_pair(X1,X1)) = empty_set,
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
fof(c_0_130,negated_conjecture,
unordered_pair(esk13_0,esk13_0) != singleton(esk13_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_126])])]) ).
cnf(c_0_131,lemma,
( X1 = X2
| subset(unordered_pair(X2,X2),singleton(X2)) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_132,lemma,
set_union2(singleton(X1),unordered_pair(X1,X1)) = unordered_pair(X1,X1),
inference(spm,[status(thm)],[c_0_96,c_0_129]) ).
cnf(c_0_133,negated_conjecture,
unordered_pair(esk13_0,esk13_0) != singleton(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_134,lemma,
( unordered_pair(X1,X1) = singleton(X1)
| X2 = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_131]),c_0_56]),c_0_132]) ).
cnf(c_0_135,negated_conjecture,
X1 = esk13_0,
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_136,lemma,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_135]),c_0_135]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU142+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:45:21 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 209.46/153.00 % Version : CSE_E---1.7
% 209.46/153.00 % Problem : theBenchmark.p
% 209.46/153.00 % SZS status Theorem for theBenchmark.p
% 209.46/153.00 % SZS output start CNFRefutation
% See solution above
% 210.59/154.10 % Total time : 112.011s
%------------------------------------------------------------------------------