%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU162+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 : n025.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 05:10:52 PM UTC 2026
% Result : Theorem 1.74s 1.88s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 68 ( 33 unt; 0 def)
% Number of atoms : 147 ( 77 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 134 ( 55 ~; 51 |; 14 &)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 127 ( 7 sgn 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l28_zfmisc_1,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
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(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(t65_zfmisc_1,conjecture,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
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(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(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(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(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(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
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(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(c_0_15,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[l28_zfmisc_1]) ).
fof(c_0_16,lemma,
! [X318,X319] :
( ( set_difference(X318,X319) != empty_set
| subset(X318,X319) )
& ( ~ subset(X318,X319)
| set_difference(X318,X319) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
fof(c_0_17,lemma,
! [X417,X418] : subset(X417,set_union2(X417,X418)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t65_zfmisc_1])]) ).
fof(c_0_19,lemma,
! [X314,X315] :
( in(X314,X315)
| disjoint(singleton(X314),X315) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
fof(c_0_20,lemma,
! [X411] : unordered_pair(X411,X411) = singleton(X411),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_21,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_22,plain,
! [X202,X203] : set_intersection2(X202,X203) = set_intersection2(X203,X202),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_23,lemma,
! [X395,X396] : set_difference(X395,set_difference(X395,X396)) = set_intersection2(X395,X396),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
cnf(c_0_24,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_26,plain,
! [X200,X201] : set_union2(X200,X201) = set_union2(X201,X200),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_27,negated_conjecture,
( ( set_difference(esk22_0,singleton(esk23_0)) != esk22_0
| in(esk23_0,esk22_0) )
& ( set_difference(esk22_0,singleton(esk23_0)) = esk22_0
| ~ in(esk23_0,esk22_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_28,lemma,
! [X419,X420] :
( ( ~ disjoint(X419,X420)
| set_difference(X419,X420) = X419 )
& ( set_difference(X419,X420) != X419
| disjoint(X419,X420) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
cnf(c_0_29,lemma,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_31,plain,
! [X206,X207,X208,X209,X210,X211] :
( ( ~ in(X208,X207)
| X208 = X206
| X207 != singleton(X206) )
& ( X209 != X206
| in(X209,X207)
| X207 != singleton(X206) )
& ( ~ in(esk1_2(X210,X211),X211)
| esk1_2(X210,X211) != X210
| X211 = singleton(X210) )
& ( in(esk1_2(X210,X211),X211)
| esk1_2(X210,X211) = X210
| X211 = singleton(X210) ) ),
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_32,plain,
! [X285,X286,X287,X288,X289,X290,X291,X292] :
( ( in(X288,X285)
| ~ in(X288,X287)
| X287 != set_difference(X285,X286) )
& ( ~ in(X288,X286)
| ~ in(X288,X287)
| X287 != set_difference(X285,X286) )
& ( ~ in(X289,X285)
| in(X289,X286)
| in(X289,X287)
| X287 != set_difference(X285,X286) )
& ( ~ in(esk16_3(X290,X291,X292),X292)
| ~ in(esk16_3(X290,X291,X292),X290)
| in(esk16_3(X290,X291,X292),X291)
| X292 = set_difference(X290,X291) )
& ( in(esk16_3(X290,X291,X292),X290)
| in(esk16_3(X290,X291,X292),X292)
| X292 = set_difference(X290,X291) )
& ( ~ in(esk16_3(X290,X291,X292),X291)
| in(esk16_3(X290,X291,X292),X292)
| X292 = set_difference(X290,X291) ) ),
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_21])])])])])]) ).
fof(c_0_33,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_34,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_36,lemma,
! [X389,X390] : set_difference(set_union2(X389,X390),X390) = set_difference(X389,X390),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
cnf(c_0_37,lemma,
set_difference(X1,set_union2(X1,X2)) = empty_set,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_38,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_39,plain,
! [X381] : set_difference(X381,empty_set) = X381,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_40,negated_conjecture,
( set_difference(esk22_0,singleton(esk23_0)) = esk22_0
| ~ in(esk23_0,esk22_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_41,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_42,lemma,
( in(X1,X2)
| disjoint(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_43,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_44,lemma,
! [X309] : singleton(X309) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_0_45,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_46,plain,
! [X213,X214,X215] :
( ( X213 != empty_set
| ~ in(X214,X213) )
& ( in(esk2_1(X215),X215)
| X215 = 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_33])])])])]) ).
cnf(c_0_47,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_34,c_0_35]),c_0_35]) ).
cnf(c_0_48,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,lemma,
set_difference(X1,set_union2(X2,X1)) = empty_set,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_50,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_51,negated_conjecture,
( set_difference(esk22_0,unordered_pair(esk23_0,esk23_0)) = esk22_0
| ~ in(esk23_0,esk22_0) ),
inference(rw,[status(thm)],[c_0_40,c_0_30]) ).
cnf(c_0_52,lemma,
( set_difference(unordered_pair(X1,X1),X2) = unordered_pair(X1,X1)
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_53,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_43,c_0_30]) ).
cnf(c_0_54,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_56,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_57,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_47,c_0_48]),c_0_49]),c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( set_difference(unordered_pair(esk23_0,esk23_0),esk22_0) = unordered_pair(esk23_0,esk23_0)
| set_difference(esk22_0,unordered_pair(esk23_0,esk23_0)) = esk22_0 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_60,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[c_0_54,c_0_30]) ).
cnf(c_0_61,negated_conjecture,
( in(esk23_0,esk22_0)
| set_difference(esk22_0,singleton(esk23_0)) != esk22_0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_62,plain,
( X1 = empty_set
| ~ in(esk2_1(X1),set_difference(X2,X1)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,lemma,
set_difference(esk22_0,unordered_pair(esk23_0,esk23_0)) = esk22_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_38]),c_0_48])]) ).
cnf(c_0_64,plain,
esk2_1(unordered_pair(X1,X1)) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_56]),c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( in(esk23_0,esk22_0)
| set_difference(esk22_0,unordered_pair(esk23_0,esk23_0)) != esk22_0 ),
inference(rw,[status(thm)],[c_0_61,c_0_30]) ).
cnf(c_0_66,lemma,
~ in(esk23_0,esk22_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_60]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_63])]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU162+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
% 0.15/0.33 % Computer : n025.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 02:46:28 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.74/1.88 % Version : CSE_E---1.7
% 1.74/1.88 % Problem : theBenchmark.p
% 1.74/1.88 % SZS status Theorem for theBenchmark.p
% 1.74/1.88 % SZS output start CNFRefutation
% See solution above
% 1.74/1.88 % Total time : 1.371s
%------------------------------------------------------------------------------