%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU144+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 : n024.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 05:10:46 PM UTC 2026
% Result : Theorem 1.15s 1.65s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 26 unt; 0 def)
% Number of atoms : 145 ( 60 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 136 ( 53 ~; 57 |; 14 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 108 ( 4 sgn 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l2_zfmisc_1,conjecture,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
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(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(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
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(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_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(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(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
inference(assume_negation,[status(cth)],[l2_zfmisc_1]) ).
fof(c_0_14,negated_conjecture,
( ( ~ subset(singleton(esk8_0),esk9_0)
| ~ in(esk8_0,esk9_0) )
& ( subset(singleton(esk8_0),esk9_0)
| in(esk8_0,esk9_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_15,lemma,
! [X273] : unordered_pair(X273,X273) = singleton(X273),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_16,lemma,
! [X217,X218] :
( ~ subset(X217,X218)
| set_union2(X217,X218) = X218 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(c_0_17,negated_conjecture,
( subset(singleton(esk8_0),esk9_0)
| in(esk8_0,esk9_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X137,X138] : set_union2(X137,X138) = set_union2(X138,X137),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_20,plain,
! [X143,X144,X145,X146,X147,X148] :
( ( ~ in(X145,X144)
| X145 = X143
| X144 != singleton(X143) )
& ( X146 != X143
| in(X146,X144)
| X144 != singleton(X143) )
& ( ~ in(esk1_2(X147,X148),X148)
| esk1_2(X147,X148) != X147
| X148 = singleton(X147) )
& ( in(esk1_2(X147,X148),X148)
| esk1_2(X147,X148) = X147
| X148 = singleton(X147) ) ),
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_21,negated_conjecture,
( ~ subset(singleton(esk8_0),esk9_0)
| ~ in(esk8_0,esk9_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( in(esk8_0,esk9_0)
| subset(unordered_pair(esk8_0,esk8_0),esk9_0) ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( ~ in(esk8_0,esk9_0)
| ~ subset(unordered_pair(esk8_0,esk8_0),esk9_0) ),
inference(rw,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( set_union2(esk9_0,unordered_pair(esk8_0,esk8_0)) = esk9_0
| in(esk8_0,esk9_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
fof(c_0_28,plain,
! [X172,X173,X174,X175,X176] :
( ( ~ subset(X172,X173)
| ~ in(X174,X172)
| in(X174,X173) )
& ( in(esk5_2(X175,X176),X175)
| subset(X175,X176) )
& ( ~ in(esk5_2(X175,X176),X176)
| subset(X175,X176) ) ),
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_29,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_30,negated_conjecture,
( set_union2(esk9_0,unordered_pair(esk8_0,esk8_0)) = esk9_0
| ~ subset(unordered_pair(esk8_0,esk8_0),esk9_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,lemma,
! [X277,X278] : subset(X277,set_union2(X277,X278)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_33,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( set_union2(esk9_0,unordered_pair(esk8_0,esk8_0)) = esk9_0
| in(esk5_2(unordered_pair(esk8_0,esk8_0),esk9_0),unordered_pair(esk8_0,esk8_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_35,plain,
! [X178,X179,X180,X181,X182,X183,X184,X185] :
( ( in(X181,X178)
| ~ in(X181,X180)
| X180 != set_intersection2(X178,X179) )
& ( in(X181,X179)
| ~ in(X181,X180)
| X180 != set_intersection2(X178,X179) )
& ( ~ in(X182,X178)
| ~ in(X182,X179)
| in(X182,X180)
| X180 != set_intersection2(X178,X179) )
& ( ~ in(esk6_3(X183,X184,X185),X185)
| ~ in(esk6_3(X183,X184,X185),X183)
| ~ in(esk6_3(X183,X184,X185),X184)
| X185 = set_intersection2(X183,X184) )
& ( in(esk6_3(X183,X184,X185),X183)
| in(esk6_3(X183,X184,X185),X185)
| X185 = set_intersection2(X183,X184) )
& ( in(esk6_3(X183,X184,X185),X184)
| in(esk6_3(X183,X184,X185),X185)
| X185 = set_intersection2(X183,X184) ) ),
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_xboole_0])])])])])]) ).
fof(c_0_36,lemma,
! [X259,X260] : set_difference(X259,set_difference(X259,X260)) = set_intersection2(X259,X260),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
cnf(c_0_37,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,negated_conjecture,
( set_union2(esk9_0,unordered_pair(esk8_0,esk8_0)) = esk9_0
| esk5_2(unordered_pair(esk8_0,esk8_0),esk9_0) = esk8_0 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_42,lemma,
! [X210,X211] :
( ( set_difference(X210,X211) != empty_set
| subset(X210,X211) )
& ( ~ subset(X210,X211)
| set_difference(X210,X211) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
cnf(c_0_43,lemma,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_24]) ).
cnf(c_0_44,negated_conjecture,
set_union2(esk9_0,unordered_pair(esk8_0,esk8_0)) = esk9_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_23]),c_0_30]) ).
fof(c_0_45,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_46,lemma,
! [X207] : singleton(X207) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_0_47,plain,
( in(X1,X2)
| X3 != set_difference(X4,set_difference(X4,X2))
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,lemma,
subset(unordered_pair(esk8_0,esk8_0),esk9_0),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_50,plain,
! [X247] : set_difference(X247,empty_set) = X247,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(c_0_51,plain,
! [X150,X151,X152] :
( ( X150 != empty_set
| ~ in(X151,X150) )
& ( in(esk2_1(X152),X152)
| X152 = 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_45])])])])]) ).
cnf(c_0_52,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X3,set_difference(X3,X2))) ),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_54,lemma,
set_difference(unordered_pair(esk8_0,esk8_0),esk9_0) = empty_set,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_56,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[c_0_52,c_0_18]) ).
cnf(c_0_58,lemma,
( in(X1,esk9_0)
| ~ in(X1,unordered_pair(esk8_0,esk8_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_59,plain,
esk2_1(unordered_pair(X1,X1)) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_56]),c_0_57]) ).
cnf(c_0_60,negated_conjecture,
~ in(esk8_0,esk9_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_49])]) ).
cnf(c_0_61,lemma,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_56]),c_0_59]),c_0_60]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU144+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.08 % 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
% 0.06/0.26 % Computer : n024.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Mon May 4 21:44:56 EDT 2026
% 0.06/0.26 % CPUTime :
% 0.06/0.27 % start to proof: theBenchmark
% 1.15/1.65 % Version : CSE_E---1.7
% 1.15/1.65 % Problem : theBenchmark.p
% 1.15/1.65 % SZS status Theorem for theBenchmark.p
% 1.15/1.65 % SZS output start CNFRefutation
% See solution above
% 1.15/1.65 % Total time : 1.362s
%------------------------------------------------------------------------------