%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU146+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n005.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 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 68 ( 22 unt; 0 def)
% Number of atoms : 178 ( 69 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 182 ( 72 ~; 69 |; 31 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 7 sgn 73 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
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/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(l4_zfmisc_1,conjecture,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_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(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
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(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(c_0_14,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_15,lemma,
! [X272,X273,X275,X276,X277] :
( ( disjoint(X272,X273)
| in(esk14_2(X272,X273),set_intersection2(X272,X273)) )
& ( ~ in(X277,set_intersection2(X275,X276))
| ~ disjoint(X275,X276) ) ),
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_14])])])])]) ).
fof(c_0_16,lemma,
! [X269,X270] : set_difference(X269,set_difference(X269,X270)) = set_intersection2(X269,X270),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_17,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_18,plain,
! [X243] : set_intersection2(X243,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
cnf(c_0_19,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,lemma,
! [X258,X259,X261,X262,X263] :
( ( in(esk13_2(X258,X259),X258)
| disjoint(X258,X259) )
& ( in(esk13_2(X258,X259),X259)
| disjoint(X258,X259) )
& ( ~ in(X263,X261)
| ~ in(X263,X262)
| ~ disjoint(X261,X262) ) ),
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_17])])])])])]) ).
cnf(c_0_22,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X257] : set_difference(X257,empty_set) = X257,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_24,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,lemma,
( in(esk13_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_27,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_28,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_29,lemma,
( in(esk13_2(X1,X2),X2)
| ~ in(X3,set_difference(X1,set_difference(X1,X2))) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
set_difference(X1,X1) = empty_set,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_31,plain,
! [X155,X156,X157] :
( ( X155 != empty_set
| ~ in(X156,X155) )
& ( in(esk2_1(X157),X157)
| X157 = 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_28])])])])]) ).
fof(c_0_32,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
inference(assume_negation,[status(cth)],[l4_zfmisc_1]) ).
fof(c_0_33,plain,
! [X148,X149,X150,X151,X152,X153] :
( ( ~ in(X150,X149)
| X150 = X148
| X149 != singleton(X148) )
& ( X151 != X148
| in(X151,X149)
| X149 != singleton(X148) )
& ( ~ in(esk1_2(X152,X153),X153)
| esk1_2(X152,X153) != X152
| X153 = singleton(X152) )
& ( in(esk1_2(X152,X153),X153)
| esk1_2(X152,X153) = X152
| X153 = singleton(X152) ) ),
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_34,lemma,
! [X283] : unordered_pair(X283,X283) = singleton(X283),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_35,plain,
! [X177,X178,X179,X180,X181] :
( ( ~ subset(X177,X178)
| ~ in(X179,X177)
| in(X179,X178) )
& ( in(esk5_2(X180,X181),X180)
| subset(X180,X181) )
& ( ~ in(esk5_2(X180,X181),X181)
| subset(X180,X181) ) ),
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_36,lemma,
( in(esk13_2(X1,X1),X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27]) ).
cnf(c_0_37,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_38,negated_conjecture,
( ( esk8_0 != empty_set
| ~ subset(esk8_0,singleton(esk9_0)) )
& ( esk8_0 != singleton(esk9_0)
| ~ subset(esk8_0,singleton(esk9_0)) )
& ( subset(esk8_0,singleton(esk9_0))
| esk8_0 = empty_set
| esk8_0 = singleton(esk9_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])]) ).
cnf(c_0_39,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,lemma,
( X1 = empty_set
| in(esk13_2(X1,X1),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( subset(esk8_0,singleton(esk9_0))
| esk8_0 = empty_set
| esk8_0 = singleton(esk9_0) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,lemma,
( X1 = empty_set
| in(esk13_2(X1,X1),X2)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( esk8_0 = empty_set
| esk8_0 = unordered_pair(esk9_0,esk9_0)
| subset(esk8_0,unordered_pair(esk9_0,esk9_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_40]),c_0_40]) ).
fof(c_0_47,lemma,
! [X213,X214] :
( ( ~ subset(singleton(X213),X214)
| in(X213,X214) )
& ( ~ in(X213,X214)
| subset(singleton(X213),X214) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
cnf(c_0_48,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = esk8_0
| esk8_0 = empty_set
| in(esk13_2(esk8_0,esk8_0),unordered_pair(esk9_0,esk9_0)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_50,plain,
! [X146,X147] :
( ( subset(X146,X147)
| X146 != X147 )
& ( subset(X147,X146)
| X146 != X147 )
& ( ~ subset(X146,X147)
| ~ subset(X147,X146)
| X146 = X147 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_51,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = esk8_0
| esk13_2(esk8_0,esk8_0) = esk9_0
| esk8_0 = empty_set ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( esk8_0 != singleton(esk9_0)
| ~ subset(esk8_0,singleton(esk9_0)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_55,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_51,c_0_40]) ).
cnf(c_0_56,lemma,
( unordered_pair(esk9_0,esk9_0) = esk8_0
| esk8_0 = empty_set
| in(esk9_0,esk8_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_52]) ).
cnf(c_0_57,negated_conjecture,
( unordered_pair(esk9_0,esk9_0) = esk8_0
| esk8_0 = empty_set
| ~ subset(unordered_pair(esk9_0,esk9_0),esk8_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_46]) ).
fof(c_0_58,plain,
! [X224] : subset(X224,X224),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_59,negated_conjecture,
( esk8_0 != empty_set
| ~ subset(esk8_0,singleton(esk9_0)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_60,negated_conjecture,
( esk8_0 != unordered_pair(esk9_0,esk9_0)
| ~ subset(esk8_0,unordered_pair(esk9_0,esk9_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_40]),c_0_40]) ).
cnf(c_0_61,lemma,
( unordered_pair(esk9_0,esk9_0) = esk8_0
| esk8_0 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
cnf(c_0_62,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_63,lemma,
! [X247] : subset(empty_set,X247),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_64,negated_conjecture,
( esk8_0 != empty_set
| ~ subset(esk8_0,unordered_pair(esk9_0,esk9_0)) ),
inference(rw,[status(thm)],[c_0_59,c_0_40]) ).
cnf(c_0_65,negated_conjecture,
esk8_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_66,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_65]),c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU146+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n005.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 03:08:30 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------