%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU162+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %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 : 600s
% DateTime : Tue Jul 19 09:17:19 EDT 2022
% Result : Theorem 0.25s 1.43s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 20 unt; 0 def)
% Number of atoms : 86 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 73 ( 35 ~; 23 |; 8 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 9 sgn 48 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_boole) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t48_xboole_1) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t4_xboole_0) ).
fof(t65_zfmisc_1,conjecture,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t65_zfmisc_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t3_boole) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t3_xboole_1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l2_zfmisc_1) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l1_zfmisc_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',symmetry_r1_xboole_0) ).
fof(l28_zfmisc_1,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l28_zfmisc_1) ).
fof(t83_xboole_1,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t83_xboole_1) ).
fof(l25_zfmisc_1,lemma,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l25_zfmisc_1) ).
fof(c_0_12,plain,
! [X2] : set_intersection2(X2,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(c_0_13,lemma,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_14,lemma,
! [X4,X5,X4,X5,X7] :
( ( disjoint(X4,X5)
| in(esk10_2(X4,X5),set_intersection2(X4,X5)) )
& ( ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t4_xboole_0])])])])])])]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(assume_negation,[status(cth)],[t65_zfmisc_1]) ).
cnf(c_0_16,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(c_0_19,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(c_0_20,lemma,
! [X3,X4,X3,X4] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X3,X4)
| subset(singleton(X3),X4) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])])])]) ).
fof(c_0_21,lemma,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_0_22,lemma,
( in(esk10_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_23,negated_conjecture,
( ( set_difference(esk1_0,singleton(esk2_0)) != esk1_0
| in(esk2_0,esk1_0) )
& ( set_difference(esk1_0,singleton(esk2_0)) = esk1_0
| ~ in(esk2_0,esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_24,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
cnf(c_0_30,lemma,
( disjoint(X1,X2)
| in(esk10_2(X1,X2),set_difference(X1,set_difference(X1,X2))) ),
inference(rw,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_31,negated_conjecture,
( set_difference(esk1_0,singleton(esk2_0)) = esk1_0
| ~ in(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
set_difference(X1,X1) = empty_set,
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,lemma,
~ in(X1,empty_set),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
fof(c_0_34,lemma,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[l28_zfmisc_1])])]) ).
cnf(c_0_35,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( disjoint(esk1_0,singleton(esk2_0))
| ~ in(esk2_0,esk1_0) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_37,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_38,lemma,
! [X3,X4,X3,X4] :
( ( ~ disjoint(X3,X4)
| set_difference(X3,X4) = X3 )
& ( set_difference(X3,X4) != X3
| disjoint(X3,X4) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])])])]) ).
cnf(c_0_39,negated_conjecture,
disjoint(singleton(esk2_0),esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
fof(c_0_40,lemma,
! [X3,X4] :
( ~ disjoint(singleton(X3),X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l25_zfmisc_1])]) ).
cnf(c_0_41,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,negated_conjecture,
disjoint(esk1_0,singleton(esk2_0)),
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_43,lemma,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( in(esk2_0,esk1_0)
| set_difference(esk1_0,singleton(esk2_0)) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_45,lemma,
set_difference(esk1_0,singleton(esk2_0)) = esk1_0,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,lemma,
~ in(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_43,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU162+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 01:06:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.25/1.43 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.25/1.43 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.25/1.43 # Preprocessing time : 0.020 s
% 0.25/1.43
% 0.25/1.43 # Proof found!
% 0.25/1.43 # SZS status Theorem
% 0.25/1.43 # SZS output start CNFRefutation
% See solution above
% 0.25/1.43 # Proof object total steps : 48
% 0.25/1.43 # Proof object clause steps : 23
% 0.25/1.43 # Proof object formula steps : 25
% 0.25/1.43 # Proof object conjectures : 9
% 0.25/1.43 # Proof object clause conjectures : 6
% 0.25/1.43 # Proof object formula conjectures : 3
% 0.25/1.43 # Proof object initial clauses used : 13
% 0.25/1.43 # Proof object initial formulas used : 12
% 0.25/1.43 # Proof object generating inferences : 6
% 0.25/1.43 # Proof object simplifying inferences : 10
% 0.25/1.43 # Training examples: 0 positive, 0 negative
% 0.25/1.43 # Parsed axioms : 92
% 0.25/1.43 # Removed by relevancy pruning/SinE : 38
% 0.25/1.43 # Initial clauses : 92
% 0.25/1.43 # Removed in clause preprocessing : 1
% 0.25/1.43 # Initial clauses in saturation : 91
% 0.25/1.43 # Processed clauses : 113
% 0.25/1.43 # ...of these trivial : 5
% 0.25/1.43 # ...subsumed : 14
% 0.25/1.43 # ...remaining for further processing : 94
% 0.25/1.43 # Other redundant clauses eliminated : 20
% 0.25/1.43 # Clauses deleted for lack of memory : 0
% 0.25/1.43 # Backward-subsumed : 2
% 0.25/1.43 # Backward-rewritten : 2
% 0.25/1.43 # Generated clauses : 526
% 0.25/1.43 # ...of the previous two non-trivial : 386
% 0.25/1.43 # Contextual simplify-reflections : 1
% 0.25/1.43 # Paramodulations : 482
% 0.25/1.43 # Factorizations : 14
% 0.25/1.43 # Equation resolutions : 30
% 0.25/1.43 # Current number of processed clauses : 87
% 0.25/1.43 # Positive orientable unit clauses : 19
% 0.25/1.43 # Positive unorientable unit clauses: 2
% 0.25/1.43 # Negative unit clauses : 3
% 0.25/1.43 # Non-unit-clauses : 63
% 0.25/1.43 # Current number of unprocessed clauses: 336
% 0.25/1.43 # ...number of literals in the above : 867
% 0.25/1.43 # Current number of archived formulas : 0
% 0.25/1.43 # Current number of archived clauses : 5
% 0.25/1.43 # Clause-clause subsumption calls (NU) : 481
% 0.25/1.43 # Rec. Clause-clause subsumption calls : 365
% 0.25/1.43 # Non-unit clause-clause subsumptions : 12
% 0.25/1.43 # Unit Clause-clause subsumption calls : 70
% 0.25/1.43 # Rewrite failures with RHS unbound : 0
% 0.25/1.43 # BW rewrite match attempts : 15
% 0.25/1.43 # BW rewrite match successes : 10
% 0.25/1.43 # Condensation attempts : 0
% 0.25/1.43 # Condensation successes : 0
% 0.25/1.43 # Termbank termtop insertions : 9435
% 0.25/1.43
% 0.25/1.43 # -------------------------------------------------
% 0.25/1.43 # User time : 0.029 s
% 0.25/1.43 # System time : 0.002 s
% 0.25/1.43 # Total time : 0.031 s
% 0.25/1.43 # Maximum resident set size: 3424 pages
%------------------------------------------------------------------------------