TSTP Solution File: SET926^20 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET926^20 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.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 21 02:56:33 EDT 2024
% Result : Theorem 0.21s 0.50s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 23
% Syntax : Number of formulae : 42 ( 16 unt; 15 typ; 0 def)
% Number of atoms : 87 ( 10 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 288 ( 26 ~; 21 |; 5 &; 224 @)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 44 ( 28 ^ 16 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_23,type,
mactual: mworld ).
thf(decl_24,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_25,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(decl_27,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_29,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_32,type,
eiw_di: $i > mworld > $o ).
thf(decl_33,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_35,type,
empty_set: $i ).
thf(decl_36,type,
qmltpeq: $i > $i > mworld > $o ).
thf(decl_37,type,
in: $i > $i > mworld > $o ).
thf(decl_39,type,
singleton: $i > $i ).
thf(decl_40,type,
set_difference: $i > $i > $i ).
thf(decl_44,type,
esk4_0: $i ).
thf(decl_45,type,
esk5_0: $i ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(mor_def,axiom,
( mor
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
| ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_def) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X7: $i > mworld > $o,X3: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ X3 )
=> ( X7 @ X6 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(mequiv_def,axiom,
( mequiv
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
<=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(mnot_def,axiom,
( mnot
= ( ^ [X2: mworld > $o,X3: mworld] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(t69_zfmisc_1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X32: $i] :
( mforall_di
@ ^ [X33: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X32 ) @ X33 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X32 ) @ X33 ) @ ( singleton @ X32 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(l36_zfmisc_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [X28: $i] :
( mforall_di
@ ^ [X29: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X28 ) @ X29 ) @ empty_set ) @ ( in @ X28 @ X29 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(l34_zfmisc_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [X26: $i] :
( mforall_di
@ ^ [X27: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X26 ) @ X27 ) @ ( singleton @ X26 ) ) @ ( mnot @ ( in @ X26 @ X27 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(c_0_8,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_9,plain,
( mor
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor_def]) ).
thf(c_0_10,plain,
( mforall_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ Z1 )
=> ( Z0 @ X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_11,plain,
( mequiv
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
<=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv_def]) ).
thf(c_0_12,plain,
( mnot
= ( ^ [Z0: mworld > $o,Z1: mworld] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot_def]) ).
thf(c_0_13,negated_conjecture,
~ ! [X71: $i] :
( ( eiw_di @ X71 @ mactual )
=> ! [X70: $i] :
( ( eiw_di @ X70 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X71 ) @ X70 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ X71 ) @ X70 ) @ ( singleton @ X71 ) @ mactual ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t69_zfmisc_1])]),c_0_8]),c_0_9]),c_0_10]) ).
thf(c_0_14,plain,
! [X67: $i] :
( ( eiw_di @ X67 @ mactual )
=> ! [X66: $i] :
( ( eiw_di @ X66 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X67 ) @ X66 ) @ empty_set @ mactual )
<=> ( in @ X67 @ X66 @ mactual ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[l36_zfmisc_1]),c_0_8]),c_0_11]),c_0_10]) ).
thf(c_0_15,plain,
! [X65: $i] :
( ( eiw_di @ X65 @ mactual )
=> ! [X64: $i] :
( ( eiw_di @ X64 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X65 ) @ X64 ) @ ( singleton @ X65 ) @ mactual )
<=> ~ ( in @ X65 @ X64 @ mactual ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[l34_zfmisc_1]),c_0_8]),c_0_12]),c_0_11]),c_0_10])]) ).
thf(c_0_16,negated_conjecture,
( ( eiw_di @ esk4_0 @ mactual )
& ( eiw_di @ esk5_0 @ mactual )
& ~ ( qmltpeq @ ( set_difference @ ( singleton @ esk4_0 ) @ esk5_0 ) @ empty_set @ mactual )
& ~ ( qmltpeq @ ( set_difference @ ( singleton @ esk4_0 ) @ esk5_0 ) @ ( singleton @ esk4_0 ) @ mactual ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
thf(c_0_17,plain,
! [X104: $i,X105: $i] :
( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X104 ) @ X105 ) @ empty_set @ mactual )
| ( in @ X104 @ X105 @ mactual )
| ~ ( eiw_di @ X105 @ mactual )
| ~ ( eiw_di @ X104 @ mactual ) )
& ( ~ ( in @ X104 @ X105 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ X104 ) @ X105 ) @ empty_set @ mactual )
| ~ ( eiw_di @ X105 @ mactual )
| ~ ( eiw_di @ X104 @ mactual ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
thf(c_0_18,plain,
! [X102: $i,X103: $i] :
( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X102 ) @ X103 ) @ ( singleton @ X102 ) @ mactual )
| ~ ( in @ X102 @ X103 @ mactual )
| ~ ( eiw_di @ X103 @ mactual )
| ~ ( eiw_di @ X102 @ mactual ) )
& ( ( in @ X102 @ X103 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ X102 ) @ X103 ) @ ( singleton @ X102 ) @ mactual )
| ~ ( eiw_di @ X103 @ mactual )
| ~ ( eiw_di @ X102 @ mactual ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
thf(c_0_19,negated_conjecture,
~ ( qmltpeq @ ( set_difference @ ( singleton @ esk4_0 ) @ esk5_0 ) @ empty_set @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_20,plain,
! [X9: $i,X6: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X9 ) @ empty_set @ mactual )
| ~ ( in @ X6 @ X9 @ mactual )
| ~ ( eiw_di @ X9 @ mactual )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,negated_conjecture,
eiw_di @ esk5_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,negated_conjecture,
eiw_di @ esk4_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_23,negated_conjecture,
~ ( qmltpeq @ ( set_difference @ ( singleton @ esk4_0 ) @ esk5_0 ) @ ( singleton @ esk4_0 ) @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_24,plain,
! [X9: $i,X6: $i] :
( ( in @ X6 @ X9 @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X9 ) @ ( singleton @ X6 ) @ mactual )
| ~ ( eiw_di @ X9 @ mactual )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_25,negated_conjecture,
~ ( in @ esk4_0 @ esk5_0 @ mactual ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]),c_0_22])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET926^20 : TPTP v8.2.0. Released v8.1.0.
% 0.12/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n017.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 : 300
% 0.13/0.35 % DateTime : Mon May 20 11:05:53 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.21/0.48 Running higher-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.50 # Version: 3.1.0-ho
% 0.21/0.50 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.21/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.50 # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.50 # Starting new_ho_12 with 300s (1) cores
% 0.21/0.50 # Starting new_bool_2 with 300s (1) cores
% 0.21/0.50 # post_as_ho3 with pid 31709 completed with status 0
% 0.21/0.50 # Result found by post_as_ho3
% 0.21/0.50 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.21/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.50 # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.50 # No SInE strategy applied
% 0.21/0.50 # Search class: HGHNS-FFMM21-SHSSMFNN
% 0.21/0.50 # partial match(2): HGUNS-FFMF21-SHSSMFNN
% 0.21/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.50 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.50 # new_ho_10 with pid 31715 completed with status 0
% 0.21/0.50 # Result found by new_ho_10
% 0.21/0.50 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.21/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.50 # Starting post_as_ho3 with 300s (1) cores
% 0.21/0.50 # No SInE strategy applied
% 0.21/0.50 # Search class: HGHNS-FFMM21-SHSSMFNN
% 0.21/0.50 # partial match(2): HGUNS-FFMF21-SHSSMFNN
% 0.21/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.50 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.50 # Preprocessing time : 0.001 s
% 0.21/0.50 # Presaturation interreduction done
% 0.21/0.50
% 0.21/0.50 # Proof found!
% 0.21/0.50 # SZS status Theorem
% 0.21/0.50 # SZS output start CNFRefutation
% See solution above
% 0.21/0.50 # Parsed axioms : 49
% 0.21/0.50 # Removed by relevancy pruning/SinE : 0
% 0.21/0.50 # Initial clauses : 46
% 0.21/0.50 # Removed in clause preprocessing : 20
% 0.21/0.50 # Initial clauses in saturation : 26
% 0.21/0.50 # Processed clauses : 49
% 0.21/0.50 # ...of these trivial : 0
% 0.21/0.50 # ...subsumed : 1
% 0.21/0.50 # ...remaining for further processing : 48
% 0.21/0.50 # Other redundant clauses eliminated : 0
% 0.21/0.50 # Clauses deleted for lack of memory : 0
% 0.21/0.50 # Backward-subsumed : 0
% 0.21/0.50 # Backward-rewritten : 0
% 0.21/0.50 # Generated clauses : 13
% 0.21/0.50 # ...of the previous two non-redundant : 7
% 0.21/0.50 # ...aggressively subsumed : 0
% 0.21/0.50 # Contextual simplify-reflections : 0
% 0.21/0.50 # Paramodulations : 13
% 0.21/0.50 # Factorizations : 0
% 0.21/0.50 # NegExts : 0
% 0.21/0.50 # Equation resolutions : 0
% 0.21/0.50 # Disequality decompositions : 0
% 0.21/0.50 # Total rewrite steps : 5
% 0.21/0.50 # ...of those cached : 2
% 0.21/0.50 # Propositional unsat checks : 0
% 0.21/0.50 # Propositional check models : 0
% 0.21/0.50 # Propositional check unsatisfiable : 0
% 0.21/0.50 # Propositional clauses : 0
% 0.21/0.50 # Propositional clauses after purity: 0
% 0.21/0.50 # Propositional unsat core size : 0
% 0.21/0.50 # Propositional preprocessing time : 0.000
% 0.21/0.50 # Propositional encoding time : 0.000
% 0.21/0.50 # Propositional solver time : 0.000
% 0.21/0.50 # Success case prop preproc time : 0.000
% 0.21/0.50 # Success case prop encoding time : 0.000
% 0.21/0.50 # Success case prop solver time : 0.000
% 0.21/0.50 # Current number of processed clauses : 22
% 0.21/0.50 # Positive orientable unit clauses : 8
% 0.21/0.50 # Positive unorientable unit clauses: 0
% 0.21/0.50 # Negative unit clauses : 4
% 0.21/0.50 # Non-unit-clauses : 10
% 0.21/0.50 # Current number of unprocessed clauses: 8
% 0.21/0.50 # ...number of literals in the above : 47
% 0.21/0.50 # Current number of archived formulas : 0
% 0.21/0.50 # Current number of archived clauses : 26
% 0.21/0.50 # Clause-clause subsumption calls (NU) : 112
% 0.21/0.50 # Rec. Clause-clause subsumption calls : 45
% 0.21/0.50 # Non-unit clause-clause subsumptions : 1
% 0.21/0.50 # Unit Clause-clause subsumption calls : 4
% 0.21/0.50 # Rewrite failures with RHS unbound : 0
% 0.21/0.50 # BW rewrite match attempts : 0
% 0.21/0.50 # BW rewrite match successes : 0
% 0.21/0.50 # Condensation attempts : 49
% 0.21/0.50 # Condensation successes : 0
% 0.21/0.50 # Termbank termtop insertions : 6160
% 0.21/0.50 # Search garbage collected termcells : 2063
% 0.21/0.50
% 0.21/0.50 # -------------------------------------------------
% 0.21/0.50 # User time : 0.009 s
% 0.21/0.50 # System time : 0.002 s
% 0.21/0.50 # Total time : 0.011 s
% 0.21/0.50 # Maximum resident set size: 2140 pages
% 0.21/0.50
% 0.21/0.50 # -------------------------------------------------
% 0.21/0.50 # User time : 0.011 s
% 0.21/0.50 # System time : 0.004 s
% 0.21/0.50 # Total time : 0.015 s
% 0.21/0.50 # Maximum resident set size: 1784 pages
% 0.21/0.50 % E---3.1 exiting
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------