TSTP Solution File: SET019^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET019^4 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n003.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 02:52:30 EDT 2024
% Result : Theorem 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 19
% Syntax : Number of formulae : 35 ( 16 unt; 12 typ; 0 def)
% Number of atoms : 77 ( 10 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 199 ( 17 ~; 14 |; 10 &; 146 @)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 38 ( 28 ^ 10 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_23,type,
mactual: mworld ).
thf(decl_24,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_26,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_28,type,
mimplies: ( 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_37,type,
equal_set: $i > $i > mworld > $o ).
thf(decl_39,type,
subset: $i > $i > mworld > $o ).
thf(decl_52,type,
esk5_0: $i ).
thf(decl_53,type,
esk6_0: $i ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(mand_def,axiom,
( mand
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
& ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_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/sandbox/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/sandbox/benchmark/theBenchmark.p',mequiv_def) ).
thf(thI02,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X65: $i] :
( mforall_di
@ ^ [X66: $i] : ( mimplies @ ( mand @ ( subset @ X65 @ X66 ) @ ( subset @ X66 @ X65 ) ) @ ( equal_set @ X65 @ X66 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI02) ).
thf(equal_set_0,axiom,
( mlocal
@ ( mforall_di
@ ^ [X50: $i] :
( mforall_di
@ ^ [X51: $i] : ( mequiv @ ( equal_set @ X50 @ X51 ) @ ( mand @ ( subset @ X50 @ X51 ) @ ( subset @ X51 @ X50 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set_0) ).
thf(c_0_7,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_8,plain,
( mand
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand_def]) ).
thf(c_0_9,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_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,negated_conjecture,
~ ! [X158: $i] :
( ( eiw_di @ X158 @ mactual )
=> ! [X157: $i] :
( ( eiw_di @ X157 @ mactual )
=> ( ( ( subset @ X158 @ X157 @ mactual )
& ( subset @ X157 @ X158 @ mactual ) )
=> ( equal_set @ X158 @ X157 @ mactual ) ) ) ),
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)],[inference(assume_negation,[status(cth)],[thI02])]),c_0_7]),c_0_8]),c_0_9]),c_0_10]) ).
thf(c_0_13,plain,
! [X133: $i] :
( ( eiw_di @ X133 @ mactual )
=> ! [X132: $i] :
( ( eiw_di @ X132 @ mactual )
=> ( ( equal_set @ X133 @ X132 @ mactual )
<=> ( ( subset @ X133 @ X132 @ mactual )
& ( subset @ X132 @ X133 @ mactual ) ) ) ) ),
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)],[equal_set_0]),c_0_7]),c_0_8]),c_0_11]),c_0_10]) ).
thf(c_0_14,negated_conjecture,
( ( eiw_di @ esk5_0 @ mactual )
& ( eiw_di @ esk6_0 @ mactual )
& ( subset @ esk5_0 @ esk6_0 @ mactual )
& ( subset @ esk6_0 @ esk5_0 @ mactual )
& ~ ( equal_set @ esk5_0 @ esk6_0 @ mactual ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
thf(c_0_15,plain,
! [X225: $i,X226: $i] :
( ( ( subset @ X225 @ X226 @ mactual )
| ~ ( equal_set @ X225 @ X226 @ mactual )
| ~ ( eiw_di @ X226 @ mactual )
| ~ ( eiw_di @ X225 @ mactual ) )
& ( ( subset @ X226 @ X225 @ mactual )
| ~ ( equal_set @ X225 @ X226 @ mactual )
| ~ ( eiw_di @ X226 @ mactual )
| ~ ( eiw_di @ X225 @ mactual ) )
& ( ~ ( subset @ X225 @ X226 @ mactual )
| ~ ( subset @ X226 @ X225 @ mactual )
| ( equal_set @ X225 @ X226 @ mactual )
| ~ ( eiw_di @ X226 @ mactual )
| ~ ( eiw_di @ X225 @ 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_13])])])])]) ).
thf(c_0_16,negated_conjecture,
~ ( equal_set @ esk5_0 @ esk6_0 @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,plain,
! [X9: $i,X6: $i] :
( ( equal_set @ X6 @ X9 @ mactual )
| ~ ( subset @ X6 @ X9 @ mactual )
| ~ ( subset @ X9 @ X6 @ mactual )
| ~ ( eiw_di @ X9 @ mactual )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
subset @ esk6_0 @ esk5_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
subset @ esk5_0 @ esk6_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,negated_conjecture,
eiw_di @ esk6_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_21,negated_conjecture,
eiw_di @ esk5_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET019^4 : TPTP v8.2.0. Released v8.1.0.
% 0.11/0.14 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 20 11:23:22 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.18/0.47 Running higher-order theorem proving
% 0.18/0.47 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.18/0.49 # Version: 3.1.0-ho
% 0.18/0.49 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.18/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.49 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.49 # Starting post_as_ho3 with 300s (1) cores
% 0.18/0.49 # Starting new_ho_12 with 300s (1) cores
% 0.18/0.49 # Starting new_bool_2 with 300s (1) cores
% 0.18/0.49 # new_ho_10_cnf2 with pid 4186 completed with status 0
% 0.18/0.49 # Result found by new_ho_10_cnf2
% 0.18/0.49 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.18/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.49 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.49 # No SInE strategy applied
% 0.18/0.49 # Search class: HGHNS-FFMS21-SHSSMFNN
% 0.18/0.49 # partial match(2): HGUNS-FFMF21-SHSSMFNN
% 0.18/0.49 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.49 # Starting new_ho_10 with 811s (1) cores
% 0.18/0.49 # Starting new_ho_10_cnf2 with 151s (1) cores
% 0.18/0.49 # Starting ho_unfolding_6 with 136s (1) cores
% 0.18/0.49 # Starting sh4l with 136s (1) cores
% 0.18/0.49 # Starting ehoh_best_nonlift_rwall with 136s (1) cores
% 0.18/0.49 # ho_unfolding_6 with pid 4196 completed with status 0
% 0.18/0.49 # Result found by ho_unfolding_6
% 0.18/0.49 # Preprocessing class: HSMSSMSSMLLNHSN.
% 0.18/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.50 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.50 # No SInE strategy applied
% 0.18/0.50 # Search class: HGHNS-FFMS21-SHSSMFNN
% 0.18/0.50 # partial match(2): HGUNS-FFMF21-SHSSMFNN
% 0.18/0.50 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.50 # Starting new_ho_10 with 811s (1) cores
% 0.18/0.50 # Starting new_ho_10_cnf2 with 151s (1) cores
% 0.18/0.50 # Starting ho_unfolding_6 with 136s (1) cores
% 0.18/0.50 # Preprocessing time : 0.002 s
% 0.18/0.50
% 0.18/0.50 # Proof found!
% 0.18/0.50 # SZS status Theorem
% 0.18/0.50 # SZS output start CNFRefutation
% See solution above
% 0.18/0.50 # Parsed axioms : 73
% 0.18/0.50 # Removed by relevancy pruning/SinE : 0
% 0.18/0.50 # Initial clauses : 88
% 0.18/0.50 # Removed in clause preprocessing : 27
% 0.18/0.50 # Initial clauses in saturation : 61
% 0.18/0.50 # Processed clauses : 14
% 0.18/0.50 # ...of these trivial : 0
% 0.18/0.50 # ...subsumed : 0
% 0.18/0.50 # ...remaining for further processing : 14
% 0.18/0.50 # Other redundant clauses eliminated : 0
% 0.18/0.50 # Clauses deleted for lack of memory : 0
% 0.18/0.50 # Backward-subsumed : 0
% 0.18/0.50 # Backward-rewritten : 0
% 0.18/0.50 # Generated clauses : 9
% 0.18/0.50 # ...of the previous two non-redundant : 6
% 0.18/0.50 # ...aggressively subsumed : 0
% 0.18/0.50 # Contextual simplify-reflections : 0
% 0.18/0.50 # Paramodulations : 9
% 0.18/0.50 # Factorizations : 0
% 0.18/0.50 # NegExts : 0
% 0.18/0.50 # Equation resolutions : 0
% 0.18/0.50 # Disequality decompositions : 0
% 0.18/0.50 # Total rewrite steps : 4
% 0.18/0.50 # ...of those cached : 0
% 0.18/0.50 # Propositional unsat checks : 0
% 0.18/0.50 # Propositional check models : 0
% 0.18/0.50 # Propositional check unsatisfiable : 0
% 0.18/0.50 # Propositional clauses : 0
% 0.18/0.50 # Propositional clauses after purity: 0
% 0.18/0.50 # Propositional unsat core size : 0
% 0.18/0.50 # Propositional preprocessing time : 0.000
% 0.18/0.50 # Propositional encoding time : 0.000
% 0.18/0.50 # Propositional solver time : 0.000
% 0.18/0.50 # Success case prop preproc time : 0.000
% 0.18/0.50 # Success case prop encoding time : 0.000
% 0.18/0.50 # Success case prop solver time : 0.000
% 0.18/0.50 # Current number of processed clauses : 14
% 0.18/0.50 # Positive orientable unit clauses : 6
% 0.18/0.50 # Positive unorientable unit clauses: 0
% 0.18/0.50 # Negative unit clauses : 1
% 0.18/0.50 # Non-unit-clauses : 7
% 0.18/0.50 # Current number of unprocessed clauses: 53
% 0.18/0.50 # ...number of literals in the above : 247
% 0.18/0.50 # Current number of archived formulas : 0
% 0.18/0.50 # Current number of archived clauses : 0
% 0.18/0.50 # Clause-clause subsumption calls (NU) : 20
% 0.18/0.50 # Rec. Clause-clause subsumption calls : 3
% 0.18/0.50 # Non-unit clause-clause subsumptions : 0
% 0.18/0.50 # Unit Clause-clause subsumption calls : 0
% 0.18/0.50 # Rewrite failures with RHS unbound : 0
% 0.18/0.50 # BW rewrite match attempts : 0
% 0.18/0.50 # BW rewrite match successes : 0
% 0.18/0.50 # Condensation attempts : 14
% 0.18/0.50 # Condensation successes : 0
% 0.18/0.50 # Termbank termtop insertions : 14561
% 0.18/0.50 # Search garbage collected termcells : 5890
% 0.18/0.50
% 0.18/0.50 # -------------------------------------------------
% 0.18/0.50 # User time : 0.012 s
% 0.18/0.50 # System time : 0.005 s
% 0.18/0.50 # Total time : 0.017 s
% 0.18/0.50 # Maximum resident set size: 2772 pages
% 0.18/0.50
% 0.18/0.50 # -------------------------------------------------
% 0.18/0.50 # User time : 0.025 s
% 0.18/0.50 # System time : 0.015 s
% 0.18/0.50 # Total time : 0.040 s
% 0.18/0.50 # Maximum resident set size: 1832 pages
% 0.18/0.50 % E---3.1 exiting
% 0.18/0.50 % E exiting
%------------------------------------------------------------------------------