TSTP Solution File: SET027^3 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET027^3 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n026.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 02:52:35 EDT 2024
% Result : Theorem 0.21s 0.49s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 20
% Syntax : Number of formulae : 40 ( 14 unt; 13 typ; 0 def)
% Number of atoms : 73 ( 10 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 199 ( 13 ~; 12 |; 7 &; 160 @)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 54 ( 30 ^ 24 !; 0 ?; 54 :)
% 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,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_34,type,
member: $i > $i > mworld > $o ).
thf(decl_35,type,
subset: $i > $i > mworld > $o ).
thf(decl_36,type,
esk1_0: $i ).
thf(decl_37,type,
esk2_0: $i ).
thf(decl_38,type,
esk3_0: $i ).
thf(decl_39,type,
esk4_2: $i > $i > $i ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_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(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X6: $i > mworld > $o,X3: mworld] :
! [X7: $i] : ( X6 @ X7 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(mand_def,axiom,
( mand
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
& ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(subset_defn,axiom,
( mlocal
@ ( mforall_di
@ ^ [X9: $i] :
( mforall_di
@ ^ [X10: $i] :
( mequiv @ ( subset @ X9 @ X10 )
@ ( mforall_di
@ ^ [X11: $i] : ( mimplies @ ( member @ X11 @ X9 ) @ ( member @ X11 @ X10 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(prove_transitivity_of_subset,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X13: $i] :
( mforall_di
@ ^ [X10: $i] :
( mforall_di
@ ^ [X11: $i] : ( mimplies @ ( mand @ ( subset @ X13 @ X10 ) @ ( subset @ X10 @ X11 ) ) @ ( subset @ X13 @ X11 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).
thf(c_0_7,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_8,plain,
( mequiv
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
<=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv_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] :
! [X7: $i] : ( Z0 @ X7 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_11,plain,
( mand
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand_def]) ).
thf(c_0_12,plain,
! [X19: $i,X18: $i] :
( ( subset @ X19 @ X18 @ mactual )
<=> ! [X17: $i] :
( ( member @ X17 @ X19 @ mactual )
=> ( member @ X17 @ X18 @ 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)],[subset_defn]),c_0_7]),c_0_8]),c_0_9]),c_0_10]) ).
thf(c_0_13,negated_conjecture,
~ ! [X16: $i,X15: $i,X14: $i] :
( ( ( subset @ X16 @ X15 @ mactual )
& ( subset @ X15 @ X14 @ mactual ) )
=> ( subset @ X16 @ X14 @ 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)],[prove_transitivity_of_subset])]),c_0_7]),c_0_11]),c_0_9]),c_0_10]) ).
thf(c_0_14,plain,
! [X24: $i,X25: $i,X26: $i,X27: $i,X28: $i] :
( ( ~ ( subset @ X24 @ X25 @ mactual )
| ~ ( member @ X26 @ X24 @ mactual )
| ( member @ X26 @ X25 @ mactual ) )
& ( ( member @ ( esk4_2 @ X27 @ X28 ) @ X27 @ mactual )
| ( subset @ X27 @ X28 @ mactual ) )
& ( ~ ( member @ ( esk4_2 @ X27 @ X28 ) @ X28 @ mactual )
| ( subset @ X27 @ X28 @ mactual ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_12])])])])])])]) ).
thf(c_0_15,negated_conjecture,
( ( subset @ esk1_0 @ esk2_0 @ mactual )
& ( subset @ esk2_0 @ esk3_0 @ mactual )
& ~ ( subset @ esk1_0 @ esk3_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_16,plain,
! [X10: $i,X9: $i,X7: $i] :
( ( member @ X10 @ X9 @ mactual )
| ~ ( subset @ X7 @ X9 @ mactual )
| ~ ( member @ X10 @ X7 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,negated_conjecture,
subset @ esk2_0 @ esk3_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,plain,
! [X7: $i,X9: $i] :
( ( subset @ X7 @ X9 @ mactual )
| ~ ( member @ ( esk4_2 @ X7 @ X9 ) @ X9 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
! [X7: $i] :
( ( member @ X7 @ esk3_0 @ mactual )
| ~ ( member @ X7 @ esk2_0 @ mactual ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,negated_conjecture,
subset @ esk1_0 @ esk2_0 @ mactual,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,negated_conjecture,
! [X7: $i] :
( ( subset @ X7 @ esk3_0 @ mactual )
| ~ ( member @ ( esk4_2 @ X7 @ esk3_0 ) @ esk2_0 @ mactual ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_22,negated_conjecture,
! [X7: $i] :
( ( member @ X7 @ esk2_0 @ mactual )
| ~ ( member @ X7 @ esk1_0 @ mactual ) ),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
thf(c_0_23,negated_conjecture,
! [X7: $i] :
( ( subset @ X7 @ esk3_0 @ mactual )
| ~ ( member @ ( esk4_2 @ X7 @ esk3_0 ) @ esk1_0 @ mactual ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_24,plain,
! [X7: $i,X9: $i] :
( ( member @ ( esk4_2 @ X7 @ X9 ) @ X7 @ mactual )
| ( subset @ X7 @ X9 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_25,negated_conjecture,
~ ( subset @ esk1_0 @ esk3_0 @ mactual ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET027^3 : TPTP v8.2.0. Released v8.1.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 12:30:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.21/0.47 Running higher-order theorem proving
% 0.21/0.47 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
% 0.21/0.49 # Version: 3.1.0-ho
% 0.21/0.49 # Preprocessing class: HSSSSMSSMLMNHSN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.49 # Starting sh5l with 300s (1) cores
% 0.21/0.49 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.49 # Starting new_bool_2 with 300s (1) cores
% 0.21/0.49 # sh5l with pid 31207 completed with status 0
% 0.21/0.49 # Result found by sh5l
% 0.21/0.49 # Preprocessing class: HSSSSMSSMLMNHSN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.49 # Starting sh5l with 300s (1) cores
% 0.21/0.49 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.49 # Search class: HGUNF-FFSF22-SHSSMFNN
% 0.21/0.49 # partial match(1): HGHNF-FFSF22-SHSSMFNN
% 0.21/0.49 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.49 # Starting new_ho_10 with 181s (1) cores
% 0.21/0.49 # new_ho_10 with pid 31214 completed with status 0
% 0.21/0.49 # Result found by new_ho_10
% 0.21/0.49 # Preprocessing class: HSSSSMSSMLMNHSN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.49 # Starting sh5l with 300s (1) cores
% 0.21/0.49 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.49 # Search class: HGUNF-FFSF22-SHSSMFNN
% 0.21/0.49 # partial match(1): HGHNF-FFSF22-SHSSMFNN
% 0.21/0.49 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.49 # Starting new_ho_10 with 181s (1) cores
% 0.21/0.49 # Preprocessing time : 0.001 s
% 0.21/0.49 # Presaturation interreduction done
% 0.21/0.49
% 0.21/0.49 # Proof found!
% 0.21/0.49 # SZS status Theorem
% 0.21/0.49 # SZS output start CNFRefutation
% See solution above
% 0.21/0.49 # Parsed axioms : 29
% 0.21/0.49 # Removed by relevancy pruning/SinE : 21
% 0.21/0.49 # Initial clauses : 7
% 0.21/0.49 # Removed in clause preprocessing : 0
% 0.21/0.49 # Initial clauses in saturation : 7
% 0.21/0.49 # Processed clauses : 19
% 0.21/0.49 # ...of these trivial : 0
% 0.21/0.49 # ...subsumed : 0
% 0.21/0.49 # ...remaining for further processing : 19
% 0.21/0.49 # Other redundant clauses eliminated : 0
% 0.21/0.49 # Clauses deleted for lack of memory : 0
% 0.21/0.49 # Backward-subsumed : 0
% 0.21/0.49 # Backward-rewritten : 0
% 0.21/0.49 # Generated clauses : 10
% 0.21/0.49 # ...of the previous two non-redundant : 5
% 0.21/0.49 # ...aggressively subsumed : 0
% 0.21/0.49 # Contextual simplify-reflections : 0
% 0.21/0.49 # Paramodulations : 10
% 0.21/0.49 # Factorizations : 0
% 0.21/0.49 # NegExts : 0
% 0.21/0.49 # Equation resolutions : 0
% 0.21/0.49 # Disequality decompositions : 0
% 0.21/0.49 # Total rewrite steps : 3
% 0.21/0.49 # ...of those cached : 0
% 0.21/0.49 # Propositional unsat checks : 0
% 0.21/0.49 # Propositional check models : 0
% 0.21/0.49 # Propositional check unsatisfiable : 0
% 0.21/0.49 # Propositional clauses : 0
% 0.21/0.49 # Propositional clauses after purity: 0
% 0.21/0.49 # Propositional unsat core size : 0
% 0.21/0.49 # Propositional preprocessing time : 0.000
% 0.21/0.49 # Propositional encoding time : 0.000
% 0.21/0.49 # Propositional solver time : 0.000
% 0.21/0.49 # Success case prop preproc time : 0.000
% 0.21/0.49 # Success case prop encoding time : 0.000
% 0.21/0.49 # Success case prop solver time : 0.000
% 0.21/0.49 # Current number of processed clauses : 12
% 0.21/0.49 # Positive orientable unit clauses : 3
% 0.21/0.49 # Positive unorientable unit clauses: 0
% 0.21/0.49 # Negative unit clauses : 1
% 0.21/0.49 # Non-unit-clauses : 8
% 0.21/0.49 # Current number of unprocessed clauses: 0
% 0.21/0.49 # ...number of literals in the above : 0
% 0.21/0.49 # Current number of archived formulas : 0
% 0.21/0.49 # Current number of archived clauses : 7
% 0.21/0.49 # Clause-clause subsumption calls (NU) : 9
% 0.21/0.49 # Rec. Clause-clause subsumption calls : 9
% 0.21/0.49 # Non-unit clause-clause subsumptions : 0
% 0.21/0.49 # Unit Clause-clause subsumption calls : 0
% 0.21/0.49 # Rewrite failures with RHS unbound : 0
% 0.21/0.49 # BW rewrite match attempts : 6
% 0.21/0.49 # BW rewrite match successes : 0
% 0.21/0.49 # Condensation attempts : 19
% 0.21/0.49 # Condensation successes : 0
% 0.21/0.49 # Termbank termtop insertions : 1253
% 0.21/0.49 # Search garbage collected termcells : 453
% 0.21/0.49
% 0.21/0.49 # -------------------------------------------------
% 0.21/0.49 # User time : 0.005 s
% 0.21/0.49 # System time : 0.002 s
% 0.21/0.49 # Total time : 0.007 s
% 0.21/0.49 # Maximum resident set size: 1908 pages
% 0.21/0.49
% 0.21/0.49 # -------------------------------------------------
% 0.21/0.49 # User time : 0.007 s
% 0.21/0.49 # System time : 0.004 s
% 0.21/0.49 # Total time : 0.011 s
% 0.21/0.49 # Maximum resident set size: 1748 pages
% 0.21/0.49 % E---3.1 exiting
% 0.21/0.49 % E exiting
%------------------------------------------------------------------------------