TSTP Solution File: ITP132^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP132^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 : Mon May 20 22:16:27 EDT 2024
% Result : Theorem 0.43s 0.56s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 19
% Syntax : Number of formulae : 27 ( 9 unt; 15 typ; 0 def)
% Number of atoms : 36 ( 17 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 158 ( 14 ~; 11 |; 8 &; 122 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 23 ( 10 ^ 13 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
set_nat: $tType ).
thf(decl_23,type,
minus_minus_nat: nat > nat > nat ).
thf(decl_24,type,
one_one_nat: nat ).
thf(decl_25,type,
times_times_nat: nat > nat > nat ).
thf(decl_26,type,
zero_zero_nat: nat ).
thf(decl_27,type,
groups1842438620at_nat: ( nat > nat ) > set_nat > nat ).
thf(decl_29,type,
number1551313001itions: ( nat > nat ) > nat > $o ).
thf(decl_31,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_36,type,
set_ord_atMost_nat: nat > set_nat ).
thf(decl_40,type,
k: nat ).
thf(decl_41,type,
n: nat ).
thf(decl_42,type,
p: nat > nat ).
thf(decl_61,type,
esk19_2: ( nat > nat ) > nat > nat ).
thf(decl_137,type,
esk92_1: ( nat > nat ) > nat > nat ).
thf(conj_0,conjecture,
( ( minus_minus_nat
@ ( groups1842438620at_nat
@ ^ [X3: nat] : ( times_times_nat @ ( p @ X3 ) @ X3 )
@ ( set_ord_atMost_nat @ n ) )
@ k )
= ( minus_minus_nat @ n @ k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(fact_61_partitions__def,axiom,
( number1551313001itions
= ( ^ [X67: nat > nat,X10: nat] :
( ! [X3: nat] :
( ( ( X67 @ X3 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ X3 )
& ( ord_less_eq_nat @ X3 @ X10 ) ) )
& ( ( groups1842438620at_nat
@ ^ [X3: nat] : ( times_times_nat @ ( X67 @ X3 ) @ X3 )
@ ( set_ord_atMost_nat @ X10 ) )
= X10 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_partitions__def) ).
thf(fact_0_partitions,axiom,
number1551313001itions @ p @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_partitions) ).
thf(c_0_3,negated_conjecture,
( ( minus_minus_nat
@ ( groups1842438620at_nat
@ ^ [Z0: nat] : ( times_times_nat @ ( p @ Z0 ) @ Z0 )
@ ( set_ord_atMost_nat @ n ) )
@ k )
!= ( minus_minus_nat @ n @ k ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])])]) ).
thf(c_0_4,plain,
! [X799: nat > nat,X800: nat] :
( ( number1551313001itions @ X799 @ X800 )
<=> ( ! [X3: nat] :
( ( ( X799 @ X3 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ X3 )
& ( ord_less_eq_nat @ X3 @ X800 ) ) )
& ( ( groups1842438620at_nat
@ ^ [Z0: nat] : ( times_times_nat @ ( X799 @ Z0 ) @ Z0 )
@ ( set_ord_atMost_nat @ X800 ) )
= X800 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_61_partitions__def])])]) ).
thf(c_0_5,negated_conjecture,
( ( minus_minus_nat
@ ( groups1842438620at_nat
@ ^ [Z0: nat] : ( times_times_nat @ ( p @ Z0 ) @ Z0 )
@ ( set_ord_atMost_nat @ n ) )
@ k )
!= ( minus_minus_nat @ n @ k ) ),
inference(fof_nnf,[status(thm)],[c_0_3]) ).
thf(c_0_6,plain,
! [X1491: nat,X4: nat > nat] :
( ( esk92_1 @ X4 @ X1491 )
= ( times_times_nat @ ( X4 @ X1491 ) @ X1491 ) ),
introduced(definition) ).
thf(c_0_7,plain,
! [X985: nat > nat,X986: nat,X987: nat,X988: nat > nat,X989: nat] :
( ( ( ord_less_eq_nat @ one_one_nat @ X987 )
| ( ( X985 @ X987 )
= zero_zero_nat )
| ~ ( number1551313001itions @ X985 @ X986 ) )
& ( ( ord_less_eq_nat @ X987 @ X986 )
| ( ( X985 @ X987 )
= zero_zero_nat )
| ~ ( number1551313001itions @ X985 @ X986 ) )
& ( ( ( groups1842438620at_nat
@ ^ [Z0: nat] : ( times_times_nat @ ( X985 @ Z0 ) @ Z0 )
@ ( set_ord_atMost_nat @ X986 ) )
= X986 )
| ~ ( number1551313001itions @ X985 @ X986 ) )
& ( ( ( X988 @ ( esk19_2 @ X988 @ X989 ) )
!= zero_zero_nat )
| ( ( groups1842438620at_nat
@ ^ [Z0: nat] : ( times_times_nat @ ( X988 @ Z0 ) @ Z0 )
@ ( set_ord_atMost_nat @ X989 ) )
!= X989 )
| ( number1551313001itions @ X988 @ X989 ) )
& ( ~ ( ord_less_eq_nat @ one_one_nat @ ( esk19_2 @ X988 @ X989 ) )
| ~ ( ord_less_eq_nat @ ( esk19_2 @ X988 @ X989 ) @ X989 )
| ( ( groups1842438620at_nat
@ ^ [Z0: nat] : ( times_times_nat @ ( X988 @ Z0 ) @ Z0 )
@ ( set_ord_atMost_nat @ X989 ) )
!= X989 )
| ( number1551313001itions @ X988 @ X989 ) ) ),
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_4])])])])])])]) ).
thf(c_0_8,negated_conjecture,
( ( minus_minus_nat @ ( groups1842438620at_nat @ ( esk92_1 @ p ) @ ( set_ord_atMost_nat @ n ) ) @ k )
!= ( minus_minus_nat @ n @ k ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_5]),c_0_6]) ).
thf(c_0_9,plain,
! [X4: nat > nat,X1: nat] :
( ( ( groups1842438620at_nat @ ( esk92_1 @ X4 ) @ ( set_ord_atMost_nat @ X1 ) )
= X1 )
| ~ ( number1551313001itions @ X4 @ X1 ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7]),c_0_6]) ).
thf(c_0_10,plain,
number1551313001itions @ p @ n,
inference(split_conjunct,[status(thm)],[fact_0_partitions]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP132^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.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 : Sat May 18 16:34:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.49 Running higher-order theorem proving
% 0.21/0.49 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
% 0.43/0.56 # Version: 3.1.0-ho
% 0.43/0.56 # Preprocessing class: HSLSSMSSSSLNHSA.
% 0.43/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.56 # Starting pre_casc_6 with 1200s (4) cores
% 0.43/0.56 # Starting sh4 with 600s (2) cores
% 0.43/0.56 # Starting pre_casc_4 with 300s (1) cores
% 0.43/0.56 # Starting full_lambda_7 with 300s (1) cores
% 0.43/0.56 # sh4 with pid 8280 completed with status 0
% 0.43/0.56 # Result found by sh4
% 0.43/0.56 # Preprocessing class: HSLSSMSSSSLNHSA.
% 0.43/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.56 # Starting pre_casc_6 with 1200s (4) cores
% 0.43/0.56 # Starting sh4 with 600s (2) cores
% 0.43/0.56 # No SInE strategy applied
% 0.43/0.56 # Search class: HGHSM-FSLM32-MHSFFSBC
% 0.43/0.56 # Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.43/0.56 # Starting ehoh_best4 with 291s (1) cores
% 0.43/0.56 # Starting sh4 with 61s (1) cores
% 0.43/0.56 # sh4 with pid 8290 completed with status 0
% 0.43/0.56 # Result found by sh4
% 0.43/0.56 # Preprocessing class: HSLSSMSSSSLNHSA.
% 0.43/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.56 # Starting pre_casc_6 with 1200s (4) cores
% 0.43/0.56 # Starting sh4 with 600s (2) cores
% 0.43/0.56 # No SInE strategy applied
% 0.43/0.56 # Search class: HGHSM-FSLM32-MHSFFSBC
% 0.43/0.56 # Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.43/0.56 # Starting ehoh_best4 with 291s (1) cores
% 0.43/0.56 # Starting sh4 with 61s (1) cores
% 0.43/0.56 # Preprocessing time : 0.008 s
% 0.43/0.56
% 0.43/0.56 # Proof found!
% 0.43/0.56 # SZS status Theorem
% 0.43/0.56 # SZS output start CNFRefutation
% See solution above
% 0.43/0.56 # Parsed axioms : 269
% 0.43/0.56 # Removed by relevancy pruning/SinE : 0
% 0.43/0.56 # Initial clauses : 524
% 0.43/0.56 # Removed in clause preprocessing : 51
% 0.43/0.56 # Initial clauses in saturation : 473
% 0.43/0.56 # Processed clauses : 122
% 0.43/0.56 # ...of these trivial : 17
% 0.43/0.56 # ...subsumed : 16
% 0.43/0.56 # ...remaining for further processing : 89
% 0.43/0.56 # Other redundant clauses eliminated : 47
% 0.43/0.56 # Clauses deleted for lack of memory : 0
% 0.43/0.56 # Backward-subsumed : 2
% 0.43/0.56 # Backward-rewritten : 3
% 0.43/0.56 # Generated clauses : 121
% 0.43/0.56 # ...of the previous two non-redundant : 62
% 0.43/0.56 # ...aggressively subsumed : 0
% 0.43/0.56 # Contextual simplify-reflections : 0
% 0.43/0.56 # Paramodulations : 53
% 0.43/0.56 # Factorizations : 0
% 0.43/0.56 # NegExts : 0
% 0.43/0.56 # Equation resolutions : 48
% 0.43/0.56 # Disequality decompositions : 0
% 0.43/0.56 # Total rewrite steps : 67
% 0.43/0.56 # ...of those cached : 50
% 0.43/0.56 # Propositional unsat checks : 0
% 0.43/0.56 # Propositional check models : 0
% 0.43/0.56 # Propositional check unsatisfiable : 0
% 0.43/0.56 # Propositional clauses : 0
% 0.43/0.56 # Propositional clauses after purity: 0
% 0.43/0.56 # Propositional unsat core size : 0
% 0.43/0.56 # Propositional preprocessing time : 0.000
% 0.43/0.56 # Propositional encoding time : 0.000
% 0.43/0.56 # Propositional solver time : 0.000
% 0.43/0.56 # Success case prop preproc time : 0.000
% 0.43/0.56 # Success case prop encoding time : 0.000
% 0.43/0.56 # Success case prop solver time : 0.000
% 0.43/0.56 # Current number of processed clauses : 48
% 0.43/0.56 # Positive orientable unit clauses : 25
% 0.43/0.56 # Positive unorientable unit clauses: 0
% 0.43/0.56 # Negative unit clauses : 5
% 0.43/0.56 # Non-unit-clauses : 18
% 0.43/0.56 # Current number of unprocessed clauses: 413
% 0.43/0.56 # ...number of literals in the above : 1319
% 0.43/0.56 # Current number of archived formulas : 0
% 0.43/0.56 # Current number of archived clauses : 5
% 0.43/0.56 # Clause-clause subsumption calls (NU) : 197
% 0.43/0.56 # Rec. Clause-clause subsumption calls : 160
% 0.43/0.56 # Non-unit clause-clause subsumptions : 15
% 0.43/0.56 # Unit Clause-clause subsumption calls : 21
% 0.43/0.56 # Rewrite failures with RHS unbound : 0
% 0.43/0.56 # BW rewrite match attempts : 11
% 0.43/0.56 # BW rewrite match successes : 3
% 0.43/0.56 # Condensation attempts : 122
% 0.43/0.56 # Condensation successes : 0
% 0.43/0.56 # Termbank termtop insertions : 34232
% 0.43/0.56 # Search garbage collected termcells : 9341
% 0.43/0.56
% 0.43/0.56 # -------------------------------------------------
% 0.43/0.56 # User time : 0.038 s
% 0.43/0.56 # System time : 0.007 s
% 0.43/0.56 # Total time : 0.045 s
% 0.43/0.56 # Maximum resident set size: 4148 pages
% 0.43/0.56
% 0.43/0.56 # -------------------------------------------------
% 0.43/0.56 # User time : 0.061 s
% 0.43/0.56 # System time : 0.012 s
% 0.43/0.56 # Total time : 0.073 s
% 0.43/0.56 # Maximum resident set size: 2144 pages
% 0.43/0.56 % E---3.1 exiting
% 0.43/0.56 % E exiting
%------------------------------------------------------------------------------