TSTP Solution File: NUM925^3 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM925^3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 : Sat May 4 08:58:25 EDT 2024
% Result : Theorem 0.59s 1.04s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 29
% Syntax : Number of formulae : 58 ( 32 unt; 18 typ; 0 def)
% Number of atoms : 55 ( 40 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 178 ( 16 ~; 7 |; 4 &; 147 @)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 ^ 23 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
int: $tType ).
thf(decl_29,type,
one_one_int: int ).
thf(decl_30,type,
one_one_nat: nat ).
thf(decl_32,type,
plus_plus_int: int > int > int ).
thf(decl_33,type,
plus_plus_nat: nat > nat > nat ).
thf(decl_38,type,
zero_zero_int: int ).
thf(decl_45,type,
bit0: int > int ).
thf(decl_46,type,
bit1: int > int ).
thf(decl_48,type,
pls: int ).
thf(decl_49,type,
nat_1: int > nat ).
thf(decl_50,type,
number_number_of_int: int > int ).
thf(decl_51,type,
number_number_of_nat: int > nat ).
thf(decl_54,type,
semiri1621563631at_int: nat > int ).
thf(decl_57,type,
ord_less_int: int > int > $o ).
thf(decl_60,type,
ord_less_eq_int: int > int > $o ).
thf(decl_63,type,
power_power_int: int > nat > int ).
thf(decl_73,type,
n: nat ).
thf(fact_25_semiring__norm_I110_J,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p',fact_25_semiring__norm_I110_J) ).
thf(fact_98_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p',fact_98_Pls__def) ).
thf(fact_177_number__of__is__id,axiom,
! [X10: int] :
( ( number_number_of_int @ X10 )
= X10 ),
file('/export/starexec/sandbox/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p',fact_177_number__of__is__id) ).
thf(fact_55_Numeral1__eq1__nat,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p',fact_55_Numeral1__eq1__nat) ).
thf(fact_768_transfer__nat__int__numerals_I2_J,axiom,
( one_one_nat
= ( nat_1 @ one_one_int ) ),
file('/export/starexec/sandbox/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p',fact_768_transfer__nat__int__numerals_I2_J) ).
thf(conj_0,conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
file('/export/starexec/sandbox/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p',conj_0) ).
thf(fact_103_Bit0__def,axiom,
! [X10: int] :
( ( bit0 @ X10 )
= ( plus_plus_int @ X10 @ X10 ) ),
file('/export/starexec/sandbox/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p',fact_103_Bit0__def) ).
thf(fact_231_field__power__not__zero,axiom,
! [X141: nat,X142: int] :
( ( X142 != zero_zero_int )
=> ( ( power_power_int @ X142 @ X141 )
!= zero_zero_int ) ),
file('/export/starexec/sandbox/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p',fact_231_field__power__not__zero) ).
thf(fact_19_semiring__one__add__one__is__two,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p',fact_19_semiring__one__add__one__is__two) ).
thf(fact_718_zless__le,axiom,
! [X18: int,X13: int] :
( ( ord_less_int @ X18 @ X13 )
<=> ( ( ord_less_eq_int @ X18 @ X13 )
& ( X18 != X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p',fact_718_zless__le) ).
thf(fact_0_n1pos,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
file('/export/starexec/sandbox/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p',fact_0_n1pos) ).
thf(c_0_11,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(split_conjunct,[status(thm)],[fact_25_semiring__norm_I110_J]) ).
thf(c_0_12,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).
thf(c_0_13,plain,
! [X5252: int] :
( ( number_number_of_int @ X5252 )
= X5252 ),
inference(variable_rename,[status(thm)],[fact_177_number__of__is__id]) ).
thf(c_0_14,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(split_conjunct,[status(thm)],[fact_55_Numeral1__eq1__nat]) ).
thf(c_0_15,plain,
( one_one_nat
= ( nat_1 @ one_one_int ) ),
inference(split_conjunct,[status(thm)],[fact_768_transfer__nat__int__numerals_I2_J]) ).
thf(c_0_16,plain,
( ( number_number_of_int @ ( bit1 @ zero_zero_int ) )
= one_one_int ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_17,plain,
! [X1: int] :
( ( number_number_of_int @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
thf(c_0_19,plain,
( ( nat_1 @ one_one_int )
= ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_12]) ).
thf(c_0_20,plain,
( one_one_int
= ( bit1 @ zero_zero_int ) ),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,plain,
! [X4568: int] :
( ( bit0 @ X4568 )
= ( plus_plus_int @ X4568 @ X4568 ) ),
inference(variable_rename,[status(thm)],[fact_103_Bit0__def]) ).
thf(c_0_22,plain,
! [X141: nat,X142: int] :
( ( X142 != zero_zero_int )
=> ( ( power_power_int @ X142 @ X141 )
!= zero_zero_int ) ),
inference(fof_simplification,[status(thm)],[fact_231_field__power__not__zero]) ).
thf(c_0_23,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(split_conjunct,[status(thm)],[fact_19_semiring__one__add__one__is__two]) ).
thf(c_0_25,plain,
( ( nat_1 @ ( bit1 @ zero_zero_int ) )
= ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_26,plain,
! [X1: int] :
( ( bit0 @ X1 )
= ( plus_plus_int @ X1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,plain,
! [X18: int,X13: int] :
( ( ord_less_int @ X18 @ X13 )
<=> ( ( ord_less_eq_int @ X18 @ X13 )
& ( X18 != X13 ) ) ),
inference(fof_simplification,[status(thm)],[fact_718_zless__le]) ).
thf(c_0_28,plain,
! [X4153: nat,X4154: int] :
( ( X4154 = zero_zero_int )
| ( ( power_power_int @ X4154 @ X4153 )
!= zero_zero_int ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
thf(c_0_29,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) )
= zero_zero_int ),
inference(rw,[status(thm)],[c_0_23,c_0_12]) ).
thf(c_0_30,plain,
( ( number_number_of_nat @ ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( bit1 @ zero_zero_int ) ) )
= ( plus_plus_nat @ ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) @ ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_15]),c_0_20]),c_0_25]),c_0_15]),c_0_20]),c_0_25]),c_0_12]),c_0_26]) ).
thf(c_0_31,plain,
! [X5282: int,X5283: int] :
( ( ( ord_less_eq_int @ X5282 @ X5283 )
| ~ ( ord_less_int @ X5282 @ X5283 ) )
& ( ( X5282 != X5283 )
| ~ ( ord_less_int @ X5282 @ X5283 ) )
& ( ~ ( ord_less_eq_int @ X5282 @ X5283 )
| ( X5282 = X5283 )
| ( ord_less_int @ X5282 @ X5283 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
thf(c_0_32,plain,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
thf(c_0_33,plain,
! [X1: int,X16: nat] :
( ( X1 = zero_zero_int )
| ( ( power_power_int @ X1 @ X16 )
!= zero_zero_int ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_34,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( semiri1621563631at_int @ n ) ) @ ( plus_plus_nat @ ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) @ ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) ) )
= zero_zero_int ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_20]),c_0_26]),c_0_30]) ).
thf(c_0_35,plain,
! [X1: int,X2: int] :
( ( X1 != X2 )
| ~ ( ord_less_int @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_36,plain,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( semiri1621563631at_int @ n ) ),
inference(rw,[status(thm)],[c_0_32,c_0_20]) ).
thf(c_0_37,negated_conjecture,
( ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( semiri1621563631at_int @ n ) )
= zero_zero_int ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_38,plain,
! [X1: int] :
~ ( ord_less_int @ X1 @ X1 ),
inference(er,[status(thm)],[c_0_35]) ).
thf(c_0_39,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.25 % Problem : NUM925^3 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.26 % Command : run_E %s %d THM
% 0.26/0.47 % Computer : n007.cluster.edu
% 0.26/0.47 % Model : x86_64 x86_64
% 0.26/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.47 % Memory : 8042.1875MB
% 0.26/0.47 % OS : Linux 3.10.0-693.el7.x86_64
% 0.31/0.47 % CPULimit : 300
% 0.31/0.47 % WCLimit : 300
% 0.31/0.47 % DateTime : Fri May 3 09:18:20 EDT 2024
% 0.31/0.47 % CPUTime :
% 0.44/0.74 Running higher-order theorem proving
% 0.44/0.74 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/tmp/tmp.rMtIyFAbrh/E---3.1_27814.p
% 0.59/1.04 # Version: 3.1.0-ho
% 0.59/1.04 # Preprocessing class: HMLSSMSMSSSNSFA.
% 0.59/1.04 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/1.04 # Starting sh3 with 1500s (5) cores
% 0.59/1.04 # Starting lpo1_def_fix with 300s (1) cores
% 0.59/1.04 # Starting lpo8_s with 300s (1) cores
% 0.59/1.04 # Starting lpo1_lambda_fix with 300s (1) cores
% 0.59/1.04 # lpo8_s with pid 28031 completed with status 0
% 0.59/1.04 # Result found by lpo8_s
% 0.59/1.04 # Preprocessing class: HMLSSMSMSSSNSFA.
% 0.59/1.04 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/1.04 # Starting sh3 with 1500s (5) cores
% 0.59/1.04 # Starting lpo1_def_fix with 300s (1) cores
% 0.59/1.04 # Starting lpo8_s with 300s (1) cores
% 0.59/1.04 # SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.59/1.04 # Search class: HGHSM-SSLM31-DSFFFFBN
% 0.59/1.04 # partial match(1): HGHSM-FSLM31-DSFFFFBN
% 0.59/1.04 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.59/1.04 # Starting lpo8_lambda_fix with 109s (1) cores
% 0.59/1.04 # lpo8_lambda_fix with pid 28096 completed with status 0
% 0.59/1.04 # Result found by lpo8_lambda_fix
% 0.59/1.04 # Preprocessing class: HMLSSMSMSSSNSFA.
% 0.59/1.04 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/1.04 # Starting sh3 with 1500s (5) cores
% 0.59/1.04 # Starting lpo1_def_fix with 300s (1) cores
% 0.59/1.04 # Starting lpo8_s with 300s (1) cores
% 0.59/1.04 # SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.59/1.04 # Search class: HGHSM-SSLM31-DSFFFFBN
% 0.59/1.04 # partial match(1): HGHSM-FSLM31-DSFFFFBN
% 0.59/1.04 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.59/1.04 # Starting lpo8_lambda_fix with 109s (1) cores
% 0.59/1.04 # Preprocessing time : 0.021 s
% 0.59/1.04 # Presaturation interreduction done
% 0.59/1.04
% 0.59/1.04 # Proof found!
% 0.59/1.04 # SZS status Theorem
% 0.59/1.04 # SZS output start CNFRefutation
% See solution above
% 0.59/1.04 # Parsed axioms : 1266
% 0.59/1.04 # Removed by relevancy pruning/SinE : 93
% 0.59/1.04 # Initial clauses : 1713
% 0.59/1.04 # Removed in clause preprocessing : 114
% 0.59/1.04 # Initial clauses in saturation : 1599
% 0.59/1.04 # Processed clauses : 1821
% 0.59/1.04 # ...of these trivial : 209
% 0.59/1.04 # ...subsumed : 388
% 0.59/1.04 # ...remaining for further processing : 1223
% 0.59/1.04 # Other redundant clauses eliminated : 162
% 0.59/1.04 # Clauses deleted for lack of memory : 0
% 0.59/1.04 # Backward-subsumed : 12
% 0.59/1.04 # Backward-rewritten : 100
% 0.59/1.04 # Generated clauses : 173
% 0.59/1.04 # ...of the previous two non-redundant : 156
% 0.59/1.04 # ...aggressively subsumed : 0
% 0.59/1.04 # Contextual simplify-reflections : 2
% 0.59/1.04 # Paramodulations : 26
% 0.59/1.04 # Factorizations : 0
% 0.59/1.04 # NegExts : 0
% 0.59/1.04 # Equation resolutions : 162
% 0.59/1.04 # Disequality decompositions : 0
% 0.59/1.04 # Total rewrite steps : 2384
% 0.59/1.04 # ...of those cached : 1989
% 0.59/1.04 # Propositional unsat checks : 0
% 0.59/1.04 # Propositional check models : 0
% 0.59/1.04 # Propositional check unsatisfiable : 0
% 0.59/1.04 # Propositional clauses : 0
% 0.59/1.04 # Propositional clauses after purity: 0
% 0.59/1.04 # Propositional unsat core size : 0
% 0.59/1.04 # Propositional preprocessing time : 0.000
% 0.59/1.04 # Propositional encoding time : 0.000
% 0.59/1.04 # Propositional solver time : 0.000
% 0.59/1.04 # Success case prop preproc time : 0.000
% 0.59/1.04 # Success case prop encoding time : 0.000
% 0.59/1.04 # Success case prop solver time : 0.000
% 0.59/1.04 # Current number of processed clauses : 71
% 0.59/1.04 # Positive orientable unit clauses : 37
% 0.59/1.04 # Positive unorientable unit clauses: 0
% 0.59/1.04 # Negative unit clauses : 24
% 0.59/1.04 # Non-unit-clauses : 10
% 0.59/1.04 # Current number of unprocessed clauses: 830
% 0.59/1.04 # ...number of literals in the above : 1910
% 0.59/1.04 # Current number of archived formulas : 0
% 0.59/1.04 # Current number of archived clauses : 1008
% 0.59/1.04 # Clause-clause subsumption calls (NU) : 143405
% 0.59/1.04 # Rec. Clause-clause subsumption calls : 94463
% 0.59/1.04 # Non-unit clause-clause subsumptions : 331
% 0.59/1.04 # Unit Clause-clause subsumption calls : 1132
% 0.59/1.04 # Rewrite failures with RHS unbound : 0
% 0.59/1.04 # BW rewrite match attempts : 371
% 0.59/1.04 # BW rewrite match successes : 274
% 0.59/1.04 # Condensation attempts : 1821
% 0.59/1.04 # Condensation successes : 1
% 0.59/1.04 # Termbank termtop insertions : 152536
% 0.59/1.04 # Search garbage collected termcells : 28402
% 0.59/1.04
% 0.59/1.04 # -------------------------------------------------
% 0.59/1.04 # User time : 0.231 s
% 0.59/1.04 # System time : 0.019 s
% 0.59/1.04 # Total time : 0.250 s
% 0.59/1.04 # Maximum resident set size: 9332 pages
% 0.59/1.04
% 0.59/1.04 # -------------------------------------------------
% 0.59/1.04 # User time : 0.273 s
% 0.59/1.04 # System time : 0.024 s
% 0.59/1.04 # Total time : 0.297 s
% 0.59/1.04 # Maximum resident set size: 4052 pages
% 0.59/1.04 % E---3.1 exiting
% 0.59/1.04 % E exiting
%------------------------------------------------------------------------------