TSTP Solution File: ITP131^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP131^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n024.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 : ContradictoryAxioms 0.21s 0.56s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 17 unt; 9 typ; 0 def)
% Number of atoms : 35 ( 10 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 149 ( 11 ~; 8 |; 1 &; 126 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 2 ^ 22 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
plus_plus_nat: nat > nat > nat ).
thf(decl_24,type,
times_times_nat: nat > nat > nat ).
thf(decl_27,type,
ord_less_nat: nat > nat > $o ).
thf(decl_28,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_29,type,
i: nat ).
thf(decl_30,type,
k: nat ).
thf(decl_31,type,
n: nat ).
thf(decl_32,type,
p: nat > nat ).
thf(fact_136_mult_Ocommute,axiom,
( times_times_nat
= ( ^ [X17: nat,X18: nat] : ( times_times_nat @ X18 @ X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_mult_Ocommute) ).
thf(fact_193_less__or__eq__imp__le,axiom,
! [X5: nat,X3: nat] :
( ( ( ord_less_nat @ X5 @ X3 )
| ( X5 = X3 ) )
=> ( ord_less_eq_nat @ X5 @ X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_less__or__eq__imp__le) ).
thf(fact_149_le__antisym,axiom,
! [X5: nat,X3: nat] :
( ( ord_less_eq_nat @ X5 @ X3 )
=> ( ( ord_less_eq_nat @ X3 @ X5 )
=> ( X5 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_le__antisym) ).
thf(fact_2_upper__bound,axiom,
ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ) @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_upper__bound) ).
thf(fact_3_lower__bound,axiom,
ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_lower__bound) ).
thf(fact_142_less__irrefl__nat,axiom,
! [X3: nat] :
~ ( ord_less_nat @ X3 @ X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_less__irrefl__nat) ).
thf(c_0_6,plain,
! [X544: nat,X545: nat] :
( ( times_times_nat @ X544 @ X545 )
= ( times_times_nat @ X545 @ X544 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_136_mult_Ocommute])]) ).
thf(c_0_7,plain,
! [X894: nat,X895: nat] :
( ( times_times_nat @ X894 @ X895 )
= ( times_times_nat @ X895 @ X894 ) ),
inference(variable_rename,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X1034: nat,X1035: nat] :
( ( ~ ( ord_less_nat @ X1034 @ X1035 )
| ( ord_less_eq_nat @ X1034 @ X1035 ) )
& ( ( X1034 != X1035 )
| ( ord_less_eq_nat @ X1034 @ X1035 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_193_less__or__eq__imp__le])])])]) ).
thf(c_0_9,plain,
! [X928: nat,X929: nat] :
( ~ ( ord_less_eq_nat @ X928 @ X929 )
| ~ ( ord_less_eq_nat @ X929 @ X928 )
| ( X928 = X929 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_149_le__antisym])])]) ).
thf(c_0_10,plain,
ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ) @ n,
inference(split_conjunct,[status(thm)],[fact_2_upper__bound]) ).
thf(c_0_11,plain,
! [X3: nat,X2: nat] :
( ( times_times_nat @ X2 @ X3 )
= ( times_times_nat @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X2: nat,X3: nat] :
( ( ord_less_eq_nat @ X2 @ X3 )
| ~ ( ord_less_nat @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ),
inference(split_conjunct,[status(thm)],[fact_3_lower__bound]) ).
thf(c_0_14,plain,
! [X3: nat] :
~ ( ord_less_nat @ X3 @ X3 ),
inference(fof_simplification,[status(thm)],[fact_142_less__irrefl__nat]) ).
thf(c_0_15,plain,
! [X3: nat,X2: nat] :
( ( X2 = X3 )
| ~ ( ord_less_eq_nat @ X2 @ X3 )
| ~ ( ord_less_eq_nat @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_16,plain,
ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) ) @ n,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
thf(c_0_17,plain,
ord_less_eq_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11]),c_0_11]) ).
thf(c_0_18,plain,
! [X912: nat] :
~ ( ord_less_nat @ X912 @ X912 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_14])]) ).
thf(c_0_19,plain,
ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_11]) ).
thf(c_0_20,plain,
( ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) )
= n ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
thf(c_0_21,plain,
! [X2: nat] :
~ ( ord_less_nat @ X2 @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP131^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 17:01:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.49 Running higher-order theorem proving
% 0.21/0.49 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
% 0.21/0.56 # Version: 3.1.0-ho
% 0.21/0.56 # Preprocessing class: HSLSSMSSSSSNSFA.
% 0.21/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56 # Starting new_ho_11 with 1500s (5) cores
% 0.21/0.56 # Starting post_as_ho6 with 300s (1) cores
% 0.21/0.56 # Starting sh9 with 300s (1) cores
% 0.21/0.56 # Starting sh5l with 300s (1) cores
% 0.21/0.56 # sh5l with pid 24428 completed with status 8
% 0.21/0.56 # post_as_ho6 with pid 24426 completed with status 8
% 0.21/0.56 # sh9 with pid 24427 completed with status 0
% 0.21/0.56 # Result found by sh9
% 0.21/0.56 # Preprocessing class: HSLSSMSSSSSNSFA.
% 0.21/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56 # Starting new_ho_11 with 1500s (5) cores
% 0.21/0.56 # Starting post_as_ho6 with 300s (1) cores
% 0.21/0.56 # Starting sh9 with 300s (1) cores
% 0.21/0.56 # No SInE strategy applied
% 0.21/0.56 # Search class: HGHSM-FSLM31-MSFFFFBN
% 0.21/0.56 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.56 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.56 # new_ho_10 with pid 24457 completed with status 0
% 0.21/0.56 # Result found by new_ho_10
% 0.21/0.56 # Preprocessing class: HSLSSMSSSSSNSFA.
% 0.21/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.56 # Starting new_ho_11 with 1500s (5) cores
% 0.21/0.56 # Starting post_as_ho6 with 300s (1) cores
% 0.21/0.56 # Starting sh9 with 300s (1) cores
% 0.21/0.56 # No SInE strategy applied
% 0.21/0.56 # Search class: HGHSM-FSLM31-MSFFFFBN
% 0.21/0.56 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.56 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.56 # Preprocessing time : 0.005 s
% 0.21/0.56 # Presaturation interreduction done
% 0.21/0.56
% 0.21/0.56 # Proof found!
% 0.21/0.56 # SZS status ContradictoryAxioms
% 0.21/0.56 # SZS output start CNFRefutation
% See solution above
% 0.21/0.56 # Parsed axioms : 225
% 0.21/0.56 # Removed by relevancy pruning/SinE : 0
% 0.21/0.56 # Initial clauses : 327
% 0.21/0.56 # Removed in clause preprocessing : 22
% 0.21/0.56 # Initial clauses in saturation : 305
% 0.21/0.56 # Processed clauses : 434
% 0.21/0.56 # ...of these trivial : 22
% 0.21/0.56 # ...subsumed : 109
% 0.21/0.56 # ...remaining for further processing : 303
% 0.21/0.56 # Other redundant clauses eliminated : 56
% 0.21/0.56 # Clauses deleted for lack of memory : 0
% 0.21/0.56 # Backward-subsumed : 2
% 0.21/0.56 # Backward-rewritten : 3
% 0.21/0.56 # Generated clauses : 464
% 0.21/0.56 # ...of the previous two non-redundant : 274
% 0.21/0.56 # ...aggressively subsumed : 0
% 0.21/0.56 # Contextual simplify-reflections : 0
% 0.21/0.56 # Paramodulations : 407
% 0.21/0.56 # Factorizations : 0
% 0.21/0.56 # NegExts : 0
% 0.21/0.56 # Equation resolutions : 60
% 0.21/0.56 # Disequality decompositions : 0
% 0.21/0.56 # Total rewrite steps : 215
% 0.21/0.56 # ...of those cached : 149
% 0.21/0.56 # Propositional unsat checks : 0
% 0.21/0.56 # Propositional check models : 0
% 0.21/0.56 # Propositional check unsatisfiable : 0
% 0.21/0.56 # Propositional clauses : 0
% 0.21/0.56 # Propositional clauses after purity: 0
% 0.21/0.56 # Propositional unsat core size : 0
% 0.21/0.56 # Propositional preprocessing time : 0.000
% 0.21/0.56 # Propositional encoding time : 0.000
% 0.21/0.56 # Propositional solver time : 0.000
% 0.21/0.56 # Success case prop preproc time : 0.000
% 0.21/0.56 # Success case prop encoding time : 0.000
% 0.21/0.56 # Success case prop solver time : 0.000
% 0.21/0.56 # Current number of processed clauses : 84
% 0.21/0.56 # Positive orientable unit clauses : 31
% 0.21/0.56 # Positive unorientable unit clauses: 2
% 0.21/0.56 # Negative unit clauses : 6
% 0.21/0.56 # Non-unit-clauses : 45
% 0.21/0.56 # Current number of unprocessed clauses: 312
% 0.21/0.56 # ...number of literals in the above : 665
% 0.21/0.56 # Current number of archived formulas : 0
% 0.21/0.56 # Current number of archived clauses : 172
% 0.21/0.56 # Clause-clause subsumption calls (NU) : 1923
% 0.21/0.56 # Rec. Clause-clause subsumption calls : 1828
% 0.21/0.56 # Non-unit clause-clause subsumptions : 73
% 0.21/0.56 # Unit Clause-clause subsumption calls : 16
% 0.21/0.56 # Rewrite failures with RHS unbound : 0
% 0.21/0.56 # BW rewrite match attempts : 79
% 0.21/0.56 # BW rewrite match successes : 53
% 0.21/0.56 # Condensation attempts : 434
% 0.21/0.56 # Condensation successes : 0
% 0.21/0.56 # Termbank termtop insertions : 26852
% 0.21/0.56 # Search garbage collected termcells : 5431
% 0.21/0.56
% 0.21/0.56 # -------------------------------------------------
% 0.21/0.56 # User time : 0.044 s
% 0.21/0.56 # System time : 0.007 s
% 0.21/0.56 # Total time : 0.051 s
% 0.21/0.56 # Maximum resident set size: 3044 pages
% 0.21/0.56
% 0.21/0.56 # -------------------------------------------------
% 0.21/0.56 # User time : 0.079 s
% 0.21/0.56 # System time : 0.025 s
% 0.21/0.56 # Total time : 0.105 s
% 0.21/0.56 # Maximum resident set size: 1960 pages
% 0.21/0.56 % E---3.1 exiting
% 0.21/0.56 % E exiting
%------------------------------------------------------------------------------