TSTP Solution File: NUN025^3 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUN025^3 : TPTP v8.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 02:15:23 EDT 2024
% Result : Theorem 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 8 unt; 5 typ; 0 def)
% Number of atoms : 140 ( 85 equ; 0 cnn)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 392 ( 56 ~; 49 |; 30 &; 247 @)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 0 ^ 54 !; 2 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
zero: $i ).
thf(decl_23,type,
s: $i > $i ).
thf(decl_24,type,
ite: $o > $i > $i > $i ).
thf(decl_25,type,
h: $i > $i ).
thf(decl_26,type,
epred1_0: $o ).
thf(n10,conjecture,
( ( ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) )
& ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) )
& ! [X4: $i] :
( ( s @ X4 )
!= zero )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X4: $i] :
( ( h @ X4 )
= ( ite @ ( X4 = zero ) @ ( s @ zero )
@ ( ite
@ ( X4
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) ) ) )
=> ? [X5: $i > $i] :
( ( ( X5 @ zero )
= ( s @ zero ) )
& ( ( X5 @ ( s @ zero ) )
= zero )
& ( ( X5 @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n10) ).
thf(c_0_1,plain,
( epred1_0
<=> ( ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) )
& ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) )
& ! [X4: $i] :
( ( s @ X4 )
!= zero )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X4: $i] :
( ( ( X4 != zero )
| ( ( ( X4
!= ( s @ zero ) )
| ( ( h @ X4 )
= ( ite @ $true @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) ) )
& ( ( X4
= ( s @ zero ) )
| ( ( h @ X4 )
= ( ite @ $true @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) ) ) ) )
& ( ( X4 = zero )
| ( ( ( X4
!= ( s @ zero ) )
| ( ( h @ X4 )
= ( ite @ $false @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) ) )
& ( ( X4
= ( s @ zero ) )
| ( ( h @ X4 )
= ( ite @ $false @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_2,plain,
( epred1_0
=> ( ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) )
& ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) )
& ! [X4: $i] :
( ( s @ X4 )
!= zero )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X4: $i] :
( ( ( X4 != zero )
| ( ( ( X4
!= ( s @ zero ) )
| ( ( h @ X4 )
= ( ite @ $true @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) ) )
& ( ( X4
= ( s @ zero ) )
| ( ( h @ X4 )
= ( ite @ $true @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) ) ) ) )
& ( ( X4 = zero )
| ( ( ( X4
!= ( s @ zero ) )
| ( ( h @ X4 )
= ( ite @ $false @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) ) )
& ( ( X4
= ( s @ zero ) )
| ( ( h @ X4 )
= ( ite @ $false @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) ) ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
~ ( epred1_0
=> ? [X5: $i > $i] :
( ( ( X5 @ zero )
= ( s @ zero ) )
& ( ( X5 @ ( s @ zero ) )
= zero )
& ( ( X5 @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[n10])])]),c_0_1]) ).
thf(c_0_4,plain,
! [X17: $o,X18: $i,X19: $i,X20: $o,X21: $i,X22: $i,X23: $i,X24: $i,X25: $i] :
( ( ~ X17
| ( ( ite @ X17 @ X18 @ X19 )
= X18 )
| ~ epred1_0 )
& ( X20
| ( ( ite @ X20 @ X21 @ X22 )
= X22 )
| ~ epred1_0 )
& ( ( ( s @ X23 )
!= zero )
| ~ epred1_0 )
& ( ( ( s @ X24 )
!= X24 )
| ~ epred1_0 )
& ( ( X25
!= ( s @ zero ) )
| ( ( h @ X25 )
= ( ite @ $true @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) )
| ( X25 != zero )
| ~ epred1_0 )
& ( ( X25
= ( s @ zero ) )
| ( ( h @ X25 )
= ( ite @ $true @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) )
| ( X25 != zero )
| ~ epred1_0 )
& ( ( X25
!= ( s @ zero ) )
| ( ( h @ X25 )
= ( ite @ $false @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) )
| ( X25 = zero )
| ~ epred1_0 )
& ( ( X25
= ( s @ zero ) )
| ( ( h @ X25 )
= ( ite @ $false @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) )
| ( X25 = zero )
| ~ epred1_0 ) ),
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_2])])])])]) ).
thf(c_0_5,negated_conjecture,
! [X16: $i > $i] :
( epred1_0
& ( ( ( X16 @ zero )
!= ( s @ zero ) )
| ( ( X16 @ ( s @ zero ) )
!= zero )
| ( ( X16 @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
thf(c_0_6,plain,
! [X2: $i,X3: $i] :
( ( ( ite @ ~ $true @ X2 @ X3 )
= X3 )
| ~ epred1_0 ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_4])])]) ).
thf(c_0_7,negated_conjecture,
epred1_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X3: $i,X2: $i] :
( ( ( ite @ $true @ X2 @ X3 )
= X2 )
| ~ epred1_0 ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_4])])]) ).
thf(c_0_9,plain,
! [X2: $i] :
( ( ( s @ X2 )
!= X2 )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_10,plain,
! [X2: $i] :
( ( X2
= ( s @ zero ) )
| ( ( h @ X2 )
= ( ite @ ~ $true @ ( s @ zero ) @ ( ite @ ~ $true @ zero @ ( s @ zero ) ) ) )
| ( X2 = zero )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_11,plain,
! [X2: $i,X3: $i] :
( ( ite @ ~ $true @ X2 @ X3 )
= X3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]) ).
thf(c_0_12,plain,
! [X2: $i] :
( ( ( s @ X2 )
!= zero )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_13,plain,
! [X2: $i] :
( ( X2
= ( s @ zero ) )
| ( ( h @ X2 )
= ( ite @ $true @ ( s @ zero ) @ ( ite @ ~ $true @ zero @ ( s @ zero ) ) ) )
| ( X2 != zero )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_14,plain,
! [X3: $i,X2: $i] :
( ( ite @ $true @ X2 @ X3 )
= X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_7])]) ).
thf(c_0_15,plain,
! [X2: $i] :
( ( s @ X2 )
!= X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_7])]) ).
thf(c_0_16,plain,
! [X2: $i] :
( ( ( h @ X2 )
= ( ite @ ~ $true @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) )
| ( X2 = zero )
| ( X2
!= ( s @ zero ) )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_17,negated_conjecture,
! [X5: $i > $i] :
( ( ( X5 @ zero )
!= ( s @ zero ) )
| ( ( X5 @ ( s @ zero ) )
!= zero )
| ( ( X5 @ ( s @ ( s @ zero ) ) )
!= ( s @ zero ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_18,plain,
! [X2: $i] :
( ( ( h @ X2 )
= ( s @ zero ) )
| ( X2
= ( s @ zero ) )
| ( X2 = zero ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]),c_0_7])]) ).
thf(c_0_19,plain,
! [X2: $i] :
( ( s @ X2 )
!= zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_7])]) ).
thf(c_0_20,plain,
( ( h @ zero )
= ( s @ zero ) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_14]),c_0_7])])]),c_0_15]) ).
thf(c_0_21,plain,
( ( h @ ( s @ zero ) )
= zero ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_14]),c_0_11]),c_0_7])])]),c_0_15]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_15]),c_0_19]),c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN025^3 : TPTP v8.2.0. Released v6.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n022.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 15:05:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.50 Running higher-order theorem proving
% 0.20/0.50 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
% 0.20/0.51 # Version: 3.1.0-ho
% 0.20/0.51 # Preprocessing class: HSSSSMSSSSSNSSA.
% 0.20/0.51 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting post_as_ho12 with 300s (1) cores
% 0.20/0.51 # Starting new_bool_9 with 300s (1) cores
% 0.20/0.51 # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.51 # Starting post_as_ho4 with 300s (1) cores
% 0.20/0.51 # Starting post_as_ho2 with 300s (1) cores
% 0.20/0.51 # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.20/0.51 # Starting full_lambda_10 with 300s (1) cores
% 0.20/0.51 # Starting new_ho_8 with 300s (1) cores
% 0.20/0.51 # post_as_ho12 with pid 22344 completed with status 0
% 0.20/0.51 # Result found by post_as_ho12
% 0.20/0.51 # Preprocessing class: HSSSSMSSSSSNSSA.
% 0.20/0.51 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting post_as_ho12 with 300s (1) cores
% 0.20/0.51 # No SInE strategy applied
% 0.20/0.51 # Search class: HGHSF-FFSF31-MSSFFSNN
% 0.20/0.51 # partial match(2): HGHPS-FFSF31-MSSFFSNN
% 0.20/0.51 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.51 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.51 # new_ho_10 with pid 22353 completed with status 0
% 0.20/0.51 # Result found by new_ho_10
% 0.20/0.51 # Preprocessing class: HSSSSMSSSSSNSSA.
% 0.20/0.51 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting post_as_ho12 with 300s (1) cores
% 0.20/0.51 # No SInE strategy applied
% 0.20/0.51 # Search class: HGHSF-FFSF31-MSSFFSNN
% 0.20/0.51 # partial match(2): HGHPS-FFSF31-MSSFFSNN
% 0.20/0.51 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.51 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.51 # Preprocessing time : 0.001 s
% 0.20/0.51 # Presaturation interreduction done
% 0.20/0.51
% 0.20/0.51 # Proof found!
% 0.20/0.51 # SZS status Theorem
% 0.20/0.51 # SZS output start CNFRefutation
% See solution above
% 0.20/0.51 # Parsed axioms : 5
% 0.20/0.51 # Removed by relevancy pruning/SinE : 0
% 0.20/0.51 # Initial clauses : 14
% 0.20/0.51 # Removed in clause preprocessing : 4
% 0.20/0.51 # Initial clauses in saturation : 10
% 0.20/0.51 # Processed clauses : 24
% 0.20/0.51 # ...of these trivial : 0
% 0.20/0.51 # ...subsumed : 2
% 0.20/0.51 # ...remaining for further processing : 21
% 0.20/0.51 # Other redundant clauses eliminated : 4
% 0.20/0.51 # Clauses deleted for lack of memory : 0
% 0.20/0.51 # Backward-subsumed : 0
% 0.20/0.51 # Backward-rewritten : 0
% 0.20/0.51 # Generated clauses : 7
% 0.20/0.51 # ...of the previous two non-redundant : 6
% 0.20/0.51 # ...aggressively subsumed : 0
% 0.20/0.51 # Contextual simplify-reflections : 0
% 0.20/0.51 # Paramodulations : 3
% 0.20/0.51 # Factorizations : 0
% 0.20/0.51 # NegExts : 0
% 0.20/0.51 # Equation resolutions : 4
% 0.20/0.51 # Disequality decompositions : 0
% 0.20/0.51 # Total rewrite steps : 22
% 0.20/0.51 # ...of those cached : 9
% 0.20/0.51 # Propositional unsat checks : 0
% 0.20/0.51 # Propositional check models : 0
% 0.20/0.51 # Propositional check unsatisfiable : 0
% 0.20/0.51 # Propositional clauses : 0
% 0.20/0.51 # Propositional clauses after purity: 0
% 0.20/0.51 # Propositional unsat core size : 0
% 0.20/0.51 # Propositional preprocessing time : 0.000
% 0.20/0.51 # Propositional encoding time : 0.000
% 0.20/0.51 # Propositional solver time : 0.000
% 0.20/0.51 # Success case prop preproc time : 0.000
% 0.20/0.51 # Success case prop encoding time : 0.000
% 0.20/0.51 # Success case prop solver time : 0.000
% 0.20/0.51 # Current number of processed clauses : 9
% 0.20/0.51 # Positive orientable unit clauses : 5
% 0.20/0.51 # Positive unorientable unit clauses: 0
% 0.20/0.51 # Negative unit clauses : 2
% 0.20/0.51 # Non-unit-clauses : 2
% 0.20/0.51 # Current number of unprocessed clauses: 1
% 0.20/0.51 # ...number of literals in the above : 2
% 0.20/0.51 # Current number of archived formulas : 0
% 0.20/0.51 # Current number of archived clauses : 9
% 0.20/0.51 # Clause-clause subsumption calls (NU) : 0
% 0.20/0.51 # Rec. Clause-clause subsumption calls : 0
% 0.20/0.51 # Non-unit clause-clause subsumptions : 0
% 0.20/0.51 # Unit Clause-clause subsumption calls : 4
% 0.20/0.51 # Rewrite failures with RHS unbound : 0
% 0.20/0.51 # BW rewrite match attempts : 0
% 0.20/0.51 # BW rewrite match successes : 0
% 0.20/0.51 # Condensation attempts : 24
% 0.20/0.51 # Condensation successes : 0
% 0.20/0.51 # Termbank termtop insertions : 1238
% 0.20/0.51 # Search garbage collected termcells : 202
% 0.20/0.51
% 0.20/0.51 # -------------------------------------------------
% 0.20/0.51 # User time : 0.004 s
% 0.20/0.51 # System time : 0.002 s
% 0.20/0.51 # Total time : 0.006 s
% 0.20/0.51 # Maximum resident set size: 1776 pages
% 0.20/0.51
% 0.20/0.51 # -------------------------------------------------
% 0.20/0.51 # User time : 0.005 s
% 0.20/0.51 # System time : 0.004 s
% 0.20/0.51 # Total time : 0.009 s
% 0.20/0.51 # Maximum resident set size: 1720 pages
% 0.20/0.51 % E---3.1 exiting
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------