TSTP Solution File: NUM666^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM666^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.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 08:56:07 EDT 2024
% Result : Theorem 0.17s 0.43s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 3 unt; 8 typ; 0 def)
% Number of atoms : 49 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 11 ~; 8 |; 0 &; 90 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 31 ( 11 ^ 20 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_22,type,
x: nat ).
thf(decl_23,type,
y: nat ).
thf(decl_24,type,
z: nat ).
thf(decl_25,type,
some: ( nat > $o ) > $o ).
thf(decl_26,type,
diffprop: nat > nat > nat > $o ).
thf(decl_27,type,
moreis: nat > nat > $o ).
thf(decl_28,type,
lessis: nat > nat > $o ).
thf(satz16a,axiom,
! [X2: nat,X3: nat,X4: nat] :
( ( lessis @ X2 @ X3 )
=> ( ( some
@ ^ [X5: nat] : ( diffprop @ X4 @ X3 @ X5 ) )
=> ( some
@ ^ [X5: nat] : ( diffprop @ X4 @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qUTPAo8aaF/E---3.1_32704.p',satz16a) ).
thf(m,axiom,
( some
@ ^ [X1: nat] : ( diffprop @ x @ y @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.qUTPAo8aaF/E---3.1_32704.p',m) ).
thf(satz13,axiom,
! [X2: nat,X3: nat] :
( ( moreis @ X2 @ X3 )
=> ( lessis @ X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.qUTPAo8aaF/E---3.1_32704.p',satz13) ).
thf(satz16d,conjecture,
( some
@ ^ [X1: nat] : ( diffprop @ x @ z @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.qUTPAo8aaF/E---3.1_32704.p',satz16d) ).
thf(n,axiom,
moreis @ y @ z,
file('/export/starexec/sandbox2/tmp/tmp.qUTPAo8aaF/E---3.1_32704.p',n) ).
thf(c_0_5,plain,
! [X2: nat,X3: nat,X4: nat] :
( ( lessis @ X2 @ X3 )
=> ( ( some
@ ^ [Z0: nat] : ( diffprop @ X4 @ X3 @ Z0 ) )
=> ( some
@ ^ [Z0: nat] : ( diffprop @ X4 @ X2 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz16a]) ).
thf(c_0_6,plain,
! [X11: nat,X12: nat,X13: nat] :
( ~ ( lessis @ X11 @ X12 )
| ~ ( some
@ ^ [Z0: nat] : ( diffprop @ X13 @ X12 @ Z0 ) )
| ( some
@ ^ [Z0: nat] : ( diffprop @ X13 @ X11 @ Z0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_7,plain,
( some
@ ^ [Z0: nat] : ( diffprop @ x @ y @ Z0 ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_8,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( some @ ( diffprop @ X3 @ X1 ) )
| ~ ( lessis @ X1 @ X2 )
| ~ ( some @ ( diffprop @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
some @ ( diffprop @ x @ y ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X14: nat,X15: nat] :
( ~ ( moreis @ X14 @ X15 )
| ( lessis @ X15 @ X14 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz13])])]) ).
thf(c_0_11,negated_conjecture,
~ ( some
@ ^ [Z0: nat] : ( diffprop @ x @ z @ Z0 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz16d])])]) ).
thf(c_0_12,plain,
! [X1: nat] :
( ( some @ ( diffprop @ x @ X1 ) )
| ~ ( lessis @ X1 @ y ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,plain,
! [X1: nat,X2: nat] :
( ( lessis @ X2 @ X1 )
| ~ ( moreis @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
~ ( some
@ ^ [Z0: nat] : ( diffprop @ x @ z @ Z0 ) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
! [X1: nat] :
( ( some @ ( diffprop @ x @ X1 ) )
| ~ ( moreis @ y @ X1 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,plain,
moreis @ y @ z,
inference(split_conjunct,[status(thm)],[n]) ).
thf(c_0_17,negated_conjecture,
~ ( some @ ( diffprop @ x @ z ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : NUM666^1 : TPTP v8.1.2. Released v3.7.0.
% 0.05/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n015.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 09:50:21 EDT 2024
% 0.17/0.31 % CPUTime :
% 0.17/0.42 Running higher-order theorem proving
% 0.17/0.42 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/tmp/tmp.qUTPAo8aaF/E---3.1_32704.p
% 0.17/0.43 # Version: 3.1.0-ho
% 0.17/0.43 # Preprocessing class: HSSSSMSSSSMNSSN.
% 0.17/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.43 # Starting sh3 with 1500s (5) cores
% 0.17/0.43 # Starting ehoh_best8_lambda with 300s (1) cores
% 0.17/0.43 # Starting sh2lt with 300s (1) cores
% 0.17/0.43 # Starting ho_unfolding_1 with 300s (1) cores
% 0.17/0.43 # ehoh_best8_lambda with pid 315 completed with status 0
% 0.17/0.43 # Result found by ehoh_best8_lambda
% 0.17/0.43 # Preprocessing class: HSSSSMSSSSMNSSN.
% 0.17/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.43 # Starting sh3 with 1500s (5) cores
% 0.17/0.43 # Starting ehoh_best8_lambda with 300s (1) cores
% 0.17/0.43 # No SInE strategy applied
% 0.17/0.43 # Search class: HHUNF-FFSF00-SSSFFFNN
% 0.17/0.43 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.43 # Starting sh3 with 163s (1) cores
% 0.17/0.43 # sh3 with pid 318 completed with status 0
% 0.17/0.43 # Result found by sh3
% 0.17/0.43 # Preprocessing class: HSSSSMSSSSMNSSN.
% 0.17/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.43 # Starting sh3 with 1500s (5) cores
% 0.17/0.43 # Starting ehoh_best8_lambda with 300s (1) cores
% 0.17/0.43 # No SInE strategy applied
% 0.17/0.43 # Search class: HHUNF-FFSF00-SSSFFFNN
% 0.17/0.43 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.43 # Starting sh3 with 163s (1) cores
% 0.17/0.43 # Preprocessing time : 0.001 s
% 0.17/0.43 # Presaturation interreduction done
% 0.17/0.43
% 0.17/0.43 # Proof found!
% 0.17/0.43 # SZS status Theorem
% 0.17/0.43 # SZS output start CNFRefutation
% See solution above
% 0.17/0.43 # Parsed axioms : 13
% 0.17/0.43 # Removed by relevancy pruning/SinE : 0
% 0.17/0.43 # Initial clauses : 13
% 0.17/0.43 # Removed in clause preprocessing : 8
% 0.17/0.43 # Initial clauses in saturation : 5
% 0.17/0.43 # Processed clauses : 12
% 0.17/0.43 # ...of these trivial : 0
% 0.17/0.43 # ...subsumed : 0
% 0.17/0.43 # ...remaining for further processing : 12
% 0.17/0.43 # Other redundant clauses eliminated : 0
% 0.17/0.43 # Clauses deleted for lack of memory : 0
% 0.17/0.43 # Backward-subsumed : 0
% 0.17/0.43 # Backward-rewritten : 0
% 0.17/0.43 # Generated clauses : 3
% 0.17/0.43 # ...of the previous two non-redundant : 2
% 0.17/0.43 # ...aggressively subsumed : 0
% 0.17/0.43 # Contextual simplify-reflections : 0
% 0.17/0.43 # Paramodulations : 3
% 0.17/0.43 # Factorizations : 0
% 0.17/0.43 # NegExts : 0
% 0.17/0.43 # Equation resolutions : 0
% 0.17/0.43 # Disequality decompositions : 0
% 0.17/0.43 # Total rewrite steps : 0
% 0.17/0.43 # ...of those cached : 0
% 0.17/0.43 # Propositional unsat checks : 0
% 0.17/0.43 # Propositional check models : 0
% 0.17/0.43 # Propositional check unsatisfiable : 0
% 0.17/0.43 # Propositional clauses : 0
% 0.17/0.43 # Propositional clauses after purity: 0
% 0.17/0.43 # Propositional unsat core size : 0
% 0.17/0.43 # Propositional preprocessing time : 0.000
% 0.17/0.43 # Propositional encoding time : 0.000
% 0.17/0.43 # Propositional solver time : 0.000
% 0.17/0.43 # Success case prop preproc time : 0.000
% 0.17/0.43 # Success case prop encoding time : 0.000
% 0.17/0.43 # Success case prop solver time : 0.000
% 0.17/0.43 # Current number of processed clauses : 7
% 0.17/0.43 # Positive orientable unit clauses : 2
% 0.17/0.43 # Positive unorientable unit clauses: 0
% 0.17/0.43 # Negative unit clauses : 1
% 0.17/0.43 # Non-unit-clauses : 4
% 0.17/0.43 # Current number of unprocessed clauses: 0
% 0.17/0.43 # ...number of literals in the above : 0
% 0.17/0.43 # Current number of archived formulas : 0
% 0.17/0.43 # Current number of archived clauses : 5
% 0.17/0.43 # Clause-clause subsumption calls (NU) : 0
% 0.17/0.43 # Rec. Clause-clause subsumption calls : 0
% 0.17/0.43 # Non-unit clause-clause subsumptions : 0
% 0.17/0.43 # Unit Clause-clause subsumption calls : 0
% 0.17/0.43 # Rewrite failures with RHS unbound : 0
% 0.17/0.43 # BW rewrite match attempts : 0
% 0.17/0.43 # BW rewrite match successes : 0
% 0.17/0.43 # Condensation attempts : 0
% 0.17/0.43 # Condensation successes : 0
% 0.17/0.43 # Termbank termtop insertions : 558
% 0.17/0.43 # Search garbage collected termcells : 80
% 0.17/0.43
% 0.17/0.43 # -------------------------------------------------
% 0.17/0.43 # User time : 0.005 s
% 0.17/0.43 # System time : 0.000 s
% 0.17/0.43 # Total time : 0.005 s
% 0.17/0.43 # Maximum resident set size: 1728 pages
% 0.17/0.43
% 0.17/0.43 # -------------------------------------------------
% 0.17/0.43 # User time : 0.006 s
% 0.17/0.43 # System time : 0.002 s
% 0.17/0.43 # Total time : 0.007 s
% 0.17/0.43 # Maximum resident set size: 1720 pages
% 0.17/0.43 % E---3.1 exiting
% 0.17/0.43 % E exiting
%------------------------------------------------------------------------------