TSTP Solution File: NUM638^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM638^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 01:15:10 EDT 2024
% Result : Theorem 0.17s 0.44s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 29 ( 8 unt; 7 typ; 0 def)
% Number of atoms : 56 ( 43 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 86 ( 23 ~; 11 |; 2 &; 41 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 12 ^ 15 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_22,type,
x: nat ).
thf(decl_23,type,
n_1: nat ).
thf(decl_24,type,
suc: nat > nat ).
thf(decl_25,type,
some: ( nat > $o ) > $o ).
thf(decl_26,type,
esk1_0: nat ).
thf(decl_27,type,
esk2_0: nat ).
thf(satz3a,conjecture,
~ ( ! [X4: nat,X2: nat] :
( ( x
= ( suc @ X4 ) )
=> ( ( x
= ( suc @ X2 ) )
=> ( X4 = X2 ) ) )
=> ~ ( some
@ ^ [X3: nat] :
( x
= ( suc @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3a) ).
thf(satz3,axiom,
! [X1: nat] :
( ( X1 != n_1 )
=> ( some
@ ^ [X3: nat] :
( X1
= ( suc @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3) ).
thf(n,axiom,
x != n_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(ax4,axiom,
! [X1: nat,X2: nat] :
( ( ( suc @ X1 )
= ( suc @ X2 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(c_0_4,negated_conjecture,
~ ~ ( ! [X4: nat,X2: nat] :
( ( x
= ( suc @ X4 ) )
=> ( ( x
= ( suc @ X2 ) )
=> ( X4 = X2 ) ) )
=> ~ ( some
@ ^ [Z0: nat] :
( x
= ( suc @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz3a])])]) ).
thf(c_0_5,plain,
! [X1: nat] :
( ( X1 != n_1 )
=> ( some
@ ^ [Z0: nat] :
( X1
= ( suc @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[satz3])]) ).
thf(c_0_6,plain,
x != n_1,
inference(fof_simplification,[status(thm)],[n]) ).
thf(c_0_7,negated_conjecture,
( ( ( x
= ( suc @ esk1_0 ) )
| ~ ( some
@ ^ [Z0: nat] :
( x
= ( suc @ Z0 ) ) ) )
& ( ( x
= ( suc @ esk2_0 ) )
| ~ ( some
@ ^ [Z0: nat] :
( x
= ( suc @ Z0 ) ) ) )
& ( ( esk1_0 != esk2_0 )
| ~ ( some
@ ^ [Z0: nat] :
( x
= ( suc @ Z0 ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
thf(c_0_8,plain,
! [X12: nat] :
( ( X12 = n_1 )
| ( some
@ ^ [Z0: nat] :
( X12
= ( suc @ Z0 ) ) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])]) ).
thf(c_0_9,plain,
x != n_1,
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X10: nat,X11: nat] :
( ( ( suc @ X10 )
!= ( suc @ X11 ) )
| ( X10 = X11 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])]) ).
thf(c_0_11,negated_conjecture,
( ( x
= ( suc @ esk1_0 ) )
| ~ ( some
@ ^ [Z0: nat] :
( x
= ( suc @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X1: nat] :
( ( X1 = n_1 )
| ( some
@ ^ [Z0: nat] :
( X1
= ( suc @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
x != n_1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X1: nat,X2: nat] :
( ( X1 = X2 )
| ( ( suc @ X1 )
!= ( suc @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
( ( suc @ esk1_0 )
= x ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
thf(c_0_16,negated_conjecture,
( ( x
= ( suc @ esk2_0 ) )
| ~ ( some
@ ^ [Z0: nat] :
( x
= ( suc @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_17,negated_conjecture,
( ( esk1_0 != esk2_0 )
| ~ ( some
@ ^ [Z0: nat] :
( x
= ( suc @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_18,negated_conjecture,
! [X1: nat] :
( ( esk1_0 = X1 )
| ( ( suc @ X1 )
!= x ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,negated_conjecture,
( ( suc @ esk2_0 )
= x ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_13]) ).
thf(c_0_20,negated_conjecture,
esk2_0 != esk1_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_12]),c_0_13]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM638^1 : TPTP v8.2.0. Released v3.7.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 20 07:30:38 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.43 Running higher-order theorem proving
% 0.17/0.43 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
% 0.17/0.44 # Version: 3.1.0-ho
% 0.17/0.44 # Preprocessing class: HSSSSMSSSSMNSSN.
% 0.17/0.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.44 # Starting sh3 with 1500s (5) cores
% 0.17/0.44 # Starting ehoh_best8_lambda with 300s (1) cores
% 0.17/0.44 # Starting sh2lt with 300s (1) cores
% 0.17/0.44 # Starting ho_unfolding_1 with 300s (1) cores
% 0.17/0.44 # ehoh_best8_lambda with pid 16835 completed with status 0
% 0.17/0.44 # Result found by ehoh_best8_lambda
% 0.17/0.44 # Preprocessing class: HSSSSMSSSSMNSSN.
% 0.17/0.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.44 # Starting sh3 with 1500s (5) cores
% 0.17/0.44 # Starting ehoh_best8_lambda with 300s (1) cores
% 0.17/0.44 # No SInE strategy applied
% 0.17/0.44 # Search class: HGHSF-FFSF11-MSSFFFNN
% 0.17/0.44 # partial match(1): HGHSF-FFSF11-SSSFFFNN
% 0.17/0.44 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.44 # Starting new_ho_10 with 163s (1) cores
% 0.17/0.44 # new_ho_10 with pid 16838 completed with status 0
% 0.17/0.44 # Result found by new_ho_10
% 0.17/0.44 # Preprocessing class: HSSSSMSSSSMNSSN.
% 0.17/0.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.44 # Starting sh3 with 1500s (5) cores
% 0.17/0.44 # Starting ehoh_best8_lambda with 300s (1) cores
% 0.17/0.44 # No SInE strategy applied
% 0.17/0.44 # Search class: HGHSF-FFSF11-MSSFFFNN
% 0.17/0.44 # partial match(1): HGHSF-FFSF11-SSSFFFNN
% 0.17/0.44 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.44 # Starting new_ho_10 with 163s (1) cores
% 0.17/0.44 # Preprocessing time : 0.001 s
% 0.17/0.44 # Presaturation interreduction done
% 0.17/0.44
% 0.17/0.44 # Proof found!
% 0.17/0.44 # SZS status Theorem
% 0.17/0.44 # SZS output start CNFRefutation
% See solution above
% 0.17/0.44 # Parsed axioms : 9
% 0.17/0.44 # Removed by relevancy pruning/SinE : 0
% 0.17/0.44 # Initial clauses : 11
% 0.17/0.44 # Removed in clause preprocessing : 5
% 0.17/0.44 # Initial clauses in saturation : 6
% 0.17/0.44 # Processed clauses : 16
% 0.17/0.44 # ...of these trivial : 0
% 0.17/0.44 # ...subsumed : 0
% 0.17/0.44 # ...remaining for further processing : 16
% 0.17/0.44 # Other redundant clauses eliminated : 0
% 0.17/0.44 # Clauses deleted for lack of memory : 0
% 0.17/0.44 # Backward-subsumed : 1
% 0.17/0.44 # Backward-rewritten : 2
% 0.17/0.44 # Generated clauses : 9
% 0.17/0.44 # ...of the previous two non-redundant : 7
% 0.17/0.44 # ...aggressively subsumed : 0
% 0.17/0.44 # Contextual simplify-reflections : 0
% 0.17/0.44 # Paramodulations : 8
% 0.17/0.44 # Factorizations : 0
% 0.17/0.44 # NegExts : 0
% 0.17/0.44 # Equation resolutions : 1
% 0.17/0.44 # Disequality decompositions : 0
% 0.17/0.44 # Total rewrite steps : 2
% 0.17/0.44 # ...of those cached : 0
% 0.17/0.44 # Propositional unsat checks : 0
% 0.17/0.44 # Propositional check models : 0
% 0.17/0.44 # Propositional check unsatisfiable : 0
% 0.17/0.44 # Propositional clauses : 0
% 0.17/0.44 # Propositional clauses after purity: 0
% 0.17/0.44 # Propositional unsat core size : 0
% 0.17/0.44 # Propositional preprocessing time : 0.000
% 0.17/0.44 # Propositional encoding time : 0.000
% 0.17/0.44 # Propositional solver time : 0.000
% 0.17/0.44 # Success case prop preproc time : 0.000
% 0.17/0.44 # Success case prop encoding time : 0.000
% 0.17/0.44 # Success case prop solver time : 0.000
% 0.17/0.44 # Current number of processed clauses : 7
% 0.17/0.44 # Positive orientable unit clauses : 2
% 0.17/0.44 # Positive unorientable unit clauses: 0
% 0.17/0.44 # Negative unit clauses : 2
% 0.17/0.44 # Non-unit-clauses : 3
% 0.17/0.44 # Current number of unprocessed clauses: 3
% 0.17/0.44 # ...number of literals in the above : 6
% 0.17/0.44 # Current number of archived formulas : 0
% 0.17/0.44 # Current number of archived clauses : 9
% 0.17/0.44 # Clause-clause subsumption calls (NU) : 4
% 0.17/0.44 # Rec. Clause-clause subsumption calls : 4
% 0.17/0.44 # Non-unit clause-clause subsumptions : 0
% 0.17/0.44 # Unit Clause-clause subsumption calls : 5
% 0.17/0.44 # Rewrite failures with RHS unbound : 0
% 0.17/0.44 # BW rewrite match attempts : 2
% 0.17/0.44 # BW rewrite match successes : 2
% 0.17/0.44 # Condensation attempts : 16
% 0.17/0.44 # Condensation successes : 0
% 0.17/0.44 # Termbank termtop insertions : 502
% 0.17/0.44 # Search garbage collected termcells : 107
% 0.17/0.44
% 0.17/0.44 # -------------------------------------------------
% 0.17/0.44 # User time : 0.001 s
% 0.17/0.44 # System time : 0.003 s
% 0.17/0.44 # Total time : 0.004 s
% 0.17/0.44 # Maximum resident set size: 1784 pages
% 0.17/0.44
% 0.17/0.44 # -------------------------------------------------
% 0.17/0.44 # User time : 0.002 s
% 0.17/0.44 # System time : 0.004 s
% 0.17/0.44 # Total time : 0.007 s
% 0.17/0.44 # Maximum resident set size: 1716 pages
% 0.17/0.44 % E---3.1 exiting
% 0.17/0.44 % E exiting
%------------------------------------------------------------------------------