TSTP Solution File: NUM645^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM645^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.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 01:15:13 EDT 2024
% Result : Theorem 0.20s 0.50s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 54 ( 25 unt; 10 typ; 0 def)
% Number of atoms : 90 ( 55 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 346 ( 52 ~; 24 |; 1 &; 262 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 20 ^ 58 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
set: $tType ).
thf(decl_22,type,
x: nat ).
thf(decl_23,type,
y: nat ).
thf(decl_24,type,
pl: nat > nat > nat ).
thf(decl_25,type,
esti: nat > set > $o ).
thf(decl_26,type,
setof: ( nat > $o ) > set ).
thf(decl_27,type,
n_1: nat ).
thf(decl_28,type,
suc: nat > nat ).
thf(decl_29,type,
esk1_1: set > nat ).
thf(ax3,axiom,
! [X4: nat] :
( ( suc @ X4 )
!= n_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(satz4b,axiom,
! [X4: nat,X5: nat] :
( ( pl @ X4 @ ( suc @ X5 ) )
= ( suc @ ( pl @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4b) ).
thf(satz4a,axiom,
! [X4: nat] :
( ( pl @ X4 @ n_1 )
= ( suc @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4a) ).
thf(ax5,axiom,
! [X3: set] :
( ( esti @ n_1 @ X3 )
=> ( ! [X4: nat] :
( ( esti @ X4 @ X3 )
=> ( esti @ ( suc @ X4 ) @ X3 ) )
=> ! [X4: nat] : ( esti @ X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(estii,axiom,
! [X1: nat > $o,X2: nat] :
( ( X1 @ X2 )
=> ( esti @ X2 @ ( setof @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',estii) ).
thf(satz7,conjecture,
( y
!= ( pl @ x @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz7) ).
thf(satz1,axiom,
! [X4: nat,X5: nat] :
( ( X4 != X5 )
=> ( ( suc @ X4 )
!= ( suc @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz1) ).
thf(estie,axiom,
! [X1: nat > $o,X2: nat] :
( ( esti @ X2 @ ( setof @ X1 ) )
=> ( X1 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',estie) ).
thf(c_0_8,plain,
! [X4: nat] :
( ( suc @ X4 )
!= n_1 ),
inference(fof_simplification,[status(thm)],[ax3]) ).
thf(c_0_9,plain,
! [X30: nat,X31: nat] :
( ( pl @ X30 @ ( suc @ X31 ) )
= ( suc @ ( pl @ X30 @ X31 ) ) ),
inference(variable_rename,[status(thm)],[satz4b]) ).
thf(c_0_10,plain,
! [X27: nat] :
( ( pl @ X27 @ n_1 )
= ( suc @ X27 ) ),
inference(variable_rename,[status(thm)],[satz4a]) ).
thf(c_0_11,plain,
! [X21: set,X23: nat] :
( ( ( esti @ ( esk1_1 @ X21 ) @ X21 )
| ( esti @ X23 @ X21 )
| ~ ( esti @ n_1 @ X21 ) )
& ( ~ ( esti @ ( suc @ ( esk1_1 @ X21 ) ) @ X21 )
| ( esti @ X23 @ X21 )
| ~ ( esti @ n_1 @ X21 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])])]) ).
thf(c_0_12,plain,
! [X24: nat > $o,X25: nat] :
( ~ ( X24 @ X25 )
| ( esti @ X25 @ ( setof @ X24 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[estii])])]) ).
thf(c_0_13,negated_conjecture,
( y
= ( pl @ x @ y ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz7])]) ).
thf(c_0_14,plain,
! [X26: nat] :
( ( suc @ X26 )
!= n_1 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).
thf(c_0_15,plain,
! [X4: nat,X5: nat] :
( ( X4 != X5 )
=> ( ( suc @ X4 )
!= ( suc @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[satz1]) ).
thf(c_0_16,plain,
! [X19: nat > $o,X20: nat] :
( ~ ( esti @ X20 @ ( setof @ X19 ) )
| ( X19 @ X20 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[estie])])]) ).
thf(c_0_17,plain,
! [X2: nat,X4: nat] :
( ( pl @ X2 @ ( suc @ X4 ) )
= ( suc @ ( pl @ X2 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_18,plain,
! [X2: nat] :
( ( pl @ X2 @ n_1 )
= ( suc @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_19,plain,
! [X2: nat,X3: set] :
( ( esti @ X2 @ X3 )
| ~ ( esti @ ( suc @ ( esk1_1 @ X3 ) ) @ X3 )
| ~ ( esti @ n_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_20,plain,
! [X1: nat > $o,X2: nat] :
( ( esti @ X2 @ ( setof @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_21,negated_conjecture,
( y
= ( pl @ x @ y ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_22,plain,
! [X2: nat] :
( ( suc @ X2 )
!= n_1 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_23,plain,
! [X28: nat,X29: nat] :
( ( X28 = X29 )
| ( ( suc @ X28 )
!= ( suc @ X29 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
thf(c_0_24,plain,
! [X2: nat,X1: nat > $o] :
( ( X1 @ X2 )
| ~ ( esti @ X2 @ ( setof @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_25,plain,
! [X2: nat,X4: nat] :
( ( pl @ ( pl @ X2 @ X4 ) @ n_1 )
= ( pl @ X2 @ ( pl @ X4 @ n_1 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
thf(c_0_26,plain,
! [X2: nat,X3: set] :
( ( esti @ X2 @ X3 )
| ~ ( esti @ ( pl @ ( esk1_1 @ X3 ) @ n_1 ) @ X3 )
| ~ ( esti @ n_1 @ X3 ) ),
inference(rw,[status(thm)],[c_0_19,c_0_18]) ).
thf(c_0_27,plain,
! [X2: nat] :
( ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) )
| ( X2
= ( pl @ x @ X2 ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_20,c_0_21]) ).
thf(c_0_28,plain,
! [X2: nat] :
( ( pl @ X2 @ n_1 )
!= n_1 ),
inference(rw,[status(thm)],[c_0_22,c_0_18]) ).
thf(c_0_29,plain,
! [X2: nat,X4: nat] :
( ( X2 = X4 )
| ( ( suc @ X2 )
!= ( suc @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_30,plain,
! [X2: nat] :
( ( X2
!= ( pl @ x @ X2 ) )
| ~ ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_24,c_0_21]) ).
thf(c_0_31,negated_conjecture,
( ( pl @ x @ ( pl @ y @ n_1 ) )
= ( pl @ y @ n_1 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
thf(c_0_32,plain,
! [X2: nat] :
( ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) )
| ~ ( esti
@ ( pl
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) )
@ n_1 )
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_33,plain,
! [X2: nat,X3: set] :
( ( esti @ ( esk1_1 @ X3 ) @ X3 )
| ( esti @ X2 @ X3 )
| ~ ( esti @ n_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_34,plain,
! [X2: nat,X4: nat] :
( ( X2 = X4 )
| ( ( pl @ X2 @ n_1 )
!= ( pl @ X4 @ n_1 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_18]),c_0_18]) ).
thf(c_0_35,negated_conjecture,
~ ( esti @ ( pl @ y @ n_1 )
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_36,plain,
! [X2: nat] :
( ( ( pl @ x
@ ( pl
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) )
@ n_1 ) )
= ( pl
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) )
@ n_1 ) )
| ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
thf(c_0_37,plain,
! [X2: nat] :
( ( esti
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) )
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) )
| ( esti @ X2
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_27]),c_0_28]) ).
thf(c_0_38,plain,
! [X2: nat,X4: nat,X5: nat] :
( ( X2
= ( pl @ X4 @ X5 ) )
| ( ( pl @ X2 @ n_1 )
!= ( pl @ X4 @ ( pl @ X5 @ n_1 ) ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
thf(c_0_39,negated_conjecture,
( ( pl @ x
@ ( pl
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) )
@ n_1 ) )
= ( pl
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) )
@ n_1 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_40,plain,
( esti
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) )
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) ),
inference(ef,[status(thm)],[c_0_37]) ).
thf(c_0_41,negated_conjecture,
! [X2: nat] :
( ( X2
= ( pl @ x
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) ) ) )
| ( ( pl @ X2 @ n_1 )
!= ( pl
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) )
@ n_1 ) ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_42,plain,
( ( pl @ x
@ ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) ) )
!= ( esk1_1
@ ( setof
@ ^ [Z0: nat] :
( Z0
!= ( pl @ x @ Z0 ) ) ) ) ),
inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_40])]) ).
thf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM645^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 07:06:23 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 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
% 0.20/0.50 # Version: 3.1.0-ho
% 0.20/0.50 # Preprocessing class: HSMSSMSSSSSNSFA.
% 0.20/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50 # Starting new_ho_14 with 1200s (4) cores
% 0.20/0.50 # Starting new_ho_13 with 600s (2) cores
% 0.20/0.50 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.20/0.50 # Starting new_bool_3 with 300s (1) cores
% 0.20/0.50 # new_ho_13 with pid 15891 completed with status 0
% 0.20/0.50 # Result found by new_ho_13
% 0.20/0.50 # Preprocessing class: HSMSSMSSSSSNSFA.
% 0.20/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50 # Starting new_ho_14 with 1200s (4) cores
% 0.20/0.50 # Starting new_ho_13 with 600s (2) cores
% 0.20/0.50 # No SInE strategy applied
% 0.20/0.50 # Search class: HGHSS-FFSF21-MSFFFSBN
% 0.20/0.50 # partial match(2): HGHSS-FFSF21-MSSFFMBN
% 0.20/0.50 # Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.20/0.50 # Starting post_as_ho12 with 270s (1) cores
% 0.20/0.50 # Starting new_ho_13 with 61s (1) cores
% 0.20/0.50 # new_ho_13 with pid 15900 completed with status 0
% 0.20/0.50 # Result found by new_ho_13
% 0.20/0.50 # Preprocessing class: HSMSSMSSSSSNSFA.
% 0.20/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50 # Starting new_ho_14 with 1200s (4) cores
% 0.20/0.50 # Starting new_ho_13 with 600s (2) cores
% 0.20/0.50 # No SInE strategy applied
% 0.20/0.50 # Search class: HGHSS-FFSF21-MSFFFSBN
% 0.20/0.50 # partial match(2): HGHSS-FFSF21-MSSFFMBN
% 0.20/0.50 # Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 0.20/0.50 # Starting post_as_ho12 with 270s (1) cores
% 0.20/0.50 # Starting new_ho_13 with 61s (1) cores
% 0.20/0.50 # Preprocessing time : 0.001 s
% 0.20/0.50 # Presaturation interreduction done
% 0.20/0.50
% 0.20/0.50 # Proof found!
% 0.20/0.50 # SZS status Theorem
% 0.20/0.50 # SZS output start CNFRefutation
% See solution above
% 0.20/0.50 # Parsed axioms : 17
% 0.20/0.50 # Removed by relevancy pruning/SinE : 0
% 0.20/0.50 # Initial clauses : 18
% 0.20/0.50 # Removed in clause preprocessing : 9
% 0.20/0.50 # Initial clauses in saturation : 11
% 0.20/0.50 # Processed clauses : 199
% 0.20/0.50 # ...of these trivial : 8
% 0.20/0.50 # ...subsumed : 122
% 0.20/0.50 # ...remaining for further processing : 69
% 0.20/0.50 # Other redundant clauses eliminated : 0
% 0.20/0.50 # Clauses deleted for lack of memory : 0
% 0.20/0.50 # Backward-subsumed : 2
% 0.20/0.50 # Backward-rewritten : 4
% 0.20/0.50 # Generated clauses : 319
% 0.20/0.50 # ...of the previous two non-redundant : 298
% 0.20/0.50 # ...aggressively subsumed : 0
% 0.20/0.50 # Contextual simplify-reflections : 0
% 0.20/0.50 # Paramodulations : 314
% 0.20/0.50 # Factorizations : 2
% 0.20/0.50 # NegExts : 0
% 0.20/0.50 # Equation resolutions : 3
% 0.20/0.50 # Disequality decompositions : 0
% 0.20/0.50 # Total rewrite steps : 579
% 0.20/0.50 # ...of those cached : 408
% 0.20/0.50 # Propositional unsat checks : 0
% 0.20/0.50 # Propositional check models : 0
% 0.20/0.50 # Propositional check unsatisfiable : 0
% 0.20/0.50 # Propositional clauses : 0
% 0.20/0.50 # Propositional clauses after purity: 0
% 0.20/0.50 # Propositional unsat core size : 0
% 0.20/0.50 # Propositional preprocessing time : 0.000
% 0.20/0.50 # Propositional encoding time : 0.000
% 0.20/0.50 # Propositional solver time : 0.000
% 0.20/0.50 # Success case prop preproc time : 0.000
% 0.20/0.50 # Success case prop encoding time : 0.000
% 0.20/0.50 # Success case prop solver time : 0.000
% 0.20/0.50 # Current number of processed clauses : 52
% 0.20/0.50 # Positive orientable unit clauses : 16
% 0.20/0.50 # Positive unorientable unit clauses: 0
% 0.20/0.50 # Negative unit clauses : 22
% 0.20/0.50 # Non-unit-clauses : 14
% 0.20/0.50 # Current number of unprocessed clauses: 101
% 0.20/0.50 # ...number of literals in the above : 125
% 0.20/0.50 # Current number of archived formulas : 0
% 0.20/0.50 # Current number of archived clauses : 17
% 0.20/0.50 # Clause-clause subsumption calls (NU) : 134
% 0.20/0.50 # Rec. Clause-clause subsumption calls : 134
% 0.20/0.50 # Non-unit clause-clause subsumptions : 23
% 0.20/0.50 # Unit Clause-clause subsumption calls : 4
% 0.20/0.50 # Rewrite failures with RHS unbound : 0
% 0.20/0.50 # BW rewrite match attempts : 19
% 0.20/0.50 # BW rewrite match successes : 3
% 0.20/0.50 # Condensation attempts : 0
% 0.20/0.50 # Condensation successes : 0
% 0.20/0.50 # Termbank termtop insertions : 11564
% 0.20/0.50 # Search garbage collected termcells : 161
% 0.20/0.50
% 0.20/0.50 # -------------------------------------------------
% 0.20/0.50 # User time : 0.015 s
% 0.20/0.50 # System time : 0.003 s
% 0.20/0.50 # Total time : 0.018 s
% 0.20/0.50 # Maximum resident set size: 1732 pages
% 0.20/0.50
% 0.20/0.50 # -------------------------------------------------
% 0.20/0.50 # User time : 0.030 s
% 0.20/0.50 # System time : 0.006 s
% 0.20/0.50 # Total time : 0.036 s
% 0.20/0.50 # Maximum resident set size: 1732 pages
% 0.20/0.50 % E---3.1 exiting
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------