TSTP Solution File: NUM647^4 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM647^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n012.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 08:55:56 EDT 2024
% Result : Theorem 0.37s 0.63s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 45 ( 23 unt; 13 typ; 0 def)
% Number of atoms : 114 ( 40 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 218 ( 31 ~; 21 |; 5 &; 140 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 64 ( 45 ^ 19 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_23,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
in: $i > $i > $o ).
thf(decl_61,type,
imp: $o > $o > $o ).
thf(decl_62,type,
d_not: $o > $o ).
thf(decl_77,type,
e_is: $i > $i > $i > $o ).
thf(decl_123,type,
nat: $i ).
thf(decl_124,type,
n_is: $i > $i > $o ).
thf(decl_125,type,
nis: $i > $i > $o ).
thf(decl_142,type,
n_pl: $i > $i > $i ).
thf(decl_184,type,
esk34_0: $i ).
thf(decl_185,type,
esk35_0: $i ).
thf(decl_186,type,
esk36_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rj8ImtPuQn/E---3.1_30661.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rj8ImtPuQn/E---3.1_30661.p',def_imp) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rj8ImtPuQn/E---3.1_30661.p',def_e_is) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rj8ImtPuQn/E---3.1_30661.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rj8ImtPuQn/E---3.1_30661.p',def_is_of) ).
thf(def_nis,axiom,
( nis
= ( ^ [X1: $i,X165: $i] : ( d_not @ ( n_is @ X1 @ X165 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rj8ImtPuQn/E---3.1_30661.p',def_nis) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rj8ImtPuQn/E---3.1_30661.p',def_n_is) ).
thf(satz8,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X203: $i] : ( in @ X203 @ nat )
@ ^ [X204: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( nis @ X204 @ X4 )
=> ( nis @ ( n_pl @ X1 @ X204 ) @ ( n_pl @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rj8ImtPuQn/E---3.1_30661.p',satz8) ).
thf(satz8a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X205: $i] : ( in @ X205 @ nat )
@ ^ [X206: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( n_is @ ( n_pl @ X1 @ X206 ) @ ( n_pl @ X1 @ X4 ) )
=> ( n_is @ X206 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rj8ImtPuQn/E---3.1_30661.p',satz8a) ).
thf(c_0_9,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_10,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_11,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_12,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_13,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_14,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_nis]) ).
thf(c_0_15,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_16,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_11]) ).
thf(c_0_17,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_18,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
thf(c_0_19,plain,
! [X506: $i] :
( ( in @ X506 @ nat )
=> ! [X505: $i] :
( ( in @ X505 @ nat )
=> ! [X504: $i] :
( ( in @ X504 @ nat )
=> ( ( ( X505 = X504 )
=> ~ $true )
=> ( ( ( n_pl @ X506 @ X505 )
= ( n_pl @ X506 @ X504 ) )
=> ~ $true ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz8]),c_0_17]),c_0_18]) ).
thf(c_0_20,plain,
! [X994: $i,X995: $i,X996: $i] :
( ( ( X995 = X996 )
| ( ( n_pl @ X994 @ X995 )
!= ( n_pl @ X994 @ X996 ) )
| ~ $true
| ~ ( in @ X996 @ nat )
| ~ ( in @ X995 @ nat )
| ~ ( in @ X994 @ nat ) )
& ( $true
| ( ( n_pl @ X994 @ X995 )
!= ( n_pl @ X994 @ X996 ) )
| ~ $true
| ~ ( in @ X996 @ nat )
| ~ ( in @ X995 @ nat )
| ~ ( in @ X994 @ nat ) ) ),
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_19])])])])]) ).
thf(c_0_21,negated_conjecture,
~ ! [X509: $i] :
( ( in @ X509 @ nat )
=> ! [X508: $i] :
( ( in @ X508 @ nat )
=> ! [X507: $i] :
( ( in @ X507 @ nat )
=> ( ( ( n_pl @ X509 @ X508 )
= ( n_pl @ X509 @ X507 ) )
=> ( X508 = X507 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz8a])]),c_0_17]),c_0_16]) ).
thf(c_0_22,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( X1 = X4 )
| ( ( n_pl @ X5 @ X1 )
!= ( n_pl @ X5 @ X4 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X5 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_23,negated_conjecture,
( ( in @ esk34_0 @ nat )
& ( in @ esk35_0 @ nat )
& ( in @ esk36_0 @ nat )
& ( ( n_pl @ esk34_0 @ esk35_0 )
= ( n_pl @ esk34_0 @ esk36_0 ) )
& ( esk35_0 != esk36_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
thf(c_0_24,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X1 = X4 )
| ( ( n_pl @ X5 @ X1 )
!= ( n_pl @ X5 @ X4 ) )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_22]) ).
thf(c_0_25,negated_conjecture,
( ( n_pl @ esk34_0 @ esk35_0 )
= ( n_pl @ esk34_0 @ esk36_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_26,negated_conjecture,
in @ esk34_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,negated_conjecture,
in @ esk36_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i] :
( ( X1 = esk36_0 )
| ( ( n_pl @ esk34_0 @ X1 )
!= ( n_pl @ esk34_0 @ esk35_0 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]) ).
thf(c_0_29,negated_conjecture,
in @ esk35_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_30,negated_conjecture,
esk35_0 != esk36_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_29])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.15 % Problem : NUM647^4 : TPTP v8.1.2. Released v7.1.0.
% 0.11/0.16 % Command : run_E %s %d THM
% 0.16/0.37 % Computer : n012.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 3 09:10:10 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.22/0.53 Running higher-order theorem proving
% 0.22/0.53 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.rj8ImtPuQn/E---3.1_30661.p
% 0.37/0.57 # Type mismatch in argument #1 of prop2 @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1) @ db(0): expected $i but got $o
% 0.37/0.57 eprover: Type error
% 0.37/0.58 # Type mismatch in argument #1 of prop2 @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1) @ db(0): expected $i but got $o
% 0.37/0.58 eprover: Type error
% 0.37/0.59 # Type mismatch in argument #1 of indeq @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ (d_11_i @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var# Type mismatch in argument #1 of @ prop2 @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1) @ db(0): expected $i but got $o
% 0.37/0.59 eprover: Type error
% 0.37/0.59 db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1)) @ db(0): expected $i but got $o
% 0.37/0.59 eprover: Type error
% 0.37/0.61 # Type mismatch in argument #1 of prop2 @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1) @ db(0): expected $i but got $o
% 0.37/0.61 eprover: Type error
% 0.37/0.62 # Type mismatch in argument #1 of prop2 @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1) @ db(0): expected $i but got $o
% 0.37/0.62 eprover: Type error
% 0.37/0.63 # Version: 3.1.0-ho
% 0.37/0.63 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.37/0.63 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.63 # Starting lpo1_fix with 900s (3) cores
% 0.37/0.63 # Starting full_lambda_9 with 300s (1) cores
% 0.37/0.63 # Starting almost_fo_4 with 300s (1) cores
% 0.37/0.63 # Starting new_ho_9 with 300s (1) cores
% 0.37/0.63 # Starting pre_casc_4 with 300s (1) cores
% 0.37/0.63 # Starting ho_unfolding_6 with 300s (1) cores
% 0.37/0.63 # almost_fo_4 with pid 30742 completed with status 0
% 0.37/0.63 # Result found by almost_fo_4
% 0.37/0.63 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.37/0.63 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.63 # Starting lpo1_fix with 900s (3) cores
% 0.37/0.63 # Starting full_lambda_9 with 300s (1) cores
% 0.37/0.63 # Starting almost_fo_4 with 300s (1) cores
% 0.37/0.63 # No SInE strategy applied
% 0.37/0.63 # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.37/0.63 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.37/0.63 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.63 # Starting full_lambda_5 with 28s (1) cores
% 0.37/0.63 # full_lambda_5 with pid 30749 completed with status 0
% 0.37/0.63 # Result found by full_lambda_5
% 0.37/0.63 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.37/0.63 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.63 # Starting lpo1_fix with 900s (3) cores
% 0.37/0.63 # Starting full_lambda_9 with 300s (1) cores
% 0.37/0.63 # Starting almost_fo_4 with 300s (1) cores
% 0.37/0.63 # No SInE strategy applied
% 0.37/0.63 # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.37/0.63 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.37/0.63 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.63 # Starting full_lambda_5 with 28s (1) cores
% 0.37/0.63 # Preprocessing time : 0.006 s
% 0.37/0.63 # Presaturation interreduction done
% 0.37/0.63
% 0.37/0.63 # Proof found!
% 0.37/0.63 # SZS status Theorem
% 0.37/0.63 # SZS output start CNFRefutation
% See solution above
% 0.37/0.63 # Parsed axioms : 327
% 0.37/0.63 # Removed by relevancy pruning/SinE : 0
% 0.37/0.63 # Initial clauses : 384
% 0.37/0.63 # Removed in clause preprocessing : 164
% 0.37/0.63 # Initial clauses in saturation : 220
% 0.37/0.63 # Processed clauses : 354
% 0.37/0.63 # ...of these trivial : 4
% 0.37/0.63 # ...subsumed : 19
% 0.37/0.63 # ...remaining for further processing : 331
% 0.37/0.63 # Other redundant clauses eliminated : 17
% 0.37/0.63 # Clauses deleted for lack of memory : 0
% 0.37/0.63 # Backward-subsumed : 0
% 0.37/0.63 # Backward-rewritten : 1
% 0.37/0.63 # Generated clauses : 379
% 0.37/0.63 # ...of the previous two non-redundant : 340
% 0.37/0.63 # ...aggressively subsumed : 0
% 0.37/0.63 # Contextual simplify-reflections : 0
% 0.37/0.63 # Paramodulations : 333
% 0.37/0.63 # Factorizations : 0
% 0.37/0.63 # NegExts : 0
% 0.37/0.63 # Equation resolutions : 20
% 0.37/0.63 # Disequality decompositions : 0
% 0.37/0.63 # Total rewrite steps : 69
% 0.37/0.63 # ...of those cached : 40
% 0.37/0.63 # Propositional unsat checks : 0
% 0.37/0.63 # Propositional check models : 0
% 0.37/0.63 # Propositional check unsatisfiable : 0
% 0.37/0.63 # Propositional clauses : 0
% 0.37/0.63 # Propositional clauses after purity: 0
% 0.37/0.63 # Propositional unsat core size : 0
% 0.37/0.63 # Propositional preprocessing time : 0.000
% 0.37/0.63 # Propositional encoding time : 0.000
% 0.37/0.63 # Propositional solver time : 0.000
% 0.37/0.63 # Success case prop preproc time : 0.000
% 0.37/0.63 # Success case prop encoding time : 0.000
% 0.37/0.63 # Success case prop solver time : 0.000
% 0.37/0.63 # Current number of processed clauses : 126
% 0.37/0.63 # Positive orientable unit clauses : 46
% 0.37/0.63 # Positive unorientable unit clauses: 2
% 0.37/0.63 # Negative unit clauses : 25
% 0.37/0.63 # Non-unit-clauses : 53
% 0.37/0.63 # Current number of unprocessed clauses: 406
% 0.37/0.63 # ...number of literals in the above : 1030
% 0.37/0.63 # Current number of archived formulas : 0
% 0.37/0.63 # Current number of archived clauses : 201
% 0.37/0.63 # Clause-clause subsumption calls (NU) : 4813
% 0.37/0.63 # Rec. Clause-clause subsumption calls : 974
% 0.37/0.63 # Non-unit clause-clause subsumptions : 17
% 0.37/0.63 # Unit Clause-clause subsumption calls : 395
% 0.37/0.63 # Rewrite failures with RHS unbound : 2
% 0.37/0.63 # BW rewrite match attempts : 50
% 0.37/0.63 # BW rewrite match successes : 19
% 0.37/0.63 # Condensation attempts : 0
% 0.37/0.63 # Condensation successes : 0
% 0.37/0.63 # Termbank termtop insertions : 45183
% 0.37/0.63 # Search garbage collected termcells : 11189
% 0.37/0.63
% 0.37/0.63 # -------------------------------------------------
% 0.37/0.63 # User time : 0.065 s
% 0.37/0.63 # System time : 0.011 s
% 0.37/0.63 # Total time : 0.076 s
% 0.37/0.63 # Maximum resident set size: 4292 pages
% 0.37/0.63
% 0.37/0.63 # -------------------------------------------------
% 0.37/0.63 # User time : 0.074 s
% 0.37/0.63 # System time : 0.013 s
% 0.37/0.63 # Total time : 0.087 s
% 0.37/0.63 # Maximum resident set size: 2164 pages
% 0.37/0.63 % E---3.1 exiting
% 0.37/0.63 % E exiting
%------------------------------------------------------------------------------