TSTP Solution File: NUM648^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM648^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 08:55:57 EDT 2024
% Result : Theorem 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of formulae : 39 ( 19 unt; 12 typ; 0 def)
% Number of atoms : 93 ( 35 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 189 ( 13 ~; 10 |; 6 &; 136 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 62 ( 41 ^ 21 !; 0 ?; 62 :)
% 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_77,type,
e_is: $i > $i > $i > $o ).
thf(decl_78,type,
amone: $i > ( $i > $o ) > $o ).
thf(decl_123,type,
nat: $i ).
thf(decl_124,type,
n_is: $i > $i > $o ).
thf(decl_142,type,
n_pl: $i > $i > $i ).
thf(decl_185,type,
esk34_0: $i ).
thf(decl_186,type,
esk35_0: $i ).
thf(decl_187,type,
esk36_0: $i ).
thf(decl_188,type,
esk37_0: $i ).
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.jbt8lqLjZL/E---3.1_16372.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jbt8lqLjZL/E---3.1_16372.p',def_is_of) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jbt8lqLjZL/E---3.1_16372.p',def_e_is) ).
thf(def_amone,axiom,
( amone
= ( ^ [X1: $i,X2: $i > $o] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ X1 )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ X1 )
@ ^ [X13: $i] :
( ( X2 @ X4 )
=> ( ( X2 @ X13 )
=> ( e_is @ X1 @ X4 @ X13 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jbt8lqLjZL/E---3.1_16372.p',def_amone) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jbt8lqLjZL/E---3.1_16372.p',def_n_is) ).
thf(satz8a,axiom,
( 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.jbt8lqLjZL/E---3.1_16372.p',satz8a) ).
thf(satz8b,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X208: $i] : ( in @ X208 @ nat )
@ ^ [X209: $i] :
( amone @ nat
@ ^ [X4: $i] : ( n_is @ X1 @ ( n_pl @ X209 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jbt8lqLjZL/E---3.1_16372.p',satz8b) ).
thf(c_0_7,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_8,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_9,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_10,plain,
( amone
= ( ^ [Z0: $i,Z1: $i > $o] :
! [X357: $i] :
( ( in @ X357 @ Z0 )
=> ! [X356: $i] :
( ( in @ X356 @ Z0 )
=> ( ( Z1 @ X357 )
=> ( ( Z1 @ X356 )
=> ( X357 = X356 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_amone]) ).
thf(c_0_11,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_12,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_9]) ).
thf(c_0_13,plain,
( amone
= ( ^ [Z0: $i,Z1: $i > $o] :
! [X357: $i] :
( ( in @ X357 @ Z0 )
=> ! [X356: $i] :
( ( in @ X356 @ Z0 )
=> ( ( Z1 @ X357 )
=> ( ( Z1 @ X356 )
=> ( X357 = X356 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_9]) ).
thf(c_0_14,plain,
! [X512: $i] :
( ( in @ X512 @ nat )
=> ! [X511: $i] :
( ( in @ X511 @ nat )
=> ! [X510: $i] :
( ( in @ X510 @ nat )
=> ( ( ( n_pl @ X512 @ X511 )
= ( n_pl @ X512 @ X510 ) )
=> ( X511 = X510 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz8a]),c_0_11]),c_0_12]) ).
thf(c_0_15,negated_conjecture,
~ ! [X516: $i] :
( ( in @ X516 @ nat )
=> ! [X515: $i] :
( ( in @ X515 @ nat )
=> ! [X513: $i] :
( ( in @ X513 @ nat )
=> ! [X514: $i] :
( ( in @ X514 @ nat )
=> ( ( X516
= ( n_pl @ X515 @ X513 ) )
=> ( ( X516
= ( n_pl @ X515 @ X514 ) )
=> ( X513 = X514 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz8b])]),c_0_11]),c_0_13]),c_0_12]) ).
thf(c_0_16,plain,
! [X1004: $i,X1005: $i,X1006: $i] :
( ~ ( in @ X1004 @ nat )
| ~ ( in @ X1005 @ nat )
| ~ ( in @ X1006 @ nat )
| ( ( n_pl @ X1004 @ X1005 )
!= ( n_pl @ X1004 @ X1006 ) )
| ( X1005 = X1006 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
thf(c_0_17,negated_conjecture,
( ( in @ esk34_0 @ nat )
& ( in @ esk35_0 @ nat )
& ( in @ esk36_0 @ nat )
& ( in @ esk37_0 @ nat )
& ( esk34_0
= ( n_pl @ esk35_0 @ esk36_0 ) )
& ( esk34_0
= ( n_pl @ esk35_0 @ esk37_0 ) )
& ( esk36_0 != esk37_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
thf(c_0_18,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ( ( n_pl @ X1 @ X4 )
!= ( n_pl @ X1 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
( esk34_0
= ( n_pl @ esk35_0 @ esk37_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
in @ esk37_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,negated_conjecture,
in @ esk35_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i] :
( ( X1 = esk37_0 )
| ( ( n_pl @ esk35_0 @ X1 )
!= esk34_0 )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
thf(c_0_23,negated_conjecture,
( esk34_0
= ( n_pl @ esk35_0 @ esk36_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_24,negated_conjecture,
in @ esk36_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,negated_conjecture,
esk36_0 != esk37_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : NUM648^4 : TPTP v8.1.2. Released v7.1.0.
% 0.08/0.11 % Command : run_E %s %d THM
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Fri May 3 09:37:24 EDT 2024
% 0.11/0.30 % CPUTime :
% 0.14/0.40 Running higher-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.jbt8lqLjZL/E---3.1_16372.p
% 0.14/0.43 # Type mismatch in argument #1 of prop2 @ ($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 $o
% 0.14/0.43 eprover: Type error
% 0.14/0.44 # Type mismatch in argument #1 of prop2 @ ($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 $o
% 0.14/0.44 eprover: Type error
% 0.14/0.44 # Type mismatch in argument #1 of indeq @ ($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 @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1)) @ db(0): expected $i but got $o
% 0.14/0.44 eprover: Type error
% 0.14/0.45 # Type mismatch in argument #1 of prop2 @ ($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 $o
% 0.14/0.45 eprover: Type error
% 0.14/0.45 # Type mismatch in argument #1 of prop2 @ ($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
% 0.14/0.46 eprover: Type error
% 0.14/0.47 # Version: 3.1.0-ho
% 0.14/0.47 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.14/0.47 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 # Starting lpo1_fix with 900s (3) cores
% 0.14/0.47 # Starting full_lambda_9 with 300s (1) cores
% 0.14/0.47 # Starting almost_fo_4 with 300s (1) cores
% 0.14/0.47 # Starting new_ho_9 with 300s (1) cores
% 0.14/0.47 # Starting pre_casc_4 with 300s (1) cores
% 0.14/0.47 # Starting ho_unfolding_6 with 300s (1) cores
% 0.14/0.47 # almost_fo_4 with pid 16526 completed with status 0
% 0.14/0.47 # Result found by almost_fo_4
% 0.14/0.47 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.14/0.47 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 # Starting lpo1_fix with 900s (3) cores
% 0.14/0.47 # Starting full_lambda_9 with 300s (1) cores
% 0.14/0.47 # Starting almost_fo_4 with 300s (1) cores
% 0.14/0.47 # No SInE strategy applied
% 0.14/0.47 # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.14/0.47 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.14/0.47 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.47 # Starting full_lambda_5 with 28s (1) cores
% 0.14/0.47 # full_lambda_5 with pid 16554 completed with status 0
% 0.14/0.47 # Result found by full_lambda_5
% 0.14/0.47 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.14/0.47 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 # Starting lpo1_fix with 900s (3) cores
% 0.14/0.47 # Starting full_lambda_9 with 300s (1) cores
% 0.14/0.47 # Starting almost_fo_4 with 300s (1) cores
% 0.14/0.47 # No SInE strategy applied
% 0.14/0.47 # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.14/0.47 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.14/0.47 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.47 # Starting full_lambda_5 with 28s (1) cores
% 0.14/0.47 # Preprocessing time : 0.004 s
% 0.14/0.47 # Presaturation interreduction done
% 0.14/0.47
% 0.14/0.47 # Proof found!
% 0.14/0.47 # SZS status Theorem
% 0.14/0.47 # SZS output start CNFRefutation
% See solution above
% 0.14/0.47 # Parsed axioms : 330
% 0.14/0.47 # Removed by relevancy pruning/SinE : 0
% 0.14/0.47 # Initial clauses : 388
% 0.14/0.47 # Removed in clause preprocessing : 165
% 0.14/0.47 # Initial clauses in saturation : 223
% 0.14/0.47 # Processed clauses : 355
% 0.14/0.47 # ...of these trivial : 4
% 0.14/0.47 # ...subsumed : 20
% 0.14/0.47 # ...remaining for further processing : 331
% 0.14/0.47 # Other redundant clauses eliminated : 14
% 0.14/0.47 # Clauses deleted for lack of memory : 0
% 0.14/0.47 # Backward-subsumed : 0
% 0.14/0.47 # Backward-rewritten : 0
% 0.14/0.47 # Generated clauses : 288
% 0.14/0.47 # ...of the previous two non-redundant : 256
% 0.14/0.47 # ...aggressively subsumed : 0
% 0.14/0.47 # Contextual simplify-reflections : 0
% 0.14/0.47 # Paramodulations : 249
% 0.14/0.47 # Factorizations : 0
% 0.14/0.47 # NegExts : 0
% 0.14/0.47 # Equation resolutions : 16
% 0.14/0.47 # Disequality decompositions : 0
% 0.14/0.47 # Total rewrite steps : 69
% 0.14/0.47 # ...of those cached : 40
% 0.14/0.47 # Propositional unsat checks : 0
% 0.14/0.47 # Propositional check models : 0
% 0.14/0.47 # Propositional check unsatisfiable : 0
% 0.14/0.47 # Propositional clauses : 0
% 0.14/0.47 # Propositional clauses after purity: 0
% 0.14/0.47 # Propositional unsat core size : 0
% 0.14/0.47 # Propositional preprocessing time : 0.000
% 0.14/0.47 # Propositional encoding time : 0.000
% 0.14/0.47 # Propositional solver time : 0.000
% 0.14/0.47 # Success case prop preproc time : 0.000
% 0.14/0.47 # Success case prop encoding time : 0.000
% 0.14/0.47 # Success case prop solver time : 0.000
% 0.14/0.47 # Current number of processed clauses : 125
% 0.14/0.47 # Positive orientable unit clauses : 47
% 0.14/0.47 # Positive unorientable unit clauses: 2
% 0.14/0.47 # Negative unit clauses : 27
% 0.14/0.47 # Non-unit-clauses : 49
% 0.14/0.47 # Current number of unprocessed clauses: 326
% 0.14/0.47 # ...number of literals in the above : 822
% 0.14/0.47 # Current number of archived formulas : 0
% 0.14/0.47 # Current number of archived clauses : 202
% 0.14/0.47 # Clause-clause subsumption calls (NU) : 4809
% 0.14/0.47 # Rec. Clause-clause subsumption calls : 1305
% 0.14/0.47 # Non-unit clause-clause subsumptions : 18
% 0.14/0.47 # Unit Clause-clause subsumption calls : 327
% 0.14/0.47 # Rewrite failures with RHS unbound : 2
% 0.14/0.47 # BW rewrite match attempts : 48
% 0.14/0.47 # BW rewrite match successes : 17
% 0.14/0.47 # Condensation attempts : 0
% 0.14/0.47 # Condensation successes : 0
% 0.14/0.47 # Termbank termtop insertions : 44351
% 0.14/0.47 # Search garbage collected termcells : 11416
% 0.14/0.47
% 0.14/0.47 # -------------------------------------------------
% 0.14/0.47 # User time : 0.037 s
% 0.14/0.47 # System time : 0.010 s
% 0.14/0.47 # Total time : 0.047 s
% 0.14/0.47 # Maximum resident set size: 4316 pages
% 0.14/0.47
% 0.14/0.47 # -------------------------------------------------
% 0.14/0.47 # User time : 0.042 s
% 0.14/0.47 # System time : 0.012 s
% 0.14/0.47 # Total time : 0.054 s
% 0.14/0.47 # Maximum resident set size: 2168 pages
% 0.14/0.47 % E---3.1 exiting
% 0.14/0.47 % E exiting
%------------------------------------------------------------------------------