TSTP Solution File: NUM728^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM728^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.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 01:15:50 EDT 2024
% Result : Theorem 0.88s 0.72s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 37 ( 16 unt; 14 typ; 0 def)
% Number of atoms : 61 ( 24 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 259 ( 7 ~; 4 |; 2 &; 239 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 45 ( 34 ^ 11 !; 0 ?; 45 :)
% 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_123,type,
nat: $i ).
thf(decl_124,type,
n_is: $i > $i > $o ).
thf(decl_162,type,
n_ts: $i > $i > $i ).
thf(decl_189,type,
frac: $i ).
thf(decl_190,type,
n_fr: $i > $i > $i ).
thf(decl_191,type,
num: $i > $i ).
thf(decl_192,type,
den: $i > $i ).
thf(decl_193,type,
n_eq: $i > $i > $o ).
thf(decl_327,type,
esk130_0: $i ).
thf(decl_328,type,
esk131_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',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/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(def_n_eq,axiom,
( n_eq
= ( ^ [X1: $i,X436: $i] : ( n_is @ ( n_ts @ ( num @ X1 ) @ ( den @ X436 ) ) @ ( n_ts @ ( num @ X436 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(satz40a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X443: $i] : ( in @ X443 @ nat )
@ ^ [X444: $i] : ( n_eq @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X444 ) @ ( n_ts @ ( den @ X1 ) @ X444 ) ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40a) ).
thf(satz40,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X441: $i] : ( in @ X441 @ nat )
@ ^ [X442: $i] : ( n_eq @ X1 @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X442 ) @ ( n_ts @ ( den @ X1 ) @ X442 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40) ).
thf(c_0_7,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_8,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_9,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_10,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_n_eq]) ).
thf(c_0_11,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_7]) ).
thf(c_0_12,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,negated_conjecture,
~ ! [X1266: $i] :
( ( in @ X1266 @ frac )
=> ! [X1265: $i] :
( ( in @ X1265 @ nat )
=> ( ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X1266 ) @ X1265 ) @ ( n_ts @ ( den @ X1266 ) @ X1265 ) ) ) @ ( den @ X1266 ) )
= ( n_ts @ ( num @ X1266 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X1266 ) @ X1265 ) @ ( n_ts @ ( den @ X1266 ) @ X1265 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz40a])]),c_0_12]),c_0_13]) ).
thf(c_0_15,plain,
! [X1264: $i] :
( ( in @ X1264 @ frac )
=> ! [X1263: $i] :
( ( in @ X1263 @ nat )
=> ( ( n_ts @ ( num @ X1264 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X1264 ) @ X1263 ) @ ( n_ts @ ( den @ X1264 ) @ X1263 ) ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X1264 ) @ X1263 ) @ ( n_ts @ ( den @ X1264 ) @ X1263 ) ) ) @ ( den @ X1264 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz40]),c_0_12]),c_0_13]) ).
thf(c_0_16,negated_conjecture,
( ( in @ esk130_0 @ frac )
& ( in @ esk131_0 @ nat )
& ( ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ esk130_0 ) @ esk131_0 ) @ ( n_ts @ ( den @ esk130_0 ) @ esk131_0 ) ) ) @ ( den @ esk130_0 ) )
!= ( n_ts @ ( num @ esk130_0 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ esk130_0 ) @ esk131_0 ) @ ( n_ts @ ( den @ esk130_0 ) @ esk131_0 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
thf(c_0_17,plain,
! [X2041: $i,X2042: $i] :
( ~ ( in @ X2041 @ frac )
| ~ ( in @ X2042 @ nat )
| ( ( n_ts @ ( num @ X2041 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X2041 ) @ X2042 ) @ ( n_ts @ ( den @ X2041 ) @ X2042 ) ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X2041 ) @ X2042 ) @ ( n_ts @ ( den @ X2041 ) @ X2042 ) ) ) @ ( den @ X2041 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
thf(c_0_18,negated_conjecture,
( ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ esk130_0 ) @ esk131_0 ) @ ( n_ts @ ( den @ esk130_0 ) @ esk131_0 ) ) ) @ ( den @ esk130_0 ) )
!= ( n_ts @ ( num @ esk130_0 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ esk130_0 ) @ esk131_0 ) @ ( n_ts @ ( den @ esk130_0 ) @ esk131_0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,plain,
! [X1: $i,X4: $i] :
( ( ( n_ts @ ( num @ X1 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X4 ) @ ( n_ts @ ( den @ X1 ) @ X4 ) ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X4 ) @ ( n_ts @ ( den @ X1 ) @ X4 ) ) ) @ ( den @ X1 ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
in @ esk131_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,negated_conjecture,
in @ esk130_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM728^4 : TPTP v8.2.0. Released v7.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n006.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 20 07:24:07 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.44 Running higher-order theorem proving
% 0.16/0.44 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.58/0.61 # Type mismatch in argument #1 of indeq @ ($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 $o
% 0.58/0.61 eprover: Type error
% 0.58/0.62 # Type mismatch in argument #1 of indeq @ ($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 $o
% 0.58/0.62 eprover: Type error
% 0.83/0.64 # Type mismatch in argument #1 of indeq @ ($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
% 0.83/0.64 eprover: Type error
% 0.88/0.72 # Version: 3.1.0-ho
% 0.88/0.72 # Preprocessing class: HSLMSMSMLMLCHSA.
% 0.88/0.72 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.88/0.72 # Starting new_ho_10 with 1500s (5) cores
% 0.88/0.72 # Starting ho_unfolding_6 with 300s (1) cores
% 0.88/0.72 # Starting sh4l with 300s (1) cores
% 0.88/0.72 # Starting ehoh_best_nonlift_nonlambdatoforall with 300s (1) cores
% 0.88/0.72 # ho_unfolding_6 with pid 9439 completed with status 0
% 0.88/0.72 # Result found by ho_unfolding_6
% 0.88/0.72 # Preprocessing class: HSLMSMSMLMLCHSA.
% 0.88/0.72 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.88/0.72 # Starting new_ho_10 with 1500s (5) cores
% 0.88/0.72 # Starting ho_unfolding_6 with 300s (1) cores
% 0.88/0.72 # No SInE strategy applied
% 0.88/0.72 # Search class: HGHSM-FSLM32-DHSMSSBN
% 0.88/0.72 # partial match(1): HGHSM-FSLM32-MHSMSSBN
% 0.88/0.72 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.88/0.72 # Starting new_ho_10 with 181s (1) cores
% 0.88/0.72 # new_ho_10 with pid 9492 completed with status 3
% 0.88/0.72 # Starting ho_unfolding_6 with 31s (1) cores
% 0.88/0.72 # ho_unfolding_6 with pid 9493 completed with status 0
% 0.88/0.72 # Result found by ho_unfolding_6
% 0.88/0.72 # Preprocessing class: HSLMSMSMLMLCHSA.
% 0.88/0.72 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.88/0.72 # Starting new_ho_10 with 1500s (5) cores
% 0.88/0.72 # Starting ho_unfolding_6 with 300s (1) cores
% 0.88/0.72 # No SInE strategy applied
% 0.88/0.72 # Search class: HGHSM-FSLM32-DHSMSSBN
% 0.88/0.72 # partial match(1): HGHSM-FSLM32-MHSMSSBN
% 0.88/0.72 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.88/0.72 # Starting new_ho_10 with 181s (1) cores
% 0.88/0.72 # new_ho_10 with pid 9492 completed with status 3
% 0.88/0.72 # Starting ho_unfolding_6 with 31s (1) cores
% 0.88/0.72 # Preprocessing time : 0.012 s
% 0.88/0.72
% 0.88/0.72 # Proof found!
% 0.88/0.72 # SZS status Theorem
% 0.88/0.72 # SZS output start CNFRefutation
% See solution above
% 0.88/0.72 # Parsed axioms : 534
% 0.88/0.72 # Removed by relevancy pruning/SinE : 0
% 0.88/0.72 # Initial clauses : 1635
% 0.88/0.72 # Removed in clause preprocessing : 1101
% 0.88/0.72 # Initial clauses in saturation : 534
% 0.88/0.72 # Processed clauses : 314
% 0.88/0.72 # ...of these trivial : 4
% 0.88/0.72 # ...subsumed : 19
% 0.88/0.72 # ...remaining for further processing : 291
% 0.88/0.72 # Other redundant clauses eliminated : 61
% 0.88/0.72 # Clauses deleted for lack of memory : 0
% 0.88/0.72 # Backward-subsumed : 0
% 0.88/0.72 # Backward-rewritten : 0
% 0.88/0.72 # Generated clauses : 3090
% 0.88/0.72 # ...of the previous two non-redundant : 3028
% 0.88/0.72 # ...aggressively subsumed : 0
% 0.88/0.72 # Contextual simplify-reflections : 0
% 0.88/0.72 # Paramodulations : 2844
% 0.88/0.72 # Factorizations : 10
% 0.88/0.72 # NegExts : 0
% 0.88/0.72 # Equation resolutions : 63
% 0.88/0.72 # Disequality decompositions : 0
% 0.88/0.72 # Total rewrite steps : 105
% 0.88/0.72 # ...of those cached : 82
% 0.88/0.72 # Propositional unsat checks : 0
% 0.88/0.72 # Propositional check models : 0
% 0.88/0.72 # Propositional check unsatisfiable : 0
% 0.88/0.72 # Propositional clauses : 0
% 0.88/0.72 # Propositional clauses after purity: 0
% 0.88/0.72 # Propositional unsat core size : 0
% 0.88/0.72 # Propositional preprocessing time : 0.000
% 0.88/0.72 # Propositional encoding time : 0.000
% 0.88/0.72 # Propositional solver time : 0.000
% 0.88/0.72 # Success case prop preproc time : 0.000
% 0.88/0.72 # Success case prop encoding time : 0.000
% 0.88/0.72 # Success case prop solver time : 0.000
% 0.88/0.72 # Current number of processed clauses : 246
% 0.88/0.72 # Positive orientable unit clauses : 73
% 0.88/0.72 # Positive unorientable unit clauses: 0
% 0.88/0.72 # Negative unit clauses : 3
% 0.88/0.72 # Non-unit-clauses : 170
% 0.88/0.72 # Current number of unprocessed clauses: 3235
% 0.88/0.72 # ...number of literals in the above : 13929
% 0.88/0.72 # Current number of archived formulas : 0
% 0.88/0.72 # Current number of archived clauses : 0
% 0.88/0.72 # Clause-clause subsumption calls (NU) : 15929
% 0.88/0.72 # Rec. Clause-clause subsumption calls : 1966
% 0.88/0.72 # Non-unit clause-clause subsumptions : 21
% 0.88/0.72 # Unit Clause-clause subsumption calls : 7
% 0.88/0.72 # Rewrite failures with RHS unbound : 0
% 0.88/0.72 # BW rewrite match attempts : 19
% 0.88/0.72 # BW rewrite match successes : 0
% 0.88/0.72 # Condensation attempts : 314
% 0.88/0.72 # Condensation successes : 2
% 0.88/0.72 # Termbank termtop insertions : 314348
% 0.88/0.72 # Search garbage collected termcells : 69673
% 0.88/0.72
% 0.88/0.72 # -------------------------------------------------
% 0.88/0.72 # User time : 0.215 s
% 0.88/0.72 # System time : 0.022 s
% 0.88/0.72 # Total time : 0.237 s
% 0.88/0.72 # Maximum resident set size: 11112 pages
% 0.88/0.72
% 0.88/0.72 # -------------------------------------------------
% 0.88/0.72 # User time : 0.230 s
% 0.88/0.72 # System time : 0.026 s
% 0.88/0.72 # Total time : 0.256 s
% 0.88/0.72 # Maximum resident set size: 2620 pages
% 0.88/0.72 % E---3.1 exiting
% 0.88/0.72 % E exiting
%------------------------------------------------------------------------------