TSTP Solution File: NUM750^4 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM750^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n002.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 01:17:03 EDT 2024
% Result : Theorem 0.50s 0.58s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 39 ( 18 unt; 14 typ; 0 def)
% Number of atoms : 88 ( 33 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 338 ( 15 ~; 12 |; 4 &; 291 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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 : 58 ( 40 ^ 18 !; 0 ?; 58 :)
% 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_124,type,
n_is: $i > $i > $o ).
thf(decl_162,type,
n_ts: $i > $i > $i ).
thf(decl_189,type,
frac: $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_198,type,
n_pf: $i > $i > $i ).
thf(decl_199,type,
esk1_0: $i ).
thf(decl_200,type,
esk2_0: $i ).
thf(decl_201,type,
esk3_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(satz62b,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X524: $i] : ( in @ X524 @ frac )
@ ^ [X525: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( n_eq @ X1 @ X525 )
=> ( n_eq @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X525 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62b) ).
thf(satz56,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X508: $i] : ( in @ X508 @ frac )
@ ^ [X509: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( n_eq @ X1 @ X509 )
=> ( ( n_eq @ X4 @ X13 )
=> ( n_eq @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X509 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56) ).
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,
~ ! [X568: $i] :
( ( in @ X568 @ frac )
=> ! [X567: $i] :
( ( in @ X567 @ frac )
=> ! [X566: $i] :
( ( in @ X566 @ frac )
=> ( ( ( n_ts @ ( num @ X568 ) @ ( den @ X567 ) )
= ( n_ts @ ( num @ X567 ) @ ( den @ X568 ) ) )
=> ( ( n_ts @ ( num @ ( n_pf @ X568 @ X566 ) ) @ ( den @ ( n_pf @ X567 @ X566 ) ) )
= ( n_ts @ ( num @ ( n_pf @ X567 @ X566 ) ) @ ( den @ ( n_pf @ X568 @ X566 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz62b])]),c_0_12]),c_0_13]) ).
thf(c_0_15,plain,
! [X578: $i] :
( ( in @ X578 @ frac )
=> ! [X577: $i] :
( ( in @ X577 @ frac )
=> ! [X576: $i] :
( ( in @ X576 @ frac )
=> ! [X575: $i] :
( ( in @ X575 @ frac )
=> ( ( ( n_ts @ ( num @ X578 ) @ ( den @ X577 ) )
= ( n_ts @ ( num @ X577 ) @ ( den @ X578 ) ) )
=> ( ( ( n_ts @ ( num @ X576 ) @ ( den @ X575 ) )
= ( n_ts @ ( num @ X575 ) @ ( den @ X576 ) ) )
=> ( ( n_ts @ ( num @ ( n_pf @ X578 @ X576 ) ) @ ( den @ ( n_pf @ X577 @ X575 ) ) )
= ( n_ts @ ( num @ ( n_pf @ X577 @ X575 ) ) @ ( den @ ( n_pf @ X578 @ X576 ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz56]),c_0_12]),c_0_13]) ).
thf(c_0_16,negated_conjecture,
( ( in @ esk1_0 @ frac )
& ( in @ esk2_0 @ frac )
& ( in @ esk3_0 @ frac )
& ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) )
= ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) )
& ( ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) )
!= ( n_ts @ ( num @ ( n_pf @ esk2_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk1_0 @ esk3_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,
! [X830: $i,X831: $i,X832: $i,X833: $i] :
( ~ ( in @ X830 @ frac )
| ~ ( in @ X831 @ frac )
| ~ ( in @ X832 @ frac )
| ~ ( in @ X833 @ frac )
| ( ( n_ts @ ( num @ X830 ) @ ( den @ X831 ) )
!= ( n_ts @ ( num @ X831 ) @ ( den @ X830 ) ) )
| ( ( n_ts @ ( num @ X832 ) @ ( den @ X833 ) )
!= ( n_ts @ ( num @ X833 ) @ ( den @ X832 ) ) )
| ( ( n_ts @ ( num @ ( n_pf @ X830 @ X832 ) ) @ ( den @ ( n_pf @ X831 @ X833 ) ) )
= ( n_ts @ ( num @ ( n_pf @ X831 @ X833 ) ) @ ( den @ ( n_pf @ X830 @ X832 ) ) ) ) ),
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_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) )
!= ( n_ts @ ( num @ ( n_pf @ esk2_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk1_0 @ esk3_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,plain,
! [X1: $i,X4: $i,X6: $i,X5: $i] :
( ( ( n_ts @ ( num @ ( n_pf @ X1 @ X5 ) ) @ ( den @ ( n_pf @ X4 @ X6 ) ) )
= ( n_ts @ ( num @ ( n_pf @ X4 @ X6 ) ) @ ( den @ ( n_pf @ X1 @ X5 ) ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X5 @ frac )
| ~ ( in @ X6 @ frac )
| ( ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) )
!= ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) )
| ( ( n_ts @ ( num @ X5 ) @ ( den @ X6 ) )
!= ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) )
= ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,negated_conjecture,
in @ esk3_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,negated_conjecture,
in @ esk2_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_23,negated_conjecture,
in @ esk1_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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]),c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM750^4 : TPTP v8.2.0. Released v7.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 07:05:53 EDT 2024
% 0.13/0.35 % 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
% 0.50/0.58 # Version: 3.1.0-ho
% 0.50/0.58 # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.50/0.58 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.50/0.58 # Starting pre_casc_4 with 1200s (4) cores
% 0.50/0.58 # Starting full_lambda_6 with 300s (1) cores
% 0.50/0.58 # Starting sh10 with 300s (1) cores
% 0.50/0.58 # Starting post_as_ho9 with 300s (1) cores
% 0.50/0.58 # Starting post_as_ho8 with 300s (1) cores
% 0.50/0.58 # pre_casc_4 with pid 14716 completed with status 0
% 0.50/0.58 # Result found by pre_casc_4
% 0.50/0.58 # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.50/0.58 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.50/0.58 # Starting pre_casc_4 with 1200s (4) cores
% 0.50/0.58 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.50/0.58 # Search class: HGUSM-FSLM31-DHSMMFBN
% 0.50/0.58 # partial match(2): HGUSM-FSLM31-DHSFFFBN
% 0.50/0.58 # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 0.50/0.58 # Starting new_bool_5 with 540s (1) cores
% 0.50/0.58 # Starting pre_casc_4 with 121s (1) cores
% 0.50/0.58 # Starting ehoh_best8_lambda with 135s (1) cores
% 0.50/0.58 # Starting new_bool_1 with 135s (1) cores
% 0.50/0.58 # new_bool_5 with pid 14741 completed with status 0
% 0.50/0.58 # Result found by new_bool_5
% 0.50/0.58 # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.50/0.58 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.50/0.58 # Starting pre_casc_4 with 1200s (4) cores
% 0.50/0.58 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.50/0.58 # Search class: HGUSM-FSLM31-DHSMMFBN
% 0.50/0.58 # partial match(2): HGUSM-FSLM31-DHSFFFBN
% 0.50/0.58 # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 0.50/0.58 # Starting new_bool_5 with 540s (1) cores
% 0.50/0.58 # Preprocessing time : 0.006 s
% 0.50/0.58 # Presaturation interreduction done
% 0.50/0.58
% 0.50/0.58 # Proof found!
% 0.50/0.58 # SZS status Theorem
% 0.50/0.58 # SZS output start CNFRefutation
% See solution above
% 0.50/0.58 # Parsed axioms : 583
% 0.50/0.58 # Removed by relevancy pruning/SinE : 446
% 0.50/0.58 # Initial clauses : 138
% 0.50/0.58 # Removed in clause preprocessing : 12
% 0.50/0.58 # Initial clauses in saturation : 126
% 0.50/0.58 # Processed clauses : 279
% 0.50/0.58 # ...of these trivial : 3
% 0.50/0.58 # ...subsumed : 51
% 0.50/0.58 # ...remaining for further processing : 225
% 0.50/0.58 # Other redundant clauses eliminated : 16
% 0.50/0.58 # Clauses deleted for lack of memory : 0
% 0.50/0.58 # Backward-subsumed : 0
% 0.50/0.58 # Backward-rewritten : 6
% 0.50/0.58 # Generated clauses : 699
% 0.50/0.58 # ...of the previous two non-redundant : 641
% 0.50/0.58 # ...aggressively subsumed : 0
% 0.50/0.58 # Contextual simplify-reflections : 0
% 0.50/0.58 # Paramodulations : 639
% 0.50/0.58 # Factorizations : 0
% 0.50/0.58 # NegExts : 1
% 0.50/0.58 # Equation resolutions : 22
% 0.50/0.58 # Disequality decompositions : 0
% 0.50/0.58 # Total rewrite steps : 304
% 0.50/0.58 # ...of those cached : 262
% 0.50/0.58 # Propositional unsat checks : 0
% 0.50/0.58 # Propositional check models : 0
% 0.50/0.58 # Propositional check unsatisfiable : 0
% 0.50/0.58 # Propositional clauses : 0
% 0.50/0.58 # Propositional clauses after purity: 0
% 0.50/0.58 # Propositional unsat core size : 0
% 0.50/0.58 # Propositional preprocessing time : 0.000
% 0.50/0.58 # Propositional encoding time : 0.000
% 0.50/0.58 # Propositional solver time : 0.000
% 0.50/0.58 # Success case prop preproc time : 0.000
% 0.50/0.58 # Success case prop encoding time : 0.000
% 0.50/0.58 # Success case prop solver time : 0.000
% 0.50/0.58 # Current number of processed clauses : 119
% 0.50/0.58 # Positive orientable unit clauses : 49
% 0.50/0.58 # Positive unorientable unit clauses: 0
% 0.50/0.58 # Negative unit clauses : 9
% 0.50/0.58 # Non-unit-clauses : 61
% 0.50/0.58 # Current number of unprocessed clauses: 556
% 0.50/0.58 # ...number of literals in the above : 2522
% 0.50/0.58 # Current number of archived formulas : 0
% 0.50/0.58 # Current number of archived clauses : 98
% 0.50/0.58 # Clause-clause subsumption calls (NU) : 6441
% 0.50/0.58 # Rec. Clause-clause subsumption calls : 1183
% 0.50/0.58 # Non-unit clause-clause subsumptions : 40
% 0.50/0.58 # Unit Clause-clause subsumption calls : 29
% 0.50/0.58 # Rewrite failures with RHS unbound : 0
% 0.50/0.58 # BW rewrite match attempts : 20
% 0.50/0.58 # BW rewrite match successes : 6
% 0.50/0.58 # Condensation attempts : 279
% 0.50/0.58 # Condensation successes : 0
% 0.50/0.58 # Termbank termtop insertions : 63618
% 0.50/0.58 # Search garbage collected termcells : 16347
% 0.50/0.58
% 0.50/0.58 # -------------------------------------------------
% 0.50/0.58 # User time : 0.049 s
% 0.50/0.58 # System time : 0.013 s
% 0.50/0.58 # Total time : 0.062 s
% 0.50/0.58 # Maximum resident set size: 5200 pages
% 0.50/0.58
% 0.50/0.58 # -------------------------------------------------
% 0.50/0.58 # User time : 0.133 s
% 0.50/0.58 # System time : 0.042 s
% 0.50/0.58 # Total time : 0.176 s
% 0.50/0.58 # Maximum resident set size: 2788 pages
% 0.50/0.58 % E---3.1 exiting
% 0.50/0.58 % E exiting
%------------------------------------------------------------------------------