TSTP Solution File: NUM721^4 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM721^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n018.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 01:15:49 EDT 2024
% Result : Theorem 0.17s 0.56s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 21
% Syntax : Number of formulae : 41 ( 17 unt; 14 typ; 0 def)
% Number of atoms : 121 ( 12 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 280 ( 15 ~; 12 |; 6 &; 228 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 57 ( 38 ^ 19 !; 0 ?; 57 :)
% 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_72,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_123,type,
nat: $i ).
thf(decl_127,type,
n_some: ( $i > $o ) > $o ).
thf(decl_147,type,
diffprop: $i > $i > $i > $o ).
thf(decl_148,type,
d_29_ii: $i > $i > $o ).
thf(decl_149,type,
iii: $i > $i > $o ).
thf(decl_162,type,
n_ts: $i > $i > $i ).
thf(decl_168,type,
esk1_0: $i ).
thf(decl_169,type,
esk2_0: $i ).
thf(decl_170,type,
esk3_0: $i ).
thf(decl_171,type,
esk4_0: $i ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_iii) ).
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_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_d_29_ii) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_some) ).
thf(satz34a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X407: $i] : ( in @ X407 @ nat )
@ ^ [X408: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( iii @ X1 @ X408 )
=> ( ( iii @ X4 @ X13 )
=> ( iii @ ( n_ts @ X1 @ X4 ) @ ( n_ts @ X408 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz34a) ).
thf(satz34,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X405: $i] : ( in @ X405 @ nat )
@ ^ [X406: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( d_29_ii @ X1 @ X406 )
=> ( ( d_29_ii @ X4 @ X13 )
=> ( d_29_ii @ ( n_ts @ X1 @ X4 ) @ ( n_ts @ X406 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz34) ).
thf(c_0_7,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
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,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_11,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_7,def_n_some]) ).
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,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_10,def_n_some]) ).
thf(c_0_14,negated_conjecture,
~ ! [X447: $i] :
( ( in @ X447 @ nat )
=> ! [X446: $i] :
( ( in @ X446 @ nat )
=> ! [X445: $i] :
( ( in @ X445 @ nat )
=> ! [X444: $i] :
( ( in @ X444 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X446 @ X447 ) )
=> ( ( l_some @ nat @ ( diffprop @ X444 @ X445 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X446 @ X444 ) @ ( n_ts @ X447 @ X445 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz34a])]),c_0_11]),c_0_12]) ).
thf(c_0_15,plain,
! [X648: $i] :
( ( in @ X648 @ nat )
=> ! [X647: $i] :
( ( in @ X647 @ nat )
=> ! [X646: $i] :
( ( in @ X646 @ nat )
=> ! [X645: $i] :
( ( in @ X645 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X648 @ X647 ) )
=> ( ( l_some @ nat @ ( diffprop @ X646 @ X645 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ X648 @ X646 ) @ ( n_ts @ X647 @ X645 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz34]),c_0_13]),c_0_12]) ).
thf(c_0_16,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( in @ esk4_0 @ nat )
& ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
& ( l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ) )
& ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ esk2_0 @ esk4_0 ) @ ( n_ts @ 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,
! [X951: $i,X952: $i,X953: $i,X954: $i] :
( ~ ( in @ X951 @ nat )
| ~ ( in @ X952 @ nat )
| ~ ( in @ X953 @ nat )
| ~ ( in @ X954 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X951 @ X952 ) )
| ~ ( l_some @ nat @ ( diffprop @ X953 @ X954 ) )
| ( l_some @ nat @ ( diffprop @ ( n_ts @ X951 @ X953 ) @ ( n_ts @ X952 @ X954 ) ) ) ),
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,
~ ( l_some @ nat @ ( diffprop @ ( n_ts @ esk2_0 @ esk4_0 ) @ ( n_ts @ esk1_0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,plain,
! [X1: $i,X4: $i,X5: $i,X6: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_ts @ X1 @ X5 ) @ ( n_ts @ X4 @ X6 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X6 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) )
| ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
l_some @ nat @ ( diffprop @ esk4_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,negated_conjecture,
l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_23,negated_conjecture,
in @ esk4_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_24,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_25,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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]),c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM721^4 : TPTP v8.2.0. Released v7.1.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 20 04:36:38 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.43 Running higher-order theorem proving
% 0.17/0.43 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
% 0.17/0.56 # Version: 3.1.0-ho
% 0.17/0.56 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.17/0.56 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.56 # Starting lpo1_fix with 900s (3) cores
% 0.17/0.56 # Starting full_lambda_9 with 300s (1) cores
% 0.17/0.56 # Starting almost_fo_4 with 300s (1) cores
% 0.17/0.56 # Starting new_ho_9 with 300s (1) cores
% 0.17/0.56 # Starting pre_casc_4 with 300s (1) cores
% 0.17/0.56 # Starting ho_unfolding_6 with 300s (1) cores
% 0.17/0.56 # full_lambda_9 with pid 30449 completed with status 0
% 0.17/0.56 # Result found by full_lambda_9
% 0.17/0.56 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.17/0.56 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.56 # Starting lpo1_fix with 900s (3) cores
% 0.17/0.56 # Starting full_lambda_9 with 300s (1) cores
% 0.17/0.56 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.17/0.56 # Search class: HGHSS-FSLM32-MHSMMSBN
% 0.17/0.56 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.17/0.56 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.56 # Starting full_lambda_5 with 25s (1) cores
% 0.17/0.56 # full_lambda_5 with pid 30454 completed with status 0
% 0.17/0.56 # Result found by full_lambda_5
% 0.17/0.56 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.17/0.56 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.56 # Starting lpo1_fix with 900s (3) cores
% 0.17/0.56 # Starting full_lambda_9 with 300s (1) cores
% 0.17/0.56 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.17/0.56 # Search class: HGHSS-FSLM32-MHSMMSBN
% 0.17/0.56 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.17/0.56 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.56 # Starting full_lambda_5 with 25s (1) cores
% 0.17/0.56 # Preprocessing time : 0.005 s
% 0.17/0.56 # Presaturation interreduction done
% 0.17/0.56
% 0.17/0.56 # Proof found!
% 0.17/0.56 # SZS status Theorem
% 0.17/0.56 # SZS output start CNFRefutation
% See solution above
% 0.17/0.56 # Parsed axioms : 467
% 0.17/0.56 # Removed by relevancy pruning/SinE : 309
% 0.17/0.56 # Initial clauses : 349
% 0.17/0.56 # Removed in clause preprocessing : 148
% 0.17/0.56 # Initial clauses in saturation : 201
% 0.17/0.56 # Processed clauses : 418
% 0.17/0.56 # ...of these trivial : 0
% 0.17/0.56 # ...subsumed : 109
% 0.17/0.56 # ...remaining for further processing : 309
% 0.17/0.56 # Other redundant clauses eliminated : 34
% 0.17/0.56 # Clauses deleted for lack of memory : 0
% 0.17/0.56 # Backward-subsumed : 0
% 0.17/0.56 # Backward-rewritten : 0
% 0.17/0.56 # Generated clauses : 974
% 0.17/0.56 # ...of the previous two non-redundant : 925
% 0.17/0.56 # ...aggressively subsumed : 0
% 0.17/0.56 # Contextual simplify-reflections : 1
% 0.17/0.56 # Paramodulations : 694
% 0.17/0.56 # Factorizations : 0
% 0.17/0.56 # NegExts : 1
% 0.17/0.56 # Equation resolutions : 40
% 0.17/0.56 # Disequality decompositions : 0
% 0.17/0.56 # Total rewrite steps : 172
% 0.17/0.56 # ...of those cached : 164
% 0.17/0.56 # Propositional unsat checks : 0
% 0.17/0.56 # Propositional check models : 0
% 0.17/0.56 # Propositional check unsatisfiable : 0
% 0.17/0.56 # Propositional clauses : 0
% 0.17/0.56 # Propositional clauses after purity: 0
% 0.17/0.56 # Propositional unsat core size : 0
% 0.17/0.56 # Propositional preprocessing time : 0.000
% 0.17/0.56 # Propositional encoding time : 0.000
% 0.17/0.56 # Propositional solver time : 0.000
% 0.17/0.56 # Success case prop preproc time : 0.000
% 0.17/0.56 # Success case prop encoding time : 0.000
% 0.17/0.56 # Success case prop solver time : 0.000
% 0.17/0.56 # Current number of processed clauses : 159
% 0.17/0.56 # Positive orientable unit clauses : 14
% 0.17/0.56 # Positive unorientable unit clauses: 0
% 0.17/0.56 # Negative unit clauses : 16
% 0.17/0.56 # Non-unit-clauses : 129
% 0.17/0.56 # Current number of unprocessed clauses: 812
% 0.17/0.56 # ...number of literals in the above : 4487
% 0.17/0.56 # Current number of archived formulas : 0
% 0.17/0.56 # Current number of archived clauses : 124
% 0.17/0.56 # Clause-clause subsumption calls (NU) : 8478
% 0.17/0.56 # Rec. Clause-clause subsumption calls : 1284
% 0.17/0.56 # Non-unit clause-clause subsumptions : 102
% 0.17/0.56 # Unit Clause-clause subsumption calls : 53
% 0.17/0.56 # Rewrite failures with RHS unbound : 0
% 0.17/0.56 # BW rewrite match attempts : 0
% 0.17/0.56 # BW rewrite match successes : 0
% 0.17/0.56 # Condensation attempts : 0
% 0.17/0.56 # Condensation successes : 0
% 0.17/0.56 # Termbank termtop insertions : 83579
% 0.17/0.56 # Search garbage collected termcells : 24172
% 0.17/0.56
% 0.17/0.56 # -------------------------------------------------
% 0.17/0.56 # User time : 0.089 s
% 0.17/0.56 # System time : 0.014 s
% 0.17/0.56 # Total time : 0.103 s
% 0.17/0.56 # Maximum resident set size: 5956 pages
% 0.17/0.56
% 0.17/0.56 # -------------------------------------------------
% 0.17/0.56 # User time : 0.103 s
% 0.17/0.56 # System time : 0.016 s
% 0.17/0.56 # Total time : 0.119 s
% 0.17/0.56 # Maximum resident set size: 2544 pages
% 0.17/0.56 % E---3.1 exiting
% 0.17/0.56 % E exiting
%------------------------------------------------------------------------------