TSTP Solution File: NUM641^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM641^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 01:15:12 EDT 2024
% Result : Theorem 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 29 ( 12 unt; 10 typ; 0 def)
% Number of atoms : 42 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 70 ( 5 ~; 2 |; 1 &; 57 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 31 ( 24 ^ 7 !; 0 ?; 31 :)
% 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_47,type,
ordsucc: $i > $i ).
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_130,type,
n_1: $i ).
thf(decl_142,type,
n_pl: $i > $i > $i ).
thf(decl_143,type,
esk1_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/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_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_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(satz4g,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( ordsucc @ X1 ) @ ( n_pl @ n_1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4g) ).
thf(satz4c,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_pl @ n_1 @ X1 ) @ ( ordsucc @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4c) ).
thf(c_0_6,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_7,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_8,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_9,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_8]) ).
thf(c_0_11,negated_conjecture,
~ ! [X279: $i] :
( ( in @ X279 @ nat )
=> ( ( ordsucc @ X279 )
= ( n_pl @ n_1 @ X279 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz4g])]),c_0_9]),c_0_10]) ).
thf(c_0_12,plain,
! [X285: $i] :
( ( in @ X285 @ nat )
=> ( ( n_pl @ n_1 @ X285 )
= ( ordsucc @ X285 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4c]),c_0_9]),c_0_10]) ).
thf(c_0_13,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( ( ordsucc @ esk1_0 )
!= ( n_pl @ n_1 @ esk1_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
thf(c_0_14,plain,
! [X349: $i] :
( ~ ( in @ X349 @ nat )
| ( ( n_pl @ n_1 @ X349 )
= ( ordsucc @ X349 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
thf(c_0_15,negated_conjecture,
( ( ordsucc @ esk1_0 )
!= ( n_pl @ n_1 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,plain,
! [X1: $i] :
( ( ( n_pl @ n_1 @ X1 )
= ( ordsucc @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM641^4 : TPTP v8.2.0. Released v7.1.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 04:39:38 EDT 2024
% 0.14/0.35 % 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
% 0.20/0.52 # Version: 3.1.0-ho
% 0.20/0.52 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.20/0.52 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 # Starting lpo1_fix with 900s (3) cores
% 0.20/0.52 # Starting full_lambda_9 with 300s (1) cores
% 0.20/0.52 # Starting almost_fo_4 with 300s (1) cores
% 0.20/0.52 # Starting new_ho_9 with 300s (1) cores
% 0.20/0.52 # Starting pre_casc_4 with 300s (1) cores
% 0.20/0.52 # Starting ho_unfolding_6 with 300s (1) cores
% 0.20/0.52 # pre_casc_4 with pid 6199 completed with status 0
% 0.20/0.52 # Result found by pre_casc_4
% 0.20/0.52 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.20/0.52 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 # Starting lpo1_fix with 900s (3) cores
% 0.20/0.52 # Starting full_lambda_9 with 300s (1) cores
% 0.20/0.52 # Starting almost_fo_4 with 300s (1) cores
% 0.20/0.52 # Starting new_ho_9 with 300s (1) cores
% 0.20/0.52 # Starting pre_casc_4 with 300s (1) cores
% 0.20/0.52 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.20/0.52 # Search class: HGUSM-FFMM31-DHSMMSBN
% 0.20/0.52 # partial match(3): HGHSM-FFMM31-SHSSMSBN
% 0.20/0.52 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.52 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.52 # new_ho_10 with pid 6205 completed with status 0
% 0.20/0.52 # Result found by new_ho_10
% 0.20/0.52 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.20/0.52 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 # Starting lpo1_fix with 900s (3) cores
% 0.20/0.52 # Starting full_lambda_9 with 300s (1) cores
% 0.20/0.52 # Starting almost_fo_4 with 300s (1) cores
% 0.20/0.52 # Starting new_ho_9 with 300s (1) cores
% 0.20/0.52 # Starting pre_casc_4 with 300s (1) cores
% 0.20/0.52 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.20/0.52 # Search class: HGUSM-FFMM31-DHSMMSBN
% 0.20/0.52 # partial match(3): HGHSM-FFMM31-SHSSMSBN
% 0.20/0.52 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.52 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.52 # Preprocessing time : 0.005 s
% 0.20/0.52 # Presaturation interreduction done
% 0.20/0.52
% 0.20/0.52 # Proof found!
% 0.20/0.52 # SZS status Theorem
% 0.20/0.52 # SZS output start CNFRefutation
% See solution above
% 0.20/0.52 # Parsed axioms : 313
% 0.20/0.52 # Removed by relevancy pruning/SinE : 244
% 0.20/0.52 # Initial clauses : 108
% 0.20/0.52 # Removed in clause preprocessing : 3
% 0.20/0.52 # Initial clauses in saturation : 105
% 0.20/0.52 # Processed clauses : 123
% 0.20/0.52 # ...of these trivial : 4
% 0.20/0.52 # ...subsumed : 6
% 0.20/0.52 # ...remaining for further processing : 113
% 0.20/0.52 # Other redundant clauses eliminated : 2
% 0.20/0.52 # Clauses deleted for lack of memory : 0
% 0.20/0.52 # Backward-subsumed : 0
% 0.20/0.52 # Backward-rewritten : 0
% 0.20/0.52 # Generated clauses : 7
% 0.20/0.52 # ...of the previous two non-redundant : 4
% 0.20/0.53 # ...aggressively subsumed : 0
% 0.20/0.53 # Contextual simplify-reflections : 0
% 0.20/0.53 # Paramodulations : 4
% 0.20/0.53 # Factorizations : 0
% 0.20/0.53 # NegExts : 0
% 0.20/0.53 # Equation resolutions : 2
% 0.20/0.53 # Disequality decompositions : 0
% 0.20/0.53 # Total rewrite steps : 16
% 0.20/0.53 # ...of those cached : 5
% 0.20/0.53 # Propositional unsat checks : 0
% 0.20/0.53 # Propositional check models : 0
% 0.20/0.53 # Propositional check unsatisfiable : 0
% 0.20/0.53 # Propositional clauses : 0
% 0.20/0.53 # Propositional clauses after purity: 0
% 0.20/0.53 # Propositional unsat core size : 0
% 0.20/0.53 # Propositional preprocessing time : 0.000
% 0.20/0.53 # Propositional encoding time : 0.000
% 0.20/0.53 # Propositional solver time : 0.000
% 0.20/0.53 # Success case prop preproc time : 0.000
% 0.20/0.53 # Success case prop encoding time : 0.000
% 0.20/0.53 # Success case prop solver time : 0.000
% 0.20/0.53 # Current number of processed clauses : 17
% 0.20/0.53 # Positive orientable unit clauses : 7
% 0.20/0.53 # Positive unorientable unit clauses: 0
% 0.20/0.53 # Negative unit clauses : 5
% 0.20/0.53 # Non-unit-clauses : 5
% 0.20/0.53 # Current number of unprocessed clauses: 81
% 0.20/0.53 # ...number of literals in the above : 244
% 0.20/0.53 # Current number of archived formulas : 0
% 0.20/0.53 # Current number of archived clauses : 95
% 0.20/0.53 # Clause-clause subsumption calls (NU) : 721
% 0.20/0.53 # Rec. Clause-clause subsumption calls : 250
% 0.20/0.53 # Non-unit clause-clause subsumptions : 6
% 0.20/0.53 # Unit Clause-clause subsumption calls : 11
% 0.20/0.53 # Rewrite failures with RHS unbound : 0
% 0.20/0.53 # BW rewrite match attempts : 1
% 0.20/0.53 # BW rewrite match successes : 0
% 0.20/0.53 # Condensation attempts : 123
% 0.20/0.53 # Condensation successes : 0
% 0.20/0.53 # Termbank termtop insertions : 14563
% 0.20/0.53 # Search garbage collected termcells : 4501
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.021 s
% 0.20/0.53 # System time : 0.006 s
% 0.20/0.53 # Total time : 0.027 s
% 0.20/0.53 # Maximum resident set size: 2816 pages
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.029 s
% 0.20/0.53 # System time : 0.009 s
% 0.20/0.53 # Total time : 0.038 s
% 0.20/0.53 # Maximum resident set size: 2136 pages
% 0.20/0.53 % E---3.1 exiting
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------