TSTP Solution File: ALG260^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ALG260^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 : Mon May 20 18:05:55 EDT 2024
% Result : Theorem 0.18s 0.53s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 38 ( 15 unt; 16 typ; 0 def)
% Number of atoms : 49 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 184 ( 12 ~; 0 |; 3 &; 153 @)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 57 ( 16 ^ 41 !; 0 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_22,type,
one: term ).
thf(decl_24,type,
lam: term > term ).
thf(decl_25,type,
sub: term > subst > term ).
thf(decl_26,type,
id: subst ).
thf(decl_27,type,
sh: subst ).
thf(decl_29,type,
comp: subst > subst > subst ).
thf(decl_30,type,
var: term > $o ).
thf(decl_68,type,
hoaslamnotvar_lthm: $o ).
thf(decl_93,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(decl_110,type,
hoaslamnotvar: $o ).
thf(decl_121,type,
lamnotvar: $o ).
thf(decl_127,type,
hoasvar: subst > term > subst > $o ).
thf(decl_142,type,
axvarid: $o ).
thf(decl_144,type,
esk1_0: subst > term > term ).
thf(hoaslamnotvar,axiom,
( hoaslamnotvar
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
@ id ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslamnotvar) ).
thf(hoasvar,axiom,
( hoasvar
= ( ^ [X3: subst,X1: term,X4: subst] : ( var @ ( sub @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasvar) ).
thf(hoaslamnotvar_lthm,axiom,
( hoaslamnotvar_lthm
<=> ( axvarid
=> ( lamnotvar
=> hoaslamnotvar ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslamnotvar_lthm) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axvarid) ).
thf(lamnotvar,axiom,
( lamnotvar
<=> ! [X1: term] :
~ ( var @ ( lam @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',lamnotvar) ).
thf(thm,conjecture,
hoaslamnotvar_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(hoaslam,axiom,
( hoaslam
= ( ^ [X3: subst,X12: subst > term > term] : ( lam @ ( X12 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslam) ).
thf(c_0_7,plain,
( hoaslamnotvar
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
@ id ) ) ),
inference(fof_simplification,[status(thm)],[hoaslamnotvar]) ).
thf(c_0_8,plain,
( hoasvar
= ( ^ [Z0: subst,Z1: term,Z2: subst] : ( var @ ( sub @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[hoasvar]) ).
thf(c_0_9,plain,
( hoaslamnotvar
= ( ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ~ ( var
@ ( sub
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
@ id ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_10,axiom,
( hoaslamnotvar_lthm
= ( ! [X1205: term] :
( ( sub @ X1205 @ id )
= X1205 )
=> ( ! [X1206: term] :
~ ( var @ ( lam @ X1206 ) )
=> ! [X1207: subst > term > term] :
( ! [X1208: subst,X1209: term,X1210: subst] :
( ( sub @ ( X1207 @ X1208 @ X1209 ) @ X1210 )
= ( X1207 @ ( comp @ X1208 @ X1210 ) @ ( sub @ X1209 @ X1210 ) ) )
=> ~ ( var
@ ( sub
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X1207 @ Z0 @ Z1 ) )
@ id ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoaslamnotvar_lthm,axvarid]),lamnotvar]),c_0_8]),c_0_9]) ).
thf(c_0_11,negated_conjecture,
~ ( ! [X3373: term] :
( ( sub @ X3373 @ id )
= X3373 )
=> ( ! [X3374: term] :
~ ( var @ ( lam @ X3374 ) )
=> ! [X3375: subst > term > term] :
( ! [X3376: subst,X3377: term,X3378: subst] :
( ( sub @ ( X3375 @ X3376 @ X3377 ) @ X3378 )
= ( X3375 @ ( comp @ X3376 @ X3378 ) @ ( sub @ X3377 @ X3378 ) ) )
=> ~ ( var @ ( sub @ ( hoaslam @ id @ X3375 ) @ id ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_10])])]) ).
thf(c_0_12,plain,
! [X3383: subst,X3384: subst > term > term] :
( ( hoaslam @ X3383 @ X3384 )
= ( lam @ ( X3384 @ sh @ one ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoaslam])]) ).
thf(c_0_13,negated_conjecture,
! [X3391: term,X3392: term,X3394: subst,X3395: term,X3396: subst] :
( ( ( sub @ X3391 @ id )
= X3391 )
& ~ ( var @ ( lam @ X3392 ) )
& ( ( sub @ ( esk1_0 @ X3394 @ X3395 ) @ X3396 )
= ( esk1_0 @ ( comp @ X3394 @ X3396 ) @ ( sub @ X3395 @ X3396 ) ) )
& ( var @ ( sub @ ( hoaslam @ id @ esk1_0 ) @ id ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).
thf(c_0_14,plain,
! [X3389: subst,X3390: subst > term > term] :
( ( hoaslam @ X3389 @ X3390 )
= ( lam @ ( X3390 @ sh @ one ) ) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
var @ ( sub @ ( hoaslam @ id @ esk1_0 ) @ id ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
! [X1: term] :
~ ( var @ ( lam @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,plain,
! [X3: subst,X12: subst > term > term] :
( ( hoaslam @ X3 @ X12 )
= ( lam @ ( X12 @ sh @ one ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
var @ ( hoaslam @ id @ esk1_0 ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,negated_conjecture,
! [X3: subst,X12: subst > term > term] :
~ ( var @ ( hoaslam @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_19,c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG260^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat May 18 22:45:23 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.18/0.47 Running higher-order theorem proving
% 0.18/0.47 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
% 0.18/0.53 # Version: 3.1.0-ho
% 0.18/0.53 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.53 # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.53 # Starting post_as_ho5 with 300s (1) cores
% 0.18/0.53 # Starting post_as_ho10 with 300s (1) cores
% 0.18/0.53 # post_as_ho1 with pid 18460 completed with status 0
% 0.18/0.53 # Result found by post_as_ho1
% 0.18/0.53 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.53 # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.53 # No SInE strategy applied
% 0.18/0.53 # Search class: HUUSM-FFSF32-SHFMMFNN
% 0.18/0.53 # partial match(2): HHUSS-FFSF32-SHFMMFNN
% 0.18/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.53 # Starting new_ho_10 with 163s (1) cores
% 0.18/0.53 # new_ho_10 with pid 18469 completed with status 0
% 0.18/0.53 # Result found by new_ho_10
% 0.18/0.53 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.53 # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.53 # No SInE strategy applied
% 0.18/0.53 # Search class: HUUSM-FFSF32-SHFMMFNN
% 0.18/0.53 # partial match(2): HHUSS-FFSF32-SHFMMFNN
% 0.18/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.53 # Starting new_ho_10 with 163s (1) cores
% 0.18/0.53 # Preprocessing time : 0.003 s
% 0.18/0.53 # Presaturation interreduction done
% 0.18/0.53
% 0.18/0.53 # Proof found!
% 0.18/0.53 # SZS status Theorem
% 0.18/0.53 # SZS output start CNFRefutation
% See solution above
% 0.18/0.53 # Parsed axioms : 238
% 0.18/0.53 # Removed by relevancy pruning/SinE : 0
% 0.30/0.53 # Initial clauses : 130
% 0.30/0.53 # Removed in clause preprocessing : 124
% 0.30/0.53 # Initial clauses in saturation : 6
% 0.30/0.53 # Processed clauses : 12
% 0.30/0.53 # ...of these trivial : 0
% 0.30/0.53 # ...subsumed : 0
% 0.30/0.53 # ...remaining for further processing : 12
% 0.30/0.53 # Other redundant clauses eliminated : 0
% 0.30/0.53 # Clauses deleted for lack of memory : 0
% 0.30/0.53 # Backward-subsumed : 0
% 0.30/0.53 # Backward-rewritten : 1
% 0.30/0.53 # Generated clauses : 4
% 0.30/0.53 # ...of the previous two non-redundant : 3
% 0.30/0.53 # ...aggressively subsumed : 0
% 0.30/0.53 # Contextual simplify-reflections : 0
% 0.30/0.53 # Paramodulations : 3
% 0.30/0.53 # Factorizations : 0
% 0.30/0.53 # NegExts : 0
% 0.30/0.53 # Equation resolutions : 0
% 0.30/0.53 # Disequality decompositions : 0
% 0.30/0.53 # Total rewrite steps : 1
% 0.30/0.53 # ...of those cached : 0
% 0.30/0.53 # Propositional unsat checks : 0
% 0.30/0.53 # Propositional check models : 0
% 0.30/0.53 # Propositional check unsatisfiable : 0
% 0.30/0.53 # Propositional clauses : 0
% 0.30/0.53 # Propositional clauses after purity: 0
% 0.30/0.53 # Propositional unsat core size : 0
% 0.30/0.53 # Propositional preprocessing time : 0.000
% 0.30/0.53 # Propositional encoding time : 0.000
% 0.30/0.53 # Propositional solver time : 0.000
% 0.30/0.53 # Success case prop preproc time : 0.000
% 0.30/0.53 # Success case prop encoding time : 0.000
% 0.30/0.53 # Success case prop solver time : 0.000
% 0.30/0.53 # Current number of processed clauses : 4
% 0.30/0.53 # Positive orientable unit clauses : 1
% 0.30/0.53 # Positive unorientable unit clauses: 1
% 0.30/0.53 # Negative unit clauses : 2
% 0.30/0.53 # Non-unit-clauses : 0
% 0.30/0.53 # Current number of unprocessed clauses: 3
% 0.30/0.53 # ...number of literals in the above : 3
% 0.30/0.53 # Current number of archived formulas : 0
% 0.30/0.53 # Current number of archived clauses : 8
% 0.30/0.53 # Clause-clause subsumption calls (NU) : 0
% 0.30/0.53 # Rec. Clause-clause subsumption calls : 0
% 0.30/0.53 # Non-unit clause-clause subsumptions : 0
% 0.30/0.53 # Unit Clause-clause subsumption calls : 1
% 0.30/0.53 # Rewrite failures with RHS unbound : 0
% 0.30/0.53 # BW rewrite match attempts : 4
% 0.30/0.53 # BW rewrite match successes : 3
% 0.30/0.53 # Condensation attempts : 12
% 0.30/0.53 # Condensation successes : 0
% 0.30/0.53 # Termbank termtop insertions : 26338
% 0.30/0.53 # Search garbage collected termcells : 1715
% 0.30/0.53
% 0.30/0.53 # -------------------------------------------------
% 0.30/0.53 # User time : 0.027 s
% 0.30/0.53 # System time : 0.012 s
% 0.30/0.53 # Total time : 0.039 s
% 0.30/0.53 # Maximum resident set size: 5788 pages
% 0.30/0.53
% 0.30/0.53 # -------------------------------------------------
% 0.30/0.53 # User time : 0.034 s
% 0.30/0.53 # System time : 0.015 s
% 0.30/0.53 # Total time : 0.049 s
% 0.30/0.53 # Maximum resident set size: 2072 pages
% 0.30/0.53 % E---3.1 exiting
% 0.30/0.53 % E exiting
%------------------------------------------------------------------------------