TSTP Solution File: ALG259^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ALG259^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 18:05:54 EDT 2024
% Result : Theorem 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 23
% Syntax : Number of formulae : 39 ( 16 unt; 17 typ; 0 def)
% Number of atoms : 37 ( 28 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 191 ( 12 ~; 0 |; 2 &; 166 @)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 75 ( 12 ^ 63 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_22,type,
one: term ).
thf(decl_23,type,
ap: term > term > 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_38,type,
hoasap: subst > term > subst > term > term ).
thf(decl_61,type,
hoaslamnotap_lthm: $o ).
thf(decl_93,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(decl_108,type,
lamnotap: $o ).
thf(decl_128,type,
hoaslamnotap: $o ).
thf(decl_144,type,
esk1_0: subst > term > term ).
thf(decl_145,type,
esk2_0: term ).
thf(decl_146,type,
esk3_0: term ).
thf(hoaslamnotap,axiom,
( hoaslamnotap
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ! [X1: term,X2: term] :
( ( hoaslam @ id
@ ^ [X3: subst,X7: term] : ( X12 @ X3 @ X7 ) )
!= ( hoasap @ id @ X1 @ id @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslamnotap) ).
thf(hoaslamnotap_lthm,axiom,
( hoaslamnotap_lthm
<=> ( lamnotap
=> hoaslamnotap ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslamnotap_lthm) ).
thf(lamnotap,axiom,
( lamnotap
<=> ! [X1: term,X2: term,X7: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',lamnotap) ).
thf(thm,conjecture,
hoaslamnotap_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(hoasap,axiom,
( hoasap
= ( ^ [X3: subst,X1: term,X4: subst,X2: term] : ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasap) ).
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_6,plain,
( hoaslamnotap
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ! [X1: term,X2: term] :
( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
!= ( hoasap @ id @ X1 @ id @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[hoaslamnotap]) ).
thf(c_0_7,axiom,
( hoaslamnotap_lthm
= ( ! [X1021: term,X1022: term,X1023: term] :
( ( lam @ X1021 )
!= ( ap @ X1022 @ X1023 ) )
=> ! [X1024: subst > term > term] :
( ! [X1025: subst,X1026: term,X1027: subst] :
( ( sub @ ( X1024 @ X1025 @ X1026 ) @ X1027 )
= ( X1024 @ ( comp @ X1025 @ X1027 ) @ ( sub @ X1026 @ X1027 ) ) )
=> ! [X1028: term,X1029: term] :
( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X1024 @ Z0 @ Z1 ) )
!= ( hoasap @ id @ X1028 @ id @ X1029 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoaslamnotap_lthm,lamnotap]),c_0_6]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X3373: term,X3374: term,X3375: term] :
( ( lam @ X3373 )
!= ( ap @ X3374 @ X3375 ) )
=> ! [X3376: subst > term > term] :
( ! [X3377: subst,X3378: term,X3379: subst] :
( ( sub @ ( X3376 @ X3377 @ X3378 ) @ X3379 )
= ( X3376 @ ( comp @ X3377 @ X3379 ) @ ( sub @ X3378 @ X3379 ) ) )
=> ! [X3380: term,X3381: term] :
( ( hoaslam @ id @ X3376 )
!= ( hoasap @ id @ X3380 @ id @ X3381 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_7])])]) ).
thf(c_0_9,plain,
! [X3382: subst,X3383: term,X3384: subst,X3385: term] :
( ( hoasap @ X3382 @ X3383 @ X3384 @ X3385 )
= ( ap @ ( sub @ X3383 @ X3384 ) @ X3385 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoasap])]) ).
thf(c_0_10,negated_conjecture,
! [X3394: term,X3395: term,X3396: term,X3398: subst,X3399: term,X3400: subst] :
( ( ( lam @ X3394 )
!= ( ap @ X3395 @ X3396 ) )
& ( ( sub @ ( esk1_0 @ X3398 @ X3399 ) @ X3400 )
= ( esk1_0 @ ( comp @ X3398 @ X3400 ) @ ( sub @ X3399 @ X3400 ) ) )
& ( ( hoaslam @ id @ esk1_0 )
= ( hoasap @ id @ esk2_0 @ id @ esk3_0 ) ) ),
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_8])])])])]) ).
thf(c_0_11,plain,
! [X3388: subst,X3389: term,X3390: subst,X3391: term] :
( ( hoasap @ X3388 @ X3389 @ X3390 @ X3391 )
= ( ap @ ( sub @ X3389 @ X3390 ) @ X3391 ) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
( ( hoaslam @ id @ esk1_0 )
= ( hoasap @ id @ esk2_0 @ id @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,plain,
! [X1: term,X3: subst,X4: subst,X2: term] :
( ( hoasap @ X3 @ X1 @ X4 @ X2 )
= ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,plain,
! [X3386: subst,X3387: subst > term > term] :
( ( hoaslam @ X3386 @ X3387 )
= ( lam @ ( X3387 @ sh @ one ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoaslam])]) ).
thf(c_0_15,negated_conjecture,
! [X1: term,X2: term,X7: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,negated_conjecture,
( ( ap @ ( sub @ esk2_0 @ id ) @ esk3_0 )
= ( hoaslam @ id @ esk1_0 ) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_17,plain,
! [X3392: subst,X3393: subst > term > term] :
( ( hoaslam @ X3392 @ X3393 )
= ( lam @ ( X3393 @ sh @ one ) ) ),
inference(variable_rename,[status(thm)],[c_0_14]) ).
thf(c_0_18,negated_conjecture,
! [X1: term] :
( ( lam @ X1 )
!= ( hoaslam @ id @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,plain,
! [X3: subst,X12: subst > term > term] :
( ( hoaslam @ X3 @ X12 )
= ( lam @ ( X12 @ sh @ one ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X3: subst,X12: subst > term > term] :
( ( hoaslam @ X3 @ X12 )
!= ( hoaslam @ id @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG259^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.09/0.30 % Computer : n014.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sat May 18 22:57:53 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.14/0.40 Running higher-order theorem proving
% 0.14/0.40 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
% 0.14/0.45 # Version: 3.1.0-ho
% 0.14/0.45 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.14/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.14/0.45 # Starting post_as_ho1 with 300s (1) cores
% 0.14/0.45 # Starting post_as_ho5 with 300s (1) cores
% 0.14/0.45 # Starting post_as_ho10 with 300s (1) cores
% 0.14/0.45 # post_as_ho10 with pid 29857 completed with status 0
% 0.14/0.45 # Result found by post_as_ho10
% 0.14/0.45 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.14/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.14/0.45 # Starting post_as_ho1 with 300s (1) cores
% 0.14/0.45 # Starting post_as_ho5 with 300s (1) cores
% 0.14/0.45 # Starting post_as_ho10 with 300s (1) cores
% 0.14/0.45 # No SInE strategy applied
% 0.14/0.45 # Search class: HUUPS-FFSF32-SHFMMFNN
% 0.14/0.45 # partial match(1): HHUPS-FFSF32-SHFMMFNN
% 0.14/0.45 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.45 # Starting new_ho_10 with 163s (1) cores
% 0.14/0.45 # new_ho_10 with pid 29862 completed with status 0
% 0.14/0.45 # Result found by new_ho_10
% 0.14/0.45 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.14/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.14/0.45 # Starting post_as_ho1 with 300s (1) cores
% 0.14/0.45 # Starting post_as_ho5 with 300s (1) cores
% 0.14/0.45 # Starting post_as_ho10 with 300s (1) cores
% 0.14/0.45 # No SInE strategy applied
% 0.14/0.45 # Search class: HUUPS-FFSF32-SHFMMFNN
% 0.14/0.45 # partial match(1): HHUPS-FFSF32-SHFMMFNN
% 0.14/0.45 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.45 # Starting new_ho_10 with 163s (1) cores
% 0.14/0.45 # Preprocessing time : 0.001 s
% 0.14/0.45 # Presaturation interreduction done
% 0.14/0.45
% 0.14/0.45 # Proof found!
% 0.14/0.45 # SZS status Theorem
% 0.14/0.45 # SZS output start CNFRefutation
% See solution above
% 0.14/0.45 # Parsed axioms : 238
% 0.14/0.45 # Removed by relevancy pruning/SinE : 0
% 0.14/0.45 # Initial clauses : 129
% 0.14/0.45 # Removed in clause preprocessing : 124
% 0.14/0.45 # Initial clauses in saturation : 5
% 0.14/0.45 # Processed clauses : 13
% 0.14/0.45 # ...of these trivial : 0
% 0.14/0.45 # ...subsumed : 0
% 0.14/0.45 # ...remaining for further processing : 13
% 0.14/0.45 # Other redundant clauses eliminated : 0
% 0.14/0.45 # Clauses deleted for lack of memory : 0
% 0.14/0.45 # Backward-subsumed : 0
% 0.14/0.45 # Backward-rewritten : 1
% 0.14/0.45 # Generated clauses : 9
% 0.14/0.45 # ...of the previous two non-redundant : 7
% 0.14/0.45 # ...aggressively subsumed : 0
% 0.14/0.45 # Contextual simplify-reflections : 0
% 0.14/0.45 # Paramodulations : 6
% 0.14/0.45 # Factorizations : 0
% 0.14/0.45 # NegExts : 0
% 0.14/0.45 # Equation resolutions : 1
% 0.14/0.45 # Disequality decompositions : 0
% 0.14/0.45 # Total rewrite steps : 2
% 0.14/0.45 # ...of those cached : 0
% 0.14/0.45 # Propositional unsat checks : 0
% 0.14/0.45 # Propositional check models : 0
% 0.14/0.45 # Propositional check unsatisfiable : 0
% 0.14/0.45 # Propositional clauses : 0
% 0.14/0.45 # Propositional clauses after purity: 0
% 0.14/0.45 # Propositional unsat core size : 0
% 0.14/0.45 # Propositional preprocessing time : 0.000
% 0.14/0.45 # Propositional encoding time : 0.000
% 0.14/0.45 # Propositional solver time : 0.000
% 0.14/0.45 # Success case prop preproc time : 0.000
% 0.14/0.45 # Success case prop encoding time : 0.000
% 0.14/0.45 # Success case prop solver time : 0.000
% 0.14/0.45 # Current number of processed clauses : 7
% 0.14/0.45 # Positive orientable unit clauses : 3
% 0.14/0.45 # Positive unorientable unit clauses: 1
% 0.14/0.45 # Negative unit clauses : 3
% 0.14/0.45 # Non-unit-clauses : 0
% 0.14/0.45 # Current number of unprocessed clauses: 4
% 0.14/0.45 # ...number of literals in the above : 4
% 0.14/0.45 # Current number of archived formulas : 0
% 0.14/0.45 # Current number of archived clauses : 6
% 0.14/0.45 # Clause-clause subsumption calls (NU) : 0
% 0.14/0.45 # Rec. Clause-clause subsumption calls : 0
% 0.14/0.45 # Non-unit clause-clause subsumptions : 0
% 0.14/0.45 # Unit Clause-clause subsumption calls : 3
% 0.14/0.45 # Rewrite failures with RHS unbound : 0
% 0.14/0.45 # BW rewrite match attempts : 6
% 0.14/0.45 # BW rewrite match successes : 3
% 0.14/0.45 # Condensation attempts : 13
% 0.14/0.45 # Condensation successes : 0
% 0.14/0.45 # Termbank termtop insertions : 26393
% 0.14/0.45 # Search garbage collected termcells : 1721
% 0.14/0.45
% 0.14/0.45 # -------------------------------------------------
% 0.14/0.45 # User time : 0.023 s
% 0.14/0.45 # System time : 0.008 s
% 0.14/0.45 # Total time : 0.031 s
% 0.14/0.45 # Maximum resident set size: 5784 pages
% 0.14/0.45
% 0.14/0.45 # -------------------------------------------------
% 0.14/0.45 # User time : 0.030 s
% 0.14/0.45 # System time : 0.011 s
% 0.14/0.45 # Total time : 0.042 s
% 0.14/0.45 # Maximum resident set size: 2072 pages
% 0.14/0.45 % E---3.1 exiting
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------