%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG261^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:44:47 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 13 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 135 ( 12 ~; 0 |; 2 &; 111 @)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 49 ( 10 ^; 39 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_24,type,
ap: term > term > term ).
thf(decl_26,type,
sub: term > subst > term ).
thf(decl_27,type,
id: subst ).
thf(decl_31,type,
var: term > $o ).
thf(decl_39,type,
hoasap: subst > term > subst > term > term ).
thf(decl_49,type,
apnotvar: $o ).
thf(decl_64,type,
hoasapnotvar: $o ).
thf(decl_128,type,
hoasvar: subst > term > subst > $o ).
thf(decl_140,type,
hoasapnotvar_lthm: $o ).
thf(decl_143,type,
axvarid: $o ).
thf(decl_145,type,
esk1_0: term ).
thf(decl_146,type,
esk2_0: term ).
thf(hoasvar,axiom,
( hoasvar
= ( ^ [X3: subst,X1: term,X4: subst] : ( var @ ( sub @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SqRYd6Qz8b/E---3.1_643796.p',hoasvar) ).
thf(hoasapnotvar,axiom,
( hoasapnotvar
<=> ! [X1: term,X2: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ),
file('/export/starexec/sandbox/tmp/tmp.SqRYd6Qz8b/E---3.1_643796.p',hoasapnotvar) ).
thf(thm,conjecture,
hoasapnotvar_lthm,
file('/export/starexec/sandbox/tmp/tmp.SqRYd6Qz8b/E---3.1_643796.p',thm) ).
thf(hoasapnotvar_lthm,axiom,
( hoasapnotvar_lthm
<=> ( axvarid
=> ( apnotvar
=> hoasapnotvar ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SqRYd6Qz8b/E---3.1_643796.p',hoasapnotvar_lthm) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.SqRYd6Qz8b/E---3.1_643796.p',axvarid) ).
thf(apnotvar,axiom,
( apnotvar
<=> ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SqRYd6Qz8b/E---3.1_643796.p',apnotvar) ).
thf(hoasap,axiom,
( hoasap
= ( ^ [X3: subst,X1: term,X4: subst,X2: term] : ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SqRYd6Qz8b/E---3.1_643796.p',hoasap) ).
thf(c_0_7,plain,
( hoasvar
= ( ^ [Z0: subst,Z1: term,Z2: subst] : ( var @ ( sub @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[hoasvar]) ).
thf(c_0_8,axiom,
( hoasapnotvar
= ( ! [X1: term,X2: term] :
~ ( var @ ( sub @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ) ) ),
inference(apply_def,[status(thm)],[hoasapnotvar,c_0_7]) ).
thf(c_0_9,negated_conjecture,
~ hoasapnotvar_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_10,axiom,
( hoasapnotvar_lthm
= ( ! [X3304: term] :
( ( sub @ X3304 @ id )
= X3304 )
=> ( ! [X3305: term,X3306: term] :
~ ( var @ ( ap @ X3305 @ X3306 ) )
=> ! [X3307: term,X3308: term] :
~ ( var @ ( sub @ ( hoasap @ id @ X3307 @ id @ X3308 ) @ id ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoasapnotvar_lthm,axvarid]),apnotvar]),c_0_8]) ).
thf(c_0_11,negated_conjecture,
~ ( ! [X3373: term] :
( ( sub @ X3373 @ id )
= X3373 )
=> ( ! [X3374: term,X3375: term] :
~ ( var @ ( ap @ X3374 @ X3375 ) )
=> ! [X3376: term,X3377: term] :
~ ( var @ ( sub @ ( hoasap @ id @ X3376 @ id @ X3377 ) @ id ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[c_0_9,c_0_10])]) ).
thf(c_0_12,plain,
! [X3378: subst,X3379: term,X3380: subst,X3381: term] :
( ( hoasap @ X3378 @ X3379 @ X3380 @ X3381 )
= ( ap @ ( sub @ X3379 @ X3380 ) @ X3381 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoasap])]) ).
thf(c_0_13,negated_conjecture,
! [X3390: term,X3391: term,X3392: term] :
( ( ( sub @ X3390 @ id )
= X3390 )
& ~ ( var @ ( ap @ X3391 @ X3392 ) )
& ( var @ ( sub @ ( hoasap @ id @ esk1_0 @ id @ esk2_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,
! [X3384: subst,X3385: term,X3386: subst,X3387: term] :
( ( hoasap @ X3384 @ X3385 @ X3386 @ X3387 )
= ( ap @ ( sub @ X3385 @ X3386 ) @ X3387 ) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
var @ ( sub @ ( hoasap @ id @ esk1_0 @ id @ esk2_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,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,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_14]) ).
thf(c_0_19,negated_conjecture,
var @ ( hoasap @ id @ esk1_0 @ id @ esk2_0 ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,negated_conjecture,
! [X1: term,X4: subst,X3: subst,X2: term] :
~ ( var @ ( hoasap @ X3 @ X1 @ X4 @ X2 ) ),
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
% 0.00/0.03 % Problem : ALG261^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:29:22 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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/tmp/tmp.SqRYd6Qz8b/E---3.1_643796.p
% 0.22/0.32 % Version: 3.5.1-ho
% 0.22/0.32 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.32 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.32 % Starting post_as_ho5 with 300s (1) cores
% 0.22/0.32 % Starting post_as_ho10 with 300s (1) cores
% 0.22/0.32 % new_ho_10_cnf2 with pid 643820 completed with status 0
% 0.22/0.32 % Result found by new_ho_10_cnf2
% 0.22/0.32 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.32 % No SInE strategy applied
% 0.22/0.32 % Search class: HUUSS-FFSF32-SHFMMFNN
% 0.22/0.32 % partial match(1): HHUSS-FFSF32-SHFMMFNN
% 0.22/0.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.32 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.32 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.22/0.32 % Starting sh5l with 136s (1) cores
% 0.22/0.32 % Starting new_bool_1 with 136s (1) cores
% 0.22/0.32 % Starting new_bool_2 with 136s (1) cores
% 0.22/0.32 % sh5l with pid 643859 completed with status 0
% 0.22/0.32 % Result found by sh5l
% 0.22/0.32 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.32 % No SInE strategy applied
% 0.22/0.32 % Search class: HUUSS-FFSF32-SHFMMFNN
% 0.22/0.32 % partial match(1): HHUSS-FFSF32-SHFMMFNN
% 0.22/0.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.32 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.32 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.22/0.32 % Starting sh5l with 136s (1) cores
% 0.22/0.32 % Preprocessing time : 0.001 s
% 0.22/0.32 % Presaturation interreduction done
% 0.22/0.32
% 0.22/0.32 % Proof found!
% 0.22/0.32 % SZS status Theorem
% 0.22/0.32 % SZS output start CNFRefutation
% See solution above
% 0.22/0.32 % Parsed axioms : 238
% 0.22/0.32 % Removed by relevancy pruning/SinE : 0
% 0.22/0.32 % Initial clauses : 129
% 0.22/0.32 % Removed in clause preprocessing : 124
% 0.22/0.32 % Initial clauses in saturation : 5
% 0.22/0.32 % Processed clauses : 11
% 0.22/0.32 % ...of these trivial : 0
% 0.22/0.32 % ...subsumed : 0
% 0.22/0.32 % ...remaining for further processing : 11
% 0.22/0.32 % Other redundant clauses eliminated : 0
% 0.22/0.32 % Clauses deleted for lack of memory : 0
% 0.22/0.32 % Backward-subsumed : 0
% 0.22/0.32 % Backward-rewritten : 0
% 0.22/0.32 % Generated clauses : 8
% 0.22/0.32 % ...of the previous two non-redundant : 6
% 0.22/0.32 % ...aggressively subsumed : 0
% 0.22/0.32 % Contextual simplify-reflections : 0
% 0.22/0.32 % Paramodulations : 6
% 0.22/0.32 % Factorizations : 0
% 0.22/0.32 % NegExts : 0
% 0.22/0.32 % Equation resolutions : 0
% 0.22/0.32 % Disequality decompositions : 0
% 0.22/0.32 % Total rewrite steps : 1
% 0.22/0.32 % ...of those cached : 0
% 0.22/0.32 % Propositional unsat checks : 0
% 0.22/0.32 % Propositional check models : 0
% 0.22/0.32 % Propositional check unsatisfiable : 0
% 0.22/0.32 % Propositional clauses : 0
% 0.22/0.32 % Propositional clauses after purity: 0
% 0.22/0.32 % Propositional unsat core size : 0
% 0.22/0.32 % Propositional preprocessing time : 0.000
% 0.22/0.32 % Propositional encoding time : 0.000
% 0.22/0.32 % Propositional solver time : 0.000
% 0.22/0.32 % Success case prop preproc time : 0.000
% 0.22/0.32 % Success case prop encoding time : 0.000
% 0.22/0.32 % Success case prop solver time : 0.000
% 0.22/0.32 % Current number of processed clauses : 5
% 0.22/0.32 % Positive orientable unit clauses : 1
% 0.22/0.32 % Positive unorientable unit clauses: 2
% 0.22/0.32 % Negative unit clauses : 2
% 0.22/0.32 % Non-unit-clauses : 0
% 0.22/0.32 % Current number of unprocessed clauses: 5
% 0.22/0.32 % ...number of literals in the above : 5
% 0.22/0.32 % Current number of archived formulas : 0
% 0.22/0.32 % Current number of archived clauses : 6
% 0.22/0.32 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.32 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.32 % Non-unit clause-clause subsumptions : 0
% 0.22/0.32 % Unit Clause-clause subsumption calls : 1
% 0.22/0.32 % Rewrite failures with RHS unbound : 2
% 0.22/0.32 % BW rewrite match attempts : 2
% 0.22/0.32 % BW rewrite match successes : 2
% 0.22/0.32 % Condensation attempts : 11
% 0.22/0.32 % Condensation successes : 0
% 0.22/0.32 % Termbank termtop insertions : 26522
% 0.22/0.32 % Search garbage collected termcells : 1674
% 0.22/0.32
% 0.22/0.32 % -------------------------------------------------
% 0.22/0.32 % User time : 0.030 s
% 0.22/0.32 % System time : 0.014 s
% 0.22/0.32 % Total time : 0.044 s
% 0.22/0.32 % Maximum resident set size: 7564 pages
% 0.22/0.32
% 0.22/0.32 % -------------------------------------------------
% 0.22/0.32 % User time : 0.057 s
% 0.22/0.32 % System time : 0.047 s
% 0.22/0.32 % Total time : 0.104 s
% 0.22/0.32 % Maximum resident set size: 5120 pages
% 0.22/0.32 % E exiting
%------------------------------------------------------------------------------