%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG260^2 : 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 : n002.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 07:44:46 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 185 ( 13 ~; 0 |; 3 &; 153 @)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 20 ( 20 >; 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_23,type,
one: term ).
thf(decl_25,type,
lam: term > term ).
thf(decl_26,type,
sub: term > subst > term ).
thf(decl_27,type,
id: subst ).
thf(decl_28,type,
sh: subst ).
thf(decl_30,type,
comp: subst > subst > subst ).
thf(decl_31,type,
var: term > $o ).
thf(decl_69,type,
hoaslamnotvar_lthm: $o ).
thf(decl_94,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(decl_111,type,
hoaslamnotvar: $o ).
thf(decl_122,type,
lamnotvar: $o ).
thf(decl_128,type,
hoasvar: subst > term > subst > $o ).
thf(decl_143,type,
axvarid: $o ).
thf(decl_145,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/sandbox/tmp/tmp.EVZNZaPMmx/E---3.1_1614444.p',hoaslamnotvar) ).
thf(hoasvar,axiom,
( hoasvar
= ( ^ [X3: subst,X1: term,X4: subst] : ( var @ ( sub @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EVZNZaPMmx/E---3.1_1614444.p',hoasvar) ).
thf(thm,conjecture,
hoaslamnotvar_lthm,
file('/export/starexec/sandbox/tmp/tmp.EVZNZaPMmx/E---3.1_1614444.p',thm) ).
thf(hoaslamnotvar_lthm,axiom,
( hoaslamnotvar_lthm
<=> ( axvarid
=> ( lamnotvar
=> hoaslamnotvar ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EVZNZaPMmx/E---3.1_1614444.p',hoaslamnotvar_lthm) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.EVZNZaPMmx/E---3.1_1614444.p',axvarid) ).
thf(lamnotvar,axiom,
( lamnotvar
<=> ! [X1: term] :
~ ( var @ ( lam @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EVZNZaPMmx/E---3.1_1614444.p',lamnotvar) ).
thf(hoaslam,axiom,
( hoaslam
= ( ^ [X3: subst,X12: subst > term > term] : ( lam @ ( X12 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EVZNZaPMmx/E---3.1_1614444.p',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,negated_conjecture,
~ hoaslamnotvar_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_11,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_12,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)],[c_0_10,c_0_11])])]) ).
thf(c_0_13,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_14,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_12])])])])]) ).
thf(c_0_15,plain,
! [X3389: subst,X3390: subst > term > term] :
( ( hoaslam @ X3389 @ X3390 )
= ( lam @ ( X3390 @ sh @ one ) ) ),
inference(variable_rename,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
var @ ( sub @ ( hoaslam @ id @ esk1_0 ) @ id ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,negated_conjecture,
! [X1: term] :
~ ( var @ ( lam @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
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_15]) ).
thf(c_0_20,negated_conjecture,
var @ ( hoaslam @ id @ esk1_0 ),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,negated_conjecture,
! [X3: subst,X12: subst > term > term] :
~ ( var @ ( hoaslam @ X3 @ X12 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_20,c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG260^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.16 % Computer : n002.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Sep 29 17:36:37 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 Running higher-order theorem proving
% 0.11/0.23 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.EVZNZaPMmx/E---3.1_1614444.p
% 0.21/0.29 % Version: 3.5.1-ho
% 0.21/0.29 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.21/0.29 % Starting post_as_ho5 with 300s (1) cores
% 0.21/0.29 % Starting post_as_ho10 with 300s (1) cores
% 0.21/0.29 % post_as_ho1 with pid 1614458 completed with status 0
% 0.21/0.29 % Result found by post_as_ho1
% 0.21/0.29 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.21/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.29 % No SInE strategy applied
% 0.21/0.29 % Search class: HUUSM-FFSF32-SHFMMFNN
% 0.21/0.29 % partial match(2): HHUSS-FFSF32-SHFMMFNN
% 0.21/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.29 % SubtermCWHack with pid 1614472 completed with status 0
% 0.21/0.29 % Result found by SubtermCWHack
% 0.21/0.29 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.21/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.29 % No SInE strategy applied
% 0.21/0.29 % Search class: HUUSM-FFSF32-SHFMMFNN
% 0.21/0.29 % partial match(2): HHUSS-FFSF32-SHFMMFNN
% 0.21/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.29 % Preprocessing time : 0.002 s
% 0.21/0.29
% 0.21/0.29 % Proof found!
% 0.21/0.29 % SZS status Theorem
% 0.21/0.29 % SZS output start CNFRefutation
% See solution above
% 0.21/0.29 % Parsed axioms : 238
% 0.21/0.29 % Removed by relevancy pruning/SinE : 0
% 0.21/0.29 % Initial clauses : 130
% 0.21/0.29 % Removed in clause preprocessing : 124
% 0.21/0.29 % Initial clauses in saturation : 6
% 0.21/0.29 % Processed clauses : 5
% 0.21/0.29 % ...of these trivial : 0
% 0.21/0.29 % ...subsumed : 0
% 0.21/0.29 % ...remaining for further processing : 5
% 0.21/0.29 % Other redundant clauses eliminated : 0
% 0.21/0.29 % Clauses deleted for lack of memory : 0
% 0.21/0.29 % Backward-subsumed : 0
% 0.21/0.29 % Backward-rewritten : 0
% 0.21/0.29 % Generated clauses : 4
% 0.21/0.29 % ...of the previous two non-redundant : 2
% 0.21/0.29 % ...aggressively subsumed : 0
% 0.21/0.29 % Contextual simplify-reflections : 0
% 0.21/0.29 % Paramodulations : 3
% 0.21/0.29 % Factorizations : 0
% 0.21/0.29 % NegExts : 0
% 0.21/0.29 % Equation resolutions : 0
% 0.21/0.29 % Disequality decompositions : 0
% 0.21/0.29 % Total rewrite steps : 1
% 0.21/0.29 % ...of those cached : 0
% 0.21/0.29 % Propositional unsat checks : 0
% 0.21/0.29 % Propositional check models : 0
% 0.21/0.29 % Propositional check unsatisfiable : 0
% 0.21/0.29 % Propositional clauses : 0
% 0.21/0.29 % Propositional clauses after purity: 0
% 0.21/0.29 % Propositional unsat core size : 0
% 0.21/0.29 % Propositional preprocessing time : 0.000
% 0.21/0.29 % Propositional encoding time : 0.000
% 0.21/0.29 % Propositional solver time : 0.000
% 0.21/0.29 % Success case prop preproc time : 0.000
% 0.21/0.29 % Success case prop encoding time : 0.000
% 0.21/0.29 % Success case prop solver time : 0.000
% 0.21/0.29 % Current number of processed clauses : 4
% 0.21/0.29 % Positive orientable unit clauses : 1
% 0.21/0.29 % Positive unorientable unit clauses: 1
% 0.21/0.29 % Negative unit clauses : 2
% 0.21/0.29 % Non-unit-clauses : 0
% 0.21/0.29 % Current number of unprocessed clauses: 3
% 0.21/0.29 % ...number of literals in the above : 3
% 0.21/0.29 % Current number of archived formulas : 0
% 0.21/0.29 % Current number of archived clauses : 1
% 0.21/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.21/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.21/0.29 % Non-unit clause-clause subsumptions : 0
% 0.21/0.29 % Unit Clause-clause subsumption calls : 1
% 0.21/0.29 % Rewrite failures with RHS unbound : 0
% 0.21/0.29 % BW rewrite match attempts : 2
% 0.21/0.29 % BW rewrite match successes : 1
% 0.21/0.29 % Condensation attempts : 0
% 0.21/0.29 % Condensation successes : 0
% 0.21/0.29 % Termbank termtop insertions : 26450
% 0.21/0.29 % Search garbage collected termcells : 1714
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.026 s
% 0.21/0.29 % System time : 0.012 s
% 0.21/0.29 % Total time : 0.038 s
% 0.21/0.29 % Maximum resident set size: 7564 pages
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.036 s
% 0.21/0.29 % System time : 0.015 s
% 0.21/0.29 % Total time : 0.051 s
% 0.21/0.29 % Maximum resident set size: 4864 pages
% 0.21/0.29 % E exiting
%------------------------------------------------------------------------------