%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG262^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 0.21s 0.29s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 4 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 71 ( 6 ~; 4 |; 1 &; 53 @)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 21 ( 5 ^; 12 !; 4 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_27,type,
id: subst ).
thf(decl_65,type,
hoasinduction_lem0: $o ).
thf(decl_107,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(decl_115,type,
hoasinduction_lem0_lthm: $o ).
thf(decl_145,type,
epred1_0: subst > term > subst > $o ).
thf(decl_146,type,
esk1_1: ( term > $o ) > term ).
thf(hoasinduction_p_and_p_prime,axiom,
( hoasinduction_p_and_p_prime
= ( ^ [X14: subst > term > subst > $o,X9: term > $o] :
! [X10: term] :
( ( X9 @ X10 )
<=> ( X14 @ id @ X10 @ id ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.n14x1GEHxQ/E---3.1_1574152.p',hoasinduction_p_and_p_prime) ).
thf(hoasinduction_lem0,axiom,
( hoasinduction_lem0
<=> ! [X15: subst > term > subst > $o] :
? [X9: term > $o] : ( hoasinduction_p_and_p_prime @ X15 @ X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.n14x1GEHxQ/E---3.1_1574152.p',hoasinduction_lem0) ).
thf(thm,conjecture,
hoasinduction_lem0_lthm,
file('/export/starexec/sandbox2/tmp/tmp.n14x1GEHxQ/E---3.1_1574152.p',thm) ).
thf(hoasinduction_lem0_lthm,axiom,
( hoasinduction_lem0_lthm
<=> hoasinduction_lem0 ),
file('/export/starexec/sandbox2/tmp/tmp.n14x1GEHxQ/E---3.1_1574152.p',hoasinduction_lem0_lthm) ).
thf(c_0_4,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Z0: subst > term > subst > $o,Z1: term > $o] :
! [X10: term] :
( ( Z1 @ X10 )
<=> ( Z0 @ id @ X10 @ id ) ) ) ),
inference(fof_simplification,[status(thm)],[hoasinduction_p_and_p_prime]) ).
thf(c_0_5,axiom,
( hoasinduction_lem0
= ( ! [X15: subst > term > subst > $o] :
? [X9: term > $o] :
! [X1037: term] :
( ( X9 @ X1037 )
<=> ( X15 @ id @ X1037 @ id ) ) ) ),
inference(apply_def,[status(thm)],[hoasinduction_lem0,c_0_4]) ).
thf(c_0_6,negated_conjecture,
~ hoasinduction_lem0_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_7,axiom,
( hoasinduction_lem0_lthm
= ( ! [X2664: subst > term > subst > $o] :
? [X2665: term > $o] :
! [X2666: term] :
( ( X2665 @ X2666 )
<=> ( X2664 @ id @ X2666 @ id ) ) ) ),
inference(apply_def,[status(thm)],[hoasinduction_lem0_lthm,c_0_5]) ).
thf(c_0_8,negated_conjecture,
~ ! [X3373: subst > term > subst > $o] :
? [X3374: term > $o] :
! [X3375: term] :
( ( X3374 @ X3375 )
<=> ( X3373 @ id @ X3375 @ id ) ),
inference(apply_def,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X3389: term > $o] :
( ( ~ ( X3389 @ ( esk1_1 @ X3389 ) )
| ~ ( epred1_0 @ id @ ( esk1_1 @ X3389 ) @ id ) )
& ( ( X3389 @ ( esk1_1 @ X3389 ) )
| ( epred1_0 @ id @ ( esk1_1 @ X3389 ) @ id ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
thf(c_0_10,negated_conjecture,
! [X6: term > $o] :
( ( X6 @ ( esk1_1 @ X6 ) )
| ( epred1_0 @ id @ ( esk1_1 @ X6 ) @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X6: term > $o] :
( ~ ( X6 @ ( esk1_1 @ X6 ) )
| ~ ( epred1_0 @ id @ ( esk1_1 @ X6 ) @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
( epred1_0 @ id
@ ( esk1_1
@ ^ [Z0: term] : ( epred1_0 @ id @ Z0 @ id ) )
@ id ),
inference(ef,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG262^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n001.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 17:39:51 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.23 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/tmp/tmp.n14x1GEHxQ/E---3.1_1574152.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 1574166 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: HGHSS-FFSF32-SHFMMMBN
% 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 1574173 completed with status 10
% 0.21/0.29 % Starting post_as_ho1 with 31s (1) cores
% 0.21/0.29 % post_as_ho1 with pid 1574176 completed with status 10
% 0.21/0.29 % Starting post_as_ho4 with 34s (1) cores
% 0.21/0.29 % post_as_ho4 with pid 1574179 completed with status 0
% 0.21/0.29 % Result found by post_as_ho4
% 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: HGHSS-FFSF32-SHFMMMBN
% 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 1574173 completed with status 10
% 0.21/0.29 % Starting post_as_ho1 with 31s (1) cores
% 0.21/0.29 % post_as_ho1 with pid 1574176 completed with status 10
% 0.21/0.29 % Starting post_as_ho4 with 34s (1) cores
% 0.21/0.29 % Preprocessing time : 0.001 s
% 0.21/0.29 % Presaturation interreduction done
% 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 : 128
% 0.21/0.29 % Removed in clause preprocessing : 124
% 0.21/0.29 % Initial clauses in saturation : 4
% 0.21/0.29 % Processed clauses : 13
% 0.21/0.29 % ...of these trivial : 0
% 0.21/0.29 % ...subsumed : 1
% 0.21/0.29 % ...remaining for further processing : 12
% 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 : 19
% 0.21/0.29 % ...of the previous two non-redundant : 12
% 0.21/0.29 % ...aggressively subsumed : 0
% 0.21/0.29 % Contextual simplify-reflections : 0
% 0.21/0.29 % Paramodulations : 9
% 0.21/0.29 % Factorizations : 2
% 0.21/0.29 % NegExts : 0
% 0.21/0.29 % Equation resolutions : 1
% 0.21/0.29 % Disequality decompositions : 0
% 0.21/0.29 % Total rewrite steps : 2
% 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 : 8
% 0.21/0.29 % Positive orientable unit clauses : 2
% 0.21/0.29 % Positive unorientable unit clauses: 2
% 0.21/0.29 % Negative unit clauses : 1
% 0.21/0.29 % Non-unit-clauses : 3
% 0.21/0.29 % Current number of unprocessed clauses: 7
% 0.21/0.29 % ...number of literals in the above : 8
% 0.21/0.29 % Current number of archived formulas : 0
% 0.21/0.29 % Current number of archived clauses : 4
% 0.21/0.29 % Clause-clause subsumption calls (NU) : 2
% 0.21/0.29 % Rec. Clause-clause subsumption calls : 2
% 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 : 3
% 0.21/0.29 % BW rewrite match successes : 0
% 0.21/0.29 % Condensation attempts : 13
% 0.21/0.29 % Condensation successes : 0
% 0.21/0.29 % Termbank termtop insertions : 27553
% 0.21/0.29 % Search garbage collected termcells : 1661
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.025 s
% 0.21/0.29 % System time : 0.009 s
% 0.21/0.29 % Total time : 0.034 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 : 0.034 s
% 0.21/0.29 % System time : 0.013 s
% 0.21/0.29 % Total time : 0.047 s
% 0.21/0.29 % Maximum resident set size: 5120 pages
% 0.21/0.29 % E exiting
%------------------------------------------------------------------------------