%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG268^4 : 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 : n003.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 07:44:48 AM UTC 2026
% Result : Theorem 0.24s 0.29s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 44 ( 4 ~; 0 |; 0 &; 38 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 ^; 11 !; 3 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_26,type,
sub: term > subst > term ).
thf(decl_29,type,
push: term > subst > subst ).
thf(decl_41,type,
hoasinduction_lem3v2_f: $o ).
thf(decl_51,type,
hoasinduction_lem3v2_f_lthm: $o ).
thf(decl_145,type,
esk1_0: term ).
thf(decl_146,type,
esk2_1: ( subst > term > term ) > term ).
thf(decl_147,type,
esk3_1: ( subst > term > term ) > subst ).
thf(thm,conjecture,
hoasinduction_lem3v2_f_lthm,
file('/export/starexec/sandbox2/tmp/tmp.gf1MNva2aV/E---3.1_2818553.p',thm) ).
thf(hoasinduction_lem3v2_f_lthm,axiom,
( hoasinduction_lem3v2_f_lthm
<=> hoasinduction_lem3v2_f ),
file('/export/starexec/sandbox2/tmp/tmp.gf1MNva2aV/E---3.1_2818553.p',hoasinduction_lem3v2_f_lthm) ).
thf(hoasinduction_lem3v2_f,axiom,
( hoasinduction_lem3v2_f
<=> ! [X2: term] :
? [X12: subst > term > term] :
! [X1: term,X3: subst] :
( ( X12 @ X3 @ X1 )
= ( sub @ X2 @ ( push @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gf1MNva2aV/E---3.1_2818553.p',hoasinduction_lem3v2_f) ).
thf(c_0_3,negated_conjecture,
~ hoasinduction_lem3v2_f_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_4,axiom,
( hoasinduction_lem3v2_f_lthm
= ( ! [X32: term] :
? [X33: subst > term > term] :
! [X34: term,X35: subst] :
( ( X33 @ X35 @ X34 )
= ( sub @ X32 @ ( push @ X34 @ X35 ) ) ) ) ),
inference(apply_def,[status(thm)],[hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_f]) ).
thf(c_0_5,negated_conjecture,
~ ! [X36: term] :
? [X37: subst > term > term] :
! [X38: term,X39: subst] :
( ( X37 @ X39 @ X38 )
= ( sub @ X36 @ ( push @ X38 @ X39 ) ) ),
inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X41: subst > term > term] :
( ( X41 @ ( esk3_1 @ X41 ) @ ( esk2_1 @ X41 ) )
!= ( sub @ esk1_0 @ ( push @ ( esk2_1 @ X41 ) @ ( esk3_1 @ X41 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
thf(c_0_7,negated_conjecture,
! [X12: subst > term > term] :
( ( X12 @ ( esk3_1 @ X12 ) @ ( esk2_1 @ X12 ) )
!= ( sub @ esk1_0 @ ( push @ ( esk2_1 @ X12 ) @ ( esk3_1 @ X12 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG268^4 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n003.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 17:36:58 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.26 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.gf1MNva2aV/E---3.1_2818553.p
% 0.24/0.29 % Version: 3.5.1-ho
% 0.24/0.29 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.24/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.24/0.29 % Starting post_as_ho5 with 300s (1) cores
% 0.24/0.29 % Starting post_as_ho10 with 300s (1) cores
% 0.24/0.29 % post_as_ho5 with pid 2818568 completed with status 0
% 0.24/0.29 % Result found by post_as_ho5
% 0.24/0.29 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.24/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.24/0.29 % Starting post_as_ho5 with 300s (1) cores
% 0.24/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.24/0.29 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.24/0.29 % Search class: HUUPF-FFSF21-MHFMMMNN
% 0.24/0.29 % partial match(5): FUUPF-FFSF21-MFFFFFNN
% 0.24/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.29 % SubtermCWHack with pid 2818570 completed with status 10
% 0.24/0.29 % Starting post_as_ho5 with 31s (1) cores
% 0.24/0.29 % post_as_ho5 with pid 2818571 completed with status 0
% 0.24/0.29 % Result found by post_as_ho5
% 0.24/0.29 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.24/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.29 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.24/0.29 % Starting post_as_ho5 with 300s (1) cores
% 0.24/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.24/0.29 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.24/0.29 % Search class: HUUPF-FFSF21-MHFMMMNN
% 0.24/0.29 % partial match(5): FUUPF-FFSF21-MFFFFFNN
% 0.24/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.29 % SubtermCWHack with pid 2818570 completed with status 10
% 0.24/0.29 % Starting post_as_ho5 with 31s (1) cores
% 0.24/0.29 % Preprocessing time : 0.002 s
% 0.24/0.29 % Presaturation interreduction done
% 0.24/0.29
% 0.24/0.29 % Proof found!
% 0.24/0.29 % SZS status Theorem
% 0.24/0.29 % SZS output start CNFRefutation
% See solution above
% 0.24/0.29 % Parsed axioms : 238
% 0.24/0.29 % Removed by relevancy pruning/SinE : 235
% 0.24/0.29 % Initial clauses : 1
% 0.24/0.29 % Removed in clause preprocessing : 0
% 0.24/0.29 % Initial clauses in saturation : 1
% 0.24/0.29 % Processed clauses : 2
% 0.24/0.29 % ...of these trivial : 0
% 0.24/0.29 % ...subsumed : 0
% 0.24/0.29 % ...remaining for further processing : 2
% 0.24/0.29 % Other redundant clauses eliminated : 0
% 0.24/0.29 % Clauses deleted for lack of memory : 0
% 0.24/0.29 % Backward-subsumed : 0
% 0.24/0.29 % Backward-rewritten : 0
% 0.24/0.29 % Generated clauses : 1
% 0.24/0.29 % ...of the previous two non-redundant : 0
% 0.24/0.29 % ...aggressively subsumed : 0
% 0.24/0.29 % Contextual simplify-reflections : 0
% 0.24/0.29 % Paramodulations : 0
% 0.24/0.29 % Factorizations : 0
% 0.24/0.29 % NegExts : 0
% 0.24/0.29 % Equation resolutions : 1
% 0.24/0.29 % Disequality decompositions : 0
% 0.24/0.29 % Total rewrite steps : 0
% 0.24/0.29 % ...of those cached : 0
% 0.24/0.29 % Propositional unsat checks : 0
% 0.24/0.29 % Propositional check models : 0
% 0.24/0.29 % Propositional check unsatisfiable : 0
% 0.24/0.29 % Propositional clauses : 0
% 0.24/0.29 % Propositional clauses after purity: 0
% 0.24/0.29 % Propositional unsat core size : 0
% 0.24/0.29 % Propositional preprocessing time : 0.000
% 0.24/0.29 % Propositional encoding time : 0.000
% 0.24/0.29 % Propositional solver time : 0.000
% 0.24/0.29 % Success case prop preproc time : 0.000
% 0.24/0.29 % Success case prop encoding time : 0.000
% 0.24/0.29 % Success case prop solver time : 0.000
% 0.24/0.29 % Current number of processed clauses : 1
% 0.24/0.29 % Positive orientable unit clauses : 0
% 0.24/0.29 % Positive unorientable unit clauses: 0
% 0.24/0.29 % Negative unit clauses : 1
% 0.24/0.29 % Non-unit-clauses : 0
% 0.24/0.29 % Current number of unprocessed clauses: 0
% 0.24/0.29 % ...number of literals in the above : 0
% 0.24/0.29 % Current number of archived formulas : 0
% 0.24/0.29 % Current number of archived clauses : 1
% 0.24/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.24/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.24/0.29 % Non-unit clause-clause subsumptions : 0
% 0.24/0.29 % Unit Clause-clause subsumption calls : 0
% 0.24/0.29 % Rewrite failures with RHS unbound : 0
% 0.24/0.29 % BW rewrite match attempts : 0
% 0.24/0.29 % BW rewrite match successes : 0
% 0.24/0.29 % Condensation attempts : 0
% 0.24/0.29 % Condensation successes : 0
% 0.24/0.29 % Termbank termtop insertions : 4973
% 0.24/0.29 % Search garbage collected termcells : 1858
% 0.24/0.29
% 0.24/0.29 % -------------------------------------------------
% 0.24/0.29 % User time : 0.006 s
% 0.24/0.29 % System time : 0.003 s
% 0.24/0.29 % Total time : 0.009 s
% 0.24/0.29 % Maximum resident set size: 4492 pages
% 0.24/0.29
% 0.24/0.29 % -------------------------------------------------
% 0.24/0.29 % User time : 0.015 s
% 0.24/0.29 % System time : 0.007 s
% 0.24/0.29 % Total time : 0.023 s
% 0.24/0.29 % Maximum resident set size: 5120 pages
% 0.24/0.29 % E exiting
%------------------------------------------------------------------------------