%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ALG256^2 : 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 : n010.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 07:44:54 AM UTC 2026
% Result : Theorem 0.23s 0.33s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 33 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 135 ( 7 ~; 3 |; 3 &; 106 @)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 10 con; 0-4 aty)
% Number of variables : 55 ( 4 ^; 51 !; 0 ?; 55 :)
% 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_39,type,
hoasap: subst > term > subst > term > term ).
thf(decl_45,type,
hoasapinj1: $o ).
thf(decl_88,type,
apinj1: $o ).
thf(decl_91,type,
hoasapinj1_lthm: $o ).
thf(decl_143,type,
axvarid: $o ).
thf(decl_145,type,
esk1_0: term ).
thf(decl_146,type,
esk2_0: term ).
thf(decl_147,type,
esk3_0: term ).
thf(decl_148,type,
esk4_0: term ).
thf(thm,conjecture,
hoasapinj1_lthm,
file('/export/starexec/sandbox2/tmp/tmp.ooXBkR3ey5/E---3.1_3181129.p',thm) ).
thf(hoasapinj1_lthm,axiom,
( hoasapinj1_lthm
<=> ( axvarid
=> ( apinj1
=> hoasapinj1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ooXBkR3ey5/E---3.1_3181129.p',hoasapinj1_lthm) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.ooXBkR3ey5/E---3.1_3181129.p',axvarid) ).
thf(apinj1,axiom,
( apinj1
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( ap @ X1 @ X7 )
= ( ap @ X2 @ X8 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ooXBkR3ey5/E---3.1_3181129.p',apinj1) ).
thf(hoasapinj1,axiom,
( hoasapinj1
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( hoasap @ id @ X1 @ id @ X7 )
= ( hoasap @ id @ X2 @ id @ X8 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ooXBkR3ey5/E---3.1_3181129.p',hoasapinj1) ).
thf(hoasap,axiom,
( hoasap
= ( ^ [X3: subst,X1: term,X4: subst,X2: term] : ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ooXBkR3ey5/E---3.1_3181129.p',hoasap) ).
thf(c_0_6,negated_conjecture,
~ hoasapinj1_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_7,axiom,
( hoasapinj1_lthm
= ( ! [X1888: term] :
( ( sub @ X1888 @ id )
= X1888 )
=> ( ! [X1889: term,X1890: term,X1891: term,X1892: term] :
( ( ( ap @ X1889 @ X1891 )
= ( ap @ X1890 @ X1892 ) )
=> ( X1889 = X1890 ) )
=> ! [X1893: term,X1894: term,X1895: term,X1896: term] :
( ( ( hoasap @ id @ X1893 @ id @ X1895 )
= ( hoasap @ id @ X1894 @ id @ X1896 ) )
=> ( X1893 = X1894 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoasapinj1_lthm,axvarid]),apinj1]),hoasapinj1]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X3373: term] :
( ( sub @ X3373 @ id )
= X3373 )
=> ( ! [X3374: term,X3375: term,X3376: term,X3377: term] :
( ( ( ap @ X3374 @ X3376 )
= ( ap @ X3375 @ X3377 ) )
=> ( X3374 = X3375 ) )
=> ! [X3378: term,X3379: term,X3380: term,X3381: term] :
( ( ( hoasap @ id @ X3378 @ id @ X3380 )
= ( hoasap @ id @ X3379 @ id @ X3381 ) )
=> ( X3378 = X3379 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_6,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,X3397: term,X3398: term] :
( ( ( sub @ X3394 @ id )
= X3394 )
& ( ( ( ap @ X3395 @ X3397 )
!= ( ap @ X3396 @ X3398 ) )
| ( X3395 = X3396 ) )
& ( ( hoasap @ id @ esk1_0 @ id @ esk3_0 )
= ( hoasap @ id @ esk2_0 @ id @ esk4_0 ) )
& ( esk1_0 != esk2_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,
( ( hoasap @ id @ esk1_0 @ id @ esk3_0 )
= ( hoasap @ id @ esk2_0 @ id @ esk4_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,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
! [X1: term,X2: term,X7: term,X8: term] :
( ( X1 = X7 )
| ( ( ap @ X1 @ X2 )
!= ( ap @ X7 @ X8 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,negated_conjecture,
( ( ap @ esk1_0 @ esk3_0 )
= ( ap @ esk2_0 @ esk4_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_13]),c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X1: term,X2: term] :
( ( X1 = esk1_0 )
| ( ( ap @ X1 @ X2 )
!= ( ap @ esk2_0 @ esk4_0 ) ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_18,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG256^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n010.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 17:33:18 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.26 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.ooXBkR3ey5/E---3.1_3181129.p
% 0.23/0.33 % Version: 3.5.1-ho
% 0.23/0.33 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.23/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.33 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.33 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.33 % Starting post_as_ho5 with 300s (1) cores
% 0.23/0.33 % Starting post_as_ho10 with 300s (1) cores
% 0.23/0.33 % new_ho_10_cnf2 with pid 3181142 completed with status 0
% 0.23/0.33 % Result found by new_ho_10_cnf2
% 0.23/0.33 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.23/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.33 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.33 % No SInE strategy applied
% 0.23/0.33 % Search class: HHUPS-FFSF32-SHFMMFNN
% 0.23/0.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.33 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.33 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.23/0.33 % Starting sh5l with 136s (1) cores
% 0.23/0.33 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.23/0.33 % Starting lpo1_def_fix with 136s (1) cores
% 0.23/0.33 % new_ho_10_cnf2 with pid 3181156 completed with status 0
% 0.23/0.33 % Result found by new_ho_10_cnf2
% 0.23/0.33 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.23/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.33 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.33 % No SInE strategy applied
% 0.23/0.33 % Search class: HHUPS-FFSF32-SHFMMFNN
% 0.23/0.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.33 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.33 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.23/0.33 % Preprocessing time : 0.001 s
% 0.23/0.33 % Presaturation interreduction done
% 0.23/0.33
% 0.23/0.33 % Proof found!
% 0.23/0.33 % SZS status Theorem
% 0.23/0.33 % SZS output start CNFRefutation
% See solution above
% 0.23/0.33 % Parsed axioms : 238
% 0.23/0.33 % Removed by relevancy pruning/SinE : 0
% 0.23/0.33 % Initial clauses : 130
% 0.23/0.33 % Removed in clause preprocessing : 124
% 0.23/0.33 % Initial clauses in saturation : 6
% 0.23/0.33 % Processed clauses : 12
% 0.23/0.33 % ...of these trivial : 0
% 0.23/0.33 % ...subsumed : 0
% 0.23/0.33 % ...remaining for further processing : 12
% 0.23/0.33 % Other redundant clauses eliminated : 0
% 0.23/0.33 % Clauses deleted for lack of memory : 0
% 0.23/0.33 % Backward-subsumed : 0
% 0.23/0.33 % Backward-rewritten : 1
% 0.23/0.33 % Generated clauses : 4
% 0.23/0.33 % ...of the previous two non-redundant : 3
% 0.23/0.33 % ...aggressively subsumed : 0
% 0.23/0.33 % Contextual simplify-reflections : 0
% 0.23/0.33 % Paramodulations : 2
% 0.23/0.33 % Factorizations : 0
% 0.23/0.33 % NegExts : 0
% 0.23/0.33 % Equation resolutions : 2
% 0.23/0.33 % Disequality decompositions : 0
% 0.23/0.33 % Total rewrite steps : 4
% 0.23/0.33 % ...of those cached : 0
% 0.23/0.33 % Propositional unsat checks : 0
% 0.23/0.33 % Propositional check models : 0
% 0.23/0.33 % Propositional check unsatisfiable : 0
% 0.23/0.33 % Propositional clauses : 0
% 0.23/0.33 % Propositional clauses after purity: 0
% 0.23/0.33 % Propositional unsat core size : 0
% 0.23/0.33 % Propositional preprocessing time : 0.000
% 0.23/0.33 % Propositional encoding time : 0.000
% 0.23/0.33 % Propositional solver time : 0.000
% 0.23/0.33 % Success case prop preproc time : 0.000
% 0.23/0.33 % Success case prop encoding time : 0.000
% 0.23/0.33 % Success case prop solver time : 0.000
% 0.23/0.33 % Current number of processed clauses : 5
% 0.23/0.33 % Positive orientable unit clauses : 2
% 0.23/0.33 % Positive unorientable unit clauses: 0
% 0.23/0.33 % Negative unit clauses : 1
% 0.23/0.33 % Non-unit-clauses : 2
% 0.23/0.33 % Current number of unprocessed clauses: 3
% 0.23/0.33 % ...number of literals in the above : 4
% 0.23/0.33 % Current number of archived formulas : 0
% 0.23/0.33 % Current number of archived clauses : 7
% 0.23/0.33 % Clause-clause subsumption calls (NU) : 1
% 0.23/0.33 % Rec. Clause-clause subsumption calls : 1
% 0.23/0.33 % Non-unit clause-clause subsumptions : 0
% 0.23/0.33 % Unit Clause-clause subsumption calls : 0
% 0.23/0.33 % Rewrite failures with RHS unbound : 0
% 0.23/0.33 % BW rewrite match attempts : 2
% 0.23/0.33 % BW rewrite match successes : 2
% 0.23/0.33 % Condensation attempts : 12
% 0.23/0.33 % Condensation successes : 0
% 0.23/0.33 % Termbank termtop insertions : 26488
% 0.23/0.33 % Search garbage collected termcells : 1713
% 0.23/0.33
% 0.23/0.33 % -------------------------------------------------
% 0.23/0.33 % User time : 0.023 s
% 0.23/0.33 % System time : 0.015 s
% 0.23/0.33 % Total time : 0.038 s
% 0.23/0.33 % Maximum resident set size: 7512 pages
% 0.23/0.33
% 0.23/0.33 % -------------------------------------------------
% 0.23/0.33 % User time : 0.037 s
% 0.23/0.33 % System time : 0.034 s
% 0.23/0.33 % Total time : 0.071 s
% 0.23/0.33 % Maximum resident set size: 4864 pages
% 0.23/0.33 % E exiting
%------------------------------------------------------------------------------