%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP216^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:04:44 AM UTC 2026
% Result : Theorem 6.82s 6.92s
% Output : CNFRefutation 6.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 15 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 53 ( 11 ~; 1 |; 0 &; 40 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 8 ^; 12 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
heap_T6362127782908069795rray_a: $tType ).
thf(decl_sort2,type,
list_a: $tType ).
thf(decl_sort3,type,
heap_e7401611519738050253t_unit: $tType ).
thf(decl_sort4,type,
option3216581401566546698it_nat: $tType ).
thf(decl_29,type,
array_of_list_a: list_a > heap_T6362127782908069795rray_a ).
thf(decl_1007,type,
heap_T5591663578999710211rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > option3216581401566546698it_nat ).
thf(decl_1017,type,
heap_T6932021131025641745rray_a: heap_T6362127782908069795rray_a > heap_e7401611519738050253t_unit > $o ).
thf(decl_1300,type,
none_P2587165478634041381it_nat: option3216581401566546698it_nat ).
thf(decl_2592,type,
h: heap_e7401611519738050253t_unit ).
thf(decl_2593,type,
xs: list_a ).
thf(fact_12_success__def,axiom,
( heap_T6932021131025641745rray_a
= ( ^ [X20: heap_T6362127782908069795rray_a,X2: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ X20 @ X2 )
!= none_P2587165478634041381it_nat ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5gg90Cu9O4/E---3.1_843033.p',fact_12_success__def) ).
thf(conj_0,conjecture,
( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
!= none_P2587165478634041381it_nat ),
file('/export/starexec/sandbox2/tmp/tmp.5gg90Cu9O4/E---3.1_843033.p',conj_0) ).
thf(fact_45_success__of__listI,axiom,
! [X70: list_a,X12: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ X70 ) @ X12 ),
file('/export/starexec/sandbox2/tmp/tmp.5gg90Cu9O4/E---3.1_843033.p',fact_45_success__of__listI) ).
thf(c_0_3,plain,
( heap_T6932021131025641745rray_a
= ( ^ [Z0: heap_T6362127782908069795rray_a,Z1: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ Z0 @ Z1 )
!= none_P2587165478634041381it_nat ) ) ),
inference(fof_simplification,[status(thm)],[fact_12_success__def]) ).
thf(c_0_4,plain,
( heap_T6932021131025641745rray_a
= ( ^ [Z0: heap_T6362127782908069795rray_a,Z1: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ Z0 @ Z1 )
!= none_P2587165478634041381it_nat ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,plain,
( ( ^ [Z0: heap_T6362127782908069795rray_a,Z1: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ Z0 @ Z1 )
!= none_P2587165478634041381it_nat ) )
= heap_T6932021131025641745rray_a ),
inference(cn,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
~ ( ( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
!= none_P2587165478634041381it_nat ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_7,plain,
! [X18951: heap_T6362127782908069795rray_a,X18952: heap_e7401611519738050253t_unit] :
( ( ( heap_T5591663578999710211rray_a @ X18951 @ X18952 )
!= none_P2587165478634041381it_nat )
<=> ( heap_T6932021131025641745rray_a @ X18951 @ X18952 ) ),
inference(arg_cong,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X18947: list_a,X18948: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ X18947 ) @ X18948 ),
inference(variable_rename,[status(thm)],[fact_45_success__of__listI]) ).
thf(c_0_9,negated_conjecture,
( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
= none_P2587165478634041381it_nat ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X1: heap_T6362127782908069795rray_a,X2: heap_e7401611519738050253t_unit] :
( ( ( heap_T5591663578999710211rray_a @ X1 @ X2 )
!= none_P2587165478634041381it_nat )
| ~ ( heap_T6932021131025641745rray_a @ X1 @ X2 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X70: list_a,X2: heap_e7401611519738050253t_unit] : ( heap_T6932021131025641745rray_a @ ( array_of_list_a @ X70 ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ xs ) @ h )
= none_P2587165478634041381it_nat ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
! [X70: list_a,X2: heap_e7401611519738050253t_unit] :
( ( heap_T5591663578999710211rray_a @ ( array_of_list_a @ X70 ) @ X2 )
!= none_P2587165478634041381it_nat ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_12,c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP216^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 % Computer : n017.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 20:11:52 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.28 Running higher-order theorem proving
% 5.45/5.51 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.5gg90Cu9O4/E---3.1_843033.p
% 6.82/6.92 % Version: 3.5.1-ho
% 6.82/6.92 % partial match(2): HMLLSMLLSSLNSFA
% 6.82/6.92 % Preprocessing class: HMLLSMLLSSLCHFA.
% 6.82/6.92 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 6.82/6.92 % Starting new_bool_8 with 1196s (4) cores
% 6.82/6.92 % Starting post_as_ho5 with 598s (2) cores
% 6.82/6.92 % Starting new_bool_9 with 299s (1) cores
% 6.82/6.92 % Starting new_bool_3 with 299s (1) cores
% 6.82/6.92 % new_bool_9 with pid 843049 completed with status 0
% 6.82/6.92 % Result found by new_bool_9
% 6.82/6.92 % partial match(2): HMLLSMLLSSLNSFA
% 6.82/6.92 % Preprocessing class: HMLLSMLLSSLCHFA.
% 6.82/6.92 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 6.82/6.92 % Starting new_bool_8 with 1196s (4) cores
% 6.82/6.92 % Starting post_as_ho5 with 598s (2) cores
% 6.82/6.92 % Starting new_bool_9 with 299s (1) cores
% 6.82/6.92 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 6.82/6.92 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 6.82/6.92 % Search class: HGUSF-FFSF21-MHFFFFNN
% 6.82/6.92 % partial match(2): FGUSF-FFSF21-MFFFFFNN
% 6.82/6.92 % Scheduled 7 strats onto 1 cores with 299 seconds (299 total)
% 6.82/6.92 % Starting SubtermCWHack with 27s (1) cores
% 6.82/6.92 % SubtermCWHack with pid 843051 completed with status 0
% 6.82/6.92 % Result found by SubtermCWHack
% 6.82/6.92 % partial match(2): HMLLSMLLSSLNSFA
% 6.82/6.92 % Preprocessing class: HMLLSMLLSSLCHFA.
% 6.82/6.92 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 6.82/6.92 % Starting new_bool_8 with 1196s (4) cores
% 6.82/6.92 % Starting post_as_ho5 with 598s (2) cores
% 6.82/6.92 % Starting new_bool_9 with 299s (1) cores
% 6.82/6.92 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 6.82/6.92 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 6.82/6.92 % Search class: HGUSF-FFSF21-MHFFFFNN
% 6.82/6.92 % partial match(2): FGUSF-FFSF21-MFFFFFNN
% 6.82/6.92 % Scheduled 7 strats onto 1 cores with 299 seconds (299 total)
% 6.82/6.92 % Starting SubtermCWHack with 27s (1) cores
% 6.82/6.92 % Preprocessing time : 0.004 s
% 6.82/6.92
% 6.82/6.92 % Proof found!
% 6.82/6.92 % SZS status Theorem
% 6.82/6.92 % SZS output start CNFRefutation
% See solution above
% 6.82/6.92 % Parsed axioms : 10879
% 6.82/6.92 % Removed by relevancy pruning/SinE : 10874
% 6.82/6.92 % Initial clauses : 5
% 6.82/6.92 % Removed in clause preprocessing : 0
% 6.82/6.92 % Initial clauses in saturation : 5
% 6.82/6.92 % Processed clauses : 8
% 6.82/6.92 % ...of these trivial : 0
% 6.82/6.92 % ...subsumed : 0
% 6.82/6.92 % ...remaining for further processing : 8
% 6.82/6.92 % Other redundant clauses eliminated : 0
% 6.82/6.92 % Clauses deleted for lack of memory : 0
% 6.82/6.92 % Backward-subsumed : 0
% 6.82/6.92 % Backward-rewritten : 0
% 6.82/6.92 % Generated clauses : 8
% 6.82/6.92 % ...of the previous two non-redundant : 6
% 6.82/6.92 % ...aggressively subsumed : 0
% 6.82/6.92 % Contextual simplify-reflections : 0
% 6.82/6.92 % Paramodulations : 2
% 6.82/6.92 % Factorizations : 0
% 6.82/6.92 % NegExts : 0
% 6.82/6.92 % Equation resolutions : 0
% 6.82/6.92 % Disequality decompositions : 0
% 6.82/6.92 % Total rewrite steps : 0
% 6.82/6.92 % ...of those cached : 0
% 6.82/6.92 % Propositional unsat checks : 0
% 6.82/6.92 % Propositional check models : 0
% 6.82/6.92 % Propositional check unsatisfiable : 0
% 6.82/6.92 % Propositional clauses : 0
% 6.82/6.92 % Propositional clauses after purity: 0
% 6.82/6.92 % Propositional unsat core size : 0
% 6.82/6.92 % Propositional preprocessing time : 0.000
% 6.82/6.92 % Propositional encoding time : 0.000
% 6.82/6.92 % Propositional solver time : 0.000
% 6.82/6.92 % Success case prop preproc time : 0.000
% 6.82/6.92 % Success case prop encoding time : 0.000
% 6.82/6.92 % Success case prop solver time : 0.000
% 6.82/6.92 % Current number of processed clauses : 6
% 6.82/6.92 % Positive orientable unit clauses : 3
% 6.82/6.92 % Positive unorientable unit clauses: 0
% 6.82/6.92 % Negative unit clauses : 1
% 6.82/6.92 % Non-unit-clauses : 2
% 6.82/6.92 % Current number of unprocessed clauses: 3
% 6.82/6.92 % ...number of literals in the above : 5
% 6.82/6.92 % Current number of archived formulas : 0
% 6.82/6.92 % Current number of archived clauses : 2
% 6.82/6.92 % Clause-clause subsumption calls (NU) : 0
% 6.82/6.92 % Rec. Clause-clause subsumption calls : 0
% 6.82/6.92 % Non-unit clause-clause subsumptions : 0
% 6.82/6.92 % Unit Clause-clause subsumption calls : 1
% 6.82/6.92 % Rewrite failures with RHS unbound : 0
% 6.82/6.92 % BW rewrite match attempts : 1
% 6.82/6.92 % BW rewrite match successes : 0
% 6.82/6.92 % Condensation attempts : 0
% 6.82/6.92 % Condensation successes : 0
% 6.82/6.92 % Termbank termtop insertions : 148127
% 6.82/6.92 % Search garbage collected termcells : 88660
% 6.82/6.92
% 6.82/6.92 % -------------------------------------------------
% 6.82/6.92 % User time : 0.064 s
% 6.82/6.92 % System time : 0.060 s
% 6.82/6.92 % Total time : 0.124 s
% 6.82/6.92 % Maximum resident set size: 32096 pages
% 6.82/6.92
% 6.82/6.92 % -------------------------------------------------
% 6.82/6.92 % User time : 1.279 s
% 6.82/6.92 % System time : 0.104 s
% 6.82/6.92 % Total time : 1.384 s
% 6.82/6.92 % Maximum resident set size: 28160 pages
% 6.82/6.92 % E exiting
%------------------------------------------------------------------------------