%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP102^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:05:31 AM UTC 2026
% Result : Theorem 4.11s 0.84s
% Output : CNFRefutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 13 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 150 ( 14 ~; 10 |; 1 &; 122 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 27 ( 0 ^; 27 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_sort3,type,
list_a: $tType ).
thf(decl_29,type,
listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).
thf(decl_34,type,
nth_a: list_a > nat > a ).
thf(decl_39,type,
size_size_list_a: list_a > nat ).
thf(decl_40,type,
ord_less_nat: nat > nat > $o ).
thf(decl_41,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_42,type,
f: nat > a ).
thf(decl_43,type,
g: nat > a ).
thf(decl_44,type,
xs: list_a ).
thf(decl_45,type,
ys: list_a ).
thf(decl_46,type,
esk1_0: nat ).
thf(conj_2,conjecture,
! [X12: nat] :
( ~ ( ord_less_nat @ X12 @ ( size_size_list_a @ xs ) )
| ( ( nth_a @ xs @ X12 )
= ( nth_a @ ys @ X12 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QbrgCC72Z7/E---3.1_3842656.p',conj_2) ).
thf(fact_102_dual__order_Ostrict__trans1,axiom,
! [X45: nat,X46: nat,X51: nat] :
( ( ord_less_eq_nat @ X45 @ X46 )
=> ( ( ord_less_nat @ X51 @ X45 )
=> ( ord_less_nat @ X51 @ X46 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QbrgCC72Z7/E---3.1_3842656.p',fact_102_dual__order_Ostrict__trans1) ).
thf(conj_1,hypothesis,
ord_less_eq_nat @ ( size_size_list_a @ xs ) @ ( size_size_list_a @ ys ),
file('/export/starexec/sandbox2/tmp/tmp.QbrgCC72Z7/E---3.1_3842656.p',conj_1) ).
thf(fact_3_i__append__nth1,axiom,
! [X9: nat,X10: list_a,X11: nat > a] :
( ( ord_less_nat @ X9 @ ( size_size_list_a @ X10 ) )
=> ( ( listIn1312259492pend_a @ X10 @ X11 @ X9 )
= ( nth_a @ X10 @ X9 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QbrgCC72Z7/E---3.1_3842656.p',fact_3_i__append__nth1) ).
thf(conj_0,hypothesis,
! [X90: nat] :
( ( listIn1312259492pend_a @ xs @ f @ X90 )
= ( listIn1312259492pend_a @ ys @ g @ X90 ) ),
file('/export/starexec/sandbox2/tmp/tmp.QbrgCC72Z7/E---3.1_3842656.p',conj_0) ).
thf(c_0_5,negated_conjecture,
~ ! [X12: nat] :
( ~ ( ord_less_nat @ X12 @ ( size_size_list_a @ xs ) )
| ( ( nth_a @ xs @ X12 )
= ( nth_a @ ys @ X12 ) ) ),
inference(assume_negation,[status(cth)],[conj_2]) ).
thf(c_0_6,plain,
! [X887: nat,X888: nat,X889: nat] :
( ~ ( ord_less_eq_nat @ X887 @ X888 )
| ~ ( ord_less_nat @ X889 @ X887 )
| ( ord_less_nat @ X889 @ X888 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_102_dual__order_Ostrict__trans1])])]) ).
thf(c_0_7,negated_conjecture,
~ ! [X12: nat] :
( ~ ( ord_less_nat @ X12 @ ( size_size_list_a @ xs ) )
| ( ( nth_a @ xs @ X12 )
= ( nth_a @ ys @ X12 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X15: nat,X12: nat,X9: nat] :
( ( ord_less_nat @ X15 @ X12 )
| ~ ( ord_less_eq_nat @ X9 @ X12 )
| ~ ( ord_less_nat @ X15 @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,hypothesis,
ord_less_eq_nat @ ( size_size_list_a @ xs ) @ ( size_size_list_a @ ys ),
inference(split_conjunct,[status(thm)],[conj_1]) ).
thf(c_0_10,negated_conjecture,
( ( ord_less_nat @ esk1_0 @ ( size_size_list_a @ xs ) )
& ( ( nth_a @ xs @ esk1_0 )
!= ( nth_a @ ys @ esk1_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
thf(c_0_11,plain,
! [X780: nat,X781: list_a,X782: nat > a] :
( ~ ( ord_less_nat @ X780 @ ( size_size_list_a @ X781 ) )
| ( ( listIn1312259492pend_a @ X781 @ X782 @ X780 )
= ( nth_a @ X781 @ X780 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_i__append__nth1])])]) ).
thf(c_0_12,hypothesis,
! [X9: nat] :
( ( ord_less_nat @ X9 @ ( size_size_list_a @ ys ) )
| ~ ( ord_less_nat @ X9 @ ( size_size_list_a @ xs ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,negated_conjecture,
ord_less_nat @ esk1_0 @ ( size_size_list_a @ xs ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,hypothesis,
! [X774: nat] :
( ( listIn1312259492pend_a @ xs @ f @ X774 )
= ( listIn1312259492pend_a @ ys @ g @ X774 ) ),
inference(variable_rename,[status(thm)],[conj_0]) ).
thf(c_0_15,plain,
! [X9: nat,X7: nat > a,X5: list_a] :
( ( ( listIn1312259492pend_a @ X5 @ X7 @ X9 )
= ( nth_a @ X5 @ X9 ) )
| ~ ( ord_less_nat @ X9 @ ( size_size_list_a @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
ord_less_nat @ esk1_0 @ ( size_size_list_a @ ys ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_17,hypothesis,
! [X9: nat] :
( ( listIn1312259492pend_a @ xs @ f @ X9 )
= ( listIn1312259492pend_a @ ys @ g @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,negated_conjecture,
! [X7: nat > a] :
( ( listIn1312259492pend_a @ ys @ X7 @ esk1_0 )
= ( nth_a @ ys @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X7: nat > a] :
( ( listIn1312259492pend_a @ xs @ X7 @ esk1_0 )
= ( nth_a @ xs @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
thf(c_0_20,negated_conjecture,
( ( nth_a @ xs @ esk1_0 )
!= ( nth_a @ ys @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_21,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP102^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 19:51:41 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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.QbrgCC72Z7/E---3.1_3842656.p
% 4.11/0.84 % Version: 3.5.1-ho
% 4.11/0.84 % Preprocessing class: HSLSSMSSSSSNHSA.
% 4.11/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.11/0.84 % Starting full_lambda_9 with 1500s (5) cores
% 4.11/0.84 % Starting new_ho_11 with 300s (1) cores
% 4.11/0.84 % Starting sh2l with 300s (1) cores
% 4.11/0.84 % Starting new_bool_6 with 300s (1) cores
% 4.11/0.84 % full_lambda_9 with pid 3842681 completed with status 0
% 4.11/0.84 % Result found by full_lambda_9
% 4.11/0.84 % Preprocessing class: HSLSSMSSSSSNHSA.
% 4.11/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.11/0.84 % Starting full_lambda_9 with 1500s (5) cores
% 4.11/0.84 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 4.11/0.84 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 4.11/0.84 % Search class: HGHSM-FSLM32-DHSFFSBN
% 4.11/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.11/0.84 % Starting SubtermCWHack with 136s (1) cores
% 4.11/0.84 % Starting full_lambda_9 with 151s (1) cores
% 4.11/0.84 % Starting sh4l with 214s (1) cores
% 4.11/0.84 % Starting pre_casc_4 with 204s (1) cores
% 4.11/0.84 % Starting lpo5_fix with 136s (1) cores
% 4.11/0.84 % lpo5_fix with pid 3842690 completed with status 0
% 4.11/0.84 % Result found by lpo5_fix
% 4.11/0.84 % Preprocessing class: HSLSSMSSSSSNHSA.
% 4.11/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.11/0.84 % Starting full_lambda_9 with 1500s (5) cores
% 4.11/0.84 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 4.11/0.84 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 4.11/0.84 % Search class: HGHSM-FSLM32-DHSFFSBN
% 4.11/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.11/0.84 % Starting SubtermCWHack with 136s (1) cores
% 4.11/0.84 % Starting full_lambda_9 with 151s (1) cores
% 4.11/0.84 % Starting sh4l with 214s (1) cores
% 4.11/0.84 % Starting pre_casc_4 with 204s (1) cores
% 4.11/0.84 % Starting lpo5_fix with 136s (1) cores
% 4.11/0.84 % Preprocessing time : 0.014 s
% 4.11/0.84
% 4.11/0.84 % Proof found!
% 4.11/0.84 % SZS status Theorem
% 4.11/0.84 % SZS output start CNFRefutation
% See solution above
% 4.11/0.84 % Parsed axioms : 282
% 4.11/0.84 % Removed by relevancy pruning/SinE : 42
% 4.11/0.84 % Initial clauses : 573
% 4.11/0.84 % Removed in clause preprocessing : 15
% 4.11/0.84 % Initial clauses in saturation : 558
% 4.11/0.84 % Processed clauses : 1054
% 4.11/0.84 % ...of these trivial : 37
% 4.11/0.84 % ...subsumed : 254
% 4.11/0.84 % ...remaining for further processing : 763
% 4.11/0.84 % Other redundant clauses eliminated : 60
% 4.11/0.84 % Clauses deleted for lack of memory : 0
% 4.11/0.84 % Backward-subsumed : 11
% 4.11/0.84 % Backward-rewritten : 0
% 4.11/0.84 % Generated clauses : 14496
% 4.11/0.84 % ...of the previous two non-redundant : 14175
% 4.11/0.84 % ...aggressively subsumed : 0
% 4.11/0.84 % Contextual simplify-reflections : 2
% 4.11/0.84 % Paramodulations : 14372
% 4.11/0.84 % Factorizations : 6
% 4.11/0.84 % NegExts : 2
% 4.11/0.84 % Equation resolutions : 71
% 4.11/0.84 % Disequality decompositions : 0
% 4.11/0.84 % Total rewrite steps : 850
% 4.11/0.84 % ...of those cached : 735
% 4.11/0.84 % Propositional unsat checks : 0
% 4.11/0.84 % Propositional check models : 0
% 4.11/0.84 % Propositional check unsatisfiable : 0
% 4.11/0.84 % Propositional clauses : 0
% 4.11/0.84 % Propositional clauses after purity: 0
% 4.11/0.84 % Propositional unsat core size : 0
% 4.11/0.84 % Propositional preprocessing time : 0.000
% 4.11/0.84 % Propositional encoding time : 0.000
% 4.11/0.84 % Propositional solver time : 0.000
% 4.11/0.84 % Success case prop preproc time : 0.000
% 4.11/0.84 % Success case prop encoding time : 0.000
% 4.11/0.84 % Success case prop solver time : 0.000
% 4.11/0.84 % Current number of processed clauses : 709
% 4.11/0.84 % Positive orientable unit clauses : 95
% 4.11/0.84 % Positive unorientable unit clauses: 1
% 4.11/0.84 % Negative unit clauses : 209
% 4.11/0.84 % Non-unit-clauses : 404
% 4.11/0.84 % Current number of unprocessed clauses: 13674
% 4.11/0.84 % ...number of literals in the above : 49212
% 4.11/0.84 % Current number of archived formulas : 0
% 4.11/0.84 % Current number of archived clauses : 12
% 4.11/0.84 % Clause-clause subsumption calls (NU) : 32303
% 4.11/0.84 % Rec. Clause-clause subsumption calls : 6964
% 4.11/0.84 % Non-unit clause-clause subsumptions : 188
% 4.11/0.84 % Unit Clause-clause subsumption calls : 19114
% 4.11/0.84 % Rewrite failures with RHS unbound : 0
% 4.11/0.84 % BW rewrite match attempts : 37
% 4.11/0.84 % BW rewrite match successes : 4
% 4.11/0.84 % Condensation attempts : 1054
% 4.11/0.84 % Condensation successes : 12
% 4.11/0.84 % Termbank termtop insertions : 685148
% 4.11/0.84 % Search garbage collected termcells : 10885
% 4.11/0.84
% 4.11/0.84 % -------------------------------------------------
% 4.11/0.84 % User time : 0.447 s
% 4.11/0.84 % System time : 0.025 s
% 4.11/0.84 % Total time : 0.472 s
% 4.11/0.84 % Maximum resident set size: 5864 pages
% 4.11/0.84
% 4.11/0.84 % -------------------------------------------------
% 4.11/0.84 % User time : 2.391 s
% 4.11/0.84 % System time : 0.119 s
% 4.11/0.84 % Total time : 2.510 s
% 4.11/0.84 % Maximum resident set size: 5376 pages
% 4.11/0.84 % E exiting
%------------------------------------------------------------------------------