%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP102^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:04:22 AM UTC 2026
% Result : Theorem 2.62s 0.68s
% Output : CNFRefutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 21 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 261 ( 28 ~; 23 |; 3 &; 197 @)
% ( 4 <=>; 6 =>; 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 : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 0 ^; 49 !; 0 ?; 49 :)
% 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_37,type,
suc: nat > nat ).
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/sandbox/tmp/tmp.uPAwCu6mk4/E---3.1_1767438.p',conj_2) ).
thf(fact_45_dual__order_Ostrict__trans,axiom,
! [X45: nat,X46: nat,X51: nat] :
( ( ord_less_nat @ X45 @ X46 )
=> ( ( ord_less_nat @ X51 @ X45 )
=> ( ord_less_nat @ X51 @ X46 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uPAwCu6mk4/E---3.1_1767438.p',fact_45_dual__order_Ostrict__trans) ).
thf(fact_213_le__imp__less__Suc,axiom,
! [X41: nat,X9: nat] :
( ( ord_less_eq_nat @ X41 @ X9 )
=> ( ord_less_nat @ X41 @ ( suc @ X9 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uPAwCu6mk4/E---3.1_1767438.p',fact_213_le__imp__less__Suc) ).
thf(fact_192_not__less__less__Suc__eq,axiom,
! [X9: nat,X41: nat] :
( ~ ( ord_less_nat @ X9 @ X41 )
=> ( ( ord_less_nat @ X9 @ ( suc @ X41 ) )
<=> ( X9 = X41 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uPAwCu6mk4/E---3.1_1767438.p',fact_192_not__less__less__Suc__eq) ).
thf(conj_1,hypothesis,
ord_less_eq_nat @ ( size_size_list_a @ xs ) @ ( size_size_list_a @ ys ),
file('/export/starexec/sandbox/tmp/tmp.uPAwCu6mk4/E---3.1_1767438.p',conj_1) ).
thf(fact_117_not__less,axiom,
! [X30: nat,X54: nat] :
( ~ ( ord_less_nat @ X30 @ X54 )
<=> ( ord_less_eq_nat @ X54 @ X30 ) ),
file('/export/starexec/sandbox/tmp/tmp.uPAwCu6mk4/E---3.1_1767438.p',fact_117_not__less) ).
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/sandbox/tmp/tmp.uPAwCu6mk4/E---3.1_1767438.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/sandbox/tmp/tmp.uPAwCu6mk4/E---3.1_1767438.p',conj_0) ).
thf(c_0_8,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_9,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_8]) ).
thf(c_0_10,plain,
! [X1075: nat,X1076: nat,X1077: nat] :
( ~ ( ord_less_nat @ X1075 @ X1076 )
| ~ ( ord_less_nat @ X1077 @ X1075 )
| ( ord_less_nat @ X1077 @ X1076 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_45_dual__order_Ostrict__trans])])]) ).
thf(c_0_11,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_9])])])]) ).
thf(c_0_12,plain,
! [X1017: nat,X1018: nat] :
( ~ ( ord_less_eq_nat @ X1017 @ X1018 )
| ( ord_less_nat @ X1017 @ ( suc @ X1018 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_213_le__imp__less__Suc])])]) ).
thf(c_0_13,plain,
! [X9: nat,X41: nat] :
( ~ ( ord_less_nat @ X9 @ X41 )
=> ( ( ord_less_nat @ X9 @ ( suc @ X41 ) )
<=> ( X9 = X41 ) ) ),
inference(fof_simplification,[status(thm)],[fact_192_not__less__less__Suc__eq]) ).
thf(c_0_14,plain,
! [X15: nat,X12: nat,X9: nat] :
( ( ord_less_nat @ X15 @ X12 )
| ~ ( ord_less_nat @ X9 @ X12 )
| ~ ( ord_less_nat @ X15 @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
ord_less_nat @ esk1_0 @ ( size_size_list_a @ xs ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X9: nat,X12: nat] :
( ( ord_less_nat @ X9 @ ( suc @ X12 ) )
| ~ ( ord_less_eq_nat @ X9 @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,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_18,plain,
! [X1249: nat,X1250: nat] :
( ( ~ ( ord_less_nat @ X1249 @ ( suc @ X1250 ) )
| ( X1249 = X1250 )
| ( ord_less_nat @ X1249 @ X1250 ) )
& ( ( X1249 != X1250 )
| ( ord_less_nat @ X1249 @ ( suc @ X1250 ) )
| ( ord_less_nat @ X1249 @ X1250 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
thf(c_0_19,negated_conjecture,
! [X9: nat] :
( ( ord_less_nat @ esk1_0 @ X9 )
| ~ ( ord_less_nat @ ( size_size_list_a @ xs ) @ X9 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_20,hypothesis,
ord_less_nat @ ( size_size_list_a @ xs ) @ ( suc @ ( size_size_list_a @ ys ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,plain,
! [X30: nat,X54: nat] :
( ~ ( ord_less_nat @ X30 @ X54 )
<=> ( ord_less_eq_nat @ X54 @ X30 ) ),
inference(fof_simplification,[status(thm)],[fact_117_not__less]) ).
thf(c_0_22,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_23,plain,
! [X9: nat,X12: nat] :
( ( X9 = X12 )
| ( ord_less_nat @ X9 @ X12 )
| ~ ( ord_less_nat @ X9 @ ( suc @ X12 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,hypothesis,
ord_less_nat @ esk1_0 @ ( suc @ ( size_size_list_a @ ys ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_25,plain,
! [X916: nat,X917: nat] :
( ( ( ord_less_nat @ X916 @ X917 )
| ( ord_less_eq_nat @ X917 @ X916 ) )
& ( ~ ( ord_less_eq_nat @ X917 @ X916 )
| ~ ( ord_less_nat @ X916 @ X917 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
thf(c_0_26,hypothesis,
! [X774: nat] :
( ( listIn1312259492pend_a @ xs @ f @ X774 )
= ( listIn1312259492pend_a @ ys @ g @ X774 ) ),
inference(variable_rename,[status(thm)],[conj_0]) ).
thf(c_0_27,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_22]) ).
thf(c_0_28,hypothesis,
( ( ( size_size_list_a @ ys )
= esk1_0 )
| ( ord_less_nat @ esk1_0 @ ( size_size_list_a @ ys ) ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_29,plain,
! [X12: nat,X9: nat] :
( ~ ( ord_less_eq_nat @ X9 @ X12 )
| ~ ( ord_less_nat @ X12 @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_30,hypothesis,
! [X9: nat] :
( ( listIn1312259492pend_a @ xs @ f @ X9 )
= ( listIn1312259492pend_a @ ys @ g @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_31,hypothesis,
! [X7: nat > a] :
( ( ( listIn1312259492pend_a @ ys @ X7 @ esk1_0 )
= ( nth_a @ ys @ esk1_0 ) )
| ( ( size_size_list_a @ ys )
= esk1_0 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_32,negated_conjecture,
! [X7: nat > a] :
( ( listIn1312259492pend_a @ xs @ X7 @ esk1_0 )
= ( nth_a @ xs @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
thf(c_0_33,negated_conjecture,
( ( nth_a @ xs @ esk1_0 )
!= ( nth_a @ ys @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_34,hypothesis,
~ ( ord_less_nat @ ( size_size_list_a @ ys ) @ ( size_size_list_a @ xs ) ),
inference(spm,[status(thm)],[c_0_29,c_0_17]) ).
thf(c_0_35,hypothesis,
( ( size_size_list_a @ ys )
= esk1_0 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33]) ).
thf(c_0_36,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_15])]),
[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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:56:22 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.uPAwCu6mk4/E---3.1_1767438.p
% 2.62/0.68 % Version: 3.5.1-ho
% 2.62/0.68 % Preprocessing class: HSLSSMSSSSSNHSA.
% 2.62/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.62/0.68 % Starting full_lambda_9 with 1500s (5) cores
% 2.62/0.68 % Starting new_ho_11 with 300s (1) cores
% 2.62/0.68 % Starting sh2l with 300s (1) cores
% 2.62/0.68 % Starting new_bool_6 with 300s (1) cores
% 2.62/0.68 % full_lambda_9 with pid 1767462 completed with status 0
% 2.62/0.68 % Result found by full_lambda_9
% 2.62/0.68 % Preprocessing class: HSLSSMSSSSSNHSA.
% 2.62/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.62/0.68 % Starting full_lambda_9 with 1500s (5) cores
% 2.62/0.68 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 2.62/0.68 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 2.62/0.68 % Search class: HGHSM-FSLM32-DHSFFSBN
% 2.62/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.62/0.68 % Starting SubtermCWHack with 136s (1) cores
% 2.62/0.68 % Starting full_lambda_9 with 151s (1) cores
% 2.62/0.68 % Starting sh4l with 214s (1) cores
% 2.62/0.68 % Starting pre_casc_4 with 204s (1) cores
% 2.62/0.68 % Starting lpo5_fix with 136s (1) cores
% 2.62/0.68 % pre_casc_4 with pid 1767471 completed with status 0
% 2.62/0.68 % Result found by pre_casc_4
% 2.62/0.68 % Preprocessing class: HSLSSMSSSSSNHSA.
% 2.62/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.62/0.68 % Starting full_lambda_9 with 1500s (5) cores
% 2.62/0.68 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 2.62/0.68 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 2.62/0.68 % Search class: HGHSM-FSLM32-DHSFFSBN
% 2.62/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.62/0.68 % Starting SubtermCWHack with 136s (1) cores
% 2.62/0.68 % Starting full_lambda_9 with 151s (1) cores
% 2.62/0.68 % Starting sh4l with 214s (1) cores
% 2.62/0.68 % Starting pre_casc_4 with 204s (1) cores
% 2.62/0.68 % Preprocessing time : 0.013 s
% 2.62/0.68 % Presaturation interreduction done
% 2.62/0.68
% 2.62/0.68 % Proof found!
% 2.62/0.68 % SZS status Theorem
% 2.62/0.68 % SZS output start CNFRefutation
% See solution above
% 2.62/0.68 % Parsed axioms : 282
% 2.62/0.68 % Removed by relevancy pruning/SinE : 42
% 2.62/0.68 % Initial clauses : 573
% 2.62/0.68 % Removed in clause preprocessing : 15
% 2.62/0.68 % Initial clauses in saturation : 558
% 2.62/0.68 % Processed clauses : 1226
% 2.62/0.68 % ...of these trivial : 17
% 2.62/0.68 % ...subsumed : 245
% 2.62/0.68 % ...remaining for further processing : 964
% 2.62/0.68 % Other redundant clauses eliminated : 56
% 2.62/0.68 % Clauses deleted for lack of memory : 0
% 2.62/0.68 % Backward-subsumed : 2
% 2.62/0.68 % Backward-rewritten : 46
% 2.62/0.68 % Generated clauses : 6693
% 2.62/0.68 % ...of the previous two non-redundant : 6407
% 2.62/0.68 % ...aggressively subsumed : 0
% 2.62/0.68 % Contextual simplify-reflections : 2
% 2.62/0.68 % Paramodulations : 6576
% 2.62/0.68 % Factorizations : 6
% 2.62/0.68 % NegExts : 2
% 2.62/0.68 % Equation resolutions : 65
% 2.62/0.68 % Disequality decompositions : 0
% 2.62/0.68 % Total rewrite steps : 449
% 2.62/0.68 % ...of those cached : 357
% 2.62/0.68 % Propositional unsat checks : 0
% 2.62/0.68 % Propositional check models : 0
% 2.62/0.68 % Propositional check unsatisfiable : 0
% 2.62/0.68 % Propositional clauses : 0
% 2.62/0.68 % Propositional clauses after purity: 0
% 2.62/0.68 % Propositional unsat core size : 0
% 2.62/0.68 % Propositional preprocessing time : 0.000
% 2.62/0.68 % Propositional encoding time : 0.000
% 2.62/0.68 % Propositional solver time : 0.000
% 2.62/0.68 % Success case prop preproc time : 0.000
% 2.62/0.68 % Success case prop encoding time : 0.000
% 2.62/0.68 % Success case prop solver time : 0.000
% 2.62/0.68 % Current number of processed clauses : 480
% 2.62/0.68 % Positive orientable unit clauses : 86
% 2.62/0.68 % Positive unorientable unit clauses: 1
% 2.62/0.68 % Negative unit clauses : 67
% 2.62/0.68 % Non-unit-clauses : 326
% 2.62/0.68 % Current number of unprocessed clauses: 6098
% 2.62/0.68 % ...number of literals in the above : 24451
% 2.62/0.68 % Current number of archived formulas : 0
% 2.62/0.68 % Current number of archived clauses : 442
% 2.62/0.68 % Clause-clause subsumption calls (NU) : 54456
% 2.62/0.68 % Rec. Clause-clause subsumption calls : 11449
% 2.62/0.68 % Non-unit clause-clause subsumptions : 166
% 2.62/0.68 % Unit Clause-clause subsumption calls : 1422
% 2.62/0.68 % Rewrite failures with RHS unbound : 0
% 2.62/0.68 % BW rewrite match attempts : 41
% 2.62/0.68 % BW rewrite match successes : 9
% 2.62/0.68 % Condensation attempts : 0
% 2.62/0.68 % Condensation successes : 0
% 2.62/0.68 % Termbank termtop insertions : 207328
% 2.62/0.68 % Search garbage collected termcells : 10885
% 2.62/0.68
% 2.62/0.68 % -------------------------------------------------
% 2.62/0.68 % User time : 0.321 s
% 2.62/0.68 % System time : 0.026 s
% 2.62/0.68 % Total time : 0.347 s
% 2.62/0.68 % Maximum resident set size: 5864 pages
% 2.62/0.68
% 2.62/0.68 % -------------------------------------------------
% 2.62/0.68 % User time : 1.561 s
% 2.62/0.68 % System time : 0.097 s
% 2.62/0.68 % Total time : 1.658 s
% 2.62/0.68 % Maximum resident set size: 5376 pages
% 2.62/0.68 % E exiting
%------------------------------------------------------------------------------