%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP145^1 : 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 : 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 08:04:30 AM UTC 2026
% Result : Theorem 1.74s 0.53s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 3 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 222 ( 13 ~; 8 |; 0 &; 198 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
list_com: $tType ).
thf(decl_sort3,type,
com: $tType ).
thf(decl_sort4,type,
set_Pr1165141447_state: $tType ).
thf(decl_sort5,type,
state: $tType ).
thf(decl_sort6,type,
produc2041926651_state: $tType ).
thf(decl_sort7,type,
produc410756839_state: $tType ).
thf(decl_36,type,
cons_com: com > list_com > list_com ).
thf(decl_41,type,
nil_com: list_com ).
thf(decl_57,type,
suc: nat > nat ).
thf(decl_58,type,
pHoare259243666_exec1: set_Pr1165141447_state ).
thf(decl_71,type,
produc1204172211_state: list_com > state > produc2041926651_state ).
thf(decl_75,type,
produc1909270103_state: produc2041926651_state > produc2041926651_state > produc410756839_state ).
thf(decl_86,type,
transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state ).
thf(decl_89,type,
transi1726587420_state: set_Pr1165141447_state > set_Pr1165141447_state ).
thf(decl_100,type,
member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o ).
thf(decl_103,type,
c: com ).
thf(decl_104,type,
f: nat > produc2041926651_state ).
thf(decl_105,type,
n: nat ).
thf(decl_106,type,
s: state ).
thf(conj_4,conjecture,
member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ),
file('/export/starexec/sandbox/tmp/tmp.Y9Pbzwsvut/E---3.1_821842.p',conj_4) ).
thf(fact_33_r__into__rtrancl,axiom,
! [X140: produc410756839_state,X141: set_Pr1165141447_state] :
( ( member1069318160_state @ X140 @ X141 )
=> ( member1069318160_state @ X140 @ ( transi1302705790_state @ X141 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Y9Pbzwsvut/E---3.1_821842.p',fact_33_r__into__rtrancl) ).
thf(fact_9_trancl__rtrancl__absorb,axiom,
! [X24: set_Pr1165141447_state] :
( ( transi1302705790_state @ ( transi1726587420_state @ X24 ) )
= ( transi1302705790_state @ X24 ) ),
file('/export/starexec/sandbox/tmp/tmp.Y9Pbzwsvut/E---3.1_821842.p',fact_9_trancl__rtrancl__absorb) ).
thf(fact_98_rtrancl__trancl__trancl,axiom,
! [X120: produc2041926651_state,X121: produc2041926651_state,X310: set_Pr1165141447_state,X166: produc2041926651_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X120 @ X121 ) @ ( transi1302705790_state @ X310 ) )
=> ( ( member1069318160_state @ ( produc1909270103_state @ X121 @ X166 ) @ ( transi1726587420_state @ X310 ) )
=> ( member1069318160_state @ ( produc1909270103_state @ X120 @ X166 ) @ ( transi1726587420_state @ X310 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Y9Pbzwsvut/E---3.1_821842.p',fact_98_rtrancl__trancl__trancl) ).
thf(conj_2,hypothesis,
! [X9: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ X9 ) @ ( f @ ( suc @ X9 ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ),
file('/export/starexec/sandbox/tmp/tmp.Y9Pbzwsvut/E---3.1_821842.p',conj_2) ).
thf(conj_3,hypothesis,
member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ),
file('/export/starexec/sandbox/tmp/tmp.Y9Pbzwsvut/E---3.1_821842.p',conj_3) ).
thf(c_0_6,negated_conjecture,
~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ),
inference(assume_negation,[status(cth)],[conj_4]) ).
thf(c_0_7,negated_conjecture,
~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X2807: produc410756839_state,X2808: set_Pr1165141447_state] :
( ~ ( member1069318160_state @ X2807 @ X2808 )
| ( member1069318160_state @ X2807 @ ( transi1302705790_state @ X2808 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_33_r__into__rtrancl])])]) ).
thf(c_0_9,plain,
! [X2971: set_Pr1165141447_state] :
( ( transi1302705790_state @ ( transi1726587420_state @ X2971 ) )
= ( transi1302705790_state @ X2971 ) ),
inference(variable_rename,[status(thm)],[fact_9_trancl__rtrancl__absorb]) ).
thf(c_0_10,negated_conjecture,
~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X4: produc410756839_state,X12: set_Pr1165141447_state] :
( ( member1069318160_state @ X4 @ ( transi1302705790_state @ X12 ) )
| ~ ( member1069318160_state @ X4 @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X12: set_Pr1165141447_state] :
( ( transi1302705790_state @ ( transi1726587420_state @ X12 ) )
= ( transi1302705790_state @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
! [X2958: produc2041926651_state,X2959: produc2041926651_state,X2960: set_Pr1165141447_state,X2961: produc2041926651_state] :
( ~ ( member1069318160_state @ ( produc1909270103_state @ X2958 @ X2959 ) @ ( transi1302705790_state @ X2960 ) )
| ~ ( member1069318160_state @ ( produc1909270103_state @ X2959 @ X2961 ) @ ( transi1726587420_state @ X2960 ) )
| ( member1069318160_state @ ( produc1909270103_state @ X2958 @ X2961 ) @ ( transi1726587420_state @ X2960 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_98_rtrancl__trancl__trancl])])]) ).
thf(c_0_14,hypothesis,
! [X2340: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ X2340 ) @ ( f @ ( suc @ X2340 ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ),
inference(variable_rename,[status(thm)],[conj_2]) ).
thf(c_0_15,negated_conjecture,
~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
! [X4: produc410756839_state,X12: set_Pr1165141447_state] :
( ( member1069318160_state @ X4 @ ( transi1302705790_state @ X12 ) )
| ~ ( member1069318160_state @ X4 @ ( transi1726587420_state @ X12 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_17,plain,
! [X10: produc2041926651_state,X18: produc2041926651_state,X15: produc2041926651_state,X12: set_Pr1165141447_state] :
( ( member1069318160_state @ ( produc1909270103_state @ X10 @ X18 ) @ ( transi1726587420_state @ X12 ) )
| ~ ( member1069318160_state @ ( produc1909270103_state @ X10 @ X15 ) @ ( transi1302705790_state @ X12 ) )
| ~ ( member1069318160_state @ ( produc1909270103_state @ X15 @ X18 ) @ ( transi1726587420_state @ X12 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,hypothesis,
! [X7: nat] : ( member1069318160_state @ ( produc1909270103_state @ ( f @ X7 ) @ ( f @ ( suc @ X7 ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,negated_conjecture,
~ ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ ( suc @ n ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,hypothesis,
! [X10: produc2041926651_state,X7: nat] :
( ( member1069318160_state @ ( produc1909270103_state @ X10 @ ( f @ ( suc @ X7 ) ) ) @ ( transi1726587420_state @ pHoare259243666_exec1 ) )
| ~ ( member1069318160_state @ ( produc1909270103_state @ X10 @ ( f @ X7 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,hypothesis,
member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( f @ n ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ),
inference(split_conjunct,[status(thm)],[conj_3]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP145^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n017.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 19:56:07 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.24 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.Y9Pbzwsvut/E---3.1_821842.p
% 1.74/0.53 % Version: 3.5.1-ho
% 1.74/0.53 % Preprocessing class: HSLSSMSMSSMNHFA.
% 1.74/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.74/0.53 % Starting new_ho_3 with 1500s (5) cores
% 1.74/0.53 % Starting sh7 with 300s (1) cores
% 1.74/0.53 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 1.74/0.53 % Starting pre_casc_7 with 300s (1) cores
% 1.74/0.53 % new_ho_3 with pid 821893 completed with status 0
% 1.74/0.53 % Result found by new_ho_3
% 1.74/0.53 % Preprocessing class: HSLSSMSMSSMNHFA.
% 1.74/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.74/0.53 % Starting new_ho_3 with 1500s (5) cores
% 1.74/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 1.74/0.53 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 1.74/0.53 % Search class: HGHSM-FSLS32-MHFFFSBN
% 1.74/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.74/0.53 % Starting SubtermCWHack with 136s (1) cores
% 1.74/0.53 % Starting new_ho_3 with 151s (1) cores
% 1.74/0.53 % Starting sh5l with 136s (1) cores
% 1.74/0.53 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 1.74/0.53 % Starting lpo1_def_fix with 136s (1) cores
% 1.74/0.53 % ehoh_best_sine_rwall with pid 821907 completed with status 0
% 1.74/0.53 % Result found by ehoh_best_sine_rwall
% 1.74/0.53 % Preprocessing class: HSLSSMSMSSMNHFA.
% 1.74/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.74/0.53 % Starting new_ho_3 with 1500s (5) cores
% 1.74/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 1.74/0.53 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 1.74/0.53 % Search class: HGHSM-FSLS32-MHFFFSBN
% 1.74/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.74/0.53 % Starting SubtermCWHack with 136s (1) cores
% 1.74/0.53 % Starting new_ho_3 with 151s (1) cores
% 1.74/0.53 % Starting sh5l with 136s (1) cores
% 1.74/0.53 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 1.74/0.53 % Preprocessing time : 0.011 s
% 1.74/0.53 % Presaturation interreduction done
% 1.74/0.53
% 1.74/0.53 % Proof found!
% 1.74/0.53 % SZS status Theorem
% 1.74/0.53 % SZS output start CNFRefutation
% See solution above
% 1.74/0.53 % Parsed axioms : 468
% 1.74/0.53 % Removed by relevancy pruning/SinE : 151
% 1.74/0.53 % Initial clauses : 763
% 1.74/0.53 % Removed in clause preprocessing : 24
% 1.74/0.53 % Initial clauses in saturation : 739
% 1.74/0.53 % Processed clauses : 2370
% 1.74/0.53 % ...of these trivial : 29
% 1.74/0.53 % ...subsumed : 912
% 1.74/0.53 % ...remaining for further processing : 1429
% 1.74/0.53 % Other redundant clauses eliminated : 583
% 1.74/0.53 % Clauses deleted for lack of memory : 0
% 1.74/0.53 % Backward-subsumed : 8
% 1.74/0.53 % Backward-rewritten : 11
% 1.74/0.53 % Generated clauses : 5718
% 1.74/0.53 % ...of the previous two non-redundant : 4819
% 1.74/0.53 % ...aggressively subsumed : 0
% 1.74/0.53 % Contextual simplify-reflections : 2
% 1.74/0.53 % Paramodulations : 4942
% 1.74/0.53 % Factorizations : 7
% 1.74/0.53 % NegExts : 13
% 1.74/0.53 % Equation resolutions : 605
% 1.74/0.53 % Disequality decompositions : 0
% 1.74/0.53 % Total rewrite steps : 786
% 1.74/0.53 % ...of those cached : 592
% 1.74/0.53 % Propositional unsat checks : 0
% 1.74/0.53 % Propositional check models : 0
% 1.74/0.53 % Propositional check unsatisfiable : 0
% 1.74/0.53 % Propositional clauses : 0
% 1.74/0.53 % Propositional clauses after purity: 0
% 1.74/0.53 % Propositional unsat core size : 0
% 1.74/0.53 % Propositional preprocessing time : 0.000
% 1.74/0.53 % Propositional encoding time : 0.000
% 1.74/0.53 % Propositional solver time : 0.000
% 1.74/0.53 % Success case prop preproc time : 0.000
% 1.74/0.53 % Success case prop encoding time : 0.000
% 1.74/0.53 % Success case prop solver time : 0.000
% 1.74/0.53 % Current number of processed clauses : 689
% 1.74/0.53 % Positive orientable unit clauses : 101
% 1.74/0.53 % Positive unorientable unit clauses: 0
% 1.74/0.53 % Negative unit clauses : 111
% 1.74/0.53 % Non-unit-clauses : 477
% 1.74/0.53 % Current number of unprocessed clauses: 3260
% 1.74/0.53 % ...number of literals in the above : 9142
% 1.74/0.53 % Current number of archived formulas : 0
% 1.74/0.53 % Current number of archived clauses : 674
% 1.74/0.53 % Clause-clause subsumption calls (NU) : 138959
% 1.74/0.53 % Rec. Clause-clause subsumption calls : 100897
% 1.74/0.53 % Non-unit clause-clause subsumptions : 578
% 1.74/0.53 % Unit Clause-clause subsumption calls : 1103
% 1.74/0.53 % Rewrite failures with RHS unbound : 0
% 1.74/0.53 % BW rewrite match attempts : 39
% 1.74/0.53 % BW rewrite match successes : 11
% 1.74/0.53 % Condensation attempts : 0
% 1.74/0.53 % Condensation successes : 0
% 1.74/0.53 % Termbank termtop insertions : 236559
% 1.74/0.53 % Search garbage collected termcells : 21984
% 1.74/0.53
% 1.74/0.53 % -------------------------------------------------
% 1.74/0.53 % User time : 0.206 s
% 1.74/0.53 % System time : 0.025 s
% 1.74/0.53 % Total time : 0.231 s
% 1.74/0.53 % Maximum resident set size: 8328 pages
% 1.74/0.53
% 1.74/0.53 % -------------------------------------------------
% 1.74/0.53 % User time : 0.879 s
% 1.74/0.53 % System time : 0.076 s
% 1.74/0.53 % Total time : 0.956 s
% 1.74/0.53 % Maximum resident set size: 6144 pages
% 1.74/0.53 % E exiting
%------------------------------------------------------------------------------