%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP059^1 : 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 : n005.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 08:04:14 AM UTC 2026
% Result : Theorem 1.53s 0.52s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 296 ( 29 ~; 18 |; 3 &; 238 @)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 37 ( 0 ^; 37 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
message_p_v: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_sort3,type,
list_c1059388851t_unit: $tType ).
thf(decl_sort4,type,
list_message_p_v: $tType ).
thf(decl_26,type,
firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
thf(decl_27,type,
minus_minus_nat: nat > nat > nat ).
thf(decl_28,type,
one_one_nat: nat ).
thf(decl_29,type,
zero_zero_nat: nat ).
thf(decl_38,type,
suc: nat > nat ).
thf(decl_39,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(decl_41,type,
ord_less_nat: nat > nat > $o ).
thf(decl_42,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_44,type,
fe: nat > list_c1059388851t_unit ).
thf(decl_46,type,
ft: nat > list_message_p_v ).
thf(decl_47,type,
index: nat ).
thf(decl_49,type,
msg: message_p_v ).
thf(decl_52,type,
nMsg: nat ).
thf(conj_0,conjecture,
ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.AoX7VB6ObV/E---3.1_2117560.p',conj_0) ).
thf(fact_193_One__nat__def,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.AoX7VB6ObV/E---3.1_2117560.p',fact_193_One__nat__def) ).
thf(fact_192_diff__less__mono,axiom,
! [X23: nat,X26: nat,X25: nat] :
( ( ord_less_nat @ X23 @ X26 )
=> ( ( ord_less_eq_nat @ X25 @ X23 )
=> ( ord_less_nat @ ( minus_minus_nat @ X23 @ X25 ) @ ( minus_minus_nat @ X26 @ X25 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AoX7VB6ObV/E---3.1_2117560.p',fact_192_diff__less__mono) ).
thf(fact_4_SmallIndex,axiom,
! [X15: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ X15 )
=> ( ord_less_nat @ X15 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AoX7VB6ObV/E---3.1_2117560.p',fact_4_SmallIndex) ).
thf(fact_156_not__less__eq__eq,axiom,
! [X17: nat,X16: nat] :
( ~ ( ord_less_eq_nat @ X17 @ X16 )
<=> ( ord_less_eq_nat @ ( suc @ X16 ) @ X17 ) ),
file('/export/starexec/sandbox2/tmp/tmp.AoX7VB6ObV/E---3.1_2117560.p',fact_156_not__less__eq__eq) ).
thf(fact_69_not__less__eq,axiom,
! [X17: nat,X16: nat] :
( ~ ( ord_less_nat @ X17 @ X16 )
<=> ( ord_less_nat @ X16 @ ( suc @ X17 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AoX7VB6ObV/E---3.1_2117560.p',fact_69_not__less__eq) ).
thf(fact_3_AssumptionSubset_I3_J,axiom,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
file('/export/starexec/sandbox2/tmp/tmp.AoX7VB6ObV/E---3.1_2117560.p',fact_3_AssumptionSubset_I3_J) ).
thf(fact_181_Suc__le__eq,axiom,
! [X17: nat,X16: nat] :
( ( ord_less_eq_nat @ ( suc @ X17 ) @ X16 )
<=> ( ord_less_nat @ X17 @ X16 ) ),
file('/export/starexec/sandbox2/tmp/tmp.AoX7VB6ObV/E---3.1_2117560.p',fact_181_Suc__le__eq) ).
thf(fact_0_AssumpOcc6_I1_J,axiom,
ord_less_nat @ zero_zero_nat @ nMsg,
file('/export/starexec/sandbox2/tmp/tmp.AoX7VB6ObV/E---3.1_2117560.p',fact_0_AssumpOcc6_I1_J) ).
thf(c_0_9,negated_conjecture,
~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_10,negated_conjecture,
~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_13,plain,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
inference(split_conjunct,[status(thm)],[fact_193_One__nat__def]) ).
thf(c_0_14,plain,
! [X1088: nat,X1089: nat,X1090: nat] :
( ~ ( ord_less_nat @ X1088 @ X1089 )
| ~ ( ord_less_eq_nat @ X1090 @ X1088 )
| ( ord_less_nat @ ( minus_minus_nat @ X1088 @ X1090 ) @ ( minus_minus_nat @ X1089 @ X1090 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_192_diff__less__mono])])]) ).
thf(c_0_15,plain,
! [X678: nat] :
( ~ ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ X678 )
| ( ord_less_nat @ X678 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_SmallIndex])])]) ).
thf(c_0_16,plain,
! [X17: nat,X16: nat] :
( ~ ( ord_less_eq_nat @ X17 @ X16 )
<=> ( ord_less_eq_nat @ ( suc @ X16 ) @ X17 ) ),
inference(fof_simplification,[status(thm)],[fact_156_not__less__eq__eq]) ).
thf(c_0_17,plain,
! [X17: nat,X16: nat] :
( ~ ( ord_less_nat @ X17 @ X16 )
<=> ( ord_less_nat @ X16 @ ( suc @ X17 ) ) ),
inference(fof_simplification,[status(thm)],[fact_69_not__less__eq]) ).
thf(c_0_18,negated_conjecture,
~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
thf(c_0_19,plain,
! [X14: nat,X10: nat,X6: nat] :
( ( ord_less_nat @ ( minus_minus_nat @ X6 @ X14 ) @ ( minus_minus_nat @ X10 @ X14 ) )
| ~ ( ord_less_nat @ X6 @ X10 )
| ~ ( ord_less_eq_nat @ X14 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
! [X6: nat] :
( ( ord_less_nat @ X6 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
| ~ ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,plain,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
inference(split_conjunct,[status(thm)],[fact_3_AssumptionSubset_I3_J]) ).
thf(c_0_22,plain,
! [X1060: nat,X1061: nat] :
( ( ~ ( ord_less_eq_nat @ ( suc @ X1060 ) @ X1061 )
| ( ord_less_nat @ X1060 @ X1061 ) )
& ( ~ ( ord_less_nat @ X1060 @ X1061 )
| ( ord_less_eq_nat @ ( suc @ X1060 ) @ X1061 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_181_Suc__le__eq])])]) ).
thf(c_0_23,plain,
! [X994: nat,X995: nat] :
( ( ( ord_less_eq_nat @ X994 @ X995 )
| ( ord_less_eq_nat @ ( suc @ X995 ) @ X994 ) )
& ( ~ ( ord_less_eq_nat @ ( suc @ X995 ) @ X994 )
| ~ ( ord_less_eq_nat @ X994 @ X995 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
thf(c_0_24,plain,
! [X807: nat,X808: nat] :
( ( ( ord_less_nat @ X807 @ X808 )
| ( ord_less_nat @ X808 @ ( suc @ X807 ) ) )
& ( ~ ( ord_less_nat @ X808 @ ( suc @ X807 ) )
| ~ ( ord_less_nat @ X807 @ X808 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
thf(c_0_25,negated_conjecture,
( ~ ( ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
| ~ ( ord_less_eq_nat @ one_one_nat @ nMsg ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_26,plain,
ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,plain,
! [X6: nat,X10: nat] :
( ( ord_less_nat @ X6 @ X10 )
| ~ ( ord_less_eq_nat @ ( suc @ X6 ) @ X10 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_28,plain,
! [X10: nat,X6: nat] :
( ( ord_less_eq_nat @ X6 @ X10 )
| ( ord_less_eq_nat @ ( suc @ X10 ) @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_29,plain,
! [X10: nat,X6: nat] :
( ~ ( ord_less_nat @ X6 @ ( suc @ X10 ) )
| ~ ( ord_less_nat @ X10 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_30,negated_conjecture,
~ ( ord_less_eq_nat @ one_one_nat @ nMsg ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
thf(c_0_31,plain,
! [X10: nat,X6: nat] :
( ( ord_less_eq_nat @ X6 @ X10 )
| ( ord_less_nat @ X10 @ X6 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_32,plain,
! [X6: nat] :
( ~ ( ord_less_nat @ X6 @ one_one_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ X6 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_13]) ).
thf(c_0_33,negated_conjecture,
ord_less_nat @ nMsg @ one_one_nat,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_34,plain,
ord_less_nat @ zero_zero_nat @ nMsg,
inference(split_conjunct,[status(thm)],[fact_0_AssumpOcc6_I1_J]) ).
thf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP059^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 19:44:31 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.19/0.27 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.AoX7VB6ObV/E---3.1_2117560.p
% 1.53/0.52 % Version: 3.5.1-ho
% 1.53/0.52 % Preprocessing class: HSLSSMSMSSSNHFA.
% 1.53/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.53/0.52 % Starting new_ho_10 with 1500s (5) cores
% 1.53/0.52 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.53/0.52 % Starting full_lambda_6 with 300s (1) cores
% 1.53/0.52 % Starting full_lambda_9 with 300s (1) cores
% 1.53/0.52 % new_ho_10 with pid 2117595 completed with status 0
% 1.53/0.52 % Result found by new_ho_10
% 1.53/0.52 % Preprocessing class: HSLSSMSMSSSNHFA.
% 1.53/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.53/0.52 % Starting new_ho_10 with 1500s (5) cores
% 1.53/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.53/0.52 % No SInE strategy applied
% 1.53/0.52 % Search class: HGHSM-FSLM31-MHFFFSBC
% 1.53/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.53/0.52 % Starting SubtermCWHack with 136s (1) cores
% 1.53/0.52 % Starting new_ho_10 with 151s (1) cores
% 1.53/0.52 % Starting almost_fo_4 with 136s (1) cores
% 1.53/0.52 % Starting new_ho_10_unif with 136s (1) cores
% 1.53/0.52 % Starting ehoh_best3_fo with 136s (1) cores
% 1.53/0.52 % almost_fo_4 with pid 2117612 completed with status 0
% 1.53/0.52 % Result found by almost_fo_4
% 1.53/0.52 % Preprocessing class: HSLSSMSMSSSNHFA.
% 1.53/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.53/0.52 % Starting new_ho_10 with 1500s (5) cores
% 1.53/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.53/0.52 % No SInE strategy applied
% 1.53/0.52 % Search class: HGHSM-FSLM31-MHFFFSBC
% 1.53/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.53/0.52 % Starting SubtermCWHack with 136s (1) cores
% 1.53/0.52 % Starting new_ho_10 with 151s (1) cores
% 1.53/0.52 % Starting almost_fo_4 with 136s (1) cores
% 1.53/0.52 % Preprocessing time : 0.007 s
% 1.53/0.52 % Presaturation interreduction done
% 1.53/0.52
% 1.53/0.52 % Proof found!
% 1.53/0.52 % SZS status Theorem
% 1.53/0.52 % SZS output start CNFRefutation
% See solution above
% 1.53/0.52 % Parsed axioms : 284
% 1.53/0.52 % Removed by relevancy pruning/SinE : 0
% 1.53/0.52 % Initial clauses : 446
% 1.53/0.52 % Removed in clause preprocessing : 54
% 1.53/0.52 % Initial clauses in saturation : 392
% 1.53/0.52 % Processed clauses : 843
% 1.53/0.52 % ...of these trivial : 27
% 1.53/0.52 % ...subsumed : 128
% 1.53/0.52 % ...remaining for further processing : 688
% 1.53/0.52 % Other redundant clauses eliminated : 96
% 1.53/0.52 % Clauses deleted for lack of memory : 0
% 1.53/0.52 % Backward-subsumed : 3
% 1.53/0.52 % Backward-rewritten : 12
% 1.53/0.52 % Generated clauses : 4448
% 1.53/0.52 % ...of the previous two non-redundant : 4003
% 1.53/0.52 % ...aggressively subsumed : 0
% 1.53/0.52 % Contextual simplify-reflections : 1
% 1.53/0.52 % Paramodulations : 4330
% 1.53/0.52 % Factorizations : 4
% 1.53/0.52 % NegExts : 0
% 1.53/0.52 % Equation resolutions : 102
% 1.53/0.52 % Disequality decompositions : 0
% 1.53/0.52 % Total rewrite steps : 947
% 1.53/0.52 % ...of those cached : 767
% 1.53/0.52 % Propositional unsat checks : 0
% 1.53/0.52 % Propositional check models : 0
% 1.53/0.52 % Propositional check unsatisfiable : 0
% 1.53/0.52 % Propositional clauses : 0
% 1.53/0.52 % Propositional clauses after purity: 0
% 1.53/0.52 % Propositional unsat core size : 0
% 1.53/0.52 % Propositional preprocessing time : 0.000
% 1.53/0.52 % Propositional encoding time : 0.000
% 1.53/0.52 % Propositional solver time : 0.000
% 1.53/0.52 % Success case prop preproc time : 0.000
% 1.53/0.52 % Success case prop encoding time : 0.000
% 1.53/0.52 % Success case prop solver time : 0.000
% 1.53/0.52 % Current number of processed clauses : 338
% 1.53/0.52 % Positive orientable unit clauses : 61
% 1.53/0.52 % Positive unorientable unit clauses: 1
% 1.53/0.52 % Negative unit clauses : 18
% 1.53/0.52 % Non-unit-clauses : 258
% 1.53/0.52 % Current number of unprocessed clauses: 3834
% 1.53/0.52 % ...number of literals in the above : 12787
% 1.53/0.52 % Current number of archived formulas : 0
% 1.53/0.52 % Current number of archived clauses : 313
% 1.53/0.52 % Clause-clause subsumption calls (NU) : 27379
% 1.53/0.52 % Rec. Clause-clause subsumption calls : 10848
% 1.53/0.52 % Non-unit clause-clause subsumptions : 59
% 1.53/0.52 % Unit Clause-clause subsumption calls : 1860
% 1.53/0.52 % Rewrite failures with RHS unbound : 0
% 1.53/0.52 % BW rewrite match attempts : 66
% 1.53/0.52 % BW rewrite match successes : 24
% 1.53/0.52 % Condensation attempts : 0
% 1.53/0.52 % Condensation successes : 0
% 1.53/0.52 % Termbank termtop insertions : 122147
% 1.53/0.52 % Search garbage collected termcells : 8836
% 1.53/0.52
% 1.53/0.52 % -------------------------------------------------
% 1.53/0.52 % User time : 0.192 s
% 1.53/0.52 % System time : 0.022 s
% 1.53/0.52 % Total time : 0.214 s
% 1.53/0.52 % Maximum resident set size: 5596 pages
% 1.53/0.52
% 1.53/0.52 % -------------------------------------------------
% 1.53/0.52 % User time : 0.776 s
% 1.53/0.52 % System time : 0.076 s
% 1.53/0.52 % Total time : 0.852 s
% 1.53/0.52 % Maximum resident set size: 5376 pages
% 1.53/0.52 % E exiting
%------------------------------------------------------------------------------