%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP131^1 : 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 : 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 08:05:37 AM UTC 2026
% Result : ContradictoryAxioms 0.65s 0.41s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 10 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 149 ( 11 ~; 8 |; 1 &; 126 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 2 ^; 22 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_24,type,
plus_plus_nat: nat > nat > nat ).
thf(decl_25,type,
times_times_nat: nat > nat > nat ).
thf(decl_28,type,
ord_less_nat: nat > nat > $o ).
thf(decl_29,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_30,type,
i: nat ).
thf(decl_31,type,
k: nat ).
thf(decl_32,type,
n: nat ).
thf(decl_33,type,
p: nat > nat ).
thf(fact_136_mult_Ocommute,axiom,
( times_times_nat
= ( ^ [X17: nat,X18: nat] : ( times_times_nat @ X18 @ X17 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DhuMgmEKZJ/E---3.1_3853389.p',fact_136_mult_Ocommute) ).
thf(fact_193_less__or__eq__imp__le,axiom,
! [X5: nat,X3: nat] :
( ( ( ord_less_nat @ X5 @ X3 )
| ( X5 = X3 ) )
=> ( ord_less_eq_nat @ X5 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.DhuMgmEKZJ/E---3.1_3853389.p',fact_193_less__or__eq__imp__le) ).
thf(fact_149_le__antisym,axiom,
! [X5: nat,X3: nat] :
( ( ord_less_eq_nat @ X5 @ X3 )
=> ( ( ord_less_eq_nat @ X3 @ X5 )
=> ( X5 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DhuMgmEKZJ/E---3.1_3853389.p',fact_149_le__antisym) ).
thf(fact_2_upper__bound,axiom,
ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ) @ n,
file('/export/starexec/sandbox/tmp/tmp.DhuMgmEKZJ/E---3.1_3853389.p',fact_2_upper__bound) ).
thf(fact_3_lower__bound,axiom,
ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ),
file('/export/starexec/sandbox/tmp/tmp.DhuMgmEKZJ/E---3.1_3853389.p',fact_3_lower__bound) ).
thf(fact_142_less__irrefl__nat,axiom,
! [X3: nat] :
~ ( ord_less_nat @ X3 @ X3 ),
file('/export/starexec/sandbox/tmp/tmp.DhuMgmEKZJ/E---3.1_3853389.p',fact_142_less__irrefl__nat) ).
thf(c_0_6,plain,
! [X544: nat,X545: nat] :
( ( times_times_nat @ X544 @ X545 )
= ( times_times_nat @ X545 @ X544 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_136_mult_Ocommute])]) ).
thf(c_0_7,plain,
! [X894: nat,X895: nat] :
( ( times_times_nat @ X894 @ X895 )
= ( times_times_nat @ X895 @ X894 ) ),
inference(variable_rename,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X1034: nat,X1035: nat] :
( ( ~ ( ord_less_nat @ X1034 @ X1035 )
| ( ord_less_eq_nat @ X1034 @ X1035 ) )
& ( ( X1034 != X1035 )
| ( ord_less_eq_nat @ X1034 @ X1035 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_193_less__or__eq__imp__le])])])]) ).
thf(c_0_9,plain,
! [X928: nat,X929: nat] :
( ~ ( ord_less_eq_nat @ X928 @ X929 )
| ~ ( ord_less_eq_nat @ X929 @ X928 )
| ( X928 = X929 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_149_le__antisym])])]) ).
thf(c_0_10,plain,
ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ) @ n,
inference(split_conjunct,[status(thm)],[fact_2_upper__bound]) ).
thf(c_0_11,plain,
! [X3: nat,X2: nat] :
( ( times_times_nat @ X2 @ X3 )
= ( times_times_nat @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X2: nat,X3: nat] :
( ( ord_less_eq_nat @ X2 @ X3 )
| ~ ( ord_less_nat @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ),
inference(split_conjunct,[status(thm)],[fact_3_lower__bound]) ).
thf(c_0_14,plain,
! [X3: nat] :
~ ( ord_less_nat @ X3 @ X3 ),
inference(fof_simplification,[status(thm)],[fact_142_less__irrefl__nat]) ).
thf(c_0_15,plain,
! [X3: nat,X2: nat] :
( ( X2 = X3 )
| ~ ( ord_less_eq_nat @ X2 @ X3 )
| ~ ( ord_less_eq_nat @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_16,plain,
ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) ) @ n,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
thf(c_0_17,plain,
ord_less_eq_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11]),c_0_11]) ).
thf(c_0_18,plain,
! [X912: nat] :
~ ( ord_less_nat @ X912 @ X912 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_14])]) ).
thf(c_0_19,plain,
ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_11]) ).
thf(c_0_20,plain,
( ( plus_plus_nat @ ( times_times_nat @ i @ ( p @ i ) ) @ ( times_times_nat @ k @ ( p @ k ) ) )
= n ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
thf(c_0_21,plain,
! [X2: nat] :
~ ( ord_less_nat @ X2 @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP131^1 : 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 : n007.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 19:56:11 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
% 0.19/0.26 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.DhuMgmEKZJ/E---3.1_3853389.p
% 0.65/0.41 % Version: 3.5.1-ho
% 0.65/0.41 % Preprocessing class: HSLSSMSSSSSNSFA.
% 0.65/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.41 % Starting new_ho_11 with 1500s (5) cores
% 0.65/0.41 % Starting post_as_ho6 with 300s (1) cores
% 0.65/0.41 % Starting sh9 with 300s (1) cores
% 0.65/0.41 % Starting sh5l with 300s (1) cores
% 0.65/0.41 % sh5l with pid 3853405 completed with status 9
% 0.65/0.41 % post_as_ho6 with pid 3853403 completed with status 9
% 0.65/0.41 % new_ho_11 with pid 3853402 completed with status 0
% 0.65/0.41 % Result found by new_ho_11
% 0.65/0.41 % Preprocessing class: HSLSSMSSSSSNSFA.
% 0.65/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.41 % Starting new_ho_11 with 1500s (5) cores
% 0.65/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.65/0.41 % No SInE strategy applied
% 0.65/0.41 % Search class: HGHSM-FSLM31-MSFFFFBN
% 0.65/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.65/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.65/0.41 % Starting new_ho_11 with 151s (1) cores
% 0.65/0.41 % Starting almost_fo_4 with 136s (1) cores
% 0.65/0.41 % Starting pre_casc_8 with 136s (1) cores
% 0.65/0.41 % Starting pre_casc_3 with 136s (1) cores
% 0.65/0.41 % almost_fo_4 with pid 3853429 completed with status 0
% 0.65/0.41 % Result found by almost_fo_4
% 0.65/0.41 % Preprocessing class: HSLSSMSSSSSNSFA.
% 0.65/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.41 % Starting new_ho_11 with 1500s (5) cores
% 0.65/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.65/0.41 % No SInE strategy applied
% 0.65/0.41 % Search class: HGHSM-FSLM31-MSFFFFBN
% 0.65/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.65/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.65/0.41 % Starting new_ho_11 with 151s (1) cores
% 0.65/0.41 % Starting almost_fo_4 with 136s (1) cores
% 0.65/0.41 % Preprocessing time : 0.006 s
% 0.65/0.41 % Presaturation interreduction done
% 0.65/0.41
% 0.65/0.41 % Proof found!
% 0.65/0.41 % SZS status ContradictoryAxioms
% 0.65/0.41 % SZS output start CNFRefutation
% See solution above
% 0.65/0.41 % Parsed axioms : 225
% 0.65/0.41 % Removed by relevancy pruning/SinE : 0
% 0.65/0.41 % Initial clauses : 327
% 0.65/0.41 % Removed in clause preprocessing : 22
% 0.65/0.41 % Initial clauses in saturation : 305
% 0.65/0.41 % Processed clauses : 591
% 0.65/0.41 % ...of these trivial : 29
% 0.65/0.41 % ...subsumed : 153
% 0.65/0.41 % ...remaining for further processing : 409
% 0.65/0.41 % Other redundant clauses eliminated : 143
% 0.65/0.41 % Clauses deleted for lack of memory : 0
% 0.65/0.41 % Backward-subsumed : 6
% 0.65/0.41 % Backward-rewritten : 3
% 0.65/0.41 % Generated clauses : 3951
% 0.65/0.41 % ...of the previous two non-redundant : 3268
% 0.65/0.41 % ...aggressively subsumed : 0
% 0.65/0.41 % Contextual simplify-reflections : 0
% 0.65/0.41 % Paramodulations : 3800
% 0.65/0.41 % Factorizations : 4
% 0.65/0.41 % NegExts : 0
% 0.65/0.41 % Equation resolutions : 150
% 0.65/0.41 % Disequality decompositions : 0
% 0.65/0.41 % Total rewrite steps : 1343
% 0.65/0.41 % ...of those cached : 1121
% 0.65/0.41 % Propositional unsat checks : 0
% 0.65/0.41 % Propositional check models : 0
% 0.65/0.41 % Propositional check unsatisfiable : 0
% 0.65/0.41 % Propositional clauses : 0
% 0.65/0.41 % Propositional clauses after purity: 0
% 0.65/0.41 % Propositional unsat core size : 0
% 0.65/0.41 % Propositional preprocessing time : 0.000
% 0.65/0.41 % Propositional encoding time : 0.000
% 0.65/0.41 % Propositional solver time : 0.000
% 0.65/0.41 % Success case prop preproc time : 0.000
% 0.65/0.41 % Success case prop encoding time : 0.000
% 0.65/0.41 % Success case prop solver time : 0.000
% 0.65/0.41 % Current number of processed clauses : 186
% 0.65/0.41 % Positive orientable unit clauses : 35
% 0.65/0.41 % Positive unorientable unit clauses: 4
% 0.65/0.41 % Negative unit clauses : 7
% 0.65/0.41 % Non-unit-clauses : 140
% 0.65/0.41 % Current number of unprocessed clauses: 3126
% 0.65/0.41 % ...number of literals in the above : 9139
% 0.65/0.41 % Current number of archived formulas : 0
% 0.65/0.41 % Current number of archived clauses : 176
% 0.65/0.41 % Clause-clause subsumption calls (NU) : 3219
% 0.65/0.41 % Rec. Clause-clause subsumption calls : 3069
% 0.65/0.41 % Non-unit clause-clause subsumptions : 98
% 0.65/0.41 % Unit Clause-clause subsumption calls : 38
% 0.65/0.41 % Rewrite failures with RHS unbound : 0
% 0.65/0.41 % BW rewrite match attempts : 71
% 0.65/0.41 % BW rewrite match successes : 51
% 0.65/0.41 % Condensation attempts : 0
% 0.65/0.41 % Condensation successes : 0
% 0.65/0.41 % Termbank termtop insertions : 66297
% 0.65/0.41 % Search garbage collected termcells : 5430
% 0.65/0.41
% 0.65/0.41 % -------------------------------------------------
% 0.65/0.41 % User time : 0.121 s
% 0.65/0.41 % System time : 0.006 s
% 0.65/0.41 % Total time : 0.126 s
% 0.65/0.41 % Maximum resident set size: 4848 pages
% 0.65/0.41
% 0.65/0.41 % -------------------------------------------------
% 0.65/0.41 % User time : 0.554 s
% 0.65/0.41 % System time : 0.070 s
% 0.65/0.41 % Total time : 0.624 s
% 0.65/0.41 % Maximum resident set size: 5120 pages
% 0.65/0.41 % E exiting
%------------------------------------------------------------------------------