%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP063^1 : 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 : n013.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 08:05:25 AM UTC 2026
% Result : Theorem 0.82s 0.40s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 215 ( 10 ~; 5 |; 1 &; 198 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 2 ^; 16 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
real: $tType ).
thf(decl_24,type,
genClo1278781456e_beta: real ).
thf(decl_27,type,
genClo1015804716orrect: nat > real > $o ).
thf(decl_31,type,
genClo1163638703lle_te: nat > nat > real ).
thf(decl_32,type,
abs_abs_real: real > real ).
thf(decl_34,type,
minus_minus_real: real > real > real ).
thf(decl_35,type,
one_one_nat: nat ).
thf(decl_37,type,
plus_plus_nat: nat > nat > nat ).
thf(decl_44,type,
ord_less_eq_real: real > real > $o ).
thf(decl_45,type,
i: nat ).
thf(decl_47,type,
p: nat ).
thf(decl_48,type,
q: nat ).
thf(fact_119_add_Ocommute,axiom,
( plus_plus_nat
= ( ^ [X98: nat,X99: nat] : ( plus_plus_nat @ X99 @ X98 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.82lvKP1nu3/E---3.1_2566196.p',fact_119_add_Ocommute) ).
thf(conj_0,conjecture,
ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta,
file('/export/starexec/sandbox/tmp/tmp.82lvKP1nu3/E---3.1_2566196.p',conj_0) ).
thf(fact_0_rts2b,axiom,
! [X1: nat,X2: nat,X3: nat] :
( ( ( genClo1015804716orrect @ X1 @ ( genClo1163638703lle_te @ X1 @ X3 ) )
& ( genClo1015804716orrect @ X2 @ ( genClo1163638703lle_te @ X2 @ X3 ) ) )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ X1 @ X3 ) @ ( genClo1163638703lle_te @ X2 @ X3 ) ) ) @ genClo1278781456e_beta ) ),
file('/export/starexec/sandbox/tmp/tmp.82lvKP1nu3/E---3.1_2566196.p',fact_0_rts2b) ).
thf(fact_2_corr__q__tq,axiom,
genClo1015804716orrect @ q @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.82lvKP1nu3/E---3.1_2566196.p',fact_2_corr__q__tq) ).
thf(fact_1_corr__p,axiom,
genClo1015804716orrect @ p @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.82lvKP1nu3/E---3.1_2566196.p',fact_1_corr__p) ).
thf(c_0_5,plain,
! [X1037: nat,X1038: nat] :
( ( plus_plus_nat @ X1037 @ X1038 )
= ( plus_plus_nat @ X1038 @ X1037 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_119_add_Ocommute])]) ).
thf(c_0_6,negated_conjecture,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_7,plain,
! [X1255: nat,X1256: nat] :
( ( plus_plus_nat @ X1255 @ X1256 )
= ( plus_plus_nat @ X1256 @ X1255 ) ),
inference(variable_rename,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X1053: nat,X1054: nat,X1055: nat] :
( ~ ( genClo1015804716orrect @ X1053 @ ( genClo1163638703lle_te @ X1053 @ X1055 ) )
| ~ ( genClo1015804716orrect @ X1054 @ ( genClo1163638703lle_te @ X1054 @ X1055 ) )
| ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ X1053 @ X1055 ) @ ( genClo1163638703lle_te @ X1054 @ X1055 ) ) ) @ genClo1278781456e_beta ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_rts2b])])]) ).
thf(c_0_10,plain,
genClo1015804716orrect @ q @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(split_conjunct,[status(thm)],[fact_2_corr__q__tq]) ).
thf(c_0_11,plain,
! [X2: nat,X1: nat] :
( ( plus_plus_nat @ X1 @ X2 )
= ( plus_plus_nat @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta ),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ X1 @ X2 ) @ ( genClo1163638703lle_te @ X3 @ X2 ) ) ) @ genClo1278781456e_beta )
| ~ ( genClo1015804716orrect @ X1 @ ( genClo1163638703lle_te @ X1 @ X2 ) )
| ~ ( genClo1015804716orrect @ X3 @ ( genClo1163638703lle_te @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
genClo1015804716orrect @ q @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ one_one_nat @ i ) ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,plain,
genClo1015804716orrect @ p @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(split_conjunct,[status(thm)],[fact_1_corr__p]) ).
thf(c_0_16,negated_conjecture,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,plain,
! [X1: nat] :
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ X1 @ ( plus_plus_nat @ one_one_nat @ i ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ one_one_nat @ i ) ) ) ) @ genClo1278781456e_beta )
| ~ ( genClo1015804716orrect @ X1 @ ( genClo1163638703lle_te @ X1 @ ( plus_plus_nat @ one_one_nat @ i ) ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,plain,
genClo1015804716orrect @ p @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ one_one_nat @ i ) ),
inference(rw,[status(thm)],[c_0_15,c_0_11]) ).
thf(c_0_19,negated_conjecture,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ one_one_nat @ i ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ one_one_nat @ i ) ) ) ) @ genClo1278781456e_beta ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_11]),c_0_11]) ).
thf(c_0_20,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP063^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n013.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 19:44:36 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.25 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.82lvKP1nu3/E---3.1_2566196.p
% 0.82/0.40 % Version: 3.5.1-ho
% 0.82/0.40 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.82/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.40 % Starting new_ho_10 with 1500s (5) cores
% 0.82/0.40 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.82/0.40 % Starting full_lambda_6 with 300s (1) cores
% 0.82/0.40 % Starting full_lambda_9 with 300s (1) cores
% 0.82/0.40 % new_ho_10 with pid 2566209 completed with status 0
% 0.82/0.40 % Result found by new_ho_10
% 0.82/0.40 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.82/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.40 % Starting new_ho_10 with 1500s (5) cores
% 0.82/0.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.82/0.40 % No SInE strategy applied
% 0.82/0.40 % Search class: HGUSM-FSLM32-MHFFFFBN
% 0.82/0.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.82/0.40 % Starting SubtermCWHack with 136s (1) cores
% 0.82/0.40 % Starting new_ho_10 with 151s (1) cores
% 0.82/0.40 % Starting full_lambda_10 with 136s (1) cores
% 0.82/0.40 % Starting new_ho_7 with 136s (1) cores
% 0.82/0.40 % Starting full_lambda_2 with 136s (1) cores
% 0.82/0.40 % new_ho_10 with pid 2566214 completed with status 0
% 0.82/0.40 % Result found by new_ho_10
% 0.82/0.40 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.82/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.40 % Starting new_ho_10 with 1500s (5) cores
% 0.82/0.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.82/0.40 % No SInE strategy applied
% 0.82/0.40 % Search class: HGUSM-FSLM32-MHFFFFBN
% 0.82/0.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.82/0.40 % Starting SubtermCWHack with 136s (1) cores
% 0.82/0.40 % Starting new_ho_10 with 151s (1) cores
% 0.82/0.40 % Preprocessing time : 0.006 s
% 0.82/0.40 % Presaturation interreduction done
% 0.82/0.40
% 0.82/0.40 % Proof found!
% 0.82/0.40 % SZS status Theorem
% 0.82/0.40 % SZS output start CNFRefutation
% See solution above
% 0.82/0.40 % Parsed axioms : 366
% 0.82/0.40 % Removed by relevancy pruning/SinE : 0
% 0.82/0.40 % Initial clauses : 479
% 0.82/0.40 % Removed in clause preprocessing : 53
% 0.82/0.40 % Initial clauses in saturation : 426
% 0.82/0.40 % Processed clauses : 848
% 0.82/0.40 % ...of these trivial : 66
% 0.82/0.40 % ...subsumed : 189
% 0.82/0.40 % ...remaining for further processing : 593
% 0.82/0.40 % Other redundant clauses eliminated : 139
% 0.82/0.40 % Clauses deleted for lack of memory : 0
% 0.82/0.40 % Backward-subsumed : 4
% 0.82/0.40 % Backward-rewritten : 14
% 0.82/0.40 % Generated clauses : 3886
% 0.82/0.40 % ...of the previous two non-redundant : 2992
% 0.82/0.40 % ...aggressively subsumed : 0
% 0.82/0.40 % Contextual simplify-reflections : 2
% 0.82/0.40 % Paramodulations : 3740
% 0.82/0.40 % Factorizations : 2
% 0.82/0.40 % NegExts : 0
% 0.82/0.40 % Equation resolutions : 150
% 0.82/0.40 % Disequality decompositions : 0
% 0.82/0.40 % Total rewrite steps : 1982
% 0.82/0.40 % ...of those cached : 1469
% 0.82/0.40 % Propositional unsat checks : 0
% 0.82/0.40 % Propositional check models : 0
% 0.82/0.40 % Propositional check unsatisfiable : 0
% 0.82/0.40 % Propositional clauses : 0
% 0.82/0.40 % Propositional clauses after purity: 0
% 0.82/0.40 % Propositional unsat core size : 0
% 0.82/0.40 % Propositional preprocessing time : 0.000
% 0.82/0.40 % Propositional encoding time : 0.000
% 0.82/0.40 % Propositional solver time : 0.000
% 0.82/0.40 % Success case prop preproc time : 0.000
% 0.82/0.40 % Success case prop encoding time : 0.000
% 0.82/0.40 % Success case prop solver time : 0.000
% 0.82/0.40 % Current number of processed clauses : 282
% 0.82/0.40 % Positive orientable unit clauses : 93
% 0.82/0.40 % Positive unorientable unit clauses: 9
% 0.82/0.40 % Negative unit clauses : 7
% 0.82/0.40 % Non-unit-clauses : 173
% 0.82/0.40 % Current number of unprocessed clauses: 2790
% 0.82/0.40 % ...number of literals in the above : 6235
% 0.82/0.40 % Current number of archived formulas : 0
% 0.82/0.40 % Current number of archived clauses : 240
% 0.82/0.40 % Clause-clause subsumption calls (NU) : 21210
% 0.82/0.40 % Rec. Clause-clause subsumption calls : 12492
% 0.82/0.40 % Non-unit clause-clause subsumptions : 181
% 0.82/0.40 % Unit Clause-clause subsumption calls : 200
% 0.82/0.40 % Rewrite failures with RHS unbound : 0
% 0.82/0.40 % BW rewrite match attempts : 234
% 0.82/0.40 % BW rewrite match successes : 163
% 0.82/0.40 % Condensation attempts : 848
% 0.82/0.40 % Condensation successes : 0
% 0.82/0.40 % Termbank termtop insertions : 65433
% 0.82/0.40 % Search garbage collected termcells : 6906
% 0.82/0.40
% 0.82/0.40 % -------------------------------------------------
% 0.82/0.40 % User time : 0.107 s
% 0.82/0.40 % System time : 0.010 s
% 0.82/0.40 % Total time : 0.117 s
% 0.82/0.40 % Maximum resident set size: 5376 pages
% 0.82/0.40
% 0.82/0.40 % -------------------------------------------------
% 0.82/0.40 % User time : 0.424 s
% 0.82/0.40 % System time : 0.043 s
% 0.82/0.40 % Total time : 0.467 s
% 0.82/0.40 % Maximum resident set size: 5376 pages
% 0.82/0.40 % E exiting
%------------------------------------------------------------------------------