%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV673+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 : Thu Sep 24 02:35:25 PM UTC 2026
% Result : Theorem 234.79s 30.60s
% Output : CNFRefutation 234.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 52 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 19 ~; 16 |; 4 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 30 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('_HAMMER_GOAL',conjecture,
! [X1503] :
( cLambda_2eRedexes_2eredexes___24t(X1503)
=> ! [X1504] :
( cLambda_2eRedexes_2eredexes___24t(X1504)
=> ! [X1505] :
( cLambda_2eRedexes_2eredexes___24t(X1505)
=> ! [X68] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X68)
=> cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1503,cCoq_2eInit_2eDatatypes_2eO),X1505,X68) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1505,cCoq_2eInit_2eDatatypes_2eS___24a1(X68)),cSubstitution_2esubst__rec__r___24a3(X1503,X1505,X68),cCoq_2eInit_2eDatatypes_2eO) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('Substitution.subst_rec_subst_rec',axiom,
! [X1503] :
( cLambda_2eRedexes_2eredexes___24t(X1503)
=> ! [X1504] :
( cLambda_2eRedexes_2eredexes___24t(X1504)
=> ! [X1505] :
( cLambda_2eRedexes_2eredexes___24t(X1505)
=> ! [X68] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X68)
=> ! [X375] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X375)
=> cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1503,X375),X1505,cCoq_2eInit_2eNat_2eadd___24a2(X375,X68)) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1505,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(X375,X68))),cSubstitution_2esubst__rec__r___24a3(X1503,X1505,X68),X375) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Substitution.subst_rec_subst_rec') ).
fof('Coq.Arith.PeanoNat.Nat.add_0_l',axiom,
! [X59] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X59)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,X59) = X59 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Arith.PeanoNat.Nat.add_0_l') ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.O') ).
fof(c_0_4,negated_conjecture,
~ ! [X1503] :
( cLambda_2eRedexes_2eredexes___24t(X1503)
=> ! [X1504] :
( cLambda_2eRedexes_2eredexes___24t(X1504)
=> ! [X1505] :
( cLambda_2eRedexes_2eredexes___24t(X1505)
=> ! [X68] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X68)
=> cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1503,cCoq_2eInit_2eDatatypes_2eO),X1505,X68) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1505,cCoq_2eInit_2eDatatypes_2eS___24a1(X68)),cSubstitution_2esubst__rec__r___24a3(X1503,X1505,X68),cCoq_2eInit_2eDatatypes_2eO) ) ) ) ),
inference(assume_negation,[status(cth)],['_HAMMER_GOAL']) ).
fof(c_0_5,plain,
! [X1560,X1561,X1562,X1563,X1564] :
( cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1561,X1560,X1564),X1562,cCoq_2eInit_2eNat_2eadd___24a2(X1564,X1563)) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1561,X1562,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(X1564,X1563))),cSubstitution_2esubst__rec__r___24a3(X1560,X1562,X1563),X1564)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1564)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1563)
| ~ cLambda_2eRedexes_2eredexes___24t(X1562)
| ~ cLambda_2eRedexes_2eredexes___24t(X1561)
| ~ cLambda_2eRedexes_2eredexes___24t(X1560) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Substitution.subst_rec_subst_rec'])])])]) ).
fof(c_0_6,plain,
! [X1641] :
( cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,X1641) = X1641
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1641) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Coq.Arith.PeanoNat.Nat.add_0_l'])])]) ).
fof(c_0_7,negated_conjecture,
( cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(esk2_0,esk1_0,cCoq_2eInit_2eDatatypes_2eO),esk3_0,esk4_0) != cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(esk2_0,esk3_0,cCoq_2eInit_2eDatatypes_2eS___24a1(esk4_0)),cSubstitution_2esubst__rec__r___24a3(esk1_0,esk3_0,esk4_0),cCoq_2eInit_2eDatatypes_2eO)
& cCoq_2eInit_2eDatatypes_2enat___24t(esk4_0)
& cLambda_2eRedexes_2eredexes___24t(esk3_0)
& cLambda_2eRedexes_2eredexes___24t(esk2_0)
& cLambda_2eRedexes_2eredexes___24t(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_8,plain,
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X5)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X4)
| ~ cLambda_2eRedexes_2eredexes___24t(X3)
| ~ cLambda_2eRedexes_2eredexes___24t(X2)
| ~ cLambda_2eRedexes_2eredexes___24t(X1)
| cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X2,X1,X5),X3,cCoq_2eInit_2eNat_2eadd___24a2(X5,X4)) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X2,X3,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(X5,X4))),cSubstitution_2esubst__rec__r___24a3(X1,X3,X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1)
| cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO),
inference(split_conjunct,[status(thm)],['$_typeof_Coq.Init.Datatypes.O']) ).
cnf(c_0_11,negated_conjecture,
cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(esk2_0,esk1_0,cCoq_2eInit_2eDatatypes_2eO),esk3_0,esk4_0) != cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(esk2_0,esk3_0,cCoq_2eInit_2eDatatypes_2eS___24a1(esk4_0)),cSubstitution_2esubst__rec__r___24a3(esk1_0,esk3_0,esk4_0),cCoq_2eInit_2eDatatypes_2eO),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X3)
| ~ cLambda_2eRedexes_2eredexes___24t(X4)
| ~ cLambda_2eRedexes_2eredexes___24t(X1)
| ~ cLambda_2eRedexes_2eredexes___24t(X2)
| cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1,X2,cCoq_2eInit_2eDatatypes_2eS___24a1(X3)),cSubstitution_2esubst__rec__r___24a3(X4,X2,X3),cCoq_2eInit_2eDatatypes_2eO) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1,X4,cCoq_2eInit_2eDatatypes_2eO),X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).
cnf(c_0_13,negated_conjecture,
cLambda_2eRedexes_2eredexes___24t(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
cLambda_2eRedexes_2eredexes___24t(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
cLambda_2eRedexes_2eredexes___24t(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
cCoq_2eInit_2eDatatypes_2enat___24t(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV673+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 07:41:14 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 234.79/30.60 % Version: 3.5.1
% 234.79/30.60 % Preprocessing class: FMLLSMLLSSSNFFN.
% 234.79/30.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 234.79/30.60 % Starting new_bool_3 with 900s (3) cores
% 234.79/30.60 % Starting new_bool_1 with 900s (3) cores
% 234.79/30.60 % Starting sh5l with 300s (1) cores
% 234.79/30.60 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 234.79/30.60 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with pid 2583175 completed with status 0
% 234.79/30.60 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y
% 234.79/30.60 % Preprocessing class: FMLLSMLLSSSNFFN.
% 234.79/30.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 234.79/30.60 % Starting new_bool_3 with 900s (3) cores
% 234.79/30.60 % Starting new_bool_1 with 900s (3) cores
% 234.79/30.60 % Starting sh5l with 300s (1) cores
% 234.79/30.60 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 234.79/30.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 234.79/30.60 % SinE strategy is gf120_h_gu_RUU_F100_L00500
% 234.79/30.60 % Search class: FGHSF-FSLM31-MFFFFFNN
% 234.79/30.60 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 234.79/30.60 % Starting SubtermCWHack with 28s (1) cores
% 234.79/30.60 % SubtermCWHack with pid 2583179 completed with status 8
% 234.79/30.60 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 31s (1) cores
% 234.79/30.60 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with pid 2583778 completed with status 0
% 234.79/30.60 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y
% 234.79/30.60 % Preprocessing class: FMLLSMLLSSSNFFN.
% 234.79/30.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 234.79/30.60 % Starting new_bool_3 with 900s (3) cores
% 234.79/30.60 % Starting new_bool_1 with 900s (3) cores
% 234.79/30.60 % Starting sh5l with 300s (1) cores
% 234.79/30.60 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 234.79/30.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 234.79/30.60 % SinE strategy is gf120_h_gu_RUU_F100_L00500
% 234.79/30.60 % Search class: FGHSF-FSLM31-MFFFFFNN
% 234.79/30.60 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 234.79/30.60 % Starting SubtermCWHack with 28s (1) cores
% 234.79/30.60 % SubtermCWHack with pid 2583179 completed with status 8
% 234.79/30.60 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 31s (1) cores
% 234.79/30.60 % Preprocessing time : 0.015 s
% 234.79/30.60
% 234.79/30.60 % Proof found!
% 234.79/30.60 % SZS status Theorem
% 234.79/30.60 % SZS output start CNFRefutation
% See solution above
% 234.79/30.60 % Parsed axioms : 2702
% 234.79/30.60 % Removed by relevancy pruning/SinE : 2443
% 234.79/30.60 % Initial clauses : 354
% 234.79/30.60 % Removed in clause preprocessing : 20
% 234.79/30.60 % Initial clauses in saturation : 334
% 234.79/30.60 % Processed clauses : 4140
% 234.79/30.60 % ...of these trivial : 178
% 234.79/30.60 % ...subsumed : 2593
% 234.79/30.60 % ...remaining for further processing : 1369
% 234.79/30.60 % Other redundant clauses eliminated : 385
% 234.79/30.60 % Clauses deleted for lack of memory : 0
% 234.79/30.60 % Backward-subsumed : 77
% 234.79/30.60 % Backward-rewritten : 17
% 234.79/30.60 % Generated clauses : 55885
% 234.79/30.60 % ...of the previous two non-redundant : 53108
% 234.79/30.60 % ...aggressively subsumed : 0
% 234.79/30.60 % Contextual simplify-reflections : 463
% 234.79/30.60 % Paramodulations : 55453
% 234.79/30.60 % Factorizations : 0
% 234.79/30.60 % NegExts : 0
% 234.79/30.60 % Equation resolutions : 432
% 234.79/30.60 % Disequality decompositions : 0
% 234.79/30.60 % Total rewrite steps : 14273
% 234.79/30.60 % ...of those cached : 14239
% 234.79/30.60 % Propositional unsat checks : 0
% 234.79/30.60 % Propositional check models : 0
% 234.79/30.60 % Propositional check unsatisfiable : 0
% 234.79/30.60 % Propositional clauses : 0
% 234.79/30.60 % Propositional clauses after purity: 0
% 234.79/30.60 % Propositional unsat core size : 0
% 234.79/30.60 % Propositional preprocessing time : 0.000
% 234.79/30.60 % Propositional encoding time : 0.000
% 234.79/30.60 % Propositional solver time : 0.000
% 234.79/30.60 % Success case prop preproc time : 0.000
% 234.79/30.60 % Success case prop encoding time : 0.000
% 234.79/30.60 % Success case prop solver time : 0.000
% 234.79/30.60 % Current number of processed clauses : 1272
% 234.79/30.60 % Positive orientable unit clauses : 34
% 234.79/30.60 % Positive unorientable unit clauses: 0
% 234.79/30.60 % Negative unit clauses : 28
% 234.79/30.60 % Non-unit-clauses : 1210
% 234.79/30.60 % Current number of unprocessed clauses: 49199
% 234.79/30.60 % ...number of literals in the above : 293454
% 234.79/30.60 % Current number of archived formulas : 0
% 234.79/30.60 % Current number of archived clauses : 94
% 234.79/30.60 % Clause-clause subsumption calls (NU) : 282514
% 234.79/30.60 % Rec. Clause-clause subsumption calls : 67676
% 234.79/30.60 % Non-unit clause-clause subsumptions : 2320
% 234.79/30.60 % Unit Clause-clause subsumption calls : 4139
% 234.79/30.60 % Rewrite failures with RHS unbound : 0
% 234.79/30.60 % BW rewrite match attempts : 12
% 234.79/30.60 % BW rewrite match successes : 10
% 234.79/30.60 % Condensation attempts : 0
% 234.79/30.60 % Condensation successes : 0
% 234.79/30.60 % Termbank termtop insertions : 1078654
% 234.79/30.60 % Search garbage collected termcells : 35025
% 234.79/30.60
% 234.79/30.60 % -------------------------------------------------
% 234.79/30.60 % User time : 28.032 s
% 234.79/30.60 % System time : 1.137 s
% 234.79/30.60 % Total time : 29.169 s
% 234.79/30.60 % Maximum resident set size: 13392 pages
% 234.79/30.60
% 234.79/30.60 % -------------------------------------------------
% 234.79/30.60 % User time : 28.227 s
% 234.79/30.60 % System time : 1.155 s
% 234.79/30.60 % Total time : 29.382 s
% 234.79/30.60 % Maximum resident set size: 10240 pages
% 234.79/30.60 % E exiting
%------------------------------------------------------------------------------