%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL812-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 : Thu Sep 24 01:16:30 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of clauses : 10 ( 7 unt; 0 nHn; 6 RR)
% Number of literals : 13 ( 0 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-5 aty)
% Number of variables : 7 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_IT_OVar_0,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_CHAINED_0,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(c_0_3,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[cls_IT_OVar_0]) ).
cnf(c_0_4,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_5,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
c_0_3 ).
cnf(c_0_6,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
cls_CHAINED_0 ).
cnf(c_0_7,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_4 ).
cnf(c_0_8,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL812-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.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 01:05:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.17/0.49 % Version: 3.5.1
% 0.17/0.49 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.17/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.17/0.49 % Starting new_bool_3 with 600s (2) cores
% 0.17/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.49 % Starting sh5l with 300s (1) cores
% 0.17/0.49 % new_bool_3 with pid 3826129 completed with status 0
% 0.17/0.49 % Result found by new_bool_3
% 0.17/0.49 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.17/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.17/0.49 % Starting new_bool_3 with 600s (2) cores
% 0.17/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.49 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.17/0.49 % Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 0.17/0.49 % Starting SubtermCWHack with 55s (1) cores
% 0.17/0.49 % Starting new_bool_3 with 61s (1) cores
% 0.17/0.49 % new_bool_3 with pid 3826133 completed with status 0
% 0.17/0.49 % Result found by new_bool_3
% 0.17/0.49 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.17/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.49 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.17/0.49 % Starting new_bool_3 with 600s (2) cores
% 0.17/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.49 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.17/0.49 % Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 0.17/0.49 % Starting SubtermCWHack with 55s (1) cores
% 0.17/0.49 % Starting new_bool_3 with 61s (1) cores
% 0.17/0.49 % Preprocessing time : 0.003 s
% 0.17/0.49 % Presaturation interreduction done
% 0.17/0.49
% 0.17/0.49 % Proof found!
% 0.17/0.49 % SZS status Unsatisfiable
% 0.17/0.49 % SZS output start CNFRefutation
% See solution above
% 0.17/0.49 % Parsed axioms : 653
% 0.17/0.49 % Removed by relevancy pruning/SinE : 310
% 0.17/0.49 % Initial clauses : 343
% 0.17/0.49 % Removed in clause preprocessing : 0
% 0.17/0.49 % Initial clauses in saturation : 343
% 0.17/0.49 % Processed clauses : 1006
% 0.17/0.49 % ...of these trivial : 53
% 0.17/0.49 % ...subsumed : 354
% 0.17/0.49 % ...remaining for further processing : 599
% 0.17/0.49 % Other redundant clauses eliminated : 7
% 0.17/0.49 % Clauses deleted for lack of memory : 0
% 0.17/0.49 % Backward-subsumed : 3
% 0.17/0.49 % Backward-rewritten : 10
% 0.17/0.49 % Generated clauses : 1832
% 0.17/0.49 % ...of the previous two non-redundant : 1510
% 0.17/0.49 % ...aggressively subsumed : 0
% 0.17/0.49 % Contextual simplify-reflections : 0
% 0.17/0.49 % Paramodulations : 1810
% 0.17/0.49 % Factorizations : 0
% 0.17/0.49 % NegExts : 0
% 0.17/0.49 % Equation resolutions : 22
% 0.17/0.49 % Disequality decompositions : 0
% 0.17/0.49 % Total rewrite steps : 880
% 0.17/0.49 % ...of those cached : 620
% 0.17/0.49 % Propositional unsat checks : 0
% 0.17/0.49 % Propositional check models : 0
% 0.17/0.49 % Propositional check unsatisfiable : 0
% 0.17/0.49 % Propositional clauses : 0
% 0.17/0.49 % Propositional clauses after purity: 0
% 0.17/0.49 % Propositional unsat core size : 0
% 0.17/0.49 % Propositional preprocessing time : 0.000
% 0.17/0.49 % Propositional encoding time : 0.000
% 0.17/0.49 % Propositional solver time : 0.000
% 0.17/0.49 % Success case prop preproc time : 0.000
% 0.17/0.49 % Success case prop encoding time : 0.000
% 0.17/0.49 % Success case prop solver time : 0.000
% 0.17/0.49 % Current number of processed clauses : 339
% 0.17/0.49 % Positive orientable unit clauses : 160
% 0.17/0.49 % Positive unorientable unit clauses: 5
% 0.17/0.49 % Negative unit clauses : 90
% 0.17/0.49 % Non-unit-clauses : 84
% 0.17/0.49 % Current number of unprocessed clauses: 1094
% 0.17/0.49 % ...number of literals in the above : 1531
% 0.17/0.49 % Current number of archived formulas : 0
% 0.17/0.49 % Current number of archived clauses : 260
% 0.17/0.49 % Clause-clause subsumption calls (NU) : 8526
% 0.17/0.49 % Rec. Clause-clause subsumption calls : 7600
% 0.17/0.49 % Non-unit clause-clause subsumptions : 83
% 0.17/0.49 % Unit Clause-clause subsumption calls : 1663
% 0.17/0.49 % Rewrite failures with RHS unbound : 0
% 0.17/0.49 % BW rewrite match attempts : 1398
% 0.17/0.49 % BW rewrite match successes : 60
% 0.17/0.49 % Condensation attempts : 0
% 0.17/0.49 % Condensation successes : 0
% 0.17/0.49 % Termbank termtop insertions : 42720
% 0.17/0.49 % Search garbage collected termcells : 1695
% 0.17/0.49
% 0.17/0.49 % -------------------------------------------------
% 0.17/0.49 % User time : 0.041 s
% 0.17/0.49 % System time : 0.009 s
% 0.17/0.49 % Total time : 0.050 s
% 0.17/0.49 % Maximum resident set size: 4632 pages
% 0.17/0.49
% 0.17/0.49 % -------------------------------------------------
% 0.17/0.49 % User time : 0.094 s
% 0.17/0.49 % System time : 0.019 s
% 0.17/0.49 % Total time : 0.113 s
% 0.17/0.49 % Maximum resident set size: 5376 pages
% 0.17/0.49 % E exiting
%------------------------------------------------------------------------------