%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL777-1 : 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 : n014.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 01:16:24 PM UTC 2026
% Result : Unsatisfiable 0.82s 0.79s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 6 RR)
% Number of literals : 8 ( 2 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-5 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_4,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_app__last_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__last_0) ).
cnf(cls_conjecture_1,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(c_0_3,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(fof_simplification,[status(thm)],[cls_conjecture_4]) ).
cnf(c_0_4,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_3 ).
cnf(c_0_5,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
cls_app__last_0 ).
cnf(c_0_6,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
cls_conjecture_1 ).
cnf(c_0_7,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_5]),c_0_6])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL777-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.51 % Computer : n014.cluster.edu
% 0.20/0.51 % Model : x86_64 x86_64
% 0.20/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.51 % Memory : 8046.5625MB
% 0.20/0.51 % OS : Linux 6.8.0-71-generic
% 0.20/0.51 % CPULimit : 300
% 0.20/0.51 % WCLimit : 300
% 0.20/0.51 % DateTime : Mon Sep 21 01:03:49 UTC 2026
% 0.24/0.52 % CPUTime :
% 0.24/0.52 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.59 Running first-order theorem proving
% 0.24/0.59 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
% 0.82/0.79 % Version: 3.5.1
% 0.82/0.79 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.82/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.82/0.79 % Starting new_bool_3 with 300s (1) cores
% 0.82/0.79 % Starting new_bool_1 with 300s (1) cores
% 0.82/0.79 % Starting sh5l with 300s (1) cores
% 0.82/0.79 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2821828 completed with status 0
% 0.82/0.79 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.82/0.79 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.82/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.82/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.82/0.79 % No SInE strategy applied
% 0.82/0.79 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.82/0.79 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.82/0.79 % Starting SubtermCWHack with 136s (1) cores
% 0.82/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.82/0.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 113s (1) cores
% 0.82/0.79 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 113s (1) cores
% 0.82/0.79 % Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 0.82/0.79 % U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 2821836 completed with status 0
% 0.82/0.79 % Result found by U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.82/0.79 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.82/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.82/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.82/0.79 % No SInE strategy applied
% 0.82/0.79 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.82/0.79 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.82/0.79 % Starting SubtermCWHack with 136s (1) cores
% 0.82/0.79 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.82/0.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 113s (1) cores
% 0.82/0.79 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 113s (1) cores
% 0.82/0.79 % Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 0.82/0.79 % Preprocessing time : 0.008 s
% 0.82/0.79 % Presaturation interreduction done
% 0.82/0.79
% 0.82/0.79 % Proof found!
% 0.82/0.79 % SZS status Unsatisfiable
% 0.82/0.79 % SZS output start CNFRefutation
% See solution above
% 0.82/0.79 % Parsed axioms : 388
% 0.82/0.79 % Removed by relevancy pruning/SinE : 0
% 0.82/0.79 % Initial clauses : 388
% 0.82/0.79 % Removed in clause preprocessing : 1
% 0.82/0.79 % Initial clauses in saturation : 387
% 0.82/0.79 % Processed clauses : 668
% 0.82/0.79 % ...of these trivial : 47
% 0.82/0.79 % ...subsumed : 42
% 0.82/0.79 % ...remaining for further processing : 579
% 0.82/0.79 % Other redundant clauses eliminated : 50
% 0.82/0.79 % Clauses deleted for lack of memory : 0
% 0.82/0.79 % Backward-subsumed : 0
% 0.82/0.79 % Backward-rewritten : 5
% 0.82/0.79 % Generated clauses : 1279
% 0.82/0.79 % ...of the previous two non-redundant : 977
% 0.82/0.79 % ...aggressively subsumed : 0
% 0.82/0.79 % Contextual simplify-reflections : 0
% 0.82/0.79 % Paramodulations : 1208
% 0.82/0.79 % Factorizations : 2
% 0.82/0.79 % NegExts : 0
% 0.82/0.79 % Equation resolutions : 69
% 0.82/0.79 % Disequality decompositions : 0
% 0.82/0.79 % Total rewrite steps : 592
% 0.82/0.79 % ...of those cached : 309
% 0.82/0.79 % Propositional unsat checks : 0
% 0.82/0.79 % Propositional check models : 0
% 0.82/0.79 % Propositional check unsatisfiable : 0
% 0.82/0.79 % Propositional clauses : 0
% 0.82/0.79 % Propositional clauses after purity: 0
% 0.82/0.79 % Propositional unsat core size : 0
% 0.82/0.79 % Propositional preprocessing time : 0.000
% 0.82/0.79 % Propositional encoding time : 0.000
% 0.82/0.79 % Propositional solver time : 0.000
% 0.82/0.79 % Success case prop preproc time : 0.000
% 0.82/0.79 % Success case prop encoding time : 0.000
% 0.82/0.79 % Success case prop solver time : 0.000
% 0.82/0.79 % Current number of processed clauses : 280
% 0.82/0.79 % Positive orientable unit clauses : 97
% 0.82/0.79 % Positive unorientable unit clauses: 2
% 0.82/0.79 % Negative unit clauses : 15
% 0.82/0.79 % Non-unit-clauses : 166
% 0.82/0.79 % Current number of unprocessed clauses: 988
% 0.82/0.79 % ...number of literals in the above : 2283
% 0.82/0.79 % Current number of archived formulas : 0
% 0.82/0.79 % Current number of archived clauses : 300
% 0.82/0.79 % Clause-clause subsumption calls (NU) : 10249
% 0.82/0.79 % Rec. Clause-clause subsumption calls : 9253
% 0.82/0.79 % Non-unit clause-clause subsumptions : 28
% 0.82/0.79 % Unit Clause-clause subsumption calls : 405
% 0.82/0.79 % Rewrite failures with RHS unbound : 0
% 0.82/0.79 % BW rewrite match attempts : 69
% 0.82/0.79 % BW rewrite match successes : 6
% 0.82/0.79 % Condensation attempts : 0
% 0.82/0.79 % Condensation successes : 0
% 0.82/0.79 % Termbank termtop insertions : 27457
% 0.82/0.79 % Search garbage collected termcells : 524
% 0.82/0.79
% 0.82/0.79 % -------------------------------------------------
% 0.82/0.79 % User time : 0.100 s
% 0.82/0.79 % System time : 0.012 s
% 0.82/0.79 % Total time : 0.112 s
% 0.82/0.79 % Maximum resident set size: 3920 pages
% 0.82/0.79
% 0.82/0.79 % -------------------------------------------------
% 0.82/0.79 % User time : 0.272 s
% 0.82/0.79 % System time : 0.046 s
% 0.82/0.79 % Total time : 0.318 s
% 0.82/0.79 % Maximum resident set size: 4864 pages
% 0.82/0.79 % E exiting
%------------------------------------------------------------------------------