%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL776-1 : 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 : n004.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 226.64s 33.46s
% Output : CNFRefutation 226.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 11 unt; 0 nHn; 13 RR)
% Number of literals : 23 ( 2 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-5 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Beta_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
cnf(cls_conjecture_4,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),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(cls_conjecture_2,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(c_0_5,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[cls_Beta_0]) ).
cnf(c_0_6,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),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_7,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
c_0_5 ).
cnf(c_0_8,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_9,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),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_6 ).
cnf(c_0_10,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_11,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_12,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
cls_conjecture_2 ).
cnf(c_0_13,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL776-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 01:03:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 226.64/33.46 % Version: 3.5.1
% 226.64/33.46 % Preprocessing class: FSLMSMSMSSSNFFN.
% 226.64/33.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 226.64/33.46 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 226.64/33.46 % Starting new_bool_3 with 600s (2) cores
% 226.64/33.46 % Starting new_bool_1 with 300s (1) cores
% 226.64/33.46 % Starting sh5l with 300s (1) cores
% 226.64/33.46 % sh5l with pid 1921790 completed with status 0
% 226.64/33.46 % Result found by sh5l
% 226.64/33.46 % Preprocessing class: FSLMSMSMSSSNFFN.
% 226.64/33.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 226.64/33.46 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 226.64/33.46 % Starting new_bool_3 with 600s (2) cores
% 226.64/33.46 % Starting new_bool_1 with 300s (1) cores
% 226.64/33.46 % Starting sh5l with 300s (1) cores
% 226.64/33.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 226.64/33.46 % SinE strategy is gf500_gu_R04_F100_L20000
% 226.64/33.46 % Search class: FGHSM-FSLM32-DFFFFFNN
% 226.64/33.46 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 226.64/33.46 % Starting SubtermCWHack with 28s (1) cores
% 226.64/33.46 % SubtermCWHack with pid 1921800 completed with status 8
% 226.64/33.46 % Starting sh5l with 31s (1) cores
% 226.64/33.46 % sh5l with pid 1922265 completed with status 0
% 226.64/33.46 % Result found by sh5l
% 226.64/33.46 % Preprocessing class: FSLMSMSMSSSNFFN.
% 226.64/33.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 226.64/33.46 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 226.64/33.46 % Starting new_bool_3 with 600s (2) cores
% 226.64/33.46 % Starting new_bool_1 with 300s (1) cores
% 226.64/33.46 % Starting sh5l with 300s (1) cores
% 226.64/33.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 226.64/33.46 % SinE strategy is gf500_gu_R04_F100_L20000
% 226.64/33.46 % Search class: FGHSM-FSLM32-DFFFFFNN
% 226.64/33.46 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 226.64/33.46 % Starting SubtermCWHack with 28s (1) cores
% 226.64/33.46 % SubtermCWHack with pid 1921800 completed with status 8
% 226.64/33.46 % Starting sh5l with 31s (1) cores
% 226.64/33.46 % Preprocessing time : 0.011 s
% 226.64/33.46 % Presaturation interreduction done
% 226.64/33.46
% 226.64/33.46 % Proof found!
% 226.64/33.46 % SZS status Unsatisfiable
% 226.64/33.46 % SZS output start CNFRefutation
% See solution above
% 226.64/33.46 % Parsed axioms : 871
% 226.64/33.46 % Removed by relevancy pruning/SinE : 180
% 226.64/33.46 % Initial clauses : 691
% 226.64/33.46 % Removed in clause preprocessing : 0
% 226.64/33.46 % Initial clauses in saturation : 691
% 226.64/33.46 % Processed clauses : 21588
% 226.64/33.46 % ...of these trivial : 222
% 226.64/33.46 % ...subsumed : 18012
% 226.64/33.46 % ...remaining for further processing : 3354
% 226.64/33.46 % Other redundant clauses eliminated : 3227
% 226.64/33.46 % Clauses deleted for lack of memory : 0
% 226.64/33.46 % Backward-subsumed : 120
% 226.64/33.46 % Backward-rewritten : 78
% 226.64/33.46 % Generated clauses : 193033
% 226.64/33.46 % ...of the previous two non-redundant : 159356
% 226.64/33.46 % ...aggressively subsumed : 0
% 226.64/33.46 % Contextual simplify-reflections : 12
% 226.64/33.46 % Paramodulations : 189736
% 226.64/33.46 % Factorizations : 26
% 226.64/33.46 % NegExts : 0
% 226.64/33.46 % Equation resolutions : 3271
% 226.64/33.46 % Disequality decompositions : 0
% 226.64/33.46 % Total rewrite steps : 114290
% 226.64/33.46 % ...of those cached : 100448
% 226.64/33.46 % Propositional unsat checks : 0
% 226.64/33.46 % Propositional check models : 0
% 226.64/33.46 % Propositional check unsatisfiable : 0
% 226.64/33.46 % Propositional clauses : 0
% 226.64/33.46 % Propositional clauses after purity: 0
% 226.64/33.46 % Propositional unsat core size : 0
% 226.64/33.46 % Propositional preprocessing time : 0.000
% 226.64/33.46 % Propositional encoding time : 0.000
% 226.64/33.46 % Propositional solver time : 0.000
% 226.64/33.46 % Success case prop preproc time : 0.000
% 226.64/33.46 % Success case prop encoding time : 0.000
% 226.64/33.46 % Success case prop solver time : 0.000
% 226.64/33.46 % Current number of processed clauses : 2619
% 226.64/33.46 % Positive orientable unit clauses : 480
% 226.64/33.46 % Positive unorientable unit clauses: 42
% 226.64/33.46 % Negative unit clauses : 499
% 226.64/33.46 % Non-unit-clauses : 1598
% 226.64/33.46 % Current number of unprocessed clauses: 138559
% 226.64/33.46 % ...number of literals in the above : 322572
% 226.64/33.46 % Current number of archived formulas : 0
% 226.64/33.46 % Current number of archived clauses : 735
% 226.64/33.46 % Clause-clause subsumption calls (NU) : 685015
% 226.64/33.46 % Rec. Clause-clause subsumption calls : 529920
% 226.64/33.46 % Non-unit clause-clause subsumptions : 6390
% 226.64/33.46 % Unit Clause-clause subsumption calls : 116294
% 226.64/33.46 % Rewrite failures with RHS unbound : 5301
% 226.64/33.46 % BW rewrite match attempts : 1410
% 226.64/33.46 % BW rewrite match successes : 209
% 226.64/33.46 % Condensation attempts : 21588
% 226.64/33.46 % Condensation successes : 268
% 226.64/33.46 % Termbank termtop insertions : 2909007
% 226.64/33.46 % Search garbage collected termcells : 1837
% 226.64/33.46
% 226.64/33.46 % -------------------------------------------------
% 226.64/33.46 % User time : 31.217 s
% 226.64/33.46 % System time : 1.126 s
% 226.64/33.46 % Total time : 32.343 s
% 226.64/33.46 % Maximum resident set size: 5264 pages
% 226.64/33.46
% 226.64/33.46 % -------------------------------------------------
% 226.64/33.46 % User time : 31.241 s
% 226.64/33.46 % System time : 1.135 s
% 226.64/33.46 % Total time : 32.376 s
% 226.64/33.46 % Maximum resident set size: 5376 pages
% 226.64/33.46 % E exiting
%------------------------------------------------------------------------------