%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL816-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 01:23:25 PM UTC 2026
% Result : Unsatisfiable 24.00s 4.00s
% Output : CNFRefutation 24.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 20 ( 15 unt; 0 nHn; 13 RR)
% Number of literals : 29 ( 4 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-5 aty)
% Number of variables : 52 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_list__app__typeI_0,axiom,
( ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X1,X3,X5)
| c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
cnf(cls_foldr__foldl_0,axiom,
c_List_Ofoldr(X1,X2,X3,X4,X5) = c_List_Ofoldl(c_COMBC(X1,X4,X5,X5),X3,c_List_Orev(X2,X4),X5,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__foldl_0) ).
cnf(cls_typing_OVar_0,axiom,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
cnf(cls_shift__eq_0,axiom,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_CHAINED_0,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(c_0_6,plain,
( ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X1,X3,X5)
| c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(fof_simplification,[status(thm)],[cls_list__app__typeI_0]) ).
cnf(c_0_7,plain,
( ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X1,X3,X5)
| c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
c_0_6 ).
cnf(c_0_8,axiom,
c_List_Ofoldr(X1,X2,X3,X4,X5) = c_List_Ofoldl(c_COMBC(X1,X4,X5,X5),X3,c_List_Orev(X2,X4),X5,X4),
cls_foldr__foldl_0 ).
cnf(c_0_9,axiom,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
cls_typing_OVar_0 ).
cnf(c_0_10,axiom,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
cls_shift__eq_0 ).
cnf(c_0_11,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_12,plain,
( ~ c_Type_Otyping(X1,X2,c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X4,c_List_Orev(X5,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X1,X3,X5)
| c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
c_Type_Otyping(c_Type_Oshift(X1,X2,X3,X4),c_Lambda_OdB_OVar(X2),X3),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
cls_CHAINED_0 ).
cnf(c_0_15,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
c_0_11 ).
cnf(c_0_16,plain,
( ~ c_Type_Otypings(c_Type_Oshift(X1,X2,c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X3,c_List_Orev(X4,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype),X5),X6,X4)
| c_Type_Otyping(c_Type_Oshift(X1,X2,c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X3,c_List_Orev(X4,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype),X5),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X6,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(rw,[status(thm)],[c_0_14,c_0_8]) ).
cnf(c_0_18,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(rw,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_19,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL816-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 01:04:05 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 24.00/4.00 % Version: 3.5.1
% 24.00/4.00 % Preprocessing class: FSLSSMSMSSSNFFN.
% 24.00/4.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.00/4.00 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 24.00/4.00 % Starting new_bool_3 with 300s (1) cores
% 24.00/4.00 % Starting new_bool_1 with 300s (1) cores
% 24.00/4.00 % Starting sh5l with 300s (1) cores
% 24.00/4.00 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 4026987 completed with status 0
% 24.00/4.00 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 24.00/4.00 % Preprocessing class: FSLSSMSMSSSNFFN.
% 24.00/4.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.00/4.00 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 24.00/4.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 24.00/4.00 % No SInE strategy applied
% 24.00/4.00 % Search class: FGHSM-FSLM32-DFFFFFNN
% 24.00/4.00 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 24.00/4.00 % Starting SubtermCWHack with 136s (1) cores
% 24.00/4.00 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 24.00/4.00 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 113s (1) cores
% 24.00/4.00 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 113s (1) cores
% 24.00/4.00 % Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 24.00/4.00 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 4026998 completed with status 0
% 24.00/4.00 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 24.00/4.00 % Preprocessing class: FSLSSMSMSSSNFFN.
% 24.00/4.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.00/4.00 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 24.00/4.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 24.00/4.00 % No SInE strategy applied
% 24.00/4.00 % Search class: FGHSM-FSLM32-DFFFFFNN
% 24.00/4.00 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 24.00/4.00 % Starting SubtermCWHack with 136s (1) cores
% 24.00/4.00 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 24.00/4.00 % Preprocessing time : 0.004 s
% 24.00/4.00 % Presaturation interreduction done
% 24.00/4.00
% 24.00/4.00 % Proof found!
% 24.00/4.00 % SZS status Unsatisfiable
% 24.00/4.00 % SZS output start CNFRefutation
% See solution above
% 24.00/4.00 % Parsed axioms : 506
% 24.00/4.00 % Removed by relevancy pruning/SinE : 0
% 24.00/4.00 % Initial clauses : 506
% 24.00/4.00 % Removed in clause preprocessing : 3
% 24.00/4.00 % Initial clauses in saturation : 503
% 24.00/4.00 % Processed clauses : 21962
% 24.00/4.00 % ...of these trivial : 339
% 24.00/4.00 % ...subsumed : 17556
% 24.00/4.00 % ...remaining for further processing : 4067
% 24.00/4.00 % Other redundant clauses eliminated : 344
% 24.00/4.00 % Clauses deleted for lack of memory : 0
% 24.00/4.00 % Backward-subsumed : 200
% 24.00/4.00 % Backward-rewritten : 106
% 24.00/4.00 % Generated clauses : 233179
% 24.00/4.00 % ...of the previous two non-redundant : 217032
% 24.00/4.00 % ...aggressively subsumed : 0
% 24.00/4.00 % Contextual simplify-reflections : 8
% 24.00/4.00 % Paramodulations : 232739
% 24.00/4.00 % Factorizations : 14
% 24.00/4.00 % NegExts : 0
% 24.00/4.00 % Equation resolutions : 426
% 24.00/4.00 % Disequality decompositions : 0
% 24.00/4.00 % Total rewrite steps : 108367
% 24.00/4.00 % ...of those cached : 95852
% 24.00/4.00 % Propositional unsat checks : 0
% 24.00/4.00 % Propositional check models : 0
% 24.00/4.00 % Propositional check unsatisfiable : 0
% 24.00/4.00 % Propositional clauses : 0
% 24.00/4.00 % Propositional clauses after purity: 0
% 24.00/4.00 % Propositional unsat core size : 0
% 24.00/4.00 % Propositional preprocessing time : 0.000
% 24.00/4.00 % Propositional encoding time : 0.000
% 24.00/4.00 % Propositional solver time : 0.000
% 24.00/4.00 % Success case prop preproc time : 0.000
% 24.00/4.00 % Success case prop encoding time : 0.000
% 24.00/4.00 % Success case prop solver time : 0.000
% 24.00/4.00 % Current number of processed clauses : 3376
% 24.00/4.00 % Positive orientable unit clauses : 350
% 24.00/4.00 % Positive unorientable unit clauses: 145
% 24.00/4.00 % Negative unit clauses : 929
% 24.00/4.00 % Non-unit-clauses : 1952
% 24.00/4.00 % Current number of unprocessed clauses: 195454
% 24.00/4.00 % ...number of literals in the above : 400852
% 24.00/4.00 % Current number of archived formulas : 0
% 24.00/4.00 % Current number of archived clauses : 694
% 24.00/4.00 % Clause-clause subsumption calls (NU) : 393524
% 24.00/4.00 % Rec. Clause-clause subsumption calls : 283234
% 24.00/4.00 % Non-unit clause-clause subsumptions : 5769
% 24.00/4.00 % Unit Clause-clause subsumption calls : 82326
% 24.00/4.00 % Rewrite failures with RHS unbound : 126
% 24.00/4.00 % BW rewrite match attempts : 8076
% 24.00/4.00 % BW rewrite match successes : 412
% 24.00/4.00 % Condensation attempts : 0
% 24.00/4.00 % Condensation successes : 0
% 24.00/4.00 % Termbank termtop insertions : 5210451
% 24.00/4.00 % Search garbage collected termcells : 925
% 24.00/4.00
% 24.00/4.00 % -------------------------------------------------
% 24.00/4.00 % User time : 3.306 s
% 24.00/4.00 % System time : 0.162 s
% 24.00/4.00 % Total time : 3.468 s
% 24.00/4.00 % Maximum resident set size: 4476 pages
% 24.00/4.00
% 24.00/4.00 % -------------------------------------------------
% 24.00/4.00 % User time : 16.650 s
% 24.00/4.00 % System time : 0.648 s
% 24.00/4.00 % Total time : 17.299 s
% 24.00/4.00 % Maximum resident set size: 4864 pages
% 24.00/4.00 % E exiting
%------------------------------------------------------------------------------