%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL837-1 : 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 : n005.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 01:16:34 PM UTC 2026
% Result : Unsatisfiable 0.29s 0.98s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 19 ( 15 unt; 0 nHn; 8 RR)
% Number of literals : 23 ( 11 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-5 aty)
% Number of variables : 33 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_subst__subst_0,axiom,
( ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(cls_One__nat__def_0,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),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))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_subst__map_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__map_0) ).
cnf(cls_CHAINED_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_zero__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
cnf(c_0_7,plain,
( ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4) ),
inference(fof_simplification,[status(thm)],[cls_subst__subst_0]) ).
cnf(c_0_8,axiom,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
cls_Suc__eq__plus1_0 ).
cnf(c_0_9,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
cls_One__nat__def_0 ).
cnf(c_0_10,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),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))),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_11,plain,
( ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4) ),
c_0_7 ).
cnf(c_0_12,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(X1),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),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))),
c_0_10 ).
cnf(c_0_14,plain,
( ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_9]),c_0_12]) ).
cnf(c_0_15,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
cls_subst__map_0 ).
cnf(c_0_16,axiom,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
cls_CHAINED_0 ).
cnf(c_0_17,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
cls_zero__less__Suc_0 ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL837-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 01:07:49 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.53 Running first-order theorem proving
% 0.26/0.53 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
% 0.29/0.98 % Version: 3.5.1
% 0.29/0.98 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.29/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.98 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.29/0.98 % Starting new_bool_3 with 300s (1) cores
% 0.29/0.98 % Starting new_bool_1 with 300s (1) cores
% 0.29/0.98 % Starting sh5l with 300s (1) cores
% 0.29/0.98 % sh5l with pid 2215698 completed with status 0
% 0.29/0.98 % Result found by sh5l
% 0.29/0.98 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.29/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.98 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.29/0.98 % Starting new_bool_3 with 300s (1) cores
% 0.29/0.98 % Starting new_bool_1 with 300s (1) cores
% 0.29/0.98 % Starting sh5l with 300s (1) cores
% 0.29/0.98 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.29/0.98 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.29/0.98 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.29/0.98 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.98 % Starting SubtermCWHack with 28s (1) cores
% 0.29/0.98 % SubtermCWHack with pid 2215706 completed with status 0
% 0.29/0.98 % Result found by SubtermCWHack
% 0.29/0.98 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.29/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.98 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.29/0.98 % Starting new_bool_3 with 300s (1) cores
% 0.29/0.98 % Starting new_bool_1 with 300s (1) cores
% 0.29/0.98 % Starting sh5l with 300s (1) cores
% 0.29/0.98 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.29/0.98 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.29/0.98 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.29/0.98 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.98 % Starting SubtermCWHack with 28s (1) cores
% 0.29/0.98 % Preprocessing time : 0.010 s
% 0.29/0.98
% 0.29/0.98 % Proof found!
% 0.29/0.98 % SZS status Unsatisfiable
% 0.29/0.98 % SZS output start CNFRefutation
% See solution above
% 0.29/0.99 % Parsed axioms : 657
% 0.29/0.99 % Removed by relevancy pruning/SinE : 179
% 0.29/0.99 % Initial clauses : 478
% 0.29/0.99 % Removed in clause preprocessing : 0
% 0.29/0.99 % Initial clauses in saturation : 478
% 0.29/0.99 % Processed clauses : 3630
% 0.29/0.99 % ...of these trivial : 224
% 0.29/0.99 % ...subsumed : 2655
% 0.29/0.99 % ...remaining for further processing : 751
% 0.29/0.99 % Other redundant clauses eliminated : 167
% 0.29/0.99 % Clauses deleted for lack of memory : 0
% 0.29/0.99 % Backward-subsumed : 9
% 0.29/0.99 % Backward-rewritten : 45
% 0.29/0.99 % Generated clauses : 20985
% 0.29/0.99 % ...of the previous two non-redundant : 16789
% 0.29/0.99 % ...aggressively subsumed : 0
% 0.29/0.99 % Contextual simplify-reflections : 0
% 0.29/0.99 % Paramodulations : 20789
% 0.29/0.99 % Factorizations : 8
% 0.29/0.99 % NegExts : 0
% 0.29/0.99 % Equation resolutions : 188
% 0.29/0.99 % Disequality decompositions : 0
% 0.29/0.99 % Total rewrite steps : 20180
% 0.29/0.99 % ...of those cached : 18568
% 0.29/0.99 % Propositional unsat checks : 0
% 0.29/0.99 % Propositional check models : 0
% 0.29/0.99 % Propositional check unsatisfiable : 0
% 0.29/0.99 % Propositional clauses : 0
% 0.29/0.99 % Propositional clauses after purity: 0
% 0.29/0.99 % Propositional unsat core size : 0
% 0.29/0.99 % Propositional preprocessing time : 0.000
% 0.29/0.99 % Propositional encoding time : 0.000
% 0.29/0.99 % Propositional solver time : 0.000
% 0.29/0.99 % Success case prop preproc time : 0.000
% 0.29/0.99 % Success case prop encoding time : 0.000
% 0.29/0.99 % Success case prop solver time : 0.000
% 0.29/0.99 % Current number of processed clauses : 697
% 0.29/0.99 % Positive orientable unit clauses : 172
% 0.29/0.99 % Positive unorientable unit clauses: 6
% 0.29/0.99 % Negative unit clauses : 125
% 0.29/0.99 % Non-unit-clauses : 394
% 0.29/0.99 % Current number of unprocessed clauses: 13558
% 0.29/0.99 % ...number of literals in the above : 29312
% 0.29/0.99 % Current number of archived formulas : 0
% 0.29/0.99 % Current number of archived clauses : 54
% 0.29/0.99 % Clause-clause subsumption calls (NU) : 33611
% 0.29/0.99 % Rec. Clause-clause subsumption calls : 25436
% 0.29/0.99 % Non-unit clause-clause subsumptions : 719
% 0.29/0.99 % Unit Clause-clause subsumption calls : 6834
% 0.29/0.99 % Rewrite failures with RHS unbound : 0
% 0.29/0.99 % BW rewrite match attempts : 476
% 0.29/0.99 % BW rewrite match successes : 42
% 0.29/0.99 % Condensation attempts : 0
% 0.29/0.99 % Condensation successes : 0
% 0.29/0.99 % Termbank termtop insertions : 333308
% 0.29/0.99 % Search garbage collected termcells : 1381
% 0.29/0.99
% 0.29/0.99 % -------------------------------------------------
% 0.29/0.99 % User time : 0.284 s
% 0.29/0.99 % System time : 0.024 s
% 0.29/0.99 % Total time : 0.308 s
% 0.29/0.99 % Maximum resident set size: 4888 pages
% 0.29/0.99
% 0.29/0.99 % -------------------------------------------------
% 0.29/0.99 % User time : 0.314 s
% 0.29/0.99 % System time : 0.032 s
% 0.29/0.99 % Total time : 0.346 s
% 0.29/0.99 % Maximum resident set size: 5120 pages
% 0.29/0.99 % E exiting
%------------------------------------------------------------------------------