%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL836-1 : 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 : n002.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 01:23:29 PM UTC 2026
% Result : Unsatisfiable 70.56s 11.16s
% Output : CNFRefutation 70.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 14 RR)
% Number of literals : 24 ( 0 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-5 aty)
% Number of variables : 14 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_SI1_0,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X3,X2,v_T____,tc_Type_Otype),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),X4)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(X3,X1,v_T____)
| 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)),X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SI1_0) ).
cnf(cls_uT_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).
cnf(cls_uIT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ 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_conjecture_0) ).
cnf(cls_CHAINED_0_02,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),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_T_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
cnf(c_0_5,plain,
( ~ c_Type_Otyping(c_Type_Oshift(X3,X2,v_T____,tc_Type_Otype),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),X4)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(X3,X1,v_T____)
| 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)),X1),X2))) ),
inference(fof_simplification,[status(thm)],[cls_SI1_0]) ).
cnf(c_0_6,plain,
( ~ c_Type_Otyping(c_Type_Oshift(X3,X2,v_T____,tc_Type_Otype),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),X4)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(X3,X1,v_T____)
| 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)),X1),X2))) ),
c_0_5 ).
cnf(c_0_7,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
cls_uT_0 ).
cnf(c_0_8,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
cls_uIT_0 ).
cnf(c_0_9,negated_conjecture,
~ 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____))),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_10,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,X1,v_T____,tc_Type_Otype),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),X2)
| 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____),X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).
cnf(c_0_11,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),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_T_H____),
cls_CHAINED_0_02 ).
cnf(c_0_12,negated_conjecture,
~ 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____))),
c_0_9 ).
cnf(c_0_13,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL836-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.47 % Computer : n002.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Mon Sep 21 01:09:47 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.56 Running first-order theorem proving
% 0.24/0.56 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
% 70.56/11.16 % Version: 3.5.1
% 70.56/11.16 % Preprocessing class: FSLMSMSMSSSNFFN.
% 70.56/11.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 70.56/11.16 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 70.56/11.16 % Starting new_bool_3 with 600s (2) cores
% 70.56/11.16 % Starting new_bool_1 with 300s (1) cores
% 70.56/11.16 % Starting sh5l with 300s (1) cores
% 70.56/11.16 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 2125587 completed with status 0
% 70.56/11.16 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 70.56/11.16 % Preprocessing class: FSLMSMSMSSSNFFN.
% 70.56/11.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 70.56/11.16 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 70.56/11.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 70.56/11.16 % No SInE strategy applied
% 70.56/11.16 % Search class: FGHSM-FSLM32-DFFFFFNN
% 70.56/11.16 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 70.56/11.16 % Starting SubtermCWHack with 109s (1) cores
% 70.56/11.16 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 70.56/11.16 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 70.56/11.16 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 70.56/11.16 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2125595 completed with status 0
% 70.56/11.16 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 70.56/11.16 % Preprocessing class: FSLMSMSMSSSNFFN.
% 70.56/11.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 70.56/11.16 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 70.56/11.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 70.56/11.16 % No SInE strategy applied
% 70.56/11.16 % Search class: FGHSM-FSLM32-DFFFFFNN
% 70.56/11.16 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 70.56/11.16 % Starting SubtermCWHack with 109s (1) cores
% 70.56/11.16 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 70.56/11.16 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 70.56/11.16 % Preprocessing time : 0.016 s
% 70.56/11.16 % Presaturation interreduction done
% 70.56/11.16
% 70.56/11.16 % Proof found!
% 70.56/11.16 % SZS status Unsatisfiable
% 70.56/11.16 % SZS output start CNFRefutation
% See solution above
% 70.56/11.16 % Parsed axioms : 625
% 70.56/11.16 % Removed by relevancy pruning/SinE : 0
% 70.56/11.16 % Initial clauses : 625
% 70.56/11.16 % Removed in clause preprocessing : 2
% 70.56/11.16 % Initial clauses in saturation : 623
% 70.56/11.16 % Processed clauses : 35261
% 70.56/11.16 % ...of these trivial : 364
% 70.56/11.16 % ...subsumed : 30696
% 70.56/11.16 % ...remaining for further processing : 4201
% 70.56/11.16 % Other redundant clauses eliminated : 2751
% 70.56/11.16 % Clauses deleted for lack of memory : 0
% 70.56/11.16 % Backward-subsumed : 134
% 70.56/11.16 % Backward-rewritten : 66
% 70.56/11.16 % Generated clauses : 349930
% 70.56/11.16 % ...of the previous two non-redundant : 318614
% 70.56/11.16 % ...aggressively subsumed : 0
% 70.56/11.16 % Contextual simplify-reflections : 20
% 70.56/11.16 % Paramodulations : 347053
% 70.56/11.16 % Factorizations : 64
% 70.56/11.16 % NegExts : 0
% 70.56/11.16 % Equation resolutions : 2813
% 70.56/11.16 % Disequality decompositions : 0
% 70.56/11.16 % Total rewrite steps : 236032
% 70.56/11.16 % ...of those cached : 228313
% 70.56/11.16 % Propositional unsat checks : 0
% 70.56/11.16 % Propositional check models : 0
% 70.56/11.16 % Propositional check unsatisfiable : 0
% 70.56/11.16 % Propositional clauses : 0
% 70.56/11.16 % Propositional clauses after purity: 0
% 70.56/11.16 % Propositional unsat core size : 0
% 70.56/11.16 % Propositional preprocessing time : 0.000
% 70.56/11.16 % Propositional encoding time : 0.000
% 70.56/11.16 % Propositional solver time : 0.000
% 70.56/11.16 % Success case prop preproc time : 0.000
% 70.56/11.16 % Success case prop encoding time : 0.000
% 70.56/11.16 % Success case prop solver time : 0.000
% 70.56/11.16 % Current number of processed clauses : 3513
% 70.56/11.16 % Positive orientable unit clauses : 558
% 70.56/11.16 % Positive unorientable unit clauses: 43
% 70.56/11.16 % Negative unit clauses : 377
% 70.56/11.16 % Non-unit-clauses : 2535
% 70.56/11.16 % Current number of unprocessed clauses: 283960
% 70.56/11.16 % ...number of literals in the above : 775102
% 70.56/11.16 % Current number of archived formulas : 0
% 70.56/11.16 % Current number of archived clauses : 689
% 70.56/11.16 % Clause-clause subsumption calls (NU) : 712161
% 70.56/11.16 % Rec. Clause-clause subsumption calls : 554664
% 70.56/11.16 % Non-unit clause-clause subsumptions : 16070
% 70.56/11.16 % Unit Clause-clause subsumption calls : 51505
% 70.56/11.16 % Rewrite failures with RHS unbound : 44
% 70.56/11.16 % BW rewrite match attempts : 18724
% 70.56/11.16 % BW rewrite match successes : 329
% 70.56/11.16 % Condensation attempts : 0
% 70.56/11.16 % Condensation successes : 0
% 70.56/11.16 % Termbank termtop insertions : 7316485
% 70.56/11.16 % Search garbage collected termcells : 1108
% 70.56/11.16
% 70.56/11.16 % -------------------------------------------------
% 70.56/11.16 % User time : 9.991 s
% 70.56/11.16 % System time : 0.309 s
% 70.56/11.16 % Total time : 10.300 s
% 70.56/11.16 % Maximum resident set size: 4812 pages
% 70.56/11.16
% 70.56/11.16 % -------------------------------------------------
% 70.56/11.16 % User time : 38.990 s
% 70.56/11.16 % System time : 1.351 s
% 70.56/11.16 % Total time : 40.341 s
% 70.56/11.16 % Maximum resident set size: 5376 pages
% 70.56/11.16 % E exiting
%------------------------------------------------------------------------------