%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL847-1 : 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 : 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 01:23:30 PM UTC 2026
% Result : Unsatisfiable 106.38s 16.19s
% Output : CNFRefutation 106.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 35 ( 20 unt; 3 nHn; 16 RR)
% Number of literals : 50 ( 13 equ; 15 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-5 aty)
% Number of variables : 90 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_set__takeWhileD_1,axiom,
( ~ c_in(X2,c_List_Oset(c_List_OtakeWhile(X1,X3,X4),X4),X4)
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).
cnf(cls_in__listsp__conv__set_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3)))
| c_List_Olistsp(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__listsp__conv__set_2) ).
cnf(cls_in__listsp__conv__set_1,axiom,
( c_in(c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3),c_List_Oset(X2,X3),X3)
| c_List_Olistsp(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__listsp__conv__set_1) ).
cnf(cls_takeWhile_Osimps_I2_J_0,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_List_OtakeWhile(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_OtakeWhile(X1,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).
cnf(cls_App_I4_J_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ta____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_I4_J_0) ).
cnf(cls_lifts__IT_0,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
cnf(cls_takeWhile_Osimps_I1_J_0,axiom,
c_List_OtakeWhile(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).
cnf(cls_map__eq__Cons__conv_3,axiom,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
cnf(cls_Nil__is__map__conv_1,axiom,
c_List_Olist_ONil(X1) = c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(c_0_11,plain,
( ~ c_in(X2,c_List_Oset(c_List_OtakeWhile(X1,X3,X4),X4),X4)
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_set__takeWhileD_1]) ).
cnf(c_0_12,plain,
( ~ hBOOL(hAPP(X1,c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3)))
| c_List_Olistsp(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[cls_in__listsp__conv__set_2]) ).
cnf(c_0_13,plain,
( ~ c_in(X2,c_List_Oset(c_List_OtakeWhile(X1,X3,X4),X4),X4)
| hBOOL(hAPP(X1,X2)) ),
c_0_11 ).
cnf(c_0_14,axiom,
( c_in(c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3),c_List_Oset(X2,X3),X3)
| c_List_Olistsp(X1,X2,X3) ),
cls_in__listsp__conv__set_1 ).
cnf(c_0_15,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_List_OtakeWhile(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_OtakeWhile(X1,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[cls_takeWhile_Osimps_I2_J_0]) ).
cnf(c_0_16,plain,
( ~ hBOOL(hAPP(X1,c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3)))
| c_List_Olistsp(X1,X2,X3) ),
c_0_12 ).
cnf(c_0_17,plain,
( hBOOL(hAPP(X2,c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,c_List_OtakeWhile(X2,X3,X4),X4)))
| c_List_Olistsp(X1,c_List_OtakeWhile(X2,X3,X4),X4) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_List_OtakeWhile(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_OtakeWhile(X1,X3,X4),X4) ),
c_0_15 ).
cnf(c_0_19,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ta____)),
cls_App_I4_J_0 ).
cnf(c_0_20,plain,
c_List_Olistsp(X1,c_List_OtakeWhile(X1,X2,X3),X3),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
c_List_OtakeWhile(c_InductTermi_OIT,c_List_Olist_OCons(v_ta____,X1,X2),X2) = c_List_Olist_OCons(v_ta____,c_List_OtakeWhile(c_InductTermi_OIT,X1,X2),X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[cls_lifts__IT_0]) ).
cnf(c_0_23,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(v_ta____,c_List_OtakeWhile(c_InductTermi_OIT,X1,X2),X2),X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,axiom,
c_List_OtakeWhile(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
cls_takeWhile_Osimps_I1_J_0 ).
cnf(c_0_25,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
c_0_22 ).
cnf(c_0_26,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(v_ta____,c_List_Olist_ONil(X1),X1),X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,axiom,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
cls_map__eq__Cons__conv_3 ).
cnf(c_0_28,axiom,
c_List_Olist_ONil(X1) = c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1),
cls_Nil__is__map__conv_1 ).
cnf(c_0_29,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_30,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_ta____,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
c_List_Omap(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3,X4) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Olist_ONil(X4),X4),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
cls_COMBC__def_0 ).
cnf(c_0_33,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
c_0_29 ).
cnf(c_0_34,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL847-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.49 % Computer : n002.cluster.edu
% 0.19/0.49 % Model : x86_64 x86_64
% 0.19/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.49 % Memory : 8046.5625MB
% 0.19/0.49 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Mon Sep 21 01:10:46 UTC 2026
% 0.19/0.50 % CPUTime :
% 0.19/0.50 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.59 Running first-order theorem proving
% 0.25/0.59 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
% 106.38/16.19 % Version: 3.5.1
% 106.38/16.19 % Preprocessing class: FSLMSMSMSSSNFFN.
% 106.38/16.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.38/16.19 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 106.38/16.19 % Starting new_bool_3 with 600s (2) cores
% 106.38/16.19 % Starting new_bool_1 with 300s (1) cores
% 106.38/16.19 % Starting sh5l with 300s (1) cores
% 106.38/16.19 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 2127524 completed with status 0
% 106.38/16.19 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 106.38/16.19 % Preprocessing class: FSLMSMSMSSSNFFN.
% 106.38/16.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.38/16.19 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 106.38/16.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 106.38/16.19 % No SInE strategy applied
% 106.38/16.19 % Search class: FGHSM-FSLM32-DFFFFFNN
% 106.38/16.19 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 106.38/16.19 % Starting SubtermCWHack with 109s (1) cores
% 106.38/16.19 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 106.38/16.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 106.38/16.19 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 106.38/16.19 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 2127533 completed with status 0
% 106.38/16.19 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 106.38/16.19 % Preprocessing class: FSLMSMSMSSSNFFN.
% 106.38/16.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.38/16.19 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 106.38/16.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 106.38/16.19 % No SInE strategy applied
% 106.38/16.19 % Search class: FGHSM-FSLM32-DFFFFFNN
% 106.38/16.19 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 106.38/16.19 % Starting SubtermCWHack with 109s (1) cores
% 106.38/16.19 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 106.38/16.19 % Preprocessing time : 0.014 s
% 106.38/16.19 % Presaturation interreduction done
% 106.38/16.19
% 106.38/16.19 % Proof found!
% 106.38/16.19 % SZS status Unsatisfiable
% 106.38/16.19 % SZS output start CNFRefutation
% See solution above
% 106.38/16.19 % Parsed axioms : 641
% 106.38/16.19 % Removed by relevancy pruning/SinE : 0
% 106.38/16.19 % Initial clauses : 641
% 106.38/16.19 % Removed in clause preprocessing : 2
% 106.38/16.19 % Initial clauses in saturation : 639
% 106.38/16.19 % Processed clauses : 24459
% 106.38/16.19 % ...of these trivial : 1370
% 106.38/16.19 % ...subsumed : 18123
% 106.38/16.19 % ...remaining for further processing : 4966
% 106.38/16.19 % Other redundant clauses eliminated : 294
% 106.38/16.19 % Clauses deleted for lack of memory : 0
% 106.38/16.19 % Backward-subsumed : 105
% 106.38/16.19 % Backward-rewritten : 83
% 106.38/16.19 % Generated clauses : 503633
% 106.38/16.19 % ...of the previous two non-redundant : 481868
% 106.38/16.19 % ...aggressively subsumed : 0
% 106.38/16.19 % Contextual simplify-reflections : 31
% 106.38/16.19 % Paramodulations : 503197
% 106.38/16.19 % Factorizations : 50
% 106.38/16.19 % NegExts : 0
% 106.38/16.19 % Equation resolutions : 386
% 106.38/16.19 % Disequality decompositions : 0
% 106.38/16.19 % Total rewrite steps : 1163035
% 106.38/16.19 % ...of those cached : 911944
% 106.38/16.19 % Propositional unsat checks : 0
% 106.38/16.19 % Propositional check models : 0
% 106.38/16.19 % Propositional check unsatisfiable : 0
% 106.38/16.19 % Propositional clauses : 0
% 106.38/16.19 % Propositional clauses after purity: 0
% 106.38/16.19 % Propositional unsat core size : 0
% 106.38/16.19 % Propositional preprocessing time : 0.000
% 106.38/16.19 % Propositional encoding time : 0.000
% 106.38/16.19 % Propositional solver time : 0.000
% 106.38/16.19 % Success case prop preproc time : 0.000
% 106.38/16.19 % Success case prop encoding time : 0.000
% 106.38/16.19 % Success case prop solver time : 0.000
% 106.38/16.19 % Current number of processed clauses : 4257
% 106.38/16.19 % Positive orientable unit clauses : 1877
% 106.38/16.19 % Positive unorientable unit clauses: 40
% 106.38/16.19 % Negative unit clauses : 251
% 106.38/16.19 % Non-unit-clauses : 2089
% 106.38/16.19 % Current number of unprocessed clauses: 457588
% 106.38/16.19 % ...number of literals in the above : 678448
% 106.38/16.19 % Current number of archived formulas : 0
% 106.38/16.19 % Current number of archived clauses : 710
% 106.38/16.19 % Clause-clause subsumption calls (NU) : 787774
% 106.38/16.19 % Rec. Clause-clause subsumption calls : 612670
% 106.38/16.19 % Non-unit clause-clause subsumptions : 6734
% 106.38/16.19 % Unit Clause-clause subsumption calls : 72500
% 106.38/16.19 % Rewrite failures with RHS unbound : 140
% 106.38/16.19 % BW rewrite match attempts : 178035
% 106.38/16.19 % BW rewrite match successes : 225
% 106.38/16.19 % Condensation attempts : 0
% 106.38/16.19 % Condensation successes : 0
% 106.38/16.19 % Termbank termtop insertions : 19668785
% 106.38/16.19 % Search garbage collected termcells : 1058
% 106.38/16.19
% 106.38/16.19 % -------------------------------------------------
% 106.38/16.19 % User time : 14.383 s
% 106.38/16.19 % System time : 0.623 s
% 106.38/16.19 % Total time : 15.006 s
% 106.38/16.19 % Maximum resident set size: 4880 pages
% 106.38/16.19
% 106.38/16.19 % -------------------------------------------------
% 106.38/16.19 % User time : 58.135 s
% 106.38/16.19 % System time : 2.263 s
% 106.38/16.19 % Total time : 60.398 s
% 106.38/16.19 % Maximum resident set size: 5376 pages
% 106.38/16.19 % E exiting
%------------------------------------------------------------------------------