%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL786-1 : 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 : n016.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 01:16:25 PM UTC 2026
% Result : Unsatisfiable 67.82s 10.33s
% Output : CNFRefutation 67.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 26 ( 14 unt; 0 nHn; 24 RR)
% Number of literals : 42 ( 4 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-5 aty)
% Number of variables : 43 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_that_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,X1,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,X1)
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_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/sandbox2/benchmark/theBenchmark.p',cls_foldr__foldl_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_list__app__typeD_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
cnf(cls_CHAINED_0,axiom,
hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_True_0,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
cnf(cls_list__app__typeD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
cnf(c_0_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,X1,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,X1)
| v_thesis____ ),
inference(fof_simplification,[status(thm)],[cls_that_0]) ).
cnf(c_0_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,X1,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,X1)
| v_thesis____ ),
c_0_7 ).
cnf(c_0_9,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_10,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2)) ),
inference(fof_simplification,[status(thm)],[cls_list__app__typeD_1]) ).
cnf(c_0_12,axiom,
hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
cls_CHAINED_0 ).
cnf(c_0_13,axiom,
v_n____ = v_i____,
cls_True_0 ).
cnf(c_0_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))) ),
inference(fof_simplification,[status(thm)],[cls_list__app__typeD_0]) ).
cnf(c_0_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(X1,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,X1)
| v_thesis____ ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_16,negated_conjecture,
~ v_thesis____,
c_0_10 ).
cnf(c_0_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2)) ),
c_0_11 ).
cnf(c_0_18,plain,
hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))) ),
c_0_14 ).
cnf(c_0_20,plain,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(X1,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_as____,X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_13]),c_0_13]),c_0_16]) ).
cnf(c_0_21,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X3,c_List_Orev(c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))) ),
inference(rw,[status(thm)],[c_0_19,c_0_9]) ).
cnf(c_0_23,plain,
~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____),tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____),tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_25,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_23,c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL786-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 01:08:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 67.82/10.33 % Version: 3.5.1
% 67.82/10.33 % Preprocessing class: FSLMSMSMSSSNFFN.
% 67.82/10.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.82/10.33 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 67.82/10.33 % Starting new_bool_3 with 600s (2) cores
% 67.82/10.33 % Starting new_bool_1 with 300s (1) cores
% 67.82/10.33 % Starting sh5l with 300s (1) cores
% 67.82/10.33 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 1240540 completed with status 0
% 67.82/10.33 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 67.82/10.33 % Preprocessing class: FSLMSMSMSSSNFFN.
% 67.82/10.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.82/10.33 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 67.82/10.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 67.82/10.33 % No SInE strategy applied
% 67.82/10.33 % Search class: FGHSM-FSLM32-DFFFFFNN
% 67.82/10.33 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 67.82/10.33 % Starting SubtermCWHack with 109s (1) cores
% 67.82/10.33 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 67.82/10.33 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 67.82/10.33 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 67.82/10.33 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1240550 completed with status 0
% 67.82/10.33 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 67.82/10.33 % Preprocessing class: FSLMSMSMSSSNFFN.
% 67.82/10.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.82/10.33 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 67.82/10.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 67.82/10.33 % No SInE strategy applied
% 67.82/10.33 % Search class: FGHSM-FSLM32-DFFFFFNN
% 67.82/10.33 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 67.82/10.33 % Starting SubtermCWHack with 109s (1) cores
% 67.82/10.33 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 67.82/10.33 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 67.82/10.33 % Preprocessing time : 0.008 s
% 67.82/10.33 % Presaturation interreduction done
% 67.82/10.33 % SatCheck found unsatisfiable ground set
% 67.82/10.33
% 67.82/10.33 % Proof found!
% 67.82/10.33 % SZS status Unsatisfiable
% 67.82/10.33 % SZS output start CNFRefutation
% See solution above
% 67.82/10.33 % Parsed axioms : 497
% 67.82/10.33 % Removed by relevancy pruning/SinE : 0
% 67.82/10.33 % Initial clauses : 497
% 67.82/10.33 % Removed in clause preprocessing : 2
% 67.82/10.33 % Initial clauses in saturation : 495
% 67.82/10.33 % Processed clauses : 27620
% 67.82/10.33 % ...of these trivial : 407
% 67.82/10.33 % ...subsumed : 22213
% 67.82/10.33 % ...remaining for further processing : 5000
% 67.82/10.33 % Other redundant clauses eliminated : 1171
% 67.82/10.33 % Clauses deleted for lack of memory : 0
% 67.82/10.33 % Backward-subsumed : 211
% 67.82/10.33 % Backward-rewritten : 132
% 67.82/10.33 % Generated clauses : 336470
% 67.82/10.33 % ...of the previous two non-redundant : 321090
% 67.82/10.33 % ...aggressively subsumed : 0
% 67.82/10.33 % Contextual simplify-reflections : 3
% 67.82/10.33 % Paramodulations : 335168
% 67.82/10.33 % Factorizations : 14
% 67.82/10.33 % NegExts : 0
% 67.82/10.33 % Equation resolutions : 1288
% 67.82/10.33 % Disequality decompositions : 0
% 67.82/10.33 % Total rewrite steps : 178138
% 67.82/10.33 % ...of those cached : 164349
% 67.82/10.33 % Propositional unsat checks : 1
% 67.82/10.33 % Propositional check models : 0
% 67.82/10.33 % Propositional check unsatisfiable : 1
% 67.82/10.33 % Propositional clauses : 298142
% 67.82/10.33 % Propositional clauses after purity: 28834
% 67.82/10.33 % Propositional unsat core size : 2
% 67.82/10.33 % Propositional preprocessing time : 0.000
% 67.82/10.33 % Propositional encoding time : 0.976
% 67.82/10.33 % Propositional solver time : 0.062
% 67.82/10.33 % Success case prop preproc time : 0.000
% 67.82/10.33 % Success case prop encoding time : 0.976
% 67.82/10.33 % Success case prop solver time : 0.062
% 67.82/10.33 % Current number of processed clauses : 4280
% 67.82/10.33 % Positive orientable unit clauses : 474
% 67.82/10.33 % Positive unorientable unit clauses: 118
% 67.82/10.33 % Negative unit clauses : 1412
% 67.82/10.33 % Non-unit-clauses : 2276
% 67.82/10.33 % Current number of unprocessed clauses: 293862
% 67.82/10.33 % ...number of literals in the above : 796320
% 67.82/10.33 % Current number of archived formulas : 0
% 67.82/10.33 % Current number of archived clauses : 722
% 67.82/10.33 % Clause-clause subsumption calls (NU) : 819210
% 67.82/10.33 % Rec. Clause-clause subsumption calls : 634083
% 67.82/10.33 % Non-unit clause-clause subsumptions : 7342
% 67.82/10.33 % Unit Clause-clause subsumption calls : 615607
% 67.82/10.33 % Rewrite failures with RHS unbound : 1350
% 67.82/10.33 % BW rewrite match attempts : 7708
% 67.82/10.33 % BW rewrite match successes : 547
% 67.82/10.33 % Condensation attempts : 0
% 67.82/10.33 % Condensation successes : 0
% 67.82/10.33 % Termbank termtop insertions : 11664970
% 67.82/10.33 % Search garbage collected termcells : 784
% 67.82/10.33
% 67.82/10.33 % -------------------------------------------------
% 67.82/10.33 % User time : 9.175 s
% 67.82/10.33 % System time : 0.348 s
% 67.82/10.33 % Total time : 9.523 s
% 67.82/10.33 % Maximum resident set size: 4488 pages
% 67.82/10.33
% 67.82/10.33 % -------------------------------------------------
% 67.82/10.33 % User time : 36.951 s
% 67.82/10.33 % System time : 1.302 s
% 67.82/10.33 % Total time : 38.253 s
% 67.82/10.33 % Maximum resident set size: 5120 pages
% 67.82/10.33 % E exiting
%------------------------------------------------------------------------------