%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL759-1 : 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 : n013.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 01:16:21 PM UTC 2026
% Result : Unsatisfiable 2.56s 1.00s
% Output : CNFRefutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 8 unt; 0 nHn; 7 RR)
% Number of literals : 17 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-5 aty)
% Number of variables : 17 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_4,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_Beta_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
cnf(cls_conjecture_1,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_ra),c_Lambda_OdB_OVar(c_Suc(X1))),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_3,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(c_0_4,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(fof_simplification,[status(thm)],[cls_conjecture_4]) ).
cnf(c_0_5,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[cls_Beta_0]) ).
cnf(c_0_6,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_4 ).
cnf(c_0_7,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
c_0_5 ).
cnf(c_0_8,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_ra),c_Lambda_OdB_OVar(c_Suc(X1))),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
cls_conjecture_1 ).
cnf(c_0_9,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2))),
cls_conjecture_3 ).
cnf(c_0_10,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL759-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 01:01:51 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 2.56/1.00 % Version: 3.5.1
% 2.56/1.00 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.56/1.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.56/1.00 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.56/1.00 % Starting new_bool_3 with 300s (1) cores
% 2.56/1.00 % Starting new_bool_1 with 300s (1) cores
% 2.56/1.00 % Starting sh5l with 300s (1) cores
% 2.56/1.00 % new_bool_1 with pid 3819023 completed with status 0
% 2.56/1.00 % Result found by new_bool_1
% 2.56/1.00 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.56/1.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.56/1.00 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.56/1.00 % Starting new_bool_3 with 300s (1) cores
% 2.56/1.00 % Starting new_bool_1 with 300s (1) cores
% 2.56/1.00 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.56/1.00 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.56/1.00 % Search class: FGHSM-FSLM32-DFFFFFNN
% 2.56/1.00 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 2.56/1.00 % Starting SubtermCWHack with 28s (1) cores
% 2.56/1.00 % SubtermCWHack with pid 3819032 completed with status 0
% 2.56/1.00 % Result found by SubtermCWHack
% 2.56/1.00 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.56/1.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.56/1.00 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.56/1.00 % Starting new_bool_3 with 300s (1) cores
% 2.56/1.00 % Starting new_bool_1 with 300s (1) cores
% 2.56/1.00 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.56/1.00 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.56/1.00 % Search class: FGHSM-FSLM32-DFFFFFNN
% 2.56/1.00 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 2.56/1.00 % Starting SubtermCWHack with 28s (1) cores
% 2.56/1.00 % Preprocessing time : 0.008 s
% 2.56/1.00
% 2.56/1.00 % Proof found!
% 2.56/1.00 % SZS status Unsatisfiable
% 2.56/1.00 % SZS output start CNFRefutation
% See solution above
% 2.56/1.00 % Parsed axioms : 637
% 2.56/1.00 % Removed by relevancy pruning/SinE : 232
% 2.56/1.00 % Initial clauses : 405
% 2.56/1.00 % Removed in clause preprocessing : 0
% 2.56/1.00 % Initial clauses in saturation : 405
% 2.56/1.00 % Processed clauses : 3014
% 2.56/1.00 % ...of these trivial : 218
% 2.56/1.00 % ...subsumed : 2204
% 2.56/1.00 % ...remaining for further processing : 592
% 2.56/1.00 % Other redundant clauses eliminated : 129
% 2.56/1.00 % Clauses deleted for lack of memory : 0
% 2.56/1.00 % Backward-subsumed : 7
% 2.56/1.00 % Backward-rewritten : 27
% 2.56/1.00 % Generated clauses : 17203
% 2.56/1.00 % ...of the previous two non-redundant : 13894
% 2.56/1.00 % ...aggressively subsumed : 0
% 2.56/1.00 % Contextual simplify-reflections : 0
% 2.56/1.00 % Paramodulations : 17046
% 2.56/1.00 % Factorizations : 8
% 2.56/1.00 % NegExts : 0
% 2.56/1.00 % Equation resolutions : 149
% 2.56/1.00 % Disequality decompositions : 0
% 2.56/1.00 % Total rewrite steps : 17596
% 2.56/1.00 % ...of those cached : 16177
% 2.56/1.00 % Propositional unsat checks : 0
% 2.56/1.00 % Propositional check models : 0
% 2.56/1.00 % Propositional check unsatisfiable : 0
% 2.56/1.00 % Propositional clauses : 0
% 2.56/1.00 % Propositional clauses after purity: 0
% 2.56/1.00 % Propositional unsat core size : 0
% 2.56/1.00 % Propositional preprocessing time : 0.000
% 2.56/1.00 % Propositional encoding time : 0.000
% 2.56/1.00 % Propositional solver time : 0.000
% 2.56/1.00 % Success case prop preproc time : 0.000
% 2.56/1.00 % Success case prop encoding time : 0.000
% 2.56/1.00 % Success case prop solver time : 0.000
% 2.56/1.00 % Current number of processed clauses : 558
% 2.56/1.00 % Positive orientable unit clauses : 133
% 2.56/1.00 % Positive unorientable unit clauses: 5
% 2.56/1.00 % Negative unit clauses : 115
% 2.56/1.00 % Non-unit-clauses : 305
% 2.56/1.00 % Current number of unprocessed clauses: 11235
% 2.56/1.00 % ...number of literals in the above : 23965
% 2.56/1.00 % Current number of archived formulas : 0
% 2.56/1.00 % Current number of archived clauses : 34
% 2.56/1.00 % Clause-clause subsumption calls (NU) : 11660
% 2.56/1.00 % Rec. Clause-clause subsumption calls : 9969
% 2.56/1.00 % Non-unit clause-clause subsumptions : 591
% 2.56/1.00 % Unit Clause-clause subsumption calls : 1659
% 2.56/1.00 % Rewrite failures with RHS unbound : 0
% 2.56/1.00 % BW rewrite match attempts : 460
% 2.56/1.00 % BW rewrite match successes : 38
% 2.56/1.00 % Condensation attempts : 0
% 2.56/1.00 % Condensation successes : 0
% 2.56/1.00 % Termbank termtop insertions : 282333
% 2.56/1.00 % Search garbage collected termcells : 1470
% 2.56/1.00
% 2.56/1.00 % -------------------------------------------------
% 2.56/1.00 % User time : 0.421 s
% 2.56/1.00 % System time : 0.023 s
% 2.56/1.00 % Total time : 0.444 s
% 2.56/1.00 % Maximum resident set size: 4612 pages
% 2.56/1.00
% 2.56/1.00 % -------------------------------------------------
% 2.56/1.00 % User time : 0.454 s
% 2.56/1.00 % System time : 0.029 s
% 2.56/1.00 % Total time : 0.483 s
% 2.56/1.00 % Maximum resident set size: 5376 pages
% 2.56/1.00 % E exiting
%------------------------------------------------------------------------------