%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL784-1 : 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 : n008.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 01:23:20 PM UTC 2026
% Result : Unsatisfiable 0.33s 0.47s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 10 RR)
% Number of literals : 15 ( 9 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 15 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_foldl__Nil_0,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
cnf(cls_Nil_0,axiom,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil_0) ).
cnf(cls_True_0,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
cnf(cls_subst__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
cnf(cls_uIT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).
cnf(c_0_6,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_7,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
cls_foldl__Nil_0 ).
cnf(c_0_8,axiom,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
cls_Nil_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,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
c_0_6 ).
cnf(c_0_10,plain,
c_List_Ofoldl(X1,X2,v_rs____,X3,tc_Lambda_OdB) = X2,
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,axiom,
v_n____ = v_i____,
cls_True_0 ).
cnf(c_0_12,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
cls_subst__eq_0 ).
cnf(c_0_13,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
cls_uIT_0 ).
cnf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 01:04:39 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.33/0.47 % Version: 3.5.1
% 0.33/0.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.33/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.33/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.33/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.33/0.47 % Starting sh5l with 300s (1) cores
% 0.33/0.47 % new_bool_3 with pid 4010139 completed with status 0
% 0.33/0.47 % Result found by new_bool_3
% 0.33/0.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.33/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.33/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.33/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.33/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.33/0.47 % Search class: FGUSM-FFLM32-DFFFFFNN
% 0.33/0.47 % partial match(1): FGUSM-FSLM32-DFFFFFNN
% 0.33/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.33/0.47 % SubtermCWHack with pid 4010143 completed with status 0
% 0.33/0.47 % Result found by SubtermCWHack
% 0.33/0.47 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.33/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.47 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.33/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.33/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.33/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.33/0.47 % Search class: FGUSM-FFLM32-DFFFFFNN
% 0.33/0.47 % partial match(1): FGUSM-FSLM32-DFFFFFNN
% 0.33/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.33/0.47 % Preprocessing time : 0.003 s
% 0.33/0.47
% 0.33/0.47 % Proof found!
% 0.33/0.47 % SZS status Unsatisfiable
% 0.33/0.47 % SZS output start CNFRefutation
% See solution above
% 0.33/0.47 % Parsed axioms : 317
% 0.33/0.47 % Removed by relevancy pruning/SinE : 190
% 0.33/0.47 % Initial clauses : 127
% 0.33/0.47 % Removed in clause preprocessing : 0
% 0.33/0.47 % Initial clauses in saturation : 127
% 0.33/0.47 % Processed clauses : 241
% 0.33/0.47 % ...of these trivial : 21
% 0.33/0.47 % ...subsumed : 118
% 0.33/0.47 % ...remaining for further processing : 101
% 0.33/0.47 % Other redundant clauses eliminated : 0
% 0.33/0.47 % Clauses deleted for lack of memory : 0
% 0.33/0.47 % Backward-subsumed : 2
% 0.33/0.47 % Backward-rewritten : 0
% 0.33/0.47 % Generated clauses : 345
% 0.33/0.47 % ...of the previous two non-redundant : 250
% 0.33/0.47 % ...aggressively subsumed : 0
% 0.33/0.47 % Contextual simplify-reflections : 0
% 0.33/0.47 % Paramodulations : 330
% 0.33/0.47 % Factorizations : 2
% 0.33/0.47 % NegExts : 0
% 0.33/0.47 % Equation resolutions : 13
% 0.33/0.47 % Disequality decompositions : 0
% 0.33/0.47 % Total rewrite steps : 213
% 0.33/0.47 % ...of those cached : 135
% 0.33/0.47 % Propositional unsat checks : 0
% 0.33/0.47 % Propositional check models : 0
% 0.33/0.47 % Propositional check unsatisfiable : 0
% 0.33/0.47 % Propositional clauses : 0
% 0.33/0.47 % Propositional clauses after purity: 0
% 0.33/0.47 % Propositional unsat core size : 0
% 0.33/0.47 % Propositional preprocessing time : 0.000
% 0.33/0.47 % Propositional encoding time : 0.000
% 0.33/0.47 % Propositional solver time : 0.000
% 0.33/0.47 % Success case prop preproc time : 0.000
% 0.33/0.47 % Success case prop encoding time : 0.000
% 0.33/0.47 % Success case prop solver time : 0.000
% 0.33/0.47 % Current number of processed clauses : 99
% 0.33/0.47 % Positive orientable unit clauses : 19
% 0.33/0.47 % Positive unorientable unit clauses: 0
% 0.33/0.47 % Negative unit clauses : 14
% 0.33/0.47 % Non-unit-clauses : 66
% 0.33/0.47 % Current number of unprocessed clauses: 136
% 0.33/0.47 % ...number of literals in the above : 291
% 0.33/0.47 % Current number of archived formulas : 0
% 0.33/0.47 % Current number of archived clauses : 2
% 0.33/0.47 % Clause-clause subsumption calls (NU) : 1017
% 0.33/0.47 % Rec. Clause-clause subsumption calls : 982
% 0.33/0.47 % Non-unit clause-clause subsumptions : 98
% 0.33/0.47 % Unit Clause-clause subsumption calls : 17
% 0.33/0.47 % Rewrite failures with RHS unbound : 0
% 0.33/0.47 % BW rewrite match attempts : 2
% 0.33/0.47 % BW rewrite match successes : 0
% 0.33/0.47 % Condensation attempts : 0
% 0.33/0.47 % Condensation successes : 0
% 0.33/0.47 % Termbank termtop insertions : 8698
% 0.33/0.47 % Search garbage collected termcells : 1091
% 0.33/0.47
% 0.33/0.47 % -------------------------------------------------
% 0.33/0.47 % User time : 0.016 s
% 0.33/0.47 % System time : 0.003 s
% 0.33/0.47 % Total time : 0.019 s
% 0.33/0.47 % Maximum resident set size: 4112 pages
% 0.33/0.47
% 0.33/0.47 % -------------------------------------------------
% 0.33/0.47 % User time : 0.026 s
% 0.33/0.47 % System time : 0.007 s
% 0.33/0.47 % Total time : 0.033 s
% 0.33/0.47 % Maximum resident set size: 5120 pages
% 0.33/0.47 % E exiting
%------------------------------------------------------------------------------