%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:03:02 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.57s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 9 unt; 0 nHn; 15 RR)
% Number of literals : 42 ( 3 equ; 24 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oadd__le__cancel__right_1,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(c_plus(X2,X4,X1),c_plus(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
cnf(cls_OrderedGroup_Oright__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X2,c_uminus(X2,X1),X1) = c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_lb(X1),v_f(X1),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_37,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
cnf(c_0_7,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(c_plus(X2,X4,X1),c_plus(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oadd__le__cancel__right_1]) ).
cnf(c_0_8,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X2,c_uminus(X2,X1),X1) = c_0 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oright__minus_0]) ).
cnf(c_0_9,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).
cnf(c_0_10,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(c_plus(X2,X4,X1),c_plus(X3,X4,X1),X1) ),
c_0_7 ).
cnf(c_0_11,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X2,c_uminus(X2,X1),X1) = c_0 ),
c_0_8 ).
cnf(c_0_12,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
c_0_9 ).
cnf(c_0_13,plain,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3)
| c_lessequals(c_0,c_plus(X1,c_uminus(X2,X3),X3),X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,negated_conjecture,
c_lessequals(v_lb(X1),v_f(X1),t_b),
cls_conjecture_0 ).
cnf(c_0_15,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_4]) ).
cnf(c_0_16,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_17,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__group__add(X1) ),
c_0_15 ).
cnf(c_0_18,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_19,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_37]) ).
cnf(c_0_20,negated_conjecture,
~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_21,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_19 ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n018.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 13:25:15 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.54 Running first-order theorem proving
% 0.23/0.54 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
% 0.23/0.57 % Version: 3.5.1
% 0.23/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.23/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.23/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.57 % Starting sh5l with 300s (1) cores
% 0.23/0.57 % new_bool_1 with pid 1989403 completed with status 0
% 0.23/0.57 % Result found by new_bool_1
% 0.23/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.23/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.23/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.57 % Search class: FHUSF-FFSF31-MFFFFFNN
% 0.23/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.57 % SubtermCWHack with pid 1989404 completed with status 0
% 0.23/0.57 % Result found by SubtermCWHack
% 0.23/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.23/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.23/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.57 % Search class: FHUSF-FFSF31-MFFFFFNN
% 0.23/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.57 % Preprocessing time : 0.002 s
% 0.23/0.57
% 0.23/0.57 % Proof found!
% 0.23/0.57 % SZS status Unsatisfiable
% 0.23/0.57 % SZS output start CNFRefutation
% See solution above
% 0.23/0.57 % Parsed axioms : 7
% 0.23/0.57 % Removed by relevancy pruning/SinE : 0
% 0.23/0.57 % Initial clauses : 7
% 0.23/0.57 % Removed in clause preprocessing : 0
% 0.23/0.57 % Initial clauses in saturation : 7
% 0.23/0.57 % Processed clauses : 13
% 0.23/0.57 % ...of these trivial : 0
% 0.23/0.57 % ...subsumed : 1
% 0.23/0.57 % ...remaining for further processing : 12
% 0.23/0.57 % Other redundant clauses eliminated : 0
% 0.23/0.57 % Clauses deleted for lack of memory : 0
% 0.23/0.57 % Backward-subsumed : 1
% 0.23/0.57 % Backward-rewritten : 0
% 0.23/0.57 % Generated clauses : 8
% 0.23/0.57 % ...of the previous two non-redundant : 7
% 0.23/0.57 % ...aggressively subsumed : 0
% 0.23/0.57 % Contextual simplify-reflections : 0
% 0.23/0.57 % Paramodulations : 8
% 0.23/0.57 % Factorizations : 0
% 0.23/0.57 % NegExts : 0
% 0.23/0.57 % Equation resolutions : 0
% 0.23/0.57 % Disequality decompositions : 0
% 0.23/0.57 % Total rewrite steps : 3
% 0.23/0.57 % ...of those cached : 1
% 0.23/0.57 % Propositional unsat checks : 0
% 0.23/0.57 % Propositional check models : 0
% 0.23/0.57 % Propositional check unsatisfiable : 0
% 0.23/0.57 % Propositional clauses : 0
% 0.23/0.57 % Propositional clauses after purity: 0
% 0.23/0.57 % Propositional unsat core size : 0
% 0.23/0.57 % Propositional preprocessing time : 0.000
% 0.23/0.57 % Propositional encoding time : 0.000
% 0.23/0.57 % Propositional solver time : 0.000
% 0.23/0.57 % Success case prop preproc time : 0.000
% 0.23/0.57 % Success case prop encoding time : 0.000
% 0.23/0.57 % Success case prop solver time : 0.000
% 0.23/0.57 % Current number of processed clauses : 11
% 0.23/0.57 % Positive orientable unit clauses : 2
% 0.23/0.57 % Positive unorientable unit clauses: 0
% 0.23/0.57 % Negative unit clauses : 2
% 0.23/0.57 % Non-unit-clauses : 7
% 0.23/0.57 % Current number of unprocessed clauses: 1
% 0.23/0.57 % ...number of literals in the above : 4
% 0.23/0.57 % Current number of archived formulas : 0
% 0.23/0.57 % Current number of archived clauses : 1
% 0.23/0.57 % Clause-clause subsumption calls (NU) : 11
% 0.23/0.57 % Rec. Clause-clause subsumption calls : 7
% 0.23/0.57 % Non-unit clause-clause subsumptions : 1
% 0.23/0.57 % Unit Clause-clause subsumption calls : 2
% 0.23/0.57 % Rewrite failures with RHS unbound : 0
% 0.23/0.57 % BW rewrite match attempts : 0
% 0.23/0.57 % BW rewrite match successes : 0
% 0.23/0.57 % Condensation attempts : 0
% 0.23/0.57 % Condensation successes : 0
% 0.23/0.57 % Termbank termtop insertions : 301
% 0.23/0.57 % Search garbage collected termcells : 13
% 0.23/0.57
% 0.23/0.57 % -------------------------------------------------
% 0.23/0.57 % User time : 0.004 s
% 0.23/0.57 % System time : 0.002 s
% 0.23/0.57 % Total time : 0.006 s
% 0.23/0.57 % Maximum resident set size: 3636 pages
% 0.23/0.57
% 0.23/0.57 % -------------------------------------------------
% 0.23/0.57 % User time : 0.005 s
% 0.23/0.57 % System time : 0.009 s
% 0.23/0.57 % Total time : 0.014 s
% 0.23/0.57 % Maximum resident set size: 4608 pages
% 0.23/0.57 % E exiting
%------------------------------------------------------------------------------