%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ANA010-2 : 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 : 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 12:03:02 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 34 ( 14 unt; 0 nHn; 26 RR)
% Number of literals : 65 ( 8 equ; 39 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(v_f(v_x(X1)),c_times(X1,c_HOL_Oabs(v_g(v_x(X1)),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(c_0,v_f(X1),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_f(X1),c_times(v_c,v_g(X1),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
cnf(c_0_9,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__of__nonneg_0]) ).
cnf(c_0_10,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(c_0_11,negated_conjecture,
~ c_lessequals(v_f(v_x(X1)),c_times(X1,c_HOL_Oabs(v_g(v_x(X1)),t_b),t_b),t_b),
inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).
cnf(c_0_12,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Oabs__mult_0]) ).
cnf(c_0_13,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
c_0_9 ).
cnf(c_0_14,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
c_0_10 ).
cnf(c_0_15,negated_conjecture,
~ c_lessequals(v_f(v_x(X1)),c_times(X1,c_HOL_Oabs(v_g(v_x(X1)),t_b),t_b),t_b),
c_0_11 ).
cnf(c_0_16,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1) ),
c_0_12 ).
cnf(c_0_17,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_18,plain,
( ~ c_lessequals(c_0,X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| c_HOL_Oabs(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(c_0_20,negated_conjecture,
~ c_lessequals(v_f(v_x(c_HOL_Oabs(X1,t_b))),c_HOL_Oabs(c_times(X1,v_g(v_x(c_HOL_Oabs(X1,t_b))),t_b),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_21,negated_conjecture,
( ~ c_lessequals(c_0,X1,t_b)
| c_HOL_Oabs(X1,t_b) = X1 ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,plain,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
c_0_19 ).
cnf(c_0_23,negated_conjecture,
c_lessequals(c_0,v_f(X1),t_b),
cls_conjecture_0 ).
cnf(c_0_24,negated_conjecture,
( ~ c_lessequals(c_0,c_times(X1,v_g(v_x(c_HOL_Oabs(X1,t_b))),t_b),t_b)
| ~ c_lessequals(v_f(v_x(c_HOL_Oabs(X1,t_b))),c_times(X1,v_g(v_x(c_HOL_Oabs(X1,t_b))),t_b),t_b) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
c_lessequals(v_f(X1),c_times(v_c,v_g(X1),t_b),t_b),
cls_conjecture_1 ).
cnf(c_0_26,negated_conjecture,
( ~ c_lessequals(v_f(X2),X1,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,X1,t_b) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
~ c_lessequals(c_0,c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,c_times(v_c,v_g(X1),t_b),t_b) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_29,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| class_Orderings_Oorder(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_OrderedGroup_Olordered__ab__group__abs_17]) ).
cnf(c_0_30,negated_conjecture,
~ class_Orderings_Oorder(t_b),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| class_Orderings_Oorder(X1) ),
c_0_29 ).
cnf(c_0_32,negated_conjecture,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_14]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA010-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 13:28:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.46 % Version: 3.5.1
% 0.11/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % Starting sh5l with 300s (1) cores
% 0.11/0.46 % new_bool_1 with pid 2516965 completed with status 0
% 0.11/0.46 % Result found by new_bool_1
% 0.11/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.46 % Search class: FHUSS-FFSF31-MFFFFFNN
% 0.11/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.46 % SubtermCWHack with pid 2516971 completed with status 0
% 0.11/0.46 % Result found by SubtermCWHack
% 0.11/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.46 % Search class: FHUSS-FFSF31-MFFFFFNN
% 0.11/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.46 % Preprocessing time : 0.001 s
% 0.11/0.46
% 0.11/0.46 % Proof found!
% 0.11/0.46 % SZS status Unsatisfiable
% 0.11/0.46 % SZS output start CNFRefutation
% See solution above
% 0.11/0.46 % Parsed axioms : 9
% 0.11/0.46 % Removed by relevancy pruning/SinE : 0
% 0.11/0.46 % Initial clauses : 9
% 0.11/0.46 % Removed in clause preprocessing : 0
% 0.11/0.46 % Initial clauses in saturation : 9
% 0.11/0.46 % Processed clauses : 25
% 0.11/0.46 % ...of these trivial : 0
% 0.11/0.46 % ...subsumed : 0
% 0.11/0.46 % ...remaining for further processing : 25
% 0.11/0.46 % Other redundant clauses eliminated : 0
% 0.11/0.46 % Clauses deleted for lack of memory : 0
% 0.11/0.46 % Backward-subsumed : 4
% 0.11/0.46 % Backward-rewritten : 0
% 0.11/0.46 % Generated clauses : 33
% 0.11/0.46 % ...of the previous two non-redundant : 32
% 0.11/0.46 % ...aggressively subsumed : 0
% 0.11/0.46 % Contextual simplify-reflections : 0
% 0.11/0.46 % Paramodulations : 33
% 0.11/0.46 % Factorizations : 0
% 0.11/0.46 % NegExts : 0
% 0.11/0.46 % Equation resolutions : 0
% 0.11/0.46 % Disequality decompositions : 0
% 0.11/0.46 % Total rewrite steps : 6
% 0.11/0.46 % ...of those cached : 5
% 0.11/0.46 % Propositional unsat checks : 0
% 0.11/0.46 % Propositional check models : 0
% 0.11/0.46 % Propositional check unsatisfiable : 0
% 0.11/0.46 % Propositional clauses : 0
% 0.11/0.46 % Propositional clauses after purity: 0
% 0.11/0.46 % Propositional unsat core size : 0
% 0.11/0.46 % Propositional preprocessing time : 0.000
% 0.11/0.46 % Propositional encoding time : 0.000
% 0.11/0.46 % Propositional solver time : 0.000
% 0.11/0.46 % Success case prop preproc time : 0.000
% 0.11/0.46 % Success case prop encoding time : 0.000
% 0.11/0.46 % Success case prop solver time : 0.000
% 0.11/0.46 % Current number of processed clauses : 21
% 0.11/0.46 % Positive orientable unit clauses : 3
% 0.11/0.46 % Positive unorientable unit clauses: 0
% 0.11/0.46 % Negative unit clauses : 6
% 0.11/0.46 % Non-unit-clauses : 12
% 0.11/0.46 % Current number of unprocessed clauses: 16
% 0.11/0.46 % ...number of literals in the above : 40
% 0.11/0.46 % Current number of archived formulas : 0
% 0.11/0.46 % Current number of archived clauses : 4
% 0.11/0.46 % Clause-clause subsumption calls (NU) : 12
% 0.11/0.46 % Rec. Clause-clause subsumption calls : 12
% 0.11/0.46 % Non-unit clause-clause subsumptions : 0
% 0.11/0.46 % Unit Clause-clause subsumption calls : 21
% 0.11/0.46 % Rewrite failures with RHS unbound : 0
% 0.11/0.46 % BW rewrite match attempts : 0
% 0.11/0.46 % BW rewrite match successes : 0
% 0.11/0.46 % Condensation attempts : 0
% 0.11/0.46 % Condensation successes : 0
% 0.11/0.46 % Termbank termtop insertions : 1016
% 0.11/0.46 % Search garbage collected termcells : 20
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.004 s
% 0.11/0.46 % System time : 0.001 s
% 0.11/0.46 % Total time : 0.006 s
% 0.11/0.46 % Maximum resident set size: 3896 pages
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.008 s
% 0.11/0.46 % System time : 0.004 s
% 0.11/0.46 % Total time : 0.012 s
% 0.11/0.46 % Maximum resident set size: 4608 pages
% 0.11/0.46 % E exiting
%------------------------------------------------------------------------------