%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA043-2 : 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 : 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 12:02:52 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.65s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 9 unt; 0 nHn; 24 RR)
% Number of literals : 68 ( 3 equ; 44 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
( ~ c_lessequals(c_0,X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
cnf(cls_OrderedGroup_Omult__left__commute_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| c_times(X2,c_times(X3,X4,X1),X1) = c_times(X3,c_times(X2,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__left__commute_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(X1),v_xa(X1)),t_b),c_HOL_Oabs(v_f(v_k(v_x(X1),v_xa(X1))),t_b),t_b),c_times(X1,c_times(c_HOL_Oabs(v_l(v_x(X1),v_xa(X1)),t_b),c_HOL_Oabs(v_h(v_k(v_x(X1),v_xa(X1))),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(X1),t_b),c_times(v_c,c_HOL_Oabs(v_h(X1),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__semiring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
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_17,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__semigroup__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
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(c_0_9,plain,
( ~ c_lessequals(c_0,X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0]) ).
cnf(c_0_10,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| c_times(X2,c_times(X3,X4,X1),X1) = c_times(X3,c_times(X2,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Omult__left__commute_0]) ).
cnf(c_0_11,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(X1),v_xa(X1)),t_b),c_HOL_Oabs(v_f(v_k(v_x(X1),v_xa(X1))),t_b),t_b),c_times(X1,c_times(c_HOL_Oabs(v_l(v_x(X1),v_xa(X1)),t_b),c_HOL_Oabs(v_h(v_k(v_x(X1),v_xa(X1))),t_b),t_b),t_b),t_b),
inference(fof_simplification,[status(thm)],[cls_conjecture_1]) ).
cnf(c_0_12,plain,
( ~ c_lessequals(c_0,X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1) ),
c_0_9 ).
cnf(c_0_13,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| c_times(X2,c_times(X3,X4,X1),X1) = c_times(X3,c_times(X2,X4,X1),X1) ),
c_0_10 ).
cnf(c_0_14,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(X1),v_xa(X1)),t_b),c_HOL_Oabs(v_f(v_k(v_x(X1),v_xa(X1))),t_b),t_b),c_times(X1,c_times(c_HOL_Oabs(v_l(v_x(X1),v_xa(X1)),t_b),c_HOL_Oabs(v_h(v_k(v_x(X1),v_xa(X1))),t_b),t_b),t_b),t_b),
c_0_11 ).
cnf(c_0_15,plain,
( ~ c_lessequals(c_0,X1,X3)
| ~ c_lessequals(X2,c_times(X4,X5,X3),X3)
| ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3)
| c_lessequals(c_times(X1,X2,X3),c_times(X4,c_times(X1,X5,X3),X3),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(X1),v_xa(X1)),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_k(v_x(X1),v_xa(X1))),t_b),c_times(X1,c_HOL_Oabs(v_h(v_k(v_x(X1),v_xa(X1))),t_b),t_b),t_b)
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(X1),t_b),c_times(v_c,c_HOL_Oabs(v_h(X1),t_b),t_b),t_b),
cls_conjecture_0 ).
cnf(c_0_18,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c_0_19,negated_conjecture,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b)
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
c_0_18 ).
cnf(c_0_21,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__semiring(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_42]) ).
cnf(c_0_22,negated_conjecture,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__semiring(X1) ),
c_0_21 ).
cnf(c_0_24,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_25,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_17]) ).
cnf(c_0_26,negated_conjecture,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_27,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Oab__semigroup__mult(X1) ),
c_0_25 ).
cnf(c_0_28,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_29,negated_conjecture,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24])]) ).
cnf(c_0_30,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
c_0_28 ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA043-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.58 % Computer : n008.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Mon Sep 21 13:26:39 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.63 Running first-order theorem proving
% 0.15/0.63 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
% 0.15/0.65 % Version: 3.5.1
% 0.15/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.65 % Starting sh5l with 300s (1) cores
% 0.15/0.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1083546 completed with status 0
% 0.15/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.65 % No SInE strategy applied
% 0.15/0.65 % Search class: FHUSF-FFSF31-DFFFFFNN
% 0.15/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.65 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.65 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.65 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 1083554 completed with status 0
% 0.15/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.15/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.65 % No SInE strategy applied
% 0.15/0.65 % Search class: FHUSF-FFSF31-DFFFFFNN
% 0.15/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.65 % Preprocessing time : 0.001 s
% 0.15/0.65 % Presaturation interreduction done
% 0.15/0.65
% 0.15/0.65 % Proof found!
% 0.15/0.65 % SZS status Unsatisfiable
% 0.15/0.65 % SZS output start CNFRefutation
% See solution above
% 0.15/0.65 % Parsed axioms : 9
% 0.15/0.65 % Removed by relevancy pruning/SinE : 0
% 0.15/0.65 % Initial clauses : 9
% 0.15/0.65 % Removed in clause preprocessing : 0
% 0.15/0.65 % Initial clauses in saturation : 9
% 0.15/0.65 % Processed clauses : 24
% 0.15/0.65 % ...of these trivial : 0
% 0.15/0.65 % ...subsumed : 0
% 0.15/0.65 % ...remaining for further processing : 24
% 0.15/0.65 % Other redundant clauses eliminated : 0
% 0.15/0.65 % Clauses deleted for lack of memory : 0
% 0.15/0.65 % Backward-subsumed : 2
% 0.15/0.65 % Backward-rewritten : 0
% 0.15/0.65 % Generated clauses : 20
% 0.15/0.65 % ...of the previous two non-redundant : 19
% 0.15/0.65 % ...aggressively subsumed : 0
% 0.15/0.65 % Contextual simplify-reflections : 0
% 0.15/0.65 % Paramodulations : 20
% 0.15/0.65 % Factorizations : 0
% 0.15/0.65 % NegExts : 0
% 0.15/0.65 % Equation resolutions : 0
% 0.15/0.65 % Disequality decompositions : 0
% 0.15/0.65 % Total rewrite steps : 3
% 0.15/0.65 % ...of those cached : 2
% 0.15/0.65 % Propositional unsat checks : 0
% 0.15/0.65 % Propositional check models : 0
% 0.15/0.65 % Propositional check unsatisfiable : 0
% 0.15/0.65 % Propositional clauses : 0
% 0.15/0.65 % Propositional clauses after purity: 0
% 0.15/0.65 % Propositional unsat core size : 0
% 0.15/0.65 % Propositional preprocessing time : 0.000
% 0.15/0.65 % Propositional encoding time : 0.000
% 0.15/0.65 % Propositional solver time : 0.000
% 0.15/0.65 % Success case prop preproc time : 0.000
% 0.15/0.65 % Success case prop encoding time : 0.000
% 0.15/0.65 % Success case prop solver time : 0.000
% 0.15/0.65 % Current number of processed clauses : 13
% 0.15/0.65 % Positive orientable unit clauses : 2
% 0.15/0.65 % Positive unorientable unit clauses: 0
% 0.15/0.65 % Negative unit clauses : 2
% 0.15/0.65 % Non-unit-clauses : 9
% 0.15/0.65 % Current number of unprocessed clauses: 13
% 0.15/0.65 % ...number of literals in the above : 53
% 0.15/0.65 % Current number of archived formulas : 0
% 0.15/0.65 % Current number of archived clauses : 11
% 0.15/0.65 % Clause-clause subsumption calls (NU) : 20
% 0.15/0.65 % Rec. Clause-clause subsumption calls : 10
% 0.15/0.65 % Non-unit clause-clause subsumptions : 1
% 0.15/0.65 % Unit Clause-clause subsumption calls : 3
% 0.15/0.65 % Rewrite failures with RHS unbound : 0
% 0.15/0.65 % BW rewrite match attempts : 0
% 0.15/0.65 % BW rewrite match successes : 0
% 0.15/0.65 % Condensation attempts : 0
% 0.15/0.65 % Condensation successes : 0
% 0.15/0.65 % Termbank termtop insertions : 861
% 0.15/0.65 % Search garbage collected termcells : 19
% 0.15/0.65
% 0.15/0.65 % -------------------------------------------------
% 0.15/0.65 % User time : 0.006 s
% 0.15/0.65 % System time : 0.002 s
% 0.15/0.65 % Total time : 0.008 s
% 0.15/0.65 % Maximum resident set size: 3644 pages
% 0.15/0.65
% 0.15/0.65 % -------------------------------------------------
% 0.15/0.65 % User time : 0.018 s
% 0.15/0.65 % System time : 0.014 s
% 0.15/0.65 % Total time : 0.032 s
% 0.15/0.65 % Maximum resident set size: 4864 pages
% 0.15/0.65 % E exiting
%------------------------------------------------------------------------------