%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA010-1 : 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 : n009.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 12:02:44 PM UTC 2026
% Result : Unsatisfiable 14.46s 2.74s
% Output : CNFRefutation 14.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 42 ( 19 unt; 0 nHn; 23 RR)
% Number of literals : 74 ( 13 equ; 36 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 1 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 : 64 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
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/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(cls_OrderedGroup_Oabs__idempotent_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_HOL_Oabs(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__idempotent_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_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/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_44,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_44) ).
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_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/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__of__nonneg_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_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(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_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(c_0_11,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_12,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_HOL_Oabs(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__idempotent_0]) ).
cnf(c_0_13,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
c_0_11 ).
cnf(c_0_14,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_15,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_16,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_HOL_Oabs(X2,X1),X1) = c_HOL_Oabs(X2,X1) ),
c_0_12 ).
cnf(c_0_17,negated_conjecture,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]) ).
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,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
c_0_15 ).
cnf(c_0_21,negated_conjecture,
c_HOL_Oabs(c_HOL_Oabs(X1,t_b),t_b) = c_HOL_Oabs(X1,t_b),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
c_0_18 ).
cnf(c_0_23,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_24,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_25,negated_conjecture,
c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_17])]) ).
cnf(c_0_26,negated_conjecture,
class_Orderings_Oorder(t_b),
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_27,plain,
( ~ c_lessequals(c_0,X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X2,X1) = X2 ),
c_0_23 ).
cnf(c_0_28,negated_conjecture,
c_lessequals(c_0,v_f(X1),t_b),
cls_conjecture_0 ).
cnf(c_0_29,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_30,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(X2,t_b),X1,t_b)
| c_lessequals(c_0,X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_31,negated_conjecture,
c_HOL_Oabs(v_f(X1),t_b) = v_f(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_17])]) ).
cnf(c_0_32,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_33,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_29 ).
cnf(c_0_34,negated_conjecture,
( ~ c_lessequals(v_f(X2),X1,t_b)
| c_lessequals(c_0,X1,t_b) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
c_lessequals(v_f(X1),c_times(v_c,v_g(X1),t_b),t_b),
cls_conjecture_1 ).
cnf(c_0_36,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_32 ).
cnf(c_0_37,negated_conjecture,
c_times(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(X2,t_b),t_b) = c_HOL_Oabs(c_times(X1,X2,t_b),t_b),
inference(spm,[status(thm)],[c_0_33,c_0_14]) ).
cnf(c_0_38,negated_conjecture,
c_lessequals(c_0,c_times(v_c,v_g(X1),t_b),t_b),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,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(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
c_HOL_Oabs(c_times(v_c,v_g(X1),t_b),t_b) = c_times(v_c,v_g(X1),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_38]),c_0_17])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA010-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n009.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 13:23:27 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.50 Running first-order theorem proving
% 0.25/0.50 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
% 14.46/2.74 % Version: 3.5.1
% 14.46/2.74 % Preprocessing class: FMLMSMSMSSSNFFN.
% 14.46/2.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.46/2.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.46/2.74 % Starting new_bool_3 with 300s (1) cores
% 14.46/2.74 % Starting new_bool_1 with 300s (1) cores
% 14.46/2.74 % Starting sh5l with 300s (1) cores
% 14.46/2.74 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1852837 completed with status 0
% 14.46/2.74 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 14.46/2.74 % Preprocessing class: FMLMSMSMSSSNFFN.
% 14.46/2.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.46/2.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.46/2.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.46/2.74 % No SInE strategy applied
% 14.46/2.74 % Search class: FGHSM-SMLM32-DFFFFFNN
% 14.46/2.74 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 14.46/2.74 % Starting SubtermCWHack with 136s (1) cores
% 14.46/2.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.46/2.74 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 14.46/2.74 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 14.46/2.74 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 14.46/2.74 % G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 1852846 completed with status 0
% 14.46/2.74 % Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 14.46/2.74 % Preprocessing class: FMLMSMSMSSSNFFN.
% 14.46/2.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.46/2.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.46/2.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.46/2.74 % No SInE strategy applied
% 14.46/2.74 % Search class: FGHSM-SMLM32-DFFFFFNN
% 14.46/2.74 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 14.46/2.74 % Starting SubtermCWHack with 136s (1) cores
% 14.46/2.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.46/2.74 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 14.46/2.74 % Preprocessing time : 0.041 s
% 14.46/2.74
% 14.46/2.74 % Proof found!
% 14.46/2.74 % SZS status Unsatisfiable
% 14.46/2.74 % SZS output start CNFRefutation
% See solution above
% 14.46/2.74 % Parsed axioms : 2788
% 14.46/2.74 % Removed by relevancy pruning/SinE : 0
% 14.46/2.74 % Initial clauses : 2788
% 14.46/2.74 % Removed in clause preprocessing : 9
% 14.46/2.74 % Initial clauses in saturation : 2779
% 14.46/2.74 % Processed clauses : 7900
% 14.46/2.74 % ...of these trivial : 481
% 14.46/2.74 % ...subsumed : 3578
% 14.46/2.74 % ...remaining for further processing : 3841
% 14.46/2.74 % Other redundant clauses eliminated : 88
% 14.46/2.74 % Clauses deleted for lack of memory : 0
% 14.46/2.74 % Backward-subsumed : 17
% 14.46/2.74 % Backward-rewritten : 163
% 14.46/2.74 % Generated clauses : 29251
% 14.46/2.74 % ...of the previous two non-redundant : 23872
% 14.46/2.74 % ...aggressively subsumed : 0
% 14.46/2.74 % Contextual simplify-reflections : 6
% 14.46/2.74 % Paramodulations : 29099
% 14.46/2.74 % Factorizations : 7
% 14.46/2.74 % NegExts : 0
% 14.46/2.74 % Equation resolutions : 145
% 14.46/2.74 % Disequality decompositions : 0
% 14.46/2.74 % Total rewrite steps : 20010
% 14.46/2.74 % ...of those cached : 18132
% 14.46/2.74 % Propositional unsat checks : 0
% 14.46/2.74 % Propositional check models : 0
% 14.46/2.74 % Propositional check unsatisfiable : 0
% 14.46/2.74 % Propositional clauses : 0
% 14.46/2.74 % Propositional clauses after purity: 0
% 14.46/2.74 % Propositional unsat core size : 0
% 14.46/2.74 % Propositional preprocessing time : 0.000
% 14.46/2.74 % Propositional encoding time : 0.000
% 14.46/2.74 % Propositional solver time : 0.000
% 14.46/2.74 % Success case prop preproc time : 0.000
% 14.46/2.74 % Success case prop encoding time : 0.000
% 14.46/2.74 % Success case prop solver time : 0.000
% 14.46/2.74 % Current number of processed clauses : 3661
% 14.46/2.74 % Positive orientable unit clauses : 956
% 14.46/2.74 % Positive unorientable unit clauses: 8
% 14.46/2.74 % Negative unit clauses : 78
% 14.46/2.74 % Non-unit-clauses : 2619
% 14.46/2.74 % Current number of unprocessed clauses: 18387
% 14.46/2.74 % ...number of literals in the above : 40695
% 14.46/2.74 % Current number of archived formulas : 0
% 14.46/2.74 % Current number of archived clauses : 188
% 14.46/2.74 % Clause-clause subsumption calls (NU) : 2798541
% 14.46/2.74 % Rec. Clause-clause subsumption calls : 1992696
% 14.46/2.74 % Non-unit clause-clause subsumptions : 3277
% 14.46/2.74 % Unit Clause-clause subsumption calls : 157135
% 14.46/2.74 % Rewrite failures with RHS unbound : 0
% 14.46/2.74 % BW rewrite match attempts : 2258
% 14.46/2.74 % BW rewrite match successes : 77
% 14.46/2.74 % Condensation attempts : 0
% 14.46/2.74 % Condensation successes : 0
% 14.46/2.74 % Termbank termtop insertions : 543541
% 14.46/2.74 % Search garbage collected termcells : 4071
% 14.46/2.74
% 14.46/2.74 % -------------------------------------------------
% 14.46/2.74 % User time : 2.012 s
% 14.46/2.74 % System time : 0.067 s
% 14.46/2.74 % Total time : 2.078 s
% 14.46/2.74 % Maximum resident set size: 8504 pages
% 14.46/2.74
% 14.46/2.74 % -------------------------------------------------
% 14.46/2.74 % User time : 9.854 s
% 14.46/2.74 % System time : 0.278 s
% 14.46/2.74 % Total time : 10.132 s
% 14.46/2.74 % Maximum resident set size: 6656 pages
% 14.46/2.74 % E exiting
%------------------------------------------------------------------------------