%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA018-2 : 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 12:02:46 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.78s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 45 ( 14 unt; 0 nHn; 38 RR)
% Number of literals : 95 ( 3 equ; 57 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 66 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( ~ class_LOrder_Ojoin__semilorder(X1)
| class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_LOrder_Ojoin__semilorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
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_2,negated_conjecture,
c_less(c_0,v_ca,t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_OrderedGroup_Omult__ac__1_0,axiom,
( ~ class_OrderedGroup_Osemigroup__mult(X1)
| c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
cnf(cls_conjecture_3,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_x(X1),t_b),c_times(v_ca,c_HOL_Oabs(v_f(X1),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
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(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(X1),t_b),c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
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(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
cnf(c_0_13,plain,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_Orderings_Oorder__less__imp__le_0]) ).
cnf(c_0_14,plain,
( ~ class_LOrder_Ojoin__semilorder(X1)
| class_Orderings_Oorder(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
cnf(c_0_15,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_LOrder_Ojoin__semilorder(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_35]) ).
cnf(c_0_16,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_17,plain,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
c_0_13 ).
cnf(c_0_18,negated_conjecture,
c_less(c_0,v_ca,t_b),
cls_conjecture_2 ).
cnf(c_0_19,plain,
( ~ class_LOrder_Ojoin__semilorder(X1)
| class_Orderings_Oorder(X1) ),
c_0_14 ).
cnf(c_0_20,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_LOrder_Ojoin__semilorder(X1) ),
c_0_15 ).
cnf(c_0_21,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(fof_simplification,[status(thm)],[cls_conjecture_4]) ).
cnf(c_0_22,plain,
( ~ class_OrderedGroup_Osemigroup__mult(X1)
| c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Omult__ac__1_0]) ).
cnf(c_0_23,plain,
( ~ c_lessequals(X4,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X3,X1) ),
c_0_16 ).
cnf(c_0_24,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_x(X1),t_b),c_times(v_ca,c_HOL_Oabs(v_f(X1),t_b),t_b),t_b),
cls_conjecture_3 ).
cnf(c_0_25,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_26,negated_conjecture,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,v_ca,t_b) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_27,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_29,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
c_0_21 ).
cnf(c_0_30,plain,
( ~ class_OrderedGroup_Osemigroup__mult(X1)
| c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) ),
c_0_22 ).
cnf(c_0_31,negated_conjecture,
( ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(X1),t_b),t_b),X2,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_HOL_Oabs(v_x(X1),t_b),X2,t_b) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,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_25 ).
cnf(c_0_33,negated_conjecture,
c_lessequals(c_0,v_ca,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_34,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_f(X1),t_b),X2,t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_HOL_Oabs(v_x(X1),t_b),c_times(v_ca,X2,t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(X1),t_b),c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),
cls_conjecture_1 ).
cnf(c_0_37,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_38,negated_conjecture,
( ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__semiring(X1) ),
c_0_37 ).
cnf(c_0_40,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_21]) ).
cnf(c_0_41,negated_conjecture,
( ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_28])]) ).
cnf(c_0_42,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Osemigroup__mult(X1) ),
c_0_40 ).
cnf(c_0_43,negated_conjecture,
~ class_Orderings_Oorder(t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_28])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA018-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.65 % Computer : n008.cluster.edu
% 0.16/0.65 % Model : x86_64 x86_64
% 0.16/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.65 % Memory : 8046.5625MB
% 0.16/0.65 % OS : Linux 6.8.0-71-generic
% 0.16/0.65 % CPULimit : 300
% 0.16/0.65 % WCLimit : 300
% 0.16/0.65 % DateTime : Mon Sep 21 13:24:25 UTC 2026
% 0.16/0.65 % CPUTime :
% 0.16/0.65 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.72 Running first-order theorem proving
% 0.21/0.72 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
% 0.21/0.78 % Version: 3.5.1
% 0.21/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.78 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.78 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.78 % Starting sh5l with 300s (1) cores
% 0.21/0.78 % sh5l with pid 1079082 completed with status 0
% 0.21/0.78 % Result found by sh5l
% 0.21/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.78 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.78 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.78 % Starting sh5l with 300s (1) cores
% 0.21/0.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.21/0.78 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.78 % Search class: FHUSS-FFSF31-MFFFFFNN
% 0.21/0.78 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.78 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.78 % SubtermCWHack with pid 1079087 completed with status 0
% 0.21/0.78 % Result found by SubtermCWHack
% 0.21/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.78 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.78 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.78 % Starting sh5l with 300s (1) cores
% 0.21/0.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.21/0.78 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.78 % Search class: FHUSS-FFSF31-MFFFFFNN
% 0.21/0.78 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.78 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.78 % Preprocessing time : 0.002 s
% 0.21/0.78
% 0.21/0.78 % Proof found!
% 0.21/0.78 % SZS status Unsatisfiable
% 0.21/0.78 % SZS output start CNFRefutation
% See solution above
% 0.21/0.78 % Parsed axioms : 13
% 0.21/0.78 % Removed by relevancy pruning/SinE : 0
% 0.21/0.78 % Initial clauses : 13
% 0.21/0.78 % Removed in clause preprocessing : 0
% 0.21/0.78 % Initial clauses in saturation : 13
% 0.21/0.78 % Processed clauses : 27
% 0.21/0.78 % ...of these trivial : 0
% 0.21/0.78 % ...subsumed : 0
% 0.21/0.78 % ...remaining for further processing : 27
% 0.21/0.78 % Other redundant clauses eliminated : 0
% 0.21/0.78 % Clauses deleted for lack of memory : 0
% 0.21/0.78 % Backward-subsumed : 7
% 0.21/0.78 % Backward-rewritten : 1
% 0.21/0.78 % Generated clauses : 21
% 0.21/0.78 % ...of the previous two non-redundant : 20
% 0.21/0.78 % ...aggressively subsumed : 0
% 0.21/0.78 % Contextual simplify-reflections : 0
% 0.21/0.78 % Paramodulations : 21
% 0.21/0.78 % Factorizations : 0
% 0.21/0.78 % NegExts : 0
% 0.21/0.78 % Equation resolutions : 0
% 0.21/0.78 % Disequality decompositions : 0
% 0.21/0.78 % Total rewrite steps : 9
% 0.21/0.78 % ...of those cached : 6
% 0.21/0.78 % Propositional unsat checks : 0
% 0.21/0.78 % Propositional check models : 0
% 0.21/0.78 % Propositional check unsatisfiable : 0
% 0.21/0.78 % Propositional clauses : 0
% 0.21/0.78 % Propositional clauses after purity: 0
% 0.21/0.78 % Propositional unsat core size : 0
% 0.21/0.78 % Propositional preprocessing time : 0.000
% 0.21/0.78 % Propositional encoding time : 0.000
% 0.21/0.78 % Propositional solver time : 0.000
% 0.21/0.78 % Success case prop preproc time : 0.000
% 0.21/0.78 % Success case prop encoding time : 0.000
% 0.21/0.78 % Success case prop solver time : 0.000
% 0.21/0.78 % Current number of processed clauses : 19
% 0.21/0.78 % Positive orientable unit clauses : 5
% 0.21/0.78 % Positive unorientable unit clauses: 0
% 0.21/0.78 % Negative unit clauses : 2
% 0.21/0.78 % Non-unit-clauses : 12
% 0.21/0.78 % Current number of unprocessed clauses: 6
% 0.21/0.78 % ...number of literals in the above : 28
% 0.21/0.78 % Current number of archived formulas : 0
% 0.21/0.78 % Current number of archived clauses : 8
% 0.21/0.78 % Clause-clause subsumption calls (NU) : 161
% 0.21/0.78 % Rec. Clause-clause subsumption calls : 139
% 0.21/0.78 % Non-unit clause-clause subsumptions : 3
% 0.21/0.78 % Unit Clause-clause subsumption calls : 4
% 0.21/0.78 % Rewrite failures with RHS unbound : 0
% 0.21/0.78 % BW rewrite match attempts : 1
% 0.21/0.78 % BW rewrite match successes : 1
% 0.21/0.78 % Condensation attempts : 0
% 0.21/0.78 % Condensation successes : 0
% 0.21/0.78 % Termbank termtop insertions : 849
% 0.21/0.78 % Search garbage collected termcells : 28
% 0.21/0.78
% 0.21/0.78 % -------------------------------------------------
% 0.21/0.78 % User time : 0.007 s
% 0.21/0.78 % System time : 0.003 s
% 0.21/0.78 % Total time : 0.010 s
% 0.21/0.78 % Maximum resident set size: 3644 pages
% 0.21/0.78
% 0.21/0.78 % -------------------------------------------------
% 0.21/0.78 % User time : 0.010 s
% 0.21/0.78 % System time : 0.009 s
% 0.21/0.78 % Total time : 0.018 s
% 0.21/0.78 % Maximum resident set size: 4608 pages
% 0.21/0.78 % E exiting
%------------------------------------------------------------------------------