%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 0.18s 10.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 53 ( 15 unt; 2 nHn; 46 RR)
% Number of literals : 100 ( 13 equ; 53 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 52 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_NatBin_OSuc__pred_H_0,axiom,
( ~ c_less(c_0,X1,tc_nat)
| X1 = c_Suc(c_minus(X1,c_1,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ c_less(c_0,X1,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X1)),t_a),c_times(X1,c_HOL_Oabs(v_h(v_xa(X1)),t_a),t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(c_Suc(X1)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(X1)),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_OrderedGroup_Oabs__eq__0_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_0,X1) = c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
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/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(cls_conjecture_1,negated_conjecture,
c_less(c_0,v_x,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
cnf(cls_Nat_Onot__gr0_0,axiom,
( X1 = c_0
| c_less(c_0,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_conjecture_0,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
( ~ c_lessequals(c_0,X3,X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_lessequals(c_0,c_times(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
cnf(c_0_15,plain,
( ~ c_less(c_0,X1,tc_nat)
| X1 = c_Suc(c_minus(X1,c_1,tc_nat)) ),
inference(fof_simplification,[status(thm)],[cls_NatBin_OSuc__pred_H_0]) ).
cnf(c_0_16,negated_conjecture,
( ~ c_less(c_0,X1,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X1)),t_a),c_times(X1,c_HOL_Oabs(v_h(v_xa(X1)),t_a),t_a),t_a) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_3]) ).
cnf(c_0_17,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(c_Suc(X1)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(X1)),t_a),t_a),t_a),
cls_conjecture_2 ).
cnf(c_0_18,plain,
( ~ c_less(c_0,X1,tc_nat)
| X1 = c_Suc(c_minus(X1,c_1,tc_nat)) ),
c_0_15 ).
cnf(c_0_19,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_0,X1) = c_0 ),
inference(fof_simplification,[status(thm)],[cls_OrderedGroup_Oabs__eq__0_1]) ).
cnf(c_0_20,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_21,negated_conjecture,
( ~ c_less(c_0,X1,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X1)),t_a),c_times(X1,c_HOL_Oabs(v_h(v_xa(X1)),t_a),t_a),t_a) ),
c_0_16 ).
cnf(c_0_22,negated_conjecture,
( ~ c_less(c_0,X1,tc_nat)
| c_lessequals(c_HOL_Oabs(v_f(X1),t_a),c_times(v_x,c_HOL_Oabs(v_h(X1),t_a),t_a),t_a) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
c_less(c_0,v_x,t_a),
cls_conjecture_1 ).
cnf(c_0_24,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(c_0,X1) = c_0 ),
c_0_19 ).
cnf(c_0_25,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
c_0_20 ).
cnf(c_0_26,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_27,plain,
( ~ class_LOrder_Ojoin__semilorder(X1)
| class_Orderings_Oorder(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
cnf(c_0_28,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_29,negated_conjecture,
~ c_less(c_0,v_xa(v_x),tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_30,axiom,
( X1 = c_0
| c_less(c_0,X1,tc_nat) ),
cls_Nat_Onot__gr0_0 ).
cnf(c_0_31,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs(c_0,X1) = c_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
tfree_tcs ).
cnf(c_0_33,plain,
( ~ c_less(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
c_0_26 ).
cnf(c_0_34,plain,
( ~ class_LOrder_Ojoin__semilorder(X1)
| class_Orderings_Oorder(X1) ),
c_0_27 ).
cnf(c_0_35,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_LOrder_Ojoin__semilorder(X1) ),
c_0_28 ).
cnf(c_0_36,negated_conjecture,
v_xa(v_x) = c_0,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
v_f(c_0) = c_0,
cls_conjecture_0 ).
cnf(c_0_38,negated_conjecture,
c_HOL_Oabs(c_0,t_a) = c_0,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
( ~ c_lessequals(c_0,X3,X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_lessequals(c_0,c_times(X3,X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_Ring__and__Field_Omult__nonneg__nonneg_0]) ).
cnf(c_0_40,negated_conjecture,
( ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_x,t_a) ),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_41,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_36]),c_0_37]),c_0_38]),c_0_23])]) ).
cnf(c_0_43,plain,
( ~ c_lessequals(c_0,X3,X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_lessequals(c_0,c_times(X3,X2,X1),X1) ),
c_0_39 ).
cnf(c_0_44,negated_conjecture,
c_lessequals(c_0,v_x,t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_32])]) ).
cnf(c_0_45,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_46,negated_conjecture,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_47,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
c_0_45 ).
cnf(c_0_48,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_40]) ).
cnf(c_0_49,negated_conjecture,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_48 ).
cnf(c_0_51,negated_conjecture,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_32])]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_25]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/10.40 % Computer : n014.cluster.edu
% 0.14/10.40 % Model : x86_64 x86_64
% 0.14/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.40 % Memory : 8046.5625MB
% 0.14/10.40 % OS : Linux 6.8.0-71-generic
% 0.14/10.40 % CPULimit : 300
% 0.14/10.40 % WCLimit : 300
% 0.14/10.40 % DateTime : Mon Sep 21 13:24:15 UTC 2026
% 0.14/10.40 % CPUTime :
% 0.14/10.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/10.46 Running first-order theorem proving
% 0.14/10.46 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.18/10.51 % Version: 3.5.1
% 0.18/10.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/10.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/10.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/10.51 % Starting new_bool_3 with 300s (1) cores
% 0.18/10.51 % Starting new_bool_1 with 300s (1) cores
% 0.18/10.51 % Starting sh5l with 300s (1) cores
% 0.18/10.51 % sh5l with pid 4157622 completed with status 0
% 0.18/10.51 % Result found by sh5l
% 0.18/10.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/10.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/10.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/10.51 % Starting new_bool_3 with 300s (1) cores
% 0.18/10.51 % Starting new_bool_1 with 300s (1) cores
% 0.18/10.51 % Starting sh5l with 300s (1) cores
% 0.18/10.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.18/10.51 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.18/10.51 % Search class: FGHSF-FFSS31-MFFFFFNN
% 0.18/10.51 % partial match(1): FGHSF-FFSS31-DFFFFFNN
% 0.18/10.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.18/10.51 % Starting SubtermCWHack with 31s (1) cores
% 0.18/10.51 % SubtermCWHack with pid 4157628 completed with status 0
% 0.18/10.51 % Result found by SubtermCWHack
% 0.18/10.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/10.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/10.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/10.51 % Starting new_bool_3 with 300s (1) cores
% 0.18/10.51 % Starting new_bool_1 with 300s (1) cores
% 0.18/10.51 % Starting sh5l with 300s (1) cores
% 0.18/10.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.18/10.51 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.18/10.51 % Search class: FGHSF-FFSS31-MFFFFFNN
% 0.18/10.51 % partial match(1): FGHSF-FFSS31-DFFFFFNN
% 0.18/10.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.18/10.51 % Starting SubtermCWHack with 31s (1) cores
% 0.18/10.51 % Preprocessing time : 0.001 s
% 0.18/10.51
% 0.18/10.51 % Proof found!
% 0.18/10.51 % SZS status Unsatisfiable
% 0.18/10.51 % SZS output start CNFRefutation
% See solution above
% 0.18/10.51 % Parsed axioms : 15
% 0.18/10.51 % Removed by relevancy pruning/SinE : 0
% 0.18/10.51 % Initial clauses : 15
% 0.18/10.51 % Removed in clause preprocessing : 0
% 0.18/10.51 % Initial clauses in saturation : 15
% 0.18/10.51 % Processed clauses : 34
% 0.18/10.51 % ...of these trivial : 0
% 0.18/10.51 % ...subsumed : 1
% 0.18/10.51 % ...remaining for further processing : 33
% 0.18/10.51 % Other redundant clauses eliminated : 0
% 0.18/10.51 % Clauses deleted for lack of memory : 0
% 0.18/10.51 % Backward-subsumed : 2
% 0.18/10.51 % Backward-rewritten : 3
% 0.18/10.51 % Generated clauses : 19
% 0.18/10.51 % ...of the previous two non-redundant : 19
% 0.18/10.51 % ...aggressively subsumed : 0
% 0.18/10.51 % Contextual simplify-reflections : 0
% 0.18/10.51 % Paramodulations : 19
% 0.18/10.51 % Factorizations : 0
% 0.18/10.51 % NegExts : 0
% 0.18/10.51 % Equation resolutions : 0
% 0.18/10.51 % Disequality decompositions : 0
% 0.18/10.51 % Total rewrite steps : 13
% 0.18/10.51 % ...of those cached : 6
% 0.18/10.51 % Propositional unsat checks : 0
% 0.18/10.51 % Propositional check models : 0
% 0.18/10.51 % Propositional check unsatisfiable : 0
% 0.18/10.51 % Propositional clauses : 0
% 0.18/10.51 % Propositional clauses after purity: 0
% 0.18/10.51 % Propositional unsat core size : 0
% 0.18/10.51 % Propositional preprocessing time : 0.000
% 0.18/10.51 % Propositional encoding time : 0.000
% 0.18/10.51 % Propositional solver time : 0.000
% 0.18/10.51 % Success case prop preproc time : 0.000
% 0.18/10.51 % Success case prop encoding time : 0.000
% 0.18/10.51 % Success case prop solver time : 0.000
% 0.18/10.51 % Current number of processed clauses : 28
% 0.18/10.51 % Positive orientable unit clauses : 8
% 0.18/10.51 % Positive unorientable unit clauses: 0
% 0.18/10.51 % Negative unit clauses : 3
% 0.18/10.51 % Non-unit-clauses : 17
% 0.18/10.51 % Current number of unprocessed clauses: 0
% 0.18/10.51 % ...number of literals in the above : 0
% 0.18/10.51 % Current number of archived formulas : 0
% 0.18/10.51 % Current number of archived clauses : 5
% 0.18/10.51 % Clause-clause subsumption calls (NU) : 61
% 0.18/10.51 % Rec. Clause-clause subsumption calls : 58
% 0.18/10.51 % Non-unit clause-clause subsumptions : 1
% 0.18/10.51 % Unit Clause-clause subsumption calls : 15
% 0.18/10.51 % Rewrite failures with RHS unbound : 0
% 0.18/10.51 % BW rewrite match attempts : 3
% 0.18/10.51 % BW rewrite match successes : 3
% 0.18/10.51 % Condensation attempts : 0
% 0.18/10.51 % Condensation successes : 0
% 0.18/10.51 % Termbank termtop insertions : 707
% 0.18/10.51 % Search garbage collected termcells : 30
% 0.18/10.51
% 0.18/10.51 % -------------------------------------------------
% 0.18/10.51 % User time : 0.003 s
% 0.18/10.51 % System time : 0.002 s
% 0.18/10.51 % Total time : 0.005 s
% 0.18/10.51 % Maximum resident set size: 3648 pages
% 0.18/10.51
% 0.18/10.51 % -------------------------------------------------
% 0.18/10.51 % User time : 0.004 s
% 0.18/10.51 % System time : 0.010 s
% 0.18/10.51 % Total time : 0.014 s
% 0.18/10.51 % Maximum resident set size: 4864 pages
% 0.18/10.51 % E exiting
%------------------------------------------------------------------------------