%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:02:47 PM UTC 2026
% Result : Unsatisfiable 0.16s 5.60s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 16 RR)
% Number of literals : 39 ( 38 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 52 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Orderings_Olinorder(X1),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Ocomm__monoid__add(X1),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(clsrel_Orderings_Olinorder_4,axiom,
ifeq(class_Orderings_Olinorder(X1),true,class_Orderings_Oorder(X1),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Opordered__ab__group__add(X1),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(X1),true,c_plus(c_0,X2,X1),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(ifeq_axiom,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
ifeq(class_Orderings_Oorder(X1),true,ifeq(c_lessequals(X2,X3,X1),true,ifeq(c_lessequals(X3,X4,X1),true,c_lessequals(X2,X4,X1),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_0,axiom,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(X2,c_minus(X3,X4,X1),X1),true,c_lessequals(c_plus(X2,X4,X1),X3,X1),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(c_plus(X2,X3,X1),X4,X1),true,c_lessequals(X2,c_minus(X4,X3,X1),X1),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
cnf(cls_conjecture_3,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(c_0_14,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Orderings_Olinorder(X1),true) = true,
clsrel_Ring__and__Field_Oordered__idom_33 ).
cnf(c_0_15,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
tfree_tcs ).
cnf(c_0_16,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_17,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Ocomm__monoid__add(X1),true) = true,
clsrel_Ring__and__Field_Oordered__idom_23 ).
cnf(c_0_18,axiom,
ifeq(class_Orderings_Olinorder(X1),true,class_Orderings_Oorder(X1),true) = true,
clsrel_Orderings_Olinorder_4 ).
cnf(c_0_19,negated_conjecture,
class_Orderings_Olinorder(t_b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_20,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Opordered__ab__group__add(X1),true) = true,
clsrel_Ring__and__Field_Oordered__idom_54 ).
cnf(c_0_21,axiom,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(X1),true,c_plus(c_0,X2,X1),X2) = X2,
cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0 ).
cnf(c_0_22,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_16]) ).
cnf(c_0_23,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_24,axiom,
ifeq(class_Orderings_Oorder(X1),true,ifeq(c_lessequals(X2,X3,X1),true,ifeq(c_lessequals(X3,X4,X1),true,c_lessequals(X2,X4,X1),true),true),true) = true,
cls_Orderings_Oorder__class_Oorder__trans_0 ).
cnf(c_0_25,negated_conjecture,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
cls_conjecture_2 ).
cnf(c_0_26,negated_conjecture,
class_Orderings_Oorder(t_b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_16]) ).
cnf(c_0_27,axiom,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(X2,c_minus(X3,X4,X1),X1),true,c_lessequals(c_plus(X2,X4,X1),X3,X1),true),true) = true,
cls_OrderedGroup_Ocompare__rls__9_0 ).
cnf(c_0_28,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
cls_conjecture_1 ).
cnf(c_0_29,negated_conjecture,
class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_15]),c_0_16]) ).
cnf(c_0_30,negated_conjecture,
c_plus(c_0,X1,t_b) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_31,axiom,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(c_plus(X2,X3,X1),X4,X1),true,c_lessequals(X2,c_minus(X4,X3,X1),X1),true),true) = true,
cls_OrderedGroup_Ocompare__rls__9_1 ).
cnf(c_0_32,negated_conjecture,
ifeq(c_lessequals(X1,v_k(v_x),t_b),true,c_lessequals(X1,v_f(v_x),t_b),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_16]),c_0_16]) ).
cnf(c_0_33,negated_conjecture,
c_lessequals(v_g(v_x),v_k(v_x),t_b) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_16]),c_0_16]),c_0_30]) ).
cnf(c_0_34,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
inference(fof_simplification,[status(thm)],[cls_conjecture_3]) ).
cnf(c_0_35,negated_conjecture,
ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_0,c_minus(X2,X1,t_b),t_b),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_30]),c_0_29]),c_0_16]) ).
cnf(c_0_36,negated_conjecture,
c_lessequals(v_g(v_x),v_f(v_x),t_b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_16]) ).
cnf(c_0_37,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
c_0_34 ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_16]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.53 % Computer : n002.cluster.edu
% 0.11/5.53 % Model : x86_64 x86_64
% 0.11/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.53 % Memory : 8046.5625MB
% 0.11/5.53 % OS : Linux 6.8.0-71-generic
% 0.11/5.54 % CPULimit : 300
% 0.11/5.54 % WCLimit : 300
% 0.11/5.54 % DateTime : Mon Sep 21 13:27:11 UTC 2026
% 0.11/5.54 % CPUTime :
% 0.11/5.54 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.58 Running first-order theorem proving
% 0.11/5.58 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
% 0.16/5.60 % Version: 3.5.1
% 0.16/5.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.60 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.60 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.60 % Starting sh5l with 300s (1) cores
% 0.16/5.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3382851 completed with status 0
% 0.16/5.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/5.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.60 % No SInE strategy applied
% 0.16/5.60 % Search class: FUUPM-FFSS31-MFFFFFNN
% 0.16/5.60 % partial match(1): FUUPM-FFSF31-MFFFFFNN
% 0.16/5.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.60 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/5.60 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 226s (1) cores
% 0.16/5.60 % Starting new_bool_3 with 226s (1) cores
% 0.16/5.60 % Starting new_bool_1 with 226s (1) cores
% 0.16/5.60 % new_bool_1 with pid 3382859 completed with status 0
% 0.16/5.60 % Result found by new_bool_1
% 0.16/5.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/5.60 % No SInE strategy applied
% 0.16/5.60 % Search class: FUUPM-FFSS31-MFFFFFNN
% 0.16/5.60 % partial match(1): FUUPM-FFSF31-MFFFFFNN
% 0.16/5.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/5.60 % Starting SubtermCWHack with 136s (1) cores
% 0.16/5.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/5.60 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 226s (1) cores
% 0.16/5.60 % Starting new_bool_3 with 226s (1) cores
% 0.16/5.60 % Starting new_bool_1 with 226s (1) cores
% 0.16/5.60 % Preprocessing time : 0.001 s
% 0.16/5.60 % Presaturation interreduction done
% 0.16/5.60
% 0.16/5.60 % Proof found!
% 0.16/5.60 % SZS status Unsatisfiable
% 0.16/5.60 % SZS output start CNFRefutation
% See solution above
% 0.16/5.60 % Parsed axioms : 14
% 0.16/5.60 % Removed by relevancy pruning/SinE : 0
% 0.16/5.60 % Initial clauses : 14
% 0.16/5.60 % Removed in clause preprocessing : 0
% 0.16/5.60 % Initial clauses in saturation : 14
% 0.16/5.60 % Processed clauses : 53
% 0.16/5.60 % ...of these trivial : 1
% 0.16/5.60 % ...subsumed : 0
% 0.16/5.60 % ...remaining for further processing : 52
% 0.16/5.60 % Other redundant clauses eliminated : 0
% 0.16/5.60 % Clauses deleted for lack of memory : 0
% 0.16/5.60 % Backward-subsumed : 0
% 0.16/5.60 % Backward-rewritten : 0
% 0.16/5.60 % Generated clauses : 61
% 0.16/5.60 % ...of the previous two non-redundant : 36
% 0.16/5.60 % ...aggressively subsumed : 0
% 0.16/5.60 % Contextual simplify-reflections : 0
% 0.16/5.60 % Paramodulations : 61
% 0.16/5.60 % Factorizations : 0
% 0.16/5.60 % NegExts : 0
% 0.16/5.60 % Equation resolutions : 0
% 0.16/5.60 % Disequality decompositions : 0
% 0.16/5.60 % Total rewrite steps : 102
% 0.16/5.60 % ...of those cached : 58
% 0.16/5.60 % Propositional unsat checks : 0
% 0.16/5.60 % Propositional check models : 0
% 0.16/5.60 % Propositional check unsatisfiable : 0
% 0.16/5.60 % Propositional clauses : 0
% 0.16/5.60 % Propositional clauses after purity: 0
% 0.16/5.60 % Propositional unsat core size : 0
% 0.16/5.60 % Propositional preprocessing time : 0.000
% 0.16/5.60 % Propositional encoding time : 0.000
% 0.16/5.60 % Propositional solver time : 0.000
% 0.16/5.60 % Success case prop preproc time : 0.000
% 0.16/5.60 % Success case prop encoding time : 0.000
% 0.16/5.60 % Success case prop solver time : 0.000
% 0.16/5.60 % Current number of processed clauses : 38
% 0.16/5.60 % Positive orientable unit clauses : 37
% 0.16/5.60 % Positive unorientable unit clauses: 0
% 0.16/5.60 % Negative unit clauses : 1
% 0.16/5.60 % Non-unit-clauses : 0
% 0.16/5.60 % Current number of unprocessed clauses: 11
% 0.16/5.60 % ...number of literals in the above : 11
% 0.16/5.60 % Current number of archived formulas : 0
% 0.16/5.60 % Current number of archived clauses : 14
% 0.16/5.60 % Clause-clause subsumption calls (NU) : 0
% 0.16/5.60 % Rec. Clause-clause subsumption calls : 0
% 0.16/5.60 % Non-unit clause-clause subsumptions : 0
% 0.16/5.60 % Unit Clause-clause subsumption calls : 0
% 0.16/5.60 % Rewrite failures with RHS unbound : 0
% 0.16/5.60 % BW rewrite match attempts : 36
% 0.16/5.60 % BW rewrite match successes : 0
% 0.16/5.60 % Condensation attempts : 0
% 0.16/5.60 % Condensation successes : 0
% 0.16/5.60 % Termbank termtop insertions : 1570
% 0.16/5.60 % Search garbage collected termcells : 2
% 0.16/5.60
% 0.16/5.60 % -------------------------------------------------
% 0.16/5.60 % User time : 0.002 s
% 0.16/5.60 % System time : 0.003 s
% 0.16/5.60 % Total time : 0.005 s
% 0.16/5.60 % Maximum resident set size: 3640 pages
% 0.16/5.60
% 0.16/5.60 % -------------------------------------------------
% 0.16/5.60 % User time : 0.013 s
% 0.16/5.60 % System time : 0.017 s
% 0.16/5.60 % Total time : 0.030 s
% 0.16/5.60 % Maximum resident set size: 4608 pages
% 0.16/5.60 % E exiting
%------------------------------------------------------------------------------