%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV254-1 : 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 : 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 02:54:06 PM UTC 2026
% Result : Unsatisfiable 3.20s 1.19s
% Output : CNFRefutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 20 unt; 0 nHn; 12 RR)
% Number of literals : 35 ( 17 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 36 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_NatArith_Oof__nat_Oof__nat__Suc_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_Suc(X2),X1) = c_plus(c_NatArith_Oof__nat(X2,X1),c_1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
cnf(cls_Finite__Set_Oof__nat__id_0,axiom,
c_NatArith_Oof__nat(X1,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Finite__Set_Oof__nat__id_0) ).
cnf(clsarity_nat_32,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsarity_nat_32) ).
cnf(cls_SetInterval_OatLeastLessThan__singleton_0,axiom,
c_SetInterval_OatLeastLessThan(X1,c_Suc(X1),tc_nat) = c_insert(X1,c_emptyset,tc_nat),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OatLeastLessThan__singleton_0) ).
cnf(cls_SetInterval_OatLeastLessThan__empty_0,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_SetInterval_OatLeastLessThan(X3,X2,X1) = c_emptyset ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OatLeastLessThan__empty_0) ).
cnf(cls_Set_Oempty__not__insert_0,axiom,
c_emptyset != c_insert(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Set_Oempty__not__insert_0) ).
cnf(clsarity_nat_3,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsarity_nat_3) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(X1,v_x(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
v_x(X1) = v_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(c_0_9,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_Suc(X2),X1) = c_plus(c_NatArith_Oof__nat(X2,X1),c_1,X1) ),
inference(fof_simplification,[status(thm)],[cls_NatArith_Oof__nat_Oof__nat__Suc_0]) ).
cnf(c_0_10,axiom,
c_NatArith_Oof__nat(X1,tc_nat) = X1,
cls_Finite__Set_Oof__nat__id_0 ).
cnf(c_0_11,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_Suc(X2),X1) = c_plus(c_NatArith_Oof__nat(X2,X1),c_1,X1) ),
c_0_9 ).
cnf(c_0_12,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
clsarity_nat_32 ).
cnf(c_0_13,axiom,
c_SetInterval_OatLeastLessThan(X1,c_Suc(X1),tc_nat) = c_insert(X1,c_emptyset,tc_nat),
cls_SetInterval_OatLeastLessThan__singleton_0 ).
cnf(c_0_14,plain,
c_Suc(X1) = c_plus(X1,c_1,tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_10]),c_0_12])]) ).
cnf(c_0_15,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_SetInterval_OatLeastLessThan(X3,X2,X1) = c_emptyset ),
inference(fof_simplification,[status(thm)],[cls_SetInterval_OatLeastLessThan__empty_0]) ).
cnf(c_0_16,plain,
c_emptyset != c_insert(X1,X2,X3),
inference(fof_simplification,[status(thm)],[cls_Set_Oempty__not__insert_0]) ).
cnf(c_0_17,plain,
c_SetInterval_OatLeastLessThan(X1,c_plus(X1,c_1,tc_nat),tc_nat) = c_insert(X1,c_emptyset,tc_nat),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_SetInterval_OatLeastLessThan(X3,X2,X1) = c_emptyset ),
c_0_15 ).
cnf(c_0_19,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat_3 ).
cnf(c_0_20,plain,
c_emptyset != c_insert(X1,X2,X3),
c_0_16 ).
cnf(c_0_21,negated_conjecture,
c_lessequals(X1,v_x(X1),tc_nat),
cls_conjecture_0 ).
cnf(c_0_22,negated_conjecture,
v_x(X1) = v_nat,
cls_conjecture_1 ).
cnf(c_0_23,plain,
~ c_lessequals(c_plus(X1,c_1,tc_nat),X1,tc_nat),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_24,negated_conjecture,
c_lessequals(X1,v_nat,tc_nat),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_23,c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV254-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 08:37:10 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 3.20/1.19 % Version: 3.5.1
% 3.20/1.19 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.20/1.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.20/1.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.20/1.19 % Starting new_bool_3 with 300s (1) cores
% 3.20/1.19 % Starting new_bool_1 with 300s (1) cores
% 3.20/1.19 % Starting sh5l with 300s (1) cores
% 3.20/1.19 % new_bool_1 with pid 603094 completed with status 9
% 3.20/1.19 % new_bool_3 with pid 603093 completed with status 9
% 3.20/1.19 % sh5l with pid 603095 completed with status 0
% 3.20/1.19 % Result found by sh5l
% 3.20/1.19 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.20/1.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.20/1.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.20/1.19 % Starting new_bool_3 with 300s (1) cores
% 3.20/1.19 % Starting new_bool_1 with 300s (1) cores
% 3.20/1.19 % Starting sh5l with 300s (1) cores
% 3.20/1.19 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 3.20/1.19 % SinE strategy is gf500_gu_R04_F100_L20000
% 3.20/1.19 % Search class: FGHSM-SMLM32-DFFFFFNN
% 3.20/1.19 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 3.20/1.19 % Starting SubtermCWHack with 28s (1) cores
% 3.20/1.19 % SubtermCWHack with pid 603105 completed with status 0
% 3.20/1.19 % Result found by SubtermCWHack
% 3.20/1.19 % Preprocessing class: FMLMSMSMSSSNFFN.
% 3.20/1.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.20/1.19 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.20/1.19 % Starting new_bool_3 with 300s (1) cores
% 3.20/1.19 % Starting new_bool_1 with 300s (1) cores
% 3.20/1.19 % Starting sh5l with 300s (1) cores
% 3.20/1.19 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 3.20/1.19 % SinE strategy is gf500_gu_R04_F100_L20000
% 3.20/1.19 % Search class: FGHSM-SMLM32-DFFFFFNN
% 3.20/1.19 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 3.20/1.19 % Starting SubtermCWHack with 28s (1) cores
% 3.20/1.19 % Preprocessing time : 0.035 s
% 3.20/1.19
% 3.20/1.19 % Proof found!
% 3.20/1.19 % SZS status Unsatisfiable
% 3.20/1.19 % SZS output start CNFRefutation
% See solution above
% 3.20/1.20 % Parsed axioms : 2789
% 3.20/1.20 % Removed by relevancy pruning/SinE : 346
% 3.20/1.20 % Initial clauses : 2443
% 3.20/1.20 % Removed in clause preprocessing : 1
% 3.20/1.20 % Initial clauses in saturation : 2442
% 3.20/1.20 % Processed clauses : 5723
% 3.20/1.20 % ...of these trivial : 37
% 3.20/1.20 % ...subsumed : 3748
% 3.20/1.20 % ...remaining for further processing : 1938
% 3.20/1.20 % Other redundant clauses eliminated : 56
% 3.20/1.20 % Clauses deleted for lack of memory : 0
% 3.20/1.20 % Backward-subsumed : 34
% 3.20/1.20 % Backward-rewritten : 37
% 3.20/1.20 % Generated clauses : 6894
% 3.20/1.20 % ...of the previous two non-redundant : 5229
% 3.20/1.20 % ...aggressively subsumed : 0
% 3.20/1.20 % Contextual simplify-reflections : 7
% 3.20/1.20 % Paramodulations : 6817
% 3.20/1.20 % Factorizations : 2
% 3.20/1.20 % NegExts : 0
% 3.20/1.20 % Equation resolutions : 75
% 3.20/1.20 % Disequality decompositions : 0
% 3.20/1.20 % Total rewrite steps : 2400
% 3.20/1.20 % ...of those cached : 2067
% 3.20/1.20 % Propositional unsat checks : 0
% 3.20/1.20 % Propositional check models : 0
% 3.20/1.20 % Propositional check unsatisfiable : 0
% 3.20/1.20 % Propositional clauses : 0
% 3.20/1.20 % Propositional clauses after purity: 0
% 3.20/1.20 % Propositional unsat core size : 0
% 3.20/1.20 % Propositional preprocessing time : 0.000
% 3.20/1.20 % Propositional encoding time : 0.000
% 3.20/1.20 % Propositional solver time : 0.000
% 3.20/1.20 % Success case prop preproc time : 0.000
% 3.20/1.20 % Success case prop encoding time : 0.000
% 3.20/1.20 % Success case prop solver time : 0.000
% 3.20/1.20 % Current number of processed clauses : 1867
% 3.20/1.20 % Positive orientable unit clauses : 406
% 3.20/1.20 % Positive unorientable unit clauses: 1
% 3.20/1.20 % Negative unit clauses : 71
% 3.20/1.20 % Non-unit-clauses : 1389
% 3.20/1.20 % Current number of unprocessed clauses: 1922
% 3.20/1.20 % ...number of literals in the above : 5472
% 3.20/1.20 % Current number of archived formulas : 0
% 3.20/1.20 % Current number of archived clauses : 71
% 3.20/1.20 % Clause-clause subsumption calls (NU) : 1184199
% 3.20/1.20 % Rec. Clause-clause subsumption calls : 1142969
% 3.20/1.20 % Non-unit clause-clause subsumptions : 3360
% 3.20/1.20 % Unit Clause-clause subsumption calls : 12916
% 3.20/1.20 % Rewrite failures with RHS unbound : 0
% 3.20/1.20 % BW rewrite match attempts : 170
% 3.20/1.20 % BW rewrite match successes : 23
% 3.20/1.20 % Condensation attempts : 0
% 3.20/1.20 % Condensation successes : 0
% 3.20/1.20 % Termbank termtop insertions : 123639
% 3.20/1.20 % Search garbage collected termcells : 4901
% 3.20/1.20
% 3.20/1.20 % -------------------------------------------------
% 3.20/1.20 % User time : 0.511 s
% 3.20/1.20 % System time : 0.042 s
% 3.20/1.20 % Total time : 0.553 s
% 3.20/1.20 % Maximum resident set size: 8500 pages
% 3.20/1.20
% 3.20/1.20 % -------------------------------------------------
% 3.20/1.20 % User time : 0.709 s
% 3.20/1.20 % System time : 0.198 s
% 3.20/1.20 % Total time : 0.907 s
% 3.20/1.20 % Maximum resident set size: 6656 pages
% 3.20/1.20 % E exiting
%------------------------------------------------------------------------------