%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE144+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:58:57 PM UTC 2026
% Result : Theorem 0.51s 0.63s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 37 unt; 0 def)
% Number of atoms : 61 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 8 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 12 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(distributivity2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(goals,conjecture,
! [X4] :
( leq(strong_iteration(one),strong_iteration(star(X4)))
& leq(strong_iteration(star(X4)),strong_iteration(one)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_10,plain,
! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_11,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_12,plain,
! [X37,X38] :
( ( leq(X37,X38)
| addition(X37,X38) != X38 )
& ( addition(X37,X38) = X38
| ~ leq(X37,X38) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_13,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X33,X34,X35] :
( leq(X35,multiplication(strong_iteration(X33),X34))
| ~ leq(X35,addition(multiplication(X33,X35),X34)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])])]) ).
fof(c_0_16,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_17,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( ~ leq(X1,addition(multiplication(X2,X1),X3))
| leq(X1,multiplication(strong_iteration(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X15] : multiplication(X15,one) = X15,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_23,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_25,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_26,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X20,X21,X22] : multiplication(addition(X20,X21),X22) = addition(multiplication(X20,X22),multiplication(X21,X22)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
cnf(c_0_29,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
addition(X1,strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_20]),c_0_29]) ).
fof(c_0_34,plain,
! [X25] : addition(one,multiplication(star(X25),X25)) = star(X25),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
cnf(c_0_35,plain,
multiplication(addition(X1,one),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_37,negated_conjecture,
~ ! [X4] :
( leq(strong_iteration(one),strong_iteration(star(X4)))
& leq(strong_iteration(star(X4)),strong_iteration(one)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_38,plain,
multiplication(addition(one,X1),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_35,c_0_29]) ).
cnf(c_0_39,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
fof(c_0_40,negated_conjecture,
( ~ leq(strong_iteration(one),strong_iteration(star(esk1_0)))
| ~ leq(strong_iteration(star(esk1_0)),strong_iteration(one)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
cnf(c_0_41,plain,
multiplication(star(X1),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_43,negated_conjecture,
( ~ leq(strong_iteration(one),strong_iteration(star(esk1_0)))
| ~ leq(strong_iteration(star(esk1_0)),strong_iteration(one)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
leq(strong_iteration(one),multiplication(strong_iteration(star(X1)),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_41]),c_0_32]),c_0_42])]) ).
cnf(c_0_45,negated_conjecture,
~ leq(strong_iteration(one),strong_iteration(star(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_27])]) ).
cnf(c_0_46,plain,
leq(strong_iteration(one),strong_iteration(star(X1))),
inference(spm,[status(thm)],[c_0_44,c_0_24]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE144+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 22:47:09 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.46 Running first-order theorem proving
% 0.14/0.46 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
% 0.51/0.63 % Version: 3.5.1
% 0.51/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.51/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.51/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.51/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.51/0.63 % Starting new_bool_1 with 300s (1) cores
% 0.51/0.63 % Starting sh5l with 300s (1) cores
% 0.51/0.63 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3763912 completed with status 0
% 0.51/0.63 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.51/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.51/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.51/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.51/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.51/0.63 % No SInE strategy applied
% 0.51/0.63 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.51/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.51/0.63 % Starting SubtermCWHack with 136s (1) cores
% 0.51/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.51/0.63 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.51/0.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.51/0.63 % Starting new_bool_3 with 136s (1) cores
% 0.51/0.63 % new_bool_3 with pid 3763920 completed with status 0
% 0.51/0.63 % Result found by new_bool_3
% 0.51/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.51/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.51/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.51/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.51/0.63 % No SInE strategy applied
% 0.51/0.63 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.51/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.51/0.63 % Starting SubtermCWHack with 136s (1) cores
% 0.51/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.51/0.63 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.51/0.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.51/0.63 % Starting new_bool_3 with 136s (1) cores
% 0.51/0.63 % Preprocessing time : 0.001 s
% 0.51/0.63 % Presaturation interreduction done
% 0.51/0.63
% 0.51/0.63 % Proof found!
% 0.51/0.63 % SZS status Theorem
% 0.51/0.63 % SZS output start CNFRefutation
% See solution above
% 0.51/0.63 % Parsed axioms : 19
% 0.51/0.63 % Removed by relevancy pruning/SinE : 0
% 0.51/0.63 % Initial clauses : 20
% 0.51/0.63 % Removed in clause preprocessing : 0
% 0.51/0.63 % Initial clauses in saturation : 20
% 0.51/0.63 % Processed clauses : 705
% 0.51/0.63 % ...of these trivial : 48
% 0.51/0.63 % ...subsumed : 390
% 0.51/0.63 % ...remaining for further processing : 267
% 0.51/0.63 % Other redundant clauses eliminated : 50
% 0.51/0.63 % Clauses deleted for lack of memory : 0
% 0.51/0.63 % Backward-subsumed : 4
% 0.51/0.63 % Backward-rewritten : 36
% 0.51/0.63 % Generated clauses : 3904
% 0.51/0.63 % ...of the previous two non-redundant : 2489
% 0.51/0.63 % ...aggressively subsumed : 0
% 0.51/0.63 % Contextual simplify-reflections : 0
% 0.51/0.63 % Paramodulations : 3853
% 0.51/0.63 % Factorizations : 0
% 0.51/0.63 % NegExts : 0
% 0.51/0.63 % Equation resolutions : 51
% 0.51/0.63 % Disequality decompositions : 0
% 0.51/0.63 % Total rewrite steps : 4103
% 0.51/0.63 % ...of those cached : 3169
% 0.51/0.63 % Propositional unsat checks : 0
% 0.51/0.63 % Propositional check models : 0
% 0.51/0.63 % Propositional check unsatisfiable : 0
% 0.51/0.63 % Propositional clauses : 0
% 0.51/0.63 % Propositional clauses after purity: 0
% 0.51/0.63 % Propositional unsat core size : 0
% 0.51/0.63 % Propositional preprocessing time : 0.000
% 0.51/0.63 % Propositional encoding time : 0.000
% 0.51/0.63 % Propositional solver time : 0.000
% 0.51/0.63 % Success case prop preproc time : 0.000
% 0.51/0.63 % Success case prop encoding time : 0.000
% 0.51/0.63 % Success case prop solver time : 0.000
% 0.51/0.63 % Current number of processed clauses : 207
% 0.51/0.63 % Positive orientable unit clauses : 86
% 0.51/0.63 % Positive unorientable unit clauses: 3
% 0.51/0.63 % Negative unit clauses : 0
% 0.51/0.63 % Non-unit-clauses : 118
% 0.51/0.63 % Current number of unprocessed clauses: 1799
% 0.51/0.63 % ...number of literals in the above : 2951
% 0.51/0.63 % Current number of archived formulas : 0
% 0.51/0.63 % Current number of archived clauses : 60
% 0.51/0.63 % Clause-clause subsumption calls (NU) : 2449
% 0.51/0.63 % Rec. Clause-clause subsumption calls : 2358
% 0.51/0.63 % Non-unit clause-clause subsumptions : 376
% 0.51/0.63 % Unit Clause-clause subsumption calls : 199
% 0.51/0.63 % Rewrite failures with RHS unbound : 0
% 0.51/0.63 % BW rewrite match attempts : 208
% 0.51/0.63 % BW rewrite match successes : 70
% 0.51/0.63 % Condensation attempts : 0
% 0.51/0.63 % Condensation successes : 0
% 0.51/0.63 % Termbank termtop insertions : 41038
% 0.51/0.63 % Search garbage collected termcells : 82
% 0.51/0.63
% 0.51/0.63 % -------------------------------------------------
% 0.51/0.63 % User time : 0.053 s
% 0.51/0.63 % System time : 0.008 s
% 0.51/0.63 % Total time : 0.061 s
% 0.51/0.63 % Maximum resident set size: 3396 pages
% 0.51/0.63
% 0.51/0.63 % -------------------------------------------------
% 0.51/0.63 % User time : 0.250 s
% 0.51/0.63 % System time : 0.031 s
% 0.51/0.63 % Total time : 0.281 s
% 0.51/0.63 % Maximum resident set size: 4608 pages
% 0.51/0.63 % E exiting
%------------------------------------------------------------------------------