%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE040+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 : n013.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 12:58:42 PM UTC 2026
% Result : Theorem 0.19s 10.55s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 31 unt; 0 def)
% Number of atoms : 59 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 10 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 75 ( 5 sgn 34 !; 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/KLE002+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(star_induction_left,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X2)
=> leq(multiplication(star(X1),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).
fof(goals,conjecture,
! [X4] :
( leq(star(X4),multiplication(star(X4),star(X4)))
& leq(multiplication(star(X4),star(X4)),star(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(c_0_9,plain,
! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_10,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_11,plain,
! [X25,X26] :
( ( leq(X25,X26)
| addition(X25,X26) != X26 )
& ( addition(X25,X26) = X26
| ~ leq(X25,X26) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_12,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_17,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X27] : leq(addition(one,multiplication(X27,star(X27))),star(X27)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
cnf(c_0_20,plain,
leq(X1,addition(X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,plain,
! [X29,X30,X31] :
( leq(multiplication(star(X29),X31),X30)
| ~ leq(addition(multiplication(X29,X30),X31),X30) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_left])])]) ).
cnf(c_0_24,plain,
leq(X1,addition(X2,addition(X3,X1))),
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_25,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_12]),c_0_18]) ).
fof(c_0_26,negated_conjecture,
~ ! [X4] :
( leq(star(X4),multiplication(star(X4),star(X4)))
& leq(multiplication(star(X4),star(X4)),star(X4)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_27,plain,
( ~ leq(addition(multiplication(X1,X2),X3),X2)
| leq(multiplication(star(X1),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
leq(multiplication(X1,star(X1)),star(X1)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_29,plain,
! [X17,X18,X19] : multiplication(X17,addition(X18,X19)) = addition(multiplication(X17,X18),multiplication(X17,X19)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_30,negated_conjecture,
( ~ leq(star(esk1_0),multiplication(star(esk1_0),star(esk1_0)))
| ~ leq(multiplication(star(esk1_0),star(esk1_0)),star(esk1_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
cnf(c_0_31,plain,
( ~ leq(addition(X2,multiplication(X1,X3)),X3)
| leq(multiplication(star(X1),X2),X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_32,plain,
addition(star(X1),multiplication(X1,star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_28]),c_0_18]) ).
cnf(c_0_33,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_34,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X15] : multiplication(X15,one) = X15,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_36,negated_conjecture,
( ~ leq(star(esk1_0),multiplication(star(esk1_0),star(esk1_0)))
| ~ leq(multiplication(star(esk1_0),star(esk1_0)),star(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
leq(multiplication(star(X1),star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_38,plain,
( multiplication(X1,addition(X2,X3)) != multiplication(X1,X3)
| leq(multiplication(X1,X2),multiplication(X1,X3)) ),
inference(spm,[status(thm)],[c_0_14,c_0_34]) ).
cnf(c_0_39,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_40,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,negated_conjecture,
~ leq(star(esk1_0),multiplication(star(esk1_0),star(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_42,plain,
leq(X1,multiplication(X1,star(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE040+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/10.42 % Computer : n013.cluster.edu
% 0.13/10.42 % Model : x86_64 x86_64
% 0.13/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.42 % Memory : 8046.5625MB
% 0.13/10.42 % OS : Linux 6.8.0-71-generic
% 0.13/10.43 % CPULimit : 300
% 0.13/10.43 % WCLimit : 300
% 0.13/10.43 % DateTime : Sun Sep 20 22:39:48 UTC 2026
% 0.13/10.43 % CPUTime :
% 0.13/10.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/10.49 Running first-order theorem proving
% 0.13/10.49 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
% 0.19/10.55 % Version: 3.5.1
% 0.19/10.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/10.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/10.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/10.55 % Starting new_bool_3 with 300s (1) cores
% 0.19/10.55 % Starting new_bool_1 with 300s (1) cores
% 0.19/10.55 % Starting sh5l with 300s (1) cores
% 0.19/10.55 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3563899 completed with status 0
% 0.19/10.55 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.19/10.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/10.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/10.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/10.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/10.55 % No SInE strategy applied
% 0.19/10.55 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.19/10.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/10.55 % Starting SubtermCWHack with 136s (1) cores
% 0.19/10.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.19/10.55 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.19/10.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.19/10.55 % Starting new_bool_3 with 136s (1) cores
% 0.19/10.55 % new_bool_3 with pid 3563907 completed with status 0
% 0.19/10.55 % Result found by new_bool_3
% 0.19/10.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/10.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/10.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/10.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/10.55 % No SInE strategy applied
% 0.19/10.55 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.19/10.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/10.55 % Starting SubtermCWHack with 136s (1) cores
% 0.19/10.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.19/10.55 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.19/10.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.19/10.55 % Starting new_bool_3 with 136s (1) cores
% 0.19/10.55 % Preprocessing time : 0.002 s
% 0.19/10.55 % Presaturation interreduction done
% 0.19/10.55
% 0.19/10.55 % Proof found!
% 0.19/10.55 % SZS status Theorem
% 0.19/10.55 % SZS output start CNFRefutation
% See solution above
% 0.19/10.55 % Parsed axioms : 17
% 0.19/10.55 % Removed by relevancy pruning/SinE : 0
% 0.19/10.55 % Initial clauses : 18
% 0.19/10.55 % Removed in clause preprocessing : 0
% 0.19/10.55 % Initial clauses in saturation : 18
% 0.19/10.55 % Processed clauses : 286
% 0.19/10.55 % ...of these trivial : 28
% 0.19/10.55 % ...subsumed : 142
% 0.19/10.55 % ...remaining for further processing : 116
% 0.19/10.55 % Other redundant clauses eliminated : 14
% 0.19/10.55 % Clauses deleted for lack of memory : 0
% 0.19/10.55 % Backward-subsumed : 0
% 0.19/10.55 % Backward-rewritten : 12
% 0.19/10.55 % Generated clauses : 1198
% 0.19/10.55 % ...of the previous two non-redundant : 819
% 0.19/10.55 % ...aggressively subsumed : 0
% 0.19/10.55 % Contextual simplify-reflections : 0
% 0.19/10.55 % Paramodulations : 1184
% 0.19/10.55 % Factorizations : 0
% 0.19/10.55 % NegExts : 0
% 0.19/10.55 % Equation resolutions : 14
% 0.19/10.55 % Disequality decompositions : 0
% 0.19/10.55 % Total rewrite steps : 1197
% 0.19/10.55 % ...of those cached : 952
% 0.19/10.55 % Propositional unsat checks : 0
% 0.19/10.55 % Propositional check models : 0
% 0.19/10.55 % Propositional check unsatisfiable : 0
% 0.19/10.55 % Propositional clauses : 0
% 0.19/10.55 % Propositional clauses after purity: 0
% 0.19/10.55 % Propositional unsat core size : 0
% 0.19/10.55 % Propositional preprocessing time : 0.000
% 0.19/10.55 % Propositional encoding time : 0.000
% 0.19/10.55 % Propositional solver time : 0.000
% 0.19/10.55 % Success case prop preproc time : 0.000
% 0.19/10.55 % Success case prop encoding time : 0.000
% 0.19/10.55 % Success case prop solver time : 0.000
% 0.19/10.55 % Current number of processed clauses : 86
% 0.19/10.55 % Positive orientable unit clauses : 40
% 0.19/10.55 % Positive unorientable unit clauses: 3
% 0.19/10.55 % Negative unit clauses : 0
% 0.19/10.55 % Non-unit-clauses : 43
% 0.19/10.55 % Current number of unprocessed clauses: 563
% 0.19/10.55 % ...number of literals in the above : 896
% 0.19/10.55 % Current number of archived formulas : 0
% 0.19/10.55 % Current number of archived clauses : 30
% 0.19/10.55 % Clause-clause subsumption calls (NU) : 757
% 0.19/10.55 % Rec. Clause-clause subsumption calls : 757
% 0.19/10.55 % Non-unit clause-clause subsumptions : 130
% 0.19/10.55 % Unit Clause-clause subsumption calls : 54
% 0.19/10.55 % Rewrite failures with RHS unbound : 0
% 0.19/10.55 % BW rewrite match attempts : 68
% 0.19/10.55 % BW rewrite match successes : 48
% 0.19/10.55 % Condensation attempts : 0
% 0.19/10.55 % Condensation successes : 0
% 0.19/10.55 % Termbank termtop insertions : 11134
% 0.19/10.55 % Search garbage collected termcells : 69
% 0.19/10.55
% 0.19/10.55 % -------------------------------------------------
% 0.19/10.55 % User time : 0.031 s
% 0.19/10.55 % System time : 0.005 s
% 0.19/10.55 % Total time : 0.036 s
% 0.19/10.55 % Maximum resident set size: 3648 pages
% 0.19/10.55
% 0.19/10.55 % -------------------------------------------------
% 0.19/10.55 % User time : 0.159 s
% 0.19/10.55 % System time : 0.024 s
% 0.19/10.55 % Total time : 0.183 s
% 0.19/10.55 % Maximum resident set size: 4864 pages
% 0.19/10.55 % E exiting
%------------------------------------------------------------------------------