%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE167+1 : 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 : n016.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 12:59:00 PM UTC 2026
% Result : Theorem 0.24s 5.63s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 39 unt; 0 def)
% Number of atoms : 61 ( 45 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 7 |; 4 &)
% ( 1 <=>; 2 =>; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 3 sgn 42 !; 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(goals,conjecture,
! [X4,X5] :
( leq(X4,multiplication(X4,star(X5)))
& ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,star(X5)),X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
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(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(star_unfold1,axiom,
! [X1] : addition(one,multiplication(X1,star(X1))) = star(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
fof(c_0_12,plain,
! [X32,X33,X34] : addition(X34,addition(X33,X32)) = addition(addition(X34,X33),X32),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_13,plain,
! [X35] : addition(X35,X35) = X35,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_14,negated_conjecture,
~ ! [X4,X5] :
( leq(X4,multiplication(X4,star(X5)))
& ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,star(X5)),X4) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_15,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
fof(c_0_16,plain,
! [X36] : multiplication(X36,one) = X36,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_17,plain,
! [X30,X31] : addition(X30,X31) = addition(X31,X30),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_18,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X26] : addition(one,multiplication(star(X26),X26)) = star(X26),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(c_0_21,negated_conjecture,
( ( ~ leq(esk1_0,multiplication(esk1_0,star(esk2_0)))
| ~ leq(multiplication(esk1_0,star(esk2_0)),esk1_0) )
& ( ~ leq(esk1_0,multiplication(esk1_0,star(esk2_0)))
| multiplication(esk1_0,esk2_0) = zero ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
fof(c_0_22,plain,
! [X14,X15] :
( ( leq(X14,X15)
| addition(X14,X15) != X15 )
& ( addition(X14,X15) = X15
| ~ leq(X14,X15) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_23,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,plain,
! [X16,X17,X18] : multiplication(X16,multiplication(X17,X18)) = multiplication(multiplication(X16,X17),X18),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_29,negated_conjecture,
( ~ leq(esk1_0,multiplication(esk1_0,star(esk2_0)))
| multiplication(esk1_0,esk2_0) = zero ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_32,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_33,plain,
! [X28] : multiplication(zero,X28) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_34,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
multiplication(esk1_0,esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_25]),c_0_32])]) ).
cnf(c_0_36,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_37,plain,
! [X27] : addition(X27,zero) = X27,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_38,negated_conjecture,
multiplication(esk1_0,multiplication(esk2_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_40,plain,
! [X25] : addition(one,multiplication(X25,star(X25))) = star(X25),
inference(variable_rename,[status(thm)],[star_unfold1]) ).
cnf(c_0_41,negated_conjecture,
multiplication(esk1_0,addition(one,multiplication(esk2_0,X1))) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_38]),c_0_39]),c_0_25]) ).
cnf(c_0_42,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( ~ leq(esk1_0,multiplication(esk1_0,star(esk2_0)))
| ~ leq(multiplication(esk1_0,star(esk2_0)),esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_44,negated_conjecture,
multiplication(esk1_0,star(esk2_0)) = esk1_0,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
~ leq(esk1_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_44])]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_30]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE167+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/5.46 % Computer : n016.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Sun Sep 20 22:53:29 UTC 2026
% 0.19/5.46 % CPUTime :
% 0.19/5.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/5.54 Running first-order theorem proving
% 0.24/5.54 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
% 0.24/5.63 % Version: 3.5.1
% 0.24/5.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/5.63 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.63 % Starting new_bool_1 with 300s (1) cores
% 0.24/5.63 % Starting sh5l with 300s (1) cores
% 0.24/5.63 % new_bool_3 with pid 967868 completed with status 0
% 0.24/5.63 % Result found by new_bool_3
% 0.24/5.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/5.63 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/5.63 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/5.63 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.24/5.63 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/5.63 % Starting SubtermCWHack with 31s (1) cores
% 0.24/5.63 % SubtermCWHack with pid 967876 completed with status 0
% 0.24/5.63 % Result found by SubtermCWHack
% 0.24/5.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/5.63 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/5.63 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/5.63 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.24/5.63 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/5.63 % Starting SubtermCWHack with 31s (1) cores
% 0.24/5.63 % Preprocessing time : 0.002 s
% 0.24/5.63
% 0.24/5.63 % Proof found!
% 0.24/5.63 % SZS status Theorem
% 0.24/5.63 % SZS output start CNFRefutation
% See solution above
% 0.24/5.63 % Parsed axioms : 19
% 0.24/5.63 % Removed by relevancy pruning/SinE : 0
% 0.24/5.63 % Initial clauses : 21
% 0.24/5.63 % Removed in clause preprocessing : 0
% 0.24/5.63 % Initial clauses in saturation : 21
% 0.24/5.63 % Processed clauses : 173
% 0.24/5.63 % ...of these trivial : 10
% 0.24/5.63 % ...subsumed : 59
% 0.24/5.63 % ...remaining for further processing : 104
% 0.24/5.63 % Other redundant clauses eliminated : 2
% 0.24/5.63 % Clauses deleted for lack of memory : 0
% 0.24/5.63 % Backward-subsumed : 16
% 0.24/5.63 % Backward-rewritten : 11
% 0.24/5.63 % Generated clauses : 1181
% 0.24/5.63 % ...of the previous two non-redundant : 868
% 0.24/5.63 % ...aggressively subsumed : 0
% 0.24/5.63 % Contextual simplify-reflections : 0
% 0.24/5.63 % Paramodulations : 1179
% 0.24/5.63 % Factorizations : 0
% 0.24/5.63 % NegExts : 0
% 0.24/5.63 % Equation resolutions : 2
% 0.24/5.63 % Disequality decompositions : 0
% 0.24/5.63 % Total rewrite steps : 962
% 0.24/5.63 % ...of those cached : 627
% 0.24/5.63 % Propositional unsat checks : 0
% 0.24/5.63 % Propositional check models : 0
% 0.24/5.63 % Propositional check unsatisfiable : 0
% 0.24/5.63 % Propositional clauses : 0
% 0.24/5.63 % Propositional clauses after purity: 0
% 0.24/5.63 % Propositional unsat core size : 0
% 0.24/5.63 % Propositional preprocessing time : 0.000
% 0.24/5.63 % Propositional encoding time : 0.000
% 0.24/5.63 % Propositional solver time : 0.000
% 0.24/5.63 % Success case prop preproc time : 0.000
% 0.24/5.63 % Success case prop encoding time : 0.000
% 0.24/5.63 % Success case prop solver time : 0.000
% 0.24/5.63 % Current number of processed clauses : 77
% 0.24/5.63 % Positive orientable unit clauses : 46
% 0.24/5.63 % Positive unorientable unit clauses: 4
% 0.24/5.63 % Negative unit clauses : 6
% 0.24/5.63 % Non-unit-clauses : 21
% 0.24/5.63 % Current number of unprocessed clauses: 704
% 0.24/5.63 % ...number of literals in the above : 918
% 0.24/5.63 % Current number of archived formulas : 0
% 0.24/5.63 % Current number of archived clauses : 27
% 0.24/5.63 % Clause-clause subsumption calls (NU) : 117
% 0.24/5.63 % Rec. Clause-clause subsumption calls : 115
% 0.24/5.63 % Non-unit clause-clause subsumptions : 23
% 0.24/5.63 % Unit Clause-clause subsumption calls : 74
% 0.24/5.63 % Rewrite failures with RHS unbound : 0
% 0.24/5.63 % BW rewrite match attempts : 58
% 0.24/5.63 % BW rewrite match successes : 42
% 0.24/5.63 % Condensation attempts : 0
% 0.24/5.63 % Condensation successes : 0
% 0.24/5.63 % Termbank termtop insertions : 10836
% 0.24/5.63 % Search garbage collected termcells : 101
% 0.24/5.63
% 0.24/5.63 % -------------------------------------------------
% 0.24/5.63 % User time : 0.025 s
% 0.24/5.63 % System time : 0.008 s
% 0.24/5.63 % Total time : 0.033 s
% 0.24/5.63 % Maximum resident set size: 3652 pages
% 0.24/5.63
% 0.24/5.63 % -------------------------------------------------
% 0.24/5.63 % User time : 0.027 s
% 0.24/5.63 % System time : 0.015 s
% 0.24/5.63 % Total time : 0.042 s
% 0.24/5.63 % Maximum resident set size: 4608 pages
% 0.24/5.63 % E exiting
%------------------------------------------------------------------------------