%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE139+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 : n011.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 12:58:55 PM UTC 2026
% Result : Theorem 0.55s 0.55s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 1 sgn 30 !; 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(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] : strong_iteration(X4) = addition(multiplication(strong_iteration(X4),X4),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(isolation,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',isolation) ).
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(c_0_8,plain,
! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_9,plain,
! [X25] : addition(one,multiplication(star(X25),X25)) = star(X25),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(c_0_10,negated_conjecture,
~ ! [X4] : strong_iteration(X4) = addition(multiplication(strong_iteration(X4),X4),one),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_11,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X20,X21,X22] : multiplication(addition(X20,X21),X22) = addition(multiplication(X20,X22),multiplication(X21,X22)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
fof(c_0_14,negated_conjecture,
strong_iteration(esk1_0) != addition(multiplication(strong_iteration(esk1_0),esk1_0),one),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_15,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_16,plain,
addition(one,addition(multiplication(star(X1),X1),X2)) = addition(star(X1),X2),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X36] : strong_iteration(X36) = addition(star(X36),multiplication(strong_iteration(X36),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
fof(c_0_19,plain,
! [X12,X13,X14] : multiplication(X12,multiplication(X13,X14)) = multiplication(multiplication(X12,X13),X14),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_20,plain,
! [X23] : multiplication(zero,X23) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_21,negated_conjecture,
strong_iteration(esk1_0) != addition(multiplication(strong_iteration(esk1_0),esk1_0),one),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
addition(one,multiplication(addition(star(X1),X2),X1)) = addition(star(X1),multiplication(X2,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
addition(one,multiplication(strong_iteration(esk1_0),esk1_0)) != strong_iteration(esk1_0),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]),c_0_24]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE139+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 22:45:55 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.55/0.55 % Version: 3.5.1
% 0.55/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.55/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.55/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.55/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.55/0.55 % Starting sh5l with 300s (1) cores
% 0.55/0.55 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 355534 completed with status 0
% 0.55/0.55 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.55/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.55/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.55/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.55/0.55 % No SInE strategy applied
% 0.55/0.55 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.55/0.55 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.55/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.55/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.55/0.55 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.55/0.55 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 0.55/0.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.55/0.55 % G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with pid 355543 completed with status 0
% 0.55/0.55 % Result found by G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y
% 0.55/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.55/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.55/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.55/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.55/0.55 % No SInE strategy applied
% 0.55/0.55 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.55/0.55 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.55/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.55/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.55/0.55 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.55/0.55 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 0.55/0.55 % Preprocessing time : 0.001 s
% 0.55/0.55 % Presaturation interreduction done
% 0.55/0.55
% 0.55/0.55 % Proof found!
% 0.55/0.55 % SZS status Theorem
% 0.55/0.55 % SZS output start CNFRefutation
% See solution above
% 0.55/0.55 % Parsed axioms : 19
% 0.55/0.55 % Removed by relevancy pruning/SinE : 0
% 0.55/0.55 % Initial clauses : 20
% 0.55/0.55 % Removed in clause preprocessing : 0
% 0.55/0.55 % Initial clauses in saturation : 20
% 0.55/0.55 % Processed clauses : 1294
% 0.55/0.55 % ...of these trivial : 103
% 0.55/0.55 % ...subsumed : 897
% 0.55/0.55 % ...remaining for further processing : 294
% 0.55/0.55 % Other redundant clauses eliminated : 0
% 0.55/0.55 % Clauses deleted for lack of memory : 0
% 0.55/0.55 % Backward-subsumed : 43
% 0.55/0.55 % Backward-rewritten : 34
% 0.55/0.55 % Generated clauses : 9550
% 0.55/0.55 % ...of the previous two non-redundant : 6917
% 0.55/0.55 % ...aggressively subsumed : 0
% 0.55/0.55 % Contextual simplify-reflections : 1
% 0.55/0.55 % Paramodulations : 9550
% 0.55/0.55 % Factorizations : 0
% 0.55/0.55 % NegExts : 0
% 0.55/0.55 % Equation resolutions : 0
% 0.55/0.55 % Disequality decompositions : 0
% 0.55/0.55 % Total rewrite steps : 9932
% 0.55/0.55 % ...of those cached : 7959
% 0.55/0.55 % Propositional unsat checks : 0
% 0.55/0.55 % Propositional check models : 0
% 0.55/0.55 % Propositional check unsatisfiable : 0
% 0.55/0.55 % Propositional clauses : 0
% 0.55/0.55 % Propositional clauses after purity: 0
% 0.55/0.55 % Propositional unsat core size : 0
% 0.55/0.55 % Propositional preprocessing time : 0.000
% 0.55/0.55 % Propositional encoding time : 0.000
% 0.55/0.55 % Propositional solver time : 0.000
% 0.55/0.55 % Success case prop preproc time : 0.000
% 0.55/0.55 % Success case prop encoding time : 0.000
% 0.55/0.55 % Success case prop solver time : 0.000
% 0.55/0.55 % Current number of processed clauses : 197
% 0.55/0.55 % Positive orientable unit clauses : 93
% 0.55/0.55 % Positive unorientable unit clauses: 8
% 0.55/0.55 % Negative unit clauses : 19
% 0.55/0.55 % Non-unit-clauses : 77
% 0.55/0.55 % Current number of unprocessed clauses: 5498
% 0.55/0.55 % ...number of literals in the above : 9113
% 0.55/0.55 % Current number of archived formulas : 0
% 0.55/0.55 % Current number of archived clauses : 97
% 0.55/0.55 % Clause-clause subsumption calls (NU) : 1080
% 0.55/0.55 % Rec. Clause-clause subsumption calls : 1075
% 0.55/0.55 % Non-unit clause-clause subsumptions : 264
% 0.55/0.55 % Unit Clause-clause subsumption calls : 365
% 0.55/0.55 % Rewrite failures with RHS unbound : 0
% 0.55/0.55 % BW rewrite match attempts : 255
% 0.55/0.55 % BW rewrite match successes : 121
% 0.55/0.55 % Condensation attempts : 1294
% 0.55/0.55 % Condensation successes : 57
% 0.55/0.55 % Termbank termtop insertions : 96010
% 0.55/0.55 % Search garbage collected termcells : 71
% 0.55/0.55
% 0.55/0.55 % -------------------------------------------------
% 0.55/0.55 % User time : 0.096 s
% 0.55/0.55 % System time : 0.011 s
% 0.55/0.55 % Total time : 0.107 s
% 0.55/0.55 % Maximum resident set size: 3600 pages
% 0.55/0.55
% 0.55/0.55 % -------------------------------------------------
% 0.55/0.55 % User time : 0.513 s
% 0.55/0.55 % System time : 0.043 s
% 0.55/0.55 % Total time : 0.556 s
% 0.55/0.55 % Maximum resident set size: 4864 pages
% 0.55/0.55 % E exiting
%------------------------------------------------------------------------------