%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE141+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:58:56 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 26 unt; 0 def)
% Number of atoms : 58 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 17 ~; 12 |; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 4 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(goals,conjecture,
! [X4] :
( leq(strong_iteration(one),multiplication(strong_iteration(one),X4))
& leq(multiplication(strong_iteration(one),X4),strong_iteration(one)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(c_0_10,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_11,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_12,plain,
( ~ leq(X1,addition(multiplication(X2,X1),X3))
| leq(X1,multiplication(strong_iteration(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X10] : addition(X10,zero) = X10,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_15,plain,
( ~ leq(X1,addition(X1,X2))
| leq(X1,multiplication(strong_iteration(one),X2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,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])])]) ).
fof(c_0_18,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_19,negated_conjecture,
~ ! [X4] :
( leq(strong_iteration(one),multiplication(strong_iteration(one),X4))
& leq(multiplication(strong_iteration(one),X4),strong_iteration(one)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_20,plain,
( ~ leq(X1,X1)
| leq(X1,multiplication(strong_iteration(one),zero)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,negated_conjecture,
( ~ leq(strong_iteration(one),multiplication(strong_iteration(one),esk1_0))
| ~ leq(multiplication(strong_iteration(one),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_19])])])]) ).
fof(c_0_24,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_25,plain,
! [X36] : strong_iteration(X36) = addition(star(X36),multiplication(strong_iteration(X36),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
cnf(c_0_26,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
leq(X1,multiplication(strong_iteration(one),zero)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_28,negated_conjecture,
( ~ leq(strong_iteration(one),multiplication(strong_iteration(one),esk1_0))
| ~ leq(multiplication(strong_iteration(one),esk1_0),strong_iteration(one)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X12,X13,X14] : multiplication(X12,multiplication(X13,X14)) = multiplication(multiplication(X12,X13),X14),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_31,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
addition(X1,multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),zero),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_33,plain,
! [X23] : multiplication(zero,X23) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_34,negated_conjecture,
( ~ leq(strong_iteration(one),multiplication(strong_iteration(one),esk1_0))
| addition(strong_iteration(one),multiplication(strong_iteration(one),esk1_0)) != strong_iteration(one) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_21]),c_0_29]) ).
cnf(c_0_35,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( addition(strong_iteration(one),multiplication(strong_iteration(one),esk1_0)) != strong_iteration(one)
| addition(strong_iteration(one),multiplication(strong_iteration(one),esk1_0)) != multiplication(strong_iteration(one),esk1_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_21]) ).
cnf(c_0_39,plain,
multiplication(strong_iteration(one),X1) = strong_iteration(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_36]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_22]),c_0_39]),c_0_39]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE141+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 22:47:03 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.45 % Version: 3.5.1
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.45 % Starting sh5l with 300s (1) cores
% 0.12/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1392116 completed with status 0
% 0.12/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.45 % No SInE strategy applied
% 0.12/0.45 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.12/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.45 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.12/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1392122 completed with status 0
% 0.12/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.45 % No SInE strategy applied
% 0.12/0.45 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.12/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.45 % Preprocessing time : 0.002 s
% 0.12/0.45 % Presaturation interreduction done
% 0.12/0.45
% 0.12/0.45 % Proof found!
% 0.12/0.45 % SZS status Theorem
% 0.12/0.45 % SZS output start CNFRefutation
% See solution above
% 0.12/0.45 % Parsed axioms : 19
% 0.12/0.45 % Removed by relevancy pruning/SinE : 0
% 0.12/0.45 % Initial clauses : 20
% 0.12/0.45 % Removed in clause preprocessing : 0
% 0.12/0.45 % Initial clauses in saturation : 20
% 0.12/0.45 % Processed clauses : 106
% 0.12/0.45 % ...of these trivial : 8
% 0.12/0.45 % ...subsumed : 15
% 0.12/0.45 % ...remaining for further processing : 83
% 0.12/0.45 % Other redundant clauses eliminated : 0
% 0.12/0.45 % Clauses deleted for lack of memory : 0
% 0.12/0.45 % Backward-subsumed : 2
% 0.12/0.45 % Backward-rewritten : 23
% 0.12/0.45 % Generated clauses : 506
% 0.12/0.45 % ...of the previous two non-redundant : 381
% 0.12/0.45 % ...aggressively subsumed : 0
% 0.12/0.45 % Contextual simplify-reflections : 1
% 0.12/0.45 % Paramodulations : 506
% 0.12/0.45 % Factorizations : 0
% 0.12/0.45 % NegExts : 0
% 0.12/0.45 % Equation resolutions : 0
% 0.12/0.45 % Disequality decompositions : 0
% 0.12/0.45 % Total rewrite steps : 365
% 0.12/0.45 % ...of those cached : 213
% 0.12/0.45 % Propositional unsat checks : 0
% 0.12/0.45 % Propositional check models : 0
% 0.12/0.45 % Propositional check unsatisfiable : 0
% 0.12/0.45 % Propositional clauses : 0
% 0.12/0.45 % Propositional clauses after purity: 0
% 0.12/0.45 % Propositional unsat core size : 0
% 0.12/0.45 % Propositional preprocessing time : 0.000
% 0.12/0.45 % Propositional encoding time : 0.000
% 0.12/0.45 % Propositional solver time : 0.000
% 0.12/0.45 % Success case prop preproc time : 0.000
% 0.12/0.45 % Success case prop encoding time : 0.000
% 0.12/0.45 % Success case prop solver time : 0.000
% 0.12/0.45 % Current number of processed clauses : 38
% 0.12/0.45 % Positive orientable unit clauses : 25
% 0.12/0.45 % Positive unorientable unit clauses: 3
% 0.12/0.45 % Negative unit clauses : 0
% 0.12/0.45 % Non-unit-clauses : 10
% 0.12/0.45 % Current number of unprocessed clauses: 309
% 0.12/0.45 % ...number of literals in the above : 461
% 0.12/0.45 % Current number of archived formulas : 0
% 0.12/0.45 % Current number of archived clauses : 45
% 0.12/0.45 % Clause-clause subsumption calls (NU) : 55
% 0.12/0.45 % Rec. Clause-clause subsumption calls : 55
% 0.12/0.45 % Non-unit clause-clause subsumptions : 8
% 0.12/0.45 % Unit Clause-clause subsumption calls : 11
% 0.12/0.45 % Rewrite failures with RHS unbound : 0
% 0.12/0.45 % BW rewrite match attempts : 57
% 0.12/0.45 % BW rewrite match successes : 50
% 0.12/0.45 % Condensation attempts : 0
% 0.12/0.45 % Condensation successes : 0
% 0.12/0.45 % Termbank termtop insertions : 5904
% 0.12/0.45 % Search garbage collected termcells : 81
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.012 s
% 0.12/0.45 % System time : 0.005 s
% 0.12/0.45 % Total time : 0.017 s
% 0.12/0.45 % Maximum resident set size: 3652 pages
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.053 s
% 0.12/0.45 % System time : 0.018 s
% 0.12/0.45 % Total time : 0.071 s
% 0.12/0.45 % Maximum resident set size: 4608 pages
% 0.12/0.45 % E exiting
%------------------------------------------------------------------------------