%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE137+1 : 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 : 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 0.13s 0.49s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 20 unt; 0 def)
% Number of atoms : 36 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 6 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 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 : 42 ( 3 sgn 24 !; 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_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(goals,conjecture,
! [X4] : leq(X4,strong_iteration(one)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(c_0_7,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_8,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_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)],[idempotence]) ).
cnf(c_0_11,plain,
( ~ leq(X1,addition(multiplication(X2,X1),X3))
| leq(X1,multiplication(strong_iteration(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,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_14,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,negated_conjecture,
~ ! [X4] : leq(X4,strong_iteration(one)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_17,plain,
( ~ leq(X1,addition(X1,X2))
| leq(X1,multiplication(strong_iteration(one),X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_20,plain,
! [X15] : multiplication(X15,one) = X15,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_21,negated_conjecture,
~ leq(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_16])])])]) ).
cnf(c_0_22,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_23,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
~ leq(esk1_0,strong_iteration(one)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE137+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 22:45:40 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.13/0.49 % Version: 3.5.1
% 0.13/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.49 % Starting sh5l with 300s (1) cores
% 0.13/0.49 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 354746 completed with status 0
% 0.13/0.49 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.49 % No SInE strategy applied
% 0.13/0.49 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.13/0.49 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.49 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.13/0.49 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 0.13/0.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.13/0.49 % G-E--_300_C18_F1_SE_CS_SP_S0Y with pid 354752 completed with status 0
% 0.13/0.49 % Result found by G-E--_300_C18_F1_SE_CS_SP_S0Y
% 0.13/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.49 % No SInE strategy applied
% 0.13/0.49 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.13/0.49 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.49 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.13/0.49 % Preprocessing time : 0.002 s
% 0.13/0.49
% 0.13/0.49 % Proof found!
% 0.13/0.49 % SZS status Theorem
% 0.13/0.49 % SZS output start CNFRefutation
% See solution above
% 0.13/0.49 % Parsed axioms : 19
% 0.13/0.49 % Removed by relevancy pruning/SinE : 0
% 0.13/0.50 % Initial clauses : 20
% 0.13/0.50 % Removed in clause preprocessing : 0
% 0.13/0.50 % Initial clauses in saturation : 20
% 0.13/0.50 % Processed clauses : 60
% 0.13/0.50 % ...of these trivial : 5
% 0.13/0.50 % ...subsumed : 13
% 0.13/0.50 % ...remaining for further processing : 42
% 0.13/0.50 % Other redundant clauses eliminated : 0
% 0.13/0.50 % Clauses deleted for lack of memory : 0
% 0.13/0.50 % Backward-subsumed : 0
% 0.13/0.50 % Backward-rewritten : 5
% 0.13/0.50 % Generated clauses : 310
% 0.13/0.50 % ...of the previous two non-redundant : 189
% 0.13/0.50 % ...aggressively subsumed : 0
% 0.13/0.50 % Contextual simplify-reflections : 0
% 0.13/0.50 % Paramodulations : 310
% 0.13/0.50 % Factorizations : 0
% 0.13/0.50 % NegExts : 0
% 0.13/0.50 % Equation resolutions : 0
% 0.13/0.50 % Disequality decompositions : 0
% 0.13/0.50 % Total rewrite steps : 259
% 0.13/0.50 % ...of those cached : 147
% 0.13/0.50 % Propositional unsat checks : 0
% 0.13/0.50 % Propositional check models : 0
% 0.13/0.50 % Propositional check unsatisfiable : 0
% 0.13/0.50 % Propositional clauses : 0
% 0.13/0.50 % Propositional clauses after purity: 0
% 0.13/0.50 % Propositional unsat core size : 0
% 0.13/0.50 % Propositional preprocessing time : 0.000
% 0.13/0.50 % Propositional encoding time : 0.000
% 0.13/0.50 % Propositional solver time : 0.000
% 0.13/0.50 % Success case prop preproc time : 0.000
% 0.13/0.50 % Success case prop encoding time : 0.000
% 0.13/0.50 % Success case prop solver time : 0.000
% 0.13/0.50 % Current number of processed clauses : 37
% 0.13/0.50 % Positive orientable unit clauses : 30
% 0.13/0.50 % Positive unorientable unit clauses: 2
% 0.13/0.50 % Negative unit clauses : 1
% 0.13/0.50 % Non-unit-clauses : 4
% 0.13/0.50 % Current number of unprocessed clauses: 147
% 0.13/0.50 % ...number of literals in the above : 190
% 0.13/0.50 % Current number of archived formulas : 0
% 0.13/0.50 % Current number of archived clauses : 5
% 0.13/0.50 % Clause-clause subsumption calls (NU) : 2
% 0.13/0.50 % Rec. Clause-clause subsumption calls : 2
% 0.13/0.50 % Non-unit clause-clause subsumptions : 0
% 0.13/0.50 % Unit Clause-clause subsumption calls : 1
% 0.13/0.50 % Rewrite failures with RHS unbound : 0
% 0.13/0.50 % BW rewrite match attempts : 24
% 0.13/0.50 % BW rewrite match successes : 17
% 0.13/0.50 % Condensation attempts : 0
% 0.13/0.50 % Condensation successes : 0
% 0.13/0.50 % Termbank termtop insertions : 3209
% 0.13/0.50 % Search garbage collected termcells : 69
% 0.13/0.50
% 0.13/0.50 % -------------------------------------------------
% 0.13/0.50 % User time : 0.010 s
% 0.13/0.50 % System time : 0.008 s
% 0.13/0.50 % Total time : 0.018 s
% 0.13/0.50 % Maximum resident set size: 3652 pages
% 0.13/0.50
% 0.13/0.50 % -------------------------------------------------
% 0.13/0.50 % User time : 0.072 s
% 0.13/0.50 % System time : 0.031 s
% 0.13/0.50 % Total time : 0.102 s
% 0.13/0.50 % Maximum resident set size: 4608 pages
% 0.13/0.50 % E exiting
%------------------------------------------------------------------------------