%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE146+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 : n010.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 12:58:57 PM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 21 unt; 0 def)
% Number of atoms : 29 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4] : leq(one,strong_iteration(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(c_0_6,negated_conjecture,
~ ! [X4] : leq(one,strong_iteration(X4)),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_7,plain,
! [X35,X36,X37] : addition(X37,addition(X36,X35)) = addition(addition(X37,X36),X35),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_8,plain,
! [X39] : addition(X39,X39) = X39,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_9,plain,
! [X17] : strong_iteration(X17) = addition(multiplication(X17,strong_iteration(X17)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_10,plain,
! [X33,X34] : addition(X33,X34) = addition(X34,X33),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_11,negated_conjecture,
~ leq(one,strong_iteration(esk1_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_12,plain,
! [X15,X16] :
( ( leq(X15,X16)
| addition(X15,X16) != X16 )
& ( addition(X15,X16) = X16
| ~ leq(X15,X16) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_13,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
~ leq(one,strong_iteration(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
addition(one,strong_iteration(esk1_0)) != strong_iteration(esk1_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE146+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:46:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.46 % Version: 3.5.1
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.46 % Starting sh5l with 300s (1) cores
% 0.09/0.46 % sh5l with pid 3675195 completed with status 0
% 0.09/0.46 % Result found by sh5l
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.46 % Starting sh5l with 300s (1) cores
% 0.09/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.46 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.46 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.09/0.46 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.46 % SubtermCWHack with pid 3675211 completed with status 0
% 0.09/0.46 % Result found by SubtermCWHack
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.46 % Starting sh5l with 300s (1) cores
% 0.09/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.46 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.46 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.09/0.46 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.46 % Preprocessing time : 0.002 s
% 0.09/0.46
% 0.09/0.46 % Proof found!
% 0.09/0.46 % SZS status Theorem
% 0.09/0.46 % SZS output start CNFRefutation
% See solution above
% 0.09/0.46 % Parsed axioms : 19
% 0.09/0.46 % Removed by relevancy pruning/SinE : 0
% 0.09/0.46 % Initial clauses : 20
% 0.09/0.46 % Removed in clause preprocessing : 0
% 0.09/0.46 % Initial clauses in saturation : 20
% 0.09/0.46 % Processed clauses : 25
% 0.09/0.46 % ...of these trivial : 1
% 0.09/0.46 % ...subsumed : 0
% 0.09/0.46 % ...remaining for further processing : 24
% 0.09/0.46 % Other redundant clauses eliminated : 0
% 0.09/0.46 % Clauses deleted for lack of memory : 0
% 0.09/0.46 % Backward-subsumed : 0
% 0.09/0.46 % Backward-rewritten : 3
% 0.09/0.46 % Generated clauses : 62
% 0.09/0.46 % ...of the previous two non-redundant : 30
% 0.09/0.46 % ...aggressively subsumed : 0
% 0.09/0.46 % Contextual simplify-reflections : 0
% 0.09/0.46 % Paramodulations : 62
% 0.09/0.46 % Factorizations : 0
% 0.09/0.46 % NegExts : 0
% 0.09/0.46 % Equation resolutions : 0
% 0.09/0.46 % Disequality decompositions : 0
% 0.09/0.46 % Total rewrite steps : 55
% 0.09/0.46 % ...of those cached : 20
% 0.09/0.46 % Propositional unsat checks : 0
% 0.09/0.46 % Propositional check models : 0
% 0.09/0.46 % Propositional check unsatisfiable : 0
% 0.09/0.46 % Propositional clauses : 0
% 0.09/0.46 % Propositional clauses after purity: 0
% 0.09/0.46 % Propositional unsat core size : 0
% 0.09/0.46 % Propositional preprocessing time : 0.000
% 0.09/0.46 % Propositional encoding time : 0.000
% 0.09/0.46 % Propositional solver time : 0.000
% 0.09/0.46 % Success case prop preproc time : 0.000
% 0.09/0.46 % Success case prop encoding time : 0.000
% 0.09/0.46 % Success case prop solver time : 0.000
% 0.09/0.46 % Current number of processed clauses : 21
% 0.09/0.46 % Positive orientable unit clauses : 17
% 0.09/0.46 % Positive unorientable unit clauses: 1
% 0.09/0.46 % Negative unit clauses : 1
% 0.09/0.46 % Non-unit-clauses : 2
% 0.09/0.46 % Current number of unprocessed clauses: 25
% 0.09/0.46 % ...number of literals in the above : 28
% 0.09/0.46 % Current number of archived formulas : 0
% 0.09/0.46 % Current number of archived clauses : 3
% 0.09/0.46 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.46 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.46 % Non-unit clause-clause subsumptions : 0
% 0.09/0.46 % Unit Clause-clause subsumption calls : 0
% 0.09/0.46 % Rewrite failures with RHS unbound : 0
% 0.09/0.46 % BW rewrite match attempts : 9
% 0.09/0.46 % BW rewrite match successes : 7
% 0.09/0.46 % Condensation attempts : 0
% 0.09/0.46 % Condensation successes : 0
% 0.09/0.46 % Termbank termtop insertions : 1308
% 0.09/0.46 % Search garbage collected termcells : 70
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.006 s
% 0.09/0.46 % System time : 0.004 s
% 0.09/0.46 % Total time : 0.010 s
% 0.09/0.46 % Maximum resident set size: 3600 pages
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.007 s
% 0.09/0.46 % System time : 0.010 s
% 0.09/0.46 % Total time : 0.017 s
% 0.09/0.46 % Maximum resident set size: 4608 pages
% 0.09/0.46 % E exiting
%------------------------------------------------------------------------------