%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE140+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 : n017.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 0.22s 10.65s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 44 unt; 0 def)
% Number of atoms : 70 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 8 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 94 ( 7 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(distributivity2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(goals,conjecture,
! [X4,X5] :
( leq(X4,X5)
=> leq(strong_iteration(X4),strong_iteration(X5)) ),
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_12,plain,
! [X34,X35,X36] : addition(X36,addition(X35,X34)) = addition(addition(X36,X35),X34),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_13,plain,
! [X37] : addition(X37,X37) = X37,
inference(variable_rename,[status(thm)],[idempotence]) ).
cnf(c_0_14,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X32,X33] : addition(X32,X33) = addition(X33,X32),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_17,plain,
! [X14,X15,X16] :
( leq(X16,multiplication(strong_iteration(X14),X15))
| ~ leq(X16,addition(multiplication(X14,X16),X15)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])])]) ).
fof(c_0_18,plain,
! [X17,X18] :
( ( leq(X17,X18)
| addition(X17,X18) != X18 )
& ( addition(X17,X18) = X18
| ~ leq(X17,X18) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_19,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X19] : strong_iteration(X19) = addition(multiplication(X19,strong_iteration(X19)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
cnf(c_0_22,plain,
( ~ leq(X1,addition(multiplication(X2,X1),X3))
| leq(X1,multiplication(strong_iteration(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_26,plain,
! [X41] : multiplication(zero,X41) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_27,plain,
! [X40] : addition(X40,zero) = X40,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_28,plain,
( addition(X1,addition(multiplication(X2,X1),X3)) != addition(multiplication(X2,X1),X3)
| leq(X1,multiplication(strong_iteration(X2),X3)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
addition(X1,addition(X2,addition(X3,X1))) = addition(X2,addition(X3,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_30,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_31,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X39] : multiplication(one,X39) = X39,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_34,plain,
! [X27,X28,X29] : multiplication(addition(X27,X28),X29) = addition(multiplication(X27,X29),multiplication(X28,X29)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
cnf(c_0_35,plain,
leq(X1,multiplication(strong_iteration(X2),addition(X3,X1))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
strong_iteration(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_37,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
leq(X1,addition(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
fof(c_0_40,negated_conjecture,
~ ! [X4,X5] :
( leq(X4,X5)
=> leq(strong_iteration(X4),strong_iteration(X5)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_41,plain,
addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)) = addition(strong_iteration(X1),X2),
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_42,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_20]) ).
fof(c_0_43,plain,
! [X38] : multiplication(X38,one) = X38,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_44,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_39,c_0_20]) ).
fof(c_0_45,negated_conjecture,
( ~ leq(strong_iteration(esk1_0),strong_iteration(esk2_0))
& leq(esk1_0,esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
cnf(c_0_46,plain,
( ~ leq(X1,addition(X3,multiplication(X2,X1)))
| leq(X1,multiplication(strong_iteration(X2),X3)) ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_47,plain,
addition(one,multiplication(addition(X1,X2),strong_iteration(X1))) = multiplication(addition(X2,one),strong_iteration(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_42]) ).
cnf(c_0_48,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,plain,
leq(X1,multiplication(addition(X2,one),X1)),
inference(spm,[status(thm)],[c_0_44,c_0_42]) ).
cnf(c_0_50,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_51,negated_conjecture,
leq(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
leq(strong_iteration(X1),strong_iteration(addition(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_53,negated_conjecture,
addition(esk1_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
~ leq(strong_iteration(esk1_0),strong_iteration(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE140+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/10.46 % Computer : n017.cluster.edu
% 0.18/10.46 % Model : x86_64 x86_64
% 0.18/10.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.46 % Memory : 8046.5625MB
% 0.18/10.46 % OS : Linux 6.8.0-71-generic
% 0.18/10.47 % CPULimit : 300
% 0.18/10.47 % WCLimit : 300
% 0.18/10.47 % DateTime : Sun Sep 20 22:41:22 UTC 2026
% 0.18/10.47 % CPUTime :
% 0.18/10.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/10.51 Running first-order theorem proving
% 0.22/10.51 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
% 0.22/10.65 % Version: 3.5.1
% 0.22/10.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/10.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/10.65 % Starting new_bool_3 with 300s (1) cores
% 0.22/10.65 % Starting new_bool_1 with 300s (1) cores
% 0.22/10.65 % Starting sh5l with 300s (1) cores
% 0.22/10.65 % new_bool_3 with pid 793291 completed with status 0
% 0.22/10.65 % Result found by new_bool_3
% 0.22/10.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/10.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/10.65 % Starting new_bool_3 with 300s (1) cores
% 0.22/10.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/10.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/10.65 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.22/10.65 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.22/10.65 % Starting SubtermCWHack with 28s (1) cores
% 0.22/10.65 % SubtermCWHack with pid 793297 completed with status 0
% 0.22/10.65 % Result found by SubtermCWHack
% 0.22/10.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/10.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/10.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/10.65 % Starting new_bool_3 with 300s (1) cores
% 0.22/10.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/10.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/10.65 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.22/10.65 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.22/10.65 % Starting SubtermCWHack with 28s (1) cores
% 0.22/10.65 % Preprocessing time : 0.001 s
% 0.22/10.65
% 0.22/10.65 % Proof found!
% 0.22/10.65 % SZS status Theorem
% 0.22/10.65 % SZS output start CNFRefutation
% See solution above
% 0.22/10.65 % Parsed axioms : 19
% 0.22/10.65 % Removed by relevancy pruning/SinE : 0
% 0.22/10.65 % Initial clauses : 21
% 0.22/10.65 % Removed in clause preprocessing : 0
% 0.22/10.65 % Initial clauses in saturation : 21
% 0.22/10.65 % Processed clauses : 3973
% 0.22/10.65 % ...of these trivial : 524
% 0.22/10.65 % ...subsumed : 2833
% 0.22/10.65 % ...remaining for further processing : 616
% 0.22/10.65 % Other redundant clauses eliminated : 16
% 0.22/10.65 % Clauses deleted for lack of memory : 0
% 0.22/10.65 % Backward-subsumed : 51
% 0.22/10.65 % Backward-rewritten : 45
% 0.22/10.65 % Generated clauses : 20373
% 0.22/10.65 % ...of the previous two non-redundant : 14677
% 0.22/10.65 % ...aggressively subsumed : 0
% 0.22/10.65 % Contextual simplify-reflections : 0
% 0.22/10.65 % Paramodulations : 20357
% 0.22/10.65 % Factorizations : 0
% 0.22/10.65 % NegExts : 0
% 0.22/10.65 % Equation resolutions : 16
% 0.22/10.65 % Disequality decompositions : 0
% 0.22/10.65 % Total rewrite steps : 17380
% 0.22/10.65 % ...of those cached : 13398
% 0.22/10.65 % Propositional unsat checks : 0
% 0.22/10.65 % Propositional check models : 0
% 0.22/10.65 % Propositional check unsatisfiable : 0
% 0.22/10.65 % Propositional clauses : 0
% 0.22/10.65 % Propositional clauses after purity: 0
% 0.22/10.65 % Propositional unsat core size : 0
% 0.22/10.65 % Propositional preprocessing time : 0.000
% 0.22/10.65 % Propositional encoding time : 0.000
% 0.22/10.65 % Propositional solver time : 0.000
% 0.22/10.65 % Success case prop preproc time : 0.000
% 0.22/10.65 % Success case prop encoding time : 0.000
% 0.22/10.65 % Success case prop solver time : 0.000
% 0.22/10.65 % Current number of processed clauses : 520
% 0.22/10.65 % Positive orientable unit clauses : 326
% 0.22/10.65 % Positive unorientable unit clauses: 4
% 0.22/10.65 % Negative unit clauses : 103
% 0.22/10.65 % Non-unit-clauses : 87
% 0.22/10.65 % Current number of unprocessed clauses: 10468
% 0.22/10.65 % ...number of literals in the above : 15401
% 0.22/10.65 % Current number of archived formulas : 0
% 0.22/10.65 % Current number of archived clauses : 96
% 0.22/10.65 % Clause-clause subsumption calls (NU) : 1491
% 0.22/10.65 % Rec. Clause-clause subsumption calls : 1485
% 0.22/10.65 % Non-unit clause-clause subsumptions : 235
% 0.22/10.65 % Unit Clause-clause subsumption calls : 1669
% 0.22/10.65 % Rewrite failures with RHS unbound : 0
% 0.22/10.65 % BW rewrite match attempts : 1011
% 0.22/10.65 % BW rewrite match successes : 91
% 0.22/10.65 % Condensation attempts : 0
% 0.22/10.65 % Condensation successes : 0
% 0.22/10.65 % Termbank termtop insertions : 193145
% 0.22/10.65 % Search garbage collected termcells : 88
% 0.22/10.65
% 0.22/10.65 % -------------------------------------------------
% 0.22/10.65 % User time : 0.106 s
% 0.22/10.65 % System time : 0.013 s
% 0.22/10.65 % Total time : 0.118 s
% 0.22/10.65 % Maximum resident set size: 3652 pages
% 0.22/10.65
% 0.22/10.65 % -------------------------------------------------
% 0.22/10.65 % User time : 0.108 s
% 0.22/10.65 % System time : 0.017 s
% 0.22/10.65 % Total time : 0.124 s
% 0.22/10.65 % Maximum resident set size: 4608 pages
% 0.22/10.65 % E exiting
%------------------------------------------------------------------------------