%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE148+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 : n016.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 12:58:58 PM UTC 2026
% Result : Theorem 0.15s 5.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 37 unt; 0 def)
% Number of atoms : 59 ( 43 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 7 |; 4 &)
% ( 1 <=>; 2 =>; 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; 4 con; 0-2 aty)
% Number of variables : 66 ( 3 sgn 40 !; 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(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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(goals,conjecture,
! [X4,X5] :
( leq(X4,multiplication(X4,strong_iteration(X5)))
& ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,strong_iteration(X5)),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(c_0_11,plain,
! [X36,X37,X38] : addition(X38,addition(X37,X36)) = addition(addition(X38,X37),X36),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_12,plain,
! [X39] : addition(X39,X39) = X39,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_13,plain,
! [X28] : strong_iteration(X28) = addition(multiplication(X28,strong_iteration(X28)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_14,plain,
! [X34,X35] : addition(X34,X35) = addition(X35,X34),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_15,negated_conjecture,
~ ! [X4,X5] :
( leq(X4,multiplication(X4,strong_iteration(X5)))
& ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,strong_iteration(X5)),X4) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_16,plain,
! [X22,X23,X24] : multiplication(X22,addition(X23,X24)) = addition(multiplication(X22,X23),multiplication(X22,X24)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
fof(c_0_17,plain,
! [X40] : multiplication(X40,one) = X40,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_18,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_22,negated_conjecture,
( ( ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0)))
| ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0) )
& ( ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0)))
| multiplication(esk1_0,esk2_0) = zero ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
fof(c_0_23,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_24,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_28,plain,
! [X19,X20,X21] : multiplication(X19,multiplication(X20,X21)) = multiplication(multiplication(X19,X20),X21),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_29,negated_conjecture,
( ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0)))
| multiplication(esk1_0,esk2_0) = zero ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_21]) ).
cnf(c_0_32,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_33,plain,
! [X31] : multiplication(zero,X31) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_34,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
multiplication(esk1_0,esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_21]),c_0_32])]) ).
cnf(c_0_36,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_37,plain,
! [X30] : addition(X30,zero) = X30,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_38,negated_conjecture,
multiplication(esk1_0,multiplication(esk2_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,negated_conjecture,
multiplication(esk1_0,addition(one,multiplication(esk2_0,X1))) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_38]),c_0_39]),c_0_21]) ).
cnf(c_0_41,negated_conjecture,
( ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0)))
| ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_42,negated_conjecture,
multiplication(esk1_0,strong_iteration(esk2_0)) = esk1_0,
inference(spm,[status(thm)],[c_0_40,c_0_27]) ).
cnf(c_0_43,negated_conjecture,
~ leq(esk1_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_30]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE148+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/5.36 % Computer : n016.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sun Sep 20 22:51:30 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 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
% 0.15/5.44 % Version: 3.5.1
% 0.15/5.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.44 % Starting sh5l with 300s (1) cores
% 0.15/5.44 % new_bool_3 with pid 965405 completed with status 0
% 0.15/5.44 % Result found by new_bool_3
% 0.15/5.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.44 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.15/5.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.44 % SubtermCWHack with pid 965411 completed with status 0
% 0.15/5.44 % Result found by SubtermCWHack
% 0.15/5.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.44 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.15/5.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.44 % Preprocessing time : 0.001 s
% 0.15/5.44
% 0.15/5.44 % Proof found!
% 0.15/5.44 % SZS status Theorem
% 0.15/5.44 % SZS output start CNFRefutation
% See solution above
% 0.15/5.44 % Parsed axioms : 19
% 0.15/5.44 % Removed by relevancy pruning/SinE : 0
% 0.15/5.44 % Initial clauses : 21
% 0.15/5.44 % Removed in clause preprocessing : 0
% 0.15/5.44 % Initial clauses in saturation : 21
% 0.15/5.44 % Processed clauses : 169
% 0.15/5.44 % ...of these trivial : 10
% 0.15/5.44 % ...subsumed : 60
% 0.15/5.44 % ...remaining for further processing : 99
% 0.15/5.44 % Other redundant clauses eliminated : 2
% 0.15/5.44 % Clauses deleted for lack of memory : 0
% 0.15/5.44 % Backward-subsumed : 15
% 0.15/5.44 % Backward-rewritten : 11
% 0.15/5.44 % Generated clauses : 1180
% 0.15/5.44 % ...of the previous two non-redundant : 866
% 0.15/5.44 % ...aggressively subsumed : 0
% 0.15/5.44 % Contextual simplify-reflections : 0
% 0.15/5.44 % Paramodulations : 1178
% 0.15/5.44 % Factorizations : 0
% 0.15/5.44 % NegExts : 0
% 0.15/5.44 % Equation resolutions : 2
% 0.15/5.44 % Disequality decompositions : 0
% 0.15/5.44 % Total rewrite steps : 975
% 0.15/5.44 % ...of those cached : 641
% 0.15/5.44 % Propositional unsat checks : 0
% 0.15/5.44 % Propositional check models : 0
% 0.15/5.44 % Propositional check unsatisfiable : 0
% 0.15/5.44 % Propositional clauses : 0
% 0.15/5.44 % Propositional clauses after purity: 0
% 0.15/5.44 % Propositional unsat core size : 0
% 0.15/5.44 % Propositional preprocessing time : 0.000
% 0.15/5.44 % Propositional encoding time : 0.000
% 0.15/5.44 % Propositional solver time : 0.000
% 0.15/5.44 % Success case prop preproc time : 0.000
% 0.15/5.44 % Success case prop encoding time : 0.000
% 0.15/5.44 % Success case prop solver time : 0.000
% 0.15/5.44 % Current number of processed clauses : 73
% 0.15/5.44 % Positive orientable unit clauses : 45
% 0.15/5.44 % Positive unorientable unit clauses: 4
% 0.15/5.44 % Negative unit clauses : 3
% 0.15/5.44 % Non-unit-clauses : 21
% 0.15/5.44 % Current number of unprocessed clauses: 706
% 0.15/5.44 % ...number of literals in the above : 934
% 0.15/5.44 % Current number of archived formulas : 0
% 0.15/5.44 % Current number of archived clauses : 26
% 0.15/5.44 % Clause-clause subsumption calls (NU) : 111
% 0.15/5.44 % Rec. Clause-clause subsumption calls : 108
% 0.15/5.44 % Non-unit clause-clause subsumptions : 25
% 0.15/5.44 % Unit Clause-clause subsumption calls : 57
% 0.15/5.44 % Rewrite failures with RHS unbound : 0
% 0.15/5.44 % BW rewrite match attempts : 58
% 0.15/5.44 % BW rewrite match successes : 42
% 0.15/5.44 % Condensation attempts : 0
% 0.15/5.44 % Condensation successes : 0
% 0.15/5.44 % Termbank termtop insertions : 10799
% 0.15/5.44 % Search garbage collected termcells : 101
% 0.15/5.44
% 0.15/5.44 % -------------------------------------------------
% 0.15/5.44 % User time : 0.010 s
% 0.15/5.44 % System time : 0.003 s
% 0.15/5.44 % Total time : 0.013 s
% 0.15/5.44 % Maximum resident set size: 3652 pages
% 0.15/5.44
% 0.15/5.44 % -------------------------------------------------
% 0.15/5.44 % User time : 0.011 s
% 0.15/5.44 % System time : 0.009 s
% 0.15/5.44 % Total time : 0.019 s
% 0.15/5.44 % Maximum resident set size: 4864 pages
% 0.15/5.44 % E exiting
%------------------------------------------------------------------------------