%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE150+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 : n012.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 0.07s 0.35s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 20 unt; 0 def)
% Number of atoms : 36 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 5 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 1 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(goals,conjecture,
! [X4] :
( leq(addition(one,multiplication(X4,zero)),strong_iteration(multiplication(X4,zero)))
& leq(strong_iteration(multiplication(X4,zero)),addition(one,multiplication(X4,zero))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
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(c_0_7,plain,
! [X32] : strong_iteration(X32) = addition(multiplication(X32,strong_iteration(X32)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_8,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_9,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X12,X13,X14] : multiplication(X12,multiplication(X13,X14)) = multiplication(multiplication(X12,X13),X14),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_12,negated_conjecture,
~ ! [X4] :
( leq(addition(one,multiplication(X4,zero)),strong_iteration(multiplication(X4,zero)))
& leq(strong_iteration(multiplication(X4,zero)),addition(one,multiplication(X4,zero))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_13,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X23] : multiplication(zero,X23) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_16,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_17,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_18,negated_conjecture,
( ~ leq(addition(one,multiplication(esk1_0,zero)),strong_iteration(multiplication(esk1_0,zero)))
| ~ leq(strong_iteration(multiplication(esk1_0,zero)),addition(one,multiplication(esk1_0,zero))) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_19,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ~ leq(addition(one,multiplication(esk1_0,zero)),strong_iteration(multiplication(esk1_0,zero)))
| ~ leq(strong_iteration(multiplication(esk1_0,zero)),addition(one,multiplication(esk1_0,zero))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
strong_iteration(multiplication(X1,zero)) = addition(one,multiplication(X1,zero)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 20 22:46:36 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.32 Running first-order theorem proving
% 0.07/0.32 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
% 0.07/0.35 % Version: 3.5.1
% 0.07/0.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.35 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.35 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.35 % Starting sh5l with 300s (1) cores
% 0.07/0.35 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1024043 completed with status 0
% 0.07/0.35 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.07/0.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.35 % No SInE strategy applied
% 0.07/0.35 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.07/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.07/0.35 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.07/0.35 % Starting new_bool_3 with 136s (1) cores
% 0.07/0.35 % new_bool_3 with pid 1024054 completed with status 0
% 0.07/0.35 % Result found by new_bool_3
% 0.07/0.35 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.35 % No SInE strategy applied
% 0.07/0.35 % Search class: FHHSM-FFSF21-MFFFFFNN
% 0.07/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.07/0.35 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.07/0.35 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.07/0.35 % Starting new_bool_3 with 136s (1) cores
% 0.07/0.35 % Preprocessing time : 0.001 s
% 0.07/0.35 % Presaturation interreduction done
% 0.07/0.35
% 0.07/0.35 % Proof found!
% 0.07/0.35 % SZS status Theorem
% 0.07/0.35 % SZS output start CNFRefutation
% See solution above
% 0.07/0.35 % Parsed axioms : 19
% 0.07/0.35 % Removed by relevancy pruning/SinE : 0
% 0.07/0.35 % Initial clauses : 20
% 0.07/0.35 % Removed in clause preprocessing : 0
% 0.07/0.35 % Initial clauses in saturation : 20
% 0.07/0.35 % Processed clauses : 238
% 0.07/0.35 % ...of these trivial : 26
% 0.07/0.35 % ...subsumed : 94
% 0.07/0.35 % ...remaining for further processing : 118
% 0.07/0.35 % Other redundant clauses eliminated : 9
% 0.07/0.35 % Clauses deleted for lack of memory : 0
% 0.07/0.35 % Backward-subsumed : 2
% 0.07/0.35 % Backward-rewritten : 11
% 0.07/0.35 % Generated clauses : 1152
% 0.07/0.35 % ...of the previous two non-redundant : 808
% 0.07/0.35 % ...aggressively subsumed : 0
% 0.07/0.35 % Contextual simplify-reflections : 0
% 0.07/0.35 % Paramodulations : 1143
% 0.07/0.35 % Factorizations : 0
% 0.07/0.35 % NegExts : 0
% 0.07/0.35 % Equation resolutions : 9
% 0.07/0.35 % Disequality decompositions : 0
% 0.07/0.35 % Total rewrite steps : 788
% 0.07/0.35 % ...of those cached : 546
% 0.07/0.35 % Propositional unsat checks : 0
% 0.07/0.35 % Propositional check models : 0
% 0.07/0.35 % Propositional check unsatisfiable : 0
% 0.07/0.35 % Propositional clauses : 0
% 0.07/0.35 % Propositional clauses after purity: 0
% 0.07/0.35 % Propositional unsat core size : 0
% 0.07/0.35 % Propositional preprocessing time : 0.000
% 0.07/0.35 % Propositional encoding time : 0.000
% 0.07/0.35 % Propositional solver time : 0.000
% 0.07/0.35 % Success case prop preproc time : 0.000
% 0.07/0.35 % Success case prop encoding time : 0.000
% 0.07/0.35 % Success case prop solver time : 0.000
% 0.07/0.35 % Current number of processed clauses : 85
% 0.07/0.35 % Positive orientable unit clauses : 47
% 0.07/0.35 % Positive unorientable unit clauses: 3
% 0.07/0.35 % Negative unit clauses : 0
% 0.07/0.35 % Non-unit-clauses : 35
% 0.07/0.35 % Current number of unprocessed clauses: 609
% 0.07/0.35 % ...number of literals in the above : 896
% 0.07/0.35 % Current number of archived formulas : 0
% 0.07/0.35 % Current number of archived clauses : 33
% 0.07/0.35 % Clause-clause subsumption calls (NU) : 441
% 0.07/0.35 % Rec. Clause-clause subsumption calls : 441
% 0.07/0.35 % Non-unit clause-clause subsumptions : 90
% 0.07/0.35 % Unit Clause-clause subsumption calls : 29
% 0.07/0.35 % Rewrite failures with RHS unbound : 0
% 0.07/0.35 % BW rewrite match attempts : 90
% 0.07/0.35 % BW rewrite match successes : 54
% 0.07/0.35 % Condensation attempts : 0
% 0.07/0.35 % Condensation successes : 0
% 0.07/0.35 % Termbank termtop insertions : 10766
% 0.07/0.35 % Search garbage collected termcells : 83
% 0.07/0.35
% 0.07/0.35 % -------------------------------------------------
% 0.07/0.35 % User time : 0.009 s
% 0.07/0.35 % System time : 0.004 s
% 0.07/0.35 % Total time : 0.013 s
% 0.07/0.35 % Maximum resident set size: 3396 pages
% 0.07/0.35
% 0.07/0.35 % -------------------------------------------------
% 0.07/0.35 % User time : 0.048 s
% 0.07/0.35 % System time : 0.013 s
% 0.07/0.35 % Total time : 0.061 s
% 0.07/0.35 % Maximum resident set size: 4608 pages
% 0.07/0.35 % E exiting
%------------------------------------------------------------------------------