%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE170+1.002 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:59:00 PM UTC 2026
% Result : Theorem 6.10s 1.54s
% Output : CNFRefutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 53 unt; 0 def)
% Number of atoms : 65 ( 38 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 5 |; 1 &)
% ( 1 <=>; 0 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 91 ( 6 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(star_unfold_left,axiom,
! [X1] : leq(addition(one,multiplication(star(X1),X1)),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(a,conjecture,
leq(multiplication(a,a),star(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).
fof(c_0_11,plain,
! [X6,X7,X8] : addition(X8,addition(X7,X6)) = addition(addition(X8,X7),X6),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_12,plain,
! [X10] : addition(X10,X10) = X10,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_13,plain,
! [X24,X25] :
( ( leq(X24,X25)
| addition(X24,X25) != X25 )
& ( addition(X24,X25) = X25
| ~ leq(X24,X25) ) ),
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_11]) ).
cnf(c_0_15,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X4,X5] : addition(X4,X5) = addition(X5,X4),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_17,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X27] : leq(addition(one,multiplication(star(X27),X27)),star(X27)),
inference(variable_rename,[status(thm)],[star_unfold_left]) ).
fof(c_0_21,plain,
! [X26] : leq(addition(one,multiplication(X26,star(X26))),star(X26)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
cnf(c_0_22,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_24,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_25,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X19,X20,X21] : multiplication(addition(X19,X20),X21) = addition(multiplication(X19,X21),multiplication(X20,X21)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_27,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
leq(X1,addition(X2,addition(X3,X1))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]),c_0_19]) ).
fof(c_0_30,plain,
! [X16,X17,X18] : multiplication(X16,addition(X17,X18)) = addition(multiplication(X16,X17),multiplication(X16,X18)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_31,plain,
! [X14] : multiplication(X14,one) = X14,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_32,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_27]),c_0_14]),c_0_19]) ).
fof(c_0_34,plain,
! [X15] : multiplication(one,X15) = X15,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_35,plain,
leq(multiplication(star(X1),X1),star(X1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
( multiplication(addition(X1,X3),X2) != multiplication(X3,X2)
| leq(multiplication(X1,X2),multiplication(X3,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_39,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_18,c_0_33]) ).
cnf(c_0_40,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
addition(star(X1),multiplication(star(X1),X1)) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_35]),c_0_19]) ).
cnf(c_0_42,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_19]) ).
cnf(c_0_43,plain,
leq(X1,multiplication(star(X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_44,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
leq(addition(X1,one),star(X1)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,plain,
addition(X1,star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_45]),c_0_14]),c_0_39]) ).
fof(c_0_47,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(assume_negation,[status(cth)],[a]) ).
cnf(c_0_48,plain,
leq(multiplication(X1,X2),multiplication(star(X1),X2)),
inference(spm,[status(thm)],[c_0_38,c_0_46]) ).
cnf(c_0_49,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(spm,[status(thm)],[c_0_44,c_0_19]) ).
fof(c_0_50,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
cnf(c_0_51,plain,
leq(multiplication(X1,addition(one,X1)),star(X1)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_52,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(fof_nnf,[status(thm)],[c_0_50]) ).
cnf(c_0_53,plain,
leq(multiplication(X1,X2),addition(X3,multiplication(X1,addition(X4,X2)))),
inference(spm,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_54,plain,
addition(star(X1),multiplication(X1,addition(one,X1))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_51]),c_0_19]) ).
cnf(c_0_55,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_56,plain,
leq(multiplication(X1,X1),star(X1)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE170+1.002 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 % Computer : n004.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 20 22:49:04 UTC 2026
% 0.20/0.41 % CPUTime :
% 0.20/0.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 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
% 6.10/1.54 % Version: 3.5.1
% 6.10/1.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 6.10/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.10/1.54 % Starting new_bool_3 with 300s (1) cores
% 6.10/1.54 % Starting new_bool_1 with 300s (1) cores
% 6.10/1.54 % Starting sh5l with 300s (1) cores
% 6.10/1.54 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1659868 completed with status 0
% 6.10/1.54 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 6.10/1.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 6.10/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.10/1.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.10/1.54 % No SInE strategy applied
% 6.10/1.54 % Search class: FHUSM-FFSF21-MFFFFFNN
% 6.10/1.54 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 6.10/1.54 % Starting SubtermCWHack with 136s (1) cores
% 6.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.10/1.54 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 6.10/1.54 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 6.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 6.10/1.54 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 1659876 completed with status 0
% 6.10/1.54 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 6.10/1.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 6.10/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.10/1.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.10/1.54 % No SInE strategy applied
% 6.10/1.54 % Search class: FHUSM-FFSF21-MFFFFFNN
% 6.10/1.54 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 6.10/1.54 % Starting SubtermCWHack with 136s (1) cores
% 6.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.10/1.54 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 6.10/1.54 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 6.10/1.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 6.10/1.54 % Preprocessing time : 0.002 s
% 6.10/1.54 % Presaturation interreduction done
% 6.10/1.54
% 6.10/1.54 % Proof found!
% 6.10/1.54 % SZS status Theorem
% 6.10/1.54 % SZS output start CNFRefutation
% See solution above
% 6.10/1.54 % Parsed axioms : 17
% 6.10/1.54 % Removed by relevancy pruning/SinE : 0
% 6.10/1.54 % Initial clauses : 18
% 6.10/1.54 % Removed in clause preprocessing : 0
% 6.10/1.54 % Initial clauses in saturation : 18
% 6.10/1.54 % Processed clauses : 3952
% 6.10/1.54 % ...of these trivial : 497
% 6.10/1.54 % ...subsumed : 2712
% 6.10/1.54 % ...remaining for further processing : 743
% 6.10/1.54 % Other redundant clauses eliminated : 37
% 6.10/1.54 % Clauses deleted for lack of memory : 0
% 6.10/1.54 % Backward-subsumed : 5
% 6.10/1.54 % Backward-rewritten : 103
% 6.10/1.54 % Generated clauses : 33650
% 6.10/1.54 % ...of the previous two non-redundant : 23923
% 6.10/1.54 % ...aggressively subsumed : 0
% 6.10/1.54 % Contextual simplify-reflections : 0
% 6.10/1.54 % Paramodulations : 33613
% 6.10/1.54 % Factorizations : 0
% 6.10/1.54 % NegExts : 0
% 6.10/1.54 % Equation resolutions : 37
% 6.10/1.54 % Disequality decompositions : 0
% 6.10/1.54 % Total rewrite steps : 36703
% 6.10/1.54 % ...of those cached : 32438
% 6.10/1.54 % Propositional unsat checks : 0
% 6.10/1.54 % Propositional check models : 0
% 6.10/1.54 % Propositional check unsatisfiable : 0
% 6.10/1.54 % Propositional clauses : 0
% 6.10/1.54 % Propositional clauses after purity: 0
% 6.10/1.54 % Propositional unsat core size : 0
% 6.10/1.54 % Propositional preprocessing time : 0.000
% 6.10/1.54 % Propositional encoding time : 0.000
% 6.10/1.54 % Propositional solver time : 0.000
% 6.10/1.54 % Success case prop preproc time : 0.000
% 6.10/1.54 % Success case prop encoding time : 0.000
% 6.10/1.54 % Success case prop solver time : 0.000
% 6.10/1.54 % Current number of processed clauses : 617
% 6.10/1.54 % Positive orientable unit clauses : 256
% 6.10/1.54 % Positive unorientable unit clauses: 7
% 6.10/1.54 % Negative unit clauses : 0
% 6.10/1.54 % Non-unit-clauses : 354
% 6.10/1.54 % Current number of unprocessed clauses: 19820
% 6.10/1.54 % ...number of literals in the above : 33601
% 6.10/1.54 % Current number of archived formulas : 0
% 6.10/1.54 % Current number of archived clauses : 126
% 6.10/1.54 % Clause-clause subsumption calls (NU) : 40826
% 6.10/1.54 % Rec. Clause-clause subsumption calls : 40739
% 6.10/1.54 % Non-unit clause-clause subsumptions : 2618
% 6.10/1.54 % Unit Clause-clause subsumption calls : 1460
% 6.10/1.54 % Rewrite failures with RHS unbound : 0
% 6.10/1.54 % BW rewrite match attempts : 1275
% 6.10/1.54 % BW rewrite match successes : 114
% 6.10/1.54 % Condensation attempts : 0
% 6.10/1.54 % Condensation successes : 0
% 6.10/1.54 % Termbank termtop insertions : 403286
% 6.10/1.54 % Search garbage collected termcells : 47
% 6.10/1.54
% 6.10/1.54 % -------------------------------------------------
% 6.10/1.54 % User time : 0.791 s
% 6.10/1.54 % System time : 0.040 s
% 6.10/1.54 % Total time : 0.830 s
% 6.10/1.54 % Maximum resident set size: 3648 pages
% 6.10/1.54
% 6.10/1.54 % -------------------------------------------------
% 6.10/1.54 % User time : 3.927 s
% 6.10/1.54 % System time : 0.176 s
% 6.10/1.54 % Total time : 4.103 s
% 6.10/1.54 % Maximum resident set size: 4864 pages
% 6.10/1.54 % E exiting
%------------------------------------------------------------------------------