0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : eprover --auto -s --tableau=1 [--tableau-equality=1] --tableau-depth=10 %s 0.13/0.34 % Computer : n017.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Thu Jul 2 08:22:21 EDT 2020 0.13/0.34 % CPUTime : 0.13/0.35 % Running in FOF/CNF-non-UEQ mode 0.20/0.38 # No SInE strategy applied 0.20/0.38 # Auto-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S 0.20/0.38 # and selection function SelectNewComplexAHP. 0.20/0.38 # 0.20/0.38 # Presaturation interreduction done 0.20/0.38 # Number of axioms: 18 Number of unprocessed: 18 0.20/0.38 # Tableaux proof search. 0.20/0.38 # 18 beginning clauses after preprocessing and clausification 0.20/0.38 # Creating start rules for all conjectures. 0.20/0.38 # 14 unit axioms, 1 start rules, and 4 other extension candidates. 0.20/0.38 ## Beginning tableaux proof search with 1 start rule applications. 0.58/0.79 # Beginning deep saturation check 0.58/0.79 # Saturate returned empty clause 0x3694840. 0.58/0.79 # Success 0.58/0.79 # SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p 0.58/0.79 # SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 0.58/0.79 # Begin clausification derivation 0.58/0.79 fof(a, conjecture, leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', a)). 0.58/0.79 fof(star_induction_left, axiom, ![X1, X3, X2]:(leq(multiplication(star(X1),X2),X3)<=leq(addition(multiplication(X1,X3),X2),X3)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', star_induction_left)). 0.58/0.79 fof(star_induction_right, axiom, ![X1, X3, X2]:(leq(addition(multiplication(X1,X3),X2),X1)=>leq(multiplication(X2,star(X3)),X1)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', star_induction_right)). 0.58/0.79 fof(order, axiom, ![X1, X3]:(X3=addition(X1,X3)<=>leq(X1,X3)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', order)). 0.58/0.79 fof(additive_commutativity, axiom, ![X1, X3]:addition(X3,X1)=addition(X1,X3), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', additive_commutativity)). 0.58/0.79 fof(right_distributivity, axiom, ![X1, X3, X2]:addition(multiplication(X1,X3),multiplication(X1,X2))=multiplication(X1,addition(X3,X2)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', right_distributivity)). 0.58/0.79 fof(additive_associativity, axiom, ![X2, X3, X1]:addition(X1,addition(X3,X2))=addition(addition(X1,X3),X2), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', additive_associativity)). 0.58/0.79 fof(left_distributivity, axiom, ![X1, X3, X2]:multiplication(addition(X1,X3),X2)=addition(multiplication(X1,X2),multiplication(X3,X2)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', left_distributivity)). 0.58/0.79 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)). 0.58/0.79 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)). 0.58/0.79 fof(multiplicative_associativity, axiom, ![X1, X3, X2]:multiplication(X1,multiplication(X3,X2))=multiplication(multiplication(X1,X3),X2), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', multiplicative_associativity)). 0.58/0.79 fof(additive_idempotence, axiom, ![X1]:X1=addition(X1,X1), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', additive_idempotence)). 0.58/0.79 fof(additive_identity, axiom, ![X1]:X1=addition(X1,zero), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', additive_identity)). 0.58/0.79 fof(multiplicative_left_identity, axiom, ![X1]:multiplication(one,X1)=X1, file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', multiplicative_left_identity)). 0.58/0.79 fof(multiplicative_right_identity, axiom, ![X1]:X1=multiplication(X1,one), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', multiplicative_right_identity)). 0.58/0.79 fof(left_annihilation, axiom, ![X1]:multiplication(zero,X1)=zero, file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', left_annihilation)). 0.58/0.79 fof(right_annihilation, axiom, ![X1]:zero=multiplication(X1,zero), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax', right_annihilation)). 0.58/0.79 fof(c_0_17, negated_conjecture, ~(leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a))), inference(assume_negation,[status(cth)],[a])). 0.58/0.79 fof(c_0_18, plain, ![X27, X28, X29]:(~leq(addition(multiplication(X27,X28),X29),X28)|leq(multiplication(star(X27),X29),X28)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[star_induction_left])])])). 0.58/0.79 fof(c_0_19, plain, ![X13, X14, X15]:(~leq(addition(multiplication(X13,X14),X15),X13)|leq(multiplication(X15,star(X14)),X13)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])])). 0.58/0.79 fof(c_0_20, plain, ![X32, X33]:((X33!=addition(X32,X33)|leq(X32,X33))&(~leq(X32,X33)|X33=addition(X32,X33))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])). 0.58/0.79 fof(c_0_21, negated_conjecture, ~leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)), inference(fof_simplification,[status(thm)],[c_0_17])). 0.58/0.79 fof(c_0_22, plain, ![X30, X31]:addition(X31,X30)=addition(X30,X31), inference(variable_rename,[status(thm)],[additive_commutativity])). 0.58/0.79 fof(c_0_23, plain, ![X19, X20, X21]:addition(multiplication(X19,X20),multiplication(X19,X21))=multiplication(X19,addition(X20,X21)), inference(variable_rename,[status(thm)],[right_distributivity])). 0.58/0.79 fof(c_0_24, plain, ![X6, X7, X8]:addition(X8,addition(X7,X6))=addition(addition(X8,X7),X6), inference(variable_rename,[status(thm)],[additive_associativity])). 0.58/0.79 fof(c_0_25, plain, ![X23, X24, X25]:multiplication(addition(X23,X24),X25)=addition(multiplication(X23,X25),multiplication(X24,X25)), inference(variable_rename,[status(thm)],[left_distributivity])). 0.58/0.79 fof(c_0_26, plain, ![X4]:leq(addition(one,multiplication(star(X4),X4)),star(X4)), inference(variable_rename,[status(thm)],[star_unfold_left])). 0.58/0.79 fof(c_0_27, plain, ![X10]:leq(addition(one,multiplication(X10,star(X10))),star(X10)), inference(variable_rename,[status(thm)],[star_unfold_right])). 0.58/0.79 fof(c_0_28, plain, ![X16, X17, X18]:multiplication(X16,multiplication(X17,X18))=multiplication(multiplication(X16,X17),X18), inference(variable_rename,[status(thm)],[multiplicative_associativity])). 0.58/0.79 fof(c_0_29, plain, ![X12]:X12=addition(X12,X12), inference(variable_rename,[status(thm)],[additive_idempotence])). 0.58/0.79 fof(c_0_30, plain, ![X22]:X22=addition(X22,zero), inference(variable_rename,[status(thm)],[additive_identity])). 0.58/0.79 fof(c_0_31, plain, ![X5]:multiplication(one,X5)=X5, inference(variable_rename,[status(thm)],[multiplicative_left_identity])). 0.58/0.79 fof(c_0_32, plain, ![X9]:X9=multiplication(X9,one), inference(variable_rename,[status(thm)],[multiplicative_right_identity])). 0.58/0.79 fof(c_0_33, plain, ![X11]:multiplication(zero,X11)=zero, inference(variable_rename,[status(thm)],[left_annihilation])). 0.58/0.79 fof(c_0_34, plain, ![X26]:zero=multiplication(X26,zero), inference(variable_rename,[status(thm)],[right_annihilation])). 0.58/0.79 cnf(c_0_35, plain, (leq(multiplication(star(X1),X3),X2)|~leq(addition(multiplication(X1,X2),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_18]), ['final']). 0.58/0.79 cnf(c_0_36, plain, (leq(multiplication(X3,star(X2)),X1)|~leq(addition(multiplication(X1,X2),X3),X1)), inference(split_conjunct,[status(thm)],[c_0_19]), ['final']). 0.58/0.79 cnf(c_0_37, plain, (leq(X2,X1)|X1!=addition(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_20]), ['final']). 0.58/0.79 cnf(c_0_38, plain, (X2=addition(X1,X2)|~leq(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_20]), ['final']). 0.58/0.79 cnf(c_0_39, negated_conjecture, (~leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a))), inference(split_conjunct,[status(thm)],[c_0_21]), ['final']). 0.58/0.79 cnf(c_0_40, plain, (addition(X1,X2)=addition(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_22]), ['final']). 0.58/0.79 cnf(c_0_41, plain, (addition(multiplication(X1,X2),multiplication(X1,X3))=multiplication(X1,addition(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_23]), ['final']). 0.58/0.79 cnf(c_0_42, plain, (addition(X1,addition(X2,X3))=addition(addition(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_24]), ['final']). 0.58/0.79 cnf(c_0_43, plain, (multiplication(addition(X1,X2),X3)=addition(multiplication(X1,X3),multiplication(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_25]), ['final']). 0.58/0.79 cnf(c_0_44, plain, (leq(addition(one,multiplication(star(X1),X1)),star(X1))), inference(split_conjunct,[status(thm)],[c_0_26]), ['final']). 0.58/0.79 cnf(c_0_45, plain, (leq(addition(one,multiplication(X1,star(X1))),star(X1))), inference(split_conjunct,[status(thm)],[c_0_27]), ['final']). 0.58/0.79 cnf(c_0_46, plain, (multiplication(X1,multiplication(X2,X3))=multiplication(multiplication(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_28]), ['final']). 0.58/0.79 cnf(c_0_47, plain, (X1=addition(X1,X1)), inference(split_conjunct,[status(thm)],[c_0_29]), ['final']). 0.58/0.79 cnf(c_0_48, plain, (X1=addition(X1,zero)), inference(split_conjunct,[status(thm)],[c_0_30]), ['final']). 0.58/0.79 cnf(c_0_49, plain, (multiplication(one,X1)=X1), inference(split_conjunct,[status(thm)],[c_0_31]), ['final']). 0.58/0.79 cnf(c_0_50, plain, (X1=multiplication(X1,one)), inference(split_conjunct,[status(thm)],[c_0_32]), ['final']). 0.58/0.79 cnf(c_0_51, plain, (multiplication(zero,X1)=zero), inference(split_conjunct,[status(thm)],[c_0_33]), ['final']). 0.58/0.79 cnf(c_0_52, plain, (zero=multiplication(X1,zero)), inference(split_conjunct,[status(thm)],[c_0_34]), ['final']). 0.58/0.79 0.58/0.79 # End clausification derivation 0.58/0.79 # Begin listing active clauses obtained from FOF to CNF conversion 0.58/0.79 cnf(i_0_13, plain, (multiplication(X1,zero)=zero)). 0.58/0.79 cnf(i_0_6, plain, (multiplication(zero,X1)=zero)). 0.58/0.79 cnf(i_0_4, plain, (multiplication(X1,one)=X1)). 0.58/0.79 cnf(i_0_2, plain, (multiplication(one,X1)=X1)). 0.58/0.79 cnf(i_0_11, plain, (addition(X1,zero)=X1)). 0.58/0.79 cnf(i_0_7, plain, (addition(X1,X1)=X1)). 0.58/0.79 cnf(i_0_9, plain, (multiplication(multiplication(X1,X2),X3)=multiplication(X1,multiplication(X2,X3)))). 0.58/0.79 cnf(i_0_5, plain, (leq(addition(one,multiplication(X1,star(X1))),star(X1)))). 0.58/0.79 cnf(i_0_1, plain, (leq(addition(one,multiplication(star(X1),X1)),star(X1)))). 0.58/0.79 cnf(i_0_12, plain, (addition(multiplication(X1,X2),multiplication(X3,X2))=multiplication(addition(X1,X3),X2))). 0.58/0.79 cnf(i_0_3, plain, (addition(addition(X1,X2),X3)=addition(X1,addition(X2,X3)))). 0.58/0.79 cnf(i_0_10, plain, (addition(multiplication(X1,X2),multiplication(X1,X3))=multiplication(X1,addition(X2,X3)))). 0.58/0.79 cnf(i_0_15, plain, (addition(X1,X2)=addition(X2,X1))). 0.58/0.79 cnf(i_0_18, negated_conjecture, (~leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)))). 0.58/0.79 cnf(i_0_16, plain, (addition(X1,X2)=X2|~leq(X1,X2))). 0.58/0.79 cnf(i_0_17, plain, (leq(X1,X2)|addition(X1,X2)!=X2)). 0.58/0.79 cnf(i_0_8, plain, (leq(multiplication(X1,star(X2)),X3)|~leq(addition(multiplication(X3,X2),X1),X3))). 0.58/0.79 cnf(i_0_14, plain, (leq(multiplication(star(X1),X2),X3)|~leq(addition(multiplication(X1,X3),X2),X3))). 0.58/0.79 # End listing active clauses. There is an equivalent clause to each of these in the clausification! 0.58/0.79 # Begin printing tableau 0.58/0.79 # 2,0,0,1 x c 0.58/0.79 cnf(i_0_22, plain, (leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)))). 0.58/0.79 # 1,2,17,0 0.58/0.79 cnf(i_0_19, plain, (~leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)))). 0.58/0.79 # 0,1,18,0 0.58/0.79 cnf(i_0_18, watchlist, (~leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)))). 0.58/0.79 0.58/0.79 # 2,0,0,0 c s 0.58/0.79 cnf(i_0_23, plain, (addition(multiplication(a,multiplication(a,multiplication(a,a))),star(a))!=star(a))). 0.58/0.79 # 1,2,17,0 0.58/0.79 cnf(i_0_19, plain, (~leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)))). 0.58/0.79 # 0,1,18,0 0.58/0.79 cnf(i_0_18, watchlist, (~leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)))). 0.58/0.79 0.58/0.79 # End printing tableau 0.58/0.79 # SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 0.58/0.79 # Branches closed with saturation will be marked with an "s" 0.58/0.79 # Proof search success! 0.58/0.79 # Exiting... 0.58/0.79 EOF