%------------------------------------------------------------------------------ % File : Etableau---0.67 % Problem : LCL562+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp:raw % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s % 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 : Mon Sep 7 12:01:26 PM UTC 2026 % Result : Theorem 7.03s 1.37s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL562+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s % 0.09/0.36 % Computer : n017.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sun Sep 6 01:04:37 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.41 # No SInE strategy applied % 0.09/0.41 # Auto-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI % 0.09/0.41 # and selection function SelectComplexExceptUniqMaxHorn. % 0.09/0.41 # % 0.09/0.41 # Presaturation interreduction done % 0.09/0.41 # Number of axioms: 135 Number of unprocessed: 117 % 0.09/0.41 # Tableaux proof search. % 0.09/0.41 # APR header successfully linked. % 0.09/0.41 # Hello from C++ % 0.09/0.42 # The folding up rule is enabled... % 0.09/0.42 # Local unification is enabled... % 0.09/0.42 # Any saturation attempts will use folding labels... % 0.09/0.42 # 117 beginning clauses after preprocessing and clausification % 0.09/0.42 # Creating start rules for all 1 conjectures. % 0.09/0.42 # There are 1 start rule candidates: % 0.09/0.42 # Found 29 unit axioms. % 0.09/0.42 # 1 start rule tableaux created. % 0.09/0.42 # 88 extension rule candidate clauses % 0.09/0.42 # 29 unit axiom clauses % 0.09/0.42 % 0.09/0.42 # Requested 8, 32 cores available to the main process. % 0.09/0.42 # There are not enough tableaux to fork, creating more from the initial 1 % 0.09/0.42 # Creating equality axioms % 0.09/0.42 # Ran out of tableaux, making start rules for all clauses % 0.09/0.42 # Returning from population with 117 new_tableaux and 0 remaining starting tableaux. % 0.09/0.42 # We now have 117 tableaux to operate on % 7.03/1.37 # There were 1 total branch saturation attempts. % 7.03/1.37 # There were 0 of these attempts blocked. % 7.03/1.37 # There were 0 deferred branch saturation attempts. % 7.03/1.37 # There were 0 free duplicated saturations. % 7.03/1.37 # There were 1 total successful branch saturations. % 7.03/1.37 # There were 0 successful branch saturations in interreduction. % 7.03/1.37 # There were 0 successful branch saturations on the branch. % 7.03/1.37 # There were 1 successful branch saturations after the branch. % 7.03/1.37 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.03/1.37 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.03/1.37 # Begin clausification derivation % 7.03/1.37 % 7.03/1.37 # End clausification derivation % 7.03/1.37 # Begin listing active clauses obtained from FOF to CNF conversion % 7.03/1.37 cnf(i_0_134, plain, (substitution_of_equivalents)). % 7.03/1.37 cnf(i_0_118, plain, (op_or)). % 7.03/1.37 cnf(i_0_132, plain, (op_implies_and)). % 7.03/1.37 cnf(i_0_121, plain, (op_equiv)). % 7.03/1.37 cnf(i_0_123, plain, (modus_ponens_strict_implies)). % 7.03/1.37 cnf(i_0_125, plain, (adjunction)). % 7.03/1.37 cnf(i_0_124, plain, (substitution_strict_equiv)). % 7.03/1.37 cnf(i_0_126, plain, (axiom_m1)). % 7.03/1.37 cnf(i_0_127, plain, (axiom_m2)). % 7.03/1.37 cnf(i_0_128, plain, (axiom_m3)). % 7.03/1.37 cnf(i_0_129, plain, (axiom_m4)). % 7.03/1.37 cnf(i_0_130, plain, (axiom_m5)). % 7.03/1.37 cnf(i_0_117, plain, (op_possibly)). % 7.03/1.37 cnf(i_0_120, plain, (op_strict_implies)). % 7.03/1.37 cnf(i_0_122, plain, (op_strict_equiv)). % 7.03/1.37 cnf(i_0_119, plain, (op_implies)). % 7.03/1.37 cnf(i_0_113, plain, (not(necessarily(not(X1)))=possibly(X1))). % 7.03/1.37 cnf(i_0_115, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2))). % 7.03/1.37 cnf(i_0_100, plain, (is_a_theorem(strict_implies(X1,and(X1,X1))))). % 7.03/1.37 cnf(i_0_58, plain, (not(and(X1,not(X2)))=implies(X1,X2))). % 7.03/1.37 cnf(i_0_96, plain, (is_a_theorem(strict_implies(and(X1,X2),X1)))). % 7.03/1.37 cnf(i_0_56, plain, (implies(not(X1),X2)=or(X1,X2))). % 7.03/1.37 cnf(i_0_94, plain, (is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))))). % 7.03/1.37 cnf(i_0_116, plain, (and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2))). % 7.03/1.37 cnf(i_0_98, plain, (is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))))). % 7.03/1.37 cnf(i_0_102, plain, (is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))))). % 7.03/1.37 cnf(i_0_60, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1)))). % 7.03/1.37 cnf(i_0_135, negated_conjecture, (~equivalence_2)). % 7.03/1.37 cnf(i_0_30, plain, (~is_a_theorem(implies(and(implies(esk29_0,esk30_0),implies(esk30_0,esk29_0)),implies(esk30_0,esk29_0))))). % 7.03/1.37 cnf(i_0_1, plain, (modus_ponens|~is_a_theorem(esk2_0))). % 7.03/1.37 cnf(i_0_3, plain, (is_a_theorem(esk1_0)|modus_ponens)). % 7.03/1.37 cnf(i_0_61, plain, (necessitation|~is_a_theorem(necessarily(esk56_0)))). % 7.03/1.37 cnf(i_0_62, plain, (necessitation|is_a_theorem(esk56_0))). % 7.03/1.37 cnf(i_0_103, plain, (axiom_m6|~is_a_theorem(strict_implies(esk88_0,possibly(esk88_0))))). % 7.03/1.37 cnf(i_0_77, plain, (axiom_M|~is_a_theorem(implies(necessarily(esk65_0),esk65_0)))). % 7.03/1.37 cnf(i_0_63, plain, (is_a_theorem(necessarily(X1))|~necessitation|~is_a_theorem(X1))). % 7.03/1.37 cnf(i_0_2, plain, (is_a_theorem(implies(esk1_0,esk2_0))|modus_ponens)). % 7.03/1.37 cnf(i_0_81, plain, (axiom_B|~is_a_theorem(implies(esk67_0,necessarily(possibly(esk67_0)))))). % 7.03/1.37 cnf(i_0_10, plain, (implies_1|~is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0))))). % 7.03/1.37 cnf(i_0_22, plain, (or_1|~is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))))). % 7.03/1.37 cnf(i_0_7, plain, (X1=X2|~is_a_theorem(equiv(X1,X2)))). % 7.03/1.37 cnf(i_0_74, plain, (X1=X2|~is_a_theorem(strict_equiv(X1,X2)))). % 7.03/1.37 cnf(i_0_24, plain, (or_2|~is_a_theorem(implies(esk23_0,or(esk22_0,esk23_0))))). % 7.03/1.37 cnf(i_0_34, plain, (kn1|~is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))))). % 7.03/1.37 cnf(i_0_48, plain, (r2|~is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0))))). % 7.03/1.37 cnf(i_0_16, plain, (and_1|~is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0)))). % 7.03/1.37 cnf(i_0_18, plain, (and_2|~is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)))). % 7.03/1.37 cnf(i_0_114, plain, (not(possibly(not(X1)))=necessarily(X1)|~op_necessarily)). % 7.03/1.37 cnf(i_0_36, plain, (kn2|~is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)))). % 7.03/1.37 cnf(i_0_46, plain, (r1|~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)))). % 7.03/1.37 cnf(i_0_4, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)|~modus_ponens)). % 7.03/1.37 cnf(i_0_104, plain, (is_a_theorem(strict_implies(X1,possibly(X1)))|~axiom_m6)). % 7.03/1.37 cnf(i_0_78, plain, (is_a_theorem(implies(necessarily(X1),X1))|~axiom_M)). % 7.03/1.37 cnf(i_0_79, plain, (axiom_4|~is_a_theorem(implies(necessarily(esk66_0),necessarily(necessarily(esk66_0)))))). % 7.03/1.37 cnf(i_0_83, plain, (axiom_5|~is_a_theorem(implies(possibly(esk68_0),necessarily(possibly(esk68_0)))))). % 7.03/1.37 cnf(i_0_91, plain, (axiom_s4|~is_a_theorem(strict_implies(necessarily(esk76_0),necessarily(necessarily(esk76_0)))))). % 7.03/1.37 cnf(i_0_59, plain, (or(not(X1),X2)=implies(X1,X2)|~op_implies_or)). % 7.03/1.37 cnf(i_0_67, plain, (is_a_theorem(X1)|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(X2))). % 7.03/1.37 cnf(i_0_111, plain, (axiom_m10|~is_a_theorem(strict_implies(possibly(esk94_0),necessarily(possibly(esk94_0)))))). % 7.03/1.37 cnf(i_0_109, plain, (axiom_m9|~is_a_theorem(strict_implies(possibly(possibly(esk93_0)),possibly(esk93_0))))). % 7.03/1.37 cnf(i_0_82, plain, (is_a_theorem(implies(X1,necessarily(possibly(X1))))|~axiom_B)). % 7.03/1.37 cnf(i_0_105, plain, (axiom_m7|~is_a_theorem(strict_implies(possibly(and(esk89_0,esk90_0)),esk89_0)))). % 7.03/1.37 cnf(i_0_50, plain, (r3|~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))))). % 7.03/1.37 cnf(i_0_71, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1))). % 7.03/1.37 cnf(i_0_11, plain, (is_a_theorem(implies(X1,implies(X2,X1)))|~implies_1)). % 7.03/1.37 cnf(i_0_20, plain, (and_3|~is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0)))))). % 7.03/1.37 cnf(i_0_35, plain, (is_a_theorem(implies(X1,and(X1,X1)))|~kn1)). % 7.03/1.37 cnf(i_0_25, plain, (is_a_theorem(implies(X1,or(X2,X1)))|~or_2)). % 7.03/1.37 cnf(i_0_49, plain, (is_a_theorem(implies(X1,or(X2,X1)))|~r2)). % 7.03/1.37 cnf(i_0_23, plain, (is_a_theorem(implies(X1,or(X1,X2)))|~or_1)). % 7.03/1.37 cnf(i_0_19, plain, (is_a_theorem(implies(and(X1,X2),X2))|~and_2)). % 7.03/1.37 cnf(i_0_17, plain, (is_a_theorem(implies(and(X1,X2),X1))|~and_1)). % 7.03/1.37 cnf(i_0_37, plain, (is_a_theorem(implies(and(X1,X2),X1))|~kn2)). % 7.03/1.37 cnf(i_0_47, plain, (is_a_theorem(implies(or(X1,X1),X1))|~r1)). % 7.03/1.37 cnf(i_0_107, plain, (axiom_m8|~is_a_theorem(strict_implies(strict_implies(esk91_0,esk92_0),strict_implies(possibly(esk91_0),possibly(esk92_0)))))). % 7.03/1.37 cnf(i_0_80, plain, (is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))|~axiom_4)). % 7.03/1.37 cnf(i_0_84, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))|~axiom_5)). % 7.03/1.37 cnf(i_0_92, plain, (is_a_theorem(strict_implies(necessarily(X1),necessarily(necessarily(X1))))|~axiom_s4)). % 7.03/1.37 cnf(i_0_112, plain, (is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1))))|~axiom_m10)). % 7.03/1.37 cnf(i_0_110, plain, (is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))|~axiom_m9)). % 7.03/1.37 cnf(i_0_57, plain, (not(or(not(X1),not(X2)))=and(X1,X2)|~op_and)). % 7.03/1.37 cnf(i_0_12, plain, (implies_2|~is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))))). % 7.03/1.37 cnf(i_0_106, plain, (is_a_theorem(strict_implies(possibly(and(X1,X2)),X1))|~axiom_m7)). % 7.03/1.37 cnf(i_0_75, plain, (axiom_K|~is_a_theorem(implies(strict_implies(esk63_0,esk64_0),implies(necessarily(esk63_0),necessarily(esk64_0)))))). % 7.03/1.37 cnf(i_0_87, plain, (axiom_s2|~is_a_theorem(strict_implies(possibly(and(esk72_0,esk73_0)),and(possibly(esk72_0),possibly(esk73_0)))))). % 7.03/1.37 cnf(i_0_42, plain, (cn2|~is_a_theorem(implies(esk42_0,or(esk42_0,esk43_0))))). % 7.03/1.37 cnf(i_0_44, plain, (cn3|~is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)))). % 7.03/1.37 cnf(i_0_43, plain, (is_a_theorem(implies(X1,or(X1,X2)))|~cn2)). % 7.03/1.37 cnf(i_0_45, plain, (is_a_theorem(implies(or(X1,X1),X1))|~cn3)). % 7.03/1.37 cnf(i_0_29, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X1,X2)))|~equivalence_1)). % 7.03/1.37 cnf(i_0_51, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))|~r3)). % 7.03/1.37 cnf(i_0_21, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3)). % 7.03/1.37 cnf(i_0_8, plain, (modus_tollens|~is_a_theorem(implies(or(esk6_0,not(esk5_0)),implies(esk5_0,esk6_0))))). % 7.03/1.37 cnf(i_0_89, plain, (axiom_s3|~is_a_theorem(strict_implies(strict_implies(esk74_0,esk75_0),strict_implies(not(possibly(esk75_0)),not(possibly(esk74_0))))))). % 7.03/1.37 cnf(i_0_14, plain, (implies_3|~is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0)))))). % 7.03/1.37 cnf(i_0_108, plain, (is_a_theorem(strict_implies(strict_implies(X1,X2),strict_implies(possibly(X1),possibly(X2))))|~axiom_m8)). % 7.03/1.37 cnf(i_0_40, plain, (cn1|~is_a_theorem(implies(implies(esk39_0,esk40_0),implies(implies(esk40_0,esk41_0),implies(esk39_0,esk41_0)))))). % 7.03/1.37 cnf(i_0_54, plain, (r5|~is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0)))))). % 7.03/1.37 cnf(i_0_52, plain, (r4|~is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0)))))). % 7.03/1.37 cnf(i_0_9, plain, (is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1)))|~modus_tollens)). % 7.03/1.37 cnf(i_0_28, plain, (equivalence_1|~is_a_theorem(implies(and(implies(esk27_0,esk28_0),implies(esk28_0,esk27_0)),implies(esk27_0,esk28_0))))). % 7.03/1.37 cnf(i_0_26, plain, (or_3|~is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(or(esk24_0,esk25_0),esk26_0)))))). % 7.03/1.37 cnf(i_0_38, plain, (kn3|~is_a_theorem(implies(implies(esk36_0,esk37_0),or(and(esk37_0,esk38_0),not(and(esk38_0,esk36_0))))))). % 7.03/1.37 cnf(i_0_13, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2)). % 7.03/1.37 cnf(i_0_85, plain, (axiom_s1|~is_a_theorem(implies(and(strict_implies(esk69_0,esk70_0),strict_implies(esk70_0,esk71_0)),strict_implies(esk69_0,esk71_0))))). % 7.03/1.37 cnf(i_0_76, plain, (is_a_theorem(implies(strict_implies(X1,X2),implies(necessarily(X1),necessarily(X2))))|~axiom_K)). % 7.03/1.37 cnf(i_0_88, plain, (is_a_theorem(strict_implies(possibly(and(X1,X2)),and(possibly(X1),possibly(X2))))|~axiom_s2)). % 7.03/1.37 cnf(i_0_15, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))|~implies_3)). % 7.03/1.37 cnf(i_0_90, plain, (is_a_theorem(strict_implies(strict_implies(X1,X2),strict_implies(not(possibly(X2)),not(possibly(X1)))))|~axiom_s3)). % 7.03/1.37 cnf(i_0_32, plain, (equivalence_3|~is_a_theorem(implies(implies(esk31_0,esk32_0),implies(implies(esk32_0,esk31_0),and(implies(esk31_0,esk32_0),implies(esk32_0,esk31_0))))))). % 7.03/1.37 cnf(i_0_41, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))|~cn1)). % 7.03/1.37 cnf(i_0_33, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2))))|~equivalence_3)). % 7.03/1.37 cnf(i_0_55, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))|~r5)). % 7.03/1.37 cnf(i_0_53, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))|~r4)). % 7.03/1.37 cnf(i_0_27, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2))))|~or_3)). % 7.03/1.37 cnf(i_0_39, plain, (is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))|~kn3)). % 7.03/1.37 cnf(i_0_86, plain, (is_a_theorem(implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|~axiom_s1)). % 7.03/1.37 cnf(i_0_318, plain, (X211=X211)). % 7.03/1.37 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 7.03/1.37 # Begin printing tableau % 7.03/1.37 # Found 6 steps % 7.03/1.37 cnf(i_0_113, plain, (not(necessarily(not(X6)))=possibly(X6)), inference(start_rule)). % 7.03/1.37 cnf(i_0_348, plain, (not(necessarily(not(X6)))=possibly(X6)), inference(extension_rule, [i_0_321])). % 7.03/1.37 cnf(i_0_1160, plain, (not(necessarily(not(X6)))!=possibly(X6)), inference(closure_rule, [i_0_113])). % 7.03/1.37 cnf(i_0_1158, plain, (not(necessarily(not(X6)))=not(necessarily(not(X6)))), inference(extension_rule, [i_0_323])). % 7.03/1.37 cnf(i_0_2275, plain, (not(necessarily(not(X1)))!=possibly(X1)), inference(closure_rule, [i_0_113])). % 7.03/1.37 cnf(i_0_2273, plain, (implies(not(necessarily(not(X6))),not(necessarily(not(X1))))=implies(not(necessarily(not(X6))),possibly(X1))), inference(etableau_closure_rule, [i_0_2273, ...])). % 7.03/1.37 # End printing tableau % 7.03/1.37 # SZS output end % 7.03/1.37 # Branches closed with saturation will be marked with an "s" % 7.03/1.38 # Child (1663609) has found a proof. % 7.03/1.38 % 7.03/1.38 # Proof search is over... % 7.03/1.38 # Freeing feature tree %------------------------------------------------------------------------------