%------------------------------------------------------------------------------ % File : Etableau---0.67 % Problem : LCL548+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 : n031.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 12:01:25 PM UTC 2026 % Result : Theorem 4.02s 0.96s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL548+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.03 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s % 0.07/0.34 % Computer : n031.cluster.edu % 0.07/0.34 % Model : x86_64 x86_64 % 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.34 % Memory : 8046.5625MB % 0.07/0.34 % OS : Linux 6.8.0-71-generic % 0.07/0.34 % CPULimit : 300 % 0.07/0.34 % WCLimit : 300 % 0.07/0.34 % DateTime : Fri Sep 4 15:53:24 UTC 2026 % 0.07/0.34 % CPUTime : % 0.11/0.38 # No SInE strategy applied % 0.11/0.38 # Auto-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI % 0.11/0.38 # and selection function SelectComplexExceptUniqMaxHorn. % 0.11/0.38 # % 0.11/0.38 # Presaturation interreduction done % 0.11/0.38 # Number of axioms: 147 Number of unprocessed: 115 % 0.11/0.38 # Tableaux proof search. % 0.11/0.38 # APR header successfully linked. % 0.11/0.38 # Hello from C++ % 0.11/0.39 # The folding up rule is enabled... % 0.11/0.39 # Local unification is enabled... % 0.11/0.39 # Any saturation attempts will use folding labels... % 0.11/0.39 # 115 beginning clauses after preprocessing and clausification % 0.11/0.39 # Creating start rules for all 1 conjectures. % 0.11/0.39 # There are 1 start rule candidates: % 0.11/0.39 # Found 56 unit axioms. % 0.11/0.39 # 1 start rule tableaux created. % 0.11/0.39 # 59 extension rule candidate clauses % 0.11/0.39 # 56 unit axiom clauses % 0.11/0.39 % 0.11/0.39 # Requested 8, 32 cores available to the main process. % 0.11/0.39 # There are not enough tableaux to fork, creating more from the initial 1 % 0.11/0.39 # Creating equality axioms % 0.11/0.39 # Ran out of tableaux, making start rules for all clauses % 0.11/0.39 # Returning from population with 115 new_tableaux and 0 remaining starting tableaux. % 0.11/0.39 # We now have 115 tableaux to operate on % 4.02/0.96 # There were 2 total branch saturation attempts. % 4.02/0.96 # There were 0 of these attempts blocked. % 4.02/0.96 # There were 0 deferred branch saturation attempts. % 4.02/0.96 # There were 0 free duplicated saturations. % 4.02/0.96 # There were 2 total successful branch saturations. % 4.02/0.96 # There were 0 successful branch saturations in interreduction. % 4.02/0.96 # There were 0 successful branch saturations on the branch. % 4.02/0.96 # There were 2 successful branch saturations after the branch. % 4.02/0.96 # SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.02/0.96 # SZS output start for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.02/0.96 # Begin clausification derivation % 4.02/0.96 % 4.02/0.96 # End clausification derivation % 4.02/0.96 # Begin listing active clauses obtained from FOF to CNF conversion % 4.02/0.96 cnf(i_0_64, plain, (modus_ponens)). % 4.02/0.96 cnf(i_0_78, plain, (substitution_of_equivalents)). % 4.02/0.96 cnf(i_0_65, plain, (modus_tollens)). % 4.02/0.96 cnf(i_0_66, plain, (implies_1)). % 4.02/0.96 cnf(i_0_67, plain, (implies_2)). % 4.02/0.96 cnf(i_0_68, plain, (implies_3)). % 4.02/0.96 cnf(i_0_69, plain, (and_1)). % 4.02/0.96 cnf(i_0_70, plain, (and_2)). % 4.02/0.96 cnf(i_0_71, plain, (and_3)). % 4.02/0.96 cnf(i_0_72, plain, (or_1)). % 4.02/0.96 cnf(i_0_73, plain, (or_2)). % 4.02/0.96 cnf(i_0_74, plain, (or_3)). % 4.02/0.96 cnf(i_0_75, plain, (equivalence_1)). % 4.02/0.96 cnf(i_0_76, plain, (equivalence_2)). % 4.02/0.96 cnf(i_0_77, plain, (equivalence_3)). % 4.02/0.96 cnf(i_0_61, plain, (op_or)). % 4.02/0.96 cnf(i_0_62, plain, (op_implies_and)). % 4.02/0.96 cnf(i_0_63, plain, (op_equiv)). % 4.02/0.96 cnf(i_0_136, plain, (necessitation)). % 4.02/0.96 cnf(i_0_137, plain, (axiom_K)). % 4.02/0.96 cnf(i_0_138, plain, (axiom_M)). % 4.02/0.96 cnf(i_0_139, plain, (axiom_4)). % 4.02/0.96 cnf(i_0_140, plain, (axiom_B)). % 4.02/0.96 cnf(i_0_135, plain, (op_possibly)). % 4.02/0.96 cnf(i_0_144, plain, (op_strict_implies)). % 4.02/0.96 cnf(i_0_146, plain, (op_strict_equiv)). % 4.02/0.96 cnf(i_0_143, plain, (op_implies)). % 4.02/0.96 cnf(i_0_131, plain, (not(necessarily(not(X1)))=possibly(X1))). % 4.02/0.96 cnf(i_0_96, plain, (is_a_theorem(implies(necessarily(X1),X1)))). % 4.02/0.96 cnf(i_0_133, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2))). % 4.02/0.96 cnf(i_0_100, plain, (is_a_theorem(implies(X1,necessarily(possibly(X1)))))). % 4.02/0.96 cnf(i_0_11, plain, (is_a_theorem(implies(X1,implies(X2,X1))))). % 4.02/0.96 cnf(i_0_25, plain, (is_a_theorem(implies(X1,or(X2,X1))))). % 4.02/0.96 cnf(i_0_48, plain, (r2)). % 4.02/0.97 cnf(i_0_23, plain, (is_a_theorem(implies(X1,or(X1,X2))))). % 4.02/0.97 cnf(i_0_58, plain, (not(and(X1,not(X2)))=implies(X1,X2))). % 4.02/0.97 cnf(i_0_19, plain, (is_a_theorem(implies(and(X1,X2),X2)))). % 4.02/0.97 cnf(i_0_17, plain, (is_a_theorem(implies(and(X1,X2),X1)))). % 4.02/0.97 cnf(i_0_36, plain, (kn2)). % 4.02/0.97 cnf(i_0_98, plain, (is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1)))))). % 4.02/0.97 cnf(i_0_56, plain, (implies(not(X1),X2)=or(X1,X2))). % 4.02/0.97 cnf(i_0_42, plain, (cn2)). % 4.02/0.97 cnf(i_0_31, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))))). % 4.02/0.97 cnf(i_0_29, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))))). % 4.02/0.97 cnf(i_0_21, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2)))))). % 4.02/0.97 cnf(i_0_134, plain, (and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2))). % 4.02/0.97 cnf(i_0_9, plain, (is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))))). % 4.02/0.97 cnf(i_0_13, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))))). % 4.02/0.97 cnf(i_0_94, plain, (is_a_theorem(implies(strict_implies(X1,X2),implies(necessarily(X1),necessarily(X2)))))). % 4.02/0.97 cnf(i_0_15, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))))). % 4.02/0.97 cnf(i_0_40, plain, (cn1)). % 4.02/0.97 cnf(i_0_33, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2)))))). % 4.02/0.97 cnf(i_0_27, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2)))))). % 4.02/0.97 cnf(i_0_60, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1)))). % 4.02/0.97 cnf(i_0_147, negated_conjecture, (~axiom_m9)). % 4.02/0.97 cnf(i_0_127, plain, (~is_a_theorem(strict_implies(possibly(possibly(esk93_0)),possibly(esk93_0))))). % 4.02/0.97 cnf(i_0_90, plain, (substitution_strict_equiv|esk62_0!=esk61_0)). % 4.02/0.97 cnf(i_0_82, plain, (modus_ponens_strict_implies|~is_a_theorem(esk58_0))). % 4.02/0.97 cnf(i_0_84, plain, (modus_ponens_strict_implies|is_a_theorem(esk57_0))). % 4.02/0.97 cnf(i_0_88, plain, (adjunction|is_a_theorem(esk59_0))). % 4.02/0.97 cnf(i_0_87, plain, (adjunction|is_a_theorem(esk60_0))). % 4.02/0.97 cnf(i_0_86, plain, (adjunction|~is_a_theorem(and(esk59_0,esk60_0)))). % 4.02/0.97 cnf(i_0_121, plain, (axiom_m6|~is_a_theorem(strict_implies(esk88_0,possibly(esk88_0))))). % 4.02/0.97 cnf(i_0_81, plain, (is_a_theorem(necessarily(X1))|~is_a_theorem(X1))). % 4.02/0.97 cnf(i_0_83, plain, (modus_ponens_strict_implies|is_a_theorem(strict_implies(esk57_0,esk58_0)))). % 4.02/0.97 cnf(i_0_7, plain, (X1=X2|~is_a_theorem(equiv(X1,X2)))). % 4.02/0.97 cnf(i_0_92, plain, (X1=X2|~substitution_strict_equiv|~is_a_theorem(strict_equiv(X1,X2)))). % 4.02/0.97 cnf(i_0_91, plain, (substitution_strict_equiv|is_a_theorem(strict_equiv(esk61_0,esk62_0)))). % 4.02/0.97 cnf(i_0_34, plain, (kn1|~is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))))). % 4.02/0.97 cnf(i_0_117, plain, (axiom_m4|~is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0))))). % 4.02/0.97 cnf(i_0_132, plain, (not(possibly(not(X1)))=necessarily(X1)|~op_necessarily)). % 4.02/0.97 cnf(i_0_46, plain, (r1|~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)))). % 4.02/0.97 cnf(i_0_113, plain, (axiom_m2|~is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0)))). % 4.02/0.97 cnf(i_0_122, plain, (is_a_theorem(strict_implies(X1,possibly(X1)))|~axiom_m6)). % 4.02/0.97 cnf(i_0_101, plain, (axiom_5|~is_a_theorem(implies(possibly(esk68_0),necessarily(possibly(esk68_0)))))). % 4.02/0.97 cnf(i_0_109, plain, (axiom_s4|~is_a_theorem(strict_implies(necessarily(esk76_0),necessarily(necessarily(esk76_0)))))). % 4.02/0.97 cnf(i_0_59, plain, (or(not(X1),X2)=implies(X1,X2)|~op_implies_or)). % 4.02/0.97 cnf(i_0_4, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2))). % 4.02/0.97 cnf(i_0_85, plain, (is_a_theorem(X1)|~modus_ponens_strict_implies|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(X2))). % 4.02/0.97 cnf(i_0_129, plain, (axiom_m10|~is_a_theorem(strict_implies(possibly(esk94_0),necessarily(possibly(esk94_0)))))). % 4.02/0.97 cnf(i_0_123, plain, (axiom_m7|~is_a_theorem(strict_implies(possibly(and(esk89_0,esk90_0)),esk89_0)))). % 4.02/0.97 cnf(i_0_89, plain, (is_a_theorem(and(X1,X2))|~adjunction|~is_a_theorem(X2)|~is_a_theorem(X1))). % 4.02/0.97 cnf(i_0_50, plain, (r3|~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))))). % 4.02/0.97 cnf(i_0_111, plain, (axiom_m1|~is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))))). % 4.02/0.97 cnf(i_0_35, plain, (is_a_theorem(implies(X1,and(X1,X1)))|~kn1)). % 4.02/0.97 cnf(i_0_118, plain, (is_a_theorem(strict_implies(X1,and(X1,X1)))|~axiom_m4)). % 4.02/0.97 cnf(i_0_47, plain, (is_a_theorem(implies(or(X1,X1),X1))|~r1)). % 4.02/0.97 cnf(i_0_114, plain, (is_a_theorem(strict_implies(and(X1,X2),X1))|~axiom_m2)). % 4.02/0.97 cnf(i_0_102, plain, (is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))|~axiom_5)). % 4.02/0.97 cnf(i_0_110, plain, (is_a_theorem(strict_implies(necessarily(X1),necessarily(necessarily(X1))))|~axiom_s4)). % 4.02/0.97 cnf(i_0_57, plain, (not(or(not(X1),not(X2)))=and(X1,X2)|~op_and)). % 4.02/0.97 cnf(i_0_130, plain, (is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1))))|~axiom_m10)). % 4.02/0.97 cnf(i_0_125, plain, (axiom_m8|~is_a_theorem(strict_implies(strict_implies(esk91_0,esk92_0),strict_implies(possibly(esk91_0),possibly(esk92_0)))))). % 4.02/0.97 cnf(i_0_124, plain, (is_a_theorem(strict_implies(possibly(and(X1,X2)),X1))|~axiom_m7)). % 4.02/0.97 cnf(i_0_105, plain, (axiom_s2|~is_a_theorem(strict_implies(possibly(and(esk72_0,esk73_0)),and(possibly(esk72_0),possibly(esk73_0)))))). % 4.02/0.97 cnf(i_0_45, plain, (is_a_theorem(implies(or(X1,X1),X1))|~cn3)). % 4.02/0.97 cnf(i_0_51, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))|~r3)). % 4.02/0.97 cnf(i_0_112, plain, (is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))|~axiom_m1)). % 4.02/0.97 cnf(i_0_44, plain, (cn3|~is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)))). % 4.02/0.97 cnf(i_0_107, plain, (axiom_s3|~is_a_theorem(strict_implies(strict_implies(esk74_0,esk75_0),strict_implies(not(possibly(esk75_0)),not(possibly(esk74_0))))))). % 4.02/0.97 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)))))). % 4.02/0.97 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)))))). % 4.02/0.97 cnf(i_0_115, plain, (axiom_m3|~is_a_theorem(strict_implies(and(and(esk81_0,esk82_0),esk83_0),and(esk81_0,and(esk82_0,esk83_0)))))). % 4.02/0.97 cnf(i_0_126, plain, (is_a_theorem(strict_implies(strict_implies(X1,X2),strict_implies(possibly(X1),possibly(X2))))|~axiom_m8)). % 4.02/0.97 cnf(i_0_119, plain, (axiom_m5|~is_a_theorem(strict_implies(and(strict_implies(esk85_0,esk86_0),strict_implies(esk86_0,esk87_0)),strict_implies(esk85_0,esk87_0))))). % 4.02/0.97 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))))))). % 4.02/0.97 cnf(i_0_103, 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))))). % 4.02/0.97 cnf(i_0_106, plain, (is_a_theorem(strict_implies(possibly(and(X1,X2)),and(possibly(X1),possibly(X2))))|~axiom_s2)). % 4.02/0.97 cnf(i_0_108, plain, (is_a_theorem(strict_implies(strict_implies(X1,X2),strict_implies(not(possibly(X2)),not(possibly(X1)))))|~axiom_s3)). % 4.02/0.97 cnf(i_0_55, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))|~r5)). % 4.02/0.97 cnf(i_0_53, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))|~r4)). % 4.02/0.97 cnf(i_0_116, plain, (is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))|~axiom_m3)). % 4.02/0.97 cnf(i_0_120, plain, (is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|~axiom_m5)). % 4.02/0.97 cnf(i_0_39, plain, (is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))|~kn3)). % 4.02/0.97 cnf(i_0_104, plain, (is_a_theorem(implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|~axiom_s1)). % 4.02/0.97 cnf(i_0_273, plain, (X211=X211)). % 4.02/0.97 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 4.02/0.97 # Begin printing tableau % 4.02/0.97 # Found 5 steps % 4.02/0.97 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)))))), inference(start_rule)). % 4.02/0.97 cnf(i_0_447, plain, (kn3), inference(extension_rule, [i_0_39])). % 4.02/0.97 cnf(i_0_1062, plain, (is_a_theorem(implies(implies(X7,X3),or(and(X3,X8),not(and(X8,X7)))))), inference(extension_rule, [i_0_81])). % 4.02/0.97 cnf(i_0_448, plain, (~is_a_theorem(implies(implies(esk36_0,esk37_0),or(and(esk37_0,esk38_0),not(and(esk38_0,esk36_0)))))), inference(etableau_closure_rule, [i_0_448, ...])). % 4.02/0.97 cnf(i_0_1078, plain, (is_a_theorem(necessarily(implies(implies(X7,X3),or(and(X3,X8),not(and(X8,X7))))))), inference(etableau_closure_rule, [i_0_1078, ...])). % 4.02/0.97 # End printing tableau % 4.02/0.97 # SZS output end % 4.02/0.97 # Branches closed with saturation will be marked with an "s" % 4.02/0.97 # Child (2303507) has found a proof. % 4.02/0.97 % 4.02/0.97 # Proof search is over... % 4.02/0.97 # Freeing feature tree %------------------------------------------------------------------------------