%------------------------------------------------------------------------------ % File : Etableau---0.67 % Problem : LCL573+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 : n005.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 12:01:27 PM UTC 2026 % Result : Theorem 5.04s 1.12s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL573+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 % 0.12/0.37 % Computer : n005.cluster.edu % 0.12/0.37 % Model : x86_64 x86_64 % 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.37 % Memory : 8046.5625MB % 0.12/0.37 % OS : Linux 6.8.0-71-generic % 0.12/0.37 % CPULimit : 300 % 0.12/0.37 % WCLimit : 300 % 0.12/0.37 % DateTime : Sat Sep 5 02:10:05 UTC 2026 % 0.12/0.37 % CPUTime : % 0.12/0.41 # No SInE strategy applied % 0.12/0.41 # Auto-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI % 0.12/0.41 # and selection function SelectComplexExceptUniqMaxHorn. % 0.12/0.41 # % 0.12/0.41 # Presaturation interreduction done % 0.12/0.41 # Number of axioms: 81 Number of unprocessed: 64 % 0.12/0.41 # Tableaux proof search. % 0.12/0.41 # APR header successfully linked. % 0.12/0.41 # Hello from C++ % 0.12/0.42 # The folding up rule is enabled... % 0.12/0.42 # Local unification is enabled... % 0.12/0.42 # Any saturation attempts will use folding labels... % 0.12/0.42 # 64 beginning clauses after preprocessing and clausification % 0.12/0.42 # Creating start rules for all 1 conjectures. % 0.12/0.42 # There are 1 start rule candidates: % 0.12/0.42 # Found 31 unit axioms. % 0.12/0.42 # 1 start rule tableaux created. % 0.12/0.42 # 33 extension rule candidate clauses % 0.12/0.42 # 31 unit axiom clauses % 0.12/0.42 % 0.12/0.42 # Requested 8, 32 cores available to the main process. % 0.12/0.42 # There are not enough tableaux to fork, creating more from the initial 1 % 0.12/0.42 # Creating equality axioms % 0.12/0.42 # Ran out of tableaux, making start rules for all clauses % 0.12/0.42 # Returning from population with 64 new_tableaux and 0 remaining starting tableaux. % 0.12/0.42 # We now have 64 tableaux to operate on % 5.04/1.12 # There were 3 total branch saturation attempts. % 5.04/1.12 # There were 0 of these attempts blocked. % 5.04/1.12 # There were 0 deferred branch saturation attempts. % 5.04/1.12 # There were 0 free duplicated saturations. % 5.04/1.12 # There were 3 total successful branch saturations. % 5.04/1.12 # There were 0 successful branch saturations in interreduction. % 5.04/1.12 # There were 0 successful branch saturations on the branch. % 5.04/1.12 # There were 3 successful branch saturations after the branch. % 5.04/1.12 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.04/1.12 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.04/1.12 # Begin clausification derivation % 5.04/1.12 % 5.04/1.12 # End clausification derivation % 5.04/1.12 # Begin listing active clauses obtained from FOF to CNF conversion % 5.04/1.12 cnf(i_0_63, plain, (op_or)). % 5.04/1.12 cnf(i_0_78, plain, (op_implies_and)). % 5.04/1.12 cnf(i_0_66, plain, (op_equiv)). % 5.04/1.12 cnf(i_0_68, plain, (modus_ponens_strict_implies)). % 5.04/1.12 cnf(i_0_70, plain, (adjunction)). % 5.04/1.12 cnf(i_0_69, plain, (substitution_strict_equiv)). % 5.04/1.12 cnf(i_0_71, plain, (axiom_m1)). % 5.04/1.12 cnf(i_0_72, plain, (axiom_m2)). % 5.04/1.12 cnf(i_0_73, plain, (axiom_m3)). % 5.04/1.12 cnf(i_0_74, plain, (axiom_m4)). % 5.04/1.12 cnf(i_0_75, plain, (axiom_m5)). % 5.04/1.12 cnf(i_0_76, plain, (axiom_m10)). % 5.04/1.12 cnf(i_0_62, plain, (op_possibly)). % 5.04/1.12 cnf(i_0_65, plain, (op_strict_implies)). % 5.04/1.12 cnf(i_0_67, plain, (op_strict_equiv)). % 5.04/1.12 cnf(i_0_64, plain, (op_implies)). % 5.04/1.12 cnf(i_0_80, plain, (substitution_of_equivalents)). % 5.04/1.12 cnf(i_0_58, plain, (not(necessarily(not(X1)))=possibly(X1))). % 5.04/1.12 cnf(i_0_60, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2))). % 5.04/1.12 cnf(i_0_45, plain, (is_a_theorem(strict_implies(X1,and(X1,X1))))). % 5.04/1.12 cnf(i_0_41, plain, (is_a_theorem(strict_implies(and(X1,X2),X1)))). % 5.04/1.12 cnf(i_0_3, plain, (not(and(X1,not(X2)))=implies(X1,X2))). % 5.04/1.12 cnf(i_0_57, plain, (is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))))). % 5.04/1.12 cnf(i_0_1, plain, (implies(not(X1),X2)=or(X1,X2))). % 5.04/1.12 cnf(i_0_39, plain, (is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))))). % 5.04/1.12 cnf(i_0_5, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2))). % 5.04/1.12 cnf(i_0_61, plain, (and(strict_implies(X1,X2),strict_implies(X2,X1))=strict_equiv(X1,X2))). % 5.04/1.12 cnf(i_0_43, plain, (is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))))). % 5.04/1.12 cnf(i_0_47, plain, (is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))))). % 5.04/1.12 cnf(i_0_81, negated_conjecture, (~axiom_5)). % 5.04/1.12 cnf(i_0_28, plain, (~is_a_theorem(implies(possibly(esk13_0),necessarily(possibly(esk13_0)))))). % 5.04/1.12 cnf(i_0_7, plain, (is_a_theorem(esk1_0)|necessitation)). % 5.04/1.12 cnf(i_0_6, plain, (necessitation|~is_a_theorem(necessarily(esk1_0)))). % 5.04/1.12 cnf(i_0_8, plain, (is_a_theorem(necessarily(X1))|~is_a_theorem(X1)|~necessitation)). % 5.04/1.12 cnf(i_0_48, plain, (axiom_m6|~is_a_theorem(strict_implies(esk33_0,possibly(esk33_0))))). % 5.04/1.12 cnf(i_0_22, plain, (axiom_M|~is_a_theorem(implies(necessarily(esk10_0),esk10_0)))). % 5.04/1.12 cnf(i_0_19, plain, (X1=X2|~is_a_theorem(strict_equiv(X1,X2)))). % 5.04/1.12 cnf(i_0_26, plain, (axiom_B|~is_a_theorem(implies(esk12_0,necessarily(possibly(esk12_0)))))). % 5.04/1.12 cnf(i_0_59, plain, (not(possibly(not(X1)))=necessarily(X1)|~op_necessarily)). % 5.04/1.12 cnf(i_0_12, plain, (is_a_theorem(X1)|~is_a_theorem(strict_implies(X2,X1))|~is_a_theorem(X2))). % 5.04/1.12 cnf(i_0_24, plain, (axiom_4|~is_a_theorem(implies(necessarily(esk11_0),necessarily(necessarily(esk11_0)))))). % 5.04/1.12 cnf(i_0_36, plain, (axiom_s4|~is_a_theorem(strict_implies(necessarily(esk21_0),necessarily(necessarily(esk21_0)))))). % 5.04/1.12 cnf(i_0_49, plain, (is_a_theorem(strict_implies(X1,possibly(X1)))|~axiom_m6)). % 5.04/1.12 cnf(i_0_23, plain, (is_a_theorem(implies(necessarily(X1),X1))|~axiom_M)). % 5.04/1.12 cnf(i_0_54, plain, (axiom_m9|~is_a_theorem(strict_implies(possibly(possibly(esk38_0)),possibly(esk38_0))))). % 5.04/1.12 cnf(i_0_50, plain, (axiom_m7|~is_a_theorem(strict_implies(possibly(and(esk34_0,esk35_0)),esk34_0)))). % 5.04/1.12 cnf(i_0_4, plain, (or(not(X1),X2)=implies(X1,X2)|~op_implies_or)). % 5.04/1.12 cnf(i_0_16, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1))). % 5.04/1.12 cnf(i_0_27, plain, (is_a_theorem(implies(X1,necessarily(possibly(X1))))|~axiom_B)). % 5.04/1.12 cnf(i_0_25, plain, (is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))|~axiom_4)). % 5.04/1.12 cnf(i_0_37, plain, (is_a_theorem(strict_implies(necessarily(X1),necessarily(necessarily(X1))))|~axiom_s4)). % 5.04/1.12 cnf(i_0_55, plain, (is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))|~axiom_m9)). % 5.04/1.12 cnf(i_0_52, plain, (axiom_m8|~is_a_theorem(strict_implies(strict_implies(esk36_0,esk37_0),strict_implies(possibly(esk36_0),possibly(esk37_0)))))). % 5.04/1.12 cnf(i_0_51, plain, (is_a_theorem(strict_implies(possibly(and(X1,X2)),X1))|~axiom_m7)). % 5.04/1.12 cnf(i_0_20, plain, (axiom_K|~is_a_theorem(implies(strict_implies(esk8_0,esk9_0),implies(necessarily(esk8_0),necessarily(esk9_0)))))). % 5.04/1.12 cnf(i_0_32, plain, (axiom_s2|~is_a_theorem(strict_implies(possibly(and(esk17_0,esk18_0)),and(possibly(esk17_0),possibly(esk18_0)))))). % 5.04/1.12 cnf(i_0_2, plain, (not(or(not(X1),not(X2)))=and(X1,X2)|~op_and)). % 5.04/1.12 cnf(i_0_34, plain, (axiom_s3|~is_a_theorem(strict_implies(strict_implies(esk19_0,esk20_0),strict_implies(not(possibly(esk20_0)),not(possibly(esk19_0))))))). % 5.04/1.12 cnf(i_0_30, plain, (axiom_s1|~is_a_theorem(implies(and(strict_implies(esk14_0,esk15_0),strict_implies(esk15_0,esk16_0)),strict_implies(esk14_0,esk16_0))))). % 5.04/1.12 cnf(i_0_53, plain, (is_a_theorem(strict_implies(strict_implies(X1,X2),strict_implies(possibly(X1),possibly(X2))))|~axiom_m8)). % 5.04/1.12 cnf(i_0_21, plain, (is_a_theorem(implies(strict_implies(X1,X2),implies(necessarily(X1),necessarily(X2))))|~axiom_K)). % 5.04/1.12 cnf(i_0_33, plain, (is_a_theorem(strict_implies(possibly(and(X1,X2)),and(possibly(X1),possibly(X2))))|~axiom_s2)). % 5.04/1.12 cnf(i_0_35, plain, (is_a_theorem(strict_implies(strict_implies(X1,X2),strict_implies(not(possibly(X2)),not(possibly(X1)))))|~axiom_s3)). % 5.04/1.12 cnf(i_0_31, plain, (is_a_theorem(implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))|~axiom_s1)). % 5.04/1.12 cnf(i_0_152, plain, (X100=X100)). % 5.04/1.12 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 5.04/1.12 # Begin printing tableau % 5.04/1.12 # Found 15 steps % 5.04/1.12 cnf(i_0_51, plain, (is_a_theorem(strict_implies(possibly(and(possibly(and(esk34_0,esk35_0)),esk34_0)),possibly(and(esk34_0,esk35_0))))|~axiom_m7), inference(start_rule)). % 5.04/1.12 cnf(i_0_244, plain, (is_a_theorem(strict_implies(possibly(and(possibly(and(esk34_0,esk35_0)),esk34_0)),possibly(and(esk34_0,esk35_0))))), inference(extension_rule, [i_0_8])). % 5.04/1.12 cnf(i_0_580, plain, (is_a_theorem(necessarily(strict_implies(possibly(and(possibly(and(esk34_0,esk35_0)),esk34_0)),possibly(and(esk34_0,esk35_0)))))), inference(extension_rule, [i_0_12])). % 5.04/1.12 cnf(i_0_597, plain, (is_a_theorem(implies(possibly(esk13_0),necessarily(possibly(esk13_0))))), inference(closure_rule, [i_0_28])). % 5.04/1.12 cnf(i_0_598, plain, (~is_a_theorem(strict_implies(necessarily(strict_implies(possibly(and(possibly(and(esk34_0,esk35_0)),esk34_0)),possibly(and(esk34_0,esk35_0)))),implies(possibly(esk13_0),necessarily(possibly(esk13_0)))))), inference(extension_rule, [i_0_161])). % 5.04/1.12 cnf(i_0_686, plain, (~is_a_theorem(strict_implies(possibly(and(esk34_0,esk35_0)),and(possibly(and(esk34_0,esk35_0)),possibly(and(esk34_0,esk35_0)))))), inference(closure_rule, [i_0_45])). % 5.04/1.12 cnf(i_0_582, plain, (~necessitation), inference(extension_rule, [i_0_7])). % 5.04/1.12 cnf(i_0_687, plain, (is_a_theorem(esk1_0)), inference(extension_rule, [i_0_16])). % 5.04/1.12 cnf(i_0_717, plain, (~is_a_theorem(strict_implies(possibly(and(esk34_0,esk35_0)),and(possibly(and(esk34_0,esk35_0)),possibly(and(esk34_0,esk35_0)))))), inference(closure_rule, [i_0_45])). % 5.04/1.12 cnf(i_0_245, plain, (~axiom_m7), inference(extension_rule, [i_0_50])). % 5.04/1.12 cnf(i_0_741, plain, (~is_a_theorem(strict_implies(possibly(and(esk34_0,esk35_0)),esk34_0))), inference(extension_rule, [i_0_161])). % 5.04/1.12 cnf(i_0_1649, plain, (necessarily(implies(possibly(and(esk34_0,esk35_0)),esk34_0))!=strict_implies(possibly(and(esk34_0,esk35_0)),esk34_0)), inference(closure_rule, [i_0_60])). % 5.04/1.12 cnf(i_0_685, plain, (strict_implies(possibly(and(esk34_0,esk35_0)),and(possibly(and(esk34_0,esk35_0)),possibly(and(esk34_0,esk35_0))))!=strict_implies(necessarily(strict_implies(possibly(and(possibly(and(esk34_0,esk35_0)),esk34_0)),possibly(and(esk34_0,esk35_0)))),implies(possibly(esk13_0),necessarily(possibly(esk13_0))))), inference(etableau_closure_rule, [i_0_685, ...])). % 5.04/1.12 cnf(i_0_715, plain, (is_a_theorem(and(strict_implies(possibly(and(esk34_0,esk35_0)),and(possibly(and(esk34_0,esk35_0)),possibly(and(esk34_0,esk35_0)))),esk1_0))), inference(etableau_closure_rule, [i_0_715, ...])). % 5.04/1.12 cnf(i_0_1650, plain, (~is_a_theorem(necessarily(implies(possibly(and(esk34_0,esk35_0)),esk34_0)))), inference(etableau_closure_rule, [i_0_1650, ...])). % 5.04/1.12 # End printing tableau % 5.04/1.12 # SZS output end % 5.04/1.12 # Branches closed with saturation will be marked with an "s" % 5.04/1.12 # Child (2085774) has found a proof. % 5.04/1.12 % 5.04/1.12 # Proof search is over... % 5.04/1.12 # Freeing feature tree %------------------------------------------------------------------------------