%------------------------------------------------------------------------------ % File : Etableau---0.67 % Problem : LCL453+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 : n026.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 12:01:17 PM UTC 2026 % Result : Theorem 0.81s 0.55s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL453+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 % 0.10/0.37 % Computer : n026.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.38 % CPULimit : 300 % 0.10/0.38 % WCLimit : 300 % 0.10/0.38 % DateTime : Sat Sep 5 12:40:26 UTC 2026 % 0.15/0.38 % CPUTime : % 0.15/0.42 # No SInE strategy applied % 0.15/0.42 # Auto-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI % 0.15/0.42 # and selection function SelectComplexExceptUniqMaxHorn. % 0.15/0.42 # % 0.15/0.42 # Presaturation interreduction done % 0.15/0.42 # Number of axioms: 82 Number of unprocessed: 57 % 0.15/0.42 # Tableaux proof search. % 0.15/0.42 # APR header successfully linked. % 0.15/0.42 # Hello from C++ % 0.15/0.42 # The folding up rule is enabled... % 0.15/0.42 # Local unification is enabled... % 0.15/0.42 # Any saturation attempts will use folding labels... % 0.15/0.42 # 57 beginning clauses after preprocessing and clausification % 0.15/0.42 # Creating start rules for all 1 conjectures. % 0.15/0.42 # There are 1 start rule candidates: % 0.15/0.42 # Found 41 unit axioms. % 0.15/0.42 # 1 start rule tableaux created. % 0.15/0.42 # 16 extension rule candidate clauses % 0.15/0.42 # 41 unit axiom clauses % 0.15/0.42 % 0.15/0.42 # Requested 8, 32 cores available to the main process. % 0.15/0.42 # There are not enough tableaux to fork, creating more from the initial 1 % 0.15/0.42 # Creating equality axioms % 0.15/0.42 # Ran out of tableaux, making start rules for all clauses % 0.15/0.42 # Returning from population with 57 new_tableaux and 0 remaining starting tableaux. % 0.15/0.42 # We now have 57 tableaux to operate on % 0.81/0.55 # There were 2 total branch saturation attempts. % 0.81/0.55 # There were 0 of these attempts blocked. % 0.81/0.55 # There were 0 deferred branch saturation attempts. % 0.81/0.55 # There were 0 free duplicated saturations. % 0.81/0.55 # There were 2 total successful branch saturations. % 0.81/0.55 # There were 0 successful branch saturations in interreduction. % 0.81/0.55 # There were 0 successful branch saturations on the branch. % 0.81/0.55 # There were 2 successful branch saturations after the branch. % 0.81/0.55 # SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.81/0.55 # SZS output start for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.81/0.55 # Begin clausification derivation % 0.81/0.55 % 0.81/0.55 # End clausification derivation % 0.81/0.55 # Begin listing active clauses obtained from FOF to CNF conversion % 0.81/0.55 cnf(i_0_64, plain, (modus_ponens)). % 0.81/0.55 cnf(i_0_78, plain, (substitution_of_equivalents)). % 0.81/0.55 cnf(i_0_65, plain, (modus_tollens)). % 0.81/0.55 cnf(i_0_66, plain, (implies_1)). % 0.81/0.55 cnf(i_0_67, plain, (implies_2)). % 0.81/0.55 cnf(i_0_68, plain, (implies_3)). % 0.81/0.55 cnf(i_0_69, plain, (and_1)). % 0.81/0.55 cnf(i_0_70, plain, (and_2)). % 0.81/0.55 cnf(i_0_71, plain, (and_3)). % 0.81/0.55 cnf(i_0_72, plain, (or_1)). % 0.81/0.55 cnf(i_0_73, plain, (or_2)). % 0.81/0.55 cnf(i_0_74, plain, (or_3)). % 0.81/0.55 cnf(i_0_75, plain, (equivalence_1)). % 0.81/0.55 cnf(i_0_76, plain, (equivalence_2)). % 0.81/0.55 cnf(i_0_77, plain, (equivalence_3)). % 0.81/0.55 cnf(i_0_61, plain, (op_or)). % 0.81/0.55 cnf(i_0_62, plain, (op_implies_and)). % 0.81/0.55 cnf(i_0_63, plain, (op_equiv)). % 0.81/0.55 cnf(i_0_80, plain, (op_implies)). % 0.81/0.55 cnf(i_0_58, plain, (not(and(X1,not(X2)))=implies(X1,X2))). % 0.81/0.55 cnf(i_0_11, plain, (is_a_theorem(implies(X1,implies(X2,X1))))). % 0.81/0.55 cnf(i_0_25, plain, (is_a_theorem(implies(X1,or(X2,X1))))). % 0.81/0.55 cnf(i_0_48, plain, (r2)). % 0.81/0.55 cnf(i_0_23, plain, (is_a_theorem(implies(X1,or(X1,X2))))). % 0.81/0.55 cnf(i_0_19, plain, (is_a_theorem(implies(and(X1,X2),X2)))). % 0.81/0.55 cnf(i_0_17, plain, (is_a_theorem(implies(and(X1,X2),X1)))). % 0.81/0.55 cnf(i_0_36, plain, (kn2)). % 0.81/0.55 cnf(i_0_56, plain, (implies(not(X1),X2)=or(X1,X2))). % 0.81/0.55 cnf(i_0_31, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))))). % 0.81/0.55 cnf(i_0_29, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))))). % 0.81/0.55 cnf(i_0_42, plain, (cn2)). % 0.81/0.55 cnf(i_0_21, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2)))))). % 0.81/0.55 cnf(i_0_60, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2))). % 0.81/0.55 cnf(i_0_9, plain, (is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))))). % 0.81/0.55 cnf(i_0_13, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))))). % 0.81/0.55 cnf(i_0_15, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))))). % 0.81/0.55 cnf(i_0_40, plain, (cn1)). % 0.81/0.55 cnf(i_0_33, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2)))))). % 0.81/0.55 cnf(i_0_27, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2)))))). % 0.81/0.55 cnf(i_0_82, negated_conjecture, (~cn3)). % 0.81/0.55 cnf(i_0_44, plain, (~is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)))). % 0.81/0.55 cnf(i_0_7, plain, (X1=X2|~is_a_theorem(equiv(X1,X2)))). % 0.81/0.55 cnf(i_0_34, plain, (kn1|~is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))))). % 0.81/0.55 cnf(i_0_59, plain, (or(not(X1),X2)=implies(X1,X2)|~op_implies_or)). % 0.81/0.55 cnf(i_0_46, plain, (r1|~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)))). % 0.81/0.55 cnf(i_0_4, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2))). % 0.81/0.55 cnf(i_0_35, plain, (is_a_theorem(implies(X1,and(X1,X1)))|~kn1)). % 0.81/0.55 cnf(i_0_50, plain, (r3|~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))))). % 0.81/0.55 cnf(i_0_47, plain, (is_a_theorem(implies(or(X1,X1),X1))|~r1)). % 0.81/0.55 cnf(i_0_57, plain, (not(or(not(X1),not(X2)))=and(X1,X2)|~op_and)). % 0.81/0.55 cnf(i_0_51, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))|~r3)). % 0.81/0.55 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)))))). % 0.81/0.55 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)))))). % 0.81/0.55 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))))))). % 0.81/0.55 cnf(i_0_55, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))|~r5)). % 0.81/0.55 cnf(i_0_53, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))|~r4)). % 0.81/0.55 cnf(i_0_39, plain, (is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))|~kn3)). % 0.81/0.55 cnf(i_0_117, plain, (X127=X127)). % 0.81/0.55 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.81/0.55 # Begin printing tableau % 0.81/0.55 # Found 11 steps % 0.81/0.55 cnf(i_0_35, plain, (is_a_theorem(implies(implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))),and(implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))),implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))))))|~kn1), inference(start_rule)). % 0.81/0.55 cnf(i_0_179, plain, (is_a_theorem(implies(implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))),and(implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))),implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))))))), inference(extension_rule, [i_0_4])). % 0.81/0.55 cnf(i_0_383, plain, (~is_a_theorem(implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))))), inference(closure_rule, [i_0_11])). % 0.81/0.55 cnf(i_0_381, plain, (is_a_theorem(and(implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))),implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0)))))), inference(extension_rule, [i_0_121])). % 0.81/0.55 cnf(i_0_421, plain, (is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0))), inference(closure_rule, [i_0_44])). % 0.81/0.55 cnf(i_0_422, plain, (and(implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))),implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))))!=implies(or(esk44_0,esk44_0),esk44_0)), inference(extension_rule, [i_0_7])). % 0.81/0.55 cnf(i_0_180, plain, (~kn1), inference(extension_rule, [i_0_34])). % 0.81/0.55 cnf(i_0_427, plain, (~is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))), inference(extension_rule, [i_0_4])). % 0.81/0.55 cnf(i_0_476, plain, (~is_a_theorem(implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))))), inference(closure_rule, [i_0_11])). % 0.81/0.55 cnf(i_0_425, plain, (~is_a_theorem(equiv(and(implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0))),implies(and(esk33_0,esk33_0),implies(esk33_0,and(esk33_0,esk33_0)))),implies(or(esk44_0,esk44_0),esk44_0)))), inference(etableau_closure_rule, [i_0_425, ...])). % 0.81/0.55 cnf(i_0_477, plain, (~is_a_theorem(and(esk33_0,esk33_0))), inference(etableau_closure_rule, [i_0_477, ...])). % 0.81/0.55 # End printing tableau % 0.81/0.55 # SZS output end % 0.81/0.55 # Branches closed with saturation will be marked with an "s" % 0.81/0.55 # There were 1 total branch saturation attempts. % 0.81/0.55 # There were 0 of these attempts blocked. % 0.81/0.55 # There were 0 deferred branch saturation attempts. % 0.81/0.55 # There were 0 free duplicated saturations. % 0.81/0.55 # There were 1 total successful branch saturations. % 0.81/0.55 # There were 0 successful branch saturations in interreduction. % 0.81/0.55 # There were 0 successful branch saturations on the branch. % 0.81/0.55 # There were 1 successful branch saturations after the branch. % 0.81/0.55 # SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.81/0.55 # SZS output start for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.81/0.55 # Begin clausification derivation % 0.81/0.55 % 0.81/0.55 # End clausification derivation % 0.81/0.55 # Begin listing active clauses obtained from FOF to CNF conversion % 0.81/0.55 cnf(i_0_64, plain, (modus_ponens)). % 0.81/0.55 cnf(i_0_78, plain, (substitution_of_equivalents)). % 0.81/0.55 cnf(i_0_65, plain, (modus_tollens)). % 0.81/0.55 cnf(i_0_66, plain, (implies_1)). % 0.81/0.55 cnf(i_0_67, plain, (implies_2)). % 0.81/0.55 cnf(i_0_68, plain, (implies_3)). % 0.81/0.55 cnf(i_0_69, plain, (and_1)). % 0.81/0.55 cnf(i_0_70, plain, (and_2)). % 0.81/0.55 cnf(i_0_71, plain, (and_3)). % 0.81/0.55 cnf(i_0_72, plain, (or_1)). % 0.81/0.55 cnf(i_0_73, plain, (or_2)). % 0.81/0.55 cnf(i_0_74, plain, (or_3)). % 0.81/0.55 cnf(i_0_75, plain, (equivalence_1)). % 0.81/0.55 cnf(i_0_76, plain, (equivalence_2)). % 0.81/0.55 cnf(i_0_77, plain, (equivalence_3)). % 0.81/0.55 cnf(i_0_61, plain, (op_or)). % 0.81/0.55 cnf(i_0_62, plain, (op_implies_and)). % 0.81/0.55 cnf(i_0_63, plain, (op_equiv)). % 0.81/0.55 cnf(i_0_80, plain, (op_implies)). % 0.81/0.55 cnf(i_0_58, plain, (not(and(X1,not(X2)))=implies(X1,X2))). % 0.81/0.55 cnf(i_0_11, plain, (is_a_theorem(implies(X1,implies(X2,X1))))). % 0.81/0.55 cnf(i_0_25, plain, (is_a_theorem(implies(X1,or(X2,X1))))). % 0.81/0.55 cnf(i_0_48, plain, (r2)). % 0.81/0.55 cnf(i_0_23, plain, (is_a_theorem(implies(X1,or(X1,X2))))). % 0.81/0.55 cnf(i_0_19, plain, (is_a_theorem(implies(and(X1,X2),X2)))). % 0.81/0.55 cnf(i_0_17, plain, (is_a_theorem(implies(and(X1,X2),X1)))). % 0.81/0.55 cnf(i_0_36, plain, (kn2)). % 0.81/0.55 cnf(i_0_56, plain, (implies(not(X1),X2)=or(X1,X2))). % 0.81/0.55 cnf(i_0_31, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))))). % 0.81/0.55 cnf(i_0_29, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))))). % 0.81/0.55 cnf(i_0_42, plain, (cn2)). % 0.81/0.55 cnf(i_0_21, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2)))))). % 0.81/0.55 cnf(i_0_60, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2))). % 0.81/0.55 cnf(i_0_9, plain, (is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))))). % 0.81/0.55 cnf(i_0_13, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))))). % 0.81/0.55 cnf(i_0_15, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))))). % 0.81/0.55 cnf(i_0_40, plain, (cn1)). % 0.81/0.55 cnf(i_0_33, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2)))))). % 0.81/0.55 cnf(i_0_27, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2)))))). % 0.81/0.55 cnf(i_0_82, negated_conjecture, (~cn3)). % 0.81/0.55 cnf(i_0_44, plain, (~is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)))). % 0.81/0.55 cnf(i_0_7, plain, (X1=X2|~is_a_theorem(equiv(X1,X2)))). % 0.81/0.55 cnf(i_0_34, plain, (kn1|~is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))))). % 0.81/0.55 cnf(i_0_59, plain, (or(not(X1),X2)=implies(X1,X2)|~op_implies_or)). % 0.81/0.55 cnf(i_0_46, plain, (r1|~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)))). % 0.81/0.55 cnf(i_0_4, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2))). % 0.81/0.55 cnf(i_0_35, plain, (is_a_theorem(implies(X1,and(X1,X1)))|~kn1)). % 0.81/0.55 cnf(i_0_50, plain, (r3|~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))))). % 0.81/0.55 cnf(i_0_47, plain, (is_a_theorem(implies(or(X1,X1),X1))|~r1)). % 0.81/0.55 cnf(i_0_57, plain, (not(or(not(X1),not(X2)))=and(X1,X2)|~op_and)). % 0.81/0.55 cnf(i_0_51, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))|~r3)). % 0.81/0.55 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)))))). % 0.81/0.55 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)))))). % 0.81/0.55 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))))))). % 0.81/0.55 cnf(i_0_55, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))|~r5)). % 0.81/0.55 cnf(i_0_53, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))|~r4)). % 0.81/0.55 cnf(i_0_39, plain, (is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))|~kn3)). % 0.81/0.55 cnf(i_0_117, plain, (X127=X127)). % 0.81/0.55 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.81/0.55 # Begin printing tableau % 0.81/0.55 # Found 6 steps % 0.81/0.55 cnf(i_0_58, plain, (not(and(or(esk44_0,esk44_0),not(esk44_0)))=implies(or(esk44_0,esk44_0),esk44_0)), inference(start_rule)). % 0.81/0.55 cnf(i_0_146, plain, (not(and(or(esk44_0,esk44_0),not(esk44_0)))=implies(or(esk44_0,esk44_0),esk44_0)), inference(extension_rule, [i_0_121])). % 0.81/0.55 cnf(i_0_13534, plain, (is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0))), inference(closure_rule, [i_0_44])). % 0.81/0.55 cnf(i_0_13536, plain, (~is_a_theorem(not(and(or(esk44_0,esk44_0),not(esk44_0))))), inference(extension_rule, [i_0_4])). % 0.81/0.55 cnf(i_0_13566, plain, (~is_a_theorem(implies(and(X1,not(and(or(esk44_0,esk44_0),not(esk44_0)))),not(and(or(esk44_0,esk44_0),not(esk44_0)))))), inference(closure_rule, [i_0_19])). % 0.81/0.55 cnf(i_0_13567, plain, (~is_a_theorem(and(X1,not(and(or(esk44_0,esk44_0),not(esk44_0)))))), inference(etableau_closure_rule, [i_0_13567, ...])). % 0.81/0.55 # End printing tableau % 0.81/0.55 # SZS output end % 0.81/0.55 # Branches closed with saturation will be marked with an "s" % 0.81/0.55 # Child (1768467) has found a proof. % 0.81/0.55 % 0.81/0.55 # Proof search is over... % 0.81/0.55 # Freeing feature tree %------------------------------------------------------------------------------