%------------------------------------------------------------------------------ % File : Etableau---0.67 % Problem : LCL454+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 12:01:17 PM UTC 2026 % Result : Theorem 0.10s 0.47s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL454+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 % 0.10/0.36 % Computer : n031.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 21:42:55 UTC 2026 % 0.10/0.36 % CPUTime : % 0.10/0.40 # No SInE strategy applied % 0.10/0.40 # Auto-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI % 0.10/0.40 # and selection function SelectComplexExceptUniqMaxHorn. % 0.10/0.40 # % 0.10/0.40 # Presaturation interreduction done % 0.10/0.40 # Number of axioms: 82 Number of unprocessed: 58 % 0.10/0.40 # Tableaux proof search. % 0.10/0.40 # APR header successfully linked. % 0.10/0.40 # Hello from C++ % 0.10/0.41 # The folding up rule is enabled... % 0.10/0.41 # Local unification is enabled... % 0.10/0.41 # Any saturation attempts will use folding labels... % 0.10/0.41 # 58 beginning clauses after preprocessing and clausification % 0.10/0.41 # Creating start rules for all 1 conjectures. % 0.10/0.41 # There are 1 start rule candidates: % 0.10/0.41 # Found 44 unit axioms. % 0.10/0.41 # 1 start rule tableaux created. % 0.10/0.41 # 14 extension rule candidate clauses % 0.10/0.41 # 44 unit axiom clauses % 0.10/0.41 % 0.10/0.41 # Requested 8, 32 cores available to the main process. % 0.10/0.41 # There are not enough tableaux to fork, creating more from the initial 1 % 0.10/0.41 # Creating equality axioms % 0.10/0.41 # Ran out of tableaux, making start rules for all clauses % 0.10/0.41 # Returning from population with 58 new_tableaux and 0 remaining starting tableaux. % 0.10/0.41 # We now have 58 tableaux to operate on % 0.10/0.47 # There were 1 total branch saturation attempts. % 0.10/0.47 # There were 0 of these attempts blocked. % 0.10/0.47 # There were 0 deferred branch saturation attempts. % 0.10/0.47 # There were 0 free duplicated saturations. % 0.10/0.47 # There were 1 total successful branch saturations. % 0.10/0.47 # There were 0 successful branch saturations in interreduction. % 0.10/0.47 # There were 0 successful branch saturations on the branch. % 0.10/0.47 # There were 1 successful branch saturations after the branch. % 0.10/0.47 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.10/0.47 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.10/0.47 # Begin clausification derivation % 0.10/0.47 % 0.10/0.47 # End clausification derivation % 0.10/0.47 # Begin listing active clauses obtained from FOF to CNF conversion % 0.10/0.47 cnf(i_0_64, plain, (modus_ponens)). % 0.10/0.47 cnf(i_0_78, plain, (substitution_of_equivalents)). % 0.10/0.47 cnf(i_0_65, plain, (modus_tollens)). % 0.10/0.47 cnf(i_0_66, plain, (implies_1)). % 0.10/0.47 cnf(i_0_67, plain, (implies_2)). % 0.10/0.47 cnf(i_0_68, plain, (implies_3)). % 0.10/0.47 cnf(i_0_69, plain, (and_1)). % 0.10/0.47 cnf(i_0_70, plain, (and_2)). % 0.10/0.47 cnf(i_0_71, plain, (and_3)). % 0.10/0.47 cnf(i_0_72, plain, (or_1)). % 0.10/0.47 cnf(i_0_73, plain, (or_2)). % 0.10/0.47 cnf(i_0_74, plain, (or_3)). % 0.10/0.47 cnf(i_0_75, plain, (equivalence_1)). % 0.10/0.47 cnf(i_0_76, plain, (equivalence_2)). % 0.10/0.47 cnf(i_0_77, plain, (equivalence_3)). % 0.10/0.47 cnf(i_0_61, plain, (op_or)). % 0.10/0.47 cnf(i_0_80, plain, (op_and)). % 0.10/0.47 cnf(i_0_62, plain, (op_implies_and)). % 0.10/0.47 cnf(i_0_79, plain, (op_implies_or)). % 0.10/0.47 cnf(i_0_63, plain, (op_equiv)). % 0.10/0.47 cnf(i_0_59, plain, (or(not(X1),X2)=implies(X1,X2))). % 0.10/0.47 cnf(i_0_11, plain, (is_a_theorem(implies(X1,implies(X2,X1))))). % 0.10/0.47 cnf(i_0_25, plain, (is_a_theorem(implies(X1,or(X2,X1))))). % 0.10/0.47 cnf(i_0_48, plain, (r2)). % 0.10/0.47 cnf(i_0_23, plain, (is_a_theorem(implies(X1,or(X1,X2))))). % 0.10/0.47 cnf(i_0_19, plain, (is_a_theorem(implies(and(X1,X2),X2)))). % 0.10/0.47 cnf(i_0_17, plain, (is_a_theorem(implies(and(X1,X2),X1)))). % 0.10/0.47 cnf(i_0_58, plain, (not(and(X1,not(X2)))=implies(X1,X2))). % 0.10/0.47 cnf(i_0_36, plain, (kn2)). % 0.10/0.47 cnf(i_0_57, plain, (not(implies(X1,not(X2)))=and(X1,X2))). % 0.10/0.47 cnf(i_0_56, plain, (implies(not(X1),X2)=or(X1,X2))). % 0.10/0.47 cnf(i_0_31, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))))). % 0.10/0.47 cnf(i_0_29, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))))). % 0.10/0.47 cnf(i_0_21, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2)))))). % 0.10/0.47 cnf(i_0_42, plain, (cn2)). % 0.10/0.47 cnf(i_0_60, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2))). % 0.10/0.47 cnf(i_0_9, plain, (is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))))). % 0.10/0.47 cnf(i_0_13, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))))). % 0.10/0.47 cnf(i_0_15, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))))). % 0.10/0.47 cnf(i_0_40, plain, (cn1)). % 0.10/0.47 cnf(i_0_33, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2)))))). % 0.10/0.47 cnf(i_0_27, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2)))))). % 0.10/0.47 cnf(i_0_82, negated_conjecture, (~r1)). % 0.10/0.47 cnf(i_0_46, plain, (~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)))). % 0.10/0.47 cnf(i_0_7, plain, (X1=X2|~is_a_theorem(equiv(X1,X2)))). % 0.10/0.47 cnf(i_0_34, plain, (kn1|~is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))))). % 0.10/0.47 cnf(i_0_4, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2))). % 0.10/0.47 cnf(i_0_35, plain, (is_a_theorem(implies(X1,and(X1,X1)))|~kn1)). % 0.10/0.47 cnf(i_0_50, plain, (r3|~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))))). % 0.10/0.47 cnf(i_0_51, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))|~r3)). % 0.10/0.47 cnf(i_0_44, plain, (cn3|~is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)))). % 0.10/0.47 cnf(i_0_45, plain, (is_a_theorem(implies(or(X1,X1),X1))|~cn3)). % 0.10/0.47 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)))))). % 0.10/0.47 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)))))). % 0.10/0.47 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))))))). % 0.10/0.47 cnf(i_0_55, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))|~r5)). % 0.10/0.47 cnf(i_0_53, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))|~r4)). % 0.10/0.47 cnf(i_0_39, plain, (is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))|~kn3)). % 0.10/0.47 cnf(i_0_113, plain, (X127=X127)). % 0.10/0.47 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.10/0.47 # Begin printing tableau % 0.10/0.47 # Found 8 steps % 0.10/0.47 cnf(i_0_44, plain, (cn3|~is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0))), inference(start_rule)). % 0.10/0.47 cnf(i_0_180, plain, (cn3), inference(extension_rule, [i_0_45])). % 0.10/0.47 cnf(i_0_371, plain, (is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))), inference(closure_rule, [i_0_46])). % 0.10/0.47 cnf(i_0_181, plain, (~is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0))), inference(extension_rule, [i_0_4])). % 0.10/0.47 cnf(i_0_378, plain, (~is_a_theorem(implies(esk44_0,implies(or(esk44_0,esk44_0),esk44_0)))), inference(closure_rule, [i_0_11])). % 0.10/0.47 cnf(i_0_379, plain, (~is_a_theorem(esk44_0)), inference(extension_rule, [i_0_4])). % 0.10/0.47 cnf(i_0_596, plain, (~is_a_theorem(implies(and(X1,esk44_0),esk44_0))), inference(closure_rule, [i_0_19])). % 0.10/0.47 cnf(i_0_597, plain, (~is_a_theorem(and(X1,esk44_0))), inference(etableau_closure_rule, [i_0_597, ...])). % 0.10/0.47 # End printing tableau % 0.10/0.47 # SZS output end % 0.10/0.47 # Branches closed with saturation will be marked with an "s" % 0.10/0.47 # There were 1 total branch saturation attempts. % 0.10/0.47 # There were 0 of these attempts blocked. % 0.10/0.47 # There were 0 deferred branch saturation attempts. % 0.10/0.47 # There were 0 free duplicated saturations. % 0.10/0.47 # There were 1 total successful branch saturations. % 0.10/0.47 # There were 0 successful branch saturations in interreduction. % 0.10/0.47 # There were 0 successful branch saturations on the branch. % 0.10/0.47 # There were 1 successful branch saturations after the branch. % 0.10/0.47 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.10/0.47 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.10/0.47 # Begin clausification derivation % 0.10/0.47 % 0.10/0.47 # End clausification derivation % 0.10/0.47 # Begin listing active clauses obtained from FOF to CNF conversion % 0.10/0.47 cnf(i_0_64, plain, (modus_ponens)). % 0.10/0.47 cnf(i_0_78, plain, (substitution_of_equivalents)). % 0.10/0.47 cnf(i_0_65, plain, (modus_tollens)). % 0.10/0.47 cnf(i_0_66, plain, (implies_1)). % 0.10/0.47 cnf(i_0_67, plain, (implies_2)). % 0.10/0.47 cnf(i_0_68, plain, (implies_3)). % 0.10/0.47 cnf(i_0_69, plain, (and_1)). % 0.10/0.47 cnf(i_0_70, plain, (and_2)). % 0.10/0.47 cnf(i_0_71, plain, (and_3)). % 0.10/0.47 cnf(i_0_72, plain, (or_1)). % 0.10/0.47 cnf(i_0_73, plain, (or_2)). % 0.10/0.47 cnf(i_0_74, plain, (or_3)). % 0.10/0.47 cnf(i_0_75, plain, (equivalence_1)). % 0.10/0.47 cnf(i_0_76, plain, (equivalence_2)). % 0.10/0.47 cnf(i_0_77, plain, (equivalence_3)). % 0.10/0.47 cnf(i_0_61, plain, (op_or)). % 0.10/0.47 cnf(i_0_80, plain, (op_and)). % 0.10/0.47 cnf(i_0_62, plain, (op_implies_and)). % 0.10/0.47 cnf(i_0_79, plain, (op_implies_or)). % 0.10/0.47 cnf(i_0_63, plain, (op_equiv)). % 0.10/0.47 cnf(i_0_59, plain, (or(not(X1),X2)=implies(X1,X2))). % 0.10/0.47 cnf(i_0_11, plain, (is_a_theorem(implies(X1,implies(X2,X1))))). % 0.10/0.47 cnf(i_0_25, plain, (is_a_theorem(implies(X1,or(X2,X1))))). % 0.10/0.47 cnf(i_0_48, plain, (r2)). % 0.10/0.47 cnf(i_0_23, plain, (is_a_theorem(implies(X1,or(X1,X2))))). % 0.10/0.47 cnf(i_0_19, plain, (is_a_theorem(implies(and(X1,X2),X2)))). % 0.10/0.47 cnf(i_0_17, plain, (is_a_theorem(implies(and(X1,X2),X1)))). % 0.10/0.47 cnf(i_0_58, plain, (not(and(X1,not(X2)))=implies(X1,X2))). % 0.10/0.47 cnf(i_0_36, plain, (kn2)). % 0.10/0.47 cnf(i_0_57, plain, (not(implies(X1,not(X2)))=and(X1,X2))). % 0.10/0.47 cnf(i_0_56, plain, (implies(not(X1),X2)=or(X1,X2))). % 0.10/0.47 cnf(i_0_31, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))))). % 0.10/0.47 cnf(i_0_29, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))))). % 0.10/0.47 cnf(i_0_21, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2)))))). % 0.10/0.47 cnf(i_0_42, plain, (cn2)). % 0.10/0.47 cnf(i_0_60, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2))). % 0.10/0.47 cnf(i_0_9, plain, (is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))))). % 0.10/0.47 cnf(i_0_13, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))))). % 0.10/0.47 cnf(i_0_15, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))))). % 0.10/0.47 cnf(i_0_40, plain, (cn1)). % 0.10/0.47 cnf(i_0_33, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2)))))). % 0.10/0.47 cnf(i_0_27, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2)))))). % 0.10/0.47 cnf(i_0_82, negated_conjecture, (~r1)). % 0.10/0.47 cnf(i_0_46, plain, (~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)))). % 0.10/0.47 cnf(i_0_7, plain, (X1=X2|~is_a_theorem(equiv(X1,X2)))). % 0.10/0.47 cnf(i_0_34, plain, (kn1|~is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))))). % 0.10/0.47 cnf(i_0_4, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2))). % 0.10/0.47 cnf(i_0_35, plain, (is_a_theorem(implies(X1,and(X1,X1)))|~kn1)). % 0.10/0.47 cnf(i_0_50, plain, (r3|~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))))). % 0.10/0.47 cnf(i_0_51, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))|~r3)). % 0.10/0.47 cnf(i_0_44, plain, (cn3|~is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)))). % 0.10/0.47 cnf(i_0_45, plain, (is_a_theorem(implies(or(X1,X1),X1))|~cn3)). % 0.10/0.47 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)))))). % 0.10/0.47 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)))))). % 0.10/0.47 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))))))). % 0.10/0.47 cnf(i_0_55, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))|~r5)). % 0.10/0.47 cnf(i_0_53, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))|~r4)). % 0.10/0.47 cnf(i_0_39, plain, (is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))|~kn3)). % 0.10/0.47 cnf(i_0_113, plain, (X127=X127)). % 0.10/0.47 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.10/0.47 # Begin printing tableau % 0.10/0.47 # Found 6 steps % 0.10/0.47 cnf(i_0_46, plain, (~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))), inference(start_rule)). % 0.10/0.47 cnf(i_0_166, plain, (~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))), inference(extension_rule, [i_0_4])). % 0.10/0.47 cnf(i_0_361, plain, (~is_a_theorem(implies(esk45_0,implies(or(esk45_0,esk45_0),esk45_0)))), inference(closure_rule, [i_0_11])). % 0.10/0.47 cnf(i_0_362, plain, (~is_a_theorem(esk45_0)), inference(extension_rule, [i_0_4])). % 0.10/0.47 cnf(i_0_583, plain, (~is_a_theorem(implies(and(X1,esk45_0),esk45_0))), inference(closure_rule, [i_0_19])). % 0.10/0.47 cnf(i_0_584, plain, (~is_a_theorem(and(X1,esk45_0))), inference(etableau_closure_rule, [i_0_584, ...])). % 0.10/0.47 # End printing tableau % 0.10/0.47 # SZS output end % 0.10/0.47 # Branches closed with saturation will be marked with an "s" % 0.10/0.47 # Child (3778553) has found a proof. % 0.10/0.47 % 0.10/0.48 # Proof search is over... % 0.10/0.48 # Freeing feature tree %------------------------------------------------------------------------------