%------------------------------------------------------------------------------ % File : Etableau---0.67 % Problem : MGT032+2 : TPTP v9.3.0. Released v2.0.0. % 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 : n009.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 : Tue Sep 8 06:09:47 AM UTC 2026 % Result : Theorem 0.08s 0.40s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT032+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s % 0.08/0.36 % Computer : n009.cluster.edu % 0.08/0.36 % Model : x86_64 x86_64 % 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.36 % Memory : 8046.5625MB % 0.08/0.36 % OS : Linux 6.8.0-71-generic % 0.08/0.36 % CPULimit : 300 % 0.08/0.36 % WCLimit : 300 % 0.08/0.36 % DateTime : Mon Sep 7 12:22:07 UTC 2026 % 0.08/0.36 % CPUTime : % 0.08/0.39 # No SInE strategy applied % 0.08/0.39 # Auto-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN % 0.08/0.39 # and selection function SelectComplexExceptUniqMaxHorn. % 0.08/0.39 # % 0.08/0.39 # Presaturation interreduction done % 0.08/0.39 # Number of axioms: 8 Number of unprocessed: 8 % 0.08/0.39 # Tableaux proof search. % 0.08/0.39 # APR header successfully linked. % 0.08/0.39 # Hello from C++ % 0.08/0.39 # The folding up rule is enabled... % 0.08/0.39 # Local unification is enabled... % 0.08/0.39 # Any saturation attempts will use folding labels... % 0.08/0.39 # 8 beginning clauses after preprocessing and clausification % 0.08/0.39 # Creating start rules for all 5 conjectures. % 0.08/0.39 # There are 5 start rule candidates: % 0.08/0.39 # Found 2 unit axioms. % 0.08/0.39 # Unsuccessfully attempted saturation on 1 start tableaux, moving on. % 0.08/0.39 # 5 start rule tableaux created. % 0.08/0.39 # 6 extension rule candidate clauses % 0.08/0.39 # 2 unit axiom clauses % 0.08/0.39 % 0.08/0.39 # Requested 8, 32 cores available to the main process. % 0.08/0.39 # There are not enough tableaux to fork, creating more from the initial 5 % 0.08/0.39 # Returning from population with 10 new_tableaux and 0 remaining starting tableaux. % 0.08/0.39 # We now have 10 tableaux to operate on % 0.08/0.40 # There were 1 total branch saturation attempts. % 0.08/0.40 # There were 0 of these attempts blocked. % 0.08/0.40 # There were 0 deferred branch saturation attempts. % 0.08/0.40 # There were 0 free duplicated saturations. % 0.08/0.40 # There were 1 total successful branch saturations. % 0.08/0.40 # There were 0 successful branch saturations in interreduction. % 0.08/0.40 # There were 0 successful branch saturations on the branch. % 0.08/0.40 # There were 1 successful branch saturations after the branch. % 0.08/0.40 # SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.08/0.40 # SZS output start for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.08/0.40 # Begin clausification derivation % 0.08/0.40 % 0.08/0.40 # End clausification derivation % 0.08/0.40 # Begin listing active clauses obtained from FOF to CNF conversion % 0.08/0.40 cnf(i_0_8, negated_conjecture, (environment(esk2_0))). % 0.08/0.40 cnf(i_0_7, negated_conjecture, (stable(esk2_0))). % 0.08/0.40 cnf(i_0_4, negated_conjecture, (~in_environment(esk2_0,X1)|~selection_favors(efficient_producers,first_movers,esk3_1(X1)))). % 0.08/0.40 cnf(i_0_6, negated_conjecture, (subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(X1))|~in_environment(esk2_0,X1))). % 0.08/0.40 cnf(i_0_5, negated_conjecture, (greater_or_equal(esk3_1(X1),X1)|~in_environment(esk2_0,X1))). % 0.08/0.40 cnf(i_0_3, hypothesis, (in_environment(X1,esk1_1(X1))|~stable(X1)|~environment(X1))). % 0.08/0.40 cnf(i_0_2, hypothesis, (greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))|~greater_or_equal(X1,esk1_1(X2))|~stable(X2)|~subpopulations(first_movers,efficient_producers,X2,X1)|~environment(X2))). % 0.08/0.40 cnf(i_0_1, plain, (selection_favors(X1,X2,X3)|~greater(growth_rate(X1,X3),growth_rate(X2,X3))|~subpopulations(X2,X1,X4,X3)|~environment(X4))). % 0.08/0.40 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.08/0.40 # Begin printing tableau % 0.08/0.40 # Found 5 steps % 0.08/0.40 cnf(i_0_8, negated_conjecture, (environment(esk2_0)), inference(start_rule)). % 0.08/0.40 cnf(i_0_16, plain, (environment(esk2_0)), inference(extension_rule, [i_0_3])). % 0.08/0.40 cnf(i_0_144, plain, (~stable(esk2_0)), inference(closure_rule, [i_0_7])). % 0.08/0.40 cnf(i_0_143, plain, (in_environment(esk2_0,esk1_1(esk2_0))), inference(extension_rule, [i_0_5])). % 0.08/0.40 cnf(i_0_155, plain, (greater_or_equal(esk3_1(esk1_1(esk2_0)),esk1_1(esk2_0))), inference(etableau_closure_rule, [i_0_155, ...])). % 0.08/0.40 # End printing tableau % 0.08/0.40 # SZS output end % 0.08/0.40 # Branches closed with saturation will be marked with an "s" % 0.08/0.40 # There were 1 total branch saturation attempts. % 0.08/0.40 # There were 0 of these attempts blocked. % 0.08/0.40 # There were 0 deferred branch saturation attempts. % 0.08/0.40 # There were 0 free duplicated saturations. % 0.08/0.40 # There were 1 total successful branch saturations. % 0.08/0.40 # There were 0 successful branch saturations in interreduction. % 0.08/0.40 # There were 0 successful branch saturations on the branch. % 0.08/0.40 # There were 1 successful branch saturations after the branch. % 0.08/0.40 # SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.08/0.40 # SZS output start for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.08/0.40 # Begin clausification derivation % 0.08/0.40 % 0.08/0.40 # End clausification derivation % 0.08/0.40 # Begin listing active clauses obtained from FOF to CNF conversion % 0.08/0.40 cnf(i_0_8, negated_conjecture, (environment(esk2_0))). % 0.08/0.40 cnf(i_0_7, negated_conjecture, (stable(esk2_0))). % 0.08/0.40 cnf(i_0_4, negated_conjecture, (~in_environment(esk2_0,X1)|~selection_favors(efficient_producers,first_movers,esk3_1(X1)))). % 0.08/0.40 cnf(i_0_6, negated_conjecture, (subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(X1))|~in_environment(esk2_0,X1))). % 0.08/0.40 cnf(i_0_5, negated_conjecture, (greater_or_equal(esk3_1(X1),X1)|~in_environment(esk2_0,X1))). % 0.08/0.40 cnf(i_0_3, hypothesis, (in_environment(X1,esk1_1(X1))|~stable(X1)|~environment(X1))). % 0.08/0.40 cnf(i_0_2, hypothesis, (greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))|~greater_or_equal(X1,esk1_1(X2))|~stable(X2)|~subpopulations(first_movers,efficient_producers,X2,X1)|~environment(X2))). % 0.08/0.40 cnf(i_0_1, plain, (selection_favors(X1,X2,X3)|~greater(growth_rate(X1,X3),growth_rate(X2,X3))|~subpopulations(X2,X1,X4,X3)|~environment(X4))). % 0.08/0.40 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.08/0.40 # Begin printing tableau % 0.08/0.40 # Found 5 steps % 0.08/0.40 cnf(i_0_7, negated_conjecture, (stable(esk2_0)), inference(start_rule)). % 0.08/0.40 cnf(i_0_15, plain, (stable(esk2_0)), inference(extension_rule, [i_0_3])). % 0.08/0.40 cnf(i_0_127, plain, (~environment(esk2_0)), inference(closure_rule, [i_0_8])). % 0.08/0.40 cnf(i_0_125, plain, (in_environment(esk2_0,esk1_1(esk2_0))), inference(extension_rule, [i_0_5])). % 0.08/0.40 cnf(i_0_155, plain, (greater_or_equal(esk3_1(esk1_1(esk2_0)),esk1_1(esk2_0))), inference(etableau_closure_rule, [i_0_155, ...])). % 0.08/0.40 # End printing tableau % 0.08/0.40 # SZS output end % 0.08/0.40 # Branches closed with saturation will be marked with an "s" % 0.08/0.40 # There were 2 total branch saturation attempts. % 0.08/0.40 # There were 0 of these attempts blocked. % 0.08/0.40 # There were 0 deferred branch saturation attempts. % 0.08/0.40 # There were 0 free duplicated saturations. % 0.08/0.40 # There were 2 total successful branch saturations. % 0.08/0.40 # There were 0 successful branch saturations in interreduction. % 0.08/0.40 # There were 0 successful branch saturations on the branch. % 0.08/0.40 # There were 2 successful branch saturations after the branch. % 0.08/0.40 # SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.08/0.40 # SZS output start for /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.08/0.40 # Begin clausification derivation % 0.08/0.40 % 0.08/0.40 # End clausification derivation % 0.08/0.40 # Begin listing active clauses obtained from FOF to CNF conversion % 0.08/0.40 cnf(i_0_8, negated_conjecture, (environment(esk2_0))). % 0.08/0.40 cnf(i_0_7, negated_conjecture, (stable(esk2_0))). % 0.08/0.40 cnf(i_0_4, negated_conjecture, (~in_environment(esk2_0,X1)|~selection_favors(efficient_producers,first_movers,esk3_1(X1)))). % 0.08/0.40 cnf(i_0_6, negated_conjecture, (subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(X1))|~in_environment(esk2_0,X1))). % 0.08/0.40 cnf(i_0_5, negated_conjecture, (greater_or_equal(esk3_1(X1),X1)|~in_environment(esk2_0,X1))). % 0.08/0.40 cnf(i_0_3, hypothesis, (in_environment(X1,esk1_1(X1))|~stable(X1)|~environment(X1))). % 0.08/0.40 cnf(i_0_2, hypothesis, (greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))|~greater_or_equal(X1,esk1_1(X2))|~stable(X2)|~subpopulations(first_movers,efficient_producers,X2,X1)|~environment(X2))). % 0.08/0.40 cnf(i_0_1, plain, (selection_favors(X1,X2,X3)|~greater(growth_rate(X1,X3),growth_rate(X2,X3))|~subpopulations(X2,X1,X4,X3)|~environment(X4))). % 0.08/0.40 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.08/0.40 # Begin printing tableau % 0.08/0.40 # Found 12 steps % 0.08/0.40 cnf(i_0_6, negated_conjecture, (subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(esk1_1(esk2_0)))|~in_environment(esk2_0,esk1_1(esk2_0))), inference(start_rule)). % 0.08/0.40 cnf(i_0_12, plain, (~in_environment(esk2_0,esk1_1(esk2_0))), inference(extension_rule, [i_0_3])). % 0.08/0.40 cnf(i_0_72, plain, (~stable(esk2_0)), inference(closure_rule, [i_0_7])). % 0.08/0.40 cnf(i_0_73, plain, (~environment(esk2_0)), inference(closure_rule, [i_0_8])). % 0.08/0.40 cnf(i_0_11, plain, (subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(esk1_1(esk2_0)))), inference(extension_rule, [i_0_2])). % 0.08/0.40 cnf(i_0_148, plain, (~stable(esk2_0)), inference(closure_rule, [i_0_7])). % 0.08/0.40 cnf(i_0_150, plain, (~environment(esk2_0)), inference(closure_rule, [i_0_8])). % 0.08/0.40 cnf(i_0_146, plain, (greater(growth_rate(efficient_producers,esk3_1(esk1_1(esk2_0))),growth_rate(first_movers,esk3_1(esk1_1(esk2_0))))), inference(extension_rule, [i_0_1])). % 0.08/0.40 cnf(i_0_156, plain, (~subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(esk1_1(esk2_0)))), inference(closure_rule, [i_0_11])). % 0.08/0.40 cnf(i_0_157, plain, (~environment(esk2_0)), inference(closure_rule, [i_0_8])). % 0.08/0.40 cnf(i_0_147, plain, (~greater_or_equal(esk3_1(esk1_1(esk2_0)),esk1_1(esk2_0))), inference(etableau_closure_rule, [i_0_147, ...])). % 0.08/0.40 cnf(i_0_154, plain, (selection_favors(efficient_producers,first_movers,esk3_1(esk1_1(esk2_0)))), inference(etableau_closure_rule, [i_0_154, ...])). % 0.08/0.40 # End printing tableau % 0.08/0.40 # SZS output end % 0.08/0.40 # Branches closed with saturation will be marked with an "s" % 0.08/0.40 # Child (1528012) has found a proof. % 0.08/0.40 % 0.08/0.40 # Proof search is over... % 0.08/0.40 # Freeing feature tree %------------------------------------------------------------------------------