%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : MGT026+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n028.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 06:04:30 AM UTC 2026
% Result : Theorem 0.24s 0.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT026+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.09/0.35 % Computer : n028.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 7 12:14:02 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.24/0.47 start to proof:theBenchmark.p
% 0.24/0.55 % Version : CSI_E---1.1
% 0.24/0.55 % Problem : theBenchmark.p
% 0.24/0.55 % Proof found!
% 0.24/0.55 % SZS status Theorem for theBenchmark.p
% 0.24/0.55 % SZS output start Proof
% 0.24/0.55 fof(mp_greater_or_equal, axiom, ![X5, X6]:((greater_or_equal(X5,X6)<=>(greater(X5,X6)|X5=X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', mp_greater_or_equal)).
% 0.24/0.55 fof(mp_critical_point_after_EP, axiom, ![X1]:((environment(X1)=>greater_or_equal(critical_point(X1),appear(efficient_producers,X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', mp_critical_point_after_EP)).
% 0.24/0.55 fof(prove_l8, conjecture, ![X1, X4]:((((environment(X1)&in_environment(X1,X4))&greater(X4,critical_point(X1)))=>selection_favors(efficient_producers,first_movers,X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prove_l8)).
% 0.24/0.55 fof(mp_greater_transitivity, axiom, ![X5, X6, X7]:(((greater(X5,X6)&greater(X6,X7))=>greater(X5,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', mp_greater_transitivity)).
% 0.24/0.55 fof(t6, hypothesis, ![X1, X4]:((((environment(X1)&in_environment(X1,X4))&greater_or_equal(X4,appear(efficient_producers,X1)))=>greater(cardinality_at_time(efficient_producers,X4),zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', t6)).
% 0.24/0.55 fof(d1, hypothesis, ![X1, X8]:(((environment(X1)&X8=critical_point(X1))=>(~(greater(growth_rate(efficient_producers,X8),growth_rate(first_movers,X8)))&![X4]:(((subpopulations(first_movers,efficient_producers,X1,X4)&greater(X4,X8))=>greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', d1)).
% 0.24/0.55 fof(mp2_favour_members, axiom, ![X1, X2, X3, X4]:((((((environment(X1)&subpopulation(X2,X1,X4))&subpopulation(X3,X1,X4))&greater(cardinality_at_time(X2,X4),zero))&cardinality_at_time(X3,X4)=zero)=>selection_favors(X2,X3,X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', mp2_favour_members)).
% 0.24/0.55 fof(mp_first_movers_exist, axiom, ![X1, X4]:(((environment(X1)&in_environment(X1,X4))=>greater_or_equal(cardinality_at_time(first_movers,X4),zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', mp_first_movers_exist)).
% 0.24/0.55 fof(mp_subpopulations, axiom, ![X1, X4]:(((environment(X1)&in_environment(X1,X4))=>(subpopulation(first_movers,X1,X4)&subpopulation(efficient_producers,X1,X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', mp_subpopulations)).
% 0.24/0.55 fof(mp_non_empty_fm_and_ep, axiom, ![X1, X4]:(((((environment(X1)&in_environment(X1,X4))&greater(cardinality_at_time(first_movers,X4),zero))&greater(cardinality_at_time(efficient_producers,X4),zero))=>subpopulations(first_movers,efficient_producers,X1,X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', mp_non_empty_fm_and_ep)).
% 0.24/0.55 fof(mp1_high_growth_rates, axiom, ![X1, X2, X3, X4]:((((environment(X1)&subpopulations(X2,X3,X1,X4))&greater(growth_rate(X3,X4),growth_rate(X2,X4)))=>selection_favors(X3,X2,X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', mp1_high_growth_rates)).
% 0.24/0.55 fof(c_0_11, plain, ![X27, X28]:(((~greater_or_equal(X27,X28)|(greater(X27,X28)|X27=X28))&((~greater(X27,X28)|greater_or_equal(X27,X28))&(X27!=X28|greater_or_equal(X27,X28))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_or_equal])])])])).
% 0.24/0.55 fof(c_0_12, plain, ![X23]:((~environment(X23)|greater_or_equal(critical_point(X23),appear(efficient_producers,X23)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_point_after_EP])])])).
% 0.24/0.55 fof(c_0_13, negated_conjecture, ~(![X1, X4]:((((environment(X1)&in_environment(X1,X4))&greater(X4,critical_point(X1)))=>selection_favors(efficient_producers,first_movers,X4)))), inference(assume_negation,[status(cth)],[prove_l8])).
% 0.24/0.55 cnf(c_0_14, plain, (greater(X1,X2)|X1=X2|~greater_or_equal(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.24/0.55 cnf(c_0_15, plain, (greater_or_equal(critical_point(X1),appear(efficient_producers,X1))|~environment(X1)), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.24/0.55 fof(c_0_16, negated_conjecture, (((environment(esk1_0)&in_environment(esk1_0,esk2_0))&greater(esk2_0,critical_point(esk1_0)))&~selection_favors(efficient_producers,first_movers,esk2_0)), inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])).
% 0.24/0.55 fof(c_0_17, plain, ![X24, X25, X26]:((~greater(X24,X25)|~greater(X25,X26)|greater(X24,X26))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_transitivity])])])).
% 0.24/0.55 cnf(c_0_18, plain, (appear(efficient_producers,X1)=critical_point(X1)|greater(critical_point(X1),appear(efficient_producers,X1))|~environment(X1)), inference(spm,[status(thm)],[c_0_14, c_0_15])).
% 0.24/0.55 cnf(c_0_19, negated_conjecture, (environment(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])).
% 0.24/0.55 fof(c_0_20, hypothesis, ![X32, X33]:((~environment(X32)|~in_environment(X32,X33)|~greater_or_equal(X33,appear(efficient_producers,X32))|greater(cardinality_at_time(efficient_producers,X33),zero))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6])])])).
% 0.24/0.55 cnf(c_0_21, plain, (greater(X1,X3)|~greater(X1,X2)|~greater(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_17])).
% 0.24/0.55 cnf(c_0_22, negated_conjecture, (appear(efficient_producers,esk1_0)=critical_point(esk1_0)|greater(critical_point(esk1_0),appear(efficient_producers,esk1_0))), inference(spm,[status(thm)],[c_0_18, c_0_19])).
% 0.24/0.55 cnf(c_0_23, hypothesis, (greater(cardinality_at_time(efficient_producers,X2),zero)|~environment(X1)|~in_environment(X1,X2)|~greater_or_equal(X2,appear(efficient_producers,X1))), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.24/0.55 cnf(c_0_24, plain, (greater_or_equal(X1,X2)|~greater(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.24/0.55 cnf(c_0_25, negated_conjecture, (appear(efficient_producers,esk1_0)=critical_point(esk1_0)|greater(X1,appear(efficient_producers,esk1_0))|~greater(X1,critical_point(esk1_0))), inference(spm,[status(thm)],[c_0_21, c_0_22])).
% 0.24/0.55 cnf(c_0_26, negated_conjecture, (greater(esk2_0,critical_point(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_16])).
% 0.24/0.55 cnf(c_0_27, hypothesis, (greater(cardinality_at_time(efficient_producers,X1),zero)|~in_environment(X2,X1)|~greater(X1,appear(efficient_producers,X2))|~environment(X2)), inference(spm,[status(thm)],[c_0_23, c_0_24])).
% 0.24/0.55 cnf(c_0_28, negated_conjecture, (appear(efficient_producers,esk1_0)=critical_point(esk1_0)|greater(esk2_0,appear(efficient_producers,esk1_0))), inference(spm,[status(thm)],[c_0_25, c_0_26])).
% 0.24/0.55 cnf(c_0_29, negated_conjecture, (in_environment(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_16])).
% 0.24/0.55 cnf(c_0_30, negated_conjecture, (appear(efficient_producers,esk1_0)=critical_point(esk1_0)|greater(cardinality_at_time(efficient_producers,esk2_0),zero)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28]), c_0_29]), c_0_19])])).
% 0.24/0.55 fof(c_0_31, hypothesis, ![X1, X8]:(((environment(X1)&X8=critical_point(X1))=>(~greater(growth_rate(efficient_producers,X8),growth_rate(first_movers,X8))&![X4]:(((subpopulations(first_movers,efficient_producers,X1,X4)&greater(X4,X8))=>greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4))))))), inference(fof_simplification,[status(thm)],[d1])).
% 0.24/0.55 fof(c_0_32, plain, ![X13, X14, X15, X16]:((~environment(X13)|~subpopulation(X14,X13,X16)|~subpopulation(X15,X13,X16)|~greater(cardinality_at_time(X14,X16),zero)|cardinality_at_time(X15,X16)!=zero|selection_favors(X14,X15,X16))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp2_favour_members])])])).
% 0.24/0.55 cnf(c_0_33, hypothesis, (greater(cardinality_at_time(efficient_producers,esk2_0),zero)|greater(cardinality_at_time(efficient_producers,X1),zero)|~in_environment(esk1_0,X1)|~greater(X1,critical_point(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_30]), c_0_19])])).
% 0.24/0.55 fof(c_0_34, hypothesis, ![X29, X30, X31]:(((~greater(growth_rate(efficient_producers,X30),growth_rate(first_movers,X30))|(~environment(X29)|X30!=critical_point(X29)))&(~subpopulations(first_movers,efficient_producers,X29,X31)|~greater(X31,X30)|greater(growth_rate(efficient_producers,X31),growth_rate(first_movers,X31))|(~environment(X29)|X30!=critical_point(X29))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])])])).
% 0.24/0.55 fof(c_0_35, plain, ![X19, X20]:((~environment(X19)|~in_environment(X19,X20)|greater_or_equal(cardinality_at_time(first_movers,X20),zero))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_first_movers_exist])])])).
% 0.24/0.55 cnf(c_0_36, plain, (selection_favors(X2,X4,X3)|~environment(X1)|~subpopulation(X2,X1,X3)|~subpopulation(X4,X1,X3)|~greater(cardinality_at_time(X2,X3),zero)|cardinality_at_time(X4,X3)!=zero), inference(split_conjunct,[status(thm)],[c_0_32])).
% 0.24/0.55 cnf(c_0_37, negated_conjecture, (greater(cardinality_at_time(efficient_producers,esk2_0),zero)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_26]), c_0_29])])).
% 0.24/0.55 fof(c_0_38, plain, ![X21, X22]:(((subpopulation(first_movers,X21,X22)|(~environment(X21)|~in_environment(X21,X22)))&(subpopulation(efficient_producers,X21,X22)|(~environment(X21)|~in_environment(X21,X22))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_subpopulations])])])])).
% 0.24/0.55 cnf(c_0_39, hypothesis, (greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))|~subpopulations(first_movers,efficient_producers,X1,X2)|~greater(X2,X3)|~environment(X1)|X3!=critical_point(X1)), inference(split_conjunct,[status(thm)],[c_0_34])).
% 0.24/0.55 fof(c_0_40, plain, ![X17, X18]:((~environment(X17)|~in_environment(X17,X18)|~greater(cardinality_at_time(first_movers,X18),zero)|~greater(cardinality_at_time(efficient_producers,X18),zero)|subpopulations(first_movers,efficient_producers,X17,X18))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_non_empty_fm_and_ep])])])).
% 0.24/0.55 cnf(c_0_41, plain, (greater_or_equal(cardinality_at_time(first_movers,X2),zero)|~environment(X1)|~in_environment(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_35])).
% 0.24/0.55 cnf(c_0_42, negated_conjecture, (selection_favors(efficient_producers,X1,esk2_0)|cardinality_at_time(X1,esk2_0)!=zero|~subpopulation(efficient_producers,X2,esk2_0)|~subpopulation(X1,X2,esk2_0)|~environment(X2)), inference(spm,[status(thm)],[c_0_36, c_0_37])).
% 0.24/0.55 cnf(c_0_43, plain, (subpopulation(efficient_producers,X1,X2)|~environment(X1)|~in_environment(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.24/0.55 cnf(c_0_44, hypothesis, (greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))|~greater(X1,critical_point(X2))|~subpopulations(first_movers,efficient_producers,X2,X1)|~environment(X2)), inference(er,[status(thm)],[c_0_39])).
% 0.24/0.55 cnf(c_0_45, plain, (subpopulations(first_movers,efficient_producers,X1,X2)|~environment(X1)|~in_environment(X1,X2)|~greater(cardinality_at_time(first_movers,X2),zero)|~greater(cardinality_at_time(efficient_producers,X2),zero)), inference(split_conjunct,[status(thm)],[c_0_40])).
% 0.24/0.55 cnf(c_0_46, negated_conjecture, (greater_or_equal(cardinality_at_time(first_movers,esk2_0),zero)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_29]), c_0_19])])).
% 0.24/0.55 cnf(c_0_47, negated_conjecture, (selection_favors(efficient_producers,X1,esk2_0)|cardinality_at_time(X1,esk2_0)!=zero|~in_environment(X2,esk2_0)|~subpopulation(X1,X2,esk2_0)|~environment(X2)), inference(spm,[status(thm)],[c_0_42, c_0_43])).
% 0.24/0.55 cnf(c_0_48, plain, (subpopulation(first_movers,X1,X2)|~environment(X1)|~in_environment(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.24/0.55 cnf(c_0_49, negated_conjecture, (~selection_favors(efficient_producers,first_movers,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_16])).
% 0.24/0.55 cnf(c_0_50, hypothesis, (greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))|~in_environment(X2,X1)|~greater(cardinality_at_time(first_movers,X1),zero)|~greater(cardinality_at_time(efficient_producers,X1),zero)|~greater(X1,critical_point(X2))|~environment(X2)), inference(spm,[status(thm)],[c_0_44, c_0_45])).
% 0.24/0.55 cnf(c_0_51, negated_conjecture, (cardinality_at_time(first_movers,esk2_0)=zero|greater(cardinality_at_time(first_movers,esk2_0),zero)), inference(spm,[status(thm)],[c_0_14, c_0_46])).
% 0.24/0.55 cnf(c_0_52, negated_conjecture, (cardinality_at_time(first_movers,esk2_0)!=zero|~in_environment(X1,esk2_0)|~environment(X1)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_49])).
% 0.24/0.55 fof(c_0_53, plain, ![X9, X10, X11, X12]:((~environment(X9)|~subpopulations(X10,X11,X9,X12)|~greater(growth_rate(X11,X12),growth_rate(X10,X12))|selection_favors(X11,X10,X12))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp1_high_growth_rates])])])).
% 0.24/0.55 cnf(c_0_54, negated_conjecture, (greater(growth_rate(efficient_producers,esk2_0),growth_rate(first_movers,esk2_0))|~in_environment(X1,esk2_0)|~greater(esk2_0,critical_point(X1))|~environment(X1)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_37])]), c_0_52])).
% 0.24/0.55 cnf(c_0_55, plain, (selection_favors(X3,X2,X4)|~environment(X1)|~subpopulations(X2,X3,X1,X4)|~greater(growth_rate(X3,X4),growth_rate(X2,X4))), inference(split_conjunct,[status(thm)],[c_0_53])).
% 0.24/0.55 cnf(c_0_56, negated_conjecture, (greater(growth_rate(efficient_producers,esk2_0),growth_rate(first_movers,esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_26]), c_0_29]), c_0_19])])).
% 0.24/0.55 cnf(c_0_57, negated_conjecture, (~subpopulations(first_movers,efficient_producers,X1,esk2_0)|~environment(X1)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56]), c_0_49])).
% 0.24/0.55 cnf(c_0_58, negated_conjecture, (~in_environment(X1,esk2_0)|~greater(cardinality_at_time(first_movers,esk2_0),zero)|~environment(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_45]), c_0_37])])).
% 0.24/0.55 cnf(c_0_59, negated_conjecture, (~in_environment(X1,esk2_0)|~environment(X1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_51]), c_0_52])).
% 0.24/0.55 cnf(c_0_60, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_29]), c_0_19])]), ['proof']).
% 0.24/0.55 % SZS output end Proof
% 0.24/0.55 % User time : 0.008 s
% 0.24/0.55 % System time : 0.003 s
% 0.24/0.55 % Total time : 0.011 s
% 0.24/0.55 % User time : 0.028 s
% 0.24/0.55 % System time : 0.012 s
% 0.24/0.55 % Total time : 0.040 s
% 0.24/0.55
%------------------------------------------------------------------------------