%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n027.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 11:20:13 AM UTC 2026
% Result : Unsatisfiable 2.22s 0.81s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.07/0.34 % Computer : n027.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 5 00:16:12 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.24/0.46 start to proof:theBenchmark.p
% 2.22/0.81 % Version : CSI_E---1.1
% 2.22/0.81 % Problem : theBenchmark.p
% 2.22/0.81 % Proof found!
% 2.22/0.81 # SZS status Unsatisfiable
% 2.22/0.81 % SZS output start Proof
% 2.22/0.81 cnf(condensed_detachment, axiom, (is_a_theorem(X2)|~is_a_theorem(implies(X1,X2))|~is_a_theorem(X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', condensed_detachment)).
% 2.22/0.81 cnf(necessitation1, axiom, (is_a_theorem(implies(necessary(implies(X1,X2)),implies(necessary(X1),necessary(X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', necessitation1)).
% 2.22/0.81 cnf(axiom_of_necessitation, axiom, (is_a_theorem(necessary(X1))|~is_a_theorem(X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom_of_necessitation)).
% 2.22/0.81 cnf(cn_18, axiom, (is_a_theorem(implies(X1,implies(X2,X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cn_18)).
% 2.22/0.81 cnf(cn_35, axiom, (is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cn_35)).
% 2.22/0.81 cnf(necessitation2, axiom, (is_a_theorem(implies(necessary(X1),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', necessitation2)).
% 2.22/0.81 cnf(cn_49, axiom, (is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cn_49)).
% 2.22/0.81 cnf(prove_this, negated_conjecture, (~is_a_theorem(implies(necessary(a),not(necessary(not(a)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prove_this)).
% 2.22/0.81 cnf(c_0_8, plain, (is_a_theorem(X2)|~is_a_theorem(implies(X1,X2))|~is_a_theorem(X1)), inference(fof_simplification,[status(thm)],[condensed_detachment])).
% 2.22/0.81 cnf(c_0_9, plain, (is_a_theorem(X2)|~is_a_theorem(implies(X1,X2))|~is_a_theorem(X1)), c_0_8).
% 2.22/0.81 cnf(c_0_10, axiom, (is_a_theorem(implies(necessary(implies(X1,X2)),implies(necessary(X1),necessary(X2))))), necessitation1).
% 2.22/0.81 cnf(c_0_11, plain, (is_a_theorem(necessary(X1))|~is_a_theorem(X1)), inference(fof_simplification,[status(thm)],[axiom_of_necessitation])).
% 2.22/0.81 cnf(c_0_12, plain, (is_a_theorem(implies(necessary(X1),necessary(X2)))|~is_a_theorem(necessary(implies(X1,X2)))), inference(spm,[status(thm)],[c_0_9, c_0_10])).
% 2.22/0.81 cnf(c_0_13, plain, (is_a_theorem(necessary(X1))|~is_a_theorem(X1)), c_0_11).
% 2.22/0.81 cnf(c_0_14, axiom, (is_a_theorem(implies(X1,implies(X2,X1)))), cn_18).
% 2.22/0.81 cnf(c_0_15, plain, (is_a_theorem(implies(necessary(X1),necessary(X2)))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_12, c_0_13])).
% 2.22/0.81 cnf(c_0_16, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_9, c_0_14])).
% 2.22/0.81 cnf(c_0_17, axiom, (is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3))))), cn_35).
% 2.22/0.81 cnf(c_0_18, plain, (is_a_theorem(implies(necessary(X1),necessary(X2)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_15, c_0_16])).
% 2.22/0.81 cnf(c_0_19, plain, (is_a_theorem(implies(implies(X1,X2),implies(X1,X3)))|~is_a_theorem(implies(X1,implies(X2,X3)))), inference(spm,[status(thm)],[c_0_9, c_0_17])).
% 2.22/0.81 cnf(c_0_20, plain, (is_a_theorem(implies(necessary(necessary(X1)),necessary(necessary(X2))))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_15, c_0_18])).
% 2.22/0.81 cnf(c_0_21, plain, (is_a_theorem(implies(necessary(X1),necessary(implies(X2,X1))))), inference(spm,[status(thm)],[c_0_15, c_0_14])).
% 2.22/0.81 cnf(c_0_22, plain, (is_a_theorem(implies(implies(X1,X2),implies(X1,X1)))), inference(spm,[status(thm)],[c_0_19, c_0_14])).
% 2.22/0.81 cnf(c_0_23, plain, (is_a_theorem(necessary(necessary(X1)))|~is_a_theorem(necessary(necessary(X2)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_9, c_0_20])).
% 2.22/0.81 cnf(c_0_24, plain, (is_a_theorem(necessary(implies(X1,X2)))|~is_a_theorem(necessary(X2))), inference(spm,[status(thm)],[c_0_9, c_0_21])).
% 2.22/0.81 cnf(c_0_25, plain, (is_a_theorem(implies(necessary(implies(X1,X2)),necessary(implies(X1,X1))))), inference(spm,[status(thm)],[c_0_15, c_0_22])).
% 2.22/0.81 cnf(c_0_26, plain, (is_a_theorem(necessary(necessary(X1)))|~is_a_theorem(necessary(X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_23, c_0_13])).
% 2.22/0.81 cnf(c_0_27, plain, (is_a_theorem(necessary(implies(X1,X2)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_24, c_0_13])).
% 2.22/0.81 cnf(c_0_28, plain, (is_a_theorem(necessary(implies(X1,X1)))|~is_a_theorem(necessary(implies(X1,X2)))), inference(spm,[status(thm)],[c_0_9, c_0_25])).
% 2.22/0.81 cnf(c_0_29, plain, (is_a_theorem(implies(X1,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_9, c_0_22])).
% 2.22/0.81 cnf(c_0_30, plain, (is_a_theorem(necessary(necessary(X1)))|~is_a_theorem(X1)|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_26, c_0_27])).
% 2.22/0.81 cnf(c_0_31, plain, (is_a_theorem(necessary(implies(X1,X1)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_28, c_0_27])).
% 2.22/0.81 cnf(c_0_32, plain, (is_a_theorem(implies(necessary(necessary(implies(X1,X2))),necessary(implies(necessary(X1),necessary(X2)))))), inference(spm,[status(thm)],[c_0_15, c_0_10])).
% 2.22/0.81 cnf(c_0_33, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_29, c_0_14])).
% 2.22/0.81 cnf(c_0_34, axiom, (is_a_theorem(implies(necessary(X1),X1))), necessitation2).
% 2.22/0.81 cnf(c_0_35, plain, (is_a_theorem(necessary(necessary(X1)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_30, c_0_21])).
% 2.22/0.81 cnf(c_0_36, plain, (is_a_theorem(necessary(implies(X1,X1)))), inference(spm,[status(thm)],[c_0_31, c_0_32])).
% 2.22/0.81 cnf(c_0_37, plain, (is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(X1,X2),X2)))), inference(spm,[status(thm)],[c_0_19, c_0_33])).
% 2.22/0.81 cnf(c_0_38, plain, (is_a_theorem(X1)|~is_a_theorem(necessary(X1))), inference(spm,[status(thm)],[c_0_9, c_0_34])).
% 2.22/0.81 cnf(c_0_39, plain, (is_a_theorem(necessary(implies(X1,necessary(X2))))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_24, c_0_35])).
% 2.22/0.81 cnf(c_0_40, plain, (is_a_theorem(necessary(implies(X1,implies(X2,X2))))), inference(spm,[status(thm)],[c_0_24, c_0_36])).
% 2.22/0.81 cnf(c_0_41, plain, (is_a_theorem(implies(implies(X1,X2),X2))|~is_a_theorem(implies(implies(X1,X2),X1))), inference(spm,[status(thm)],[c_0_9, c_0_37])).
% 2.22/0.81 cnf(c_0_42, plain, (is_a_theorem(implies(X1,necessary(X2)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_38, c_0_39])).
% 2.22/0.81 cnf(c_0_43, plain, (is_a_theorem(implies(X1,implies(X2,X2)))), inference(spm,[status(thm)],[c_0_38, c_0_40])).
% 2.22/0.81 cnf(c_0_44, plain, (is_a_theorem(implies(implies(X1,X2),implies(X1,X3)))|~is_a_theorem(implies(X2,X3))), inference(spm,[status(thm)],[c_0_19, c_0_16])).
% 2.22/0.81 cnf(c_0_45, plain, (is_a_theorem(implies(implies(necessary(X1),X2),X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_41, c_0_42])).
% 2.22/0.81 cnf(c_0_46, plain, (is_a_theorem(implies(implies(implies(X1,X1),X2),X2))), inference(spm,[status(thm)],[c_0_41, c_0_43])).
% 2.22/0.81 cnf(c_0_47, plain, (is_a_theorem(implies(implies(X1,necessary(X2)),implies(X1,X2)))), inference(spm,[status(thm)],[c_0_44, c_0_34])).
% 2.22/0.81 cnf(c_0_48, plain, (is_a_theorem(X1)|~is_a_theorem(implies(necessary(X2),X1))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_9, c_0_45])).
% 2.22/0.81 cnf(c_0_49, plain, (is_a_theorem(implies(necessary(implies(implies(X1,X1),X2)),necessary(X2)))), inference(spm,[status(thm)],[c_0_15, c_0_46])).
% 2.22/0.81 cnf(c_0_50, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,necessary(X2)))), inference(spm,[status(thm)],[c_0_9, c_0_47])).
% 2.22/0.81 cnf(c_0_51, plain, (is_a_theorem(necessary(X1))|~is_a_theorem(implies(implies(X2,X2),X1))), inference(spm,[status(thm)],[c_0_48, c_0_49])).
% 2.22/0.81 cnf(c_0_52, plain, (is_a_theorem(implies(implies(X1,X2),implies(X1,implies(X3,X2))))), inference(spm,[status(thm)],[c_0_44, c_0_14])).
% 2.22/0.81 cnf(c_0_53, plain, (is_a_theorem(necessary(implies(X1,implies(X2,implies(X3,X3)))))), inference(spm,[status(thm)],[c_0_24, c_0_40])).
% 2.22/0.81 cnf(c_0_54, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(necessary(X2))), inference(spm,[status(thm)],[c_0_50, c_0_16])).
% 2.22/0.81 cnf(c_0_55, plain, (is_a_theorem(necessary(implies(X1,implies(X2,X1))))), inference(spm,[status(thm)],[c_0_51, c_0_52])).
% 2.22/0.81 cnf(c_0_56, plain, (is_a_theorem(implies(X1,implies(X2,implies(X3,X3))))), inference(spm,[status(thm)],[c_0_38, c_0_53])).
% 2.22/0.81 cnf(c_0_57, plain, (is_a_theorem(implies(X1,implies(X2,implies(X3,X2))))), inference(spm,[status(thm)],[c_0_54, c_0_55])).
% 2.22/0.81 cnf(c_0_58, plain, (is_a_theorem(implies(implies(X1,X2),X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_41, c_0_16])).
% 2.22/0.81 cnf(c_0_59, plain, (is_a_theorem(implies(implies(implies(X1,implies(X2,X2)),X3),X3))), inference(spm,[status(thm)],[c_0_41, c_0_56])).
% 2.22/0.81 cnf(c_0_60, plain, (is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3))), inference(spm,[status(thm)],[c_0_41, c_0_57])).
% 2.22/0.81 cnf(c_0_61, axiom, (is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))), cn_49).
% 2.22/0.81 cnf(c_0_62, plain, (is_a_theorem(implies(necessary(implies(X1,X2)),necessary(X2)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_15, c_0_58])).
% 2.22/0.81 cnf(c_0_63, plain, (is_a_theorem(X1)|~is_a_theorem(implies(implies(X2,implies(X3,X3)),X1))), inference(spm,[status(thm)],[c_0_9, c_0_59])).
% 2.22/0.81 cnf(c_0_64, plain, (is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(X1,X2)),implies(implies(X1,implies(X2,X3)),implies(X1,X3))))), inference(spm,[status(thm)],[c_0_19, c_0_17])).
% 2.22/0.81 cnf(c_0_65, plain, (is_a_theorem(X1)|~is_a_theorem(implies(implies(X2,implies(X3,X2)),X1))), inference(spm,[status(thm)],[c_0_9, c_0_60])).
% 2.22/0.81 cnf(c_0_66, plain, (is_a_theorem(implies(implies(X1,implies(not(X2),not(X3))),implies(X1,implies(X3,X2))))), inference(spm,[status(thm)],[c_0_44, c_0_61])).
% 2.22/0.81 cnf(c_0_67, plain, (is_a_theorem(necessary(X1))|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_48, c_0_62])).
% 2.22/0.81 cnf(c_0_68, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), inference(spm,[status(thm)],[c_0_63, c_0_64])).
% 2.22/0.81 cnf(c_0_69, plain, (is_a_theorem(implies(X1,implies(X2,X3)))|~is_a_theorem(implies(X1,X3))), inference(spm,[status(thm)],[c_0_9, c_0_52])).
% 2.22/0.81 cnf(c_0_70, plain, (is_a_theorem(implies(not(X1),implies(X1,X2)))), inference(spm,[status(thm)],[c_0_65, c_0_66])).
% 2.22/0.81 cnf(c_0_71, plain, (is_a_theorem(necessary(implies(X1,X2)))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_67, c_0_68])).
% 2.22/0.81 cnf(c_0_72, plain, (is_a_theorem(implies(not(X1),implies(X2,implies(X1,X3))))), inference(spm,[status(thm)],[c_0_69, c_0_70])).
% 2.22/0.81 cnf(c_0_73, plain, (is_a_theorem(necessary(implies(not(X1),implies(X1,X2))))), inference(spm,[status(thm)],[c_0_71, c_0_72])).
% 2.22/0.81 cnf(c_0_74, plain, (is_a_theorem(implies(X1,implies(not(X2),implies(X2,X3))))), inference(spm,[status(thm)],[c_0_54, c_0_73])).
% 2.22/0.81 cnf(c_0_75, plain, (is_a_theorem(implies(implies(implies(not(X1),implies(X1,X2)),X3),X3))), inference(spm,[status(thm)],[c_0_41, c_0_74])).
% 2.22/0.81 cnf(c_0_76, plain, (is_a_theorem(X1)|~is_a_theorem(implies(implies(not(X2),implies(X2,X3)),X1))), inference(spm,[status(thm)],[c_0_9, c_0_75])).
% 2.22/0.81 cnf(c_0_77, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_9, c_0_68])).
% 2.22/0.81 cnf(c_0_78, plain, (is_a_theorem(implies(not(not(X1)),implies(X2,X1)))), inference(spm,[status(thm)],[c_0_76, c_0_66])).
% 2.22/0.81 cnf(c_0_79, plain, (is_a_theorem(implies(not(not(X1)),X1))), inference(spm,[status(thm)],[c_0_77, c_0_78])).
% 2.22/0.81 cnf(c_0_80, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(not(X2),not(X1)))), inference(spm,[status(thm)],[c_0_9, c_0_61])).
% 2.22/0.81 cnf(c_0_81, plain, (is_a_theorem(implies(not(not(necessary(X1))),X1))), inference(spm,[status(thm)],[c_0_50, c_0_79])).
% 2.22/0.81 cnf(c_0_82, plain, (is_a_theorem(implies(X1,not(necessary(not(X1)))))), inference(spm,[status(thm)],[c_0_80, c_0_81])).
% 2.22/0.81 cnf(c_0_83, negated_conjecture, (~is_a_theorem(implies(necessary(a),not(necessary(not(a)))))), inference(fof_simplification,[status(thm)],[prove_this])).
% 2.22/0.81 cnf(c_0_84, plain, (is_a_theorem(implies(necessary(X1),necessary(not(necessary(not(X1))))))), inference(spm,[status(thm)],[c_0_15, c_0_82])).
% 2.22/0.81 cnf(c_0_85, negated_conjecture, (~is_a_theorem(implies(necessary(a),not(necessary(not(a)))))), c_0_83).
% 2.22/0.81 cnf(c_0_86, plain, (is_a_theorem(implies(necessary(X1),not(necessary(not(X1)))))), inference(spm,[status(thm)],[c_0_50, c_0_84])).
% 2.22/0.81 cnf(c_0_87, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85, c_0_86])]), ['proof']).
% 2.22/0.81 % SZS output end Proof
% 2.22/0.81 % User time : 0.297 s
% 2.22/0.81 % System time : 0.016 s
% 2.22/0.81 % Total time : 0.313 s
% 2.22/0.81 % User time : 1.202 s
% 2.22/0.81 % System time : 0.040 s
% 2.22/0.81 % Total time : 1.242 s
% 2.22/0.81
%------------------------------------------------------------------------------