%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL309-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n006.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 11:20:44 AM UTC 2026
% Result : Unsatisfiable 21.15s 3.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL309-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : java -jar mcs_scs.jar %d %s
% 0.07/0.33 % Computer : n006.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 5 14:51:16 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.11/0.45 start to proof:theBenchmark.p
% 21.15/3.56 % Version : CSI_E---1.1
% 21.15/3.56 % Problem : theBenchmark.p
% 21.15/3.56 % Proof found!
% 21.15/3.56 # SZS status Unsatisfiable
% 21.15/3.56 % SZS output start Proof
% 21.15/3.56 cnf(rule_2, axiom, (theorem(X1)|~theorem(implies(X2,X1))|~theorem(X2)), file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax', rule_2)).
% 21.15/3.56 cnf(implies_definition, axiom, (implies(X1,X2)=or(not(X1),X2)), file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax', implies_definition)).
% 21.15/3.56 cnf(rule_1, axiom, (theorem(X1)|~axiom(X1)), file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax', rule_1)).
% 21.15/3.56 cnf(axiom_1_5, axiom, (axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax', axiom_1_5)).
% 21.15/3.56 cnf(axiom_1_3, axiom, (axiom(implies(X1,or(X2,X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax', axiom_1_3)).
% 21.15/3.56 cnf(axiom_1_2, axiom, (axiom(implies(or(X1,X1),X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax', axiom_1_2)).
% 21.15/3.56 cnf(axiom_1_6, axiom, (axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax', axiom_1_6)).
% 21.15/3.56 cnf(axiom_1_4, axiom, (axiom(implies(or(X1,X2),or(X2,X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL004-0.ax', axiom_1_4)).
% 21.15/3.56 cnf(prove_this, negated_conjecture, (~theorem(equivalent(or(implies(p,q),implies(p,r)),implies(p,or(q,r))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prove_this)).
% 21.15/3.56 cnf(equivalent_defn, axiom, (equivalent(X1,X2)=and(implies(X1,X2),implies(X2,X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL004-2.ax', equivalent_defn)).
% 21.15/3.56 cnf(and_defn, axiom, (and(X1,X2)=not(or(not(X1),not(X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL004-1.ax', and_defn)).
% 21.15/3.56 cnf(c_0_11, plain, (theorem(X1)|~theorem(implies(X2,X1))|~theorem(X2)), inference(fof_simplification,[status(thm)],[rule_2])).
% 21.15/3.56 cnf(c_0_12, plain, (theorem(X1)|~theorem(implies(X2,X1))|~theorem(X2)), c_0_11).
% 21.15/3.56 cnf(c_0_13, axiom, (implies(X1,X2)=or(not(X1),X2)), implies_definition).
% 21.15/3.56 cnf(c_0_14, plain, (theorem(X1)|~axiom(X1)), inference(fof_simplification,[status(thm)],[rule_1])).
% 21.15/3.56 cnf(c_0_15, plain, (theorem(X1)|~theorem(X2)|~theorem(or(not(X2),X1))), inference(rw,[status(thm)],[c_0_12, c_0_13])).
% 21.15/3.56 cnf(c_0_16, plain, (theorem(X1)|~axiom(X1)), c_0_14).
% 21.15/3.56 cnf(c_0_17, axiom, (axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))), axiom_1_5).
% 21.15/3.56 cnf(c_0_18, axiom, (axiom(implies(X1,or(X2,X1)))), axiom_1_3).
% 21.15/3.56 cnf(c_0_19, plain, (theorem(X1)|~theorem(X2)|~axiom(or(not(X2),X1))), inference(spm,[status(thm)],[c_0_15, c_0_16])).
% 21.15/3.56 cnf(c_0_20, plain, (axiom(or(not(or(X1,or(X2,X3))),or(X2,or(X1,X3))))), inference(rw,[status(thm)],[c_0_17, c_0_13])).
% 21.15/3.56 cnf(c_0_21, axiom, (axiom(implies(or(X1,X1),X1))), axiom_1_2).
% 21.15/3.56 cnf(c_0_22, plain, (axiom(or(not(X1),or(X2,X1)))), inference(rw,[status(thm)],[c_0_18, c_0_13])).
% 21.15/3.56 cnf(c_0_23, plain, (theorem(or(X1,or(X2,X3)))|~theorem(or(X2,or(X1,X3)))), inference(spm,[status(thm)],[c_0_19, c_0_20])).
% 21.15/3.56 cnf(c_0_24, axiom, (axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))), axiom_1_6).
% 21.15/3.56 cnf(c_0_25, plain, (axiom(or(not(or(X1,X1)),X1))), inference(rw,[status(thm)],[c_0_21, c_0_13])).
% 21.15/3.56 cnf(c_0_26, plain, (theorem(or(X1,X2))|~theorem(X2)), inference(spm,[status(thm)],[c_0_19, c_0_22])).
% 21.15/3.56 cnf(c_0_27, plain, (theorem(or(X1,or(X2,X3)))|~axiom(or(X2,or(X1,X3)))), inference(spm,[status(thm)],[c_0_23, c_0_16])).
% 21.15/3.56 cnf(c_0_28, axiom, (axiom(implies(or(X1,X2),or(X2,X1)))), axiom_1_4).
% 21.15/3.56 cnf(c_0_29, plain, (axiom(or(not(or(not(X1),X2)),or(not(or(X3,X1)),or(X3,X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_13]), c_0_13]), c_0_13])).
% 21.15/3.56 cnf(c_0_30, plain, (theorem(X1)|~theorem(or(X1,X1))), inference(spm,[status(thm)],[c_0_19, c_0_25])).
% 21.15/3.56 cnf(c_0_31, plain, (theorem(or(X1,or(X2,X3)))|~theorem(or(X1,X3))), inference(spm,[status(thm)],[c_0_23, c_0_26])).
% 21.15/3.56 cnf(c_0_32, plain, (theorem(or(X1,X2))|~theorem(X3)|~axiom(or(X1,or(not(X3),X2)))), inference(spm,[status(thm)],[c_0_15, c_0_27])).
% 21.15/3.56 cnf(c_0_33, plain, (axiom(or(not(or(X1,X2)),or(X2,X1)))), inference(rw,[status(thm)],[c_0_28, c_0_13])).
% 21.15/3.56 cnf(c_0_34, plain, (theorem(or(not(or(X1,X2)),or(X1,X3)))|~theorem(or(not(X2),X3))), inference(spm,[status(thm)],[c_0_19, c_0_29])).
% 21.15/3.56 cnf(c_0_35, plain, (theorem(or(X1,X2))|~theorem(or(or(X1,X2),X2))), inference(spm,[status(thm)],[c_0_30, c_0_31])).
% 21.15/3.56 cnf(c_0_36, negated_conjecture, (~theorem(equivalent(or(implies(p,q),implies(p,r)),implies(p,or(q,r))))), inference(fof_simplification,[status(thm)],[prove_this])).
% 21.15/3.56 cnf(c_0_37, axiom, (equivalent(X1,X2)=and(implies(X1,X2),implies(X2,X1))), equivalent_defn).
% 21.15/3.56 cnf(c_0_38, axiom, (and(X1,X2)=not(or(not(X1),not(X2)))), and_defn).
% 21.15/3.56 cnf(c_0_39, plain, (theorem(or(not(or(X1,not(X2))),X1))|~theorem(X2)), inference(spm,[status(thm)],[c_0_32, c_0_33])).
% 21.15/3.56 cnf(c_0_40, plain, (theorem(or(X1,X2))|~theorem(or(not(X3),X2))|~theorem(or(X1,X3))), inference(spm,[status(thm)],[c_0_15, c_0_34])).
% 21.15/3.56 cnf(c_0_41, plain, (theorem(or(X1,X2))|~theorem(or(X2,X1))), inference(spm,[status(thm)],[c_0_19, c_0_33])).
% 21.15/3.56 cnf(c_0_42, plain, (theorem(or(X1,or(not(or(X1,X2)),X3)))|~theorem(or(not(X2),X3))), inference(spm,[status(thm)],[c_0_23, c_0_34])).
% 21.15/3.56 cnf(c_0_43, plain, (theorem(or(X1,or(X2,X3)))|~axiom(or(X2,or(or(X1,or(X2,X3)),X3)))), inference(spm,[status(thm)],[c_0_35, c_0_27])).
% 21.15/3.56 cnf(c_0_44, negated_conjecture, (~theorem(equivalent(or(implies(p,q),implies(p,r)),implies(p,or(q,r))))), c_0_36).
% 21.15/3.56 cnf(c_0_45, plain, (equivalent(X1,X2)=not(or(not(or(not(X1),X2)),not(or(not(X2),X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_13]), c_0_13]), c_0_38])).
% 21.15/3.56 cnf(c_0_46, plain, (theorem(X1)|~theorem(or(X1,not(X2)))|~theorem(X2)), inference(spm,[status(thm)],[c_0_15, c_0_39])).
% 21.15/3.56 cnf(c_0_47, plain, (theorem(or(X1,or(X2,X3)))|~theorem(or(X1,or(X2,X4)))|~theorem(or(not(X4),X3))), inference(spm,[status(thm)],[c_0_40, c_0_34])).
% 21.15/3.56 cnf(c_0_48, plain, (theorem(or(or(not(or(X1,X2)),X3),X1))|~theorem(or(not(X2),X3))), inference(spm,[status(thm)],[c_0_41, c_0_42])).
% 21.15/3.56 cnf(c_0_49, plain, (theorem(or(X1,X2))|~theorem(or(X1,X3))|~axiom(or(not(X3),X2))), inference(spm,[status(thm)],[c_0_40, c_0_16])).
% 21.15/3.56 cnf(c_0_50, plain, (theorem(or(X1,or(not(X2),X2)))), inference(spm,[status(thm)],[c_0_43, c_0_22])).
% 21.15/3.56 cnf(c_0_51, negated_conjecture, (~theorem(not(or(not(or(not(or(or(not(p),q),or(not(p),r))),or(not(p),or(q,r)))),not(or(not(or(not(p),or(q,r))),or(or(not(p),q),or(not(p),r)))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_13]), c_0_13]), c_0_13]), c_0_45])).
% 21.15/3.56 cnf(c_0_52, plain, (theorem(not(or(not(X1),not(X2))))|~theorem(X1)|~theorem(X2)), inference(spm,[status(thm)],[c_0_46, c_0_39])).
% 21.15/3.56 cnf(c_0_53, plain, (theorem(or(or(not(or(or(X1,X2),X3)),X4),or(X1,X5)))|~theorem(or(not(X2),X5))|~theorem(or(not(X3),X4))), inference(spm,[status(thm)],[c_0_47, c_0_48])).
% 21.15/3.56 cnf(c_0_54, plain, (theorem(or(X1,or(X2,X3)))|~theorem(or(X1,or(X3,X2)))), inference(spm,[status(thm)],[c_0_49, c_0_33])).
% 21.15/3.56 cnf(c_0_55, plain, (theorem(or(not(X1),or(X2,X1)))), inference(spm,[status(thm)],[c_0_23, c_0_50])).
% 21.15/3.56 cnf(c_0_56, negated_conjecture, (~theorem(or(not(or(or(not(p),q),or(not(p),r))),or(not(p),or(q,r))))|~theorem(or(not(or(not(p),or(q,r))),or(or(not(p),q),or(not(p),r))))), inference(spm,[status(thm)],[c_0_51, c_0_52])).
% 21.15/3.56 cnf(c_0_57, plain, (theorem(or(not(or(or(X1,X2),X3)),or(X1,X4)))|~theorem(or(not(X3),or(X1,X4)))|~theorem(or(not(X2),X4))), inference(spm,[status(thm)],[c_0_35, c_0_53])).
% 21.15/3.56 cnf(c_0_58, plain, (theorem(or(not(X1),or(X1,X2)))), inference(spm,[status(thm)],[c_0_54, c_0_55])).
% 21.15/3.56 cnf(c_0_59, plain, (theorem(or(or(X1,X2),X3))|~theorem(or(X3,X2))), inference(spm,[status(thm)],[c_0_41, c_0_31])).
% 21.15/3.56 cnf(c_0_60, negated_conjecture, (~theorem(or(not(or(not(p),or(q,r))),or(or(not(p),q),or(not(p),r))))|~theorem(or(not(or(not(p),r)),or(not(p),or(q,r))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_58])])).
% 21.15/3.56 cnf(c_0_61, plain, (theorem(or(X1,or(or(X2,X3),X4)))|~theorem(or(or(X1,X4),X3))), inference(spm,[status(thm)],[c_0_23, c_0_59])).
% 21.15/3.56 cnf(c_0_62, negated_conjecture, (~theorem(or(or(not(or(not(p),or(q,r))),or(not(p),r)),q))|~theorem(or(not(or(not(p),r)),or(not(p),or(q,r))))), inference(spm,[status(thm)],[c_0_60, c_0_61])).
% 21.15/3.56 cnf(c_0_63, plain, (theorem(or(or(X1,X2),X3))|~axiom(or(X1,or(X3,X2)))), inference(spm,[status(thm)],[c_0_41, c_0_27])).
% 21.15/3.56 cnf(c_0_64, plain, (theorem(or(X1,or(X2,or(X3,X4))))|~theorem(or(X1,or(X3,or(X2,X4))))), inference(spm,[status(thm)],[c_0_49, c_0_20])).
% 21.15/3.56 cnf(c_0_65, negated_conjecture, (~theorem(or(not(or(not(p),r)),or(not(p),or(q,r))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_20])])).
% 21.15/3.56 cnf(c_0_66, plain, (theorem(or(X1,or(X2,or(X3,X4))))|~axiom(or(X1,or(X3,or(X2,X4))))), inference(spm,[status(thm)],[c_0_64, c_0_16])).
% 21.15/3.56 cnf(c_0_67, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_66]), c_0_22])]), ['proof']).
% 21.15/3.56 % SZS output end Proof
% 21.15/3.56 % User time : 2.706 s
% 21.15/3.56 % System time : 0.091 s
% 21.15/3.56 % Total time : 2.797 s
% 21.15/3.56 % User time : 14.505 s
% 21.15/3.56 % System time : 0.295 s
% 21.15/3.56 % Total time : 14.800 s
% 21.15/3.56
%------------------------------------------------------------------------------