%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n013.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 11:20:25 AM UTC 2026
% Result : Unsatisfiable 1.15s 1.32s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.09/0.35 % Computer : n013.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 : Sat Sep 5 16:48:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.24/0.47 start to proof:theBenchmark.p
% 1.15/1.32 % Version : CSI_E---1.1
% 1.15/1.32 % Problem : theBenchmark.p
% 1.15/1.32 % Proof found!
% 1.15/1.32 # SZS status Unsatisfiable
% 1.15/1.32 % SZS output start Proof
% 1.15/1.32 cnf(wajsberg_4, axiom, (implies(implies(not(X1),not(X2)),implies(X2,X1))=truth), file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax', wajsberg_4)).
% 1.15/1.32 cnf(or_definition, axiom, (or(X1,X2)=implies(not(X1),X2)), file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax', or_definition)).
% 1.15/1.32 cnf(wajsberg_2, axiom, (implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))=truth), file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax', wajsberg_2)).
% 1.15/1.32 cnf(wajsberg_1, axiom, (implies(truth,X1)=X1), file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax', wajsberg_1)).
% 1.15/1.32 cnf(false_definition, axiom, (not(truth)=falsehood), file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax', false_definition)).
% 1.15/1.32 cnf(wajsberg_3, axiom, (implies(implies(X1,X2),X2)=implies(implies(X2,X1),X1)), file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax', wajsberg_3)).
% 1.15/1.32 cnf(or_commutativity, axiom, (or(X1,X2)=or(X2,X1)), file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax', or_commutativity)).
% 1.15/1.32 cnf(and_star_definition, axiom, (and_star(X1,X2)=not(or(not(X1),not(X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax', and_star_definition)).
% 1.15/1.32 cnf(and_definition, axiom, (and(X1,X2)=not(or(not(X1),not(X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax', and_definition)).
% 1.15/1.32 cnf(or_associativity, axiom, (or(or(X1,X2),X3)=or(X1,or(X2,X3))), file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax', or_associativity)).
% 1.15/1.32 cnf(and_star_commutativity, axiom, (and_star(X1,X2)=and_star(X2,X1)), file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax', and_star_commutativity)).
% 1.15/1.32 cnf(xor_definition, axiom, (xor(X1,X2)=or(and(X1,not(X2)),and(not(X1),X2))), file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax', xor_definition)).
% 1.15/1.32 cnf(prove_alternative_wajsberg_axiom, negated_conjecture, (xor(x,xor(truth,y))!=xor(xor(x,truth),y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prove_alternative_wajsberg_axiom)).
% 1.15/1.32 cnf(xor_commutativity, axiom, (xor(X1,X2)=xor(X2,X1)), file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax', xor_commutativity)).
% 1.15/1.32 cnf(c_0_14, axiom, (implies(implies(not(X1),not(X2)),implies(X2,X1))=truth), wajsberg_4).
% 1.15/1.32 cnf(c_0_15, axiom, (or(X1,X2)=implies(not(X1),X2)), or_definition).
% 1.15/1.32 cnf(c_0_16, axiom, (implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))=truth), wajsberg_2).
% 1.15/1.32 cnf(c_0_17, axiom, (implies(truth,X1)=X1), wajsberg_1).
% 1.15/1.32 cnf(c_0_18, plain, (implies(or(X1,not(X2)),implies(X2,X1))=truth), inference(rw,[status(thm)],[c_0_14, c_0_15])).
% 1.15/1.32 cnf(c_0_19, axiom, (not(truth)=falsehood), false_definition).
% 1.15/1.32 cnf(c_0_20, plain, (implies(X1,implies(implies(X1,X2),X2))=truth), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17]), c_0_17])).
% 1.15/1.32 cnf(c_0_21, axiom, (implies(implies(X1,X2),X2)=implies(implies(X2,X1),X1)), wajsberg_3).
% 1.15/1.32 cnf(c_0_22, plain, (implies(or(X1,falsehood),X1)=truth), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_17]), c_0_19])).
% 1.15/1.32 cnf(c_0_23, axiom, (or(X1,X2)=or(X2,X1)), or_commutativity).
% 1.15/1.32 cnf(c_0_24, plain, (implies(X1,X1)=truth), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17, c_0_20]), c_0_17])).
% 1.15/1.32 cnf(c_0_25, axiom, (and_star(X1,X2)=not(or(not(X1),not(X2)))), and_star_definition).
% 1.15/1.32 cnf(c_0_26, axiom, (and(X1,X2)=not(or(not(X1),not(X2)))), and_definition).
% 1.15/1.32 cnf(c_0_27, plain, (implies(implies(X1,truth),truth)=implies(X1,X1)), inference(spm,[status(thm)],[c_0_21, c_0_17])).
% 1.15/1.32 cnf(c_0_28, plain, (implies(or(falsehood,X1),X1)=truth), inference(spm,[status(thm)],[c_0_22, c_0_23])).
% 1.15/1.32 cnf(c_0_29, plain, (or(X1,not(X1))=truth), inference(spm,[status(thm)],[c_0_15, c_0_24])).
% 1.15/1.32 cnf(c_0_30, plain, (and(X1,X2)=and_star(X1,X2)), inference(rw,[status(thm)],[c_0_25, c_0_26])).
% 1.15/1.32 cnf(c_0_31, plain, (implies(implies(X1,truth),truth)=truth), inference(rw,[status(thm)],[c_0_27, c_0_24])).
% 1.15/1.32 cnf(c_0_32, plain, (not(falsehood)=truth), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_17])).
% 1.15/1.32 cnf(c_0_33, plain, (not(or(not(X1),not(X2)))=and_star(X1,X2)), inference(rw,[status(thm)],[c_0_26, c_0_30])).
% 1.15/1.32 cnf(c_0_34, plain, (implies(X1,truth)=truth), inference(spm,[status(thm)],[c_0_20, c_0_31])).
% 1.15/1.32 cnf(c_0_35, plain, (or(falsehood,X1)=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_32]), c_0_17])).
% 1.15/1.32 cnf(c_0_36, plain, (not(or(falsehood,not(X1)))=and_star(X1,truth)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_19]), c_0_23])).
% 1.15/1.32 cnf(c_0_37, plain, (or(X1,truth)=truth), inference(spm,[status(thm)],[c_0_15, c_0_34])).
% 1.15/1.32 cnf(c_0_38, axiom, (or(or(X1,X2),X3)=or(X1,or(X2,X3))), or_associativity).
% 1.15/1.32 cnf(c_0_39, plain, (implies(or(not(X1),X2),implies(X1,X2))=truth), inference(spm,[status(thm)],[c_0_18, c_0_23])).
% 1.15/1.32 cnf(c_0_40, plain, (or(X1,falsehood)=X1), inference(spm,[status(thm)],[c_0_23, c_0_35])).
% 1.15/1.32 cnf(c_0_41, plain, (not(not(X1))=and_star(X1,truth)), inference(rw,[status(thm)],[c_0_36, c_0_35])).
% 1.15/1.32 cnf(c_0_42, plain, (implies(falsehood,X1)=or(truth,X1)), inference(spm,[status(thm)],[c_0_15, c_0_19])).
% 1.15/1.32 cnf(c_0_43, plain, (or(truth,X1)=truth), inference(spm,[status(thm)],[c_0_23, c_0_37])).
% 1.15/1.32 cnf(c_0_44, plain, (or(not(X1),or(not(X2),X3))=implies(and_star(X1,X2),X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_33]), c_0_38])).
% 1.15/1.32 cnf(c_0_45, plain, (or(X1,implies(X1,falsehood))=truth), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40]), c_0_15])).
% 1.15/1.32 cnf(c_0_46, plain, (implies(X1,and_star(X1,truth))=truth), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_29]), c_0_17]), c_0_41])).
% 1.15/1.32 cnf(c_0_47, axiom, (and_star(X1,X2)=and_star(X2,X1)), and_star_commutativity).
% 1.15/1.32 cnf(c_0_48, axiom, (xor(X1,X2)=or(and(X1,not(X2)),and(not(X1),X2))), xor_definition).
% 1.15/1.32 cnf(c_0_49, plain, (implies(falsehood,X1)=truth), inference(rw,[status(thm)],[c_0_42, c_0_43])).
% 1.15/1.32 cnf(c_0_50, plain, (implies(and_star(X1,X2),X2)=truth), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_37]), c_0_15]), c_0_40])).
% 1.15/1.32 cnf(c_0_51, plain, (implies(X1,and_star(truth,X1))=truth), inference(spm,[status(thm)],[c_0_46, c_0_47])).
% 1.15/1.32 cnf(c_0_52, plain, (or(and_star(X1,not(X2)),and_star(not(X1),X2))=xor(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48, c_0_30]), c_0_30])).
% 1.15/1.32 cnf(c_0_53, plain, (implies(implies(X1,falsehood),falsehood)=X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_49]), c_0_17])).
% 1.15/1.32 cnf(c_0_54, plain, (implies(and_star(X1,X2),X1)=truth), inference(spm,[status(thm)],[c_0_50, c_0_47])).
% 1.15/1.32 cnf(c_0_55, plain, (or(falsehood,or(not(X1),X2))=implies(and_star(X1,truth),X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_36]), c_0_38])).
% 1.15/1.32 cnf(c_0_56, plain, (and_star(truth,X1)=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_51]), c_0_17]), c_0_50]), c_0_17])).
% 1.15/1.32 cnf(c_0_57, plain, (or(and_star(X1,not(X2)),or(and_star(not(X1),X2),X3))=or(xor(X1,X2),X3)), inference(spm,[status(thm)],[c_0_38, c_0_52])).
% 1.15/1.32 cnf(c_0_58, plain, (and_star(falsehood,X1)=falsehood), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_17])).
% 1.15/1.32 cnf(c_0_59, plain, (or(not(X1),X2)=implies(and_star(X1,truth),X2)), inference(rw,[status(thm)],[c_0_55, c_0_35])).
% 1.15/1.32 cnf(c_0_60, plain, (and_star(X1,truth)=X1), inference(spm,[status(thm)],[c_0_47, c_0_56])).
% 1.15/1.32 cnf(c_0_61, plain, (or(X1,or(X2,X3))=or(X2,or(X3,X1))), inference(spm,[status(thm)],[c_0_38, c_0_23])).
% 1.15/1.32 cnf(c_0_62, plain, (or(xor(truth,X1),X2)=implies(X1,X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_19]), c_0_56]), c_0_58]), c_0_35]), c_0_59]), c_0_60])).
% 1.15/1.32 cnf(c_0_63, plain, (implies(X1,falsehood)=not(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_15]), c_0_40])).
% 1.15/1.32 cnf(c_0_64, plain, (or(X1,or(falsehood,not(X2)))=implies(and_star(X2,truth),X1)), inference(spm,[status(thm)],[c_0_55, c_0_61])).
% 1.15/1.32 cnf(c_0_65, plain, (not(not(X1))=X1), inference(rw,[status(thm)],[c_0_41, c_0_60])).
% 1.15/1.32 cnf(c_0_66, plain, (not(X1)=xor(truth,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_62]), c_0_63])).
% 1.15/1.32 cnf(c_0_67, plain, (or(X1,not(X2))=implies(and_star(X2,truth),X1)), inference(rw,[status(thm)],[c_0_64, c_0_35])).
% 1.15/1.32 cnf(c_0_68, plain, (xor(truth,xor(truth,X1))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_66]), c_0_66])).
% 1.15/1.32 cnf(c_0_69, plain, (xor(truth,implies(X1,xor(truth,X2)))=and_star(X2,X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_67]), c_0_60]), c_0_66]), c_0_66])).
% 1.15/1.32 cnf(c_0_70, plain, (implies(xor(truth,X1),X2)=or(X1,X2)), inference(rw,[status(thm)],[c_0_15, c_0_66])).
% 1.15/1.32 cnf(c_0_71, plain, (implies(X1,xor(truth,X2))=xor(truth,and_star(X2,X1))), inference(spm,[status(thm)],[c_0_68, c_0_69])).
% 1.15/1.32 cnf(c_0_72, plain, (or(X1,xor(truth,X2))=implies(X2,X1)), inference(spm,[status(thm)],[c_0_23, c_0_62])).
% 1.15/1.32 cnf(c_0_73, plain, (xor(truth,and_star(X1,xor(truth,X2)))=implies(X1,X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_72])).
% 1.15/1.32 cnf(c_0_74, plain, (xor(truth,implies(X1,X2))=and_star(X1,xor(truth,X2))), inference(spm,[status(thm)],[c_0_68, c_0_73])).
% 1.15/1.32 cnf(c_0_75, plain, (or(and_star(X1,xor(truth,X2)),or(and_star(xor(truth,X1),X2),X3))=or(xor(X1,X2),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_66]), c_0_66])).
% 1.15/1.32 cnf(c_0_76, plain, (and_star(xor(truth,X1),xor(truth,X2))=xor(truth,or(X1,X2))), inference(spm,[status(thm)],[c_0_74, c_0_70])).
% 1.15/1.32 cnf(c_0_77, plain, (implies(or(X1,X2),or(and_star(X1,X2),X3))=or(xor(xor(truth,X1),X2),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_68]), c_0_76]), c_0_62])).
% 1.15/1.32 cnf(c_0_78, plain, (implies(or(X1,X2),and_star(X1,X2))=xor(xor(truth,X1),X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_40]), c_0_40])).
% 1.15/1.32 cnf(c_0_79, plain, (implies(or(X1,X2),and_star(X2,X1))=xor(X1,xor(truth,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_76]), c_0_62]), c_0_71]), c_0_70]), c_0_72]), c_0_68])).
% 1.15/1.32 cnf(c_0_80, negated_conjecture, (xor(x,xor(truth,y))!=xor(xor(x,truth),y)), prove_alternative_wajsberg_axiom).
% 1.15/1.32 cnf(c_0_81, axiom, (xor(X1,X2)=xor(X2,X1)), xor_commutativity).
% 1.15/1.32 cnf(c_0_82, plain, (xor(xor(truth,X1),X2)=xor(X1,xor(truth,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_47]), c_0_78])).
% 1.15/1.32 cnf(c_0_83, negated_conjecture, (xor(y,xor(truth,x))!=xor(x,xor(truth,y))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81]), c_0_81])).
% 1.15/1.32 cnf(c_0_84, plain, (xor(X1,xor(truth,X2))=xor(X2,xor(truth,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_76]), c_0_62]), c_0_71]), c_0_70]), c_0_72]), c_0_78]), c_0_68]), c_0_82]), c_0_82])).
% 1.15/1.32 cnf(c_0_85, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83, c_0_84])]), ['proof']).
% 1.15/1.32 % SZS output end Proof
% 1.15/1.32 % User time : 0.777 s
% 1.15/1.32 % System time : 0.057 s
% 1.15/1.32 % Total time : 0.835 s
% 1.15/1.32
%------------------------------------------------------------------------------