%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 : Thu Sep 24 01:09:28 PM UTC 2026
% Result : Unsatisfiable 51.46s 6.94s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n012.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 21 00:07:51 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 51.46/6.94 % Refutation found
% 51.46/6.94 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 51.46/6.94 % SZS output start CNFRefutation for theBenchmark
% 51.46/6.94 fof(f1,axiom,(
% 51.46/6.94 (![X]: (not(X) = xor(X,truth) ))),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f2,axiom,(
% 51.46/6.94 (![X]: (xor(X,falsehood) = X ))),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f5,axiom,(
% 51.46/6.94 (![X]: (and_star(X,falsehood) = falsehood ))),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f6,axiom,(
% 51.46/6.94 (![X]: (and_star(xor(truth,X),X) = falsehood ))),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f7,axiom,(
% 51.46/6.94 (![X,Y]: (xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ))),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f8,axiom,(
% 51.46/6.94 (![X,Y]: (and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ))),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f9,axiom,(
% 51.46/6.94 (![X,Y]: (xor(X,Y) = xor(Y,X) ))),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f10,axiom,(
% 51.46/6.94 (![X,Y,Z]: (and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) ))),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f11,axiom,(
% 51.46/6.94 (![X,Y]: (and_star(X,Y) = and_star(Y,X) ))),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f12,axiom,(
% 51.46/6.94 not(truth) = falsehood ),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f13,axiom,(
% 51.46/6.94 (![X,Y]: (implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ))),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f14,negated_conjecture,(
% 51.46/6.94 implies(implies(x,y),implies(implies(y,z),implies(x,z))) != truth ),
% 51.46/6.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 51.46/6.94 fof(f15,plain,(
% 51.46/6.94 ![X0]: (not(X0)=xor(X0,truth))),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f1])).
% 51.46/6.94 fof(f16,plain,(
% 51.46/6.94 ![X0]: (xor(X0,falsehood)=X0)),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f2])).
% 51.46/6.94 fof(f19,plain,(
% 51.46/6.94 ![X0]: (and_star(X0,falsehood)=falsehood)),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f5])).
% 51.46/6.94 fof(f20,plain,(
% 51.46/6.94 ![X0]: (and_star(xor(truth,X0),X0)=falsehood)),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f6])).
% 51.46/6.94 fof(f21,plain,(
% 51.46/6.94 ![X0,X1]: (xor(X0,xor(truth,X1))=xor(xor(X0,truth),X1))),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f7])).
% 51.46/6.94 fof(f22,plain,(
% 51.46/6.94 ![X0,X1]: (and_star(xor(and_star(xor(truth,X0),X1),truth),X1)=and_star(xor(and_star(xor(truth,X1),X0),truth),X0))),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f8])).
% 51.46/6.94 fof(f23,plain,(
% 51.46/6.94 ![X0,X1]: (xor(X0,X1)=xor(X1,X0))),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f9])).
% 51.46/6.94 fof(f24,plain,(
% 51.46/6.94 ![X0,X1,X2]: (and_star(and_star(X0,X1),X2)=and_star(X0,and_star(X1,X2)))),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f10])).
% 51.46/6.94 fof(f25,plain,(
% 51.46/6.94 ![X0,X1]: (and_star(X0,X1)=and_star(X1,X0))),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f11])).
% 51.46/6.94 fof(f26,plain,(
% 51.46/6.94 not(truth)=falsehood),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f12])).
% 51.46/6.94 fof(f27,plain,(
% 51.46/6.94 ![X0,X1]: (implies(X0,X1)=xor(truth,and_star(X0,xor(truth,X1))))),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f13])).
% 51.46/6.94 fof(f28,plain,(
% 51.46/6.94 ~implies(implies(x,y),implies(implies(y,z),implies(x,z)))=truth),
% 51.46/6.94 inference(cnf_transformation,[status(thm)],[f14])).
% 51.46/6.94 fof(f35,plain,(
% 51.46/6.94 ![X0,X1]: (xor(X0,xor(truth,X1))=xor(not(X0),X1))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f15,f21])).
% 51.46/6.94 fof(f36,plain,(
% 51.46/6.94 ![X0,X1]: (and_star(not(and_star(xor(truth,X0),X1)),X1)=and_star(xor(and_star(xor(truth,X1),X0),truth),X0))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f15,f22])).
% 51.46/6.94 fof(f37,plain,(
% 51.46/6.94 ![X0,X1]: (and_star(not(and_star(xor(truth,X0),X1)),X1)=and_star(not(and_star(xor(truth,X1),X0)),X0))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f15,f36])).
% 51.46/6.94 fof(f52,plain,(
% 51.46/6.94 ![X0]: (not(X0)=xor(truth,X0))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f15,f23])).
% 51.46/6.94 fof(f53,plain,(
% 51.46/6.94 ![X0]: (X0=xor(falsehood,X0))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f16,f23])).
% 51.46/6.94 fof(f60,plain,(
% 51.46/6.94 ![X0]: (and_star(xor(X0,truth),X0)=falsehood)),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f23,f20])).
% 51.46/6.94 fof(f67,plain,(
% 51.46/6.94 ![X0,X1]: (implies(X0,X1)=not(and_star(X0,xor(truth,X1))))),
% 51.46/6.94 inference(backward_demodulation,[status(thm)],[f52,f27])).
% 51.46/6.94 fof(f68,plain,(
% 51.46/6.94 ![X0,X1]: (and_star(not(and_star(xor(truth,X0),X1)),X1)=and_star(not(and_star(not(X1),X0)),X0))),
% 51.46/6.94 inference(backward_demodulation,[status(thm)],[f52,f37])).
% 51.46/6.94 fof(f69,plain,(
% 51.46/6.94 ![X0,X1]: (xor(X0,not(X1))=xor(not(X0),X1))),
% 51.46/6.94 inference(backward_demodulation,[status(thm)],[f52,f35])).
% 51.46/6.94 fof(f70,plain,(
% 51.46/6.94 ![X0]: (and_star(not(X0),X0)=falsehood)),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f15,f60])).
% 51.46/6.94 fof(f72,plain,(
% 51.46/6.94 ![X0,X1]: (implies(X0,X1)=not(and_star(X0,not(X1))))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f52,f67])).
% 51.46/6.94 fof(f73,plain,(
% 51.46/6.94 ![X0,X1]: (and_star(not(and_star(not(X0),X1)),X1)=and_star(not(and_star(not(X1),X0)),X0))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f52,f68])).
% 51.46/6.94 fof(f74,plain,(
% 51.46/6.94 truth=not(falsehood)),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f15,f53])).
% 51.46/6.94 fof(f84,plain,(
% 51.46/6.94 ![X0]: (falsehood=and_star(falsehood,X0))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f19,f25])).
% 51.46/6.94 fof(f152,plain,(
% 51.46/6.94 ![X0,X1]: (and_star(falsehood,X0)=and_star(not(X1),and_star(X1,X0)))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f70,f24])).
% 51.46/6.94 fof(f155,plain,(
% 51.46/6.94 ![X0,X1]: (falsehood=and_star(not(X0),and_star(X0,X1)))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f84,f152])).
% 51.46/6.94 fof(f260,plain,(
% 51.46/6.94 ![X0,X1,X2]: (implies(and_star(X0,X1),X2)=not(and_star(X0,and_star(X1,not(X2)))))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f24,f72])).
% 51.46/6.94 fof(f264,plain,(
% 51.46/6.94 ![X0,X1]: (implies(X0,X1)=not(and_star(not(X1),X0)))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f25,f72])).
% 51.46/6.94 fof(f279,plain,(
% 51.46/6.94 ![X0,X1]: (and_star(not(and_star(not(X0),X1)),X1)=and_star(implies(X0,X1),X0))),
% 51.46/6.94 inference(backward_demodulation,[status(thm)],[f264,f73])).
% 51.46/6.94 fof(f287,plain,(
% 51.46/6.94 ![X0,X1]: (and_star(implies(X0,X1),X0)=and_star(implies(X1,X0),X1))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f264,f279])).
% 51.46/6.94 fof(f298,plain,(
% 51.46/6.94 ![X0]: (xor(X0,not(truth))=not(not(X0)))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f15,f69])).
% 51.46/6.94 fof(f311,plain,(
% 51.46/6.94 ![X0]: (xor(X0,falsehood)=not(not(X0)))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f26,f298])).
% 51.46/6.94 fof(f313,plain,(
% 51.46/6.94 ![X0]: (X0=not(not(X0)))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f16,f311])).
% 51.46/6.94 fof(f325,plain,(
% 51.46/6.94 ![X0,X1]: (and_star(X0,not(X1))=not(implies(X0,X1)))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f72,f313])).
% 51.46/6.94 fof(f329,plain,(
% 51.46/6.94 ![X0,X1]: (implies(X0,not(X1))=not(and_star(X0,X1)))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f313,f72])).
% 51.46/6.94 fof(f338,plain,(
% 51.46/6.94 ![X0,X1]: (implies(X0,X1)=implies(not(X1),not(X0)))),
% 51.46/6.94 inference(backward_demodulation,[status(thm)],[f329,f264])).
% 51.46/6.94 fof(f340,plain,(
% 51.46/6.94 ![X0,X1,X2]: (implies(and_star(X0,X1),X2)=implies(X0,not(and_star(X1,not(X2)))))),
% 51.46/6.94 inference(backward_demodulation,[status(thm)],[f329,f260])).
% 51.46/6.94 fof(f345,plain,(
% 51.46/6.94 ![X0,X1,X2]: (implies(and_star(X0,X1),X2)=implies(X0,implies(X1,X2)))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f72,f340])).
% 51.46/6.94 fof(f448,plain,(
% 51.46/6.94 ![X0,X1]: (implies(not(X0),not(and_star(X0,X1)))=not(falsehood))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f155,f329])).
% 51.46/6.94 fof(f458,plain,(
% 51.46/6.94 ![X0,X1]: (implies(X0,not(X1))=not(and_star(X1,X0)))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f25,f329])).
% 51.46/6.94 fof(f474,plain,(
% 51.46/6.94 ![X0,X1]: (implies(and_star(X0,X1),X0)=not(falsehood))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f338,f448])).
% 51.46/6.94 fof(f475,plain,(
% 51.46/6.94 ![X0,X1]: (implies(X0,implies(X1,X0))=not(falsehood))),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f345,f474])).
% 51.46/6.94 fof(f476,plain,(
% 51.46/6.94 ![X0,X1]: (implies(X0,implies(X1,X0))=truth)),
% 51.46/6.94 inference(forward_demodulation,[status(thm)],[f74,f475])).
% 51.46/6.94 fof(f586,plain,(
% 51.46/6.94 ![X0,X1,X2]: (implies(X0,implies(X1,X2))=implies(and_star(X1,not(X2)),not(X0)))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f325,f338])).
% 51.46/6.94 fof(f595,plain,(
% 51.46/6.94 ![X0,X1]: (and_star(implies(not(X0),not(X1)),not(X0))=and_star(implies(X0,X1),not(X1)))),
% 51.46/6.94 inference(paramodulation,[status(thm)],[f338,f287])).
% 51.46/6.94 fof(f600,plain,(
% 51.46/6.94 ![X0,X1,X2]: (implies(X0,implies(X1,X2))=implies(X1,implies(not(X2),not(X0))))),
% 23.50/7.02 inference(forward_demodulation,[status(thm)],[f345,f586])).
% 23.50/7.02 fof(f601,plain,(
% 23.50/7.02 ![X0,X1,X2]: (implies(X0,implies(X1,X2))=implies(X1,implies(X0,X2)))),
% 23.50/7.02 inference(forward_demodulation,[status(thm)],[f338,f600])).
% 23.50/7.02 fof(f608,plain,(
% 23.50/7.02 ![X0,X1]: (and_star(implies(X0,X1),not(X1))=and_star(implies(X1,X0),not(X0)))),
% 23.50/7.02 inference(forward_demodulation,[status(thm)],[f338,f595])).
% 23.50/7.02 fof(f2978,plain,(
% 23.50/7.02 ~implies(implies(x,y),implies(x,implies(implies(y,z),z)))=truth),
% 23.50/7.02 inference(paramodulation,[status(thm)],[f601,f28])).
% 23.50/7.02 fof(f2996,plain,(
% 23.50/7.02 ![X0,X1,X2]: (implies(implies(X0,X1),implies(X0,implies(X2,X1)))=truth)),
% 23.50/7.02 inference(paramodulation,[status(thm)],[f601,f476])).
% 23.50/7.02 fof(f5284,plain,(
% 23.50/7.02 ![X0,X1]: (implies(not(X0),not(implies(X1,X0)))=not(and_star(implies(X0,X1),not(X1))))),
% 23.50/7.02 inference(paramodulation,[status(thm)],[f608,f458])).
% 23.50/7.02 fof(f5425,plain,(
% 23.50/7.02 ![X0,X1]: (implies(implies(X0,X1),X1)=not(and_star(implies(X1,X0),not(X0))))),
% 23.50/7.02 inference(forward_demodulation,[status(thm)],[f338,f5284])).
% 23.50/7.02 fof(f5426,plain,(
% 23.50/7.02 ![X0,X1]: (implies(implies(X0,X1),X1)=implies(not(X0),not(implies(X1,X0))))),
% 23.50/7.02 inference(forward_demodulation,[status(thm)],[f458,f5425])).
% 23.50/7.02 fof(f5427,plain,(
% 23.50/7.02 ![X0,X1]: (implies(implies(X0,X1),X1)=implies(implies(X1,X0),X0))),
% 23.50/7.02 inference(forward_demodulation,[status(thm)],[f338,f5426])).
% 23.50/7.02 fof(f28545,plain,(
% 23.50/7.02 ![X0,X1,X2]: (implies(implies(X0,X1),implies(X0,implies(implies(X1,X2),X2)))=truth)),
% 23.50/7.02 inference(paramodulation,[status(thm)],[f5427,f2996])).
% 23.50/7.02 fof(f28683,plain,(
% 23.50/7.02 ~truth=truth),
% 23.50/7.02 inference(backward_demodulation,[status(thm)],[f28545,f2978])).
% 23.50/7.02 fof(f28809,plain,(
% 23.50/7.02 $false),
% 23.50/7.02 inference(trivial_equality_resolution,[status(thm)],[f28683])).
% 23.50/7.02 % SZS output end CNFRefutation for theBenchmark.p
% 23.50/7.06 % Elapsed time: 6.664854 seconds
% 23.50/7.06 % CPU time: 52.582866 seconds
% 23.50/7.06 % Total memory used: 337.032 MB
% 23.50/7.06 % Net memory used: 325.686 MB
%------------------------------------------------------------------------------