%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL138-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Thu Sep 24 01:09:26 PM UTC 2026
% Result : Unsatisfiable 36.56s 5.29s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL138-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n013.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Mon Sep 21 00:06:36 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 % Drodi V4.1.1
% 36.56/5.29 % Refutation found
% 36.56/5.29 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 36.56/5.29 % SZS output start CNFRefutation for theBenchmark
% 36.56/5.29 fof(f1,axiom,(
% 36.56/5.29 (![X]: (implies(truth,X) = X ))),
% 36.56/5.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 36.56/5.29 fof(f2,axiom,(
% 36.56/5.29 (![X,Y,Z]: (implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ))),
% 36.56/5.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 36.56/5.29 fof(f3,axiom,(
% 36.56/5.29 (![X,Y]: (implies(implies(X,Y),Y) = implies(implies(Y,X),X) ))),
% 36.56/5.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 36.56/5.29 fof(f5,negated_conjecture,(
% 36.56/5.29 implies(x,implies(y,z)) != implies(y,implies(x,z)) ),
% 36.56/5.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 36.56/5.29 fof(f6,plain,(
% 36.56/5.29 ![X0]: (implies(truth,X0)=X0)),
% 36.56/5.29 inference(cnf_transformation,[status(thm)],[f1])).
% 36.56/5.29 fof(f7,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))=truth)),
% 36.56/5.29 inference(cnf_transformation,[status(thm)],[f2])).
% 36.56/5.29 fof(f8,plain,(
% 36.56/5.29 ![X0,X1]: (implies(implies(X0,X1),X1)=implies(implies(X1,X0),X0))),
% 36.56/5.29 inference(cnf_transformation,[status(thm)],[f3])).
% 36.56/5.29 fof(f10,plain,(
% 36.56/5.29 ~implies(x,implies(y,z))=implies(y,implies(x,z))),
% 36.56/5.29 inference(cnf_transformation,[status(thm)],[f5])).
% 36.56/5.29 fof(f20,plain,(
% 36.56/5.29 ![X0]: (implies(implies(X0,truth),truth)=implies(X0,X0))),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f6,f8])).
% 36.56/5.29 fof(f83,plain,(
% 36.56/5.29 ![X0,X1]: (implies(X0,implies(implies(X0,X1),implies(truth,X1)))=truth)),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f6,f7])).
% 36.56/5.29 fof(f89,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(X0,X1),X1),implies(implies(X0,X2),implies(implies(X1,X0),X2)))=truth)),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f8,f7])).
% 36.56/5.29 fof(f101,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(X0,implies(X1,X2)),implies(implies(implies(X2,X1),X1),implies(X0,X2)))=truth)),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f8,f7])).
% 36.56/5.29 fof(f110,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(X0,X1),X2),implies(implies(X2,X1),implies(implies(X1,X0),X0)))=truth)),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f8,f7])).
% 36.56/5.29 fof(f113,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X0)),implies(X2,X0))=implies(truth,implies(implies(X0,X1),implies(X2,X1))))),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f7,f8])).
% 36.56/5.29 fof(f115,plain,(
% 36.56/5.29 ![X0,X1]: (implies(X0,implies(implies(X0,X1),X1))=truth)),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f6,f83])).
% 36.56/5.29 fof(f122,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X0)),implies(X2,X0))=implies(implies(X0,X1),implies(X2,X1)))),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f6,f113])).
% 36.56/5.29 fof(f129,plain,(
% 36.56/5.29 ![X0,X1]: (implies(implies(implies(X0,implies(X1,X0)),implies(X1,truth)),implies(X1,truth))=implies(implies(truth,X0),implies(X1,X0)))),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f6,f122])).
% 36.56/5.29 fof(f136,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(X2,implies(X1,X0))),implies(X2,implies(X1,X0)))=implies(implies(implies(X1,X0),X0),implies(X2,X0)))),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f8,f122])).
% 36.56/5.29 fof(f175,plain,(
% 36.56/5.29 ![X0,X1]: (implies(implies(implies(X0,implies(X1,X0)),implies(X1,truth)),implies(X1,truth))=implies(X0,implies(X1,X0)))),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f6,f129])).
% 36.56/5.29 fof(f478,plain,(
% 36.56/5.29 ![X0]: (implies(implies(truth,X0),X0)=truth)),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f6,f115])).
% 36.56/5.29 fof(f481,plain,(
% 36.56/5.29 ![X0]: (implies(X0,implies(X0,X0))=truth)),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f20,f115])).
% 36.56/5.29 fof(f556,plain,(
% 36.56/5.29 ![X0]: (implies(X0,X0)=truth)),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f6,f478])).
% 36.56/5.29 fof(f576,plain,(
% 36.56/5.29 ![X0,X1]: (implies(implies(implies(X0,implies(X1,X0)),implies(X1,truth)),truth)=implies(X0,implies(X1,X0)))),
% 36.56/5.29 inference(backward_demodulation,[status(thm)],[f578,f175])).
% 36.56/5.29 fof(f578,plain,(
% 36.56/5.29 ![X0]: (implies(X0,truth)=truth)),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f556,f481])).
% 36.56/5.29 fof(f759,plain,(
% 36.56/5.29 ![X0,X1]: (truth=implies(X0,implies(X1,X0)))),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f578,f576])).
% 36.56/5.29 fof(f1098,plain,(
% 36.56/5.29 ![X0,X1,X2,X3]: (implies(implies(implies(implies(X0,X1),X2),X2),implies(truth,implies(implies(X2,implies(X0,X1)),implies(implies(X1,X3),implies(X0,X3)))))=truth)),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f7,f89])).
% 36.56/5.29 fof(f1167,plain,(
% 36.56/5.29 ![X0,X1,X2,X3]: (implies(implies(implies(implies(X0,X1),X2),X2),implies(implies(X2,implies(X0,X1)),implies(implies(X1,X3),implies(X0,X3))))=truth)),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f6,f1098])).
% 36.56/5.29 fof(f2048,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(X0,X1),implies(X2,X1)),implies(implies(implies(X1,X2),X2),implies(implies(X1,X0),X0)))=truth)),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f8,f101])).
% 36.56/5.29 fof(f2569,plain,(
% 36.56/5.29 ![X0,X1]: (implies(truth,implies(implies(implies(X0,X1),X1),implies(implies(X1,X0),X0)))=truth)),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f556,f110])).
% 36.56/5.29 fof(f2629,plain,(
% 36.56/5.29 ![X0,X1]: (implies(implies(implies(X0,X1),X1),implies(implies(X1,X0),X0))=truth)),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f6,f2569])).
% 36.56/5.29 fof(f2750,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(implies(implies(X0,X2),X2),implies(implies(X0,implies(X1,X0)),implies(X1,X0))))=truth)),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f8,f2048])).
% 36.56/5.29 fof(f2917,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(implies(implies(X0,X2),X2),implies(truth,implies(X1,X0))))=truth)),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f759,f2750])).
% 36.56/5.29 fof(f2918,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(implies(implies(X0,X2),X2),implies(X1,X0)))=truth)),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f6,f2917])).
% 36.56/5.29 fof(f4634,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(implies(implies(X0,X2),X2),implies(X1,X0))),implies(implies(implies(X0,X2),X2),implies(X1,X0)))=implies(truth,implies(implies(implies(X0,X1),X1),implies(X2,X0))))),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f2918,f8])).
% 36.56/5.29 fof(f5000,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(truth,implies(implies(implies(X0,X1),X1),implies(X2,X0)))=implies(truth,implies(implies(implies(X0,X2),X2),implies(X1,X0))))),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f2918,f4634])).
% 36.56/5.29 fof(f5001,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(X0,X1),X1),implies(X2,X0))=implies(truth,implies(implies(implies(X0,X2),X2),implies(X1,X0))))),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f6,f5000])).
% 36.56/5.29 fof(f5002,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(X0,X1),X1),implies(X2,X0))=implies(implies(implies(X0,X2),X2),implies(X1,X0)))),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f6,f5001])).
% 36.56/5.29 fof(f7788,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(X0,X1),X1),implies(X2,X1))=implies(implies(implies(X1,X2),X2),implies(X0,X1)))),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f8,f5002])).
% 36.56/5.29 fof(f7898,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(implies(X0,X1),X1),implies(implies(X1,X0),X0)),implies(implies(implies(X1,X0),implies(X0,implies(X1,X0))),implies(implies(implies(X1,X0),X2),implies(X0,X2))))=truth)),
% 36.56/5.29 inference(paramodulation,[status(thm)],[f5002,f1167])).
% 36.56/5.29 fof(f8334,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(truth,implies(implies(implies(X0,X1),implies(X1,implies(X0,X1))),implies(implies(implies(X0,X1),X2),implies(X1,X2))))=truth)),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f2629,f7898])).
% 36.56/5.29 fof(f8335,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(X0,X1),implies(X1,implies(X0,X1))),implies(implies(implies(X0,X1),X2),implies(X1,X2)))=truth)),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f6,f8334])).
% 36.56/5.29 fof(f8336,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(truth,implies(implies(implies(X0,X1),X2),implies(X1,X2)))=truth)),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f759,f8335])).
% 36.56/5.29 fof(f8352,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(X0,X1),X2),implies(X1,X2))=truth)),
% 36.56/5.29 inference(forward_demodulation,[status(thm)],[f6,f8336])).
% 36.56/5.29 fof(f9929,plain,(
% 36.56/5.29 ![X0,X1,X2]: (implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(X1,implies(X2,X0))),implies(X1,implies(X2,X0)))=implies(implies(implies(X2,X0),X0),implies(X1,X0)))),
% 37.30/5.34 inference(paramodulation,[status(thm)],[f5002,f136])).
% 37.30/5.34 fof(f10195,plain,(
% 37.30/5.34 ![X0,X1,X2]: (implies(truth,implies(X0,implies(X1,X2)))=implies(implies(implies(X1,X2),X2),implies(X0,X2)))),
% 37.30/5.34 inference(forward_demodulation,[status(thm)],[f8352,f9929])).
% 37.30/5.34 fof(f10200,plain,(
% 37.30/5.34 ![X0,X1,X2]: (implies(X0,implies(X1,X2))=implies(implies(implies(X2,X0),X0),implies(X1,X2)))),
% 37.30/5.34 inference(backward_demodulation,[status(thm)],[f10212,f7788])).
% 37.30/5.34 fof(f10212,plain,(
% 37.30/5.34 ![X0,X1,X2]: (implies(X0,implies(X1,X2))=implies(implies(implies(X1,X2),X2),implies(X0,X2)))),
% 37.30/5.34 inference(forward_demodulation,[status(thm)],[f6,f10195])).
% 37.30/5.34 fof(f11472,plain,(
% 37.30/5.34 ![X0,X1,X2]: (implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))=truth)),
% 37.30/5.34 inference(backward_demodulation,[status(thm)],[f10200,f101])).
% 37.30/5.34 fof(f13412,plain,(
% 37.30/5.34 ![X0,X1,X2]: (implies(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2))),implies(X1,implies(X0,X2)))=implies(truth,implies(X0,implies(X1,X2))))),
% 37.30/5.34 inference(paramodulation,[status(thm)],[f11472,f8])).
% 37.30/5.34 fof(f13689,plain,(
% 37.30/5.34 ![X0,X1,X2]: (implies(truth,implies(X0,implies(X1,X2)))=implies(truth,implies(X1,implies(X0,X2))))),
% 37.30/5.34 inference(forward_demodulation,[status(thm)],[f11472,f13412])).
% 37.30/5.34 fof(f13690,plain,(
% 37.30/5.34 ![X0,X1,X2]: (implies(X0,implies(X1,X2))=implies(truth,implies(X1,implies(X0,X2))))),
% 37.30/5.34 inference(forward_demodulation,[status(thm)],[f6,f13689])).
% 37.30/5.34 fof(f13692,plain,(
% 37.30/5.34 ![X0,X1,X2]: (implies(X0,implies(X1,X2))=implies(X1,implies(X0,X2)))),
% 37.30/5.34 inference(forward_demodulation,[status(thm)],[f6,f13690])).
% 37.30/5.34 fof(f13693,plain,(
% 37.30/5.34 $false),
% 37.30/5.34 inference(backward_subsumption_resolution,[status(thm)],[f10,f13692])).
% 37.30/5.34 % SZS output end CNFRefutation for theBenchmark.p
% 30.93/6.62 % Elapsed time: 5.818310 seconds
% 30.93/6.62 % CPU time: 17.880039 seconds
% 30.93/6.62 % Total memory used: 205.644 MB
% 30.93/6.62 % Net memory used: 198.504 MB
%------------------------------------------------------------------------------