%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL156-1 : 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 : n018.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 01:09:27 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL156-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:09:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.03/0.37 % Drodi V4.1.1
% 0.03/0.39 % Refutation found
% 0.03/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.03/0.39 fof(f1,axiom,(
% 0.03/0.39 (![X]: (implies(truth,X) = X ))),
% 0.03/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.39 fof(f2,axiom,(
% 0.03/0.39 (![X,Y,Z]: (implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ))),
% 0.03/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.39 fof(f3,axiom,(
% 0.03/0.39 (![X,Y]: (implies(implies(X,Y),Y) = implies(implies(Y,X),X) ))),
% 0.03/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.39 fof(f4,axiom,(
% 0.03/0.39 (![X,Y]: (implies(implies(not(X),not(Y)),implies(Y,X)) = truth ))),
% 0.03/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.39 fof(f5,axiom,(
% 0.03/0.39 (![X,Y]: (or(X,Y) = implies(not(X),Y) ))),
% 0.03/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.39 fof(f7,axiom,(
% 0.03/0.39 (![X,Y]: (or(X,Y) = or(Y,X) ))),
% 0.03/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.39 fof(f8,axiom,(
% 0.03/0.39 (![X,Y]: (and(X,Y) = not(or(not(X),not(Y))) ))),
% 0.03/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.39 fof(f13,axiom,(
% 0.03/0.39 (![X,Y]: (and_star(X,Y) = not(or(not(X),not(Y))) ))),
% 0.03/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.39 fof(f15,axiom,(
% 0.03/0.39 (![X,Y]: (and_star(X,Y) = and_star(Y,X) ))),
% 0.03/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.39 fof(f16,axiom,(
% 0.03/0.39 not(truth) = falsehood ),
% 0.03/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.39 fof(f17,negated_conjecture,(
% 0.03/0.39 and_star(x,truth) != x ),
% 0.03/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.03/0.39 fof(f18,plain,(
% 0.03/0.39 ![X0]: (implies(truth,X0)=X0)),
% 0.03/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.03/0.39 fof(f19,plain,(
% 0.03/0.39 ![X0,X1,X2]: (implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))=truth)),
% 0.03/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.03/0.39 fof(f20,plain,(
% 0.03/0.39 ![X0,X1]: (implies(implies(X0,X1),X1)=implies(implies(X1,X0),X0))),
% 0.03/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.03/0.39 fof(f21,plain,(
% 0.03/0.39 ![X0,X1]: (implies(implies(not(X0),not(X1)),implies(X1,X0))=truth)),
% 0.03/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.03/0.39 fof(f22,plain,(
% 0.03/0.39 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 0.03/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.03/0.39 fof(f24,plain,(
% 0.03/0.39 ![X0,X1]: (or(X0,X1)=or(X1,X0))),
% 0.03/0.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.03/0.39 fof(f25,plain,(
% 0.03/0.39 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1))))),
% 0.03/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.03/0.39 fof(f30,plain,(
% 0.03/0.39 ![X0,X1]: (and_star(X0,X1)=not(or(not(X0),not(X1))))),
% 0.03/0.39 inference(cnf_transformation,[status(thm)],[f13])).
% 0.03/0.39 fof(f32,plain,(
% 0.03/0.39 ![X0,X1]: (and_star(X0,X1)=and_star(X1,X0))),
% 0.03/0.39 inference(cnf_transformation,[status(thm)],[f15])).
% 0.03/0.39 fof(f33,plain,(
% 0.03/0.39 not(truth)=falsehood),
% 0.03/0.39 inference(cnf_transformation,[status(thm)],[f16])).
% 0.03/0.39 fof(f34,plain,(
% 0.03/0.39 ~and_star(x,truth)=x),
% 0.03/0.39 inference(cnf_transformation,[status(thm)],[f17])).
% 0.03/0.39 fof(f35,definition,(
% 0.03/0.39 sF0_fnc=and_star(x,truth)),
% 0.03/0.39 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.03/0.39 fof(f36,plain,(
% 0.03/0.39 ~sF0_fnc=x),
% 0.03/0.39 inference(definition_folding,[],[f34,f35])).
% 0.03/0.39 fof(f37,plain,(
% 0.03/0.39 ![X0,X1]: (implies(or(X0,not(X1)),implies(X1,X0))=truth)),
% 0.03/0.39 inference(backward_demodulation,[status(thm)],[f22,f21])).
% 0.03/0.39 fof(f38,plain,(
% 0.03/0.39 ![X0,X1]: (and_star(X0,X1)=and(X0,X1))),
% 0.03/0.39 inference(forward_demodulation,[status(thm)],[f25,f30])).
% 0.03/0.39 fof(f43,plain,(
% 0.03/0.39 ![X0,X1]: (and(X0,X1)=and_star(X1,X0))),
% 0.03/0.39 inference(forward_demodulation,[status(thm)],[f38,f32])).
% 0.03/0.39 fof(f44,plain,(
% 0.03/0.39 sF0_fnc=and(truth,x)),
% 0.03/0.39 inference(forward_demodulation,[status(thm)],[f43,f35])).
% 0.03/0.39 fof(f58,plain,(
% 0.03/0.39 ![X0,X1]: (implies(X0,implies(implies(X0,X1),implies(truth,X1)))=truth)),
% 0.03/0.39 inference(paramodulation,[status(thm)],[f18,f19])).
% 0.03/0.39 fof(f65,plain,(
% 0.03/0.39 ![X0,X1]: (implies(X0,implies(implies(X0,X1),X1))=truth)),
% 0.03/0.39 inference(forward_demodulation,[status(thm)],[f18,f58])).
% 0.03/0.39 fof(f70,plain,(
% 0.03/0.39 ![X0]: (or(truth,X0)=implies(falsehood,X0))),
% 0.03/0.39 inference(paramodulation,[status(thm)],[f33,f22])).
% 0.03/0.39 fof(f76,plain,(
% 0.03/0.39 ![X0]: (or(X0,truth)=implies(falsehood,X0))),
% 0.03/0.39 inference(paramodulation,[status(thm)],[f24,f70])).
% 0.03/0.39 fof(f90,plain,(
% 0.03/0.40 ![X0]: (implies(X0,X0)=implies(implies(X0,truth),truth))),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f18,f20])).
% 0.03/0.40 fof(f105,plain,(
% 0.03/0.40 ![X0]: (implies(implies(truth,X0),X0)=truth)),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f18,f65])).
% 0.03/0.40 fof(f123,plain,(
% 0.03/0.40 ![X0]: (truth=implies(implies(X0,truth),truth))),
% 0.03/0.40 inference(backward_demodulation,[status(thm)],[f124,f90])).
% 0.03/0.40 fof(f124,plain,(
% 0.03/0.40 ![X0]: (implies(X0,X0)=truth)),
% 0.03/0.40 inference(forward_demodulation,[status(thm)],[f18,f105])).
% 0.03/0.40 fof(f135,plain,(
% 0.03/0.40 ![X0]: (or(X0,not(X0))=truth)),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f22,f124])).
% 0.03/0.40 fof(f162,plain,(
% 0.03/0.40 ![X0]: (implies(X0,truth)=truth)),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f123,f65])).
% 0.03/0.40 fof(f195,plain,(
% 0.03/0.40 ![X0]: (or(X0,truth)=truth)),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f22,f162])).
% 0.03/0.40 fof(f212,plain,(
% 0.03/0.40 ![X0]: (truth=implies(falsehood,X0))),
% 0.03/0.40 inference(backward_demodulation,[status(thm)],[f195,f76])).
% 0.03/0.40 fof(f269,plain,(
% 0.03/0.40 ![X0]: (implies(implies(X0,falsehood),falsehood)=implies(truth,X0))),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f212,f20])).
% 0.03/0.40 fof(f274,plain,(
% 0.03/0.40 ![X0]: (implies(implies(X0,falsehood),falsehood)=X0)),
% 0.03/0.40 inference(forward_demodulation,[status(thm)],[f18,f269])).
% 0.03/0.40 fof(f369,plain,(
% 0.03/0.40 ![X0]: (implies(or(X0,falsehood),falsehood)=not(X0))),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f22,f274])).
% 0.03/0.40 fof(f395,plain,(
% 0.03/0.40 ![X0]: (and(truth,X0)=not(or(falsehood,not(X0))))),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f33,f25])).
% 0.03/0.40 fof(f470,plain,(
% 0.03/0.40 ![X0]: (implies(or(falsehood,X0),falsehood)=not(X0))),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f24,f369])).
% 0.03/0.40 fof(f503,plain,(
% 0.03/0.40 implies(truth,falsehood)=not(not(falsehood))),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f135,f470])).
% 0.03/0.40 fof(f517,plain,(
% 0.03/0.40 falsehood=not(not(falsehood))),
% 0.03/0.40 inference(forward_demodulation,[status(thm)],[f18,f503])).
% 0.03/0.40 fof(f531,plain,(
% 0.03/0.40 ![X0]: (or(not(falsehood),X0)=implies(falsehood,X0))),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f517,f22])).
% 0.03/0.40 fof(f540,plain,(
% 0.03/0.40 ![X0]: (or(not(falsehood),X0)=truth)),
% 0.03/0.40 inference(forward_demodulation,[status(thm)],[f212,f531])).
% 0.03/0.40 fof(f766,plain,(
% 0.03/0.40 ![X0]: (implies(truth,implies(X0,not(falsehood)))=truth)),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f540,f37])).
% 0.03/0.40 fof(f804,plain,(
% 0.03/0.40 ![X0]: (implies(X0,not(falsehood))=truth)),
% 0.03/0.40 inference(forward_demodulation,[status(thm)],[f18,f766])).
% 0.03/0.40 fof(f821,plain,(
% 0.03/0.40 not(falsehood)=truth),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f18,f804])).
% 0.03/0.40 fof(f882,plain,(
% 0.03/0.40 ![X0]: (or(falsehood,X0)=implies(truth,X0))),
% 0.03/0.40 inference(paramodulation,[status(thm)],[f821,f22])).
% 0.03/0.40 fof(f894,plain,(
% 0.03/0.40 ![X0]: (implies(X0,falsehood)=not(X0))),
% 0.03/0.40 inference(backward_demodulation,[status(thm)],[f909,f470])).
% 0.03/0.40 fof(f901,plain,(
% 0.03/0.40 ![X0]: (and(truth,X0)=not(not(X0)))),
% 0.03/0.40 inference(backward_demodulation,[status(thm)],[f909,f395])).
% 0.03/0.40 fof(f909,plain,(
% 0.03/0.40 ![X0]: (or(falsehood,X0)=X0)),
% 0.03/0.40 inference(forward_demodulation,[status(thm)],[f18,f882])).
% 0.03/0.40 fof(f911,plain,(
% 0.03/0.40 ![X0]: (not(implies(X0,falsehood))=X0)),
% 0.03/0.40 inference(backward_demodulation,[status(thm)],[f894,f274])).
% 0.03/0.40 fof(f926,plain,(
% 0.03/0.40 sF0_fnc=not(not(x))),
% 0.03/0.40 inference(backward_demodulation,[status(thm)],[f901,f44])).
% 0.03/0.40 fof(f942,plain,(
% 0.03/0.40 ![X0]: (not(not(X0))=X0)),
% 0.03/0.40 inference(forward_demodulation,[status(thm)],[f894,f911])).
% 0.03/0.40 fof(f950,plain,(
% 0.03/0.40 sF0_fnc=x),
% 0.03/0.40 inference(forward_demodulation,[status(thm)],[f942,f926])).
% 0.03/0.40 fof(f951,plain,(
% 0.03/0.40 $false),
% 0.03/0.40 inference(forward_subsumption_resolution,[status(thm)],[f950,f36])).
% 0.03/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.03/0.41 % Elapsed time: 0.039227 seconds
% 0.03/0.41 % CPU time: 0.167656 seconds
% 0.03/0.41 % Total memory used: 8.315 MB
% 0.03/0.41 % Net memory used: 8.148 MB
%------------------------------------------------------------------------------