%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL153-1 : 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 : 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 : Thu Sep 24 01:09:27 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.61s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL153-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.58 % Computer : n006.cluster.edu
% 0.08/0.58 % Model : x86_64 x86_64
% 0.08/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.58 % Memory : 8046.5625MB
% 0.08/0.58 % OS : Linux 6.8.0-71-generic
% 0.08/0.58 % CPULimit : 300
% 0.08/0.58 % WCLimit : 300
% 0.08/0.58 % DateTime : Mon Sep 21 00:07:28 UTC 2026
% 0.08/0.58 % CPUTime :
% 0.08/0.58 % Drodi V4.1.1
% 0.08/0.61 % Refutation found
% 0.08/0.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.61 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.61 fof(f1,axiom,(
% 0.08/0.61 (![X]: (implies(truth,X) = X ))),
% 0.08/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.61 fof(f2,axiom,(
% 0.08/0.61 (![X,Y,Z]: (implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ))),
% 0.08/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.61 fof(f3,axiom,(
% 0.08/0.61 (![X,Y]: (implies(implies(X,Y),Y) = implies(implies(Y,X),X) ))),
% 0.08/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.61 fof(f4,axiom,(
% 0.08/0.61 (![X,Y]: (implies(implies(not(X),not(Y)),implies(Y,X)) = truth ))),
% 0.08/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.61 fof(f5,axiom,(
% 0.08/0.61 (![X,Y]: (or(X,Y) = implies(not(X),Y) ))),
% 0.08/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.61 fof(f7,axiom,(
% 0.08/0.61 (![X,Y]: (or(X,Y) = or(Y,X) ))),
% 0.08/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.61 fof(f8,axiom,(
% 0.08/0.61 (![X,Y]: (and(X,Y) = not(or(not(X),not(Y))) ))),
% 0.08/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.61 fof(f10,axiom,(
% 0.08/0.61 (![X,Y]: (and(X,Y) = and(Y,X) ))),
% 0.08/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.61 fof(f11,axiom,(
% 0.08/0.61 (![X,Y]: (xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ))),
% 0.08/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.61 fof(f16,axiom,(
% 0.08/0.61 not(truth) = falsehood ),
% 0.08/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.61 fof(f17,negated_conjecture,(
% 0.08/0.61 not(x) != xor(x,truth) ),
% 0.08/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.61 fof(f18,plain,(
% 0.08/0.61 ![X0]: (implies(truth,X0)=X0)),
% 0.08/0.61 inference(cnf_transformation,[status(thm)],[f1])).
% 0.08/0.61 fof(f19,plain,(
% 0.08/0.61 ![X0,X1,X2]: (implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))=truth)),
% 0.08/0.61 inference(cnf_transformation,[status(thm)],[f2])).
% 0.08/0.61 fof(f20,plain,(
% 0.08/0.61 ![X0,X1]: (implies(implies(X0,X1),X1)=implies(implies(X1,X0),X0))),
% 0.08/0.61 inference(cnf_transformation,[status(thm)],[f3])).
% 0.08/0.61 fof(f21,plain,(
% 0.08/0.61 ![X0,X1]: (implies(implies(not(X0),not(X1)),implies(X1,X0))=truth)),
% 0.08/0.61 inference(cnf_transformation,[status(thm)],[f4])).
% 0.08/0.61 fof(f22,plain,(
% 0.08/0.61 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 0.08/0.61 inference(cnf_transformation,[status(thm)],[f5])).
% 0.08/0.61 fof(f24,plain,(
% 0.08/0.61 ![X0,X1]: (or(X0,X1)=or(X1,X0))),
% 0.08/0.61 inference(cnf_transformation,[status(thm)],[f7])).
% 0.08/0.61 fof(f25,plain,(
% 0.08/0.61 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1))))),
% 0.08/0.61 inference(cnf_transformation,[status(thm)],[f8])).
% 0.08/0.61 fof(f27,plain,(
% 0.08/0.61 ![X0,X1]: (and(X0,X1)=and(X1,X0))),
% 0.08/0.61 inference(cnf_transformation,[status(thm)],[f10])).
% 0.08/0.61 fof(f28,plain,(
% 0.08/0.61 ![X0,X1]: (xor(X0,X1)=or(and(X0,not(X1)),and(not(X0),X1)))),
% 0.08/0.61 inference(cnf_transformation,[status(thm)],[f11])).
% 0.08/0.61 fof(f33,plain,(
% 0.08/0.61 not(truth)=falsehood),
% 0.08/0.61 inference(cnf_transformation,[status(thm)],[f16])).
% 0.08/0.61 fof(f34,plain,(
% 0.08/0.61 ~not(x)=xor(x,truth)),
% 0.08/0.61 inference(cnf_transformation,[status(thm)],[f17])).
% 0.08/0.61 fof(f35,definition,(
% 0.08/0.61 sF0_fnc=not(x)),
% 0.08/0.61 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.08/0.61 fof(f36,definition,(
% 0.08/0.61 sF1_fnc=xor(x,truth)),
% 0.08/0.61 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.08/0.61 fof(f37,plain,(
% 0.08/0.61 ~sF0_fnc=sF1_fnc),
% 0.08/0.61 inference(definition_folding,[],[f34,f36,f35])).
% 0.08/0.61 fof(f38,plain,(
% 0.08/0.61 ![X0,X1]: (implies(or(X0,not(X1)),implies(X1,X0))=truth)),
% 0.08/0.61 inference(backward_demodulation,[status(thm)],[f22,f21])).
% 0.08/0.61 fof(f54,plain,(
% 0.08/0.61 ![X0,X1]: (implies(X0,implies(implies(X0,X1),implies(truth,X1)))=truth)),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f18,f19])).
% 0.08/0.61 fof(f61,plain,(
% 0.08/0.61 ![X0,X1]: (implies(X0,implies(implies(X0,X1),X1))=truth)),
% 0.08/0.61 inference(forward_demodulation,[status(thm)],[f18,f54])).
% 0.08/0.61 fof(f75,plain,(
% 0.08/0.61 ![X0]: (or(truth,X0)=implies(falsehood,X0))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f33,f22])).
% 0.08/0.61 fof(f85,plain,(
% 0.08/0.61 ![X0]: (implies(X0,X0)=implies(implies(X0,truth),truth))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f18,f20])).
% 0.08/0.61 fof(f103,plain,(
% 0.08/0.61 ![X0]: (or(X0,truth)=implies(falsehood,X0))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f24,f75])).
% 0.08/0.61 fof(f132,plain,(
% 0.08/0.61 ![X0]: (implies(implies(truth,X0),X0)=truth)),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f18,f61])).
% 0.08/0.61 fof(f152,plain,(
% 0.08/0.61 ![X0]: (truth=implies(implies(X0,truth),truth))),
% 0.08/0.61 inference(backward_demodulation,[status(thm)],[f153,f85])).
% 0.08/0.61 fof(f153,plain,(
% 0.08/0.61 ![X0]: (implies(X0,X0)=truth)),
% 0.08/0.61 inference(forward_demodulation,[status(thm)],[f18,f132])).
% 0.08/0.61 fof(f201,plain,(
% 0.08/0.61 ![X0]: (or(X0,not(X0))=truth)),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f22,f153])).
% 0.08/0.61 fof(f310,plain,(
% 0.08/0.61 ![X0]: (and(X0,truth)=not(or(not(X0),falsehood)))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f33,f25])).
% 0.08/0.61 fof(f334,plain,(
% 0.08/0.61 ![X0]: (implies(X0,truth)=truth)),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f152,f61])).
% 0.08/0.61 fof(f376,plain,(
% 0.08/0.61 ![X0]: (or(X0,truth)=truth)),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f22,f334])).
% 0.08/0.61 fof(f393,plain,(
% 0.08/0.61 ![X0]: (truth=implies(falsehood,X0))),
% 0.08/0.61 inference(backward_demodulation,[status(thm)],[f376,f103])).
% 0.08/0.61 fof(f462,plain,(
% 0.08/0.61 ![X0]: (implies(implies(X0,falsehood),falsehood)=implies(truth,X0))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f393,f20])).
% 0.08/0.61 fof(f468,plain,(
% 0.08/0.61 ![X0]: (implies(implies(X0,falsehood),falsehood)=X0)),
% 0.08/0.61 inference(forward_demodulation,[status(thm)],[f18,f462])).
% 0.08/0.61 fof(f571,plain,(
% 0.08/0.61 ![X0]: (implies(or(X0,falsehood),falsehood)=not(X0))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f22,f468])).
% 0.08/0.61 fof(f599,plain,(
% 0.08/0.61 ![X0]: (xor(X0,truth)=or(and(X0,falsehood),and(not(X0),truth)))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f33,f28])).
% 0.08/0.61 fof(f690,plain,(
% 0.08/0.61 ![X0]: (implies(or(falsehood,X0),falsehood)=not(X0))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f24,f571])).
% 0.08/0.61 fof(f738,plain,(
% 0.08/0.61 implies(truth,falsehood)=not(not(falsehood))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f201,f690])).
% 0.08/0.61 fof(f753,plain,(
% 0.08/0.61 falsehood=not(not(falsehood))),
% 0.08/0.61 inference(forward_demodulation,[status(thm)],[f18,f738])).
% 0.08/0.61 fof(f810,plain,(
% 0.08/0.61 ![X0]: (or(not(falsehood),X0)=implies(falsehood,X0))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f753,f22])).
% 0.08/0.61 fof(f822,plain,(
% 0.08/0.61 ![X0]: (or(not(falsehood),X0)=truth)),
% 0.08/0.61 inference(forward_demodulation,[status(thm)],[f393,f810])).
% 0.08/0.61 fof(f833,plain,(
% 0.08/0.61 ![X0]: (and(falsehood,X0)=not(truth))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f822,f25])).
% 0.08/0.61 fof(f840,plain,(
% 0.08/0.61 ![X0]: (implies(truth,implies(X0,not(falsehood)))=truth)),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f822,f38])).
% 0.08/0.61 fof(f854,plain,(
% 0.08/0.61 ![X0]: (and(falsehood,X0)=falsehood)),
% 0.08/0.61 inference(forward_demodulation,[status(thm)],[f33,f833])).
% 0.08/0.61 fof(f858,plain,(
% 0.08/0.61 ![X0]: (implies(X0,not(falsehood))=truth)),
% 0.08/0.61 inference(forward_demodulation,[status(thm)],[f18,f840])).
% 0.08/0.61 fof(f863,plain,(
% 0.08/0.61 ![X0]: (and(X0,falsehood)=falsehood)),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f27,f854])).
% 0.08/0.61 fof(f871,plain,(
% 0.08/0.61 ![X0]: (xor(X0,truth)=or(falsehood,and(not(X0),truth)))),
% 0.08/0.61 inference(backward_demodulation,[status(thm)],[f863,f599])).
% 0.08/0.61 fof(f923,plain,(
% 0.08/0.61 not(falsehood)=truth),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f18,f858])).
% 0.08/0.61 fof(f1147,plain,(
% 0.08/0.61 ![X0]: (or(falsehood,X0)=implies(truth,X0))),
% 0.08/0.61 inference(paramodulation,[status(thm)],[f923,f22])).
% 0.08/0.61 fof(f1159,plain,(
% 0.08/0.61 ![X0]: (implies(X0,falsehood)=not(X0))),
% 0.08/0.61 inference(backward_demodulation,[status(thm)],[f1177,f690])).
% 0.08/0.61 fof(f1161,plain,(
% 0.08/0.61 ![X0]: (xor(X0,truth)=and(not(X0),truth))),
% 0.08/0.61 inference(backward_demodulation,[status(thm)],[f1177,f871])).
% 0.08/0.61 fof(f1177,plain,(
% 0.08/0.61 ![X0]: (or(falsehood,X0)=X0)),
% 0.08/0.61 inference(forward_demodulation,[status(thm)],[f18,f1147])).
% 0.08/0.61 fof(f1178,plain,(
% 0.08/0.61 ![X0]: (not(or(X0,falsehood))=not(X0))),
% 0.08/0.61 inference(backward_demodulation,[status(thm)],[f1159,f571])).
% 0.08/0.61 fof(f1179,plain,(
% 0.08/0.61 ![X0]: (not(implies(X0,falsehood))=X0)),
% 0.08/0.61 inference(backward_demodulation,[status(thm)],[f1159,f468])).
% 0.08/0.61 fof(f1209,plain,(
% 0.08/0.61 ![X0]: (and(X0,truth)=not(not(X0)))),
% 0.08/0.61 inference(backward_demodulation,[status(thm)],[f1178,f310])).
% 0.08/0.61 fof(f1215,plain,(
% 0.08/0.61 ![X0]: (not(not(X0))=X0)),
% 0.08/0.61 inference(forward_demodulation,[status(thm)],[f1159,f1179])).
% 0.08/0.61 fof(f1233,plain,(
% 0.08/0.61 ![X0]: (xor(X0,truth)=not(X0))),
% 0.08/0.61 inference(backward_demodulation,[status(thm)],[f1235,f1161])).
% 0.08/0.61 fof(f1235,plain,(
% 0.08/0.61 ![X0]: (and(X0,truth)=X0)),
% 0.08/0.61 inference(forward_demodulation,[status(thm)],[f1215,f1209])).
% 0.08/0.61 fof(f1240,plain,(
% 0.08/0.61 sF1_fnc=not(x)),
% 0.08/0.61 inference(backward_demodulation,[status(thm)],[f1233,f36])).
% 0.08/0.61 fof(f1241,plain,(
% 0.08/0.61 sF1_fnc=sF0_fnc),
% 0.08/0.61 inference(forward_demodulation,[status(thm)],[f35,f1240])).
% 0.08/0.61 fof(f1242,plain,(
% 0.08/0.61 $false),
% 0.08/0.61 inference(forward_subsumption_resolution,[status(thm)],[f1241,f37])).
% 0.08/0.61 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.63 % Elapsed time: 0.045182 seconds
% 0.08/0.63 % CPU time: 0.199408 seconds
% 0.08/0.63 % Total memory used: 10.650 MB
% 0.08/0.63 % Net memory used: 10.590 MB
%------------------------------------------------------------------------------