%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 01:09:22 PM UTC 2026
% Result : Unsatisfiable 10.73s 16.98s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.57 % CPULimit : 300
% 0.09/15.57 % WCLimit : 300
% 0.09/15.57 % DateTime : Mon Sep 21 00:05:42 UTC 2026
% 0.09/15.58 % CPUTime :
% 0.09/15.59 % Drodi V4.1.1
% 10.73/16.98 % Refutation found
% 10.73/16.98 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 10.73/16.98 % SZS output start CNFRefutation for theBenchmark
% 10.73/16.98 fof(f2,axiom,(
% 10.73/16.98 (![X]: (implies(truth,X) = X ))),
% 10.73/16.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.73/16.98 fof(f4,axiom,(
% 10.73/16.98 (![X,Y]: (implies(implies(X,Y),Y) = implies(implies(Y,X),X) ))),
% 10.73/16.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.73/16.98 fof(f6,axiom,(
% 10.73/16.98 (![X]: (implies(X,X) = truth ))),
% 10.73/16.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.73/16.98 fof(f9,axiom,(
% 10.73/16.98 (![X,Y]: (implies(X,implies(Y,X)) = truth ))),
% 10.73/16.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.73/16.98 fof(f12,axiom,(
% 10.73/16.98 (![X,Y,Z]: (implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ))),
% 10.73/16.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.73/16.98 fof(f13,axiom,(
% 10.73/16.98 (![X]: (implies(X,not(truth)) = not(X) ))),
% 10.73/16.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.73/16.98 fof(f14,axiom,(
% 10.73/16.98 (![X]: (not(not(X)) = X ))),
% 10.73/16.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.73/16.98 fof(f15,axiom,(
% 10.73/16.98 (![X,Y]: (implies(not(X),not(Y)) = implies(Y,X) ))),
% 10.73/16.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.73/16.98 fof(f16,negated_conjecture,(
% 10.73/16.98 implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth ),
% 10.73/16.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.73/16.98 fof(f18,plain,(
% 10.73/16.98 ![X0]: (implies(truth,X0)=X0)),
% 10.73/16.98 inference(cnf_transformation,[status(thm)],[f2])).
% 10.73/16.98 fof(f20,plain,(
% 10.73/16.98 ![X0,X1]: (implies(implies(X0,X1),X1)=implies(implies(X1,X0),X0))),
% 10.73/16.98 inference(cnf_transformation,[status(thm)],[f4])).
% 10.73/16.98 fof(f22,plain,(
% 10.73/16.98 ![X0]: (implies(X0,X0)=truth)),
% 10.73/16.98 inference(cnf_transformation,[status(thm)],[f6])).
% 10.73/16.98 fof(f25,plain,(
% 10.73/16.98 ![X0,X1]: (implies(X0,implies(X1,X0))=truth)),
% 10.73/16.98 inference(cnf_transformation,[status(thm)],[f9])).
% 10.73/16.98 fof(f28,plain,(
% 10.73/16.98 ![X0,X1,X2]: (implies(X0,implies(X1,X2))=implies(X1,implies(X0,X2)))),
% 10.73/16.98 inference(cnf_transformation,[status(thm)],[f12])).
% 10.73/16.98 fof(f29,plain,(
% 10.73/16.98 ![X0]: (implies(X0,not(truth))=not(X0))),
% 10.73/16.98 inference(cnf_transformation,[status(thm)],[f13])).
% 10.73/16.98 fof(f30,plain,(
% 10.73/16.98 ![X0]: (not(not(X0))=X0)),
% 10.73/16.98 inference(cnf_transformation,[status(thm)],[f14])).
% 10.73/16.98 fof(f31,plain,(
% 10.73/16.98 ![X0,X1]: (implies(not(X0),not(X1))=implies(X1,X0))),
% 10.73/16.98 inference(cnf_transformation,[status(thm)],[f15])).
% 10.73/16.98 fof(f32,plain,(
% 10.73/16.98 ~implies(implies(implies(a,b),implies(b,a)),implies(b,a))=truth),
% 10.73/16.98 inference(cnf_transformation,[status(thm)],[f16])).
% 10.73/16.98 fof(f33,definition,(
% 10.73/16.98 sF2_fnc=implies(a,b)),
% 10.73/16.98 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 10.73/16.98 fof(f34,definition,(
% 10.73/16.98 sF3_fnc=implies(b,a)),
% 10.73/16.98 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 10.73/16.98 fof(f35,definition,(
% 10.73/16.98 sF1_fnc=implies(sF2_fnc,sF3_fnc)),
% 10.73/16.98 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 10.73/16.98 fof(f36,definition,(
% 10.73/16.98 sF0_fnc=implies(sF1_fnc,sF3_fnc)),
% 10.73/16.98 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 10.73/16.98 fof(f37,plain,(
% 10.73/16.98 ~sF0_fnc=truth),
% 10.73/16.98 inference(definition_folding,[],[f32,f36,f35,f34,f33])).
% 10.73/16.98 fof(f77,plain,(
% 10.73/16.98 implies(sF3_fnc,a)=implies(implies(a,b),b)),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f34,f20])).
% 10.73/16.98 fof(f91,plain,(
% 10.73/16.98 implies(sF3_fnc,a)=implies(sF2_fnc,b)),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f33,f77])).
% 10.73/16.98 fof(f95,plain,(
% 10.73/16.98 implies(implies(a,sF3_fnc),sF3_fnc)=implies(implies(sF2_fnc,b),a)),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f91,f20])).
% 10.73/16.98 fof(f113,plain,(
% 10.73/16.98 ![X0,X1,X2]: (implies(X0,implies(implies(X1,X2),X2))=implies(implies(X2,X1),implies(X0,X1)))),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f20,f28])).
% 10.73/16.98 fof(f538,plain,(
% 10.73/16.98 implies(a,sF3_fnc)=truth),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f34,f25])).
% 10.73/16.98 fof(f539,plain,(
% 10.73/16.98 implies(b,sF2_fnc)=truth),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f33,f25])).
% 10.73/16.98 fof(f554,plain,(
% 10.73/16.98 ![X0,X1,X2]: (implies(X0,implies(truth,implies(X1,X2)))=implies(implies(implies(X1,X2),X2),implies(X0,X2)))),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f25,f113])).
% 10.73/16.98 fof(f580,plain,(
% 10.73/16.98 implies(truth,sF3_fnc)=implies(implies(sF2_fnc,b),a)),
% 10.73/16.98 inference(backward_demodulation,[status(thm)],[f538,f95])).
% 10.73/16.98 fof(f594,plain,(
% 10.73/16.98 ![X0,X1,X2]: (implies(X0,implies(X1,X2))=implies(implies(implies(X1,X2),X2),implies(X0,X2)))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f18,f554])).
% 10.73/16.98 fof(f636,plain,(
% 10.73/16.98 sF3_fnc=implies(implies(sF2_fnc,b),a)),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f18,f580])).
% 10.73/16.98 fof(f2105,plain,(
% 10.73/16.98 ![X0,X1]: (implies(X0,implies(X1,not(truth)))=implies(not(implies(X1,not(truth))),implies(X0,not(truth))))),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f29,f594])).
% 10.73/16.98 fof(f2152,plain,(
% 10.73/16.98 ![X0,X1]: (implies(X0,not(X1))=implies(not(implies(X1,not(truth))),implies(X0,not(truth))))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f29,f2105])).
% 10.73/16.98 fof(f2153,plain,(
% 10.73/16.98 ![X0,X1]: (implies(X0,not(X1))=implies(not(not(X1)),implies(X0,not(truth))))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f29,f2152])).
% 10.73/16.98 fof(f2154,plain,(
% 10.73/16.98 ![X0,X1]: (implies(X0,not(X1))=implies(X1,implies(X0,not(truth))))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f30,f2153])).
% 10.73/16.98 fof(f2155,plain,(
% 10.73/16.98 ![X0,X1]: (implies(X0,not(X1))=implies(X1,not(X0)))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f29,f2154])).
% 10.73/16.98 fof(f2523,plain,(
% 10.73/16.98 ![X0,X1]: (implies(implies(not(X0),X1),X1)=implies(X0,not(implies(X1,not(X0)))))),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f20,f2155])).
% 10.73/16.98 fof(f2572,plain,(
% 10.73/16.98 ![X0,X1,X2]: (implies(X0,implies(X1,not(X2)))=implies(X1,implies(X2,not(X0))))),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f2155,f28])).
% 10.73/16.98 fof(f2721,plain,(
% 10.73/16.98 ![X0,X1,X2]: (implies(not(X0),implies(X1,not(X2)))=implies(X1,implies(X2,X0)))),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f30,f2572])).
% 10.73/16.98 fof(f4141,plain,(
% 10.73/16.98 ![X0,X1]: (implies(implies(implies(not(not(X0)),X1),X1),not(implies(X1,not(not(X0)))))=implies(X0,not(implies(not(implies(X1,not(not(X0)))),not(X0)))))),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f2523,f2523])).
% 10.73/16.98 fof(f4280,plain,(
% 10.73/16.98 ![X0,X1]: (implies(implies(implies(X0,X1),X1),not(implies(X1,not(not(X0)))))=implies(X0,not(implies(not(implies(X1,not(not(X0)))),not(X0)))))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f30,f4141])).
% 10.73/16.98 fof(f4281,plain,(
% 10.73/16.98 ![X0,X1]: (implies(implies(implies(X0,X1),X1),not(implies(X1,X0)))=implies(X0,not(implies(not(implies(X1,not(not(X0)))),not(X0)))))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f30,f4280])).
% 10.73/16.98 fof(f4282,plain,(
% 10.73/16.98 ![X0,X1]: (implies(implies(implies(X0,X1),X1),not(implies(X1,X0)))=implies(X0,not(implies(X0,implies(X1,not(not(X0)))))))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f31,f4281])).
% 10.73/16.98 fof(f4283,plain,(
% 10.73/16.98 ![X0,X1]: (implies(implies(implies(X0,X1),X1),not(implies(X1,X0)))=implies(X0,not(implies(X0,implies(X1,X0)))))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f30,f4282])).
% 10.73/16.98 fof(f4284,plain,(
% 10.73/16.98 ![X0,X1]: (implies(implies(implies(X0,X1),X1),not(implies(X1,X0)))=implies(X0,not(truth)))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f25,f4283])).
% 10.73/16.98 fof(f4285,plain,(
% 10.73/16.98 ![X0,X1]: (implies(implies(implies(X0,X1),X1),not(implies(X1,X0)))=not(X0))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f29,f4284])).
% 10.73/16.98 fof(f5180,plain,(
% 10.73/16.98 implies(implies(truth,sF2_fnc),not(implies(sF2_fnc,b)))=not(b)),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f539,f4285])).
% 10.73/16.98 fof(f5366,plain,(
% 10.73/16.98 implies(sF2_fnc,not(implies(sF2_fnc,b)))=not(b)),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f18,f5180])).
% 10.73/16.98 fof(f5803,plain,(
% 10.73/16.98 ![X0]: (implies(not(X0),not(b))=implies(sF2_fnc,implies(implies(sF2_fnc,b),X0)))),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f5366,f2721])).
% 10.73/16.98 fof(f5846,plain,(
% 10.73/16.98 ![X0]: (implies(b,X0)=implies(sF2_fnc,implies(implies(sF2_fnc,b),X0)))),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f31,f5803])).
% 10.73/16.98 fof(f7349,plain,(
% 10.73/16.98 implies(b,a)=implies(sF2_fnc,sF3_fnc)),
% 10.73/16.98 inference(paramodulation,[status(thm)],[f636,f5846])).
% 10.73/16.98 fof(f7426,plain,(
% 10.73/16.98 sF3_fnc=implies(sF2_fnc,sF3_fnc)),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f34,f7349])).
% 10.73/16.98 fof(f7446,plain,(
% 10.73/16.98 sF0_fnc=implies(sF1_fnc,sF1_fnc)),
% 10.73/16.98 inference(backward_demodulation,[status(thm)],[f7730,f36])).
% 10.73/16.98 fof(f7730,plain,(
% 10.73/16.98 sF3_fnc=sF1_fnc),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f35,f7426])).
% 10.73/16.98 fof(f7866,plain,(
% 10.73/16.98 sF0_fnc=truth),
% 10.73/16.98 inference(forward_demodulation,[status(thm)],[f22,f7446])).
% 10.73/17.00 fof(f7867,plain,(
% 10.73/17.00 $false),
% 10.73/17.00 inference(forward_subsumption_resolution,[status(thm)],[f7866,f37])).
% 10.73/17.00 % SZS output end CNFRefutation for theBenchmark.p
% 2.72/17.02 % Elapsed time: 1.427966 seconds
% 2.72/17.02 % CPU time: 11.152468 seconds
% 2.72/17.02 % Total memory used: 127.931 MB
% 2.72/17.02 % Net memory used: 125.367 MB
%------------------------------------------------------------------------------