%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL208-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 01:09:36 PM UTC 2026
% Result : Unsatisfiable 16.93s 2.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL208-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 00:14:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 16.93/2.58 % Refutation found
% 16.93/2.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 16.93/2.58 % SZS output start CNFRefutation for theBenchmark
% 16.93/2.58 fof(f1,axiom,(
% 16.93/2.58 (![A]: (axiom(implies(or(A,A),A)) ))),
% 16.93/2.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.93/2.58 fof(f2,axiom,(
% 16.93/2.58 (![A,B]: (axiom(implies(A,or(B,A))) ))),
% 16.93/2.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.93/2.58 fof(f3,axiom,(
% 16.93/2.58 (![A,B]: (axiom(implies(or(A,B),or(B,A))) ))),
% 16.93/2.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.93/2.58 fof(f4,axiom,(
% 16.93/2.58 (![A,B,C]: (axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ))),
% 16.93/2.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.93/2.58 fof(f5,axiom,(
% 16.93/2.58 (![A,B,C]: (axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ))),
% 16.93/2.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.93/2.58 fof(f6,axiom,(
% 16.93/2.58 (![X,Y]: (implies(X,Y) = or(not(X),Y) ))),
% 16.93/2.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.93/2.58 fof(f7,axiom,(
% 16.93/2.58 (![X]: (( theorem(X)| ~ axiom(X) ) ))),
% 16.93/2.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.93/2.58 fof(f8,axiom,(
% 16.93/2.58 (![X,Y]: (( theorem(X)| ~ theorem(implies(Y,X))| ~ theorem(Y) ) ))),
% 16.93/2.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.93/2.58 fof(f9,negated_conjecture,(
% 16.93/2.58 ~ theorem(implies(or(p,q),implies(not(p),q))) ),
% 16.93/2.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 16.93/2.58 fof(f10,plain,(
% 16.93/2.58 ![X0]: (axiom(implies(or(X0,X0),X0)))),
% 16.93/2.58 inference(cnf_transformation,[status(thm)],[f1])).
% 16.93/2.58 fof(f11,plain,(
% 16.93/2.58 ![X0,X1]: (axiom(implies(X0,or(X1,X0))))),
% 16.93/2.58 inference(cnf_transformation,[status(thm)],[f2])).
% 16.93/2.58 fof(f12,plain,(
% 16.93/2.58 ![X0,X1]: (axiom(implies(or(X0,X1),or(X1,X0))))),
% 16.93/2.58 inference(cnf_transformation,[status(thm)],[f3])).
% 16.93/2.58 fof(f13,plain,(
% 16.93/2.58 ![X0,X1,X2]: (axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 16.93/2.58 inference(cnf_transformation,[status(thm)],[f4])).
% 16.93/2.58 fof(f14,plain,(
% 16.93/2.58 ![X0,X1,X2]: (axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 16.93/2.58 inference(cnf_transformation,[status(thm)],[f5])).
% 16.93/2.58 fof(f15,plain,(
% 16.93/2.58 ![X0,X1]: (implies(X0,X1)=or(not(X0),X1))),
% 16.93/2.58 inference(cnf_transformation,[status(thm)],[f6])).
% 16.93/2.58 fof(f16,plain,(
% 16.93/2.58 ![X0]: (theorem(X0)|~axiom(X0))),
% 16.93/2.58 inference(cnf_transformation,[status(thm)],[f7])).
% 16.93/2.58 fof(f17,plain,(
% 16.93/2.58 ![Y]: ((![X]: (theorem(X)|~theorem(implies(Y,X))))|~theorem(Y))),
% 16.93/2.58 inference(miniscoping,[status(thm)],[f8])).
% 16.93/2.58 fof(f18,plain,(
% 16.93/2.58 ![X0,X1]: (theorem(X0)|~theorem(implies(X1,X0))|~theorem(X1))),
% 16.93/2.58 inference(cnf_transformation,[status(thm)],[f17])).
% 16.93/2.58 fof(f19,plain,(
% 16.93/2.58 ~theorem(implies(or(p,q),implies(not(p),q)))),
% 16.93/2.58 inference(cnf_transformation,[status(thm)],[f9])).
% 16.93/2.58 fof(f20,plain,(
% 16.93/2.58 ![X0]: (theorem(implies(or(X0,X0),X0)))),
% 16.93/2.58 inference(resolution,[status(thm)],[f10,f16])).
% 16.93/2.58 fof(f22,plain,(
% 16.93/2.58 ![X0]: (theorem(X0)|~theorem(or(X0,X0)))),
% 16.93/2.58 inference(resolution,[status(thm)],[f20,f18])).
% 16.93/2.58 fof(f24,plain,(
% 16.93/2.58 ![X0,X1]: (theorem(implies(X0,or(X1,X0))))),
% 16.93/2.58 inference(resolution,[status(thm)],[f11,f16])).
% 16.93/2.58 fof(f27,plain,(
% 16.93/2.58 ![X0,X1]: (theorem(or(X0,X1))|~theorem(X1))),
% 16.93/2.58 inference(resolution,[status(thm)],[f24,f18])).
% 16.93/2.58 fof(f29,plain,(
% 16.93/2.58 ![X0,X1]: (theorem(implies(or(X0,X1),or(X1,X0))))),
% 16.93/2.58 inference(resolution,[status(thm)],[f12,f16])).
% 16.93/2.58 fof(f32,plain,(
% 16.93/2.58 ![X0,X1,X2]: (theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))))),
% 16.93/2.58 inference(resolution,[status(thm)],[f13,f16])).
% 16.93/2.58 fof(f41,plain,(
% 16.93/2.58 ![X0,X1,X2]: (theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))))),
% 16.93/2.58 inference(resolution,[status(thm)],[f14,f16])).
% 16.93/2.58 fof(f51,plain,(
% 16.93/2.58 ![X0,X1]: (theorem(or(X0,X1))|~theorem(or(X1,X0)))),
% 16.93/2.58 inference(resolution,[status(thm)],[f29,f18])).
% 16.93/2.58 fof(f52,plain,(
% 16.93/2.58 ![X0,X1]: (theorem(implies(implies(X0,X1),or(X1,not(X0)))))),
% 16.93/2.58 inference(paramodulation,[status(thm)],[f15,f29])).
% 16.93/2.58 fof(f53,plain,(
% 16.93/2.58 ![X0,X1]: (theorem(implies(or(X0,not(X1)),implies(X1,X0))))),
% 16.93/2.58 inference(paramodulation,[status(thm)],[f15,f29])).
% 16.93/2.58 fof(f60,plain,(
% 16.93/2.58 ![X0,X1,X2]: (theorem(or(X0,or(X1,X2)))|~theorem(or(X1,or(X0,X2))))),
% 16.93/2.58 inference(resolution,[status(thm)],[f32,f18])).
% 16.93/2.58 fof(f61,plain,(
% 16.93/2.58 ![X0,X1,X2]: (theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))))),
% 16.93/2.58 inference(paramodulation,[status(thm)],[f15,f32])).
% 16.93/2.58 fof(f65,plain,(
% 16.93/2.59 ![X0,X1,X2]: (theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))))),
% 16.93/2.59 inference(forward_demodulation,[status(thm)],[f15,f61])).
% 16.93/2.59 fof(f87,plain,(
% 16.93/2.59 ![X0,X1,X2]: (theorem(implies(or(X0,X1),or(X0,X2)))|~theorem(implies(X1,X2)))),
% 16.93/2.59 inference(resolution,[status(thm)],[f41,f18])).
% 16.93/2.59 fof(f94,plain,(
% 16.93/2.59 ![X0,X1]: (theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))))),
% 16.93/2.59 inference(paramodulation,[status(thm)],[f15,f52])).
% 16.93/2.59 fof(f95,plain,(
% 16.93/2.59 ![X0,X1]: (theorem(implies(X0,X1))|~theorem(or(X1,not(X0))))),
% 16.93/2.59 inference(resolution,[status(thm)],[f53,f18])).
% 16.93/2.59 fof(f102,plain,(
% 16.93/2.59 ![X0,X1,X2]: (theorem(or(X0,or(X1,X2)))|~theorem(or(X0,X2)))),
% 16.93/2.59 inference(resolution,[status(thm)],[f60,f27])).
% 16.93/2.59 fof(f103,plain,(
% 16.93/2.59 ![X0,X1,X2]: (theorem(or(X0,or(not(X1),X2)))|~theorem(implies(X1,or(X0,X2))))),
% 16.93/2.59 inference(paramodulation,[status(thm)],[f15,f60])).
% 16.93/2.59 fof(f105,plain,(
% 16.93/2.59 ![X0,X1,X2]: (theorem(or(X0,implies(X1,X2)))|~theorem(implies(X1,or(X0,X2))))),
% 16.93/2.59 inference(forward_demodulation,[status(thm)],[f15,f103])).
% 16.93/2.59 fof(f136,plain,(
% 16.93/2.59 ![X0,X1]: (~theorem(or(or(X0,X1),X1))|theorem(or(X0,X1)))),
% 16.93/2.59 inference(resolution,[status(thm)],[f102,f22])).
% 16.93/2.59 fof(f168,plain,(
% 16.93/2.59 ![X0,X1,X2]: (~theorem(implies(X0,X1))|theorem(or(X2,X1))|~theorem(or(X2,X0)))),
% 16.93/2.59 inference(resolution,[status(thm)],[f87,f18])).
% 16.93/2.59 fof(f194,plain,(
% 16.93/2.59 ![X0,X1,X2]: (~theorem(implies(X0,or(or(X1,implies(X0,X2)),X2)))|theorem(or(X1,implies(X0,X2))))),
% 16.93/2.59 inference(resolution,[status(thm)],[f105,f136])).
% 16.93/2.59 fof(f197,plain,(
% 16.93/2.59 ![X0,X1,X2]: (theorem(implies(X0,implies(X1,X2)))|~theorem(implies(X1,or(not(X0),X2))))),
% 16.93/2.59 inference(paramodulation,[status(thm)],[f15,f105])).
% 16.93/2.59 fof(f198,plain,(
% 16.93/2.59 ![X0,X1,X2]: (theorem(implies(X0,implies(X1,X2)))|~theorem(implies(X1,implies(X0,X2))))),
% 16.93/2.59 inference(forward_demodulation,[status(thm)],[f15,f197])).
% 16.93/2.59 fof(f290,plain,(
% 16.93/2.59 ![X0,X1,X2]: (~theorem(implies(X0,not(X1)))|~theorem(or(X2,X0))|theorem(implies(X1,X2)))),
% 16.93/2.59 inference(resolution,[status(thm)],[f168,f95])).
% 16.93/2.59 fof(f293,plain,(
% 16.93/2.59 ![X0,X1]: (~theorem(implies(X0,X1))|~theorem(or(X1,X0))|theorem(X1))),
% 16.93/2.59 inference(resolution,[status(thm)],[f168,f22])).
% 16.93/2.59 fof(f388,plain,(
% 16.93/2.59 ~theorem(implies(not(p),implies(or(p,q),q)))),
% 16.93/2.59 inference(resolution,[status(thm)],[f198,f19])).
% 16.93/2.59 fof(f604,plain,(
% 16.93/2.59 ![X0,X1]: (theorem(or(X0,implies(X1,X1))))),
% 16.93/2.59 inference(resolution,[status(thm)],[f194,f24])).
% 16.93/2.59 fof(f618,plain,(
% 16.93/2.59 ![X0,X1]: (~theorem(implies(implies(X0,X0),X1))|theorem(X1))),
% 16.93/2.59 inference(resolution,[status(thm)],[f604,f293])).
% 16.93/2.59 fof(f825,plain,(
% 16.93/2.59 ![X0,X1]: (theorem(or(X0,implies(or(X0,X1),X1))))),
% 16.93/2.59 inference(resolution,[status(thm)],[f618,f65])).
% 16.93/2.59 fof(f826,plain,(
% 16.93/2.59 ![X0]: (theorem(implies(X0,not(not(X0)))))),
% 16.93/2.59 inference(resolution,[status(thm)],[f618,f94])).
% 16.93/2.59 fof(f904,plain,(
% 16.93/2.59 ![X0,X1]: (~theorem(or(X0,X1))|theorem(implies(not(X1),X0)))),
% 16.93/2.59 inference(resolution,[status(thm)],[f826,f290])).
% 16.93/2.59 fof(f1575,plain,(
% 16.93/2.59 ![X0,X1]: (theorem(or(implies(or(X0,X1),X1),X0)))),
% 16.93/2.59 inference(resolution,[status(thm)],[f825,f51])).
% 16.93/2.59 fof(f2540,plain,(
% 16.93/2.59 ![X0,X1]: (theorem(implies(not(X0),implies(or(X0,X1),X1))))),
% 16.93/2.59 inference(resolution,[status(thm)],[f904,f1575])).
% 16.93/2.59 fof(f3786,plain,(
% 16.93/2.59 $false),
% 16.93/2.59 inference(backward_subsumption_resolution,[status(thm)],[f388,f2540])).
% 16.93/2.59 % SZS output end CNFRefutation for theBenchmark.p
% 2.98/2.62 % Elapsed time: 2.231000 seconds
% 2.98/2.62 % CPU time: 17.395213 seconds
% 2.98/2.62 % Total memory used: 228.959 MB
% 2.98/2.62 % Net memory used: 211.017 MB
%------------------------------------------------------------------------------