%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG138+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 11:49:41 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG138+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 13:03:29 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.39 fof(f1,axiom,(
% 0.13/0.39 ( ( op(e0,e0) = e0| op(e0,e0) = e1| op(e0,e0) = e2| op(e0,e0) = e3 )& ( op(e0,e1) = e0| op(e0,e1) = e1| op(e0,e1) = e2| op(e0,e1) = e3 )& ( op(e0,e2) = e0| op(e0,e2) = e1| op(e0,e2) = e2| op(e0,e2) = e3 )& ( op(e0,e3) = e0| op(e0,e3) = e1| op(e0,e3) = e2| op(e0,e3) = e3 )& ( op(e1,e0) = e0| op(e1,e0) = e1| op(e1,e0) = e2| op(e1,e0) = e3 )& ( op(e1,e1) = e0| op(e1,e1) = e1| op(e1,e1) = e2| op(e1,e1) = e3 )& ( op(e1,e2) = e0| op(e1,e2) = e1| op(e1,e2) = e2| op(e1,e2) = e3 )& ( op(e1,e3) = e0| op(e1,e3) = e1| op(e1,e3) = e2| op(e1,e3) = e3 )& ( op(e2,e0) = e0| op(e2,e0) = e1| op(e2,e0) = e2| op(e2,e0) = e3 )& ( op(e2,e1) = e0| op(e2,e1) = e1| op(e2,e1) = e2| op(e2,e1) = e3 )& ( op(e2,e2) = e0| op(e2,e2) = e1| op(e2,e2) = e2| op(e2,e2) = e3 )& ( op(e2,e3) = e0| op(e2,e3) = e1| op(e2,e3) = e2| op(e2,e3) = e3 )& ( op(e3,e0) = e0| op(e3,e0) = e1| op(e3,e0) = e2| op(e3,e0) = e3 )& ( op(e3,e1) = e0| op(e3,e1) = e1| op(e3,e1) = e2| op(e3,e1) = e3 )& ( op(e3,e2) = e0| op(e3,e2) = e1| op(e3,e2) = e2| op(e3,e2) = e3 )& ( op(e3,e3) = e0| op(e3,e3) = e1| op(e3,e3) = e2| op(e3,e3) = e3 ) ) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f2,axiom,(
% 0.13/0.39 ( ( op(e0,e0) = e0| op(e0,e1) = e0| op(e0,e2) = e0| op(e0,e3) = e0 )& ( op(e0,e0) = e0| op(e1,e0) = e0| op(e2,e0) = e0| op(e3,e0) = e0 )& ( op(e0,e0) = e1| op(e0,e1) = e1| op(e0,e2) = e1| op(e0,e3) = e1 )& ( op(e0,e0) = e1| op(e1,e0) = e1| op(e2,e0) = e1| op(e3,e0) = e1 )& ( op(e0,e0) = e2| op(e0,e1) = e2| op(e0,e2) = e2| op(e0,e3) = e2 )& ( op(e0,e0) = e2| op(e1,e0) = e2| op(e2,e0) = e2| op(e3,e0) = e2 )& ( op(e0,e0) = e3| op(e0,e1) = e3| op(e0,e2) = e3| op(e0,e3) = e3 )& ( op(e0,e0) = e3| op(e1,e0) = e3| op(e2,e0) = e3| op(e3,e0) = e3 )& ( op(e1,e0) = e0| op(e1,e1) = e0| op(e1,e2) = e0| op(e1,e3) = e0 )& ( op(e0,e1) = e0| op(e1,e1) = e0| op(e2,e1) = e0| op(e3,e1) = e0 )& ( op(e1,e0) = e1| op(e1,e1) = e1| op(e1,e2) = e1| op(e1,e3) = e1 )& ( op(e0,e1) = e1| op(e1,e1) = e1| op(e2,e1) = e1| op(e3,e1) = e1 )& ( op(e1,e0) = e2| op(e1,e1) = e2| op(e1,e2) = e2| op(e1,e3) = e2 )& ( op(e0,e1) = e2| op(e1,e1) = e2| op(e2,e1) = e2| op(e3,e1) = e2 )& ( op(e1,e0) = e3| op(e1,e1) = e3| op(e1,e2) = e3| op(e1,e3) = e3 )& ( op(e0,e1) = e3| op(e1,e1) = e3| op(e2,e1) = e3| op(e3,e1) = e3 )& ( op(e2,e0) = e0| op(e2,e1) = e0| op(e2,e2) = e0| op(e2,e3) = e0 )& ( op(e0,e2) = e0| op(e1,e2) = e0| op(e2,e2) = e0| op(e3,e2) = e0 )& ( op(e2,e0) = e1| op(e2,e1) = e1| op(e2,e2) = e1| op(e2,e3) = e1 )& ( op(e0,e2) = e1| op(e1,e2) = e1| op(e2,e2) = e1| op(e3,e2) = e1 )& ( op(e2,e0) = e2| op(e2,e1) = e2| op(e2,e2) = e2| op(e2,e3) = e2 )& ( op(e0,e2) = e2| op(e1,e2) = e2| op(e2,e2) = e2| op(e3,e2) = e2 )& ( op(e2,e0) = e3| op(e2,e1) = e3| op(e2,e2) = e3| op(e2,e3) = e3 )& ( op(e0,e2) = e3| op(e1,e2) = e3| op(e2,e2) = e3| op(e3,e2) = e3 )& ( op(e3,e0) = e0| op(e3,e1) = e0| op(e3,e2) = e0| op(e3,e3) = e0 )& ( op(e0,e3) = e0| op(e1,e3) = e0| op(e2,e3) = e0| op(e3,e3) = e0 )& ( op(e3,e0) = e1| op(e3,e1) = e1| op(e3,e2) = e1| op(e3,e3) = e1 )& ( op(e0,e3) = e1| op(e1,e3) = e1| op(e2,e3) = e1| op(e3,e3) = e1 )& ( op(e3,e0) = e2| op(e3,e1) = e2| op(e3,e2) = e2| op(e3,e3) = e2 )& ( op(e0,e3) = e2| op(e1,e3) = e2| op(e2,e3) = e2| op(e3,e3) = e2 )& ( op(e3,e0) = e3| op(e3,e1) = e3| op(e3,e2) = e3| op(e3,e3) = e3 )& ( op(e0,e3) = e3| op(e1,e3) = e3| op(e2,e3) = e3| op(e3,e3) = e3 ) ) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f3,axiom,(
% 0.13/0.39 ( op(e0,e0) != op(e1,e0)& op(e0,e0) != op(e2,e0)& op(e0,e0) != op(e3,e0)& op(e1,e0) != op(e2,e0)& op(e1,e0) != op(e3,e0)& op(e2,e0) != op(e3,e0)& op(e0,e1) != op(e1,e1)& op(e0,e1) != op(e2,e1)& op(e0,e1) != op(e3,e1)& op(e1,e1) != op(e2,e1)& op(e1,e1) != op(e3,e1)& op(e2,e1) != op(e3,e1)& op(e0,e2) != op(e1,e2)& op(e0,e2) != op(e2,e2)& op(e0,e2) != op(e3,e2)& op(e1,e2) != op(e2,e2)& op(e1,e2) != op(e3,e2)& op(e2,e2) != op(e3,e2)& op(e0,e3) != op(e1,e3)& op(e0,e3) != op(e2,e3)& op(e0,e3) != op(e3,e3)& op(e1,e3) != op(e2,e3)& op(e1,e3) != op(e3,e3)& op(e2,e3) != op(e3,e3)& op(e0,e0) != op(e0,e1)& op(e0,e0) != op(e0,e2)& op(e0,e0) != op(e0,e3)& op(e0,e1) != op(e0,e2)& op(e0,e1) != op(e0,e3)& op(e0,e2) != op(e0,e3)& op(e1,e0) != op(e1,e1)& op(e1,e0) != op(e1,e2)& op(e1,e0) != op(e1,e3)& op(e1,e1) != op(e1,e2)& op(e1,e1) != op(e1,e3)& op(e1,e2) != op(e1,e3)& op(e2,e0) != op(e2,e1)& op(e2,e0) != op(e2,e2)& op(e2,e0) != op(e2,e3)& op(e2,e1) != op(e2,e2)& op(e2,e1) != op(e2,e3)& op(e2,e2) != op(e2,e3)& op(e3,e0) != op(e3,e1)& op(e3,e0) != op(e3,e2)& op(e3,e0) != op(e3,e3)& op(e3,e1) != op(e3,e2)& op(e3,e1) != op(e3,e3)& op(e3,e2) != op(e3,e3) ) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f4,axiom,(
% 0.13/0.39 ( e0 != e1& e0 != e2& e0 != e3& e1 != e2& e1 != e3& e2 != e3 ) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f5,axiom,(
% 0.13/0.39 ( op(e0,e0) = e0& op(e1,e1) = e1& op(e2,e2) = e2& op(e3,e3) = e3 ) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f6,axiom,(
% 0.13/0.39 ~ ( e0 = op(e2,e3)& e1 = op(op(e2,e3),e3) ) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f12,axiom,(
% 0.13/0.39 ~ ( e1 = op(e2,e3)& e0 = op(op(e2,e3),e3) ) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f33,plain,(
% 0.13/0.39 op(e0,e3)=e0|op(e0,e3)=e1|op(e0,e3)=e2|op(e0,e3)=e3),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.39 fof(f37,plain,(
% 0.13/0.39 op(e1,e3)=e0|op(e1,e3)=e1|op(e1,e3)=e2|op(e1,e3)=e3),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.39 fof(f41,plain,(
% 0.13/0.39 op(e2,e3)=e0|op(e2,e3)=e1|op(e2,e3)=e2|op(e2,e3)=e3),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.39 fof(f71,plain,(
% 0.13/0.39 op(e0,e3)=e0|op(e1,e3)=e0|op(e2,e3)=e0|op(e3,e3)=e0),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/0.39 fof(f96,plain,(
% 0.13/0.39 ~op(e0,e3)=op(e1,e3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f98,plain,(
% 0.13/0.39 ~op(e0,e3)=op(e3,e3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f99,plain,(
% 0.13/0.39 ~op(e1,e3)=op(e2,e3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f100,plain,(
% 0.13/0.39 ~op(e1,e3)=op(e3,e3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f101,plain,(
% 0.13/0.39 ~op(e2,e3)=op(e3,e3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f104,plain,(
% 0.13/0.39 ~op(e0,e0)=op(e0,e3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f112,plain,(
% 0.13/0.39 ~op(e1,e1)=op(e1,e3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f119,plain,(
% 0.13/0.39 ~op(e2,e2)=op(e2,e3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f128,plain,(
% 0.13/0.39 ~e0=e3),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/0.39 fof(f132,plain,(
% 0.13/0.39 op(e0,e0)=e0),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.39 fof(f133,plain,(
% 0.13/0.39 op(e1,e1)=e1),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.39 fof(f134,plain,(
% 0.13/0.39 op(e2,e2)=e2),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.39 fof(f135,plain,(
% 0.13/0.39 op(e3,e3)=e3),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.39 fof(f136,plain,(
% 0.13/0.39 (~e0=op(e2,e3)|~e1=op(op(e2,e3),e3))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.13/0.39 fof(f137,plain,(
% 0.13/0.39 ~e0=op(e2,e3)|~e1=op(op(e2,e3),e3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f136])).
% 0.13/0.39 fof(f148,plain,(
% 0.13/0.39 (~e1=op(e2,e3)|~e0=op(op(e2,e3),e3))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.13/0.39 fof(f149,plain,(
% 0.13/0.39 ~e1=op(e2,e3)|~e0=op(op(e2,e3),e3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f148])).
% 0.13/0.39 fof(f184,plain,(
% 0.13/0.39 ~e0=op(e0,e3)),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f132,f104])).
% 0.13/0.39 fof(f199,plain,(
% 0.13/0.39 ~e1=op(e1,e3)),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f133,f112])).
% 0.13/0.39 fof(f214,plain,(
% 0.13/0.39 ~e2=op(e2,e3)),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f134,f119])).
% 0.13/0.39 fof(f232,plain,(
% 0.13/0.39 ~op(e2,e3)=e3),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f135,f101])).
% 0.13/0.39 fof(f233,plain,(
% 0.13/0.39 ~op(e1,e3)=e3),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f135,f100])).
% 0.13/0.39 fof(f234,plain,(
% 0.13/0.39 ~op(e0,e3)=e3),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f135,f98])).
% 0.13/0.39 fof(f241,plain,(
% 0.13/0.39 op(e0,e3)=e0|op(e1,e3)=e0|op(e2,e3)=e0|e3=e0),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f135,f71])).
% 0.13/0.39 fof(f244,plain,(
% 0.13/0.39 op(e0,e3)=e1|op(e0,e3)=e2|op(e0,e3)=e3),
% 0.13/0.39 inference(backward_subsumption_resolution,[status(thm)],[f33,f184])).
% 0.13/0.39 fof(f256,plain,(
% 0.13/0.39 op(e1,e3)=e0|op(e1,e3)=e2|op(e1,e3)=e3),
% 0.13/0.39 inference(backward_subsumption_resolution,[status(thm)],[f37,f199])).
% 0.13/0.39 fof(f269,plain,(
% 0.13/0.39 op(e2,e3)=e0|op(e2,e3)=e1|op(e2,e3)=e3),
% 0.13/0.39 inference(backward_subsumption_resolution,[status(thm)],[f41,f214])).
% 0.13/0.39 fof(f293,plain,(
% 0.13/0.39 op(e1,e3)=e0|op(e2,e3)=e0|e3=e0),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f241,f184])).
% 0.13/0.39 fof(f295,plain,(
% 0.13/0.39 op(e0,e3)=e1|op(e0,e3)=e2),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f244,f234])).
% 0.13/0.39 fof(f301,plain,(
% 0.13/0.39 op(e1,e3)=e0|op(e1,e3)=e2),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f256,f233])).
% 0.13/0.39 fof(f305,plain,(
% 0.13/0.39 op(e2,e3)=e0|op(e2,e3)=e1),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f269,f232])).
% 0.13/0.39 fof(f333,plain,(
% 0.13/0.39 ~op(e0,e3)=e2|op(e1,e3)=e0),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f301,f96])).
% 0.13/0.39 fof(f462,plain,(
% 0.13/0.39 ~e1=op(e2,e3)|~e0=op(e1,e3)|op(e2,e3)=e0),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f305,f149])).
% 0.13/0.39 fof(f463,plain,(
% 0.13/0.39 op(e2,e3)=e0|e3=e0),
% 0.13/0.39 inference(backward_subsumption_resolution,[status(thm)],[f293,f464])).
% 0.13/0.39 fof(f464,plain,(
% 0.13/0.39 ~e0=op(e1,e3)|op(e2,e3)=e0),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f462,f305])).
% 0.13/0.39 fof(f467,plain,(
% 0.13/0.39 ~e0=op(e2,e3)|~e1=op(e0,e3)),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f480,f137])).
% 0.13/0.39 fof(f470,plain,(
% 0.13/0.39 ~op(e1,e3)=e0),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f480,f99])).
% 0.13/0.39 fof(f480,plain,(
% 0.13/0.39 op(e2,e3)=e0),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f463,f128])).
% 0.13/0.39 fof(f482,plain,(
% 0.13/0.39 ~e0=e0|~e1=op(e0,e3)),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f480,f467])).
% 0.13/0.39 fof(f484,plain,(
% 0.13/0.39 op(e0,e3)=e2),
% 0.13/0.39 inference(backward_subsumption_resolution,[status(thm)],[f295,f486])).
% 0.13/0.39 fof(f486,plain,(
% 0.13/0.39 ~e1=op(e0,e3)),
% 0.13/0.39 inference(trivial_equality_resolution,[status(thm)],[f482])).
% 0.13/0.39 fof(f492,plain,(
% 0.13/0.39 ~op(e0,e3)=e2),
% 0.13/0.39 inference(backward_subsumption_resolution,[status(thm)],[f333,f470])).
% 0.13/0.39 fof(f558,plain,(
% 0.13/0.39 ~e2=e2),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f484,f492])).
% 0.13/0.39 fof(f559,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(trivial_equality_resolution,[status(thm)],[f558])).
% 0.13/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.39 % Elapsed time: 0.025717 seconds
% 0.13/0.39 % CPU time: 0.050609 seconds
% 0.13/0.39 % Total memory used: 2.882 MB
% 0.13/0.39 % Net memory used: 2.834 MB
%------------------------------------------------------------------------------