%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG054+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 : n016.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 11:49:32 AM UTC 2026
% Result : Theorem 0.13s 10.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG054+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n016.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Mon Sep 21 12:59:35 UTC 2026
% 0.10/10.37 % CPUTime :
% 0.10/10.39 % Drodi V4.1.1
% 0.13/10.43 % Refutation found
% 0.13/10.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/10.43 % SZS output start CNFRefutation for theBenchmark
% 0.13/10.43 fof(f2,axiom,(
% 0.13/10.43 ( op(unit,e0) = e0& op(e0,unit) = e0& op(unit,e1) = e1& op(e1,unit) = e1& op(unit,e2) = e2& op(e2,unit) = e2& op(unit,e3) = e3& op(e3,unit) = e3& op(unit,e4) = e4& op(e4,unit) = e4& ( unit = e0| unit = e1| unit = e2| unit = e3| unit = e4 ) ) ),
% 0.13/10.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/10.43 fof(f4,axiom,(
% 0.13/10.43 ( op(e0,e0) != op(e1,e0)& op(e0,e0) != op(e2,e0)& op(e0,e0) != op(e3,e0)& op(e0,e0) != op(e4,e0)& op(e1,e0) != op(e2,e0)& op(e1,e0) != op(e3,e0)& op(e1,e0) != op(e4,e0)& op(e2,e0) != op(e3,e0)& op(e2,e0) != op(e4,e0)& op(e3,e0) != op(e4,e0)& op(e0,e1) != op(e1,e1)& op(e0,e1) != op(e2,e1)& op(e0,e1) != op(e3,e1)& op(e0,e1) != op(e4,e1)& op(e1,e1) != op(e2,e1)& op(e1,e1) != op(e3,e1)& op(e1,e1) != op(e4,e1)& op(e2,e1) != op(e3,e1)& op(e2,e1) != op(e4,e1)& op(e3,e1) != op(e4,e1)& op(e0,e2) != op(e1,e2)& op(e0,e2) != op(e2,e2)& op(e0,e2) != op(e3,e2)& op(e0,e2) != op(e4,e2)& op(e1,e2) != op(e2,e2)& op(e1,e2) != op(e3,e2)& op(e1,e2) != op(e4,e2)& op(e2,e2) != op(e3,e2)& op(e2,e2) != op(e4,e2)& op(e3,e2) != op(e4,e2)& op(e0,e3) != op(e1,e3)& op(e0,e3) != op(e2,e3)& op(e0,e3) != op(e3,e3)& op(e0,e3) != op(e4,e3)& op(e1,e3) != op(e2,e3)& op(e1,e3) != op(e3,e3)& op(e1,e3) != op(e4,e3)& op(e2,e3) != op(e3,e3)& op(e2,e3) != op(e4,e3)& op(e3,e3) != op(e4,e3)& op(e0,e4) != op(e1,e4)& op(e0,e4) != op(e2,e4)& op(e0,e4) != op(e3,e4)& op(e0,e4) != op(e4,e4)& op(e1,e4) != op(e2,e4)& op(e1,e4) != op(e3,e4)& op(e1,e4) != op(e4,e4)& op(e2,e4) != op(e3,e4)& op(e2,e4) != op(e4,e4)& op(e3,e4) != op(e4,e4)& op(e0,e0) != op(e0,e1)& op(e0,e0) != op(e0,e2)& op(e0,e0) != op(e0,e3)& op(e0,e0) != op(e0,e4)& op(e0,e1) != op(e0,e2)& op(e0,e1) != op(e0,e3)& op(e0,e1) != op(e0,e4)& op(e0,e2) != op(e0,e3)& op(e0,e2) != op(e0,e4)& op(e0,e3) != op(e0,e4)& op(e1,e0) != op(e1,e1)& op(e1,e0) != op(e1,e2)& op(e1,e0) != op(e1,e3)& op(e1,e0) != op(e1,e4)& op(e1,e1) != op(e1,e2)& op(e1,e1) != op(e1,e3)& op(e1,e1) != op(e1,e4)& op(e1,e2) != op(e1,e3)& op(e1,e2) != op(e1,e4)& op(e1,e3) != op(e1,e4)& op(e2,e0) != op(e2,e1)& op(e2,e0) != op(e2,e2)& op(e2,e0) != op(e2,e3)& op(e2,e0) != op(e2,e4)& op(e2,e1) != op(e2,e2)& op(e2,e1) != op(e2,e3)& op(e2,e1) != op(e2,e4)& op(e2,e2) != op(e2,e3)& op(e2,e2) != op(e2,e4)& op(e2,e3) != op(e2,e4)& op(e3,e0) != op(e3,e1)& op(e3,e0) != op(e3,e2)& op(e3,e0) != op(e3,e3)& op(e3,e0) != op(e3,e4)& op(e3,e1) != op(e3,e2)& op(e3,e1) != op(e3,e3)& op(e3,e1) != op(e3,e4)& op(e3,e2) != op(e3,e3)& op(e3,e2) != op(e3,e4)& op(e3,e3) != op(e3,e4)& op(e4,e0) != op(e4,e1)& op(e4,e0) != op(e4,e2)& op(e4,e0) != op(e4,e3)& op(e4,e0) != op(e4,e4)& op(e4,e1) != op(e4,e2)& op(e4,e1) != op(e4,e3)& op(e4,e1) != op(e4,e4)& op(e4,e2) != op(e4,e3)& op(e4,e2) != op(e4,e4)& op(e4,e3) != op(e4,e4) ) ),
% 0.13/10.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/10.43 fof(f5,axiom,(
% 0.13/10.43 ( e0 != e1& e0 != e2& e0 != e3& e0 != e4& e1 != e2& e1 != e3& e1 != e4& e2 != e3& e2 != e4& e3 != e4 ) ),
% 0.13/10.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/10.43 fof(f6,axiom,(
% 0.13/10.43 ( e0 = op(e1,op(op(e1,e1),op(e1,e1)))& e2 = op(op(e1,e1),op(e1,e1))& e3 = op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1)))& e4 = op(e1,e1) ) ),
% 0.13/10.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/10.43 fof(f7,conjecture,(
% 0.13/10.43 ~ ( ( op(e0,e0) = e0| op(e1,e1) = e0| op(e2,e2) = e0| op(e3,e3) = e0| op(e4,e4) = e0 )& ( op(e0,e0) = e1| op(e1,e1) = e1| op(e2,e2) = e1| op(e3,e3) = e1| op(e4,e4) = e1 )& ( op(e0,e0) = e2| op(e1,e1) = e2| op(e2,e2) = e2| op(e3,e3) = e2| op(e4,e4) = e2 )& ( op(e0,e0) = e3| op(e1,e1) = e3| op(e2,e2) = e3| op(e3,e3) = e3| op(e4,e4) = e3 )& ( op(e0,e0) = e4| op(e1,e1) = e4| op(e2,e2) = e4| op(e3,e3) = e4| op(e4,e4) = e4 )& ( op(e0,e0) != e0| op(e0,e0) = e0 )& ( op(e0,e0) != e1| op(e0,e1) = e0 )& ( op(e0,e0) != e2| op(e0,e2) = e0 )& ( op(e0,e0) != e3| op(e0,e3) = e0 )& ( op(e0,e0) != e4| op(e0,e4) = e0 )& ( op(e1,e1) != e0| op(e1,e0) = e1 )& ( op(e1,e1) != e1| op(e1,e1) = e1 )& ( op(e1,e1) != e2| op(e1,e2) = e1 )& ( op(e1,e1) != e3| op(e1,e3) = e1 )& ( op(e1,e1) != e4| op(e1,e4) = e1 )& ( op(e2,e2) != e0| op(e2,e0) = e2 )& ( op(e2,e2) != e1| op(e2,e1) = e2 )& ( op(e2,e2) != e2| op(e2,e2) = e2 )& ( op(e2,e2) != e3| op(e2,e3) = e2 )& ( op(e2,e2) != e4| op(e2,e4) = e2 )& ( op(e3,e3) != e0| op(e3,e0) = e3 )& ( op(e3,e3) != e1| op(e3,e1) = e3 )& ( op(e3,e3) != e2| op(e3,e2) = e3 )& ( op(e3,e3) != e3| op(e3,e3) = e3 )& ( op(e3,e3) != e4| op(e3,e4) = e3 )& ( op(e4,e4) != e0| op(e4,e0) = e4 )& ( op(e4,e4) != e1| op(e4,e1) = e4 )& ( op(e4,e4) != e2| op(e4,e2) = e4 )& ( op(e4,e4) != e3| op(e4,e3) = e4 )& ( op(e4,e4) != e4| op(e4,e4) = e4 ) ) ),
% 0.13/10.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/10.43 fof(f8,negated_conjecture,(
% 0.13/10.43 ~(~ ( ( op(e0,e0) = e0| op(e1,e1) = e0| op(e2,e2) = e0| op(e3,e3) = e0| op(e4,e4) = e0 )& ( op(e0,e0) = e1| op(e1,e1) = e1| op(e2,e2) = e1| op(e3,e3) = e1| op(e4,e4) = e1 )& ( op(e0,e0) = e2| op(e1,e1) = e2| op(e2,e2) = e2| op(e3,e3) = e2| op(e4,e4) = e2 )& ( op(e0,e0) = e3| op(e1,e1) = e3| op(e2,e2) = e3| op(e3,e3) = e3| op(e4,e4) = e3 )& ( op(e0,e0) = e4| op(e1,e1) = e4| op(e2,e2) = e4| op(e3,e3) = e4| op(e4,e4) = e4 )& ( op(e0,e0) != e0| op(e0,e0) = e0 )& ( op(e0,e0) != e1| op(e0,e1) = e0 )& ( op(e0,e0) != e2| op(e0,e2) = e0 )& ( op(e0,e0) != e3| op(e0,e3) = e0 )& ( op(e0,e0) != e4| op(e0,e4) = e0 )& ( op(e1,e1) != e0| op(e1,e0) = e1 )& ( op(e1,e1) != e1| op(e1,e1) = e1 )& ( op(e1,e1) != e2| op(e1,e2) = e1 )& ( op(e1,e1) != e3| op(e1,e3) = e1 )& ( op(e1,e1) != e4| op(e1,e4) = e1 )& ( op(e2,e2) != e0| op(e2,e0) = e2 )& ( op(e2,e2) != e1| op(e2,e1) = e2 )& ( op(e2,e2) != e2| op(e2,e2) = e2 )& ( op(e2,e2) != e3| op(e2,e3) = e2 )& ( op(e2,e2) != e4| op(e2,e4) = e2 )& ( op(e3,e3) != e0| op(e3,e0) = e3 )& ( op(e3,e3) != e1| op(e3,e1) = e3 )& ( op(e3,e3) != e2| op(e3,e2) = e3 )& ( op(e3,e3) != e3| op(e3,e3) = e3 )& ( op(e3,e3) != e4| op(e3,e4) = e3 )& ( op(e4,e4) != e0| op(e4,e0) = e4 )& ( op(e4,e4) != e1| op(e4,e1) = e4 )& ( op(e4,e4) != e2| op(e4,e2) = e4 )& ( op(e4,e4) != e3| op(e4,e3) = e4 )& ( op(e4,e4) != e4| op(e4,e4) = e4 ) ) )),
% 0.13/10.43 inference(negated_conjecture,[status(cth)],[f7])).
% 0.13/10.43 fof(f41,plain,(
% 0.13/10.43 op(e3,unit)=e3),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/10.43 fof(f43,plain,(
% 0.13/10.43 op(e4,unit)=e4),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/10.43 fof(f44,plain,(
% 0.13/10.43 unit=e0|unit=e1|unit=e2|unit=e3|unit=e4),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/10.43 fof(f111,plain,(
% 0.13/10.43 ~op(e1,e1)=op(e4,e1)),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/10.43 fof(f122,plain,(
% 0.13/10.43 ~op(e2,e2)=op(e3,e2)),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/10.43 fof(f186,plain,(
% 0.13/10.43 ~op(e4,e0)=op(e4,e2)),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/10.43 fof(f192,plain,(
% 0.13/10.43 ~op(e4,e2)=op(e4,e3)),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/10.43 fof(f203,plain,(
% 0.13/10.43 ~e2=e4),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/10.43 fof(f206,plain,(
% 0.13/10.43 e2=op(op(e1,e1),op(e1,e1))),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/10.43 fof(f207,plain,(
% 0.13/10.43 e3=op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1)))),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/10.43 fof(f208,plain,(
% 0.13/10.43 e4=op(e1,e1)),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/10.43 fof(f236,plain,(
% 0.13/10.43 ~op(e4,e4)=e2|op(e4,e2)=e4),
% 0.13/10.43 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/10.43 fof(f240,plain,(
% 0.13/10.43 e3=op(e2,op(op(e1,e1),op(e1,e1)))),
% 0.13/10.43 inference(forward_demodulation,[status(thm)],[f206,f207])).
% 0.13/10.43 fof(f246,plain,(
% 0.13/10.43 ~e3=op(e3,e2)),
% 0.13/10.43 inference(backward_demodulation,[status(thm)],[f260,f122])).
% 0.13/10.43 fof(f260,plain,(
% 0.13/10.43 e3=op(e2,e2)),
% 0.13/10.43 inference(forward_demodulation,[status(thm)],[f206,f240])).
% 0.13/10.43 fof(f261,plain,(
% 0.13/10.43 e2=op(op(e1,e1),e4)),
% 0.13/10.43 inference(backward_demodulation,[status(thm)],[f208,f206])).
% 0.13/10.43 fof(f266,plain,(
% 0.13/10.43 ~e4=op(e4,e1)),
% 0.13/10.43 inference(backward_demodulation,[status(thm)],[f208,f111])).
% 0.13/10.43 fof(f362,plain,(
% 0.13/10.43 ~e2=e2|op(e4,e2)=e4),
% 0.13/10.43 inference(backward_demodulation,[status(thm)],[f380,f236])).
% 0.13/10.43 fof(f380,plain,(
% 0.13/10.43 e2=op(e4,e4)),
% 0.13/10.43 inference(forward_demodulation,[status(thm)],[f208,f261])).
% 0.13/10.43 fof(f451,plain,(
% 0.13/10.43 ~e4=op(e4,e3)),
% 0.13/10.43 inference(backward_demodulation,[status(thm)],[f456,f192])).
% 0.13/10.44 fof(f453,plain,(
% 0.13/10.44 ~op(e4,e0)=e4),
% 0.13/10.44 inference(backward_demodulation,[status(thm)],[f456,f186])).
% 0.13/10.44 fof(f456,plain,(
% 0.13/10.44 op(e4,e2)=e4),
% 0.13/10.44 inference(trivial_equality_resolution,[status(thm)],[f362])).
% 0.13/10.44 fof(f498,plain,(
% 0.13/10.44 op(e4,e4)=e4|unit=e0|unit=e1|unit=e2|unit=e3),
% 0.13/10.44 inference(paramodulation,[status(thm)],[f44,f43])).
% 0.13/10.44 fof(f512,plain,(
% 0.13/10.44 e2=e4|unit=e0|unit=e1|unit=e2|unit=e3),
% 0.13/10.44 inference(forward_demodulation,[status(thm)],[f380,f498])).
% 0.13/10.44 fof(f513,plain,(
% 0.13/10.44 unit=e0|unit=e1|unit=e2|unit=e3),
% 0.13/10.44 inference(forward_subsumption_resolution,[status(thm)],[f512,f203])).
% 0.13/10.44 fof(f616,plain,(
% 0.13/10.44 op(e4,e3)=e4|unit=e0|unit=e1|unit=e2),
% 0.13/10.44 inference(paramodulation,[status(thm)],[f513,f43])).
% 0.13/10.44 fof(f629,plain,(
% 0.13/10.44 unit=e0|unit=e1|unit=e2),
% 0.13/10.44 inference(forward_subsumption_resolution,[status(thm)],[f616,f451])).
% 0.13/10.44 fof(f632,plain,(
% 0.13/10.44 op(e3,e2)=e3|unit=e0|unit=e1),
% 0.13/10.44 inference(paramodulation,[status(thm)],[f629,f41])).
% 0.13/10.44 fof(f642,plain,(
% 0.13/10.44 unit=e0|unit=e1),
% 0.13/10.44 inference(forward_subsumption_resolution,[status(thm)],[f632,f246])).
% 0.13/10.44 fof(f647,plain,(
% 0.13/10.44 op(e4,e1)=e4|unit=e0),
% 0.13/10.44 inference(paramodulation,[status(thm)],[f642,f43])).
% 0.13/10.44 fof(f659,plain,(
% 0.13/10.44 op(e4,e0)=e4),
% 0.13/10.44 inference(backward_demodulation,[status(thm)],[f669,f43])).
% 0.13/10.44 fof(f669,plain,(
% 0.13/10.44 unit=e0),
% 0.13/10.44 inference(forward_subsumption_resolution,[status(thm)],[f647,f266])).
% 0.13/10.44 fof(f674,plain,(
% 0.13/10.44 $false),
% 0.13/10.44 inference(forward_subsumption_resolution,[status(thm)],[f659,f453])).
% 0.13/10.44 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/10.45 % Elapsed time: 0.071333 seconds
% 0.13/10.45 % CPU time: 0.289296 seconds
% 0.13/10.45 % Total memory used: 91.615 MB
% 0.13/10.45 % Net memory used: 91.439 MB
%------------------------------------------------------------------------------