%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG441-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 11:50:11 AM UTC 2026
% Result : Unsatisfiable 47.62s 6.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG441-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % 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 13:21:54 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 47.62/6.48 % Refutation found
% 47.62/6.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 47.62/6.48 % SZS output start CNFRefutation for theBenchmark
% 47.62/6.48 fof(f1,axiom,(
% 47.62/6.48 (![A,B]: (m(A,A,B) = B ))),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f2,axiom,(
% 47.62/6.48 (![A,B]: (m(A,B,B) = A ))),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f3,axiom,(
% 47.62/6.48 (![A]: (u(A,A) = A ))),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f5,axiom,(
% 47.62/6.48 (![A,B]: (u(A,B) = u(B,A) ))),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f6,axiom,(
% 47.62/6.48 (![A,B]: (v(A,A,A,B) = v(A,A,B,A) ))),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f7,axiom,(
% 47.62/6.48 (![A,B]: (v(A,A,B,A) = v(A,B,A,A) ))),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f8,axiom,(
% 47.62/6.48 (![A,B]: (v(A,B,A,A) = v(B,A,A,A) ))),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f9,axiom,(
% 47.62/6.48 (![A,B]: (u(A,B) = v(A,A,A,B) ))),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f10,axiom,(
% 47.62/6.48 (![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (( ~ r(X0,X1,X2)| ~ r(X3,X4,X5)| ~ r(X6,X7,X8)| r(m(X0,X3,X6),m(X1,X4,X7),m(X2,X5,X8)) ) ))),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f11,axiom,(
% 47.62/6.48 (![X0,X1,X2,X3,X4,X5]: (( ~ r(X0,X1,X2)| ~ r(X3,X4,X5)| r(u(X0,X3),u(X1,X4),u(X2,X5)) ) ))),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f12,axiom,(
% 47.62/6.48 (![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11]: (( ~ r(X0,X1,X2)| ~ r(X3,X4,X5)| ~ r(X6,X7,X8)| ~ r(X9,X10,X11)| r(v(X0,X3,X6,X9),v(X1,X4,X7,X10),v(X2,X5,X8,X11)) ) ))),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f13,axiom,(
% 47.62/6.48 r(a,a,b) ),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f14,axiom,(
% 47.62/6.48 r(a,b,a) ),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f15,axiom,(
% 47.62/6.48 r(b,a,a) ),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f16,negated_conjecture,(
% 47.62/6.48 ~ r(a,a,a) ),
% 47.62/6.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 47.62/6.48 fof(f17,plain,(
% 47.62/6.48 ![X0,X1]: (m(X0,X0,X1)=X1)),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f1])).
% 47.62/6.48 fof(f18,plain,(
% 47.62/6.48 ![X0,X1]: (m(X0,X1,X1)=X0)),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f2])).
% 47.62/6.48 fof(f19,plain,(
% 47.62/6.48 ![X0]: (u(X0,X0)=X0)),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f3])).
% 47.62/6.48 fof(f21,plain,(
% 47.62/6.48 ![X0,X1]: (u(X0,X1)=u(X1,X0))),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f5])).
% 47.62/6.48 fof(f22,plain,(
% 47.62/6.48 ![X0,X1]: (v(X0,X0,X0,X1)=v(X0,X0,X1,X0))),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f6])).
% 47.62/6.48 fof(f23,plain,(
% 47.62/6.48 ![X0,X1]: (v(X0,X0,X1,X0)=v(X0,X1,X0,X0))),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f7])).
% 47.62/6.48 fof(f24,plain,(
% 47.62/6.48 ![X0,X1]: (v(X0,X1,X0,X0)=v(X1,X0,X0,X0))),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f8])).
% 47.62/6.48 fof(f25,plain,(
% 47.62/6.48 ![X0,X1]: (u(X0,X1)=v(X0,X0,X0,X1))),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f9])).
% 47.62/6.48 fof(f26,plain,(
% 47.62/6.48 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (~r(X0,X1,X2)|~r(X3,X4,X5)|~r(X6,X7,X8)|r(m(X0,X3,X6),m(X1,X4,X7),m(X2,X5,X8)))),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f10])).
% 47.62/6.48 fof(f27,plain,(
% 47.62/6.48 ![X0,X1,X2,X3,X4,X5]: (~r(X0,X1,X2)|~r(X3,X4,X5)|r(u(X0,X3),u(X1,X4),u(X2,X5)))),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f11])).
% 47.62/6.48 fof(f28,plain,(
% 47.62/6.48 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11]: (~r(X0,X1,X2)|~r(X3,X4,X5)|~r(X6,X7,X8)|~r(X9,X10,X11)|r(v(X0,X3,X6,X9),v(X1,X4,X7,X10),v(X2,X5,X8,X11)))),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f12])).
% 47.62/6.48 fof(f29,plain,(
% 47.62/6.48 r(a,a,b)),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f13])).
% 47.62/6.48 fof(f30,plain,(
% 47.62/6.48 r(a,b,a)),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f14])).
% 47.62/6.48 fof(f31,plain,(
% 47.62/6.48 r(b,a,a)),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f15])).
% 47.62/6.48 fof(f32,plain,(
% 47.62/6.48 ~r(a,a,a)),
% 47.62/6.48 inference(cnf_transformation,[status(thm)],[f16])).
% 47.62/6.48 fof(f40,plain,(
% 47.62/6.48 ![X0,X1]: (u(X0,X1)=v(X0,X0,X1,X0))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f25,f22])).
% 47.62/6.48 fof(f43,plain,(
% 47.62/6.48 ![X0,X1]: (u(X0,X1)=v(X0,X1,X0,X0))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f40,f23])).
% 47.62/6.48 fof(f48,plain,(
% 47.62/6.48 ![X0,X1]: (u(X0,X1)=v(X1,X0,X0,X0))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f43,f24])).
% 47.62/6.48 fof(f57,plain,(
% 47.62/6.48 ![X0,X1,X2,X3,X4,X5]: (~r(X0,X1,X2)|~r(X3,X4,X5)|r(m(a,X0,X3),m(a,X1,X4),m(b,X2,X5)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f26,f29])).
% 47.62/6.48 fof(f58,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(u(b,X0),u(a,X1),u(a,X2)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f27,f31])).
% 47.62/6.48 fof(f59,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(u(a,X0),u(b,X1),u(a,X2)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f27,f30])).
% 47.62/6.48 fof(f62,plain,(
% 47.62/6.48 r(u(b,a),u(a,b),u(a,a))),
% 47.62/6.48 inference(resolution,[status(thm)],[f58,f30])).
% 47.62/6.48 fof(f67,plain,(
% 47.62/6.48 r(u(a,b),u(a,b),u(a,a))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f21,f62])).
% 47.62/6.48 fof(f68,plain,(
% 47.62/6.48 r(u(a,b),u(a,b),a)),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f19,f67])).
% 47.62/6.48 fof(f73,plain,(
% 47.62/6.48 ![X0,X1,X2,X3,X4,X5]: (~r(X0,X1,X2)|~r(X3,X4,X5)|r(m(u(a,b),X0,X3),m(u(a,b),X1,X4),m(a,X2,X5)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f68,f26])).
% 47.62/6.48 fof(f83,plain,(
% 47.62/6.48 r(u(a,a),u(b,a),u(a,b))),
% 47.62/6.48 inference(resolution,[status(thm)],[f59,f29])).
% 47.62/6.48 fof(f91,plain,(
% 47.62/6.48 r(a,u(b,a),u(a,b))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f19,f83])).
% 47.62/6.48 fof(f92,plain,(
% 47.62/6.48 r(a,u(a,b),u(a,b))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f21,f91])).
% 47.62/6.48 fof(f96,plain,(
% 47.62/6.48 ![X0,X1,X2,X3,X4,X5]: (~r(X0,X1,X2)|~r(X3,X4,X5)|r(m(a,X0,X3),m(u(a,b),X1,X4),m(u(a,b),X2,X5)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f92,f26])).
% 47.62/6.48 fof(f169,plain,(
% 47.62/6.48 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (~r(X0,X1,X2)|~r(X3,X4,X5)|~r(X6,X7,X8)|r(v(b,X0,X3,X6),v(a,X1,X4,X7),v(a,X2,X5,X8)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f28,f31])).
% 47.62/6.48 fof(f454,plain,(
% 47.62/6.48 ![X0,X1,X2,X3,X4,X5]: (~r(X0,X1,X2)|~r(X3,X4,X5)|r(v(b,b,X0,X3),v(a,a,X1,X4),v(a,a,X2,X5)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f169,f31])).
% 47.62/6.48 fof(f460,plain,(
% 47.62/6.48 ![X0,X1,X2,X3,X4,X5]: (~r(X0,X1,X2)|~r(X3,X4,X5)|r(v(b,a,X0,X3),v(a,b,X1,X4),v(a,a,X2,X5)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f169,f30])).
% 47.62/6.48 fof(f874,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(v(b,b,a,X0),v(a,a,b,X1),v(a,a,a,X2)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f454,f30])).
% 47.62/6.48 fof(f875,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(v(b,b,a,X0),v(a,a,a,X1),v(a,a,b,X2)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f454,f29])).
% 47.62/6.48 fof(f898,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(v(b,b,a,X0),v(a,a,b,X1),u(a,X2)))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f25,f874])).
% 47.62/6.48 fof(f899,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(v(b,b,a,X0),u(a,X1),v(a,a,b,X2)))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f25,f875])).
% 47.62/6.48 fof(f1011,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(v(b,a,a,X0),v(a,b,a,X1),v(a,a,b,X2)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f460,f29])).
% 47.62/6.48 fof(f18455,plain,(
% 47.62/6.48 r(v(b,b,a,a),v(a,a,b,a),u(a,b))),
% 47.62/6.48 inference(resolution,[status(thm)],[f898,f29])).
% 47.62/6.48 fof(f18637,plain,(
% 47.62/6.48 r(v(b,b,a,a),u(a,b),u(a,b))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f40,f18455])).
% 47.62/6.48 fof(f18764,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(a,v(b,b,a,a),X0),m(u(a,b),u(a,b),X1),m(u(a,b),u(a,b),X2)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f18637,f96])).
% 47.62/6.48 fof(f18814,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(a,v(b,b,a,a),X0),X1,m(u(a,b),u(a,b),X2)))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f17,f18764])).
% 47.62/6.48 fof(f18815,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(a,v(b,b,a,a),X0),X1,X2))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f17,f18814])).
% 47.62/6.48 fof(f19637,plain,(
% 47.62/6.48 r(v(b,b,a,a),u(a,a),v(a,a,b,b))),
% 47.62/6.48 inference(resolution,[status(thm)],[f899,f29])).
% 47.62/6.48 fof(f19826,plain,(
% 47.62/6.48 r(v(b,b,a,a),a,v(a,a,b,b))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f19,f19637])).
% 47.62/6.48 fof(f23174,plain,(
% 47.62/6.48 r(m(a,v(b,b,a,a),v(b,b,a,a)),a,v(a,a,b,b))),
% 47.62/6.48 inference(resolution,[status(thm)],[f19826,f18815])).
% 47.62/6.48 fof(f23248,plain,(
% 47.62/6.48 r(a,a,v(a,a,b,b))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f18,f23174])).
% 47.62/6.48 fof(f23340,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(a,a,X0),m(a,a,X1),m(b,v(a,a,b,b),X2)))),
% 47.62/6.48 inference(resolution,[status(thm)],[f23248,f57])).
% 47.62/6.48 fof(f23388,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(X0,m(a,a,X1),m(b,v(a,a,b,b),X2)))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f17,f23340])).
% 47.62/6.48 fof(f23389,plain,(
% 47.62/6.48 ![X0,X1,X2]: (~r(X0,X1,X2)|r(X0,X1,m(b,v(a,a,b,b),X2)))),
% 47.62/6.48 inference(forward_demodulation,[status(thm)],[f17,f23388])).
% 47.62/6.51 fof(f23847,plain,(
% 47.62/6.51 r(v(b,a,a,a),v(a,b,a,a),v(a,a,b,b))),
% 47.62/6.51 inference(resolution,[status(thm)],[f1011,f29])).
% 47.62/6.51 fof(f24032,plain,(
% 47.62/6.51 r(u(a,b),v(a,b,a,a),v(a,a,b,b))),
% 47.62/6.51 inference(forward_demodulation,[status(thm)],[f48,f23847])).
% 47.62/6.51 fof(f24033,plain,(
% 47.62/6.51 r(u(a,b),u(a,b),v(a,a,b,b))),
% 47.62/6.51 inference(forward_demodulation,[status(thm)],[f43,f24032])).
% 47.62/6.51 fof(f37604,plain,(
% 47.62/6.51 r(u(a,b),u(a,b),m(b,v(a,a,b,b),v(a,a,b,b)))),
% 47.62/6.51 inference(resolution,[status(thm)],[f24033,f23389])).
% 47.62/6.51 fof(f37694,plain,(
% 47.62/6.51 r(u(a,b),u(a,b),b)),
% 47.62/6.51 inference(forward_demodulation,[status(thm)],[f18,f37604])).
% 47.62/6.51 fof(f39085,plain,(
% 47.62/6.51 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(u(a,b),u(a,b),X0),m(u(a,b),u(a,b),X1),m(a,b,X2)))),
% 47.62/6.51 inference(resolution,[status(thm)],[f37694,f73])).
% 47.62/6.51 fof(f39138,plain,(
% 47.62/6.51 ![X0,X1,X2]: (~r(X0,X1,X2)|r(X0,m(u(a,b),u(a,b),X1),m(a,b,X2)))),
% 47.62/6.51 inference(forward_demodulation,[status(thm)],[f17,f39085])).
% 47.62/6.51 fof(f39139,plain,(
% 47.62/6.51 ![X0,X1,X2]: (~r(X0,X1,X2)|r(X0,X1,m(a,b,X2)))),
% 47.62/6.51 inference(forward_demodulation,[status(thm)],[f17,f39138])).
% 47.62/6.51 fof(f44653,plain,(
% 47.62/6.51 r(a,a,m(a,b,b))),
% 47.62/6.51 inference(resolution,[status(thm)],[f39139,f29])).
% 47.62/6.51 fof(f44716,plain,(
% 47.62/6.51 r(a,a,a)),
% 47.62/6.51 inference(forward_demodulation,[status(thm)],[f18,f44653])).
% 47.62/6.51 fof(f44717,plain,(
% 47.62/6.51 $false),
% 47.62/6.51 inference(forward_subsumption_resolution,[status(thm)],[f44716,f32])).
% 47.62/6.51 % SZS output end CNFRefutation for theBenchmark.p
% 47.62/6.52 % Elapsed time: 6.149366 seconds
% 47.62/6.52 % CPU time: 48.463220 seconds
% 47.62/6.52 % Total memory used: 309.271 MB
% 47.62/6.52 % Net memory used: 274.531 MB
%------------------------------------------------------------------------------