%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG440-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 4.96s 1.84s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG440-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.49 % Computer : n010.cluster.edu
% 0.17/0.49 % Model : x86_64 x86_64
% 0.17/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.49 % Memory : 8046.5625MB
% 0.17/0.49 % OS : Linux 6.8.0-71-generic
% 0.17/0.49 % CPULimit : 300
% 0.17/0.49 % WCLimit : 300
% 0.17/0.49 % DateTime : Mon Sep 21 13:21:29 UTC 2026
% 0.17/0.49 % CPUTime :
% 0.17/0.51 % Drodi V4.1.1
% 4.96/1.84 % Refutation found
% 4.96/1.84 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.96/1.84 % SZS output start CNFRefutation for theBenchmark
% 4.96/1.84 fof(f1,axiom,(
% 4.96/1.84 (![A,B]: (m(A,A,B) = B ))),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f2,axiom,(
% 4.96/1.84 (![A,B]: (m(A,B,B) = A ))),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f4,axiom,(
% 4.96/1.84 (![A]: (v(A,A) = A ))),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f5,axiom,(
% 4.96/1.84 (![A,B]: (u(A,A,B) = u(A,B,A) ))),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f6,axiom,(
% 4.96/1.84 (![A,B]: (u(A,A,B) = u(B,A,A) ))),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f7,axiom,(
% 4.96/1.84 (![A,B]: (v(A,B) = v(B,A) ))),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f8,axiom,(
% 4.96/1.84 (![A,B]: (u(A,A,B) = v(A,B) ))),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f9,axiom,(
% 4.96/1.84 (![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)) ) ))),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f10,axiom,(
% 4.96/1.84 (![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (( ~ r(X0,X1,X2)| ~ r(X3,X4,X5)| ~ r(X6,X7,X8)| r(u(X0,X3,X6),u(X1,X4,X7),u(X2,X5,X8)) ) ))),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f11,axiom,(
% 4.96/1.84 (![X0,X1,X2,X3,X4,X5]: (( ~ r(X0,X1,X2)| ~ r(X3,X4,X5)| r(v(X0,X3),v(X1,X4),v(X2,X5)) ) ))),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f12,axiom,(
% 4.96/1.84 r(a,a,b) ),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f13,axiom,(
% 4.96/1.84 r(a,b,a) ),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f14,axiom,(
% 4.96/1.84 r(b,a,a) ),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f15,negated_conjecture,(
% 4.96/1.84 ~ r(a,a,a) ),
% 4.96/1.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.96/1.84 fof(f16,plain,(
% 4.96/1.84 ![X0,X1]: (m(X0,X0,X1)=X1)),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f1])).
% 4.96/1.84 fof(f17,plain,(
% 4.96/1.84 ![X0,X1]: (m(X0,X1,X1)=X0)),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f2])).
% 4.96/1.84 fof(f19,plain,(
% 4.96/1.84 ![X0]: (v(X0,X0)=X0)),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f4])).
% 4.96/1.84 fof(f20,plain,(
% 4.96/1.84 ![X0,X1]: (u(X0,X0,X1)=u(X0,X1,X0))),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f5])).
% 4.96/1.84 fof(f21,plain,(
% 4.96/1.84 ![X0,X1]: (u(X0,X0,X1)=u(X1,X0,X0))),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f6])).
% 4.96/1.84 fof(f22,plain,(
% 4.96/1.84 ![X0,X1]: (v(X0,X1)=v(X1,X0))),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f7])).
% 4.96/1.84 fof(f23,plain,(
% 4.96/1.84 ![X0,X1]: (u(X0,X0,X1)=v(X0,X1))),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f8])).
% 4.96/1.84 fof(f24,plain,(
% 4.96/1.84 ![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)))),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f9])).
% 4.96/1.84 fof(f25,plain,(
% 4.96/1.84 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (~r(X0,X1,X2)|~r(X3,X4,X5)|~r(X6,X7,X8)|r(u(X0,X3,X6),u(X1,X4,X7),u(X2,X5,X8)))),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f10])).
% 4.96/1.84 fof(f26,plain,(
% 4.96/1.84 ![X0,X1,X2,X3,X4,X5]: (~r(X0,X1,X2)|~r(X3,X4,X5)|r(v(X0,X3),v(X1,X4),v(X2,X5)))),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f11])).
% 4.96/1.84 fof(f27,plain,(
% 4.96/1.84 r(a,a,b)),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f12])).
% 4.96/1.84 fof(f28,plain,(
% 4.96/1.84 r(a,b,a)),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f13])).
% 4.96/1.84 fof(f29,plain,(
% 4.96/1.84 r(b,a,a)),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f14])).
% 4.96/1.84 fof(f30,plain,(
% 4.96/1.84 ~r(a,a,a)),
% 4.96/1.84 inference(cnf_transformation,[status(thm)],[f15])).
% 4.96/1.84 fof(f39,plain,(
% 4.96/1.84 ![X0,X1]: (v(X0,X1)=u(X0,X1,X0))),
% 4.96/1.84 inference(backward_demodulation,[status(thm)],[f23,f20])).
% 4.96/1.84 fof(f41,plain,(
% 4.96/1.84 ![X0,X1]: (v(X0,X1)=u(X1,X0,X0))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f23,f21])).
% 4.96/1.84 fof(f48,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(v(b,X0),v(a,X1),v(a,X2)))),
% 4.96/1.84 inference(resolution,[status(thm)],[f26,f29])).
% 4.96/1.84 fof(f49,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(v(a,X0),v(b,X1),v(a,X2)))),
% 4.96/1.84 inference(resolution,[status(thm)],[f26,f28])).
% 4.96/1.84 fof(f52,plain,(
% 4.96/1.84 r(v(b,a),v(a,b),v(a,a))),
% 4.96/1.84 inference(resolution,[status(thm)],[f48,f28])).
% 4.96/1.84 fof(f53,plain,(
% 4.96/1.84 r(v(b,a),v(a,a),v(a,b))),
% 4.96/1.84 inference(resolution,[status(thm)],[f48,f27])).
% 4.96/1.84 fof(f57,plain,(
% 4.96/1.84 r(v(b,a),v(b,a),v(a,a))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f22,f52])).
% 4.96/1.84 fof(f58,plain,(
% 4.96/1.84 r(v(b,a),v(b,a),a)),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f19,f57])).
% 4.96/1.84 fof(f59,plain,(
% 4.96/1.84 r(v(b,a),a,v(a,b))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f19,f53])).
% 4.96/1.84 fof(f60,plain,(
% 4.96/1.84 r(v(b,a),a,v(b,a))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f22,f59])).
% 4.96/1.84 fof(f67,plain,(
% 4.96/1.84 ![X0,X1,X2,X3,X4,X5]: (~r(X0,X1,X2)|~r(X3,X4,X5)|r(m(v(b,a),X0,X3),m(a,X1,X4),m(v(b,a),X2,X5)))),
% 4.96/1.84 inference(resolution,[status(thm)],[f24,f60])).
% 4.96/1.84 fof(f69,plain,(
% 4.96/1.84 ![X0,X1,X2,X3,X4,X5]: (~r(X0,X1,X2)|~r(X3,X4,X5)|r(m(b,X0,X3),m(a,X1,X4),m(a,X2,X5)))),
% 4.96/1.84 inference(resolution,[status(thm)],[f24,f29])).
% 4.96/1.84 fof(f76,plain,(
% 4.96/1.84 r(v(a,a),v(b,a),v(a,b))),
% 4.96/1.84 inference(resolution,[status(thm)],[f49,f27])).
% 4.96/1.84 fof(f83,plain,(
% 4.96/1.84 r(a,v(b,a),v(a,b))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f19,f76])).
% 4.96/1.84 fof(f84,plain,(
% 4.96/1.84 r(a,v(b,a),v(b,a))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f22,f83])).
% 4.96/1.84 fof(f86,plain,(
% 4.96/1.84 ![X0,X1,X2,X3,X4,X5]: (~r(X0,X1,X2)|~r(X3,X4,X5)|r(m(a,X0,X3),m(v(b,a),X1,X4),m(v(b,a),X2,X5)))),
% 4.96/1.84 inference(resolution,[status(thm)],[f84,f24])).
% 4.96/1.84 fof(f123,plain,(
% 4.96/1.84 ![X0,X1,X2,X3,X4,X5]: (~r(X0,X1,X2)|~r(X3,X4,X5)|r(u(b,X0,X3),u(a,X1,X4),u(a,X2,X5)))),
% 4.96/1.84 inference(resolution,[status(thm)],[f25,f29])).
% 4.96/1.84 fof(f514,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(u(b,a,X0),u(a,b,X1),u(a,a,X2)))),
% 4.96/1.84 inference(resolution,[status(thm)],[f123,f28])).
% 4.96/1.84 fof(f533,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(u(b,a,X0),u(a,b,X1),v(a,X2)))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f23,f514])).
% 4.96/1.84 fof(f1105,plain,(
% 4.96/1.84 r(u(b,a,a),u(a,b,a),v(a,b))),
% 4.96/1.84 inference(resolution,[status(thm)],[f533,f27])).
% 4.96/1.84 fof(f1169,plain,(
% 4.96/1.84 r(v(a,b),u(a,b,a),v(a,b))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f41,f1105])).
% 4.96/1.84 fof(f1170,plain,(
% 4.96/1.84 r(v(b,a),u(a,b,a),v(a,b))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f22,f1169])).
% 4.96/1.84 fof(f1171,plain,(
% 4.96/1.84 r(v(b,a),v(a,b),v(a,b))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f39,f1170])).
% 4.96/1.84 fof(f1172,plain,(
% 4.96/1.84 r(v(b,a),v(b,a),v(a,b))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f22,f1171])).
% 4.96/1.84 fof(f1173,plain,(
% 4.96/1.84 r(v(b,a),v(b,a),v(b,a))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f22,f1172])).
% 4.96/1.84 fof(f3341,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(v(b,a),v(b,a),X0),m(a,v(b,a),X1),m(v(b,a),v(b,a),X2)))),
% 4.96/1.84 inference(resolution,[status(thm)],[f67,f1173])).
% 4.96/1.84 fof(f3394,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(X0,m(a,v(b,a),X1),m(v(b,a),v(b,a),X2)))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f16,f3341])).
% 4.96/1.84 fof(f3395,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(X0,m(a,v(b,a),X1),X2))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f16,f3394])).
% 4.96/1.84 fof(f3441,plain,(
% 4.96/1.84 r(v(b,a),m(a,v(b,a),v(b,a)),a)),
% 4.96/1.84 inference(resolution,[status(thm)],[f3395,f58])).
% 4.96/1.84 fof(f3478,plain,(
% 4.96/1.84 r(v(b,a),a,a)),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f17,f3441])).
% 4.96/1.84 fof(f3503,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(b,v(b,a),X0),m(a,a,X1),m(a,a,X2)))),
% 4.96/1.84 inference(resolution,[status(thm)],[f3478,f69])).
% 4.96/1.84 fof(f3548,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(b,v(b,a),X0),X1,m(a,a,X2)))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f16,f3503])).
% 4.96/1.84 fof(f3549,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(b,v(b,a),X0),X1,X2))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f16,f3548])).
% 4.96/1.84 fof(f6426,plain,(
% 4.96/1.84 r(m(b,v(b,a),v(b,a)),v(b,a),v(b,a))),
% 4.96/1.84 inference(resolution,[status(thm)],[f3549,f1173])).
% 4.96/1.84 fof(f6489,plain,(
% 4.96/1.84 r(b,v(b,a),v(b,a))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f17,f6426])).
% 4.96/1.84 fof(f6738,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(a,b,X0),m(v(b,a),v(b,a),X1),m(v(b,a),v(b,a),X2)))),
% 4.96/1.84 inference(resolution,[status(thm)],[f6489,f86])).
% 4.96/1.84 fof(f6775,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(a,b,X0),X1,m(v(b,a),v(b,a),X2)))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f16,f6738])).
% 4.96/1.84 fof(f6776,plain,(
% 4.96/1.84 ![X0,X1,X2]: (~r(X0,X1,X2)|r(m(a,b,X0),X1,X2))),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f16,f6775])).
% 4.96/1.84 fof(f7085,plain,(
% 4.96/1.84 r(m(a,b,b),a,a)),
% 4.96/1.84 inference(resolution,[status(thm)],[f6776,f29])).
% 4.96/1.84 fof(f7136,plain,(
% 4.96/1.84 r(a,a,a)),
% 4.96/1.84 inference(forward_demodulation,[status(thm)],[f17,f7085])).
% 4.96/1.84 fof(f7137,plain,(
% 4.96/1.84 $false),
% 4.96/1.84 inference(forward_subsumption_resolution,[status(thm)],[f7136,f30])).
% 4.96/1.84 % SZS output end CNFRefutation for theBenchmark.p
% 9.82/1.87 % Elapsed time: 1.356593 seconds
% 9.82/1.87 % CPU time: 10.167840 seconds
% 9.82/1.87 % Total memory used: 119.387 MB
% 9.82/1.87 % Net memory used: 112.984 MB
%------------------------------------------------------------------------------