%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYO683-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/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 03:44:46 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO683-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 21 12:09:40 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.42 % Drodi V4.1.1
% 0.18/0.48 % Refutation found
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.48 fof(f1,axiom,(
% 0.18/0.48 (![E,A_4]: (( ~ 'E'('0',f(A_4))| ~ 'E'('0',f(suc(A_4)))| iLEQ(suc(A_4),suc(A_4)) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f2,axiom,(
% 0.18/0.48 (![E,A_3]: (( ~ 'E'(s('0'),f(A_3))| ~ 'E'(s('0'),f(suc(A_3)))| iLEQ(suc(A_3),suc(A_3)) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f3,axiom,(
% 0.18/0.48 (![LE,A]: ('LE'(f(A),s(s(s(s('0'))))) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f4,axiom,(
% 0.18/0.48 (![E,A_2]: (( ~ 'E'(s(s('0')),f(A_2))| ~ 'E'(s(s('0')),f(suc(A_2)))| iLEQ(suc(A_2),suc(A_2)) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f5,axiom,(
% 0.18/0.48 (![E,B_159,B_162,B_160,B_161,A_1]: (( ~ 'E'(s(s(s('0'))),f(suc(B_159)))| ~ 'E'(s(s(s('0'))),f(B_162))| ~ iLEQ(suc(B_160),suc(B_161))| ~ 'E'(s(s(s('0'))),f(suc(B_162)))| ~ 'E'(s(s(s('0'))),f(B_159))| ~ 'E'(s(s(s('0'))),f(B_161))| ~ 'E'(s(s(s('0'))),f(B_160))| ~ iLEQ(suc(B_159),suc(B_160))| ~ 'E'(s(s(s('0'))),f(A_1))| ~ 'E'(s(s(s('0'))),f(suc(B_161)))| ~ iLEQ(suc(B_161),suc(B_162))| ~ 'E'(s(s(s('0'))),f(suc(B_160)))| ~ 'E'(s(s(s('0'))),f(suc(A_1)))| ~ iLEQ(suc(A_1),suc(B_159)) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f6,axiom,(
% 0.18/0.48 (![LE,B_247,E]: (( ~ 'LE'(f(suc(B_247)),s(s(s('0'))))| 'E'(s(s('0')),f(suc(B_247)))| 'LE'(f(B_247),s(s('0'))) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f7,axiom,(
% 0.18/0.48 (![LE,B_247,E]: (( ~ 'LE'(f(B_247),s(s(s('0'))))| 'E'(s(s('0')),f(B_247))| 'LE'(f(B_247),s(s('0'))) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f8,axiom,(
% 0.18/0.48 (![LE,B_158,E]: (( ~ 'LE'(f(suc(B_158)),s(s(s(s('0')))))| 'E'(s(s(s('0'))),f(suc(B_158)))| 'LE'(f(B_158),s(s(s('0')))) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f9,axiom,(
% 0.18/0.48 (![LE]: (~ 'LE'(f(z),'0') ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f10,axiom,(
% 0.18/0.48 (![LE,B_309,E]: (( ~ 'LE'(f(suc(B_309)),s('0'))| 'E'('0',f(suc(B_309)))| 'LE'(f(B_309),'0') ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f11,axiom,(
% 0.18/0.48 (![E,B_249,B_250,A_2,B_248,B_251]: (( ~ 'E'(s(s('0')),f(suc(B_249)))| ~ 'E'(s(s('0')),f(B_250))| ~ iLEQ(suc(A_2),suc(B_248))| ~ 'E'(s(s('0')),f(B_248))| ~ 'E'(s(s('0')),f(suc(B_251)))| ~ iLEQ(suc(B_249),suc(B_250))| ~ 'E'(s(s('0')),f(suc(A_2)))| ~ 'E'(s(s('0')),f(B_251))| ~ 'E'(s(s('0')),f(suc(B_248)))| ~ 'E'(s(s('0')),f(suc(B_250)))| ~ iLEQ(suc(B_248),suc(B_249))| ~ 'E'(s(s('0')),f(B_249))| ~ 'E'(s(s('0')),f(A_2))| ~ iLEQ(suc(B_250),suc(B_251)) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f12,axiom,(
% 0.18/0.48 (![LE,B_158,E]: (( ~ 'LE'(f(B_158),s(s(s(s('0')))))| 'E'(s(s(s('0'))),f(B_158))| 'LE'(f(B_158),s(s(s('0')))) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f13,axiom,(
% 0.18/0.48 (![E,A_1]: (( ~ 'E'(s(s(s('0'))),f(A_1))| ~ 'E'(s(s(s('0'))),f(suc(A_1)))| iLEQ(suc(A_1),suc(A_1)) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f14,axiom,(
% 0.18/0.48 (![LE,B_291,E]: (( ~ 'LE'(f(suc(B_291)),s(s('0')))| 'E'(s('0'),f(suc(B_291)))| 'LE'(f(B_291),s('0')) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f15,axiom,(
% 0.18/0.48 (![LE,B_291,E]: (( ~ 'LE'(f(B_291),s(s('0')))| 'E'(s('0'),f(B_291))| 'LE'(f(B_291),s('0')) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f16,axiom,(
% 0.18/0.48 (![E,B_310,B_311,B_313,B_312,A_4]: (( ~ 'E'('0',f(suc(B_310)))| ~ 'E'('0',f(suc(B_311)))| ~ 'E'('0',f(B_311))| ~ 'E'('0',f(suc(B_313)))| ~ 'E'('0',f(B_310))| ~ 'E'('0',f(B_312))| ~ 'E'('0',f(suc(B_312)))| ~ 'E'('0',f(B_313))| ~ iLEQ(suc(B_311),suc(B_312))| ~ iLEQ(suc(B_310),suc(B_311))| ~ iLEQ(suc(A_4),suc(B_310))| ~ 'E'('0',f(suc(A_4)))| ~ iLEQ(suc(B_312),suc(B_313))| ~ 'E'('0',f(A_4)) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f17,axiom,(
% 0.18/0.48 (![LE,B_309,E]: (( ~ 'LE'(f(B_309),s('0'))| 'E'('0',f(B_309))| 'LE'(f(B_309),'0') ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f18,axiom,(
% 0.18/0.48 (![E,B_294,B_295,B_292,A_3,B_293]: (( ~ 'E'(s('0'),f(suc(B_294)))| ~ 'E'(s('0'),f(B_295))| ~ 'E'(s('0'),f(suc(B_295)))| ~ 'E'(s('0'),f(suc(B_292)))| ~ 'E'(s('0'),f(suc(A_3)))| ~ 'E'(s('0'),f(B_294))| ~ 'E'(s('0'),f(B_292))| ~ iLEQ(suc(A_3),suc(B_292))| ~ 'E'(s('0'),f(B_293))| ~ iLEQ(suc(B_294),suc(B_295))| ~ 'E'(s('0'),f(A_3))| ~ 'E'(s('0'),f(suc(B_293)))| ~ iLEQ(suc(B_293),suc(B_294))| ~ iLEQ(suc(B_292),suc(B_293)) ) ))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.48 fof(f19,plain,(
% 0.18/0.48 ![A_4]: ((~'E'('0',f(A_4))|~'E'('0',f(suc(A_4))))|iLEQ(suc(A_4),suc(A_4)))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f1])).
% 0.18/0.48 fof(f20,plain,(
% 0.18/0.48 ![E,X0]: (~'E'('0',f(X0))|~'E'('0',f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f19])).
% 0.18/0.48 fof(f21,plain,(
% 0.18/0.48 ![A_3]: ((~'E'(s('0'),f(A_3))|~'E'(s('0'),f(suc(A_3))))|iLEQ(suc(A_3),suc(A_3)))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f2])).
% 0.18/0.48 fof(f22,plain,(
% 0.18/0.48 ![E,X0]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f21])).
% 0.18/0.48 fof(f23,plain,(
% 0.18/0.48 ![A]: 'LE'(f(A),s(s(s(s('0')))))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f3])).
% 0.18/0.48 fof(f24,plain,(
% 0.18/0.48 ![LE,X0]: ('LE'(f(X0),s(s(s(s('0'))))))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f23])).
% 0.18/0.48 fof(f25,plain,(
% 0.18/0.48 ![A_2]: ((~'E'(s(s('0')),f(A_2))|~'E'(s(s('0')),f(suc(A_2))))|iLEQ(suc(A_2),suc(A_2)))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f4])).
% 0.18/0.48 fof(f26,plain,(
% 0.18/0.48 ![E,X0]: (~'E'(s(s('0')),f(X0))|~'E'(s(s('0')),f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f25])).
% 0.18/0.48 fof(f27,plain,(
% 0.18/0.48 ![B_159,A_1]: (((![B_160]: ((![B_162,B_161]: ((((((((((~'E'(s(s(s('0'))),f(suc(B_159)))|~'E'(s(s(s('0'))),f(B_162)))|~iLEQ(suc(B_160),suc(B_161)))|~'E'(s(s(s('0'))),f(suc(B_162))))|~'E'(s(s(s('0'))),f(B_159)))|~'E'(s(s(s('0'))),f(B_161)))|~'E'(s(s(s('0'))),f(B_160)))|~iLEQ(suc(B_159),suc(B_160)))|~'E'(s(s(s('0'))),f(A_1)))|~'E'(s(s(s('0'))),f(suc(B_161))))|~iLEQ(suc(B_161),suc(B_162))))|~'E'(s(s(s('0'))),f(suc(B_160)))))|~'E'(s(s(s('0'))),f(suc(A_1))))|~iLEQ(suc(A_1),suc(B_159)))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f5])).
% 0.18/0.48 fof(f28,plain,(
% 0.18/0.48 ![E,X0,X1,X2,X3,X4]: (~'E'(s(s(s('0'))),f(suc(X0)))|~'E'(s(s(s('0'))),f(X1))|~iLEQ(suc(X2),suc(X3))|~'E'(s(s(s('0'))),f(suc(X1)))|~'E'(s(s(s('0'))),f(X0))|~'E'(s(s(s('0'))),f(X3))|~'E'(s(s(s('0'))),f(X2))|~iLEQ(suc(X0),suc(X2))|~'E'(s(s(s('0'))),f(X4))|~'E'(s(s(s('0'))),f(suc(X3)))|~iLEQ(suc(X3),suc(X1))|~'E'(s(s(s('0'))),f(suc(X2)))|~'E'(s(s(s('0'))),f(suc(X4)))|~iLEQ(suc(X4),suc(X0)))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f27])).
% 0.18/0.48 fof(f29,plain,(
% 0.18/0.48 ![B_247]: ((~'LE'(f(suc(B_247)),s(s(s('0'))))|'E'(s(s('0')),f(suc(B_247))))|'LE'(f(B_247),s(s('0'))))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f6])).
% 0.18/0.48 fof(f30,plain,(
% 0.18/0.48 ![LE,X0,E]: (~'LE'(f(suc(X0)),s(s(s('0'))))|'E'(s(s('0')),f(suc(X0)))|'LE'(f(X0),s(s('0'))))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f29])).
% 0.18/0.48 fof(f31,plain,(
% 0.18/0.48 ![B_247]: ((~'LE'(f(B_247),s(s(s('0'))))|'E'(s(s('0')),f(B_247)))|'LE'(f(B_247),s(s('0'))))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f7])).
% 0.18/0.48 fof(f32,plain,(
% 0.18/0.48 ![LE,X0,E]: (~'LE'(f(X0),s(s(s('0'))))|'E'(s(s('0')),f(X0))|'LE'(f(X0),s(s('0'))))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f31])).
% 0.18/0.48 fof(f33,plain,(
% 0.18/0.48 ![B_158]: ((~'LE'(f(suc(B_158)),s(s(s(s('0')))))|'E'(s(s(s('0'))),f(suc(B_158))))|'LE'(f(B_158),s(s(s('0')))))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f8])).
% 0.18/0.48 fof(f34,plain,(
% 0.18/0.48 ![LE,X0,E]: (~'LE'(f(suc(X0)),s(s(s(s('0')))))|'E'(s(s(s('0'))),f(suc(X0)))|'LE'(f(X0),s(s(s('0')))))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f33])).
% 0.18/0.48 fof(f35,plain,(
% 0.18/0.48 ![LE]: (~'LE'(f(z),'0'))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f9])).
% 0.18/0.48 fof(f36,plain,(
% 0.18/0.48 ![B_309]: ((~'LE'(f(suc(B_309)),s('0'))|'E'('0',f(suc(B_309))))|'LE'(f(B_309),'0'))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f10])).
% 0.18/0.48 fof(f37,plain,(
% 0.18/0.48 ![LE,X0,E]: (~'LE'(f(suc(X0)),s('0'))|'E'('0',f(suc(X0)))|'LE'(f(X0),'0'))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f36])).
% 0.18/0.48 fof(f38,plain,(
% 0.18/0.48 ![B_250,B_251]: ((![A_2]: ((![B_249]: ((![B_248]: ((((((((((~'E'(s(s('0')),f(suc(B_249)))|~'E'(s(s('0')),f(B_250)))|~iLEQ(suc(A_2),suc(B_248)))|~'E'(s(s('0')),f(B_248)))|~'E'(s(s('0')),f(suc(B_251))))|~iLEQ(suc(B_249),suc(B_250)))|~'E'(s(s('0')),f(suc(A_2))))|~'E'(s(s('0')),f(B_251)))|~'E'(s(s('0')),f(suc(B_248))))|~'E'(s(s('0')),f(suc(B_250))))|~iLEQ(suc(B_248),suc(B_249))))|~'E'(s(s('0')),f(B_249))))|~'E'(s(s('0')),f(A_2))))|~iLEQ(suc(B_250),suc(B_251)))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f11])).
% 0.18/0.48 fof(f39,plain,(
% 0.18/0.48 ![E,X0,X1,X2,X3,X4]: (~'E'(s(s('0')),f(suc(X0)))|~'E'(s(s('0')),f(X1))|~iLEQ(suc(X2),suc(X3))|~'E'(s(s('0')),f(X3))|~'E'(s(s('0')),f(suc(X4)))|~iLEQ(suc(X0),suc(X1))|~'E'(s(s('0')),f(suc(X2)))|~'E'(s(s('0')),f(X4))|~'E'(s(s('0')),f(suc(X3)))|~'E'(s(s('0')),f(suc(X1)))|~iLEQ(suc(X3),suc(X0))|~'E'(s(s('0')),f(X0))|~'E'(s(s('0')),f(X2))|~iLEQ(suc(X1),suc(X4)))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f38])).
% 0.18/0.48 fof(f40,plain,(
% 0.18/0.48 ![B_158]: ((~'LE'(f(B_158),s(s(s(s('0')))))|'E'(s(s(s('0'))),f(B_158)))|'LE'(f(B_158),s(s(s('0')))))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f12])).
% 0.18/0.48 fof(f41,plain,(
% 0.18/0.48 ![LE,X0,E]: (~'LE'(f(X0),s(s(s(s('0')))))|'E'(s(s(s('0'))),f(X0))|'LE'(f(X0),s(s(s('0')))))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f40])).
% 0.18/0.48 fof(f42,plain,(
% 0.18/0.48 ![A_1]: ((~'E'(s(s(s('0'))),f(A_1))|~'E'(s(s(s('0'))),f(suc(A_1))))|iLEQ(suc(A_1),suc(A_1)))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f13])).
% 0.18/0.48 fof(f43,plain,(
% 0.18/0.48 ![E,X0]: (~'E'(s(s(s('0'))),f(X0))|~'E'(s(s(s('0'))),f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f42])).
% 0.18/0.48 fof(f44,plain,(
% 0.18/0.48 ![B_291]: ((~'LE'(f(suc(B_291)),s(s('0')))|'E'(s('0'),f(suc(B_291))))|'LE'(f(B_291),s('0')))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f14])).
% 0.18/0.48 fof(f45,plain,(
% 0.18/0.48 ![LE,X0,E]: (~'LE'(f(suc(X0)),s(s('0')))|'E'(s('0'),f(suc(X0)))|'LE'(f(X0),s('0')))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f44])).
% 0.18/0.48 fof(f46,plain,(
% 0.18/0.48 ![B_291]: ((~'LE'(f(B_291),s(s('0')))|'E'(s('0'),f(B_291)))|'LE'(f(B_291),s('0')))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f15])).
% 0.18/0.48 fof(f47,plain,(
% 0.18/0.48 ![LE,X0,E]: (~'LE'(f(X0),s(s('0')))|'E'(s('0'),f(X0))|'LE'(f(X0),s('0')))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f46])).
% 0.18/0.48 fof(f48,plain,(
% 0.18/0.48 ![A_4]: ((![B_313,B_312]: (((![B_310]: ((![B_311]: (((((((((~'E'('0',f(suc(B_310)))|~'E'('0',f(suc(B_311))))|~'E'('0',f(B_311)))|~'E'('0',f(suc(B_313))))|~'E'('0',f(B_310)))|~'E'('0',f(B_312)))|~'E'('0',f(suc(B_312))))|~'E'('0',f(B_313)))|~iLEQ(suc(B_311),suc(B_312)))|~iLEQ(suc(B_310),suc(B_311))))|~iLEQ(suc(A_4),suc(B_310))))|~'E'('0',f(suc(A_4))))|~iLEQ(suc(B_312),suc(B_313))))|~'E'('0',f(A_4)))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f16])).
% 0.18/0.48 fof(f49,plain,(
% 0.18/0.48 ![E,X0,X1,X2,X3,X4]: (~'E'('0',f(suc(X0)))|~'E'('0',f(suc(X1)))|~'E'('0',f(X1))|~'E'('0',f(suc(X2)))|~'E'('0',f(X0))|~'E'('0',f(X3))|~'E'('0',f(suc(X3)))|~'E'('0',f(X2))|~iLEQ(suc(X1),suc(X3))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X4),suc(X0))|~'E'('0',f(suc(X4)))|~iLEQ(suc(X3),suc(X2))|~'E'('0',f(X4)))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f48])).
% 0.18/0.48 fof(f50,plain,(
% 0.18/0.48 ![B_309]: ((~'LE'(f(B_309),s('0'))|'E'('0',f(B_309)))|'LE'(f(B_309),'0'))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f17])).
% 0.18/0.48 fof(f51,plain,(
% 0.18/0.48 ![LE,X0,E]: (~'LE'(f(X0),s('0'))|'E'('0',f(X0))|'LE'(f(X0),'0'))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f50])).
% 0.18/0.48 fof(f52,plain,(
% 0.18/0.48 ![B_292,B_293]: ((![B_294]: (((![A_3]: ((![B_295]: (((((((((~'E'(s('0'),f(suc(B_294)))|~'E'(s('0'),f(B_295)))|~'E'(s('0'),f(suc(B_295))))|~'E'(s('0'),f(suc(B_292))))|~'E'(s('0'),f(suc(A_3))))|~'E'(s('0'),f(B_294)))|~'E'(s('0'),f(B_292)))|~iLEQ(suc(A_3),suc(B_292)))|~'E'(s('0'),f(B_293)))|~iLEQ(suc(B_294),suc(B_295))))|~'E'(s('0'),f(A_3))))|~'E'(s('0'),f(suc(B_293))))|~iLEQ(suc(B_293),suc(B_294))))|~iLEQ(suc(B_292),suc(B_293)))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f18])).
% 0.18/0.48 fof(f53,plain,(
% 0.18/0.48 ![E,X0,X1,X2,X3,X4]: (~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X1))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(suc(X2)))|~'E'(s('0'),f(suc(X3)))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(X2))|~iLEQ(suc(X3),suc(X2))|~'E'(s('0'),f(X4))|~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(X3))|~'E'(s('0'),f(suc(X4)))|~iLEQ(suc(X4),suc(X0))|~iLEQ(suc(X2),suc(X4)))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f52])).
% 0.18/0.48 fof(f56,plain,(
% 0.18/0.48 ![E,X0,LE]: ('E'(s(s(s('0'))),f(X0))|'LE'(f(X0),s(s(s('0')))))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f41,f24])).
% 0.18/0.48 fof(f59,plain,(
% 0.18/0.48 ![E,X0,LE]: ('E'(s(s(s('0'))),f(suc(X0)))|'LE'(f(X0),s(s(s('0')))))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f34,f24])).
% 0.18/0.48 fof(f60,plain,(
% 0.18/0.48 ![LE,X0,E]: ('LE'(f(X0),s(s(s('0'))))|~'E'(s(s(s('0'))),f(X0))|iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(resolution,[status(thm)],[f59,f43])).
% 0.18/0.48 fof(f61,plain,(
% 0.18/0.48 ![LE,X0,E,X1]: ('LE'(f(X0),s(s(s('0'))))|~'E'(s(s(s('0'))),f(suc(X1)))|~'E'(s(s(s('0'))),f(X0))|~iLEQ(suc(X0),suc(X0))|~'E'(s(s(s('0'))),f(X1))|~'E'(s(s(s('0'))),f(X0))|~'E'(s(s(s('0'))),f(X0))|~iLEQ(suc(X1),suc(X0))|~'E'(s(s(s('0'))),f(X0))|~iLEQ(suc(X0),suc(X0))|~iLEQ(suc(X0),suc(X1)))),
% 0.18/0.48 inference(resolution,[status(thm)],[f59,f28])).
% 0.18/0.48 fof(f69,plain,(
% 0.18/0.48 ![LE,X0]: ('LE'(f(X0),s(s(s('0'))))|iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f60,f56])).
% 0.18/0.48 fof(f70,plain,(
% 0.18/0.48 ![LE,X0,E,X1]: ('LE'(f(X0),s(s(s('0'))))|~'E'(s(s(s('0'))),f(suc(X1)))|~'E'(s(s(s('0'))),f(X0))|~iLEQ(suc(X0),suc(X0))|~'E'(s(s(s('0'))),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1)))),
% 0.18/0.48 inference(duplicate_literals_removal,[status(thm)],[f61])).
% 0.18/0.48 fof(f71,plain,(
% 0.18/0.48 ![LE,X0,E,X1]: ('LE'(f(X0),s(s(s('0'))))|~'E'(s(s(s('0'))),f(suc(X1)))|~iLEQ(suc(X0),suc(X0))|~'E'(s(s(s('0'))),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1)))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f70,f56])).
% 0.18/0.48 fof(f83,plain,(
% 0.18/0.48 ![X0,E,LE]: (iLEQ(suc(X0),suc(X0))|'E'(s(s('0')),f(X0))|'LE'(f(X0),s(s('0'))))),
% 0.18/0.48 inference(resolution,[status(thm)],[f69,f32])).
% 0.18/0.48 fof(f86,plain,(
% 0.18/0.48 ![E,X0,X1]: (~'E'(s(s('0')),f(suc(X0)))|~'E'(s(s('0')),f(X1))|~iLEQ(suc(X1),suc(X1))|~'E'(s(s('0')),f(X1))|~'E'(s(s('0')),f(suc(X1)))|~iLEQ(suc(X0),suc(X1))|~'E'(s(s('0')),f(X1))|~iLEQ(suc(X1),suc(X0))|~'E'(s(s('0')),f(X0))|~'E'(s(s('0')),f(X1))|~iLEQ(suc(X1),suc(X1)))),
% 0.18/0.48 inference(factoring,[status(thm)],[f39])).
% 0.18/0.48 fof(f87,plain,(
% 0.18/0.48 ![E,X0,X1]: (~'E'(s(s('0')),f(suc(X0)))|~'E'(s(s('0')),f(X1))|~iLEQ(suc(X1),suc(X1))|~'E'(s(s('0')),f(suc(X1)))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X1),suc(X0))|~'E'(s(s('0')),f(X0)))),
% 0.18/0.48 inference(duplicate_literals_removal,[status(thm)],[f86])).
% 0.18/0.48 fof(f88,plain,(
% 0.18/0.48 ![E,X0,X1]: (~'E'(s(s('0')),f(suc(X0)))|~'E'(s(s('0')),f(X1))|~'E'(s(s('0')),f(suc(X1)))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X1),suc(X0))|~'E'(s(s('0')),f(X0)))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f87,f26])).
% 0.18/0.48 fof(f123,plain,(
% 0.18/0.48 ![E,X0]: (~'E'('0',f(suc(X0)))|~'E'('0',f(suc(X0)))|~'E'('0',f(X0))|~'E'('0',f(X0))|~'E'('0',f(X0))|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X0))|~'E'('0',f(X0)))),
% 0.18/0.48 inference(factoring,[status(thm)],[f49])).
% 0.18/0.48 fof(f148,plain,(
% 0.18/0.48 ![E,X0]: (~'E'('0',f(suc(X0)))|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(duplicate_literals_removal,[status(thm)],[f123])).
% 0.18/0.48 fof(f149,plain,(
% 0.18/0.48 ![E,X0]: (~'E'('0',f(suc(X0)))|~'E'('0',f(X0)))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f148,f20])).
% 0.18/0.48 fof(f150,plain,(
% 0.18/0.48 ![E,X0,X1]: (~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X1))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(X1))|~iLEQ(suc(X1),suc(X1))|~'E'(s('0'),f(X1))|~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X1),suc(X1)))),
% 0.18/0.48 inference(factoring,[status(thm)],[f53])).
% 0.18/0.48 fof(f151,plain,(
% 0.18/0.48 ![E,X0,X1]: (~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X1))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X0))|~iLEQ(suc(X1),suc(X1))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X1),suc(X0)))),
% 0.18/0.48 inference(duplicate_literals_removal,[status(thm)],[f150])).
% 0.18/0.48 fof(f152,plain,(
% 0.18/0.48 ![E,X0,X1]: (~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X1))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X0))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X1),suc(X0)))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f151,f22])).
% 0.18/0.48 fof(f184,plain,(
% 0.18/0.48 ![LE,X0,E,X1]: ('LE'(f(X0),s(s(s('0'))))|~'E'(s(s(s('0'))),f(suc(X1)))|~'E'(s(s(s('0'))),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1)))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f71,f69])).
% 0.18/0.48 fof(f186,plain,(
% 0.18/0.48 ![LE,X0,E,X1]: ('LE'(f(X0),s(s(s('0'))))|~'E'(s(s(s('0'))),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1))|'LE'(f(X1),s(s(s('0')))))),
% 0.18/0.48 inference(resolution,[status(thm)],[f184,f59])).
% 0.18/0.48 fof(f188,plain,(
% 0.18/0.48 ![LE,X0,X1]: ('LE'(f(X0),s(s(s('0'))))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1))|'LE'(f(X1),s(s(s('0')))))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f186,f56])).
% 0.18/0.48 fof(f192,plain,(
% 0.18/0.48 ![LE,X0]: ('LE'(f(X0),s(s(s('0'))))|~iLEQ(suc(X0),suc(X0))|'LE'(f(X0),s(s(s('0'))))|'LE'(f(X0),s(s(s('0')))))),
% 0.18/0.48 inference(resolution,[status(thm)],[f188,f69])).
% 0.18/0.48 fof(f199,plain,(
% 0.18/0.48 ![LE,X0]: ('LE'(f(X0),s(s(s('0'))))|~iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(duplicate_literals_removal,[status(thm)],[f192])).
% 0.18/0.48 fof(f200,plain,(
% 0.18/0.48 ![LE,X0]: ('LE'(f(X0),s(s(s('0')))))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f199,f69])).
% 0.18/0.48 fof(f201,plain,(
% 0.18/0.48 ![E,X0,LE]: ('E'(s(s('0')),f(suc(X0)))|'LE'(f(X0),s(s('0'))))),
% 0.18/0.48 inference(backward_subsumption_resolution,[status(thm)],[f30,f200])).
% 0.18/0.48 fof(f202,plain,(
% 0.18/0.48 ![E,X0,LE]: ('E'(s(s('0')),f(X0))|'LE'(f(X0),s(s('0'))))),
% 0.18/0.48 inference(backward_subsumption_resolution,[status(thm)],[f32,f200])).
% 0.18/0.48 fof(f211,plain,(
% 0.18/0.48 ![LE,X0,E]: ('LE'(f(X0),s(s('0')))|~'E'(s(s('0')),f(X0))|iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(resolution,[status(thm)],[f201,f26])).
% 0.18/0.48 fof(f216,plain,(
% 0.18/0.48 ![LE,X0]: ('LE'(f(X0),s(s('0')))|iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f211,f83])).
% 0.18/0.48 fof(f257,plain,(
% 0.18/0.48 ![E,X0,X1,LE]: (~'E'(s(s('0')),f(suc(X0)))|~'E'(s(s('0')),f(X1))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X1),suc(X0))|~'E'(s(s('0')),f(X0))|'LE'(f(X1),s(s('0'))))),
% 0.18/0.48 inference(resolution,[status(thm)],[f88,f201])).
% 0.18/0.48 fof(f259,plain,(
% 0.18/0.48 ![E,X0,X1,LE]: (~'E'(s(s('0')),f(suc(X0)))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X1),suc(X0))|~'E'(s(s('0')),f(X0))|'LE'(f(X1),s(s('0'))))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f257,f202])).
% 0.18/0.48 fof(f263,plain,(
% 0.18/0.48 ![X0,X1,E,LE]: (~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X1),suc(X0))|~'E'(s(s('0')),f(X0))|'LE'(f(X1),s(s('0')))|'LE'(f(X0),s(s('0'))))),
% 0.18/0.48 inference(resolution,[status(thm)],[f259,f201])).
% 0.18/0.48 fof(f265,plain,(
% 0.18/0.48 ![X0,X1,LE]: (~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X1),suc(X0))|'LE'(f(X1),s(s('0')))|'LE'(f(X0),s(s('0'))))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f263,f202])).
% 0.18/0.48 fof(f272,plain,(
% 0.18/0.48 ![X0,LE]: (~iLEQ(suc(X0),suc(X0))|'LE'(f(X0),s(s('0')))|'LE'(f(X0),s(s('0')))|'LE'(f(X0),s(s('0'))))),
% 0.18/0.48 inference(resolution,[status(thm)],[f265,f216])).
% 0.18/0.48 fof(f285,plain,(
% 0.18/0.48 ![X0,LE]: (~iLEQ(suc(X0),suc(X0))|'LE'(f(X0),s(s('0'))))),
% 0.18/0.48 inference(duplicate_literals_removal,[status(thm)],[f272])).
% 0.18/0.48 fof(f286,plain,(
% 0.18/0.48 ![LE,X0]: ('LE'(f(X0),s(s('0'))))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f285,f216])).
% 0.18/0.48 fof(f287,plain,(
% 0.18/0.48 ![E,X0,LE]: ('E'(s('0'),f(suc(X0)))|'LE'(f(X0),s('0')))),
% 0.18/0.48 inference(backward_subsumption_resolution,[status(thm)],[f45,f286])).
% 0.18/0.48 fof(f288,plain,(
% 0.18/0.48 ![E,X0,LE]: ('E'(s('0'),f(X0))|'LE'(f(X0),s('0')))),
% 0.18/0.48 inference(backward_subsumption_resolution,[status(thm)],[f47,f286])).
% 0.18/0.48 fof(f291,plain,(
% 0.18/0.48 ![LE,X0,E,X1]: ('LE'(f(X0),s('0'))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1)))),
% 0.18/0.48 inference(resolution,[status(thm)],[f287,f152])).
% 0.18/0.48 fof(f300,plain,(
% 0.18/0.48 ![LE,X0,E]: ('LE'(f(X0),s('0'))|~'E'(s('0'),f(X0))|iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(resolution,[status(thm)],[f287,f22])).
% 0.18/0.48 fof(f301,plain,(
% 0.18/0.48 ![LE,X0,E,X1]: ('LE'(f(X0),s('0'))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1)))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f291,f288])).
% 0.18/0.48 fof(f314,plain,(
% 0.18/0.48 ![LE,X0]: ('LE'(f(X0),s('0'))|iLEQ(suc(X0),suc(X0)))),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f300,f288])).
% 0.18/0.48 fof(f353,plain,(
% 0.18/0.48 ![LE,X0,E,X1]: ('LE'(f(X0),s('0'))|~'E'(s('0'),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1))|'LE'(f(X1),s('0')))),
% 0.18/0.48 inference(resolution,[status(thm)],[f301,f287])).
% 0.18/0.49 fof(f355,plain,(
% 0.18/0.49 ![LE,X0,X1]: ('LE'(f(X0),s('0'))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1))|'LE'(f(X1),s('0')))),
% 0.18/0.49 inference(forward_subsumption_resolution,[status(thm)],[f353,f288])).
% 0.18/0.49 fof(f360,plain,(
% 0.18/0.49 ![LE,X0]: ('LE'(f(X0),s('0'))|~iLEQ(suc(X0),suc(X0))|'LE'(f(X0),s('0'))|'LE'(f(X0),s('0')))),
% 0.18/0.49 inference(resolution,[status(thm)],[f355,f314])).
% 0.18/0.49 fof(f369,plain,(
% 0.18/0.49 ![LE,X0]: ('LE'(f(X0),s('0'))|~iLEQ(suc(X0),suc(X0)))),
% 0.18/0.49 inference(duplicate_literals_removal,[status(thm)],[f360])).
% 0.18/0.49 fof(f370,plain,(
% 0.18/0.49 ![LE,X0]: ('LE'(f(X0),s('0')))),
% 0.18/0.49 inference(forward_subsumption_resolution,[status(thm)],[f369,f314])).
% 0.18/0.49 fof(f371,plain,(
% 0.18/0.49 ![E,X0,LE]: ('E'('0',f(suc(X0)))|'LE'(f(X0),'0'))),
% 0.18/0.49 inference(backward_subsumption_resolution,[status(thm)],[f37,f370])).
% 0.18/0.49 fof(f372,plain,(
% 0.18/0.49 ![E,X0,LE]: ('E'('0',f(X0))|'LE'(f(X0),'0'))),
% 0.18/0.49 inference(backward_subsumption_resolution,[status(thm)],[f51,f370])).
% 0.18/0.49 fof(f373,plain,(
% 0.18/0.49 ![LE,X0,E]: ('LE'(f(X0),'0')|~'E'('0',f(X0)))),
% 0.18/0.49 inference(resolution,[status(thm)],[f371,f149])).
% 0.18/0.49 fof(f376,plain,(
% 0.18/0.49 ![LE,X0]: ('LE'(f(X0),'0'))),
% 0.18/0.49 inference(forward_subsumption_resolution,[status(thm)],[f373,f372])).
% 0.18/0.49 fof(f377,plain,(
% 0.18/0.49 $false),
% 0.18/0.49 inference(backward_subsumption_resolution,[status(thm)],[f35,f376])).
% 0.18/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.18/0.51 % Elapsed time: 0.093094 seconds
% 0.18/0.51 % CPU time: 0.557759 seconds
% 0.18/0.51 % Total memory used: 9.257 MB
% 0.18/0.51 % Net memory used: 8.581 MB
%------------------------------------------------------------------------------