%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYO680-1 : 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 : n014.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 03:44:45 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.46s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO680-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 12:08:50 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.15/0.46 % Refutation found
% 0.15/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.46 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.46 fof(f1,axiom,(
% 0.15/0.46 (![E,A_4]: (( ~ 'E'('0',f(A_4))| ~ 'E'('0',f(suc(A_4)))| iLEQ(suc(A_4),suc(A_4)) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f2,axiom,(
% 0.15/0.46 (![LE,A]: ('LE'(f(A),s(s(s(s('0'))))) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f3,axiom,(
% 0.15/0.46 (![E,A_3]: (( ~ 'E'(s('0'),f(A_3))| ~ 'E'(s('0'),f(suc(A_3)))| iLEQ(suc(A_3),suc(A_3)) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f4,axiom,(
% 0.15/0.46 (![LE,B_60,E]: (( ~ 'LE'(f(suc(B_60)),s('0'))| 'E'('0',f(suc(B_60)))| 'LE'(f(B_60),'0') ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f5,axiom,(
% 0.15/0.46 (![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)) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f6,axiom,(
% 0.15/0.46 (![E,B_42,B_43,A_2]: (( ~ 'E'(s(s('0')),f(suc(B_42)))| ~ 'E'(s(s('0')),f(B_42))| ~ iLEQ(suc(B_42),suc(B_43))| ~ 'E'(s(s('0')),f(suc(A_2)))| ~ 'E'(s(s('0')),f(suc(B_43)))| ~ iLEQ(suc(A_2),suc(B_42))| ~ 'E'(s(s('0')),f(B_43))| ~ 'E'(s(s('0')),f(A_2)) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f7,axiom,(
% 0.15/0.46 (![B_24,B_25,E,A_1]: (( ~ iLEQ(suc(B_24),suc(B_25))| ~ 'E'(s(s(s('0'))),f(B_25))| ~ 'E'(s(s(s('0'))),f(B_24))| ~ iLEQ(suc(A_1),suc(B_24))| ~ 'E'(s(s(s('0'))),f(A_1))| ~ 'E'(s(s(s('0'))),f(suc(B_24)))| ~ 'E'(s(s(s('0'))),f(suc(B_25)))| ~ 'E'(s(s(s('0'))),f(suc(A_1))) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f8,axiom,(
% 0.15/0.46 (![LE,B_53,E]: (( ~ 'LE'(f(B_53),s(s('0')))| 'E'(s('0'),f(B_53))| 'LE'(f(B_53),s('0')) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f9,axiom,(
% 0.15/0.46 (![LE]: (~ 'LE'(f(z),'0') ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f10,axiom,(
% 0.15/0.46 (![LE,B_41,E]: (( ~ 'LE'(f(suc(B_41)),s(s(s('0'))))| 'E'(s(s('0')),f(suc(B_41)))| 'LE'(f(B_41),s(s('0'))) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f11,axiom,(
% 0.15/0.46 (![E,B_61,B_62,A_4]: (( ~ 'E'('0',f(suc(B_61)))| ~ iLEQ(suc(B_61),suc(B_62))| ~ iLEQ(suc(A_4),suc(B_61))| ~ 'E'('0',f(suc(B_62)))| ~ 'E'('0',f(B_61))| ~ 'E'('0',f(suc(A_4)))| ~ 'E'('0',f(B_62))| ~ 'E'('0',f(A_4)) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f12,axiom,(
% 0.15/0.46 (![LE,B_23,E]: (( ~ 'LE'(f(B_23),s(s(s(s('0')))))| 'E'(s(s(s('0'))),f(B_23))| 'LE'(f(B_23),s(s(s('0')))) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f13,axiom,(
% 0.15/0.46 (![LE,B_41,E]: (( ~ 'LE'(f(B_41),s(s(s('0'))))| 'E'(s(s('0')),f(B_41))| 'LE'(f(B_41),s(s('0'))) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f14,axiom,(
% 0.15/0.46 (![B_54,B_55,E,A_3]: (( ~ iLEQ(suc(B_54),suc(B_55))| ~ 'E'(s('0'),f(suc(A_3)))| ~ iLEQ(suc(A_3),suc(B_54))| ~ 'E'(s('0'),f(suc(B_55)))| ~ 'E'(s('0'),f(A_3))| ~ 'E'(s('0'),f(B_55))| ~ 'E'(s('0'),f(suc(B_54)))| ~ 'E'(s('0'),f(B_54)) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f15,axiom,(
% 0.15/0.46 (![LE,B_23,E]: (( ~ 'LE'(f(suc(B_23)),s(s(s(s('0')))))| 'E'(s(s(s('0'))),f(suc(B_23)))| 'LE'(f(B_23),s(s(s('0')))) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f16,axiom,(
% 0.15/0.46 (![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)) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f17,axiom,(
% 0.15/0.46 (![LE,B_60,E]: (( ~ 'LE'(f(B_60),s('0'))| 'E'('0',f(B_60))| 'LE'(f(B_60),'0') ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f18,axiom,(
% 0.15/0.46 (![LE,B_53,E]: (( ~ 'LE'(f(suc(B_53)),s(s('0')))| 'E'(s('0'),f(suc(B_53)))| 'LE'(f(B_53),s('0')) ) ))),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f19,plain,(
% 0.15/0.46 ![A_4]: ((~'E'('0',f(A_4))|~'E'('0',f(suc(A_4))))|iLEQ(suc(A_4),suc(A_4)))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f1])).
% 0.15/0.46 fof(f20,plain,(
% 0.15/0.46 ![E,X0]: (~'E'('0',f(X0))|~'E'('0',f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f19])).
% 0.15/0.46 fof(f21,plain,(
% 0.15/0.46 ![A]: 'LE'(f(A),s(s(s(s('0')))))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f2])).
% 0.15/0.46 fof(f22,plain,(
% 0.15/0.46 ![LE,X0]: ('LE'(f(X0),s(s(s(s('0'))))))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f21])).
% 0.15/0.46 fof(f23,plain,(
% 0.15/0.46 ![A_3]: ((~'E'(s('0'),f(A_3))|~'E'(s('0'),f(suc(A_3))))|iLEQ(suc(A_3),suc(A_3)))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f3])).
% 0.15/0.46 fof(f24,plain,(
% 0.15/0.46 ![E,X0]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f23])).
% 0.15/0.46 fof(f25,plain,(
% 0.15/0.46 ![B_60]: ((~'LE'(f(suc(B_60)),s('0'))|'E'('0',f(suc(B_60))))|'LE'(f(B_60),'0'))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f4])).
% 0.15/0.46 fof(f26,plain,(
% 0.15/0.46 ![LE,X0,E]: (~'LE'(f(suc(X0)),s('0'))|'E'('0',f(suc(X0)))|'LE'(f(X0),'0'))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f25])).
% 0.15/0.46 fof(f27,plain,(
% 0.15/0.46 ![A_2]: ((~'E'(s(s('0')),f(A_2))|~'E'(s(s('0')),f(suc(A_2))))|iLEQ(suc(A_2),suc(A_2)))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f5])).
% 0.15/0.46 fof(f28,plain,(
% 0.15/0.46 ![E,X0]: (~'E'(s(s('0')),f(X0))|~'E'(s(s('0')),f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.46 fof(f29,plain,(
% 0.15/0.46 ![A_2]: ((![B_43]: ((![B_42]: (((((~'E'(s(s('0')),f(suc(B_42)))|~'E'(s(s('0')),f(B_42)))|~iLEQ(suc(B_42),suc(B_43)))|~'E'(s(s('0')),f(suc(A_2))))|~'E'(s(s('0')),f(suc(B_43))))|~iLEQ(suc(A_2),suc(B_42))))|~'E'(s(s('0')),f(B_43))))|~'E'(s(s('0')),f(A_2)))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f6])).
% 0.15/0.46 fof(f30,plain,(
% 0.15/0.46 ![E,X0,X1,X2]: (~'E'(s(s('0')),f(suc(X0)))|~'E'(s(s('0')),f(X0))|~iLEQ(suc(X0),suc(X1))|~'E'(s(s('0')),f(suc(X2)))|~'E'(s(s('0')),f(suc(X1)))|~iLEQ(suc(X2),suc(X0))|~'E'(s(s('0')),f(X1))|~'E'(s(s('0')),f(X2)))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f29])).
% 0.15/0.46 fof(f31,plain,(
% 0.15/0.46 ![A_1]: ((![B_25]: ((![B_24]: (((((~iLEQ(suc(B_24),suc(B_25))|~'E'(s(s(s('0'))),f(B_25)))|~'E'(s(s(s('0'))),f(B_24)))|~iLEQ(suc(A_1),suc(B_24)))|~'E'(s(s(s('0'))),f(A_1)))|~'E'(s(s(s('0'))),f(suc(B_24)))))|~'E'(s(s(s('0'))),f(suc(B_25)))))|~'E'(s(s(s('0'))),f(suc(A_1))))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f7])).
% 0.15/0.46 fof(f32,plain,(
% 0.15/0.46 ![X0,X1,E,X2]: (~iLEQ(suc(X0),suc(X1))|~'E'(s(s(s('0'))),f(X1))|~'E'(s(s(s('0'))),f(X0))|~iLEQ(suc(X2),suc(X0))|~'E'(s(s(s('0'))),f(X2))|~'E'(s(s(s('0'))),f(suc(X0)))|~'E'(s(s(s('0'))),f(suc(X1)))|~'E'(s(s(s('0'))),f(suc(X2))))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f31])).
% 0.15/0.46 fof(f33,plain,(
% 0.15/0.46 ![B_53]: ((~'LE'(f(B_53),s(s('0')))|'E'(s('0'),f(B_53)))|'LE'(f(B_53),s('0')))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f8])).
% 0.15/0.46 fof(f34,plain,(
% 0.15/0.46 ![LE,X0,E]: (~'LE'(f(X0),s(s('0')))|'E'(s('0'),f(X0))|'LE'(f(X0),s('0')))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f33])).
% 0.15/0.46 fof(f35,plain,(
% 0.15/0.46 ![LE]: (~'LE'(f(z),'0'))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f9])).
% 0.15/0.46 fof(f36,plain,(
% 0.15/0.46 ![B_41]: ((~'LE'(f(suc(B_41)),s(s(s('0'))))|'E'(s(s('0')),f(suc(B_41))))|'LE'(f(B_41),s(s('0'))))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f10])).
% 0.15/0.46 fof(f37,plain,(
% 0.15/0.46 ![LE,X0,E]: (~'LE'(f(suc(X0)),s(s(s('0'))))|'E'(s(s('0')),f(suc(X0)))|'LE'(f(X0),s(s('0'))))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f36])).
% 0.15/0.46 fof(f38,plain,(
% 0.15/0.46 ![A_4]: ((![B_62]: (((![B_61]: ((((~'E'('0',f(suc(B_61)))|~iLEQ(suc(B_61),suc(B_62)))|~iLEQ(suc(A_4),suc(B_61)))|~'E'('0',f(suc(B_62))))|~'E'('0',f(B_61))))|~'E'('0',f(suc(A_4))))|~'E'('0',f(B_62))))|~'E'('0',f(A_4)))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f11])).
% 0.15/0.46 fof(f39,plain,(
% 0.15/0.46 ![E,X0,X1,X2]: (~'E'('0',f(suc(X0)))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X2),suc(X0))|~'E'('0',f(suc(X1)))|~'E'('0',f(X0))|~'E'('0',f(suc(X2)))|~'E'('0',f(X1))|~'E'('0',f(X2)))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f38])).
% 0.15/0.46 fof(f40,plain,(
% 0.15/0.46 ![B_23]: ((~'LE'(f(B_23),s(s(s(s('0')))))|'E'(s(s(s('0'))),f(B_23)))|'LE'(f(B_23),s(s(s('0')))))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f12])).
% 0.15/0.46 fof(f41,plain,(
% 0.15/0.46 ![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')))))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f40])).
% 0.15/0.46 fof(f42,plain,(
% 0.15/0.46 ![B_41]: ((~'LE'(f(B_41),s(s(s('0'))))|'E'(s(s('0')),f(B_41)))|'LE'(f(B_41),s(s('0'))))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f13])).
% 0.15/0.46 fof(f43,plain,(
% 0.15/0.46 ![LE,X0,E]: (~'LE'(f(X0),s(s(s('0'))))|'E'(s(s('0')),f(X0))|'LE'(f(X0),s(s('0'))))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f42])).
% 0.15/0.46 fof(f44,plain,(
% 0.15/0.46 ![B_54]: (((![B_55]: ((![A_3]: ((((~iLEQ(suc(B_54),suc(B_55))|~'E'(s('0'),f(suc(A_3))))|~iLEQ(suc(A_3),suc(B_54)))|~'E'(s('0'),f(suc(B_55))))|~'E'(s('0'),f(A_3))))|~'E'(s('0'),f(B_55))))|~'E'(s('0'),f(suc(B_54))))|~'E'(s('0'),f(B_54)))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f14])).
% 0.15/0.46 fof(f45,plain,(
% 0.15/0.46 ![X0,X1,E,X2]: (~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(suc(X2)))|~iLEQ(suc(X2),suc(X0))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X2))|~'E'(s('0'),f(X1))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X0)))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f44])).
% 0.15/0.46 fof(f46,plain,(
% 0.15/0.46 ![B_23]: ((~'LE'(f(suc(B_23)),s(s(s(s('0')))))|'E'(s(s(s('0'))),f(suc(B_23))))|'LE'(f(B_23),s(s(s('0')))))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f15])).
% 0.15/0.46 fof(f47,plain,(
% 0.15/0.46 ![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')))))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f46])).
% 0.15/0.46 fof(f48,plain,(
% 0.15/0.46 ![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)))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f16])).
% 0.15/0.46 fof(f49,plain,(
% 0.15/0.46 ![E,X0]: (~'E'(s(s(s('0'))),f(X0))|~'E'(s(s(s('0'))),f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f48])).
% 0.15/0.46 fof(f50,plain,(
% 0.15/0.46 ![B_60]: ((~'LE'(f(B_60),s('0'))|'E'('0',f(B_60)))|'LE'(f(B_60),'0'))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f17])).
% 0.15/0.46 fof(f51,plain,(
% 0.15/0.46 ![LE,X0,E]: (~'LE'(f(X0),s('0'))|'E'('0',f(X0))|'LE'(f(X0),'0'))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f50])).
% 0.15/0.46 fof(f52,plain,(
% 0.15/0.46 ![B_53]: ((~'LE'(f(suc(B_53)),s(s('0')))|'E'(s('0'),f(suc(B_53))))|'LE'(f(B_53),s('0')))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f18])).
% 0.15/0.46 fof(f53,plain,(
% 0.15/0.46 ![LE,X0,E]: (~'LE'(f(suc(X0)),s(s('0')))|'E'(s('0'),f(suc(X0)))|'LE'(f(X0),s('0')))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f52])).
% 0.15/0.46 fof(f58,plain,(
% 0.15/0.46 ![E,X0]: (~'E'('0',f(suc(X0)))|~iLEQ(suc(X0),suc(X0))|~'E'('0',f(suc(X0)))|~'E'('0',f(X0))|~'E'('0',f(X0))|~'E'('0',f(X0)))),
% 0.15/0.46 inference(factoring,[status(thm)],[f39])).
% 0.15/0.46 fof(f59,plain,(
% 0.15/0.46 ![E,X0]: (~'E'('0',f(suc(X0)))|~iLEQ(suc(X0),suc(X0))|~'E'('0',f(X0)))),
% 0.15/0.46 inference(duplicate_literals_removal,[status(thm)],[f58])).
% 0.15/0.46 fof(f60,plain,(
% 0.15/0.46 ![E,X0]: (~'E'('0',f(suc(X0)))|~'E'('0',f(X0)))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f59,f20])).
% 0.15/0.46 fof(f61,plain,(
% 0.15/0.46 ![E,X0,LE]: ('E'(s(s(s('0'))),f(X0))|'LE'(f(X0),s(s(s('0')))))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f41,f22])).
% 0.15/0.46 fof(f78,plain,(
% 0.15/0.46 ![E,X0,LE]: ('E'(s(s(s('0'))),f(suc(X0)))|'LE'(f(X0),s(s(s('0')))))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f47,f22])).
% 0.15/0.46 fof(f79,plain,(
% 0.15/0.46 ![LE,X0,E]: ('LE'(f(X0),s(s(s('0'))))|~'E'(s(s(s('0'))),f(X0))|iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(resolution,[status(thm)],[f78,f49])).
% 0.15/0.46 fof(f80,plain,(
% 0.15/0.46 ![LE,X0,X1,E]: ('LE'(f(X0),s(s(s('0'))))|~iLEQ(suc(X1),suc(X0))|~'E'(s(s(s('0'))),f(X0))|~'E'(s(s(s('0'))),f(X1))|~iLEQ(suc(X0),suc(X1))|~'E'(s(s(s('0'))),f(X0))|~'E'(s(s(s('0'))),f(suc(X1))))),
% 0.15/0.46 inference(resolution,[status(thm)],[f78,f32])).
% 0.15/0.46 fof(f84,plain,(
% 0.15/0.46 ![LE,X0]: ('LE'(f(X0),s(s(s('0'))))|iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f79,f61])).
% 0.15/0.46 fof(f85,plain,(
% 0.15/0.46 ![LE,X0,X1,E]: ('LE'(f(X0),s(s(s('0'))))|~iLEQ(suc(X1),suc(X0))|~'E'(s(s(s('0'))),f(X0))|~'E'(s(s(s('0'))),f(X1))|~iLEQ(suc(X0),suc(X1))|~'E'(s(s(s('0'))),f(suc(X1))))),
% 0.15/0.46 inference(duplicate_literals_removal,[status(thm)],[f80])).
% 0.15/0.46 fof(f86,plain,(
% 0.15/0.46 ![LE,X0,X1,E]: ('LE'(f(X0),s(s(s('0'))))|~iLEQ(suc(X1),suc(X0))|~'E'(s(s(s('0'))),f(X1))|~iLEQ(suc(X0),suc(X1))|~'E'(s(s(s('0'))),f(suc(X1))))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f85,f61])).
% 0.15/0.46 fof(f92,plain,(
% 0.15/0.46 ![X0,E,LE]: (iLEQ(suc(X0),suc(X0))|'E'(s(s('0')),f(X0))|'LE'(f(X0),s(s('0'))))),
% 0.15/0.46 inference(resolution,[status(thm)],[f84,f43])).
% 0.15/0.46 fof(f111,plain,(
% 0.15/0.46 ![LE,X0,X1,E]: ('LE'(f(X0),s(s(s('0'))))|~iLEQ(suc(X1),suc(X0))|~'E'(s(s(s('0'))),f(X1))|~iLEQ(suc(X0),suc(X1))|'LE'(f(X1),s(s(s('0')))))),
% 0.15/0.46 inference(resolution,[status(thm)],[f86,f78])).
% 0.15/0.46 fof(f114,plain,(
% 0.15/0.46 ![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')))))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f111,f61])).
% 0.15/0.46 fof(f119,plain,(
% 0.15/0.46 ![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')))))),
% 0.15/0.46 inference(resolution,[status(thm)],[f114,f84])).
% 0.15/0.46 fof(f128,plain,(
% 0.15/0.46 ![LE,X0]: ('LE'(f(X0),s(s(s('0'))))|~iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(duplicate_literals_removal,[status(thm)],[f119])).
% 0.15/0.46 fof(f129,plain,(
% 0.15/0.46 ![LE,X0]: ('LE'(f(X0),s(s(s('0')))))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f128,f84])).
% 0.15/0.46 fof(f130,plain,(
% 0.15/0.46 ![E,X0,LE]: ('E'(s(s('0')),f(suc(X0)))|'LE'(f(X0),s(s('0'))))),
% 0.15/0.46 inference(backward_subsumption_resolution,[status(thm)],[f37,f129])).
% 0.15/0.46 fof(f131,plain,(
% 0.15/0.46 ![E,X0,LE]: ('E'(s(s('0')),f(X0))|'LE'(f(X0),s(s('0'))))),
% 0.15/0.46 inference(backward_subsumption_resolution,[status(thm)],[f43,f129])).
% 0.15/0.46 fof(f133,plain,(
% 0.15/0.46 ![LE,X0,E,X1]: ('LE'(f(X0),s(s('0')))|~'E'(s(s('0')),f(suc(X1)))|~'E'(s(s('0')),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1))|~'E'(s(s('0')),f(X0))|~'E'(s(s('0')),f(X0)))),
% 0.15/0.46 inference(resolution,[status(thm)],[f130,f30])).
% 0.15/0.46 fof(f137,plain,(
% 0.15/0.46 ![LE,X0,E]: ('LE'(f(X0),s(s('0')))|~'E'(s(s('0')),f(X0))|iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(resolution,[status(thm)],[f130,f28])).
% 0.15/0.46 fof(f138,plain,(
% 0.15/0.46 ![LE,X0,E,X1]: ('LE'(f(X0),s(s('0')))|~'E'(s(s('0')),f(suc(X1)))|~'E'(s(s('0')),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1))|~'E'(s(s('0')),f(X0)))),
% 0.15/0.46 inference(duplicate_literals_removal,[status(thm)],[f133])).
% 0.15/0.46 fof(f140,plain,(
% 0.15/0.46 ![LE,X0]: ('LE'(f(X0),s(s('0')))|iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f137,f92])).
% 0.15/0.46 fof(f142,plain,(
% 0.15/0.46 ![X0,E,LE]: (iLEQ(suc(X0),suc(X0))|'E'(s('0'),f(X0))|'LE'(f(X0),s('0')))),
% 0.15/0.46 inference(resolution,[status(thm)],[f140,f34])).
% 0.15/0.46 fof(f161,plain,(
% 0.15/0.46 ![LE,X0,E,X1]: ('LE'(f(X0),s(s('0')))|~'E'(s(s('0')),f(suc(X1)))|~'E'(s(s('0')),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1)))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f138,f131])).
% 0.15/0.46 fof(f163,plain,(
% 0.15/0.46 ![LE,X0,E,X1]: ('LE'(f(X0),s(s('0')))|~'E'(s(s('0')),f(X1))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1))|'LE'(f(X1),s(s('0'))))),
% 0.15/0.46 inference(resolution,[status(thm)],[f161,f130])).
% 0.15/0.46 fof(f165,plain,(
% 0.15/0.46 ![LE,X0,X1]: ('LE'(f(X0),s(s('0')))|~iLEQ(suc(X1),suc(X0))|~iLEQ(suc(X0),suc(X1))|'LE'(f(X1),s(s('0'))))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f163,f131])).
% 0.15/0.46 fof(f168,plain,(
% 0.15/0.46 ![LE,X0]: ('LE'(f(X0),s(s('0')))|~iLEQ(suc(X0),suc(X0))|'LE'(f(X0),s(s('0')))|'LE'(f(X0),s(s('0'))))),
% 0.15/0.46 inference(resolution,[status(thm)],[f165,f140])).
% 0.15/0.46 fof(f173,plain,(
% 0.15/0.46 ![LE,X0]: ('LE'(f(X0),s(s('0')))|~iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(duplicate_literals_removal,[status(thm)],[f168])).
% 0.15/0.46 fof(f174,plain,(
% 0.15/0.46 ![LE,X0]: ('LE'(f(X0),s(s('0'))))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f173,f140])).
% 0.15/0.46 fof(f175,plain,(
% 0.15/0.46 ![E,X0,LE]: ('E'(s('0'),f(suc(X0)))|'LE'(f(X0),s('0')))),
% 0.15/0.46 inference(backward_subsumption_resolution,[status(thm)],[f53,f174])).
% 0.15/0.46 fof(f176,plain,(
% 0.15/0.46 ![E,X0,LE]: ('E'(s('0'),f(X0))|'LE'(f(X0),s('0')))),
% 0.15/0.46 inference(backward_subsumption_resolution,[status(thm)],[f34,f174])).
% 0.15/0.46 fof(f177,plain,(
% 0.15/0.46 ![LE,X0,X1,X2,E]: ('LE'(f(X0),s('0'))|~iLEQ(suc(X1),suc(X2))|~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(suc(X2)))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(X2))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X1)))),
% 0.15/0.46 inference(resolution,[status(thm)],[f175,f45])).
% 0.15/0.46 fof(f178,plain,(
% 0.15/0.46 ![LE,X0,E]: ('LE'(f(X0),s('0'))|~'E'(s('0'),f(X0))|iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(resolution,[status(thm)],[f175,f24])).
% 0.15/0.46 fof(f179,plain,(
% 0.15/0.46 ![LE,X0]: ('LE'(f(X0),s('0'))|iLEQ(suc(X0),suc(X0)))),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f178,f142])).
% 0.15/0.46 fof(f190,plain,(
% 0.15/0.46 ![LE,X0,X1,X2,E]: ('LE'(f(X0),s('0'))|~iLEQ(suc(X1),suc(X2))|~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(suc(X2)))|~'E'(s('0'),f(X2))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X1)))),
% 0.15/0.47 inference(forward_subsumption_resolution,[status(thm)],[f177,f176])).
% 0.15/0.47 fof(f192,plain,(
% 0.15/0.47 ![LE,X0,X1,X2,E]: ('LE'(f(X0),s('0'))|~iLEQ(suc(X1),suc(X2))|~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(X2))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X1))|'LE'(f(X2),s('0')))),
% 0.15/0.47 inference(resolution,[status(thm)],[f190,f175])).
% 0.15/0.47 fof(f194,plain,(
% 0.15/0.47 ![LE,X0,X1,X2,E]: ('LE'(f(X0),s('0'))|~iLEQ(suc(X1),suc(X2))|~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X1))|'LE'(f(X2),s('0')))),
% 0.15/0.47 inference(forward_subsumption_resolution,[status(thm)],[f192,f176])).
% 0.15/0.47 fof(f199,plain,(
% 0.15/0.47 ![LE,X0,X1,X2,E]: ('LE'(f(X0),s('0'))|~iLEQ(suc(X1),suc(X2))|~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(X1))|'LE'(f(X2),s('0'))|'LE'(f(X1),s('0')))),
% 0.15/0.47 inference(resolution,[status(thm)],[f194,f175])).
% 0.15/0.47 fof(f201,plain,(
% 0.15/0.47 ![LE,X0,X1,X2]: ('LE'(f(X0),s('0'))|~iLEQ(suc(X1),suc(X2))|~iLEQ(suc(X0),suc(X1))|'LE'(f(X2),s('0'))|'LE'(f(X1),s('0')))),
% 0.15/0.47 inference(forward_subsumption_resolution,[status(thm)],[f199,f176])).
% 0.15/0.47 fof(f206,plain,(
% 0.15/0.47 ![LE,X0,X1]: ('LE'(f(X0),s('0'))|~iLEQ(suc(X0),suc(X1))|'LE'(f(X1),s('0'))|'LE'(f(X1),s('0'))|'LE'(f(X1),s('0')))),
% 0.15/0.47 inference(resolution,[status(thm)],[f201,f179])).
% 0.15/0.47 fof(f213,plain,(
% 0.15/0.47 ![LE,X0,X1]: ('LE'(f(X0),s('0'))|~iLEQ(suc(X0),suc(X1))|'LE'(f(X1),s('0')))),
% 0.15/0.47 inference(duplicate_literals_removal,[status(thm)],[f206])).
% 0.15/0.47 fof(f218,plain,(
% 0.15/0.47 ![LE,X0]: ('LE'(f(X0),s('0'))|'LE'(f(X0),s('0'))|'LE'(f(X0),s('0')))),
% 0.15/0.47 inference(resolution,[status(thm)],[f213,f179])).
% 0.15/0.47 fof(f225,plain,(
% 0.15/0.47 ![LE,X0]: ('LE'(f(X0),s('0')))),
% 0.15/0.47 inference(duplicate_literals_removal,[status(thm)],[f218])).
% 0.15/0.47 fof(f226,plain,(
% 0.15/0.47 ![E,X0,LE]: ('E'('0',f(suc(X0)))|'LE'(f(X0),'0'))),
% 0.15/0.47 inference(backward_subsumption_resolution,[status(thm)],[f26,f225])).
% 0.15/0.47 fof(f227,plain,(
% 0.15/0.47 ![E,X0,LE]: ('E'('0',f(X0))|'LE'(f(X0),'0'))),
% 0.15/0.47 inference(backward_subsumption_resolution,[status(thm)],[f51,f225])).
% 0.15/0.47 fof(f229,plain,(
% 0.15/0.47 ![LE,X0,E]: ('LE'(f(X0),'0')|~'E'('0',f(X0)))),
% 0.15/0.47 inference(resolution,[status(thm)],[f226,f60])).
% 0.15/0.47 fof(f230,plain,(
% 0.15/0.47 ![LE,X0]: ('LE'(f(X0),'0'))),
% 0.15/0.47 inference(forward_subsumption_resolution,[status(thm)],[f229,f227])).
% 0.15/0.47 fof(f232,plain,(
% 0.15/0.47 $false),
% 0.15/0.47 inference(backward_subsumption_resolution,[status(thm)],[f35,f230])).
% 0.15/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.47 % Elapsed time: 0.092317 seconds
% 0.15/0.47 % CPU time: 0.582336 seconds
% 0.15/0.47 % Total memory used: 10.845 MB
% 0.15/0.47 % Net memory used: 9.680 MB
%------------------------------------------------------------------------------