%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYO657-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 03:44:43 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO657-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 12:09:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.39 fof(f1,axiom,(
% 0.10/0.39 (![E,A_2,B_6]: (( ~ 'E'('0',f(suc(A_2)))| ~ 'E'('0',f(A_2))| ~ iLEQ(suc(A_2),suc(B_6))| ~ 'E'('0',f(B_6))| ~ 'E'('0',f(suc(B_6)))| 'E'(f(A_2),f(suc(A_2)))| 'E'(f(B_6),f(suc(B_6))) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f2,axiom,(
% 0.10/0.39 (![LE,B_2,E]: (( ~ 'LE'(f(suc(suc(B_2))),s(s('0')))| 'E'(s('0'),f(suc(suc(B_2))))| 'LE'(f(B_2),s('0')) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f3,axiom,(
% 0.10/0.39 (![LE,A]: ('LE'(f(A),s(s('0'))) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f4,axiom,(
% 0.10/0.39 (![E,A_1]: (( ~ 'E'(s('0'),f(A_1))| ~ 'E'(s('0'),f(suc(A_1)))| 'E'(f(A_1),f(suc(A_1)))| iLEQ(suc(A_1),suc(A_1)) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f7,axiom,(
% 0.10/0.39 (![LE,B_2,E]: (( ~ 'LE'(f(B_2),s(s('0')))| 'E'(s('0'),f(B_2))| 'LE'(f(B_2),s('0')) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f8,axiom,(
% 0.10/0.39 (![LE,B_5,E]: (( ~ 'LE'(f(B_5),s('0'))| 'E'('0',f(B_5))| 'LE'(f(B_5),'0') ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f9,axiom,(
% 0.10/0.39 (![E,A_2]: (( ~ 'E'('0',f(suc(suc(A_2))))| ~ 'E'('0',f(suc(A_2)))| ~ 'E'(f(A_2),f(suc(A_2)))| ~ 'E'('0',f(A_2))| iLEQ(suc(A_2),suc(A_2)) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f10,axiom,(
% 0.10/0.39 (![E,A_2,B_6]: (( ~ 'E'('0',f(suc(A_2)))| ~ 'E'('0',f(suc(suc(A_2))))| ~ 'E'('0',f(A_2))| ~ iLEQ(suc(A_2),suc(B_6))| ~ 'E'('0',f(B_6))| ~ 'E'(f(A_2),f(suc(A_2)))| ~ 'E'('0',f(suc(B_6)))| 'E'(f(B_6),f(suc(B_6))) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f11,axiom,(
% 0.10/0.39 (![E,A_2]: (( ~ 'E'('0',f(A_2))| ~ 'E'('0',f(suc(A_2)))| 'E'(f(A_2),f(suc(A_2)))| iLEQ(suc(A_2),suc(A_2)) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f12,axiom,(
% 0.10/0.39 (![E,A_2,B_6]: (( ~ 'E'('0',f(suc(A_2)))| ~ 'E'('0',f(suc(suc(B_6))))| ~ 'E'('0',f(suc(suc(A_2))))| ~ 'E'('0',f(A_2))| ~ iLEQ(suc(A_2),suc(B_6))| ~ 'E'('0',f(B_6))| ~ 'E'(f(A_2),f(suc(A_2)))| ~ 'E'(f(B_6),f(suc(B_6)))| ~ 'E'('0',f(suc(B_6))) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f13,axiom,(
% 0.10/0.39 (![LE,B_5,E]: (( ~ 'LE'(f(suc(B_5)),s('0'))| 'E'('0',f(suc(B_5)))| 'LE'(f(B_5),'0') ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f14,axiom,(
% 0.10/0.39 (![LE,B_5,E]: (( ~ 'LE'(f(suc(suc(B_5))),s('0'))| 'E'('0',f(suc(suc(B_5))))| 'LE'(f(B_5),'0') ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f15,axiom,(
% 0.10/0.39 (![LE]: (~ 'LE'(f(z),'0') ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f16,axiom,(
% 0.10/0.39 (![LE,B_2,E]: (( ~ 'LE'(f(suc(B_2)),s(s('0')))| 'E'(s('0'),f(suc(B_2)))| 'LE'(f(B_2),s('0')) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f17,axiom,(
% 0.10/0.39 (![A_1,B_3,E]: (( ~ iLEQ(suc(A_1),suc(B_3))| ~ 'E'(s('0'),f(A_1))| ~ 'E'(s('0'),f(suc(A_1)))| ~ 'E'(s('0'),f(suc(B_3)))| ~ 'E'(s('0'),f(B_3))| 'E'(f(A_1),f(suc(A_1)))| 'E'(f(B_3),f(suc(B_3))) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f18,axiom,(
% 0.10/0.39 (![E,A_1]: (( ~ 'E'(s('0'),f(suc(suc(A_1))))| ~ 'E'(s('0'),f(suc(A_1)))| ~ 'E'(f(A_1),f(suc(A_1)))| ~ 'E'(s('0'),f(A_1))| iLEQ(suc(A_1),suc(A_1)) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f19,axiom,(
% 0.10/0.39 (![A_1,B_3,E]: (( ~ iLEQ(suc(A_1),suc(B_3))| ~ 'E'(s('0'),f(A_1))| ~ 'E'(s('0'),f(suc(suc(B_3))))| ~ 'E'(s('0'),f(suc(A_1)))| ~ 'E'(s('0'),f(suc(B_3)))| ~ 'E'(s('0'),f(B_3))| ~ 'E'(f(B_3),f(suc(B_3)))| 'E'(f(A_1),f(suc(A_1))) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f20,axiom,(
% 0.10/0.39 (![A_1,B_3,E]: (( ~ iLEQ(suc(A_1),suc(B_3))| ~ 'E'(s('0'),f(suc(suc(A_1))))| ~ 'E'(s('0'),f(A_1))| ~ 'E'(s('0'),f(suc(suc(B_3))))| ~ 'E'(s('0'),f(suc(A_1)))| ~ 'E'(s('0'),f(suc(B_3)))| ~ 'E'(s('0'),f(B_3))| ~ 'E'(f(B_3),f(suc(B_3)))| ~ 'E'(f(A_1),f(suc(A_1))) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f21,plain,(
% 0.10/0.39 ![B_6]: ((![A_2]: (((((~'E'('0',f(suc(A_2)))|~'E'('0',f(A_2)))|~iLEQ(suc(A_2),suc(B_6)))|~'E'('0',f(B_6)))|~'E'('0',f(suc(B_6))))|'E'(f(A_2),f(suc(A_2)))))|'E'(f(B_6),f(suc(B_6))))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f1])).
% 0.10/0.39 fof(f22,plain,(
% 0.10/0.39 ![E,X0,X1]: (~'E'('0',f(suc(X0)))|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X1))|~'E'('0',f(X1))|~'E'('0',f(suc(X1)))|'E'(f(X0),f(suc(X0)))|'E'(f(X1),f(suc(X1))))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f21])).
% 0.10/0.39 fof(f23,plain,(
% 0.10/0.39 ![B_2]: ((~'LE'(f(suc(suc(B_2))),s(s('0')))|'E'(s('0'),f(suc(suc(B_2)))))|'LE'(f(B_2),s('0')))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f2])).
% 0.10/0.39 fof(f24,plain,(
% 0.10/0.39 ![LE,X0,E]: (~'LE'(f(suc(suc(X0))),s(s('0')))|'E'(s('0'),f(suc(suc(X0))))|'LE'(f(X0),s('0')))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f23])).
% 0.10/0.39 fof(f25,plain,(
% 0.10/0.39 ![A]: 'LE'(f(A),s(s('0')))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f3])).
% 0.10/0.39 fof(f26,plain,(
% 0.10/0.39 ![LE,X0]: ('LE'(f(X0),s(s('0'))))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f25])).
% 0.10/0.39 fof(f27,plain,(
% 0.10/0.39 ![A_1]: (((~'E'(s('0'),f(A_1))|~'E'(s('0'),f(suc(A_1))))|'E'(f(A_1),f(suc(A_1))))|iLEQ(suc(A_1),suc(A_1)))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f4])).
% 0.10/0.39 fof(f28,plain,(
% 0.10/0.39 ![E,X0]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|'E'(f(X0),f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f27])).
% 0.10/0.39 fof(f33,plain,(
% 0.10/0.39 ![B_2]: ((~'LE'(f(B_2),s(s('0')))|'E'(s('0'),f(B_2)))|'LE'(f(B_2),s('0')))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f7])).
% 0.10/0.39 fof(f34,plain,(
% 0.10/0.39 ![LE,X0,E]: (~'LE'(f(X0),s(s('0')))|'E'(s('0'),f(X0))|'LE'(f(X0),s('0')))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f33])).
% 0.10/0.39 fof(f35,plain,(
% 0.10/0.39 ![B_5]: ((~'LE'(f(B_5),s('0'))|'E'('0',f(B_5)))|'LE'(f(B_5),'0'))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f8])).
% 0.10/0.39 fof(f36,plain,(
% 0.10/0.39 ![LE,X0,E]: (~'LE'(f(X0),s('0'))|'E'('0',f(X0))|'LE'(f(X0),'0'))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f35])).
% 0.10/0.39 fof(f37,plain,(
% 0.10/0.39 ![A_2]: ((((~'E'('0',f(suc(suc(A_2))))|~'E'('0',f(suc(A_2))))|~'E'(f(A_2),f(suc(A_2))))|~'E'('0',f(A_2)))|iLEQ(suc(A_2),suc(A_2)))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f9])).
% 0.10/0.39 fof(f38,plain,(
% 0.10/0.39 ![E,X0]: (~'E'('0',f(suc(suc(X0))))|~'E'('0',f(suc(X0)))|~'E'(f(X0),f(suc(X0)))|~'E'('0',f(X0))|iLEQ(suc(X0),suc(X0)))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f37])).
% 0.10/0.39 fof(f39,plain,(
% 0.10/0.39 ![B_6]: (((![A_2]: (((((~'E'('0',f(suc(A_2)))|~'E'('0',f(suc(suc(A_2)))))|~'E'('0',f(A_2)))|~iLEQ(suc(A_2),suc(B_6)))|~'E'('0',f(B_6)))|~'E'(f(A_2),f(suc(A_2)))))|~'E'('0',f(suc(B_6))))|'E'(f(B_6),f(suc(B_6))))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f10])).
% 0.10/0.39 fof(f40,plain,(
% 0.10/0.39 ![E,X0,X1]: (~'E'('0',f(suc(X0)))|~'E'('0',f(suc(suc(X0))))|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X1))|~'E'('0',f(X1))|~'E'(f(X0),f(suc(X0)))|~'E'('0',f(suc(X1)))|'E'(f(X1),f(suc(X1))))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f39])).
% 0.10/0.39 fof(f41,plain,(
% 0.10/0.39 ![A_2]: (((~'E'('0',f(A_2))|~'E'('0',f(suc(A_2))))|'E'(f(A_2),f(suc(A_2))))|iLEQ(suc(A_2),suc(A_2)))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f11])).
% 0.10/0.39 fof(f42,plain,(
% 0.10/0.39 ![E,X0]: (~'E'('0',f(X0))|~'E'('0',f(suc(X0)))|'E'(f(X0),f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f41])).
% 0.10/0.39 fof(f43,plain,(
% 0.10/0.39 ![B_6]: (((![A_2]: ((((((~'E'('0',f(suc(A_2)))|~'E'('0',f(suc(suc(B_6)))))|~'E'('0',f(suc(suc(A_2)))))|~'E'('0',f(A_2)))|~iLEQ(suc(A_2),suc(B_6)))|~'E'('0',f(B_6)))|~'E'(f(A_2),f(suc(A_2)))))|~'E'(f(B_6),f(suc(B_6))))|~'E'('0',f(suc(B_6))))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f12])).
% 0.10/0.39 fof(f44,plain,(
% 0.10/0.39 ![E,X0,X1]: (~'E'('0',f(suc(X0)))|~'E'('0',f(suc(suc(X1))))|~'E'('0',f(suc(suc(X0))))|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X1))|~'E'('0',f(X1))|~'E'(f(X0),f(suc(X0)))|~'E'(f(X1),f(suc(X1)))|~'E'('0',f(suc(X1))))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f43])).
% 0.10/0.39 fof(f45,plain,(
% 0.10/0.39 ![B_5]: ((~'LE'(f(suc(B_5)),s('0'))|'E'('0',f(suc(B_5))))|'LE'(f(B_5),'0'))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f13])).
% 0.10/0.39 fof(f46,plain,(
% 0.10/0.39 ![LE,X0,E]: (~'LE'(f(suc(X0)),s('0'))|'E'('0',f(suc(X0)))|'LE'(f(X0),'0'))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f45])).
% 0.10/0.39 fof(f47,plain,(
% 0.10/0.39 ![B_5]: ((~'LE'(f(suc(suc(B_5))),s('0'))|'E'('0',f(suc(suc(B_5)))))|'LE'(f(B_5),'0'))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f14])).
% 0.10/0.39 fof(f48,plain,(
% 0.10/0.39 ![LE,X0,E]: (~'LE'(f(suc(suc(X0))),s('0'))|'E'('0',f(suc(suc(X0))))|'LE'(f(X0),'0'))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f47])).
% 0.10/0.39 fof(f49,plain,(
% 0.10/0.39 ![LE]: (~'LE'(f(z),'0'))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f15])).
% 0.10/0.39 fof(f50,plain,(
% 0.10/0.39 ![B_2]: ((~'LE'(f(suc(B_2)),s(s('0')))|'E'(s('0'),f(suc(B_2))))|'LE'(f(B_2),s('0')))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f16])).
% 0.10/0.39 fof(f51,plain,(
% 0.10/0.39 ![LE,X0,E]: (~'LE'(f(suc(X0)),s(s('0')))|'E'(s('0'),f(suc(X0)))|'LE'(f(X0),s('0')))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f50])).
% 0.10/0.39 fof(f52,plain,(
% 0.10/0.39 ![B_3]: ((![A_1]: (((((~iLEQ(suc(A_1),suc(B_3))|~'E'(s('0'),f(A_1)))|~'E'(s('0'),f(suc(A_1))))|~'E'(s('0'),f(suc(B_3))))|~'E'(s('0'),f(B_3)))|'E'(f(A_1),f(suc(A_1)))))|'E'(f(B_3),f(suc(B_3))))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f17])).
% 0.10/0.39 fof(f53,plain,(
% 0.10/0.39 ![X0,X1,E]: (~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X1))|'E'(f(X0),f(suc(X0)))|'E'(f(X1),f(suc(X1))))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f52])).
% 0.10/0.40 fof(f54,plain,(
% 0.10/0.40 ![A_1]: ((((~'E'(s('0'),f(suc(suc(A_1))))|~'E'(s('0'),f(suc(A_1))))|~'E'(f(A_1),f(suc(A_1))))|~'E'(s('0'),f(A_1)))|iLEQ(suc(A_1),suc(A_1)))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f18])).
% 0.10/0.40 fof(f55,plain,(
% 0.10/0.40 ![E,X0]: (~'E'(s('0'),f(suc(suc(X0))))|~'E'(s('0'),f(suc(X0)))|~'E'(f(X0),f(suc(X0)))|~'E'(s('0'),f(X0))|iLEQ(suc(X0),suc(X0)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f54])).
% 0.10/0.40 fof(f56,plain,(
% 0.10/0.40 ![A_1]: ((![B_3]: ((((((~iLEQ(suc(A_1),suc(B_3))|~'E'(s('0'),f(A_1)))|~'E'(s('0'),f(suc(suc(B_3)))))|~'E'(s('0'),f(suc(A_1))))|~'E'(s('0'),f(suc(B_3))))|~'E'(s('0'),f(B_3)))|~'E'(f(B_3),f(suc(B_3)))))|'E'(f(A_1),f(suc(A_1))))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f19])).
% 0.10/0.40 fof(f57,plain,(
% 0.10/0.40 ![X0,X1,E]: (~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(suc(X1))))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X1))|~'E'(f(X1),f(suc(X1)))|'E'(f(X0),f(suc(X0))))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f56])).
% 0.10/0.40 fof(f58,plain,(
% 0.10/0.40 ![A_1]: ((![B_3]: (((((((~iLEQ(suc(A_1),suc(B_3))|~'E'(s('0'),f(suc(suc(A_1)))))|~'E'(s('0'),f(A_1)))|~'E'(s('0'),f(suc(suc(B_3)))))|~'E'(s('0'),f(suc(A_1))))|~'E'(s('0'),f(suc(B_3))))|~'E'(s('0'),f(B_3)))|~'E'(f(B_3),f(suc(B_3)))))|~'E'(f(A_1),f(suc(A_1))))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f20])).
% 0.10/0.40 fof(f59,plain,(
% 0.10/0.40 ![X0,X1,E]: (~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(suc(suc(X0))))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(suc(X1))))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X1))|~'E'(f(X1),f(suc(X1)))|~'E'(f(X0),f(suc(X0))))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f58])).
% 0.10/0.40 fof(f60,plain,(
% 0.10/0.40 ![E,X0,LE]: ('E'(s('0'),f(X0))|'LE'(f(X0),s('0')))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f34,f26])).
% 0.10/0.40 fof(f63,plain,(
% 0.10/0.40 ![E,X0,LE]: ('E'(s('0'),f(suc(suc(X0))))|'LE'(f(X0),s('0')))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f24,f26])).
% 0.10/0.40 fof(f65,plain,(
% 0.10/0.40 ![E,X0,LE]: ('E'(s('0'),f(suc(X0)))|'LE'(f(X0),s('0')))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f51,f26])).
% 0.10/0.40 fof(f66,plain,(
% 0.10/0.40 ![E,X0]: (~'E'('0',f(suc(suc(X0))))|~'E'('0',f(suc(X0)))|~'E'('0',f(X0))|iLEQ(suc(X0),suc(X0)))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f38,f42])).
% 0.10/0.40 fof(f67,plain,(
% 0.10/0.40 ![E,X0]: (~'E'(s('0'),f(suc(suc(X0))))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X0))|iLEQ(suc(X0),suc(X0)))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f55,f28])).
% 0.10/0.40 fof(f69,plain,(
% 0.10/0.40 ![E,X0]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X0))|'E'(f(X0),f(suc(X0)))|'E'(f(X0),f(suc(X0)))|~'E'(s('0'),f(suc(suc(X0))))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X0)))),
% 0.10/0.40 inference(resolution,[status(thm)],[f53,f67])).
% 0.10/0.40 fof(f71,plain,(
% 0.10/0.40 ![E,X0]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|'E'(f(X0),f(suc(X0)))|~'E'(s('0'),f(suc(suc(X0)))))),
% 0.10/0.40 inference(duplicate_literals_removal,[status(thm)],[f69])).
% 0.10/0.40 fof(f74,plain,(
% 0.10/0.40 ![E,X0,X1]: (~'E'('0',f(suc(X0)))|~'E'('0',f(suc(suc(X0))))|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X1))|~'E'('0',f(X1))|~'E'('0',f(suc(X1)))|'E'(f(X1),f(suc(X1))))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f40,f22])).
% 0.10/0.40 fof(f75,plain,(
% 0.10/0.40 ![E,X0,X1]: (~'E'('0',f(suc(X0)))|~'E'('0',f(suc(suc(X1))))|~'E'('0',f(suc(suc(X0))))|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X1))|~'E'('0',f(X1))|~'E'(f(X0),f(suc(X0)))|~'E'('0',f(suc(X1))))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f44,f74])).
% 0.10/0.40 fof(f76,plain,(
% 0.10/0.40 ![X0,X1,E]: (~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(suc(X1))))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X1))|'E'(f(X0),f(suc(X0))))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f57,f53])).
% 0.10/0.40 fof(f77,plain,(
% 0.10/0.40 ![X0,X1,E]: (~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(suc(suc(X0))))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(suc(X1))))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X1))|~'E'(f(X1),f(suc(X1))))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f59,f76])).
% 0.10/0.40 fof(f78,plain,(
% 0.10/0.40 ![E,X0]: (~'E'(s('0'),f(suc(suc(X0))))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(suc(X0))))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X0))|~'E'(f(X0),f(suc(X0)))|~'E'(s('0'),f(suc(suc(X0))))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X0)))),
% 0.10/0.40 inference(resolution,[status(thm)],[f77,f67])).
% 0.10/0.40 fof(f80,plain,(
% 0.10/0.40 ![E,X0]: (~'E'(s('0'),f(suc(suc(X0))))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|~'E'(f(X0),f(suc(X0))))),
% 0.10/0.40 inference(duplicate_literals_removal,[status(thm)],[f78])).
% 0.10/0.40 fof(f81,plain,(
% 0.10/0.40 ![E,X0]: (~'E'(s('0'),f(suc(suc(X0))))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0))))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f80,f71])).
% 0.10/0.40 fof(f85,plain,(
% 0.10/0.40 ![E,X0,LE]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|'LE'(f(X0),s('0')))),
% 0.10/0.40 inference(resolution,[status(thm)],[f81,f63])).
% 0.10/0.40 fof(f89,plain,(
% 0.10/0.40 ![E,X0,LE]: (~'E'(s('0'),f(suc(X0)))|'LE'(f(X0),s('0')))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f85,f60])).
% 0.10/0.40 fof(f91,plain,(
% 0.10/0.40 ![E,X0,LE]: ('E'('0',f(suc(suc(X0))))|'LE'(f(X0),'0'))),
% 0.10/0.40 inference(backward_subsumption_resolution,[status(thm)],[f48,f94])).
% 0.10/0.40 fof(f92,plain,(
% 0.10/0.40 ![E,X0,LE]: ('E'('0',f(suc(X0)))|'LE'(f(X0),'0'))),
% 0.10/0.40 inference(backward_subsumption_resolution,[status(thm)],[f46,f94])).
% 0.10/0.40 fof(f93,plain,(
% 0.10/0.40 ![E,X0,LE]: ('E'('0',f(X0))|'LE'(f(X0),'0'))),
% 0.10/0.40 inference(backward_subsumption_resolution,[status(thm)],[f36,f94])).
% 0.10/0.40 fof(f94,plain,(
% 0.10/0.40 ![LE,X0]: ('LE'(f(X0),s('0')))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f89,f65])).
% 0.10/0.40 fof(f95,plain,(
% 0.10/0.40 ![E]: ('E'('0',f(z)))),
% 0.10/0.40 inference(resolution,[status(thm)],[f93,f49])).
% 0.10/0.40 fof(f103,definition,(
% 0.10/0.40 ![E]: (sQ2_spl <=> ('E'(f(z),f(suc(z)))))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f105,plain,(
% 0.10/0.40 ![E]: (~'E'(f(z),f(suc(z)))|sQ2_spl)),
% 0.10/0.40 inference(component_clause,[status(thm)],[f103])).
% 0.10/0.40 fof(f106,definition,(
% 0.10/0.40 ![E]: (sQ3_spl <=> ('E'('0',f(suc(suc(z))))))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f107,plain,(
% 0.10/0.40 ![E]: ('E'('0',f(suc(suc(z))))|~sQ3_spl)),
% 0.10/0.40 inference(component_clause,[status(thm)],[f106])).
% 0.10/0.40 fof(f108,plain,(
% 0.10/0.40 ![E]: (~'E'('0',f(suc(suc(z))))|sQ3_spl)),
% 0.10/0.40 inference(component_clause,[status(thm)],[f106])).
% 0.10/0.40 fof(f109,definition,(
% 0.10/0.40 ![E]: (sQ4_spl <=> ('E'('0',f(suc(z)))))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f111,plain,(
% 0.10/0.40 ![E]: (~'E'('0',f(suc(z)))|sQ4_spl)),
% 0.10/0.40 inference(component_clause,[status(thm)],[f109])).
% 0.10/0.40 fof(f118,plain,(
% 0.10/0.40 ![LE,X0,E,X1]: ('LE'(f(X0),'0')|~'E'('0',f(suc(X0)))|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X1))|~'E'('0',f(X1))|~'E'('0',f(suc(X1)))|'E'(f(X1),f(suc(X1))))),
% 0.10/0.40 inference(resolution,[status(thm)],[f91,f74])).
% 0.10/0.40 fof(f138,plain,(
% 0.10/0.40 ![LE,X0,E,X1]: ('LE'(f(X0),'0')|~'E'('0',f(suc(X0)))|~iLEQ(suc(X0),suc(X1))|~'E'('0',f(X1))|~'E'('0',f(suc(X1)))|'E'(f(X1),f(suc(X1))))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f118,f93])).
% 0.10/0.40 fof(f145,plain,(
% 0.10/0.40 ![LE]: ('LE'(f(z),'0')|sQ4_spl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f92,f111])).
% 0.10/0.40 fof(f163,plain,(
% 0.10/0.40 $false|sQ4_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f145,f49])).
% 0.10/0.40 fof(f164,plain,(
% 0.10/0.40 sQ4_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f163])).
% 0.10/0.40 fof(f197,definition,(
% 0.10/0.40 ![E]: (sQ6_spl <=> ('E'('0',f(z))))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f199,plain,(
% 0.10/0.40 ![E]: (~'E'('0',f(z))|sQ6_spl)),
% 0.10/0.40 inference(component_clause,[status(thm)],[f197])).
% 0.10/0.40 fof(f210,definition,(
% 0.10/0.40 sQ9_spl <=> (iLEQ(suc(z),suc(z)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f211,plain,(
% 0.10/0.40 iLEQ(suc(z),suc(z))|~sQ9_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f210])).
% 0.10/0.40 fof(f212,plain,(
% 0.10/0.40 ~iLEQ(suc(z),suc(z))|sQ9_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f210])).
% 0.10/0.40 fof(f225,plain,(
% 0.10/0.40 $false|sQ6_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f199,f95])).
% 0.10/0.40 fof(f226,plain,(
% 0.10/0.40 sQ6_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f225])).
% 0.10/0.40 fof(f230,plain,(
% 0.10/0.40 ![LE]: ('LE'(f(z),'0')|sQ3_spl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f108,f91])).
% 0.10/0.40 fof(f232,plain,(
% 0.10/0.40 $false|sQ3_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f230,f49])).
% 0.10/0.40 fof(f233,plain,(
% 0.10/0.40 sQ3_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f232])).
% 0.10/0.40 fof(f238,plain,(
% 0.10/0.40 ![E]: (~'E'('0',f(suc(z)))|~'E'('0',f(z))|~iLEQ(suc(z),suc(z))|~'E'('0',f(z))|~'E'(f(z),f(suc(z)))|~'E'('0',f(suc(z)))|~sQ3_spl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f107,f75])).
% 0.10/0.40 fof(f255,plain,(
% 0.10/0.40 ~sQ4_spl|~sQ6_spl|~sQ9_spl|~sQ2_spl|~sQ3_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f238,f109,f197,f210,f103,f106])).
% 0.10/0.40 fof(f302,plain,(
% 0.10/0.40 ![E]: (~'E'('0',f(suc(suc(z))))|~'E'('0',f(suc(z)))|~'E'('0',f(z))|sQ9_spl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f212,f66])).
% 0.10/0.40 fof(f303,plain,(
% 0.10/0.40 ~sQ3_spl|~sQ4_spl|~sQ6_spl|sQ9_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f302,f106,f109,f197,f210])).
% 0.10/0.40 fof(f336,plain,(
% 0.10/0.40 ![LE,X0,X1,E]: ('LE'(f(X0),'0')|~iLEQ(suc(X0),suc(X1))|~'E'('0',f(X1))|~'E'('0',f(suc(X1)))|'E'(f(X1),f(suc(X1))))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f138,f92])).
% 0.10/0.40 fof(f337,plain,(
% 0.10/0.40 ![LE,X0,E]: ('LE'(f(X0),'0')|~iLEQ(suc(X0),suc(z))|~'E'('0',f(z))|~'E'('0',f(suc(z)))|sQ2_spl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f336,f105])).
% 0.10/0.40 fof(f339,definition,(
% 0.10/0.40 ![LE,X0]: (sQ26_spl <=> ('LE'(f(X0),'0')|~iLEQ(suc(X0),suc(z))))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f340,plain,(
% 0.10/0.40 ![LE,X0]: ('LE'(f(X0),'0')|~iLEQ(suc(X0),suc(z))|~sQ26_spl)),
% 0.10/0.40 inference(component_clause,[status(thm)],[f339])).
% 0.10/0.40 fof(f342,plain,(
% 0.10/0.40 sQ26_spl|~sQ6_spl|~sQ4_spl|sQ2_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f337,f339,f197,f109,f103])).
% 0.10/0.40 fof(f344,plain,(
% 0.10/0.40 ![LE]: ('LE'(f(z),'0')|~sQ26_spl|~sQ9_spl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f340,f211])).
% 0.10/0.40 fof(f346,plain,(
% 0.10/0.40 $false|~sQ26_spl|~sQ9_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f344,f49])).
% 0.10/0.40 fof(f347,plain,(
% 0.10/0.40 ~sQ26_spl|~sQ9_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f346])).
% 0.10/0.40 fof(f348,plain,(
% 0.10/0.40 $false),
% 0.10/0.40 inference(sat_refutation,[status(thm)],[f164,f226,f233,f255,f303,f342,f347])).
% 0.10/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.41 % Elapsed time: 0.037310 seconds
% 0.10/0.41 % CPU time: 0.128352 seconds
% 0.10/0.41 % Total memory used: 3.611 MB
% 0.10/0.41 % Net memory used: 3.328 MB
%------------------------------------------------------------------------------