%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYO664-1 : 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 : n009.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 03:44:44 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO664-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 12:08:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.38 fof(f1,axiom,(
% 0.09/0.38 (![E,B_45,B_46,B_43,A_1,B_44]: (( ~ 'E'(s('0'),f(suc(B_45)))| ~ 'E'(s('0'),f(B_45))| ~ 'E'(s('0'),f(suc(B_46)))| ~ 'E'(s('0'),f(suc(B_43)))| ~ 'E'(s('0'),f(A_1))| ~ 'E'(s('0'),f(suc(A_1)))| ~ iLEQ(suc(A_1),suc(B_43))| ~ 'E'(s('0'),f(B_43))| ~ iLEQ(suc(B_44),suc(B_45))| ~ 'E'(s('0'),f(B_46))| ~ 'E'(s('0'),f(B_44))| ~ iLEQ(suc(B_45),suc(B_46))| ~ iLEQ(suc(B_43),suc(B_44))| ~ 'E'(s('0'),f(suc(B_44))) ) ))),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f2,axiom,(
% 0.09/0.38 (![LE]: (~ 'LE'(f(z),'0') ))),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f3,axiom,(
% 0.09/0.38 (![LE,B_42,E]: (( ~ 'LE'(f(B_42),s(s('0')))| 'E'(s('0'),f(B_42))| 'LE'(f(B_42),s('0')) ) ))),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f4,axiom,(
% 0.09/0.38 (![E,B_63,B_61,A_2,B_62,B_64]: (( ~ 'E'('0',f(B_63))| ~ 'E'('0',f(suc(B_61)))| ~ 'E'('0',f(suc(A_2)))| ~ iLEQ(suc(A_2),suc(B_61))| ~ iLEQ(suc(B_61),suc(B_62))| ~ 'E'('0',f(suc(B_63)))| ~ 'E'('0',f(A_2))| ~ iLEQ(suc(B_62),suc(B_63))| ~ 'E'('0',f(B_64))| ~ iLEQ(suc(B_63),suc(B_64))| ~ 'E'('0',f(suc(B_62)))| ~ 'E'('0',f(B_61))| ~ 'E'('0',f(suc(B_64)))| ~ 'E'('0',f(B_62)) ) ))),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f5,axiom,(
% 0.09/0.38 (![LE,A]: ('LE'(f(A),s(s('0'))) ))),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f6,axiom,(
% 0.09/0.38 (![E,A_2]: (( ~ 'E'('0',f(A_2))| ~ 'E'('0',f(suc(A_2)))| iLEQ(suc(A_2),suc(A_2)) ) ))),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f7,axiom,(
% 0.09/0.38 (![LE,B_60,E]: (( ~ 'LE'(f(suc(B_60)),s('0'))| 'E'('0',f(suc(B_60)))| 'LE'(f(B_60),'0') ) ))),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f8,axiom,(
% 0.09/0.38 (![LE,B_60,E]: (( ~ 'LE'(f(B_60),s('0'))| 'E'('0',f(B_60))| 'LE'(f(B_60),'0') ) ))),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f9,axiom,(
% 0.09/0.38 (![E,A_1]: (( ~ 'E'(s('0'),f(A_1))| ~ 'E'(s('0'),f(suc(A_1)))| iLEQ(suc(A_1),suc(A_1)) ) ))),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f10,axiom,(
% 0.09/0.38 (![LE,B_42,E]: (( ~ 'LE'(f(suc(B_42)),s(s('0')))| 'E'(s('0'),f(suc(B_42)))| 'LE'(f(B_42),s('0')) ) ))),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f11,plain,(
% 0.09/0.38 ![B_44]: ((![B_43]: ((![B_45,B_46]: ((((((![A_1]: ((((((~'E'(s('0'),f(suc(B_45)))|~'E'(s('0'),f(B_45)))|~'E'(s('0'),f(suc(B_46))))|~'E'(s('0'),f(suc(B_43))))|~'E'(s('0'),f(A_1)))|~'E'(s('0'),f(suc(A_1))))|~iLEQ(suc(A_1),suc(B_43))))|~'E'(s('0'),f(B_43)))|~iLEQ(suc(B_44),suc(B_45)))|~'E'(s('0'),f(B_46)))|~'E'(s('0'),f(B_44)))|~iLEQ(suc(B_45),suc(B_46))))|~iLEQ(suc(B_43),suc(B_44))))|~'E'(s('0'),f(suc(B_44))))),
% 0.09/0.38 inference(miniscoping,[status(thm)],[f1])).
% 0.09/0.38 fof(f12,plain,(
% 0.09/0.38 ![E,X0,X1,X2,X3,X4]: (~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(suc(X2)))|~'E'(s('0'),f(X3))|~'E'(s('0'),f(suc(X3)))|~iLEQ(suc(X3),suc(X2))|~'E'(s('0'),f(X2))|~iLEQ(suc(X4),suc(X0))|~'E'(s('0'),f(X1))|~'E'(s('0'),f(X4))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X2),suc(X4))|~'E'(s('0'),f(suc(X4))))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f11])).
% 0.09/0.38 fof(f13,plain,(
% 0.09/0.38 ![LE]: (~'LE'(f(z),'0'))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f2])).
% 0.09/0.38 fof(f14,plain,(
% 0.09/0.38 ![B_42]: ((~'LE'(f(B_42),s(s('0')))|'E'(s('0'),f(B_42)))|'LE'(f(B_42),s('0')))),
% 0.09/0.38 inference(miniscoping,[status(thm)],[f3])).
% 0.09/0.38 fof(f15,plain,(
% 0.09/0.38 ![LE,X0,E]: (~'LE'(f(X0),s(s('0')))|'E'(s('0'),f(X0))|'LE'(f(X0),s('0')))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/0.38 fof(f16,plain,(
% 0.09/0.38 ![B_62]: ((![B_64]: ((![B_61]: (((![B_63]: ((((![A_2]: ((((((~'E'('0',f(B_63))|~'E'('0',f(suc(B_61))))|~'E'('0',f(suc(A_2))))|~iLEQ(suc(A_2),suc(B_61)))|~iLEQ(suc(B_61),suc(B_62)))|~'E'('0',f(suc(B_63))))|~'E'('0',f(A_2))))|~iLEQ(suc(B_62),suc(B_63)))|~'E'('0',f(B_64)))|~iLEQ(suc(B_63),suc(B_64))))|~'E'('0',f(suc(B_62))))|~'E'('0',f(B_61))))|~'E'('0',f(suc(B_64)))))|~'E'('0',f(B_62)))),
% 0.09/0.38 inference(miniscoping,[status(thm)],[f4])).
% 0.09/0.38 fof(f17,plain,(
% 0.09/0.38 ![E,X0,X1,X2,X3,X4]: (~'E'('0',f(X0))|~'E'('0',f(suc(X1)))|~'E'('0',f(suc(X2)))|~iLEQ(suc(X2),suc(X1))|~iLEQ(suc(X1),suc(X3))|~'E'('0',f(suc(X0)))|~'E'('0',f(X2))|~iLEQ(suc(X3),suc(X0))|~'E'('0',f(X4))|~iLEQ(suc(X0),suc(X4))|~'E'('0',f(suc(X3)))|~'E'('0',f(X1))|~'E'('0',f(suc(X4)))|~'E'('0',f(X3)))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f16])).
% 0.09/0.38 fof(f18,plain,(
% 0.09/0.38 ![A]: 'LE'(f(A),s(s('0')))),
% 0.09/0.38 inference(miniscoping,[status(thm)],[f5])).
% 0.09/0.38 fof(f19,plain,(
% 0.09/0.38 ![LE,X0]: ('LE'(f(X0),s(s('0'))))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f18])).
% 0.09/0.38 fof(f20,plain,(
% 0.09/0.38 ![A_2]: ((~'E'('0',f(A_2))|~'E'('0',f(suc(A_2))))|iLEQ(suc(A_2),suc(A_2)))),
% 0.09/0.38 inference(miniscoping,[status(thm)],[f6])).
% 0.09/0.38 fof(f21,plain,(
% 0.09/0.38 ![E,X0]: (~'E'('0',f(X0))|~'E'('0',f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f20])).
% 0.09/0.38 fof(f22,plain,(
% 0.09/0.38 ![B_60]: ((~'LE'(f(suc(B_60)),s('0'))|'E'('0',f(suc(B_60))))|'LE'(f(B_60),'0'))),
% 0.09/0.38 inference(miniscoping,[status(thm)],[f7])).
% 0.09/0.38 fof(f23,plain,(
% 0.09/0.38 ![LE,X0,E]: (~'LE'(f(suc(X0)),s('0'))|'E'('0',f(suc(X0)))|'LE'(f(X0),'0'))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f22])).
% 0.09/0.39 fof(f24,plain,(
% 0.09/0.39 ![B_60]: ((~'LE'(f(B_60),s('0'))|'E'('0',f(B_60)))|'LE'(f(B_60),'0'))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f8])).
% 0.09/0.39 fof(f25,plain,(
% 0.09/0.39 ![LE,X0,E]: (~'LE'(f(X0),s('0'))|'E'('0',f(X0))|'LE'(f(X0),'0'))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f24])).
% 0.09/0.39 fof(f26,plain,(
% 0.09/0.39 ![A_1]: ((~'E'(s('0'),f(A_1))|~'E'(s('0'),f(suc(A_1))))|iLEQ(suc(A_1),suc(A_1)))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f9])).
% 0.09/0.39 fof(f27,plain,(
% 0.09/0.39 ![E,X0]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|iLEQ(suc(X0),suc(X0)))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f26])).
% 0.09/0.39 fof(f28,plain,(
% 0.09/0.39 ![B_42]: ((~'LE'(f(suc(B_42)),s(s('0')))|'E'(s('0'),f(suc(B_42))))|'LE'(f(B_42),s('0')))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f10])).
% 0.09/0.39 fof(f29,plain,(
% 0.09/0.39 ![LE,X0,E]: (~'LE'(f(suc(X0)),s(s('0')))|'E'(s('0'),f(suc(X0)))|'LE'(f(X0),s('0')))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f28])).
% 0.09/0.39 fof(f30,plain,(
% 0.09/0.39 ![E,X0,LE]: ('E'(s('0'),f(X0))|'LE'(f(X0),s('0')))),
% 0.09/0.39 inference(backward_subsumption_resolution,[status(thm)],[f15,f19])).
% 0.09/0.39 fof(f31,plain,(
% 0.09/0.39 ![E,X0,LE]: ('E'(s('0'),f(suc(X0)))|'LE'(f(X0),s('0')))),
% 0.09/0.39 inference(forward_subsumption_resolution,[status(thm)],[f29,f19])).
% 0.09/0.39 fof(f32,plain,(
% 0.09/0.39 ![E,X0,X1,X2,X3]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(suc(X2)))|~'E'(s('0'),f(X3))|~'E'(s('0'),f(suc(X3)))|~iLEQ(suc(X3),suc(X2))|~'E'(s('0'),f(X2))|~'E'(s('0'),f(X1))|~'E'(s('0'),f(X0))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X2),suc(X0))|~'E'(s('0'),f(suc(X0))))),
% 0.09/0.39 inference(resolution,[status(thm)],[f27,f12])).
% 0.09/0.39 fof(f33,plain,(
% 0.09/0.39 ![E,X0,X1,X2,X3]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(suc(X2)))|~'E'(s('0'),f(X3))|~'E'(s('0'),f(suc(X3)))|~iLEQ(suc(X3),suc(X2))|~'E'(s('0'),f(X2))|~'E'(s('0'),f(X1))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X2),suc(X0)))),
% 0.09/0.39 inference(duplicate_literals_removal,[status(thm)],[f32])).
% 0.09/0.39 fof(f34,plain,(
% 0.09/0.39 ![E,X0,X1,X2]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(suc(X2)))|~'E'(s('0'),f(X2))|~'E'(s('0'),f(suc(X2)))|~'E'(s('0'),f(X2))|~'E'(s('0'),f(X1))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X2),suc(X0))|~'E'(s('0'),f(X2))|~'E'(s('0'),f(suc(X2))))),
% 0.09/0.39 inference(resolution,[status(thm)],[f33,f27])).
% 0.09/0.39 fof(f35,plain,(
% 0.09/0.39 ![E,X0,X1,X2]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(suc(X2)))|~'E'(s('0'),f(X2))|~'E'(s('0'),f(X1))|~iLEQ(suc(X0),suc(X1))|~iLEQ(suc(X2),suc(X0)))),
% 0.09/0.39 inference(duplicate_literals_removal,[status(thm)],[f34])).
% 0.09/0.39 fof(f36,plain,(
% 0.09/0.39 ![E,X0,X1]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(X1))|~iLEQ(suc(X0),suc(X1))|~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0))))),
% 0.09/0.39 inference(resolution,[status(thm)],[f35,f27])).
% 0.09/0.39 fof(f37,plain,(
% 0.09/0.39 ![E,X0,X1]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0)))|~'E'(s('0'),f(suc(X1)))|~'E'(s('0'),f(X1))|~iLEQ(suc(X0),suc(X1)))),
% 0.09/0.39 inference(duplicate_literals_removal,[status(thm)],[f36])).
% 0.09/0.39 fof(f38,plain,(
% 0.09/0.39 ![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'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0))))),
% 0.09/0.39 inference(resolution,[status(thm)],[f37,f27])).
% 0.09/0.39 fof(f39,plain,(
% 0.09/0.39 ![E,X0]: (~'E'(s('0'),f(X0))|~'E'(s('0'),f(suc(X0))))),
% 0.09/0.39 inference(duplicate_literals_removal,[status(thm)],[f38])).
% 0.09/0.39 fof(f40,plain,(
% 0.09/0.39 ![E,X0,LE]: (~'E'(s('0'),f(X0))|'LE'(f(X0),s('0')))),
% 0.09/0.39 inference(resolution,[status(thm)],[f39,f31])).
% 0.09/0.39 fof(f42,plain,(
% 0.09/0.39 ![E,X0,LE]: ('E'('0',f(suc(X0)))|'LE'(f(X0),'0'))),
% 0.09/0.39 inference(backward_subsumption_resolution,[status(thm)],[f23,f44])).
% 0.09/0.39 fof(f43,plain,(
% 0.09/0.39 ![E,X0,LE]: ('E'('0',f(X0))|'LE'(f(X0),'0'))),
% 0.09/0.39 inference(backward_subsumption_resolution,[status(thm)],[f25,f44])).
% 0.09/0.39 fof(f44,plain,(
% 0.09/0.39 ![LE,X0]: ('LE'(f(X0),s('0')))),
% 0.09/0.39 inference(forward_subsumption_resolution,[status(thm)],[f40,f30])).
% 0.09/0.39 fof(f45,plain,(
% 0.09/0.39 ![LE,X0,E]: ('LE'(f(X0),'0')|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X0))|~iLEQ(suc(X0),suc(X0))|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X0))|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X0))|~'E'('0',f(X0))|~'E'('0',f(X0)))),
% 0.09/0.39 inference(resolution,[status(thm)],[f42,f17])).
% 0.09/0.39 fof(f55,plain,(
% 0.09/0.39 ![LE,X0,E]: ('LE'(f(X0),'0')|~'E'('0',f(X0))|iLEQ(suc(X0),suc(X0)))),
% 0.09/0.39 inference(resolution,[status(thm)],[f42,f21])).
% 0.09/0.39 fof(f64,plain,(
% 0.09/0.39 ![LE,X0,E]: ('LE'(f(X0),'0')|~'E'('0',f(X0))|~iLEQ(suc(X0),suc(X0)))),
% 0.09/0.39 inference(duplicate_literals_removal,[status(thm)],[f45])).
% 0.09/0.39 fof(f65,plain,(
% 0.09/0.39 ![LE,X0]: ('LE'(f(X0),'0')|~iLEQ(suc(X0),suc(X0)))),
% 0.09/0.39 inference(forward_subsumption_resolution,[status(thm)],[f64,f43])).
% 0.09/0.39 fof(f75,plain,(
% 0.09/0.39 ![LE,X0]: ('LE'(f(X0),'0'))),
% 0.09/0.39 inference(backward_subsumption_resolution,[status(thm)],[f65,f76])).
% 0.09/0.39 fof(f76,plain,(
% 0.09/0.39 ![LE,X0]: ('LE'(f(X0),'0')|iLEQ(suc(X0),suc(X0)))),
% 0.09/0.39 inference(forward_subsumption_resolution,[status(thm)],[f55,f43])).
% 0.09/0.39 fof(f82,plain,(
% 0.09/0.39 $false),
% 0.09/0.39 inference(backward_subsumption_resolution,[status(thm)],[f13,f75])).
% 0.09/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.40 % Elapsed time: 0.035498 seconds
% 0.09/0.40 % CPU time: 0.111958 seconds
% 0.09/0.40 % Total memory used: 2.842 MB
% 0.09/0.40 % Net memory used: 2.630 MB
%------------------------------------------------------------------------------