%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE151-10 : 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 : n004.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 12:58:25 PM UTC 2026
% Result : Unsatisfiable 15.36s 2.50s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE151-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n004.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 20 22:46:35 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 15.36/2.50 % Refutation found
% 15.36/2.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 15.36/2.50 % SZS output start CNFRefutation for theBenchmark
% 15.36/2.50 fof(f1,axiom,(
% 15.36/2.50 (![A,B,C]: (ifeq3(A,A,B,C) = B ))),
% 15.36/2.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.36/2.50 fof(f3,axiom,(
% 15.36/2.50 (![A,B,C]: (ifeq(A,A,B,C) = B ))),
% 15.36/2.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.36/2.50 fof(f4,axiom,(
% 15.36/2.50 (![A,B]: (addition(A,B) = addition(B,A) ))),
% 15.36/2.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.36/2.50 fof(f7,axiom,(
% 15.36/2.50 (![A]: (addition(A,A) = A ))),
% 15.36/2.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.36/2.50 fof(f8,axiom,(
% 15.36/2.50 (![A,B,C]: (multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ))),
% 15.36/2.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.36/2.50 fof(f9,axiom,(
% 15.36/2.50 (![A]: (multiplication(A,one) = A ))),
% 15.36/2.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.36/2.50 fof(f11,axiom,(
% 15.36/2.50 (![A,B,C]: (multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ))),
% 15.36/2.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.36/2.50 fof(f18,axiom,(
% 15.36/2.50 (![A]: (strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ))),
% 15.36/2.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.36/2.50 fof(f19,axiom,(
% 15.36/2.50 (![C,A,B]: (ifeq(leq(C,addition(multiplication(A,C),B)),true,leq(C,multiplication(strong_iteration(A),B)),true) = true ))),
% 15.36/2.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.36/2.50 fof(f22,axiom,(
% 15.36/2.50 (![A,B]: (ifeq3(addition(A,B),B,leq(A,B),true) = true ))),
% 15.36/2.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.36/2.50 fof(f23,negated_conjecture,(
% 15.36/2.50 leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) != true ),
% 15.36/2.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.36/2.50 fof(f24,plain,(
% 15.36/2.50 ![X0,X1,X2]: (ifeq3(X0,X0,X1,X2)=X1)),
% 15.36/2.50 inference(cnf_transformation,[status(thm)],[f1])).
% 15.36/2.50 fof(f26,plain,(
% 15.36/2.50 ![X0,X1,X2]: (ifeq(X0,X0,X1,X2)=X1)),
% 15.36/2.50 inference(cnf_transformation,[status(thm)],[f3])).
% 15.36/2.50 fof(f27,plain,(
% 15.36/2.50 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 15.36/2.50 inference(cnf_transformation,[status(thm)],[f4])).
% 15.36/2.50 fof(f30,plain,(
% 15.36/2.50 ![X0]: (addition(X0,X0)=X0)),
% 15.36/2.50 inference(cnf_transformation,[status(thm)],[f7])).
% 15.36/2.50 fof(f31,plain,(
% 15.36/2.50 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 15.36/2.50 inference(cnf_transformation,[status(thm)],[f8])).
% 15.36/2.50 fof(f32,plain,(
% 15.36/2.50 ![X0]: (multiplication(X0,one)=X0)),
% 15.36/2.50 inference(cnf_transformation,[status(thm)],[f9])).
% 15.36/2.50 fof(f34,plain,(
% 15.36/2.50 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 15.36/2.50 inference(cnf_transformation,[status(thm)],[f11])).
% 15.36/2.50 fof(f41,plain,(
% 15.36/2.50 ![X0]: (strong_iteration(X0)=addition(multiplication(X0,strong_iteration(X0)),one))),
% 15.36/2.50 inference(cnf_transformation,[status(thm)],[f18])).
% 15.36/2.50 fof(f42,plain,(
% 15.36/2.50 ![X0,X1,X2]: (ifeq(leq(X0,addition(multiplication(X1,X0),X2)),true,leq(X0,multiplication(strong_iteration(X1),X2)),true)=true)),
% 15.36/2.50 inference(cnf_transformation,[status(thm)],[f19])).
% 15.36/2.50 fof(f45,plain,(
% 15.36/2.50 ![X0,X1]: (ifeq3(addition(X0,X1),X1,leq(X0,X1),true)=true)),
% 15.36/2.50 inference(cnf_transformation,[status(thm)],[f22])).
% 15.36/2.50 fof(f46,plain,(
% 15.36/2.50 ~leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0))=true),
% 15.36/2.50 inference(cnf_transformation,[status(thm)],[f23])).
% 15.36/2.50 fof(f47,definition,(
% 15.36/2.50 sF3_fnc=multiplication(sK1_goals_X1,sK2_goals_X0)),
% 15.36/2.50 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 15.36/2.50 fof(f48,definition,(
% 15.36/2.50 sF2_fnc=strong_iteration(sF3_fnc)),
% 15.36/2.50 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 15.36/2.50 fof(f49,definition,(
% 15.36/2.50 sF1_fnc=multiplication(sK2_goals_X0,sF2_fnc)),
% 15.36/2.50 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 15.36/2.50 fof(f50,definition,(
% 15.36/2.50 sF6_fnc=multiplication(sK2_goals_X0,sK1_goals_X1)),
% 15.36/2.50 introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition])).
% 15.36/2.54 fof(f51,definition,(
% 15.36/2.54 sF5_fnc=strong_iteration(sF6_fnc)),
% 15.36/2.54 introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition])).
% 15.36/2.54 fof(f52,definition,(
% 15.36/2.54 sF4_fnc=multiplication(sF5_fnc,sK2_goals_X0)),
% 15.36/2.54 introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition])).
% 15.36/2.54 fof(f53,definition,(
% 15.36/2.54 sF0_fnc=leq(sF1_fnc,sF4_fnc)),
% 15.36/2.54 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 15.36/2.54 fof(f54,plain,(
% 15.36/2.54 ~sF0_fnc=true),
% 15.36/2.54 inference(definition_folding,[],[f46,f53,f52,f51,f50,f49,f48,f47])).
% 15.36/2.54 fof(f57,plain,(
% 15.36/2.54 ![X0]: (multiplication(sK2_goals_X0,multiplication(sK1_goals_X1,X0))=multiplication(sF6_fnc,X0))),
% 15.36/2.54 inference(paramodulation,[status(thm)],[f50,f31])).
% 15.36/2.54 fof(f59,plain,(
% 15.36/2.54 ![X0]: (multiplication(sK1_goals_X1,multiplication(sK2_goals_X0,X0))=multiplication(sF3_fnc,X0))),
% 15.36/2.54 inference(paramodulation,[status(thm)],[f47,f31])).
% 15.36/2.54 fof(f122,plain,(
% 15.36/2.54 multiplication(sK1_goals_X1,sF1_fnc)=multiplication(sF3_fnc,sF2_fnc)),
% 15.36/2.54 inference(paramodulation,[status(thm)],[f49,f59])).
% 15.36/2.54 fof(f200,plain,(
% 15.36/2.54 ![X0,X1]: (multiplication(sK2_goals_X0,addition(X0,multiplication(sK1_goals_X1,X1)))=addition(multiplication(sK2_goals_X0,X0),multiplication(sF6_fnc,X1)))),
% 15.36/2.54 inference(paramodulation,[status(thm)],[f57,f34])).
% 15.36/2.54 fof(f702,plain,(
% 15.36/2.54 ![X0]: (strong_iteration(X0)=addition(one,multiplication(X0,strong_iteration(X0))))),
% 15.36/2.54 inference(forward_demodulation,[status(thm)],[f27,f41])).
% 15.36/2.54 fof(f707,plain,(
% 15.36/2.54 strong_iteration(sF3_fnc)=addition(one,multiplication(sF3_fnc,sF2_fnc))),
% 15.36/2.54 inference(paramodulation,[status(thm)],[f48,f702])).
% 15.36/2.54 fof(f713,plain,(
% 15.36/2.54 sF2_fnc=addition(one,multiplication(sF3_fnc,sF2_fnc))),
% 15.36/2.54 inference(forward_demodulation,[status(thm)],[f48,f707])).
% 15.36/2.54 fof(f714,plain,(
% 15.36/2.54 sF2_fnc=addition(one,multiplication(sK1_goals_X1,sF1_fnc))),
% 15.36/2.54 inference(forward_demodulation,[status(thm)],[f122,f713])).
% 15.36/2.54 fof(f748,plain,(
% 15.36/2.54 ![X0,X1,X2]: (ifeq(leq(X0,addition(X1,multiplication(X2,X0))),true,leq(X0,multiplication(strong_iteration(X2),X1)),true)=true)),
% 15.36/2.54 inference(paramodulation,[status(thm)],[f27,f42])).
% 15.36/2.54 fof(f1377,plain,(
% 15.36/2.54 ![X0]: (ifeq3(X0,X0,leq(X0,X0),true)=true)),
% 15.36/2.54 inference(paramodulation,[status(thm)],[f30,f45])).
% 15.36/2.54 fof(f1387,plain,(
% 15.36/2.54 ![X0]: (leq(X0,X0)=true)),
% 15.36/2.54 inference(forward_demodulation,[status(thm)],[f24,f1377])).
% 15.36/2.54 fof(f15222,plain,(
% 15.36/2.54 multiplication(sK2_goals_X0,sF2_fnc)=addition(multiplication(sK2_goals_X0,one),multiplication(sF6_fnc,sF1_fnc))),
% 15.36/2.54 inference(paramodulation,[status(thm)],[f714,f200])).
% 15.36/2.54 fof(f15322,plain,(
% 15.36/2.54 sF1_fnc=addition(multiplication(sK2_goals_X0,one),multiplication(sF6_fnc,sF1_fnc))),
% 15.36/2.54 inference(forward_demodulation,[status(thm)],[f49,f15222])).
% 15.36/2.54 fof(f15323,plain,(
% 15.36/2.54 sF1_fnc=addition(sK2_goals_X0,multiplication(sF6_fnc,sF1_fnc))),
% 15.36/2.54 inference(forward_demodulation,[status(thm)],[f32,f15322])).
% 15.36/2.54 fof(f16422,plain,(
% 15.36/2.54 ifeq(leq(sF1_fnc,sF1_fnc),true,leq(sF1_fnc,multiplication(strong_iteration(sF6_fnc),sK2_goals_X0)),true)=true),
% 15.36/2.54 inference(paramodulation,[status(thm)],[f15323,f748])).
% 15.36/2.54 fof(f16455,plain,(
% 15.36/2.54 ifeq(true,true,leq(sF1_fnc,multiplication(strong_iteration(sF6_fnc),sK2_goals_X0)),true)=true),
% 15.36/2.54 inference(forward_demodulation,[status(thm)],[f1387,f16422])).
% 15.36/2.54 fof(f16456,plain,(
% 15.36/2.54 leq(sF1_fnc,multiplication(strong_iteration(sF6_fnc),sK2_goals_X0))=true),
% 15.36/2.54 inference(forward_demodulation,[status(thm)],[f26,f16455])).
% 15.36/2.54 fof(f16457,plain,(
% 15.36/2.54 leq(sF1_fnc,multiplication(sF5_fnc,sK2_goals_X0))=true),
% 15.36/2.54 inference(forward_demodulation,[status(thm)],[f51,f16456])).
% 15.36/2.54 fof(f16458,plain,(
% 15.36/2.54 leq(sF1_fnc,sF4_fnc)=true),
% 15.36/2.54 inference(forward_demodulation,[status(thm)],[f52,f16457])).
% 15.36/2.54 fof(f16481,plain,(
% 15.36/2.54 sF0_fnc=true),
% 15.36/2.54 inference(backward_demodulation,[status(thm)],[f16458,f53])).
% 15.36/2.54 fof(f16487,plain,(
% 15.36/2.54 $false),
% 15.36/2.54 inference(forward_subsumption_resolution,[status(thm)],[f16481,f54])).
% 15.36/2.54 % SZS output end CNFRefutation for theBenchmark.p
% 15.36/2.60 % Elapsed time: 2.138580 seconds
% 15.36/2.60 % CPU time: 16.598351 seconds
% 15.36/2.60 % Total memory used: 243.338 MB
% 15.36/2.60 % Net memory used: 240.695 MB
%------------------------------------------------------------------------------