%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:06:47 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n015.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Mon Sep 21 13:51:51 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.35 % Drodi V4.1.1
% 0.12/0.62 % Refutation found
% 0.12/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.62 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.62 fof(f1,axiom,(
% 0.12/0.62 (![X,Y,Z]: (add(X,multiply(Y,multiply(X,Z))) = X ))),
% 0.12/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.62 fof(f2,axiom,(
% 0.12/0.62 (![X,Y,Z]: (add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y ))),
% 0.12/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.62 fof(f4,axiom,(
% 0.12/0.62 (![X,Y,Z]: (multiply(X,add(Y,add(X,Z))) = X ))),
% 0.12/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.62 fof(f5,axiom,(
% 0.12/0.62 (![X,Y,Z]: (multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y ))),
% 0.12/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.62 fof(f6,axiom,(
% 0.12/0.62 (![X,Y]: (add(multiply(X,Y),multiply(X,inverse(Y))) = X ))),
% 0.12/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.62 fof(f7,axiom,(
% 0.12/0.62 (![X,Y]: (add(X,Y) = add(Y,X) ))),
% 0.12/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.62 fof(f8,axiom,(
% 0.12/0.62 (![X,Y]: (multiply(X,Y) = multiply(Y,X) ))),
% 0.12/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.62 fof(f9,axiom,(
% 0.12/0.62 (![X,Y,Z]: (add(add(X,Y),Z) = add(X,add(Y,Z)) ))),
% 0.12/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.62 fof(f10,axiom,(
% 0.12/0.62 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.12/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.62 fof(f11,negated_conjecture,(
% 0.12/0.62 add(b,inverse(b)) != add(a,inverse(a)) ),
% 0.12/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.62 fof(f12,plain,(
% 0.12/0.62 ![X0,X1,X2]: (add(X0,multiply(X1,multiply(X0,X2)))=X0)),
% 0.12/0.62 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.62 fof(f13,plain,(
% 0.12/0.62 ![X0,X1,X2]: (add(add(multiply(X0,X1),multiply(X1,X2)),X1)=X1)),
% 0.12/0.62 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.62 fof(f15,plain,(
% 0.12/0.62 ![X0,X1,X2]: (multiply(X0,add(X1,add(X0,X2)))=X0)),
% 0.12/0.62 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.62 fof(f16,plain,(
% 0.12/0.62 ![X0,X1,X2]: (multiply(multiply(add(X0,X1),add(X1,X2)),X1)=X1)),
% 0.12/0.62 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.62 fof(f17,plain,(
% 0.12/0.62 ![X0,X1]: (add(multiply(X0,X1),multiply(X0,inverse(X1)))=X0)),
% 0.12/0.62 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.62 fof(f18,plain,(
% 0.12/0.62 ![X0,X1]: (add(X0,X1)=add(X1,X0))),
% 0.12/0.62 inference(cnf_transformation,[status(thm)],[f7])).
% 0.12/0.62 fof(f19,plain,(
% 0.12/0.62 ![X0,X1]: (multiply(X0,X1)=multiply(X1,X0))),
% 0.12/0.62 inference(cnf_transformation,[status(thm)],[f8])).
% 0.12/0.62 fof(f20,plain,(
% 0.12/0.62 ![X0,X1,X2]: (add(add(X0,X1),X2)=add(X0,add(X1,X2)))),
% 0.12/0.62 inference(cnf_transformation,[status(thm)],[f9])).
% 0.12/0.62 fof(f21,plain,(
% 0.12/0.62 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.12/0.62 inference(cnf_transformation,[status(thm)],[f10])).
% 0.12/0.62 fof(f22,plain,(
% 0.12/0.62 ~add(b,inverse(b))=add(a,inverse(a))),
% 0.12/0.62 inference(cnf_transformation,[status(thm)],[f11])).
% 0.12/0.62 fof(f23,definition,(
% 0.12/0.62 sF1_fnc=inverse(b)),
% 0.12/0.62 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.12/0.62 fof(f24,definition,(
% 0.12/0.62 sF0_fnc=add(b,sF1_fnc)),
% 0.12/0.62 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.12/0.62 fof(f25,definition,(
% 0.12/0.62 sF3_fnc=inverse(a)),
% 0.12/0.62 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 0.12/0.62 fof(f26,definition,(
% 0.12/0.62 sF2_fnc=add(a,sF3_fnc)),
% 0.12/0.62 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 0.12/0.62 fof(f27,plain,(
% 0.12/0.62 ~sF0_fnc=sF2_fnc),
% 0.12/0.62 inference(definition_folding,[],[f22,f26,f25,f24,f23])).
% 0.12/0.62 fof(f28,plain,(
% 0.12/0.62 ![X0,X1,X2]: (add(multiply(X0,X1),add(multiply(X1,X2),X1))=X1)),
% 0.12/0.62 inference(backward_demodulation,[status(thm)],[f20,f13])).
% 0.12/0.62 fof(f29,plain,(
% 0.12/0.62 ![X0,X1,X2]: (multiply(add(X0,X1),multiply(add(X1,X2),X1))=X1)),
% 0.12/0.62 inference(backward_demodulation,[status(thm)],[f21,f16])).
% 0.12/0.62 fof(f40,plain,(
% 0.12/0.62 ![X0,X1,X2]: (add(X0,multiply(X1,multiply(X2,X0)))=X0)),
% 0.12/0.62 inference(paramodulation,[status(thm)],[f19,f12])).
% 0.12/0.62 fof(f65,plain,(
% 0.12/0.62 ![X0]: (multiply(b,add(X0,sF0_fnc))=b)),
% 0.12/0.62 inference(paramodulation,[status(thm)],[f24,f15])).
% 0.12/0.62 fof(f66,plain,(
% 0.12/0.62 ![X0,X1]: (multiply(X0,add(X1,X0))=X0)),
% 0.12/0.62 inference(paramodulation,[status(thm)],[f40,f15])).
% 0.12/0.62 fof(f73,plain,(
% 0.12/0.62 ![X0,X1]: (add(X0,multiply(X1,X0))=X0)),
% 0.12/0.62 inference(paramodulation,[status(thm)],[f15,f12])).
% 0.12/0.63 fof(f86,plain,(
% 0.12/0.63 multiply(sF1_fnc,sF0_fnc)=sF1_fnc),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f24,f66])).
% 0.12/0.63 fof(f423,plain,(
% 0.12/0.63 ![X0,X1,X2]: (add(add(multiply(X0,X1),X0),multiply(X2,X0))=X0)),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f18,f28])).
% 0.12/0.63 fof(f432,plain,(
% 0.12/0.63 ![X0]: (add(sF1_fnc,add(multiply(sF0_fnc,X0),sF0_fnc))=sF0_fnc)),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f86,f28])).
% 0.12/0.63 fof(f441,plain,(
% 0.12/0.63 ![X0,X1,X2]: (add(multiply(X0,add(multiply(X1,X2),X1)),X1)=add(multiply(X1,X2),X1))),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f28,f28])).
% 0.12/0.63 fof(f468,plain,(
% 0.12/0.63 ![X0,X1,X2]: (add(multiply(X0,X1),add(X0,multiply(X2,X0)))=X0)),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f20,f423])).
% 0.12/0.63 fof(f471,plain,(
% 0.12/0.63 ![X0,X1]: (add(multiply(X0,X1),X0)=X0)),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f73,f468])).
% 0.12/0.63 fof(f481,plain,(
% 0.12/0.63 add(sF1_fnc,sF0_fnc)=sF0_fnc),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f471,f432])).
% 0.12/0.63 fof(f490,plain,(
% 0.12/0.63 ![X0,X1,X2]: (add(multiply(X0,X1),X1)=add(multiply(X1,X2),X1))),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f471,f441])).
% 0.12/0.63 fof(f491,plain,(
% 0.12/0.63 ![X0,X1]: (add(multiply(X0,X1),X1)=X1)),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f471,f490])).
% 0.12/0.63 fof(f527,plain,(
% 0.12/0.63 ![X0]: (multiply(sF1_fnc,add(X0,sF0_fnc))=sF1_fnc)),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f481,f15])).
% 0.12/0.63 fof(f630,plain,(
% 0.12/0.63 ![X0,X1,X2]: (multiply(multiply(add(X0,X1),X0),add(X2,X0))=X0)),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f19,f29])).
% 0.12/0.63 fof(f697,plain,(
% 0.12/0.63 ![X0,X1,X2]: (multiply(add(X0,X1),multiply(X0,add(X2,X0)))=X0)),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f21,f630])).
% 0.12/0.63 fof(f700,plain,(
% 0.12/0.63 ![X0,X1]: (multiply(add(X0,X1),X0)=X0)),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f66,f697])).
% 0.12/0.63 fof(f771,plain,(
% 0.12/0.63 ![X0,X1]: (multiply(X0,multiply(X1,X0))=multiply(X1,X0))),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f491,f700])).
% 0.12/0.63 fof(f1600,plain,(
% 0.12/0.63 ![X0]: (multiply(add(X0,sF0_fnc),b)=multiply(b,add(X0,sF0_fnc)))),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f65,f771])).
% 0.12/0.63 fof(f1612,plain,(
% 0.12/0.63 ![X0]: (multiply(add(X0,sF0_fnc),sF1_fnc)=multiply(sF1_fnc,add(X0,sF0_fnc)))),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f527,f771])).
% 0.12/0.63 fof(f1652,plain,(
% 0.12/0.63 ![X0]: (multiply(add(X0,sF0_fnc),b)=b)),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f65,f1600])).
% 0.12/0.63 fof(f1664,plain,(
% 0.12/0.63 ![X0]: (multiply(add(X0,sF0_fnc),sF1_fnc)=sF1_fnc)),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f527,f1612])).
% 0.12/0.63 fof(f1711,plain,(
% 0.12/0.63 ![X0]: (add(b,multiply(add(X0,sF0_fnc),inverse(b)))=add(X0,sF0_fnc))),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f1652,f17])).
% 0.12/0.63 fof(f1720,plain,(
% 0.12/0.63 ![X0]: (add(b,multiply(add(X0,sF0_fnc),sF1_fnc))=add(X0,sF0_fnc))),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f23,f1711])).
% 0.12/0.63 fof(f1721,plain,(
% 0.12/0.63 ![X0]: (add(b,sF1_fnc)=add(X0,sF0_fnc))),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f1664,f1720])).
% 0.12/0.63 fof(f1738,plain,(
% 0.12/0.63 ![X0]: (sF0_fnc=add(X0,sF0_fnc))),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f24,f1721])).
% 0.12/0.63 fof(f1764,plain,(
% 0.12/0.63 ![X0]: (multiply(sF0_fnc,X0)=X0)),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f1738,f700])).
% 0.12/0.63 fof(f1934,plain,(
% 0.12/0.63 ![X0]: (add(multiply(sF0_fnc,X0),inverse(X0))=sF0_fnc)),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f1764,f17])).
% 0.12/0.63 fof(f1963,plain,(
% 0.12/0.63 ![X0]: (add(X0,inverse(X0))=sF0_fnc)),
% 0.12/0.63 inference(forward_demodulation,[status(thm)],[f1764,f1934])).
% 0.12/0.63 fof(f1973,plain,(
% 0.12/0.63 add(a,sF3_fnc)=sF0_fnc),
% 0.12/0.63 inference(paramodulation,[status(thm)],[f25,f1963])).
% 0.12/0.63 fof(f1991,plain,(
% 0.12/0.63 sF2_fnc=sF0_fnc),
% 0.12/0.63 inference(backward_demodulation,[status(thm)],[f1973,f26])).
% 0.12/0.63 fof(f2001,plain,(
% 0.12/0.63 $false),
% 0.12/0.63 inference(forward_subsumption_resolution,[status(thm)],[f1991,f27])).
% 0.12/0.63 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.64 % Elapsed time: 0.294433 seconds
% 0.12/0.64 % CPU time: 2.137288 seconds
% 0.12/0.64 % Total memory used: 31.751 MB
% 0.12/0.64 % Net memory used: 31.187 MB
%------------------------------------------------------------------------------