%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:06:44 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.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 13:50:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.39 fof(f1,axiom,(
% 0.15/0.39 (![X,Y]: (add(X,Y) = add(Y,X) ))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f2,axiom,(
% 0.15/0.39 (![X,Y]: (multiply(X,Y) = multiply(Y,X) ))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f3,axiom,(
% 0.15/0.39 (![X,Y,Z]: (add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f4,axiom,(
% 0.15/0.39 (![X,Y,Z]: (multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f5,axiom,(
% 0.15/0.39 (![X]: (add(X,additive_identity) = X ))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f6,axiom,(
% 0.15/0.39 (![X]: (multiply(X,multiplicative_identity) = X ))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f7,axiom,(
% 0.15/0.39 (![X]: (add(X,inverse(X)) = multiplicative_identity ))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f8,axiom,(
% 0.15/0.39 (![X]: (multiply(X,inverse(X)) = additive_identity ))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f9,negated_conjecture,(
% 0.15/0.39 multiply(a,add(a,b)) != a ),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f10,plain,(
% 0.15/0.39 ![X0,X1]: (add(X0,X1)=add(X1,X0))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.15/0.39 fof(f11,plain,(
% 0.15/0.39 ![X0,X1]: (multiply(X0,X1)=multiply(X1,X0))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.15/0.39 fof(f12,plain,(
% 0.15/0.39 ![X0,X1,X2]: (add(X0,multiply(X1,X2))=multiply(add(X0,X1),add(X0,X2)))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.15/0.39 fof(f13,plain,(
% 0.15/0.39 ![X0,X1,X2]: (multiply(X0,add(X1,X2))=add(multiply(X0,X1),multiply(X0,X2)))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.15/0.39 fof(f14,plain,(
% 0.15/0.39 ![X0]: (add(X0,additive_identity)=X0)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.15/0.39 fof(f15,plain,(
% 0.15/0.39 ![X0]: (multiply(X0,multiplicative_identity)=X0)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.15/0.39 fof(f16,plain,(
% 0.15/0.39 ![X0]: (add(X0,inverse(X0))=multiplicative_identity)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.15/0.39 fof(f17,plain,(
% 0.15/0.39 ![X0]: (multiply(X0,inverse(X0))=additive_identity)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.15/0.39 fof(f18,plain,(
% 0.15/0.39 ~multiply(a,add(a,b))=a),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.15/0.39 fof(f19,definition,(
% 0.15/0.39 sF1_fnc=add(a,b)),
% 0.15/0.39 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.15/0.39 fof(f20,definition,(
% 0.15/0.39 sF0_fnc=multiply(a,sF1_fnc)),
% 0.15/0.39 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.15/0.39 fof(f21,plain,(
% 0.15/0.39 ~sF0_fnc=a),
% 0.15/0.39 inference(definition_folding,[],[f18,f20,f19])).
% 0.15/0.39 fof(f40,plain,(
% 0.15/0.39 ![X0]: (X0=multiply(multiplicative_identity,X0))),
% 0.15/0.39 inference(paramodulation,[status(thm)],[f15,f11])).
% 0.15/0.39 fof(f62,plain,(
% 0.15/0.39 ![X0,X1]: (add(X0,multiply(inverse(X0),X1))=multiply(multiplicative_identity,add(X0,X1)))),
% 0.15/0.39 inference(paramodulation,[status(thm)],[f16,f12])).
% 0.15/0.39 fof(f68,plain,(
% 0.15/0.39 ![X0,X1]: (add(X0,multiply(X1,inverse(X0)))=multiply(add(X0,X1),multiplicative_identity))),
% 0.15/0.39 inference(paramodulation,[status(thm)],[f16,f12])).
% 0.15/0.39 fof(f75,plain,(
% 0.15/0.39 ![X0,X1]: (add(X0,multiply(inverse(X0),X1))=add(X0,X1))),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f40,f62])).
% 0.15/0.39 fof(f77,plain,(
% 0.15/0.39 ![X0,X1]: (add(X0,multiply(X1,inverse(X0)))=add(X0,X1))),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f15,f68])).
% 0.15/0.39 fof(f80,plain,(
% 0.15/0.39 ![X0]: (add(X0,inverse(X0))=add(X0,multiplicative_identity))),
% 0.15/0.39 inference(paramodulation,[status(thm)],[f15,f75])).
% 0.15/0.39 fof(f91,plain,(
% 0.15/0.39 ![X0]: (multiplicative_identity=add(X0,multiplicative_identity))),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f16,f80])).
% 0.15/0.39 fof(f99,plain,(
% 0.15/0.39 ![X0]: (multiplicative_identity=add(multiplicative_identity,X0))),
% 0.15/0.39 inference(paramodulation,[status(thm)],[f10,f91])).
% 0.15/0.39 fof(f144,plain,(
% 0.15/0.39 ![X0]: (add(X0,additive_identity)=add(X0,X0))),
% 0.15/0.39 inference(paramodulation,[status(thm)],[f17,f77])).
% 0.15/0.39 fof(f157,plain,(
% 0.15/0.39 ![X0]: (X0=add(X0,X0))),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f14,f144])).
% 0.15/0.39 fof(f174,plain,(
% 0.15/0.39 ![X0,X1]: (add(X0,multiply(X0,X1))=multiply(X0,add(X0,X1)))),
% 0.15/0.39 inference(paramodulation,[status(thm)],[f157,f12])).
% 0.15/0.39 fof(f183,plain,(
% 0.15/0.39 ![X0,X1]: (multiply(X0,add(multiplicative_identity,X1))=add(X0,multiply(X0,X1)))),
% 0.15/0.39 inference(paramodulation,[status(thm)],[f15,f13])).
% 0.15/0.39 fof(f201,plain,(
% 0.15/0.39 ![X0,X1]: (multiply(X0,multiplicative_identity)=add(X0,multiply(X0,X1)))),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f99,f183])).
% 0.15/0.39 fof(f202,plain,(
% 0.15/0.39 ![X0,X1]: (X0=multiply(X0,add(X0,X1)))),
% 0.15/0.39 inference(backward_demodulation,[status(thm)],[f203,f174])).
% 0.15/0.39 fof(f203,plain,(
% 0.15/0.39 ![X0,X1]: (X0=add(X0,multiply(X0,X1)))),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f15,f201])).
% 0.15/0.39 fof(f456,plain,(
% 0.15/0.39 a=multiply(a,sF1_fnc)),
% 0.15/0.39 inference(paramodulation,[status(thm)],[f19,f202])).
% 0.15/0.39 fof(f477,plain,(
% 0.15/0.39 sF0_fnc=a),
% 0.15/0.39 inference(backward_demodulation,[status(thm)],[f456,f20])).
% 0.15/0.39 fof(f483,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(forward_subsumption_resolution,[status(thm)],[f477,f21])).
% 0.15/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.42 % Elapsed time: 0.045028 seconds
% 0.15/0.42 % CPU time: 0.107353 seconds
% 0.15/0.42 % Total memory used: 3.584 MB
% 0.15/0.42 % Net memory used: 3.556 MB
%------------------------------------------------------------------------------