%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : BOO012-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 0.09s 0.96s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.94 % Computer : n006.cluster.edu
% 0.09/0.94 % Model : x86_64 x86_64
% 0.09/0.94 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.94 % Memory : 8046.5625MB
% 0.09/0.94 % OS : Linux 6.8.0-71-generic
% 0.09/0.94 % CPULimit : 300
% 0.09/0.94 % WCLimit : 300
% 0.09/0.94 % DateTime : Mon Sep 21 13:48:02 UTC 2026
% 0.09/0.94 % CPUTime :
% 0.09/0.95 % Drodi V4.1.1
% 0.09/0.96 % Refutation found
% 0.09/0.96 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.96 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.96 fof(f5,axiom,(
% 0.09/0.96 (![X,Y,Z]: (multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ))),
% 0.09/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.96 fof(f6,axiom,(
% 0.09/0.96 (![X,Y,Z]: (multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ))),
% 0.09/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.96 fof(f7,axiom,(
% 0.09/0.96 (![X]: (add(X,inverse(X)) = multiplicative_identity ))),
% 0.09/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.96 fof(f9,axiom,(
% 0.09/0.96 (![X]: (multiply(X,inverse(X)) = additive_identity ))),
% 0.09/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.96 fof(f11,axiom,(
% 0.09/0.96 (![X]: (multiply(X,multiplicative_identity) = X ))),
% 0.09/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.96 fof(f12,axiom,(
% 0.09/0.96 (![X]: (multiply(multiplicative_identity,X) = X ))),
% 0.09/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.96 fof(f13,axiom,(
% 0.09/0.96 (![X]: (add(X,additive_identity) = X ))),
% 0.09/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.96 fof(f14,axiom,(
% 0.09/0.96 (![X]: (add(additive_identity,X) = X ))),
% 0.09/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.96 fof(f15,negated_conjecture,(
% 0.09/0.96 inverse(inverse(x)) != x ),
% 0.09/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.96 fof(f20,plain,(
% 0.09/0.96 ![X0,X1,X2]: (multiply(add(X0,X1),X2)=add(multiply(X0,X2),multiply(X1,X2)))),
% 0.09/0.96 inference(cnf_transformation,[status(thm)],[f5])).
% 0.09/0.96 fof(f21,plain,(
% 0.09/0.96 ![X0,X1,X2]: (multiply(X0,add(X1,X2))=add(multiply(X0,X1),multiply(X0,X2)))),
% 0.09/0.96 inference(cnf_transformation,[status(thm)],[f6])).
% 0.09/0.96 fof(f22,plain,(
% 0.09/0.96 ![X0]: (add(X0,inverse(X0))=multiplicative_identity)),
% 0.09/0.96 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/0.96 fof(f24,plain,(
% 0.09/0.96 ![X0]: (multiply(X0,inverse(X0))=additive_identity)),
% 0.09/0.96 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/0.96 fof(f26,plain,(
% 0.09/0.96 ![X0]: (multiply(X0,multiplicative_identity)=X0)),
% 0.09/0.96 inference(cnf_transformation,[status(thm)],[f11])).
% 0.09/0.96 fof(f27,plain,(
% 0.09/0.96 ![X0]: (multiply(multiplicative_identity,X0)=X0)),
% 0.09/0.96 inference(cnf_transformation,[status(thm)],[f12])).
% 0.09/0.96 fof(f28,plain,(
% 0.09/0.96 ![X0]: (add(X0,additive_identity)=X0)),
% 0.09/0.96 inference(cnf_transformation,[status(thm)],[f13])).
% 0.09/0.96 fof(f29,plain,(
% 0.09/0.96 ![X0]: (add(additive_identity,X0)=X0)),
% 0.09/0.96 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/0.96 fof(f30,plain,(
% 0.09/0.96 ~inverse(inverse(x))=x),
% 0.09/0.96 inference(cnf_transformation,[status(thm)],[f15])).
% 0.09/0.96 fof(f31,definition,(
% 0.09/0.96 sF1_fnc=inverse(x)),
% 0.09/0.96 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.09/0.96 fof(f32,definition,(
% 0.09/0.96 sF0_fnc=inverse(sF1_fnc)),
% 0.09/0.96 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.09/0.96 fof(f33,plain,(
% 0.09/0.96 ~sF0_fnc=x),
% 0.09/0.96 inference(definition_folding,[],[f30,f32,f31])).
% 0.09/0.96 fof(f115,plain,(
% 0.09/0.96 multiply(sF1_fnc,sF0_fnc)=additive_identity),
% 0.09/0.96 inference(paramodulation,[status(thm)],[f32,f24])).
% 0.09/0.96 fof(f116,plain,(
% 0.09/0.96 multiply(x,sF1_fnc)=additive_identity),
% 0.09/0.96 inference(paramodulation,[status(thm)],[f31,f24])).
% 0.09/0.96 fof(f124,plain,(
% 0.09/0.96 ![X0]: (multiply(add(X0,sF1_fnc),sF0_fnc)=add(multiply(X0,sF0_fnc),additive_identity))),
% 0.09/0.96 inference(paramodulation,[status(thm)],[f115,f20])).
% 0.09/0.96 fof(f128,plain,(
% 0.09/0.96 ![X0]: (multiply(add(X0,sF1_fnc),sF0_fnc)=multiply(X0,sF0_fnc))),
% 0.09/0.96 inference(forward_demodulation,[status(thm)],[f28,f124])).
% 0.09/0.96 fof(f188,plain,(
% 0.09/0.96 ![X0]: (multiply(x,add(sF1_fnc,X0))=add(additive_identity,multiply(x,X0)))),
% 0.09/0.96 inference(paramodulation,[status(thm)],[f116,f21])).
% 0.09/0.96 fof(f224,plain,(
% 0.09/0.96 ![X0]: (multiply(x,add(sF1_fnc,X0))=multiply(x,X0))),
% 0.09/0.96 inference(forward_demodulation,[status(thm)],[f29,f188])).
% 0.09/0.96 fof(f238,plain,(
% 0.09/0.96 add(sF1_fnc,sF0_fnc)=multiplicative_identity),
% 0.09/0.96 inference(paramodulation,[status(thm)],[f32,f22])).
% 0.09/0.96 fof(f239,plain,(
% 0.09/0.96 add(x,sF1_fnc)=multiplicative_identity),
% 0.09/0.96 inference(paramodulation,[status(thm)],[f31,f22])).
% 0.09/0.96 fof(f306,plain,(
% 0.09/0.96 multiply(multiplicative_identity,sF0_fnc)=multiply(x,sF0_fnc)),
% 0.09/0.96 inference(paramodulation,[status(thm)],[f239,f128])).
% 0.09/0.96 fof(f311,plain,(
% 0.09/0.96 sF0_fnc=multiply(x,sF0_fnc)),
% 0.09/0.96 inference(forward_demodulation,[status(thm)],[f27,f306])).
% 0.09/0.96 fof(f680,plain,(
% 0.09/0.96 multiply(x,multiplicative_identity)=multiply(x,sF0_fnc)),
% 0.09/0.96 inference(paramodulation,[status(thm)],[f238,f224])).
% 0.09/0.96 fof(f690,plain,(
% 0.09/0.96 sF0_fnc=x),
% 0.09/0.96 inference(backward_demodulation,[status(thm)],[f691,f311])).
% 0.09/0.96 fof(f691,plain,(
% 0.09/0.96 x=multiply(x,sF0_fnc)),
% 0.09/0.96 inference(forward_demodulation,[status(thm)],[f26,f680])).
% 0.09/0.96 fof(f697,plain,(
% 0.09/0.96 $false),
% 0.09/0.96 inference(forward_subsumption_resolution,[status(thm)],[f690,f33])).
% 0.09/0.96 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.99 % Elapsed time: 0.037568 seconds
% 0.09/0.99 % CPU time: 0.115891 seconds
% 0.09/0.99 % Total memory used: 4.892 MB
% 0.09/0.99 % Net memory used: 4.846 MB
%------------------------------------------------------------------------------