%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 12:36:14 PM UTC 2026
% Result : Unsatisfiable 0.28s 0.87s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n006.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 20:05:28 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.28/0.87 % Refutation found
% 0.28/0.87 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.28/0.87 % SZS output start CNFRefutation for theBenchmark
% 0.28/0.87 fof(f1,axiom,(
% 0.28/0.87 (![X]: (multiply(identity,X) = X ))),
% 0.28/0.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.87 fof(f2,axiom,(
% 0.28/0.87 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.28/0.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.87 fof(f3,axiom,(
% 0.28/0.87 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.28/0.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.87 fof(f5,axiom,(
% 0.28/0.87 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 0.28/0.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.87 fof(f10,axiom,(
% 0.28/0.87 (![X,Y]: (least_upper_bound(X,greatest_lower_bound(X,Y)) = X ))),
% 0.28/0.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.87 fof(f12,axiom,(
% 0.28/0.87 (![X,Y,Z]: (multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ))),
% 0.28/0.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.87 fof(f14,axiom,(
% 0.28/0.87 (![Y,Z,X]: (multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ))),
% 0.28/0.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.87 fof(f16,hypothesis,(
% 0.28/0.87 greatest_lower_bound(a,b) = b ),
% 0.28/0.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.87 fof(f17,negated_conjecture,(
% 0.28/0.87 least_upper_bound(inverse(a),inverse(b)) != inverse(b) ),
% 0.28/0.87 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.28/0.87 fof(f18,plain,(
% 0.28/0.87 ![X0]: (multiply(identity,X0)=X0)),
% 0.28/0.87 inference(cnf_transformation,[status(thm)],[f1])).
% 0.28/0.87 fof(f19,plain,(
% 0.28/0.87 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.28/0.87 inference(cnf_transformation,[status(thm)],[f2])).
% 0.28/0.87 fof(f20,plain,(
% 0.28/0.87 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.28/0.87 inference(cnf_transformation,[status(thm)],[f3])).
% 0.28/0.87 fof(f22,plain,(
% 0.28/0.87 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 0.28/0.87 inference(cnf_transformation,[status(thm)],[f5])).
% 0.28/0.87 fof(f27,plain,(
% 0.28/0.87 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X0,X1))=X0)),
% 0.28/0.87 inference(cnf_transformation,[status(thm)],[f10])).
% 0.28/0.87 fof(f29,plain,(
% 0.28/0.87 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X1),multiply(X0,X2)))),
% 0.28/0.87 inference(cnf_transformation,[status(thm)],[f12])).
% 0.28/0.87 fof(f31,plain,(
% 0.28/0.87 ![X0,X1,X2]: (multiply(least_upper_bound(X0,X1),X2)=least_upper_bound(multiply(X0,X2),multiply(X1,X2)))),
% 0.28/0.87 inference(cnf_transformation,[status(thm)],[f14])).
% 0.28/0.87 fof(f33,plain,(
% 0.28/0.87 greatest_lower_bound(a,b)=b),
% 0.28/0.87 inference(cnf_transformation,[status(thm)],[f16])).
% 0.28/0.87 fof(f34,plain,(
% 0.28/0.87 ~least_upper_bound(inverse(a),inverse(b))=inverse(b)),
% 0.28/0.87 inference(cnf_transformation,[status(thm)],[f17])).
% 0.28/0.87 fof(f35,definition,(
% 0.28/0.87 sF1_fnc=inverse(a)),
% 0.28/0.87 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.28/0.87 fof(f36,definition,(
% 0.28/0.87 sF2_fnc=inverse(b)),
% 0.28/0.87 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 0.28/0.87 fof(f37,definition,(
% 0.28/0.87 sF0_fnc=least_upper_bound(sF1_fnc,sF2_fnc)),
% 0.28/0.87 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.28/0.87 fof(f38,plain,(
% 0.28/0.87 ~sF0_fnc=sF2_fnc),
% 0.28/0.87 inference(definition_folding,[],[f34,f37,f36,f35])).
% 0.28/0.87 fof(f67,plain,(
% 0.28/0.87 least_upper_bound(a,b)=a),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f33,f27])).
% 0.28/0.87 fof(f68,plain,(
% 0.28/0.87 least_upper_bound(b,a)=a),
% 0.28/0.87 inference(forward_demodulation,[status(thm)],[f22,f67])).
% 0.28/0.87 fof(f143,plain,(
% 0.28/0.87 multiply(sF2_fnc,b)=identity),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f36,f19])).
% 0.28/0.87 fof(f144,plain,(
% 0.28/0.87 multiply(sF1_fnc,a)=identity),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f35,f19])).
% 0.28/0.87 fof(f167,plain,(
% 0.28/0.87 ![X0]: (multiply(least_upper_bound(sF2_fnc,X0),b)=least_upper_bound(identity,multiply(X0,b)))),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f143,f31])).
% 0.28/0.87 fof(f174,plain,(
% 0.28/0.87 ![X0]: (multiply(sF1_fnc,least_upper_bound(X0,a))=least_upper_bound(multiply(sF1_fnc,X0),identity))),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f144,f29])).
% 0.28/0.87 fof(f177,plain,(
% 0.28/0.87 ![X0]: (multiply(sF1_fnc,least_upper_bound(X0,a))=least_upper_bound(identity,multiply(sF1_fnc,X0)))),
% 0.28/0.87 inference(forward_demodulation,[status(thm)],[f22,f174])).
% 0.28/0.87 fof(f299,plain,(
% 0.28/0.87 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f19,f20])).
% 0.28/0.87 fof(f309,plain,(
% 0.28/0.87 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.28/0.87 inference(forward_demodulation,[status(thm)],[f18,f299])).
% 0.28/0.87 fof(f877,plain,(
% 0.28/0.87 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f309,f309])).
% 0.28/0.87 fof(f878,plain,(
% 0.28/0.87 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f19,f309])).
% 0.28/0.87 fof(f3610,plain,(
% 0.28/0.87 ![X0]: (X0=multiply(X0,identity))),
% 0.28/0.87 inference(backward_demodulation,[status(thm)],[f877,f878])).
% 0.28/0.87 fof(f3656,plain,(
% 0.28/0.87 ![X0]: (inverse(inverse(X0))=multiply(X0,identity))),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f877,f3610])).
% 0.28/0.87 fof(f3677,plain,(
% 0.28/0.87 ![X0]: (inverse(inverse(X0))=X0)),
% 0.28/0.87 inference(forward_demodulation,[status(thm)],[f3610,f3656])).
% 0.28/0.87 fof(f15272,plain,(
% 0.28/0.87 multiply(sF1_fnc,least_upper_bound(b,a))=multiply(least_upper_bound(sF2_fnc,sF1_fnc),b)),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f167,f177])).
% 0.28/0.87 fof(f15324,plain,(
% 0.28/0.87 multiply(sF1_fnc,a)=multiply(least_upper_bound(sF2_fnc,sF1_fnc),b)),
% 0.28/0.87 inference(forward_demodulation,[status(thm)],[f68,f15272])).
% 0.28/0.87 fof(f15325,plain,(
% 0.28/0.87 identity=multiply(least_upper_bound(sF2_fnc,sF1_fnc),b)),
% 0.28/0.87 inference(forward_demodulation,[status(thm)],[f144,f15324])).
% 0.28/0.87 fof(f15326,plain,(
% 0.28/0.87 identity=multiply(least_upper_bound(sF1_fnc,sF2_fnc),b)),
% 0.28/0.87 inference(forward_demodulation,[status(thm)],[f22,f15325])).
% 0.28/0.87 fof(f15327,plain,(
% 0.28/0.87 identity=multiply(sF0_fnc,b)),
% 0.28/0.87 inference(forward_demodulation,[status(thm)],[f37,f15326])).
% 0.28/0.87 fof(f15413,plain,(
% 0.28/0.87 b=multiply(inverse(sF0_fnc),identity)),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f15327,f309])).
% 0.28/0.87 fof(f15436,plain,(
% 0.28/0.87 b=inverse(sF0_fnc)),
% 0.28/0.87 inference(forward_demodulation,[status(thm)],[f3610,f15413])).
% 0.28/0.87 fof(f15447,plain,(
% 0.28/0.87 inverse(b)=sF0_fnc),
% 0.28/0.87 inference(paramodulation,[status(thm)],[f15436,f3677])).
% 0.28/0.87 fof(f15452,plain,(
% 0.28/0.87 sF2_fnc=sF0_fnc),
% 0.28/0.87 inference(backward_demodulation,[status(thm)],[f15447,f36])).
% 0.28/0.87 fof(f15462,plain,(
% 0.28/0.87 $false),
% 0.28/0.87 inference(forward_subsumption_resolution,[status(thm)],[f15452,f38])).
% 0.28/0.87 % SZS output end CNFRefutation for theBenchmark.p
% 0.28/0.92 % Elapsed time: 0.452162 seconds
% 0.28/0.92 % CPU time: 3.205960 seconds
% 0.28/0.92 % Total memory used: 43.103 MB
% 0.28/0.92 % Net memory used: 42.369 MB
%------------------------------------------------------------------------------