%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:37:14 PM UTC 2026
% Result : Theorem 0.13s 5.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n011.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sun Sep 20 20:35:01 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 0.13/5.65 % Refutation found
% 0.13/5.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.65 % SZS output start CNFRefutation for theBenchmark
% 0.13/5.65 fof(f6,axiom,(
% 0.13/5.65 (! [C,B,A] : mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) )),
% 0.13/5.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f7,axiom,(
% 0.13/5.65 (! [B,A] : mult(A,mult(B,B)) = mult(mult(A,B),B) )),
% 0.13/5.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f8,axiom,(
% 0.13/5.65 (! [A] : mult(A,unit) = A )),
% 0.13/5.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f9,axiom,(
% 0.13/5.65 (! [A] : mult(unit,A) = A )),
% 0.13/5.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f10,axiom,(
% 0.13/5.65 mult(op_a,op_b) = unit ),
% 0.13/5.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f11,axiom,(
% 0.13/5.65 mult(op_b,op_a) = unit ),
% 0.13/5.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f12,conjecture,(
% 0.13/5.65 (! [X0] :( mult(mult(X0,op_a),op_b) = X0& mult(mult(X0,op_b),op_a) = X0 ) )),
% 0.13/5.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.65 fof(f13,negated_conjecture,(
% 0.13/5.66 ~((! [X0] :( mult(mult(X0,op_a),op_b) = X0& mult(mult(X0,op_b),op_a) = X0 ) ))),
% 0.13/5.66 inference(negated_conjecture,[status(cth)],[f12])).
% 0.13/5.66 fof(f19,plain,(
% 0.13/5.66 ![X0,X1,X2]: (mult(mult(mult(X0,X1),X2),X1)=mult(X0,mult(mult(X1,X2),X1)))),
% 0.13/5.66 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/5.66 fof(f20,plain,(
% 0.13/5.66 ![X0,X1]: (mult(X0,mult(X1,X1))=mult(mult(X0,X1),X1))),
% 0.13/5.66 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/5.66 fof(f21,plain,(
% 0.13/5.66 ![X0]: (mult(X0,unit)=X0)),
% 0.13/5.66 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/5.66 fof(f22,plain,(
% 0.13/5.66 ![X0]: (mult(unit,X0)=X0)),
% 0.13/5.66 inference(cnf_transformation,[status(thm)],[f9])).
% 0.13/5.66 fof(f23,plain,(
% 0.13/5.66 mult(op_a,op_b)=unit),
% 0.13/5.66 inference(cnf_transformation,[status(thm)],[f10])).
% 0.13/5.66 fof(f24,plain,(
% 0.13/5.66 mult(op_b,op_a)=unit),
% 0.13/5.66 inference(cnf_transformation,[status(thm)],[f11])).
% 0.13/5.66 fof(f25,plain,(
% 0.13/5.66 (?[X0]: (~mult(mult(X0,op_a),op_b)=X0|~mult(mult(X0,op_b),op_a)=X0))),
% 0.13/5.66 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.13/5.66 fof(f26,plain,(
% 0.13/5.66 (?[X0]: ~mult(mult(X0,op_a),op_b)=X0)|(?[X0]: ~mult(mult(X0,op_b),op_a)=X0)),
% 0.13/5.66 inference(miniscoping,[status(thm)],[f25])).
% 0.13/5.66 fof(f27,plain,(
% 0.13/5.66 ~mult(mult(sK0_skl,op_a),op_b)=sK0_skl|~mult(mult(sK1_skl,op_b),op_a)=sK1_skl),
% 0.13/5.66 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f26])).
% 0.13/5.66 fof(f28,plain,(
% 0.13/5.66 ~mult(mult(sK0_skl,op_a),op_b)=sK0_skl|~mult(mult(sK1_skl,op_b),op_a)=sK1_skl),
% 0.13/5.66 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/5.66 fof(f30,plain,(
% 0.13/5.66 mult(op_b,mult(op_a,op_a))=mult(unit,op_a)),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f24,f20])).
% 0.13/5.66 fof(f32,plain,(
% 0.13/5.66 mult(op_b,mult(op_a,op_a))=op_a),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f22,f30])).
% 0.13/5.66 fof(f36,plain,(
% 0.13/5.66 ![X0,X1]: (mult(mult(X0,X1),mult(X1,X1))=mult(X0,mult(mult(X1,X1),X1)))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f20,f19])).
% 0.13/5.66 fof(f37,plain,(
% 0.13/5.66 ![X0,X1,X2]: (mult(mult(X0,mult(mult(X1,X2),X1)),X2)=mult(mult(X0,X1),mult(mult(X2,X1),X2)))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f19,f19])).
% 0.13/5.66 fof(f39,plain,(
% 0.13/5.66 ![X0,X1,X2,X3]: (mult(mult(mult(X0,mult(mult(X1,X2),X1)),X3),X1)=mult(mult(mult(X0,X1),X2),mult(mult(X1,X3),X1)))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f19,f19])).
% 0.13/5.66 fof(f42,plain,(
% 0.13/5.66 ![X0]: (mult(mult(unit,X0),op_a)=mult(op_b,mult(mult(op_a,X0),op_a)))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f24,f19])).
% 0.13/5.66 fof(f44,plain,(
% 0.13/5.66 ![X0]: (mult(mult(unit,X0),op_b)=mult(op_a,mult(mult(op_b,X0),op_b)))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f23,f19])).
% 0.13/5.66 fof(f50,plain,(
% 0.13/5.66 ![X0,X1]: (mult(mult(X0,X1),mult(X1,X1))=mult(X0,mult(X1,mult(X1,X1))))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f20,f36])).
% 0.13/5.66 fof(f52,plain,(
% 0.13/5.66 ![X0]: (mult(X0,op_a)=mult(op_b,mult(mult(op_a,X0),op_a)))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f22,f42])).
% 0.13/5.66 fof(f53,plain,(
% 0.13/5.66 ![X0]: (mult(X0,op_b)=mult(op_a,mult(mult(op_b,X0),op_b)))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f22,f44])).
% 0.13/5.66 fof(f55,plain,(
% 0.13/5.66 mult(op_a,op_a)=mult(op_b,mult(op_a,mult(op_a,op_a)))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f20,f52])).
% 0.13/5.66 fof(f80,plain,(
% 0.13/5.66 mult(mult(op_a,op_a),op_b)=mult(op_a,mult(op_a,op_b))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f32,f53])).
% 0.13/5.66 fof(f85,plain,(
% 0.13/5.66 mult(mult(op_a,op_a),op_b)=mult(op_a,unit)),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f23,f80])).
% 0.13/5.66 fof(f86,plain,(
% 0.13/5.66 mult(mult(op_a,op_a),op_b)=op_a),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f21,f85])).
% 0.13/5.66 fof(f242,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b)=mult(mult(X0,mult(op_a,op_a)),mult(mult(op_b,mult(op_a,op_a)),op_b)))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f86,f37])).
% 0.13/5.66 fof(f253,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,mult(op_a,op_b)),mult(op_a,op_a))=mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f32,f37])).
% 0.13/5.66 fof(f285,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b)=mult(mult(X0,mult(op_a,op_a)),mult(op_a,op_b)))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f32,f242])).
% 0.13/5.66 fof(f286,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b)=mult(mult(X0,mult(op_a,op_a)),unit))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f23,f285])).
% 0.13/5.66 fof(f287,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b)=mult(X0,mult(op_a,op_a)))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f21,f286])).
% 0.13/5.66 fof(f299,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,unit),mult(op_a,op_a))=mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f23,f253])).
% 0.13/5.66 fof(f300,plain,(
% 0.13/5.66 ![X0]: (mult(X0,mult(op_a,op_a))=mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f21,f299])).
% 0.13/5.66 fof(f303,plain,(
% 0.13/5.66 ![X0]: (mult(X0,mult(op_a,op_a))=mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f86,f300])).
% 0.13/5.66 fof(f357,plain,(
% 0.13/5.66 ![X0,X1]: (mult(mult(mult(X0,mult(mult(op_a,op_a),op_b)),X1),op_b)=mult(mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))),mult(mult(op_b,X1),op_b)))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f55,f39])).
% 0.13/5.66 fof(f358,plain,(
% 0.13/5.66 ![X0,X1]: (mult(mult(mult(X0,mult(op_a,op_b)),X1),op_b)=mult(mult(mult(X0,op_b),mult(op_a,op_a)),mult(mult(op_b,X1),op_b)))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f32,f39])).
% 0.13/5.66 fof(f411,plain,(
% 0.13/5.66 ![X0,X1]: (mult(mult(mult(X0,op_a),X1),op_b)=mult(mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))),mult(mult(op_b,X1),op_b)))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f86,f357])).
% 0.13/5.66 fof(f412,plain,(
% 0.13/5.66 ![X0,X1]: (mult(mult(mult(X0,op_a),X1),op_b)=mult(mult(X0,mult(op_a,op_a)),mult(mult(op_b,X1),op_b)))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f303,f411])).
% 0.13/5.66 fof(f413,plain,(
% 0.13/5.66 ![X0,X1]: (mult(mult(mult(X0,unit),X1),op_b)=mult(mult(mult(X0,op_b),mult(op_a,op_a)),mult(mult(op_b,X1),op_b)))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f23,f358])).
% 0.13/5.66 fof(f414,plain,(
% 0.13/5.66 ![X0,X1]: (mult(mult(X0,X1),op_b)=mult(mult(mult(X0,op_b),mult(op_a,op_a)),mult(mult(op_b,X1),op_b)))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f21,f413])).
% 0.13/5.66 fof(f415,plain,(
% 0.13/5.66 ![X0,X1]: (mult(mult(X0,X1),op_b)=mult(mult(mult(mult(X0,op_b),op_a),X1),op_b))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f412,f414])).
% 0.13/5.66 fof(f1166,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,mult(op_a,op_a)),op_b)=mult(mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))),op_b))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f50,f415])).
% 0.13/5.66 fof(f1167,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,op_a),op_b)=mult(mult(mult(X0,op_b),mult(op_a,op_a)),op_b))),
% 0.13/5.66 inference(paramodulation,[status(thm)],[f20,f415])).
% 0.13/5.66 fof(f1212,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,mult(op_a,op_a)),op_b)=mult(X0,mult(mult(op_b,mult(op_a,mult(op_a,op_a))),op_b)))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f19,f1166])).
% 0.13/5.66 fof(f1213,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,mult(op_a,op_a)),op_b)=mult(X0,mult(op_b,mult(op_a,op_a))))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f287,f1212])).
% 0.13/5.66 fof(f1216,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,mult(op_a,op_a)),op_b)=mult(X0,op_a))),
% 0.13/5.66 inference(forward_demodulation,[status(thm)],[f32,f1213])).
% 0.13/5.66 fof(f1217,plain,(
% 0.13/5.66 ![X0]: (mult(mult(X0,op_a),op_b)=mult(X0,mult(mult(op_b,mult(op_a,op_a)),op_b)))),
% 0.13/5.67 inference(forward_demodulation,[status(thm)],[f19,f1167])).
% 0.13/5.67 fof(f1218,plain,(
% 0.13/5.67 ![X0]: (mult(mult(X0,op_a),op_b)=mult(X0,mult(op_b,op_a)))),
% 0.13/5.67 inference(forward_demodulation,[status(thm)],[f1216,f1217])).
% 0.13/5.67 fof(f1219,plain,(
% 0.13/5.67 ![X0]: (mult(mult(X0,op_a),op_b)=mult(X0,unit))),
% 0.13/5.67 inference(forward_demodulation,[status(thm)],[f24,f1218])).
% 0.13/5.67 fof(f1221,plain,(
% 0.13/5.67 ~sK0_skl=sK0_skl|~mult(mult(sK1_skl,op_b),op_a)=sK1_skl),
% 0.13/5.67 inference(backward_demodulation,[status(thm)],[f1227,f28])).
% 0.13/5.67 fof(f1227,plain,(
% 0.13/5.67 ![X0]: (mult(mult(X0,op_a),op_b)=X0)),
% 0.13/5.67 inference(forward_demodulation,[status(thm)],[f21,f1219])).
% 0.13/5.67 fof(f1259,plain,(
% 0.13/5.67 ~mult(mult(sK1_skl,op_b),op_a)=sK1_skl),
% 0.13/5.67 inference(trivial_equality_resolution,[status(thm)],[f1221])).
% 0.13/5.67 fof(f1261,plain,(
% 0.13/5.67 ![X0]: (mult(mult(X0,op_a),op_b)=mult(mult(X0,op_b),op_a))),
% 0.13/5.67 inference(paramodulation,[status(thm)],[f415,f1227])).
% 0.13/5.67 fof(f1295,plain,(
% 0.13/5.67 ~sK1_skl=sK1_skl),
% 0.13/5.67 inference(backward_demodulation,[status(thm)],[f1313,f1259])).
% 0.13/5.67 fof(f1313,plain,(
% 0.13/5.67 ![X0]: (X0=mult(mult(X0,op_b),op_a))),
% 0.13/5.67 inference(forward_demodulation,[status(thm)],[f1227,f1261])).
% 0.13/5.67 fof(f1330,plain,(
% 0.13/5.67 $false),
% 0.13/5.67 inference(trivial_equality_resolution,[status(thm)],[f1295])).
% 0.13/5.67 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/5.68 % Elapsed time: 0.307944 seconds
% 0.13/5.68 % CPU time: 2.279382 seconds
% 0.13/5.68 % Total memory used: 104.728 MB
% 0.13/5.68 % Net memory used: 103.886 MB
%------------------------------------------------------------------------------