%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : REL031+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:03:41 PM UTC 2026
% Result : Theorem 15.94s 2.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL031+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:02:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 15.94/2.55 % Refutation found
% 15.94/2.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 15.94/2.55 % SZS output start CNFRefutation for theBenchmark
% 15.94/2.55 fof(f1,axiom,(
% 15.94/2.55 (! [X0,X1] : join(X0,X1) = join(X1,X0) )),
% 15.94/2.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.94/2.55 fof(f2,axiom,(
% 15.94/2.55 (! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) )),
% 15.94/2.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.94/2.55 fof(f5,axiom,(
% 15.94/2.55 (! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) )),
% 15.94/2.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.94/2.55 fof(f6,axiom,(
% 15.94/2.55 (! [X0] : composition(X0,one) = X0 )),
% 15.94/2.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.94/2.55 fof(f7,axiom,(
% 15.94/2.55 (! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) )),
% 15.94/2.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.94/2.55 fof(f8,axiom,(
% 15.94/2.55 (! [X0] : converse(converse(X0)) = X0 )),
% 15.94/2.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.94/2.55 fof(f9,axiom,(
% 15.94/2.55 (! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)) )),
% 15.94/2.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.94/2.55 fof(f10,axiom,(
% 15.94/2.55 (! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) )),
% 15.94/2.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.94/2.55 fof(f17,conjecture,(
% 15.94/2.55 (! [X0,X1] :( ( join(composition(converse(X0),X0),one) = one& join(composition(converse(X1),X1),one) = one )=> join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ) )),
% 15.94/2.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.94/2.55 fof(f18,negated_conjecture,(
% 15.94/2.55 ~((! [X0,X1] :( ( join(composition(converse(X0),X0),one) = one& join(composition(converse(X1),X1),one) = one )=> join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ) ))),
% 15.94/2.55 inference(negated_conjecture,[status(cth)],[f17])).
% 15.94/2.55 fof(f19,plain,(
% 15.94/2.55 ![X0,X1]: (join(X0,X1)=join(X1,X0))),
% 15.94/2.55 inference(cnf_transformation,[status(thm)],[f1])).
% 15.94/2.55 fof(f20,plain,(
% 15.94/2.55 ![X0,X1,X2]: (join(X0,join(X1,X2))=join(join(X0,X1),X2))),
% 15.94/2.55 inference(cnf_transformation,[status(thm)],[f2])).
% 15.94/2.55 fof(f23,plain,(
% 15.94/2.55 ![X0,X1,X2]: (composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2))),
% 15.94/2.55 inference(cnf_transformation,[status(thm)],[f5])).
% 15.94/2.55 fof(f24,plain,(
% 15.94/2.55 ![X0]: (composition(X0,one)=X0)),
% 15.94/2.55 inference(cnf_transformation,[status(thm)],[f6])).
% 15.94/2.55 fof(f25,plain,(
% 15.94/2.55 ![X0,X1,X2]: (composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2)))),
% 15.94/2.55 inference(cnf_transformation,[status(thm)],[f7])).
% 15.94/2.55 fof(f26,plain,(
% 15.94/2.55 ![X0]: (converse(converse(X0))=X0)),
% 15.94/2.55 inference(cnf_transformation,[status(thm)],[f8])).
% 15.94/2.55 fof(f27,plain,(
% 15.94/2.55 ![X0,X1]: (converse(join(X0,X1))=join(converse(X0),converse(X1)))),
% 15.94/2.55 inference(cnf_transformation,[status(thm)],[f9])).
% 15.94/2.55 fof(f28,plain,(
% 15.94/2.55 ![X0,X1]: (converse(composition(X0,X1))=composition(converse(X1),converse(X0)))),
% 15.94/2.55 inference(cnf_transformation,[status(thm)],[f10])).
% 15.94/2.55 fof(f35,plain,(
% 15.94/2.55 (?[X0,X1]: ((join(composition(converse(X0),X0),one)=one&join(composition(converse(X1),X1),one)=one)&~join(composition(converse(composition(X0,X1)),composition(X0,X1)),one)=one))),
% 15.94/2.55 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 15.94/2.55 fof(f36,plain,(
% 15.94/2.55 ((join(composition(converse(sK0_skl),sK0_skl),one)=one&join(composition(converse(sK1_skl),sK1_skl),one)=one)&~join(composition(converse(composition(sK0_skl,sK1_skl)),composition(sK0_skl,sK1_skl)),one)=one)),
% 15.94/2.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f35])).
% 15.94/2.55 fof(f37,plain,(
% 15.94/2.55 join(composition(converse(sK0_skl),sK0_skl),one)=one),
% 15.94/2.55 inference(cnf_transformation,[status(thm)],[f36])).
% 15.94/2.55 fof(f38,plain,(
% 15.94/2.55 join(composition(converse(sK1_skl),sK1_skl),one)=one),
% 15.94/2.55 inference(cnf_transformation,[status(thm)],[f36])).
% 15.94/2.55 fof(f39,plain,(
% 15.94/2.55 ~join(composition(converse(composition(sK0_skl,sK1_skl)),composition(sK0_skl,sK1_skl)),one)=one),
% 15.94/2.55 inference(cnf_transformation,[status(thm)],[f36])).
% 15.94/2.55 fof(f48,plain,(
% 15.94/2.55 join(one,composition(converse(sK0_skl),sK0_skl))=one),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f19,f37])).
% 15.94/2.55 fof(f49,plain,(
% 15.94/2.55 join(one,composition(converse(sK1_skl),sK1_skl))=one),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f19,f38])).
% 15.94/2.55 fof(f50,plain,(
% 15.94/2.55 ~join(one,composition(converse(composition(sK0_skl,sK1_skl)),composition(sK0_skl,sK1_skl)))=one),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f19,f39])).
% 15.94/2.55 fof(f60,plain,(
% 15.94/2.55 ![X0]: (join(one,join(composition(converse(sK1_skl),sK1_skl),X0))=join(one,X0))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f49,f20])).
% 15.94/2.55 fof(f68,plain,(
% 15.94/2.55 ![X0,X1]: (converse(composition(X0,converse(X1)))=composition(X1,converse(X0)))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f26,f28])).
% 15.94/2.55 fof(f69,plain,(
% 15.94/2.55 ![X0,X1]: (converse(composition(converse(X0),X1))=composition(converse(X1),X0))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f26,f28])).
% 15.94/2.55 fof(f72,plain,(
% 15.94/2.55 ![X0,X1,X2]: (composition(converse(X0),composition(converse(X1),X2))=composition(converse(composition(X1,X0)),X2))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f28,f23])).
% 15.94/2.55 fof(f73,plain,(
% 15.94/2.55 ![X0,X1]: (composition(X0,composition(one,X1))=composition(X0,X1))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f24,f23])).
% 15.94/2.55 fof(f99,plain,(
% 15.94/2.55 ![X0,X1]: (converse(join(X0,X1))=join(converse(X1),converse(X0)))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f19,f27])).
% 15.94/2.55 fof(f114,plain,(
% 15.94/2.55 ![X0,X1]: (converse(join(converse(X0),X1))=join(converse(X1),X0))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f26,f99])).
% 15.94/2.55 fof(f173,plain,(
% 15.94/2.55 ![X0]: (converse(converse(X0))=composition(converse(one),X0))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f24,f69])).
% 15.94/2.55 fof(f191,plain,(
% 15.94/2.55 ![X0]: (X0=composition(converse(one),X0))),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f26,f173])).
% 15.94/2.55 fof(f201,plain,(
% 15.94/2.55 ![X0]: (composition(one,X0)=composition(converse(one),X0))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f73,f191])).
% 15.94/2.55 fof(f211,plain,(
% 15.94/2.55 ![X0]: (composition(one,X0)=X0)),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f191,f201])).
% 15.94/2.55 fof(f241,plain,(
% 15.94/2.55 ![X0,X1]: (composition(join(one,X0),X1)=join(X1,composition(X0,X1)))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f211,f25])).
% 15.94/2.55 fof(f883,plain,(
% 15.94/2.55 ![X0]: (join(one,composition(join(converse(sK1_skl),X0),sK1_skl))=join(one,composition(X0,sK1_skl)))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f25,f60])).
% 15.94/2.55 fof(f7265,plain,(
% 15.94/2.55 ![X0]: (composition(one,X0)=join(X0,composition(composition(converse(sK0_skl),sK0_skl),X0)))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f48,f241])).
% 15.94/2.55 fof(f7346,plain,(
% 15.94/2.55 ![X0]: (X0=join(X0,composition(composition(converse(sK0_skl),sK0_skl),X0)))),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f211,f7265])).
% 15.94/2.55 fof(f7347,plain,(
% 15.94/2.55 ![X0]: (X0=join(X0,composition(converse(sK0_skl),composition(sK0_skl,X0))))),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f23,f7346])).
% 15.94/2.55 fof(f8601,plain,(
% 15.94/2.55 ![X0]: (converse(converse(X0))=join(converse(composition(converse(sK0_skl),composition(sK0_skl,converse(X0)))),X0))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f7347,f114])).
% 15.94/2.55 fof(f8647,plain,(
% 15.94/2.55 ![X0]: (X0=join(converse(composition(converse(sK0_skl),composition(sK0_skl,converse(X0)))),X0))),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f26,f8601])).
% 15.94/2.55 fof(f8648,plain,(
% 15.94/2.55 ![X0]: (X0=join(X0,converse(composition(converse(sK0_skl),composition(sK0_skl,converse(X0))))))),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f19,f8647])).
% 15.94/2.55 fof(f8649,plain,(
% 15.94/2.55 ![X0]: (X0=join(X0,composition(converse(composition(sK0_skl,converse(X0))),sK0_skl)))),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f69,f8648])).
% 15.94/2.55 fof(f8650,plain,(
% 15.94/2.55 ![X0]: (X0=join(X0,composition(composition(X0,converse(sK0_skl)),sK0_skl)))),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f68,f8649])).
% 15.94/2.55 fof(f8651,plain,(
% 15.94/2.55 ![X0]: (X0=join(X0,composition(X0,composition(converse(sK0_skl),sK0_skl))))),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f23,f8650])).
% 15.94/2.55 fof(f9790,plain,(
% 15.94/2.55 join(one,composition(converse(sK1_skl),sK1_skl))=join(one,composition(composition(converse(sK1_skl),composition(converse(sK0_skl),sK0_skl)),sK1_skl))),
% 15.94/2.55 inference(paramodulation,[status(thm)],[f8651,f883])).
% 15.94/2.55 fof(f9852,plain,(
% 15.94/2.55 one=join(one,composition(composition(converse(sK1_skl),composition(converse(sK0_skl),sK0_skl)),sK1_skl))),
% 15.94/2.55 inference(forward_demodulation,[status(thm)],[f49,f9790])).
% 17.02/2.59 fof(f9853,plain,(
% 17.02/2.59 one=join(one,composition(converse(sK1_skl),composition(composition(converse(sK0_skl),sK0_skl),sK1_skl)))),
% 17.02/2.59 inference(forward_demodulation,[status(thm)],[f23,f9852])).
% 17.02/2.59 fof(f9854,plain,(
% 17.02/2.59 one=join(one,composition(converse(sK1_skl),composition(converse(sK0_skl),composition(sK0_skl,sK1_skl))))),
% 17.02/2.59 inference(forward_demodulation,[status(thm)],[f23,f9853])).
% 17.02/2.59 fof(f9855,plain,(
% 17.02/2.59 one=join(one,composition(converse(composition(sK0_skl,sK1_skl)),composition(sK0_skl,sK1_skl)))),
% 17.02/2.59 inference(forward_demodulation,[status(thm)],[f72,f9854])).
% 17.02/2.59 fof(f9856,plain,(
% 17.02/2.59 $false),
% 17.02/2.59 inference(forward_subsumption_resolution,[status(thm)],[f9855,f50])).
% 17.02/2.59 % SZS output end CNFRefutation for theBenchmark.p
% 9.35/2.64 % Elapsed time: 2.260392 seconds
% 9.35/2.64 % CPU time: 17.606258 seconds
% 9.35/2.64 % Total memory used: 277.027 MB
% 9.35/2.64 % Net memory used: 272.566 MB
%------------------------------------------------------------------------------