%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : REL010+2 : 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 : n012.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 02:03:33 PM UTC 2026
% Result : Theorem 16.38s 2.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : REL010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 03:57:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 16.38/2.49 % Refutation found
% 16.38/2.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 16.38/2.49 % SZS output start CNFRefutation for theBenchmark
% 16.38/2.49 fof(f1,axiom,(
% 16.38/2.49 (! [X0,X1] : join(X0,X1) = join(X1,X0) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f2,axiom,(
% 16.38/2.49 (! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f3,axiom,(
% 16.38/2.49 (! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f4,axiom,(
% 16.38/2.49 (! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f5,axiom,(
% 16.38/2.49 (! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f6,axiom,(
% 16.38/2.49 (! [X0] : composition(X0,one) = X0 )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f7,axiom,(
% 16.38/2.49 (! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f8,axiom,(
% 16.38/2.49 (! [X0] : converse(converse(X0)) = X0 )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f9,axiom,(
% 16.38/2.49 (! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f10,axiom,(
% 16.38/2.49 (! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f11,axiom,(
% 16.38/2.49 (! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f12,axiom,(
% 16.38/2.49 (! [X0] : top = join(X0,complement(X0)) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f13,axiom,(
% 16.38/2.49 (! [X0] : zero = meet(X0,complement(X0)) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f15,axiom,(
% 16.38/2.49 (! [X0,X1,X2] : join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f17,conjecture,(
% 16.38/2.49 (! [X0,X1,X2] :( meet(composition(X0,X1),X2) = zero=> meet(X1,composition(converse(X0),X2)) = zero ) )),
% 16.38/2.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 16.38/2.49 fof(f18,negated_conjecture,(
% 16.38/2.49 ~((! [X0,X1,X2] :( meet(composition(X0,X1),X2) = zero=> meet(X1,composition(converse(X0),X2)) = zero ) ))),
% 16.38/2.49 inference(negated_conjecture,[status(cth)],[f17])).
% 16.38/2.49 fof(f19,plain,(
% 16.38/2.49 ![X0,X1]: (join(X0,X1)=join(X1,X0))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f1])).
% 16.38/2.49 fof(f20,plain,(
% 16.38/2.49 ![X0,X1,X2]: (join(X0,join(X1,X2))=join(join(X0,X1),X2))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f2])).
% 16.38/2.49 fof(f21,plain,(
% 16.38/2.49 ![X0,X1]: (X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f3])).
% 16.38/2.49 fof(f22,plain,(
% 16.38/2.49 ![X0,X1]: (meet(X0,X1)=complement(join(complement(X0),complement(X1))))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f4])).
% 16.38/2.49 fof(f23,plain,(
% 16.38/2.49 ![X0,X1,X2]: (composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f5])).
% 16.38/2.49 fof(f24,plain,(
% 16.38/2.49 ![X0]: (composition(X0,one)=X0)),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f6])).
% 16.38/2.49 fof(f25,plain,(
% 16.38/2.49 ![X0,X1,X2]: (composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2)))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f7])).
% 16.38/2.49 fof(f26,plain,(
% 16.38/2.49 ![X0]: (converse(converse(X0))=X0)),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f8])).
% 16.38/2.49 fof(f27,plain,(
% 16.38/2.49 ![X0,X1]: (converse(join(X0,X1))=join(converse(X0),converse(X1)))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f9])).
% 16.38/2.49 fof(f28,plain,(
% 16.38/2.49 ![X0,X1]: (converse(composition(X0,X1))=composition(converse(X1),converse(X0)))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f10])).
% 16.38/2.49 fof(f29,plain,(
% 16.38/2.49 ![X0,X1]: (join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f11])).
% 16.38/2.49 fof(f30,plain,(
% 16.38/2.49 ![X0]: (top=join(X0,complement(X0)))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f12])).
% 16.38/2.49 fof(f31,plain,(
% 16.38/2.49 ![X0]: (zero=meet(X0,complement(X0)))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f13])).
% 16.38/2.49 fof(f33,plain,(
% 16.38/2.49 ![X0,X1,X2]: (join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2))=meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2))),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f15])).
% 16.38/2.49 fof(f35,plain,(
% 16.38/2.49 (?[X0,X1,X2]: (meet(composition(X0,X1),X2)=zero&~meet(X1,composition(converse(X0),X2))=zero))),
% 16.38/2.49 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 16.38/2.49 fof(f36,plain,(
% 16.38/2.49 (meet(composition(sK0_skl,sK1_skl),sK2_skl)=zero&~meet(sK1_skl,composition(converse(sK0_skl),sK2_skl))=zero)),
% 16.38/2.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl)],[f35])).
% 16.38/2.49 fof(f37,plain,(
% 16.38/2.49 meet(composition(sK0_skl,sK1_skl),sK2_skl)=zero),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f36])).
% 16.38/2.49 fof(f38,plain,(
% 16.38/2.49 ~meet(sK1_skl,composition(converse(sK0_skl),sK2_skl))=zero),
% 16.38/2.49 inference(cnf_transformation,[status(thm)],[f36])).
% 16.38/2.49 fof(f39,definition,(
% 16.38/2.49 sF2_fnc=converse(sK0_skl)),
% 16.38/2.49 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 16.38/2.49 fof(f40,definition,(
% 16.38/2.49 sF1_fnc=composition(sF2_fnc,sK2_skl)),
% 16.38/2.49 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 16.38/2.49 fof(f41,definition,(
% 16.38/2.49 sF0_fnc=meet(sK1_skl,sF1_fnc)),
% 16.38/2.49 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 16.38/2.49 fof(f42,plain,(
% 16.38/2.49 ~sF0_fnc=zero),
% 16.38/2.49 inference(definition_folding,[],[f38,f41,f40,f39])).
% 16.38/2.49 fof(f43,plain,(
% 16.38/2.49 ![X0,X1]: (X0=join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f21])).
% 16.38/2.49 fof(f44,plain,(
% 16.38/2.49 ![X0,X1]: (X0=join(complement(join(complement(X0),X1)),meet(X0,X1)))),
% 16.38/2.49 inference(backward_demodulation,[status(thm)],[f22,f43])).
% 16.38/2.49 fof(f45,plain,(
% 16.38/2.49 ![X0,X1]: (join(complement(X0),composition(converse(X1),complement(composition(X1,X0))))=complement(X0))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f29])).
% 16.38/2.49 fof(f46,plain,(
% 16.38/2.49 ![X0,X1]: (X0=join(meet(X0,X1),complement(join(complement(X0),X1))))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f44])).
% 16.38/2.49 fof(f48,plain,(
% 16.38/2.49 converse(sF2_fnc)=sK0_skl),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f39,f26])).
% 16.38/2.49 fof(f54,plain,(
% 16.38/2.49 ![X0,X1,X2]: (join(X0,join(X1,X2))=join(X2,join(X0,X1)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f19,f20])).
% 16.38/2.49 fof(f65,plain,(
% 16.38/2.49 ![X0,X1]: (join(X0,join(complement(X0),X1))=join(top,X1))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f30,f20])).
% 16.38/2.49 fof(f69,plain,(
% 16.38/2.49 ![X0,X1]: (composition(X0,composition(one,X1))=composition(X0,X1))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f24,f23])).
% 16.38/2.49 fof(f82,plain,(
% 16.38/2.49 ![X0]: (meet(X0,complement(X0))=complement(top))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f30,f22])).
% 16.38/2.49 fof(f83,plain,(
% 16.38/2.49 ![X0,X1]: (meet(X0,X1)=complement(join(complement(X1),complement(X0))))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f19,f22])).
% 16.38/2.49 fof(f87,plain,(
% 16.38/2.49 ![X0,X1]: (top=join(join(complement(X0),complement(X1)),meet(X0,X1)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f22,f30])).
% 16.38/2.49 fof(f89,plain,(
% 16.38/2.49 zero=complement(top)),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f31,f82])).
% 16.38/2.49 fof(f90,plain,(
% 16.38/2.49 ![X0,X1]: (top=join(complement(X0),join(complement(X1),meet(X0,X1))))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f20,f87])).
% 16.38/2.49 fof(f93,plain,(
% 16.38/2.49 ![X0]: (meet(X0,top)=complement(join(complement(X0),zero)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f89,f22])).
% 16.38/2.49 fof(f97,plain,(
% 16.38/2.49 ![X0]: (meet(X0,top)=complement(join(zero,complement(X0))))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f93])).
% 16.38/2.49 fof(f102,plain,(
% 16.38/2.49 ![X0]: (converse(composition(sF2_fnc,X0))=composition(converse(X0),sK0_skl))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f48,f28])).
% 16.38/2.49 fof(f104,plain,(
% 16.38/2.49 ![X0,X1]: (converse(composition(converse(X0),X1))=composition(converse(X1),X0))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f26,f28])).
% 16.38/2.49 fof(f128,plain,(
% 16.38/2.49 ![X0,X1]: (converse(join(X0,X1))=join(converse(X1),converse(X0)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f19,f27])).
% 16.38/2.49 fof(f132,plain,(
% 16.38/2.49 ![X0,X1]: (converse(join(converse(X0),X1))=join(X0,converse(X1)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f26,f27])).
% 16.38/2.49 fof(f134,plain,(
% 16.38/2.49 ![X0]: (converse(join(X0,sK0_skl))=join(converse(X0),sF2_fnc))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f39,f27])).
% 16.38/2.49 fof(f140,plain,(
% 16.38/2.49 ![X0]: (converse(join(X0,sK0_skl))=join(sF2_fnc,converse(X0)))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f134])).
% 16.38/2.49 fof(f166,plain,(
% 16.38/2.49 meet(top,top)=complement(join(zero,zero))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f89,f97])).
% 16.38/2.49 fof(f179,plain,(
% 16.38/2.49 ![X0]: (join(zero,composition(converse(X0),complement(composition(X0,top))))=complement(top))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f89,f45])).
% 16.38/2.49 fof(f193,plain,(
% 16.38/2.49 ![X0]: (join(zero,composition(converse(X0),complement(composition(X0,top))))=zero)),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f89,f179])).
% 16.38/2.49 fof(f410,plain,(
% 16.38/2.49 ![X0,X1,X2]: (join(meet(composition(converse(X0),X1),X2),meet(composition(converse(X0),meet(X1,composition(X0,X2))),X2))=meet(composition(converse(X0),meet(X1,composition(converse(converse(X0)),X2))),X2))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f26,f33])).
% 16.38/2.49 fof(f450,plain,(
% 16.38/2.49 ![X0,X1,X2]: (join(meet(composition(converse(X0),X1),X2),meet(composition(converse(X0),meet(X1,composition(X0,X2))),X2))=meet(composition(converse(X0),meet(X1,composition(X0,X2))),X2))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f26,f410])).
% 16.38/2.49 fof(f477,plain,(
% 16.38/2.49 ![X0,X1]: (meet(X0,X1)=meet(X1,X0))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f22,f83])).
% 16.38/2.49 fof(f500,plain,(
% 16.38/2.49 meet(sK2_skl,composition(sK0_skl,sK1_skl))=zero),
% 16.38/2.49 inference(backward_demodulation,[status(thm)],[f477,f37])).
% 16.38/2.49 fof(f507,plain,(
% 16.38/2.49 ![X0,X1,X2]: (join(meet(composition(converse(X0),X1),X2),meet(composition(converse(X0),meet(X1,composition(X0,X2))),X2))=meet(X2,composition(converse(X0),meet(X1,composition(X0,X2)))))),
% 16.38/2.49 inference(backward_demodulation,[status(thm)],[f477,f450])).
% 16.38/2.49 fof(f549,plain,(
% 16.38/2.49 ![X0,X1,X2]: (join(meet(composition(converse(X0),X1),X2),meet(X2,composition(converse(X0),meet(X1,composition(X0,X2)))))=meet(X2,composition(converse(X0),meet(X1,composition(X0,X2)))))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f477,f507])).
% 16.38/2.49 fof(f586,plain,(
% 16.38/2.49 ![X0]: (X0=join(zero,complement(join(complement(X0),complement(X0)))))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f31,f46])).
% 16.38/2.49 fof(f589,plain,(
% 16.38/2.49 ![X0,X1]: (X0=join(meet(X0,complement(X1)),meet(X1,X0)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f83,f46])).
% 16.38/2.49 fof(f593,plain,(
% 16.38/2.49 ![X0]: (X0=join(meet(X0,complement(complement(X0))),complement(top)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f30,f46])).
% 16.38/2.49 fof(f606,plain,(
% 16.38/2.49 ![X0]: (X0=join(zero,meet(X0,X0)))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f83,f586])).
% 16.38/2.49 fof(f607,plain,(
% 16.38/2.49 ![X0,X1]: (X0=join(meet(X1,X0),meet(X0,complement(X1))))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f589])).
% 16.38/2.49 fof(f611,plain,(
% 16.38/2.49 ![X0]: (X0=join(complement(top),meet(X0,complement(complement(X0)))))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f593])).
% 16.38/2.49 fof(f612,plain,(
% 16.38/2.49 ![X0]: (X0=join(zero,meet(X0,complement(complement(X0)))))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f89,f611])).
% 16.38/2.49 fof(f623,plain,(
% 16.38/2.49 top=join(zero,meet(top,complement(zero)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f89,f612])).
% 16.38/2.49 fof(f645,plain,(
% 16.38/2.49 ![X0,X1]: (X0=join(meet(X1,X0),meet(complement(X1),X0)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f477,f607])).
% 16.38/2.49 fof(f647,plain,(
% 16.38/2.49 ![X0]: (X0=join(meet(top,X0),meet(X0,zero)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f89,f607])).
% 16.38/2.49 fof(f728,plain,(
% 16.38/2.49 ![X0]: (X0=join(meet(X0,top),meet(X0,zero)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f477,f647])).
% 16.38/2.49 fof(f765,plain,(
% 16.38/2.49 ![X0]: (X0=join(meet(X0,top),meet(zero,X0)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f477,f728])).
% 16.38/2.49 fof(f775,plain,(
% 16.38/2.49 complement(zero)=join(meet(complement(zero),top),zero)),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f31,f765])).
% 16.38/2.49 fof(f782,plain,(
% 16.38/2.49 complement(zero)=join(zero,meet(complement(zero),top))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f775])).
% 16.38/2.49 fof(f783,plain,(
% 16.38/2.49 complement(zero)=join(zero,meet(top,complement(zero)))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f477,f782])).
% 16.38/2.49 fof(f787,plain,(
% 16.38/2.49 complement(zero)=top),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f623,f783])).
% 16.38/2.49 fof(f844,plain,(
% 16.38/2.49 ![X0]: (zero=join(meet(zero,X0),complement(join(top,X0))))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f787,f46])).
% 16.38/2.49 fof(f1060,plain,(
% 16.38/2.49 ![X0]: (complement(complement(X0))=join(meet(X0,complement(complement(X0))),zero))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f31,f645])).
% 16.38/2.49 fof(f1076,plain,(
% 16.38/2.49 ![X0]: (complement(complement(X0))=join(zero,meet(X0,complement(complement(X0)))))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f1060])).
% 16.38/2.49 fof(f1087,plain,(
% 16.38/2.49 ![X0]: (complement(complement(X0))=X0)),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f612,f1076])).
% 16.38/2.49 fof(f1102,plain,(
% 16.38/2.49 ![X0,X1]: (complement(meet(X0,X1))=join(complement(X0),complement(X1)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f22,f1087])).
% 16.38/2.49 fof(f1384,plain,(
% 16.38/2.49 ![X0,X1]: (converse(join(X0,X1))=converse(join(X1,X0)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f27,f128])).
% 16.38/2.49 fof(f1595,plain,(
% 16.38/2.49 complement(meet(top,top))=join(zero,zero)),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f166,f1087])).
% 16.38/2.49 fof(f1914,plain,(
% 16.38/2.49 ![X0]: (converse(converse(X0))=composition(converse(one),X0))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f24,f104])).
% 16.38/2.49 fof(f1951,plain,(
% 16.38/2.49 ![X0]: (X0=composition(converse(one),X0))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f26,f1914])).
% 16.38/2.49 fof(f1989,plain,(
% 16.38/2.49 ![X0]: (composition(one,X0)=composition(converse(one),X0))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f69,f1951])).
% 16.38/2.49 fof(f1990,plain,(
% 16.38/2.49 one=converse(one)),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f24,f1951])).
% 16.38/2.49 fof(f1993,plain,(
% 16.38/2.49 ![X0]: (join(complement(X0),complement(composition(one,X0)))=complement(X0))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f1951,f45])).
% 16.38/2.49 fof(f2008,plain,(
% 16.38/2.49 ![X0,X1]: (composition(join(X0,converse(one)),X1)=join(composition(X0,X1),X1))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f1951,f25])).
% 16.38/2.49 fof(f2009,plain,(
% 16.38/2.49 ![X0,X1]: (composition(join(converse(one),X0),X1)=join(X1,composition(X0,X1)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f1951,f25])).
% 16.38/2.49 fof(f2022,plain,(
% 16.38/2.49 ![X0]: (composition(one,X0)=X0)),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f1951,f1989])).
% 16.38/2.49 fof(f2028,plain,(
% 16.38/2.49 ![X0]: (complement(meet(X0,composition(one,X0)))=complement(X0))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f1102,f1993])).
% 16.38/2.49 fof(f2029,plain,(
% 16.38/2.49 complement(top)=join(zero,zero)),
% 16.38/2.49 inference(backward_demodulation,[status(thm)],[f2030,f1595])).
% 16.38/2.49 fof(f2030,plain,(
% 16.38/2.49 ![X0]: (complement(meet(X0,X0))=complement(X0))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f2022,f2028])).
% 16.38/2.49 fof(f2076,plain,(
% 16.38/2.49 ![X0,X1]: (composition(join(X0,one),X1)=join(composition(X0,X1),X1))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f1990,f2008])).
% 16.38/2.49 fof(f2078,plain,(
% 16.38/2.49 ![X0,X1]: (composition(join(X0,one),X1)=join(X1,composition(X0,X1)))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f2076])).
% 16.38/2.49 fof(f2079,plain,(
% 16.38/2.49 ![X0,X1]: (composition(join(one,X0),X1)=join(X1,composition(X0,X1)))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f1990,f2009])).
% 16.38/2.49 fof(f2107,plain,(
% 16.38/2.49 zero=join(zero,zero)),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f89,f2029])).
% 16.38/2.49 fof(f2171,plain,(
% 16.38/2.49 converse(join(one,sK0_skl))=join(sF2_fnc,one)),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f1990,f140])).
% 16.38/2.49 fof(f2192,plain,(
% 16.38/2.49 converse(join(sK0_skl,one))=join(sF2_fnc,one)),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f1384,f2171])).
% 16.38/2.49 fof(f2193,plain,(
% 16.38/2.49 converse(join(sK0_skl,one))=join(one,sF2_fnc)),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f2192])).
% 16.38/2.49 fof(f2236,plain,(
% 16.38/2.49 ![X0]: (join(zero,join(zero,X0))=join(X0,zero))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f2107,f54])).
% 16.38/2.49 fof(f2380,plain,(
% 16.38/2.49 ![X0]: (complement(complement(X0))=meet(X0,X0))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f2030,f1087])).
% 16.38/2.49 fof(f2393,plain,(
% 16.38/2.49 ![X0]: (X0=join(zero,X0))),
% 16.38/2.49 inference(backward_demodulation,[status(thm)],[f2404,f606])).
% 16.38/2.49 fof(f2404,plain,(
% 16.38/2.49 ![X0]: (X0=meet(X0,X0))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f1087,f2380])).
% 16.38/2.49 fof(f2429,plain,(
% 16.38/2.49 ![X0]: (composition(converse(X0),complement(composition(X0,top)))=zero)),
% 16.38/2.49 inference(backward_demodulation,[status(thm)],[f2393,f193])).
% 16.38/2.49 fof(f2430,plain,(
% 16.38/2.49 ![X0]: (join(zero,X0)=join(X0,zero))),
% 16.38/2.49 inference(backward_demodulation,[status(thm)],[f2393,f2236])).
% 16.38/2.49 fof(f2459,plain,(
% 16.38/2.49 ![X0]: (X0=join(X0,zero))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f2393,f2430])).
% 16.38/2.49 fof(f2518,plain,(
% 16.38/2.49 ![X0]: (top=join(complement(X0),join(complement(X0),X0)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f2404,f90])).
% 16.38/2.49 fof(f2579,plain,(
% 16.38/2.49 ![X0]: (top=join(complement(X0),join(X0,complement(X0))))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f54,f2518])).
% 16.38/2.49 fof(f2580,plain,(
% 16.38/2.49 ![X0]: (top=join(X0,join(complement(X0),complement(X0))))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f54,f2579])).
% 16.38/2.49 fof(f2581,plain,(
% 16.38/2.49 ![X0]: (top=join(top,complement(X0)))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f65,f2580])).
% 16.38/2.49 fof(f2690,plain,(
% 16.38/2.49 ![X0]: (top=join(top,X0))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f1087,f2581])).
% 16.38/2.49 fof(f2720,plain,(
% 16.38/2.49 ![X0]: (zero=join(meet(zero,X0),complement(top)))),
% 16.38/2.49 inference(backward_demodulation,[status(thm)],[f2690,f844])).
% 16.38/2.49 fof(f2739,plain,(
% 16.38/2.49 ![X0]: (zero=join(complement(top),meet(zero,X0)))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f19,f2720])).
% 16.38/2.49 fof(f2740,plain,(
% 16.38/2.49 ![X0]: (zero=join(zero,meet(zero,X0)))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f89,f2739])).
% 16.38/2.49 fof(f2753,plain,(
% 16.38/2.49 ![X0]: (zero=meet(zero,X0))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f2393,f2740])).
% 16.38/2.49 fof(f3019,plain,(
% 16.38/2.49 ![X0]: (zero=meet(X0,zero))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f477,f2753])).
% 16.38/2.49 fof(f4021,plain,(
% 16.38/2.49 ![X0]: (converse(converse(X0))=join(X0,converse(zero)))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f2459,f132])).
% 16.38/2.49 fof(f4070,plain,(
% 16.38/2.49 ![X0]: (X0=join(X0,converse(zero)))),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f26,f4021])).
% 16.38/2.49 fof(f4102,plain,(
% 16.38/2.49 zero=converse(zero)),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f2393,f4070])).
% 16.38/2.49 fof(f4177,plain,(
% 16.38/2.49 ![X0]: (converse(composition(zero,X0))=composition(converse(X0),zero))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f4102,f104])).
% 16.38/2.49 fof(f4187,plain,(
% 16.38/2.49 converse(composition(sF2_fnc,zero))=composition(zero,sK0_skl)),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f4102,f102])).
% 16.38/2.49 fof(f17011,plain,(
% 16.38/2.49 composition(join(one,sF2_fnc),complement(composition(join(sK0_skl,one),top)))=zero),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f2193,f2429])).
% 16.38/2.49 fof(f17084,plain,(
% 16.38/2.49 composition(join(one,sF2_fnc),complement(join(top,composition(sK0_skl,top))))=zero),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f2078,f17011])).
% 16.38/2.49 fof(f17085,plain,(
% 16.38/2.49 composition(join(one,sF2_fnc),complement(top))=zero),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f2690,f17084])).
% 16.38/2.49 fof(f17086,plain,(
% 16.38/2.49 composition(join(one,sF2_fnc),zero)=zero),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f89,f17085])).
% 16.38/2.49 fof(f17087,plain,(
% 16.38/2.49 join(zero,composition(sF2_fnc,zero))=zero),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f2079,f17086])).
% 16.38/2.49 fof(f17089,plain,(
% 16.38/2.49 converse(zero)=composition(zero,sK0_skl)),
% 16.38/2.49 inference(backward_demodulation,[status(thm)],[f17090,f4187])).
% 16.38/2.49 fof(f17090,plain,(
% 16.38/2.49 composition(sF2_fnc,zero)=zero),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f2393,f17087])).
% 16.38/2.49 fof(f17271,plain,(
% 16.38/2.49 zero=composition(zero,sK0_skl)),
% 16.38/2.49 inference(forward_demodulation,[status(thm)],[f4102,f17089])).
% 16.38/2.49 fof(f17698,plain,(
% 16.38/2.49 join(meet(composition(converse(sK0_skl),sK2_skl),sK1_skl),meet(sK1_skl,composition(converse(sK0_skl),zero)))=meet(sK1_skl,composition(converse(sK0_skl),meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 16.38/2.49 inference(paramodulation,[status(thm)],[f500,f549])).
% 16.38/2.49 fof(f17901,plain,(
% 16.38/2.49 join(meet(sK1_skl,composition(converse(sK0_skl),zero)),meet(composition(converse(sK0_skl),sK2_skl),sK1_skl))=meet(sK1_skl,composition(converse(sK0_skl),meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f19,f17698])).
% 17.17/2.56 fof(f17902,plain,(
% 17.17/2.56 join(meet(sK1_skl,converse(composition(zero,sK0_skl))),meet(composition(converse(sK0_skl),sK2_skl),sK1_skl))=meet(sK1_skl,composition(converse(sK0_skl),meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f4177,f17901])).
% 17.17/2.56 fof(f17903,plain,(
% 17.17/2.56 join(meet(sK1_skl,converse(zero)),meet(composition(converse(sK0_skl),sK2_skl),sK1_skl))=meet(sK1_skl,composition(converse(sK0_skl),meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f17271,f17902])).
% 17.17/2.56 fof(f17904,plain,(
% 17.17/2.56 join(meet(sK1_skl,zero),meet(composition(converse(sK0_skl),sK2_skl),sK1_skl))=meet(sK1_skl,composition(converse(sK0_skl),meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f4102,f17903])).
% 17.17/2.56 fof(f17905,plain,(
% 17.17/2.56 join(zero,meet(composition(converse(sK0_skl),sK2_skl),sK1_skl))=meet(sK1_skl,composition(converse(sK0_skl),meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f3019,f17904])).
% 17.17/2.56 fof(f17906,plain,(
% 17.17/2.56 meet(composition(converse(sK0_skl),sK2_skl),sK1_skl)=meet(sK1_skl,composition(converse(sK0_skl),meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f2393,f17905])).
% 17.17/2.56 fof(f17907,plain,(
% 17.17/2.56 meet(sK1_skl,composition(converse(sK0_skl),sK2_skl))=meet(sK1_skl,composition(converse(sK0_skl),meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f477,f17906])).
% 17.17/2.56 fof(f17908,plain,(
% 17.17/2.56 meet(sK1_skl,composition(sF2_fnc,sK2_skl))=meet(sK1_skl,composition(converse(sK0_skl),meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f39,f17907])).
% 17.17/2.56 fof(f17909,plain,(
% 17.17/2.56 meet(sK1_skl,sF1_fnc)=meet(sK1_skl,composition(converse(sK0_skl),meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f40,f17908])).
% 17.17/2.56 fof(f17910,plain,(
% 17.17/2.56 sF0_fnc=meet(sK1_skl,composition(converse(sK0_skl),meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f41,f17909])).
% 17.17/2.56 fof(f17911,plain,(
% 17.17/2.56 sF0_fnc=meet(sK1_skl,composition(sF2_fnc,meet(sK2_skl,composition(sK0_skl,sK1_skl))))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f39,f17910])).
% 17.17/2.56 fof(f17912,plain,(
% 17.17/2.56 sF0_fnc=meet(sK1_skl,composition(sF2_fnc,zero))),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f500,f17911])).
% 17.17/2.56 fof(f17913,plain,(
% 17.17/2.56 sF0_fnc=meet(sK1_skl,zero)),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f17090,f17912])).
% 17.17/2.56 fof(f17914,plain,(
% 17.17/2.56 sF0_fnc=zero),
% 17.17/2.56 inference(forward_demodulation,[status(thm)],[f3019,f17913])).
% 17.17/2.56 fof(f17915,plain,(
% 17.17/2.56 $false),
% 17.17/2.56 inference(forward_subsumption_resolution,[status(thm)],[f17914,f42])).
% 17.17/2.56 % SZS output end CNFRefutation for theBenchmark.p
% 17.17/2.57 % Elapsed time: 2.264491 seconds
% 17.17/2.57 % CPU time: 17.795590 seconds
% 17.17/2.57 % Total memory used: 400.160 MB
% 17.17/2.57 % Net memory used: 393.670 MB
%------------------------------------------------------------------------------