%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : REL044+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 : n002.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 02:03:45 PM UTC 2026
% Result : Theorem 38.29s 10.25s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL044+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n002.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 : Mon Sep 21 04:11:11 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 38.29/10.25 % Refutation found
% 38.29/10.25 % SZS status Theorem for theBenchmark: Theorem is valid
% 38.29/10.25 % SZS output start CNFRefutation for theBenchmark
% 38.29/10.25 fof(f1,axiom,(
% 38.29/10.25 (! [X0,X1] : join(X0,X1) = join(X1,X0) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f2,axiom,(
% 38.29/10.25 (! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f3,axiom,(
% 38.29/10.25 (! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f4,axiom,(
% 38.29/10.25 (! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f5,axiom,(
% 38.29/10.25 (! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f6,axiom,(
% 38.29/10.25 (! [X0] : composition(X0,one) = X0 )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f7,axiom,(
% 38.29/10.25 (! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f8,axiom,(
% 38.29/10.25 (! [X0] : converse(converse(X0)) = X0 )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f9,axiom,(
% 38.29/10.25 (! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f10,axiom,(
% 38.29/10.25 (! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f11,axiom,(
% 38.29/10.25 (! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f12,axiom,(
% 38.29/10.25 (! [X0] : top = join(X0,complement(X0)) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f13,axiom,(
% 38.29/10.25 (! [X0] : zero = meet(X0,complement(X0)) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f14,axiom,(
% 38.29/10.25 (! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f17,conjecture,(
% 38.29/10.25 (! [X0,X1,X2] :( join(composition(complement(X0),X1),complement(X2)) = complement(X2)=> join(composition(X2,converse(X1)),X0) = X0 ) )),
% 38.29/10.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 38.29/10.25 fof(f18,negated_conjecture,(
% 38.29/10.25 ~((! [X0,X1,X2] :( join(composition(complement(X0),X1),complement(X2)) = complement(X2)=> join(composition(X2,converse(X1)),X0) = X0 ) ))),
% 38.29/10.25 inference(negated_conjecture,[status(cth)],[f17])).
% 38.29/10.25 fof(f19,plain,(
% 38.29/10.25 ![X0,X1]: (join(X0,X1)=join(X1,X0))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f1])).
% 38.29/10.25 fof(f20,plain,(
% 38.29/10.25 ![X0,X1,X2]: (join(X0,join(X1,X2))=join(join(X0,X1),X2))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f2])).
% 38.29/10.25 fof(f21,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f3])).
% 38.29/10.25 fof(f22,plain,(
% 38.29/10.25 ![X0,X1]: (meet(X0,X1)=complement(join(complement(X0),complement(X1))))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f4])).
% 38.29/10.25 fof(f23,plain,(
% 38.29/10.25 ![X0,X1,X2]: (composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f5])).
% 38.29/10.25 fof(f24,plain,(
% 38.29/10.25 ![X0]: (composition(X0,one)=X0)),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f6])).
% 38.29/10.25 fof(f25,plain,(
% 38.29/10.25 ![X0,X1,X2]: (composition(join(X0,X1),X2)=join(composition(X0,X2),composition(X1,X2)))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f7])).
% 38.29/10.25 fof(f26,plain,(
% 38.29/10.25 ![X0]: (converse(converse(X0))=X0)),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f8])).
% 38.29/10.25 fof(f27,plain,(
% 38.29/10.25 ![X0,X1]: (converse(join(X0,X1))=join(converse(X0),converse(X1)))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f9])).
% 38.29/10.25 fof(f28,plain,(
% 38.29/10.25 ![X0,X1]: (converse(composition(X0,X1))=composition(converse(X1),converse(X0)))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f10])).
% 38.29/10.25 fof(f29,plain,(
% 38.29/10.25 ![X0,X1]: (join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f11])).
% 38.29/10.25 fof(f30,plain,(
% 38.29/10.25 ![X0]: (top=join(X0,complement(X0)))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f12])).
% 38.29/10.25 fof(f31,plain,(
% 38.29/10.25 ![X0]: (zero=meet(X0,complement(X0)))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f13])).
% 38.29/10.25 fof(f32,plain,(
% 38.29/10.25 ![X0,X1,X2]: (join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))))=composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))))),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f14])).
% 38.29/10.25 fof(f35,plain,(
% 38.29/10.25 (?[X0,X1,X2]: (join(composition(complement(X0),X1),complement(X2))=complement(X2)&~join(composition(X2,converse(X1)),X0)=X0))),
% 38.29/10.25 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 38.29/10.25 fof(f36,plain,(
% 38.29/10.25 (join(composition(complement(sK0_skl),sK1_skl),complement(sK2_skl))=complement(sK2_skl)&~join(composition(sK2_skl,converse(sK1_skl)),sK0_skl)=sK0_skl)),
% 38.29/10.25 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])).
% 38.29/10.25 fof(f37,plain,(
% 38.29/10.25 join(composition(complement(sK0_skl),sK1_skl),complement(sK2_skl))=complement(sK2_skl)),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f36])).
% 38.29/10.25 fof(f38,plain,(
% 38.29/10.25 ~join(composition(sK2_skl,converse(sK1_skl)),sK0_skl)=sK0_skl),
% 38.29/10.25 inference(cnf_transformation,[status(thm)],[f36])).
% 38.29/10.25 fof(f39,definition,(
% 38.29/10.25 sF2_fnc=converse(sK1_skl)),
% 38.29/10.25 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 38.29/10.25 fof(f40,definition,(
% 38.29/10.25 sF1_fnc=composition(sK2_skl,sF2_fnc)),
% 38.29/10.25 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 38.29/10.25 fof(f41,definition,(
% 38.29/10.25 sF0_fnc=join(sF1_fnc,sK0_skl)),
% 38.29/10.25 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 38.29/10.25 fof(f42,plain,(
% 38.29/10.25 ~sF0_fnc=sK0_skl),
% 38.29/10.25 inference(definition_folding,[],[f38,f41,f40,f39])).
% 38.29/10.25 fof(f43,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f19,f21])).
% 38.29/10.25 fof(f44,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(complement(join(complement(X0),X1)),meet(X0,X1)))),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f22,f43])).
% 38.29/10.25 fof(f45,plain,(
% 38.29/10.25 ![X0,X1]: (join(complement(X0),composition(converse(X1),complement(composition(X1,X0))))=complement(X0))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f19,f29])).
% 38.29/10.25 fof(f46,plain,(
% 38.29/10.25 join(complement(sK2_skl),composition(complement(sK0_skl),sK1_skl))=complement(sK2_skl)),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f19,f37])).
% 38.29/10.25 fof(f47,plain,(
% 38.29/10.25 sF0_fnc=join(sK0_skl,sF1_fnc)),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f19,f41])).
% 38.29/10.25 fof(f48,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(meet(X0,X1),complement(join(complement(X0),X1))))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f19,f44])).
% 38.29/10.25 fof(f54,plain,(
% 38.29/10.25 converse(sF2_fnc)=sK1_skl),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f39,f26])).
% 38.29/10.25 fof(f63,plain,(
% 38.29/10.25 ![X0,X1]: (meet(X0,X1)=complement(join(complement(X1),complement(X0))))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f19,f22])).
% 38.29/10.25 fof(f65,plain,(
% 38.29/10.25 ![X0,X1,X2]: (meet(join(complement(X0),complement(X1)),X2)=complement(join(meet(X0,X1),complement(X2))))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f22,f22])).
% 38.29/10.25 fof(f71,plain,(
% 38.29/10.25 ![X0,X1]: (converse(composition(converse(X0),X1))=composition(converse(X1),X0))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f26,f28])).
% 38.29/10.25 fof(f144,plain,(
% 38.29/10.25 ![X0,X1]: (composition(X0,composition(one,X1))=composition(X0,X1))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f24,f23])).
% 38.29/10.25 fof(f149,plain,(
% 38.29/10.25 ![X0,X1]: (zero=meet(join(complement(X0),complement(X1)),meet(X0,X1)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f22,f31])).
% 38.29/10.25 fof(f150,plain,(
% 38.29/10.25 ![X0,X1]: (zero=complement(join(meet(X0,X1),complement(meet(X0,X1)))))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f65,f149])).
% 38.29/10.25 fof(f151,plain,(
% 38.29/10.25 zero=complement(top)),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f30,f150])).
% 38.29/10.25 fof(f154,plain,(
% 38.29/10.25 ![X0]: (meet(top,X0)=complement(join(zero,complement(X0))))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f151,f22])).
% 38.29/10.25 fof(f157,plain,(
% 38.29/10.25 top=join(top,zero)),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f151,f30])).
% 38.29/10.25 fof(f161,plain,(
% 38.29/10.25 ![X0,X1]: (join(X0,join(complement(X0),X1))=join(top,X1))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f30,f20])).
% 38.29/10.25 fof(f164,plain,(
% 38.29/10.25 ![X0]: (join(top,join(zero,X0))=join(top,X0))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f157,f20])).
% 38.29/10.25 fof(f220,plain,(
% 38.29/10.25 ![X0,X1]: (meet(X0,X1)=meet(X1,X0))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f22,f63])).
% 38.29/10.25 fof(f322,plain,(
% 38.29/10.25 ![X0,X1]: (converse(join(converse(X0),X1))=join(X0,converse(X1)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f26,f27])).
% 38.29/10.25 fof(f337,plain,(
% 38.29/10.25 ![X0]: (join(zero,composition(converse(X0),complement(composition(X0,top))))=complement(top))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f151,f45])).
% 38.29/10.25 fof(f359,plain,(
% 38.29/10.25 ![X0]: (join(zero,composition(converse(X0),complement(composition(X0,top))))=zero)),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f151,f337])).
% 38.29/10.25 fof(f386,plain,(
% 38.29/10.25 ![X0]: (join(meet(sF1_fnc,X0),composition(meet(sK2_skl,composition(X0,converse(sF2_fnc))),meet(sF2_fnc,composition(converse(sK2_skl),X0))))=composition(meet(sK2_skl,composition(X0,converse(sF2_fnc))),meet(sF2_fnc,composition(converse(sK2_skl),X0))))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f40,f32])).
% 38.29/10.25 fof(f436,plain,(
% 38.29/10.25 ![X0]: (join(meet(sF1_fnc,X0),composition(meet(sK2_skl,composition(X0,sK1_skl)),meet(sF2_fnc,composition(converse(sK2_skl),X0))))=composition(meet(sK2_skl,composition(X0,converse(sF2_fnc))),meet(sF2_fnc,composition(converse(sK2_skl),X0))))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f54,f386])).
% 38.29/10.25 fof(f437,plain,(
% 38.29/10.25 ![X0]: (join(meet(sF1_fnc,X0),composition(meet(sK2_skl,composition(X0,sK1_skl)),meet(sF2_fnc,composition(converse(sK2_skl),X0))))=composition(meet(sK2_skl,composition(X0,sK1_skl)),meet(sF2_fnc,composition(converse(sK2_skl),X0))))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f54,f436])).
% 38.29/10.25 fof(f565,plain,(
% 38.29/10.25 ![X0,X1]: (meet(join(zero,complement(X0)),X1)=complement(join(meet(top,X0),complement(X1))))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f154,f22])).
% 38.29/10.25 fof(f580,plain,(
% 38.29/10.25 ![X0]: (join(X0,top)=join(top,complement(complement(X0))))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f30,f161])).
% 38.29/10.25 fof(f854,plain,(
% 38.29/10.25 ![X0]: (converse(converse(X0))=composition(converse(one),X0))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f24,f71])).
% 38.29/10.25 fof(f898,plain,(
% 38.29/10.25 ![X0]: (X0=composition(converse(one),X0))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f26,f854])).
% 38.29/10.25 fof(f935,plain,(
% 38.29/10.25 ![X0]: (composition(one,X0)=composition(converse(one),X0))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f144,f898])).
% 38.29/10.25 fof(f936,plain,(
% 38.29/10.25 one=converse(one)),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f24,f898])).
% 38.29/10.25 fof(f937,plain,(
% 38.29/10.25 ![X0]: (join(complement(X0),complement(composition(one,X0)))=complement(X0))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f898,f45])).
% 38.29/10.25 fof(f950,plain,(
% 38.29/10.25 ![X0,X1]: (composition(join(converse(one),X0),X1)=join(X1,composition(X0,X1)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f898,f25])).
% 38.29/10.25 fof(f964,plain,(
% 38.29/10.25 ![X0]: (composition(one,X0)=X0)),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f898,f935])).
% 38.29/10.25 fof(f971,plain,(
% 38.29/10.25 ![X0]: (join(complement(X0),complement(X0))=complement(X0))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f964,f937])).
% 38.29/10.25 fof(f1000,plain,(
% 38.29/10.25 ![X0,X1]: (composition(join(one,X0),X1)=join(X1,composition(X0,X1)))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f936,f950])).
% 38.29/10.25 fof(f1021,plain,(
% 38.29/10.25 ![X0]: (X0=join(zero,complement(join(complement(X0),complement(X0)))))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f31,f48])).
% 38.29/10.25 fof(f1024,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(meet(X0,complement(X1)),meet(X1,X0)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f63,f48])).
% 38.29/10.25 fof(f1029,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(meet(X0,join(complement(complement(X0)),X1)),complement(join(top,X1))))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f161,f48])).
% 38.29/10.25 fof(f1046,plain,(
% 38.29/10.25 ![X0]: (X0=join(zero,meet(X0,X0)))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f63,f1021])).
% 38.29/10.25 fof(f1047,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(meet(X1,X0),meet(X0,complement(X1))))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f19,f1024])).
% 38.29/10.25 fof(f1052,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(complement(join(top,X1)),meet(X0,join(complement(complement(X0)),X1))))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f19,f1029])).
% 38.29/10.25 fof(f1167,plain,(
% 38.29/10.25 ![X0]: (converse(join(one,X0))=join(one,converse(X0)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f936,f322])).
% 38.29/10.25 fof(f1202,plain,(
% 38.29/10.25 ![X0]: (join(top,X0)=join(top,meet(X0,X0)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f1046,f164])).
% 38.29/10.25 fof(f1223,plain,(
% 38.29/10.25 ![X0]: (meet(X0,X0)=complement(complement(X0)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f971,f63])).
% 38.29/10.25 fof(f1225,plain,(
% 38.29/10.25 ![X0]: (X0=join(meet(X0,complement(X0)),complement(complement(X0))))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f971,f48])).
% 38.29/10.25 fof(f1226,plain,(
% 38.29/10.25 ![X0]: (join(X0,complement(X0))=join(top,complement(X0)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f971,f161])).
% 38.29/10.25 fof(f1272,plain,(
% 38.29/10.25 ![X0]: (join(top,X0)=join(top,complement(complement(X0))))),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1223,f1202])).
% 38.29/10.25 fof(f1273,plain,(
% 38.29/10.25 ![X0]: (X0=join(complement(complement(X0)),meet(X0,complement(X0))))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f19,f1225])).
% 38.29/10.25 fof(f1274,plain,(
% 38.29/10.25 ![X0]: (X0=join(complement(complement(X0)),zero))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f31,f1273])).
% 38.29/10.25 fof(f1275,plain,(
% 38.29/10.25 ![X0]: (X0=join(zero,complement(complement(X0))))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f19,f1274])).
% 38.29/10.25 fof(f1277,plain,(
% 38.29/10.25 ![X0]: (join(X0,top)=top)),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1279,f580])).
% 38.29/10.25 fof(f1279,plain,(
% 38.29/10.25 ![X0]: (top=join(top,complement(X0)))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f30,f1226])).
% 38.29/10.25 fof(f1290,plain,(
% 38.29/10.25 ![X0,X1]: (join(X0,join(complement(X0),X1))=top)),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1312,f161])).
% 38.29/10.25 fof(f1300,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(complement(top),meet(X0,join(complement(complement(X0)),X1))))),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1312,f1052])).
% 38.29/10.25 fof(f1312,plain,(
% 38.29/10.25 ![X0]: (join(top,X0)=top)),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f1279,f1272])).
% 38.29/10.25 fof(f1315,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(zero,meet(X0,join(complement(complement(X0)),X1))))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f151,f1300])).
% 38.29/10.25 fof(f1347,plain,(
% 38.29/10.25 ![X0]: (X0=join(meet(X0,top),complement(top)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f1277,f48])).
% 38.29/10.25 fof(f1359,plain,(
% 38.29/10.25 ![X0]: (X0=join(complement(top),meet(X0,top)))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f19,f1347])).
% 38.29/10.25 fof(f1361,plain,(
% 38.29/10.25 ![X0]: (X0=join(zero,meet(X0,top)))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f151,f1359])).
% 38.29/10.25 fof(f1405,plain,(
% 38.29/10.25 ![X0]: (X0=join(zero,meet(top,X0)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f220,f1361])).
% 38.29/10.25 fof(f1415,plain,(
% 38.29/10.25 ![X0,X1]: (join(complement(X0),complement(X1))=join(zero,complement(meet(X0,X1))))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f22,f1275])).
% 38.29/10.25 fof(f1416,plain,(
% 38.29/10.25 ![X0]: (meet(top,complement(X0))=complement(X0))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f1275,f154])).
% 38.29/10.25 fof(f1443,plain,(
% 38.29/10.25 ![X0]: (complement(X0)=join(zero,complement(X0)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f1416,f1405])).
% 38.29/10.25 fof(f1452,plain,(
% 38.29/10.25 ![X0]: (X0=complement(complement(X0)))),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1443,f1275])).
% 38.29/10.25 fof(f1453,plain,(
% 38.29/10.25 ![X0]: (meet(top,X0)=complement(complement(X0)))),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1443,f154])).
% 38.29/10.25 fof(f1455,plain,(
% 38.29/10.25 ![X0,X1]: (join(complement(X0),complement(X1))=complement(meet(X0,X1)))),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1443,f1415])).
% 38.29/10.25 fof(f1460,plain,(
% 38.29/10.25 ![X0,X1]: (meet(complement(X0),X1)=complement(join(meet(top,X0),complement(X1))))),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1443,f565])).
% 38.29/10.25 fof(f1481,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(zero,meet(X0,join(X0,X1))))),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1452,f1315])).
% 38.29/10.25 fof(f1487,plain,(
% 38.29/10.25 ![X0]: (X0=join(zero,X0))),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1493,f1405])).
% 38.29/10.25 fof(f1493,plain,(
% 38.29/10.25 ![X0]: (meet(top,X0)=X0)),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f1452,f1453])).
% 38.29/10.25 fof(f1525,plain,(
% 38.29/10.25 ![X0,X1]: (meet(complement(X0),X1)=complement(join(X0,complement(X1))))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f1493,f1460])).
% 38.29/10.25 fof(f1563,plain,(
% 38.29/10.25 ![X0]: (composition(converse(X0),complement(composition(X0,top)))=zero)),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1487,f359])).
% 38.29/10.25 fof(f1566,plain,(
% 38.29/10.25 ![X0,X1]: (X0=meet(X0,join(X0,X1)))),
% 38.29/10.25 inference(backward_demodulation,[status(thm)],[f1487,f1481])).
% 38.29/10.25 fof(f2254,plain,(
% 38.29/10.25 ![X0]: (X0=join(X0,zero))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f19,f1487])).
% 38.29/10.25 fof(f2287,plain,(
% 38.29/10.25 ![X0]: (converse(converse(X0))=join(X0,converse(zero)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f2254,f322])).
% 38.29/10.25 fof(f2305,plain,(
% 38.29/10.25 ![X0]: (X0=join(X0,converse(zero)))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f26,f2287])).
% 38.29/10.25 fof(f2310,plain,(
% 38.29/10.25 zero=converse(zero)),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f1487,f2305])).
% 38.29/10.25 fof(f2363,plain,(
% 38.29/10.25 ![X0]: (converse(composition(zero,X0))=composition(converse(X0),zero))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f2310,f71])).
% 38.29/10.25 fof(f2414,plain,(
% 38.29/10.25 ![X0,X1]: (X0=meet(X0,join(X1,X0)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f19,f1566])).
% 38.29/10.25 fof(f2942,plain,(
% 38.29/10.25 ![X0,X1]: (X0=join(meet(X1,X0),meet(complement(X1),X0)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f220,f1047])).
% 38.29/10.25 fof(f2950,plain,(
% 38.29/10.25 ![X0,X1]: (meet(X0,X1)=meet(meet(X0,X1),X1))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f1047,f1566])).
% 38.29/10.25 fof(f2981,plain,(
% 38.29/10.25 ![X0,X1]: (meet(X0,X1)=meet(X1,meet(X0,X1)))),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f220,f2950])).
% 38.29/10.25 fof(f3000,plain,(
% 38.29/10.25 ![X0,X1]: (meet(X0,X1)=meet(X1,meet(X1,X0)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f220,f2981])).
% 38.29/10.25 fof(f9605,plain,(
% 38.29/10.25 ![X0,X1]: (join(X0,complement(meet(X0,X1)))=top)),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f1455,f1290])).
% 38.29/10.25 fof(f9874,plain,(
% 38.29/10.25 ![X0,X1]: (complement(meet(X0,meet(complement(X0),X1)))=top)),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f1455,f9605])).
% 38.29/10.25 fof(f10006,plain,(
% 38.29/10.25 ![X0,X1]: (meet(X0,meet(complement(X0),X1))=complement(top))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f9874,f1452])).
% 38.29/10.25 fof(f10054,plain,(
% 38.29/10.25 ![X0,X1]: (meet(X0,meet(complement(X0),X1))=zero)),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f151,f10006])).
% 38.29/10.25 fof(f10068,plain,(
% 38.29/10.25 ![X0,X1]: (meet(X0,meet(X1,complement(X0)))=zero)),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f3000,f10054])).
% 38.29/10.25 fof(f10168,plain,(
% 38.29/10.25 ![X0,X1]: (meet(complement(X0),meet(X1,X0))=zero)),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f1452,f10068])).
% 38.29/10.25 fof(f11262,plain,(
% 38.29/10.25 ![X0,X1]: (meet(complement(join(X0,X1)),X1)=zero)),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f2414,f10168])).
% 38.29/10.25 fof(f11307,plain,(
% 38.29/10.25 ![X0,X1]: (meet(X0,complement(join(X1,X0)))=zero)),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f220,f11262])).
% 38.29/10.25 fof(f11898,plain,(
% 38.29/10.25 meet(composition(complement(sK0_skl),sK1_skl),complement(complement(sK2_skl)))=zero),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f46,f11307])).
% 38.29/10.25 fof(f12024,plain,(
% 38.29/10.25 meet(complement(complement(sK2_skl)),composition(complement(sK0_skl),sK1_skl))=zero),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f220,f11898])).
% 38.29/10.25 fof(f12026,plain,(
% 38.29/10.25 meet(sK2_skl,composition(complement(sK0_skl),sK1_skl))=zero),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f1452,f12024])).
% 38.29/10.25 fof(f13357,plain,(
% 38.29/10.25 ![X0,X1]: (meet(complement(X0),complement(X1))=complement(join(X0,X1)))),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f1452,f1525])).
% 38.29/10.25 fof(f14698,plain,(
% 38.29/10.25 ![X0]: (composition(join(one,converse(X0)),complement(composition(join(one,X0),top)))=zero)),
% 38.29/10.25 inference(paramodulation,[status(thm)],[f1167,f1563])).
% 38.29/10.25 fof(f14759,plain,(
% 38.29/10.25 ![X0]: (composition(join(one,converse(X0)),complement(join(top,composition(X0,top))))=zero)),
% 38.29/10.25 inference(forward_demodulation,[status(thm)],[f1000,f14698])).
% 38.29/10.25 fof(f14760,plain,(
% 38.29/10.25 ![X0]: (composition(join(one,converse(X0)),complement(top))=zero)),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f1312,f14759])).
% 33.03/10.35 fof(f14761,plain,(
% 33.03/10.35 ![X0]: (composition(join(one,converse(X0)),zero)=zero)),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f151,f14760])).
% 33.03/10.35 fof(f14762,plain,(
% 33.03/10.35 ![X0]: (join(zero,composition(converse(X0),zero))=zero)),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f1000,f14761])).
% 33.03/10.35 fof(f14763,plain,(
% 33.03/10.35 ![X0]: (converse(composition(zero,X0))=zero)),
% 33.03/10.35 inference(backward_demodulation,[status(thm)],[f14764,f2363])).
% 33.03/10.35 fof(f14764,plain,(
% 33.03/10.35 ![X0]: (composition(converse(X0),zero)=zero)),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f1487,f14762])).
% 33.03/10.35 fof(f16913,plain,(
% 33.03/10.35 ![X0]: (converse(zero)=composition(zero,X0))),
% 33.03/10.35 inference(paramodulation,[status(thm)],[f14763,f26])).
% 33.03/10.35 fof(f17138,plain,(
% 33.03/10.35 ![X0]: (zero=composition(zero,X0))),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f2310,f16913])).
% 33.03/10.35 fof(f27916,plain,(
% 33.03/10.35 join(meet(sF1_fnc,complement(sK0_skl)),composition(zero,meet(sF2_fnc,composition(converse(sK2_skl),complement(sK0_skl)))))=composition(meet(sK2_skl,composition(complement(sK0_skl),sK1_skl)),meet(sF2_fnc,composition(converse(sK2_skl),complement(sK0_skl))))),
% 33.03/10.35 inference(paramodulation,[status(thm)],[f12026,f437])).
% 33.03/10.35 fof(f27950,plain,(
% 33.03/10.35 join(meet(sF1_fnc,complement(sK0_skl)),zero)=composition(meet(sK2_skl,composition(complement(sK0_skl),sK1_skl)),meet(sF2_fnc,composition(converse(sK2_skl),complement(sK0_skl))))),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f17138,f27916])).
% 33.03/10.35 fof(f27951,plain,(
% 33.03/10.35 meet(sF1_fnc,complement(sK0_skl))=composition(meet(sK2_skl,composition(complement(sK0_skl),sK1_skl)),meet(sF2_fnc,composition(converse(sK2_skl),complement(sK0_skl))))),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f2254,f27950])).
% 33.03/10.35 fof(f27952,plain,(
% 33.03/10.35 meet(sF1_fnc,complement(sK0_skl))=composition(zero,meet(sF2_fnc,composition(converse(sK2_skl),complement(sK0_skl))))),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f12026,f27951])).
% 33.03/10.35 fof(f27953,plain,(
% 33.03/10.35 meet(sF1_fnc,complement(sK0_skl))=zero),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f17138,f27952])).
% 33.03/10.35 fof(f28038,plain,(
% 33.03/10.35 complement(sK0_skl)=join(zero,meet(complement(sF1_fnc),complement(sK0_skl)))),
% 33.03/10.35 inference(paramodulation,[status(thm)],[f27953,f2942])).
% 33.03/10.35 fof(f28078,plain,(
% 33.03/10.35 complement(sK0_skl)=meet(complement(sF1_fnc),complement(sK0_skl))),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f1487,f28038])).
% 33.03/10.35 fof(f28079,plain,(
% 33.03/10.35 complement(sK0_skl)=meet(complement(sK0_skl),complement(sF1_fnc))),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f220,f28078])).
% 33.03/10.35 fof(f28080,plain,(
% 33.03/10.35 complement(sK0_skl)=complement(join(sK0_skl,sF1_fnc))),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f13357,f28079])).
% 33.03/10.35 fof(f28095,plain,(
% 33.03/10.35 complement(sK0_skl)=complement(sF0_fnc)),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f47,f28080])).
% 33.03/10.35 fof(f28140,plain,(
% 33.03/10.35 sF0_fnc=complement(complement(sK0_skl))),
% 33.03/10.35 inference(paramodulation,[status(thm)],[f28095,f1452])).
% 33.03/10.35 fof(f28162,plain,(
% 33.03/10.35 sF0_fnc=sK0_skl),
% 33.03/10.35 inference(forward_demodulation,[status(thm)],[f1452,f28140])).
% 33.03/10.35 fof(f28163,plain,(
% 33.03/10.35 $false),
% 33.03/10.35 inference(forward_subsumption_resolution,[status(thm)],[f28162,f42])).
% 33.03/10.35 % SZS output end CNFRefutation for theBenchmark.p
% 33.03/10.39 % Elapsed time: 5.007746 seconds
% 33.03/10.39 % CPU time: 39.560503 seconds
% 33.03/10.39 % Total memory used: 524.830 MB
% 33.03/10.39 % Net memory used: 516.515 MB
%------------------------------------------------------------------------------