%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : REL001+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 : n008.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 02:03:30 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL001+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
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 03:58:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.39 fof(f1,axiom,(
% 0.13/0.39 (! [X0,X1] : join(X0,X1) = join(X1,X0) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f2,axiom,(
% 0.13/0.39 (! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f3,axiom,(
% 0.13/0.39 (! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f4,axiom,(
% 0.13/0.39 (! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f5,axiom,(
% 0.13/0.39 (! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f6,axiom,(
% 0.13/0.39 (! [X0] : composition(X0,one) = X0 )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f8,axiom,(
% 0.13/0.39 (! [X0] : converse(converse(X0)) = X0 )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f10,axiom,(
% 0.13/0.39 (! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f11,axiom,(
% 0.13/0.39 (! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f12,axiom,(
% 0.13/0.39 (! [X0] : top = join(X0,complement(X0)) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f13,axiom,(
% 0.13/0.39 (! [X0] : zero = meet(X0,complement(X0)) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f14,conjecture,(
% 0.13/0.39 (! [X0] : join(zero,X0) = X0 )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f15,negated_conjecture,(
% 0.13/0.39 ~((! [X0] : join(zero,X0) = X0 ))),
% 0.13/0.39 inference(negated_conjecture,[status(cth)],[f14])).
% 0.13/0.39 fof(f16,plain,(
% 0.13/0.39 ![X0,X1]: (join(X0,X1)=join(X1,X0))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.39 fof(f17,plain,(
% 0.13/0.39 ![X0,X1,X2]: (join(X0,join(X1,X2))=join(join(X0,X1),X2))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/0.39 fof(f18,plain,(
% 0.13/0.39 ![X0,X1]: (X0=join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f19,plain,(
% 0.13/0.39 ![X0,X1]: (meet(X0,X1)=complement(join(complement(X0),complement(X1))))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/0.39 fof(f20,plain,(
% 0.13/0.39 ![X0,X1,X2]: (composition(X0,composition(X1,X2))=composition(composition(X0,X1),X2))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.39 fof(f21,plain,(
% 0.13/0.39 ![X0]: (composition(X0,one)=X0)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.39 fof(f23,plain,(
% 0.13/0.39 ![X0]: (converse(converse(X0))=X0)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/0.39 fof(f25,plain,(
% 0.13/0.39 ![X0,X1]: (converse(composition(X0,X1))=composition(converse(X1),converse(X0)))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.13/0.39 fof(f26,plain,(
% 0.13/0.39 ![X0,X1]: (join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))=complement(X1))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.13/0.39 fof(f27,plain,(
% 0.13/0.39 ![X0]: (top=join(X0,complement(X0)))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.13/0.39 fof(f28,plain,(
% 0.13/0.39 ![X0]: (zero=meet(X0,complement(X0)))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.39 fof(f29,plain,(
% 0.13/0.39 (?[X0]: ~join(zero,X0)=X0)),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.13/0.39 fof(f30,plain,(
% 0.13/0.39 ~join(zero,sK0_skl)=sK0_skl),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f29])).
% 0.13/0.39 fof(f31,plain,(
% 0.13/0.39 ~join(zero,sK0_skl)=sK0_skl),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f30])).
% 0.13/0.39 fof(f32,definition,(
% 0.13/0.39 sF0_fnc=join(zero,sK0_skl)),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.13/0.39 fof(f33,plain,(
% 0.13/0.39 ~sF0_fnc=sK0_skl),
% 0.13/0.39 inference(definition_folding,[],[f31,f32])).
% 0.13/0.39 fof(f34,plain,(
% 0.13/0.39 ![X0,X1]: (X0=join(meet(X0,X1),complement(join(complement(X0),X1))))),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f19,f18])).
% 0.13/0.39 fof(f40,plain,(
% 0.13/0.39 ![X0,X1]: (join(X0,join(X1,complement(join(X0,X1))))=top)),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f27,f17])).
% 0.13/0.39 fof(f41,plain,(
% 0.13/0.39 ![X0,X1,X2]: (join(X0,join(X1,X2))=join(X2,join(X0,X1)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f16,f17])).
% 0.13/0.39 fof(f44,plain,(
% 0.13/0.39 ![X0,X1]: (join(X0,join(complement(X0),X1))=join(top,X1))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f27,f17])).
% 0.13/0.39 fof(f54,plain,(
% 0.13/0.39 ![X0,X1]: (converse(composition(converse(X0),X1))=composition(converse(X1),X0))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f23,f25])).
% 0.13/0.39 fof(f58,plain,(
% 0.13/0.39 ![X0,X1]: (composition(X0,composition(one,X1))=composition(X0,X1))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f21,f20])).
% 0.13/0.39 fof(f71,plain,(
% 0.13/0.39 ![X0]: (meet(X0,complement(X0))=complement(top))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f27,f19])).
% 0.13/0.39 fof(f78,plain,(
% 0.13/0.39 zero=complement(top)),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f28,f71])).
% 0.13/0.39 fof(f161,plain,(
% 0.13/0.39 ![X0]: (join(X0,top)=join(top,complement(complement(X0))))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f27,f44])).
% 0.13/0.39 fof(f176,plain,(
% 0.13/0.39 ![X0]: (converse(converse(X0))=composition(converse(one),X0))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f21,f54])).
% 0.13/0.39 fof(f191,plain,(
% 0.13/0.39 ![X0]: (X0=composition(converse(one),X0))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f23,f176])).
% 0.13/0.39 fof(f203,plain,(
% 0.13/0.39 ![X0]: (composition(one,X0)=composition(converse(one),X0))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f58,f191])).
% 0.13/0.39 fof(f205,plain,(
% 0.13/0.39 ![X0]: (join(complement(composition(one,X0)),complement(X0))=complement(X0))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f191,f26])).
% 0.13/0.39 fof(f218,plain,(
% 0.13/0.39 ![X0]: (composition(one,X0)=X0)),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f191,f203])).
% 0.13/0.39 fof(f220,plain,(
% 0.13/0.39 ![X0]: (join(complement(X0),complement(X0))=complement(X0))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f218,f205])).
% 0.13/0.39 fof(f259,plain,(
% 0.13/0.39 ![X0]: (X0=join(meet(X0,complement(complement(X0))),complement(top)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f27,f34])).
% 0.13/0.39 fof(f268,plain,(
% 0.13/0.39 ![X0]: (X0=join(meet(X0,complement(complement(X0))),zero))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f78,f259])).
% 0.13/0.39 fof(f271,plain,(
% 0.13/0.39 join(zero,complement(top))=complement(top)),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f78,f220])).
% 0.13/0.39 fof(f275,plain,(
% 0.13/0.39 ![X0]: (meet(X0,X0)=complement(complement(X0)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f220,f19])).
% 0.13/0.39 fof(f277,plain,(
% 0.13/0.39 ![X0]: (join(X0,complement(X0))=join(top,complement(X0)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f220,f44])).
% 0.13/0.39 fof(f279,plain,(
% 0.13/0.39 join(zero,zero)=complement(top)),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f78,f271])).
% 0.13/0.39 fof(f280,plain,(
% 0.13/0.39 join(zero,zero)=zero),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f78,f279])).
% 0.13/0.39 fof(f290,plain,(
% 0.13/0.39 ![X0]: (join(X0,top)=top)),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f291,f161])).
% 0.13/0.39 fof(f291,plain,(
% 0.13/0.39 ![X0]: (top=join(top,complement(X0)))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f27,f277])).
% 0.13/0.39 fof(f297,plain,(
% 0.13/0.39 ![X0]: (X0=join(meet(X0,top),complement(top)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f290,f34])).
% 0.13/0.39 fof(f316,plain,(
% 0.13/0.39 ![X0]: (X0=join(meet(X0,top),zero))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f78,f297])).
% 0.13/0.39 fof(f335,plain,(
% 0.13/0.39 ![X0]: (X0=join(complement(complement(X0)),complement(join(complement(X0),X0))))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f275,f34])).
% 0.13/0.39 fof(f386,plain,(
% 0.13/0.39 top=join(complement(complement(top)),zero)),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f275,f316])).
% 0.13/0.39 fof(f391,plain,(
% 0.13/0.39 top=join(complement(zero),zero)),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f78,f386])).
% 0.13/0.39 fof(f399,plain,(
% 0.13/0.39 zero=join(meet(zero,zero),complement(top))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f391,f34])).
% 0.13/0.39 fof(f404,plain,(
% 0.13/0.39 zero=join(complement(complement(zero)),complement(top))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f275,f399])).
% 0.13/0.39 fof(f405,plain,(
% 0.13/0.39 zero=join(complement(complement(zero)),zero)),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f78,f404])).
% 0.13/0.39 fof(f416,plain,(
% 0.13/0.39 complement(zero)=join(meet(complement(zero),zero),complement(zero))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f405,f34])).
% 0.13/0.39 fof(f469,plain,(
% 0.13/0.39 ![X0]: (join(X0,zero)=join(zero,join(X0,zero)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f280,f41])).
% 0.13/0.39 fof(f583,plain,(
% 0.13/0.39 ![X0,X1]: (join(meet(X0,complement(complement(X0))),join(zero,X1))=join(X1,X0))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f268,f41])).
% 0.13/0.39 fof(f585,plain,(
% 0.13/0.39 ![X0]: (join(meet(X0,complement(complement(X0))),join(zero,complement(X0)))=top)),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f268,f40])).
% 0.13/0.39 fof(f591,plain,(
% 0.13/0.39 ![X0]: (X0=join(complement(complement(X0)),complement(top)))),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f592,f335])).
% 0.13/0.39 fof(f592,plain,(
% 0.13/0.39 ![X0]: (join(complement(X0),X0)=top)),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f583,f585])).
% 0.13/0.39 fof(f594,plain,(
% 0.13/0.39 ![X0]: (X0=join(complement(complement(X0)),zero))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f78,f591])).
% 0.13/0.39 fof(f602,plain,(
% 0.13/0.39 ![X0]: (meet(complement(X0),X0)=complement(top))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f592,f19])).
% 0.13/0.39 fof(f614,plain,(
% 0.13/0.39 complement(zero)=join(zero,complement(zero))),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f615,f416])).
% 0.13/0.39 fof(f615,plain,(
% 0.13/0.39 ![X0]: (meet(complement(X0),X0)=zero)),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f78,f602])).
% 0.13/0.39 fof(f626,plain,(
% 0.13/0.39 complement(zero)=top),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f27,f614])).
% 0.13/0.39 fof(f638,plain,(
% 0.13/0.39 ![X0]: (meet(X0,zero)=complement(join(complement(X0),top)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f626,f19])).
% 0.13/0.39 fof(f651,plain,(
% 0.13/0.39 ![X0]: (meet(X0,zero)=complement(top))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f290,f638])).
% 0.13/0.39 fof(f653,plain,(
% 0.13/0.39 ![X0]: (meet(X0,zero)=zero)),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f78,f651])).
% 0.13/0.39 fof(f780,plain,(
% 0.13/0.39 ![X0]: (complement(X0)=join(meet(complement(X0),zero),complement(X0)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f594,f34])).
% 0.13/0.39 fof(f786,plain,(
% 0.13/0.39 ![X0]: (join(zero,complement(complement(X0)))=X0)),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f594,f16])).
% 0.13/0.39 fof(f793,plain,(
% 0.13/0.39 ![X0]: (complement(X0)=join(zero,complement(X0)))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f653,f780])).
% 0.13/0.39 fof(f795,plain,(
% 0.13/0.39 ![X0]: (X0=join(X0,zero))),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f811,f594])).
% 0.13/0.39 fof(f811,plain,(
% 0.13/0.39 ![X0]: (complement(complement(X0))=X0)),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f793,f786])).
% 0.13/0.39 fof(f833,plain,(
% 0.13/0.39 ![X0]: (join(X0,zero)=join(zero,X0))),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f795,f469])).
% 0.13/0.39 fof(f869,plain,(
% 0.13/0.39 sF0_fnc=sK0_skl),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f876,f32])).
% 0.13/0.39 fof(f876,plain,(
% 0.13/0.39 ![X0]: (X0=join(zero,X0))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f795,f833])).
% 0.13/0.39 fof(f883,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f869,f33])).
% 0.13/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.40 % Elapsed time: 0.035608 seconds
% 0.13/0.40 % CPU time: 0.133476 seconds
% 0.13/0.40 % Total memory used: 4.485 MB
% 0.13/0.40 % Net memory used: 4.429 MB
%------------------------------------------------------------------------------