%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL045+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 02:03:27 PM UTC 2026
% Result : Theorem 11.22s 2.05s
% Output : CNFRefutation 11.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 15
% Syntax : Number of formulae : 144 ( 144 unt; 0 def)
% Number of atoms : 144 ( 143 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 188 ( 187 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [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))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0] : join(X0,composition(composition(X0,converse(X0)),X0)) = composition(composition(X0,converse(X0)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] : join(X0,composition(composition(X0,converse(X0)),X0)) = composition(composition(X0,converse(X0)),X0),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f29,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f30,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
! [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))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
? [X0] : join(X0,composition(composition(X0,converse(X0)),X0)) != composition(composition(X0,converse(X0)),X0),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f36,plain,
join(sK0_skl,composition(composition(sK0_skl,converse(sK0_skl)),sK0_skl)) != composition(composition(sK0_skl,converse(sK0_skl)),sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f35]) ).
fof(f37,plain,
join(sK0_skl,composition(composition(sK0_skl,converse(sK0_skl)),sK0_skl)) != composition(composition(sK0_skl,converse(sK0_skl)),sK0_skl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f45,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f19,f21]) ).
fof(f46,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f22,f45]) ).
fof(f47,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f19,f29]) ).
fof(f48,plain,
join(sK0_skl,composition(sK0_skl,composition(converse(sK0_skl),sK0_skl))) != composition(composition(sK0_skl,converse(sK0_skl)),sK0_skl),
inference(forward_demodulation,[status(thm)],[f23,f37]) ).
fof(f49,plain,
join(sK0_skl,composition(sK0_skl,composition(converse(sK0_skl),sK0_skl))) != composition(sK0_skl,composition(converse(sK0_skl),sK0_skl)),
inference(forward_demodulation,[status(thm)],[f23,f48]) ).
fof(f50,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f46]) ).
fof(f59,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f60,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f88,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f209,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(X1,complement(X0)))),
inference(paramodulation,[status(thm)],[f19,f50]) ).
fof(f211,plain,
! [X0,X1,X2] : join(meet(X0,X1),join(complement(join(complement(X0),X1)),X2)) = join(X0,X2),
inference(paramodulation,[status(thm)],[f50,f20]) ).
fof(f733,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f60]) ).
fof(f743,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f733]) ).
fof(f752,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f743]) ).
fof(f754,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f743,f47]) ).
fof(f762,plain,
! [X0,X1] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f743,f25]) ).
fof(f764,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f752,f743]) ).
fof(f771,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f752,f762]) ).
fof(f773,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f764,f754]) ).
fof(f791,plain,
! [X0] : converse(join(one,X0)) = join(one,converse(X0)),
inference(paramodulation,[status(thm)],[f752,f88]) ).
fof(f851,plain,
! [X0] : X0 = join(meet(X0,complement(X0)),complement(complement(X0))),
inference(paramodulation,[status(thm)],[f773,f50]) ).
fof(f860,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f851]) ).
fof(f861,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f31,f860]) ).
fof(f862,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f861]) ).
fof(f892,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f773,f22]) ).
fof(f893,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f30,f22]) ).
fof(f894,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f898,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f50]) ).
fof(f899,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X1,X0)),
inference(paramodulation,[status(thm)],[f22,f209]) ).
fof(f913,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f31,f893]) ).
fof(f919,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f894]) ).
fof(f921,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f898]) ).
fof(f922,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f899]) ).
fof(f944,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(paramodulation,[status(thm)],[f913,f47]) ).
fof(f957,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f913,f944]) ).
fof(f992,plain,
meet(top,top) = complement(zero),
inference(paramodulation,[status(thm)],[f913,f892]) ).
fof(f1003,plain,
! [X0] : top = join(complement(X0),meet(X0,X0)),
inference(paramodulation,[status(thm)],[f892,f30]) ).
fof(f1030,plain,
! [X0,X1] : join(meet(X0,X1),composition(meet(X0,composition(X1,converse(one))),meet(one,composition(converse(X0),X1)))) = composition(meet(X0,composition(X1,converse(one))),meet(one,composition(converse(X0),X1))),
inference(paramodulation,[status(thm)],[f24,f32]) ).
fof(f1046,plain,
! [X0,X1,X2] : join(meet(composition(X0,converse(X1)),X2),composition(meet(X0,composition(X2,X1)),meet(converse(X1),composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(converse(X1)))),meet(converse(X1),composition(converse(X0),X2))),
inference(paramodulation,[status(thm)],[f26,f32]) ).
fof(f1087,plain,
! [X0,X1] : join(meet(X0,X1),composition(meet(X0,composition(X1,one)),meet(one,composition(converse(X0),X1)))) = composition(meet(X0,composition(X1,converse(one))),meet(one,composition(converse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f752,f1030]) ).
fof(f1088,plain,
! [X0,X1] : join(meet(X0,X1),composition(meet(X0,X1),meet(one,composition(converse(X0),X1)))) = composition(meet(X0,composition(X1,converse(one))),meet(one,composition(converse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f24,f1087]) ).
fof(f1089,plain,
! [X0,X1] : join(meet(X0,X1),composition(meet(X0,X1),meet(one,composition(converse(X0),X1)))) = composition(meet(X0,composition(X1,one)),meet(one,composition(converse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f752,f1088]) ).
fof(f1090,plain,
! [X0,X1] : join(meet(X0,X1),composition(meet(X0,X1),meet(one,composition(converse(X0),X1)))) = composition(meet(X0,X1),meet(one,composition(converse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f24,f1089]) ).
fof(f1114,plain,
! [X0,X1,X2] : join(meet(composition(X0,converse(X1)),X2),composition(meet(X0,composition(X2,X1)),meet(converse(X1),composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,X1)),meet(converse(X1),composition(converse(X0),X2))),
inference(forward_demodulation,[status(thm)],[f26,f1046]) ).
fof(f1301,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X0),X1))),
inference(paramodulation,[status(thm)],[f773,f211]) ).
fof(f1352,plain,
! [X0,X1] : X0 = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f50,f1301]) ).
fof(f1433,plain,
! [X0] : X0 = join(meet(X0,meet(X0,X0)),complement(top)),
inference(paramodulation,[status(thm)],[f1003,f50]) ).
fof(f1449,plain,
! [X0] : X0 = join(complement(top),meet(X0,meet(X0,X0))),
inference(forward_demodulation,[status(thm)],[f19,f1433]) ).
fof(f1450,plain,
! [X0] : X0 = join(zero,meet(X0,meet(X0,X0))),
inference(forward_demodulation,[status(thm)],[f913,f1449]) ).
fof(f1455,plain,
top = join(zero,meet(top,complement(zero))),
inference(paramodulation,[status(thm)],[f992,f1450]) ).
fof(f1500,plain,
! [X0] : X0 = join(meet(X0,top),meet(X0,zero)),
inference(paramodulation,[status(thm)],[f913,f921]) ).
fof(f1634,plain,
! [X0] : X0 = join(meet(top,X0),meet(X0,zero)),
inference(paramodulation,[status(thm)],[f919,f1500]) ).
fof(f1637,plain,
! [X0] : X0 = join(meet(X0,top),meet(zero,X0)),
inference(paramodulation,[status(thm)],[f919,f1500]) ).
fof(f1659,plain,
complement(zero) = join(meet(complement(zero),top),zero),
inference(paramodulation,[status(thm)],[f31,f1637]) ).
fof(f1679,plain,
complement(zero) = join(zero,meet(complement(zero),top)),
inference(forward_demodulation,[status(thm)],[f19,f1659]) ).
fof(f1680,plain,
complement(zero) = join(zero,meet(top,complement(zero))),
inference(forward_demodulation,[status(thm)],[f919,f1679]) ).
fof(f1683,plain,
complement(zero) = top,
inference(forward_demodulation,[status(thm)],[f1455,f1680]) ).
fof(f1692,plain,
! [X0] : meet(X0,zero) = complement(join(complement(X0),top)),
inference(paramodulation,[status(thm)],[f1683,f22]) ).
fof(f1701,plain,
! [X0] : zero = join(meet(zero,X0),complement(join(X0,top))),
inference(paramodulation,[status(thm)],[f1683,f209]) ).
fof(f1702,plain,
! [X0] : zero = join(meet(zero,X0),complement(join(top,X0))),
inference(paramodulation,[status(thm)],[f1683,f50]) ).
fof(f1708,plain,
! [X0] : meet(X0,zero) = complement(join(top,complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f1692]) ).
fof(f1789,plain,
! [X0] : X0 = join(meet(X0,zero),meet(top,X0)),
inference(paramodulation,[status(thm)],[f19,f1634]) ).
fof(f1886,plain,
! [X0] : X0 = join(X0,complement(top)),
inference(paramodulation,[status(thm)],[f1003,f1352]) ).
fof(f1899,plain,
! [X0] : zero = join(zero,complement(join(top,X0))),
inference(paramodulation,[status(thm)],[f1683,f1352]) ).
fof(f1925,plain,
! [X0] : X0 = join(X0,zero),
inference(forward_demodulation,[status(thm)],[f913,f1886]) ).
fof(f1944,plain,
! [X0] : X0 = join(zero,X0),
inference(paramodulation,[status(thm)],[f19,f1925]) ).
fof(f1966,plain,
! [X0] : X0 = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1944,f862]) ).
fof(f1971,plain,
! [X0] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(backward_demodulation,[status(thm)],[f1944,f957]) ).
fof(f1974,plain,
! [X0] : zero = complement(join(top,X0)),
inference(backward_demodulation,[status(thm)],[f1944,f1899]) ).
fof(f2032,plain,
! [X0] : meet(X0,zero) = zero,
inference(backward_demodulation,[status(thm)],[f1974,f1708]) ).
fof(f2033,plain,
! [X0] : zero = join(meet(zero,X0),zero),
inference(backward_demodulation,[status(thm)],[f1974,f1702]) ).
fof(f2094,plain,
! [X0] : X0 = join(zero,meet(top,X0)),
inference(backward_demodulation,[status(thm)],[f2032,f1789]) ).
fof(f2105,plain,
! [X0] : zero = join(zero,complement(join(X0,top))),
inference(backward_demodulation,[status(thm)],[f2106,f1701]) ).
fof(f2106,plain,
! [X0] : zero = meet(zero,X0),
inference(forward_demodulation,[status(thm)],[f1925,f2033]) ).
fof(f2147,plain,
! [X0] : X0 = meet(top,X0),
inference(forward_demodulation,[status(thm)],[f1944,f2094]) ).
fof(f2163,plain,
! [X0] : zero = complement(join(X0,top)),
inference(forward_demodulation,[status(thm)],[f1944,f2105]) ).
fof(f2705,plain,
! [X0] : join(X0,top) = complement(zero),
inference(paramodulation,[status(thm)],[f2163,f1966]) ).
fof(f2722,plain,
! [X0] : join(X0,top) = top,
inference(forward_demodulation,[status(thm)],[f1683,f2705]) ).
fof(f2760,plain,
! [X0] : join(top,X0) = top,
inference(paramodulation,[status(thm)],[f19,f2722]) ).
fof(f2768,plain,
! [X0] : converse(top) = join(X0,converse(top)),
inference(paramodulation,[status(thm)],[f2722,f88]) ).
fof(f2958,plain,
converse(top) = top,
inference(paramodulation,[status(thm)],[f2760,f2768]) ).
fof(f4593,plain,
! [X0] : composition(join(one,converse(X0)),complement(composition(join(one,X0),top))) = zero,
inference(paramodulation,[status(thm)],[f791,f1971]) ).
fof(f4627,plain,
! [X0] : composition(join(one,converse(X0)),complement(join(top,composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f771,f4593]) ).
fof(f4628,plain,
! [X0] : composition(join(one,converse(X0)),complement(top)) = zero,
inference(forward_demodulation,[status(thm)],[f2760,f4627]) ).
fof(f4629,plain,
! [X0] : composition(join(one,converse(X0)),zero) = zero,
inference(forward_demodulation,[status(thm)],[f913,f4628]) ).
fof(f4630,plain,
! [X0] : join(zero,composition(converse(X0),zero)) = zero,
inference(forward_demodulation,[status(thm)],[f771,f4629]) ).
fof(f4632,plain,
! [X0] : composition(converse(X0),zero) = zero,
inference(forward_demodulation,[status(thm)],[f1944,f4630]) ).
fof(f4696,plain,
! [X0,X1] : composition(composition(X0,converse(X1)),zero) = zero,
inference(paramodulation,[status(thm)],[f59,f4632]) ).
fof(f4721,plain,
! [X0,X1] : composition(X0,composition(converse(X1),zero)) = zero,
inference(forward_demodulation,[status(thm)],[f23,f4696]) ).
fof(f4734,plain,
! [X0] : composition(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f4632,f4721]) ).
fof(f8009,plain,
! [X0] : join(meet(X0,complement(composition(X0,top))),composition(meet(X0,complement(composition(X0,top))),meet(one,zero))) = composition(meet(X0,complement(composition(X0,top))),meet(one,composition(converse(X0),complement(composition(X0,top))))),
inference(paramodulation,[status(thm)],[f1971,f1090]) ).
fof(f8126,plain,
! [X0] : join(meet(X0,complement(composition(X0,top))),composition(meet(X0,complement(composition(X0,top))),zero)) = composition(meet(X0,complement(composition(X0,top))),meet(one,composition(converse(X0),complement(composition(X0,top))))),
inference(forward_demodulation,[status(thm)],[f2032,f8009]) ).
fof(f8127,plain,
! [X0] : join(meet(X0,complement(composition(X0,top))),zero) = composition(meet(X0,complement(composition(X0,top))),meet(one,composition(converse(X0),complement(composition(X0,top))))),
inference(forward_demodulation,[status(thm)],[f4734,f8126]) ).
fof(f8128,plain,
! [X0] : meet(X0,complement(composition(X0,top))) = composition(meet(X0,complement(composition(X0,top))),meet(one,composition(converse(X0),complement(composition(X0,top))))),
inference(forward_demodulation,[status(thm)],[f1925,f8127]) ).
fof(f8129,plain,
! [X0] : meet(X0,complement(composition(X0,top))) = composition(meet(X0,complement(composition(X0,top))),meet(one,zero)),
inference(forward_demodulation,[status(thm)],[f1971,f8128]) ).
fof(f8130,plain,
! [X0] : meet(X0,complement(composition(X0,top))) = composition(meet(X0,complement(composition(X0,top))),zero),
inference(forward_demodulation,[status(thm)],[f2032,f8129]) ).
fof(f8131,plain,
! [X0] : meet(X0,complement(composition(X0,top))) = zero,
inference(forward_demodulation,[status(thm)],[f4734,f8130]) ).
fof(f8207,plain,
! [X0] : X0 = join(meet(composition(X0,top),X0),zero),
inference(paramodulation,[status(thm)],[f8131,f922]) ).
fof(f8236,plain,
! [X0] : X0 = meet(composition(X0,top),X0),
inference(forward_demodulation,[status(thm)],[f1925,f8207]) ).
fof(f8237,plain,
! [X0] : X0 = meet(X0,composition(X0,top)),
inference(forward_demodulation,[status(thm)],[f919,f8236]) ).
fof(f10826,plain,
! [X0] : join(meet(composition(X0,converse(top)),X0),composition(X0,meet(converse(top),composition(converse(X0),X0)))) = composition(meet(X0,composition(X0,top)),meet(converse(top),composition(converse(X0),X0))),
inference(paramodulation,[status(thm)],[f8237,f1114]) ).
fof(f10987,plain,
! [X0] : join(meet(X0,composition(X0,converse(top))),composition(X0,meet(converse(top),composition(converse(X0),X0)))) = composition(meet(X0,composition(X0,top)),meet(converse(top),composition(converse(X0),X0))),
inference(forward_demodulation,[status(thm)],[f919,f10826]) ).
fof(f10988,plain,
! [X0] : join(meet(X0,composition(X0,top)),composition(X0,meet(converse(top),composition(converse(X0),X0)))) = composition(meet(X0,composition(X0,top)),meet(converse(top),composition(converse(X0),X0))),
inference(forward_demodulation,[status(thm)],[f2958,f10987]) ).
fof(f10989,plain,
! [X0] : join(X0,composition(X0,meet(converse(top),composition(converse(X0),X0)))) = composition(meet(X0,composition(X0,top)),meet(converse(top),composition(converse(X0),X0))),
inference(forward_demodulation,[status(thm)],[f8237,f10988]) ).
fof(f10990,plain,
! [X0] : join(X0,composition(X0,meet(top,composition(converse(X0),X0)))) = composition(meet(X0,composition(X0,top)),meet(converse(top),composition(converse(X0),X0))),
inference(forward_demodulation,[status(thm)],[f2958,f10989]) ).
fof(f10991,plain,
! [X0] : join(X0,composition(X0,composition(converse(X0),X0))) = composition(meet(X0,composition(X0,top)),meet(converse(top),composition(converse(X0),X0))),
inference(forward_demodulation,[status(thm)],[f2147,f10990]) ).
fof(f10992,plain,
! [X0] : join(X0,composition(X0,composition(converse(X0),X0))) = composition(X0,meet(converse(top),composition(converse(X0),X0))),
inference(forward_demodulation,[status(thm)],[f8237,f10991]) ).
fof(f10993,plain,
! [X0] : join(X0,composition(X0,composition(converse(X0),X0))) = composition(X0,meet(top,composition(converse(X0),X0))),
inference(forward_demodulation,[status(thm)],[f2958,f10992]) ).
fof(f10994,plain,
composition(sK0_skl,composition(converse(sK0_skl),sK0_skl)) != composition(sK0_skl,composition(converse(sK0_skl),sK0_skl)),
inference(backward_demodulation,[status(thm)],[f10995,f49]) ).
fof(f10995,plain,
! [X0] : join(X0,composition(X0,composition(converse(X0),X0))) = composition(X0,composition(converse(X0),X0)),
inference(forward_demodulation,[status(thm)],[f2147,f10993]) ).
fof(f11180,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f10994]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL045+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.57 % Computer : n004.cluster.edu
% 0.07/0.57 % Model : x86_64 x86_64
% 0.07/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.57 % Memory : 8046.5625MB
% 0.07/0.57 % OS : Linux 6.8.0-71-generic
% 0.07/0.57 % CPULimit : 300
% 0.07/0.57 % WCLimit : 300
% 0.07/0.57 % DateTime : Mon Sep 21 04:08:23 UTC 2026
% 0.07/0.57 % CPUTime :
% 0.07/0.58 % Drodi V4.1.1
% 11.22/2.05 % Refutation found
% 11.22/2.05 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.22/2.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.22/2.11 % Elapsed time: 1.522876 seconds
% 11.22/2.11 % CPU time: 11.925381 seconds
% 11.22/2.11 % Total memory used: 225.419 MB
% 11.22/2.11 % Net memory used: 221.158 MB
%------------------------------------------------------------------------------