%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL023+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 02:03:18 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 83 unt; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 128 ( 125 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
? [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) != composition(X0,meet(X1,X2)),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f30,plain,
join(composition(meet(sK0_skl,converse(sK1_skl)),meet(sK1_skl,sK2_skl)),composition(sK0_skl,meet(sK1_skl,sK2_skl))) != composition(sK0_skl,meet(sK1_skl,sK2_skl)),
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)],[f29]) ).
fof(f31,plain,
join(composition(meet(sK0_skl,converse(sK1_skl)),meet(sK1_skl,sK2_skl)),composition(sK0_skl,meet(sK1_skl,sK2_skl))) != composition(sK0_skl,meet(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f40,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f16,f18]) ).
fof(f41,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f19,f40]) ).
fof(f42,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f16,f26]) ).
fof(f43,plain,
composition(join(meet(sK0_skl,converse(sK1_skl)),sK0_skl),meet(sK1_skl,sK2_skl)) != composition(sK0_skl,meet(sK1_skl,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f22,f31]) ).
fof(f44,plain,
composition(join(sK0_skl,meet(sK0_skl,converse(sK1_skl))),meet(sK1_skl,sK2_skl)) != composition(sK0_skl,meet(sK1_skl,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f16,f43]) ).
fof(f45,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f16,f41]) ).
fof(f54,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f16,f19]) ).
fof(f57,plain,
! [X0,X1,X2] : meet(X0,join(complement(X1),complement(X2))) = complement(join(complement(X0),meet(X1,X2))),
inference(paramodulation,[status(thm)],[f19,f19]) ).
fof(f58,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f19,f54]) ).
fof(f63,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f69,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(forward_demodulation,[status(thm)],[f17,f63]) ).
fof(f76,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f216,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f45]) ).
fof(f220,plain,
! [X0,X1,X2] : join(meet(X0,X1),join(complement(join(complement(X0),X1)),X2)) = join(X0,X2),
inference(paramodulation,[status(thm)],[f45,f17]) ).
fof(f221,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f16,f216]) ).
fof(f226,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f58,f221]) ).
fof(f278,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f21,f76]) ).
fof(f284,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f23,f278]) ).
fof(f287,plain,
! [X0,X1] : zero = meet(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f28]) ).
fof(f291,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(paramodulation,[status(thm)],[f28,f221]) ).
fof(f293,plain,
! [X0,X1] : zero = meet(meet(X0,X1),join(complement(X0),complement(X1))),
inference(forward_demodulation,[status(thm)],[f58,f287]) ).
fof(f294,plain,
! [X0,X1] : zero = complement(join(complement(meet(X0,X1)),meet(X0,X1))),
inference(forward_demodulation,[status(thm)],[f57,f293]) ).
fof(f295,plain,
! [X0,X1] : zero = complement(join(meet(X0,X1),complement(meet(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f16,f294]) ).
fof(f296,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f27,f295]) ).
fof(f305,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(paramodulation,[status(thm)],[f296,f19]) ).
fof(f308,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[status(thm)],[f16,f305]) ).
fof(f317,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f21,f284]) ).
fof(f318,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f284,f42]) ).
fof(f327,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f317,f284]) ).
fof(f335,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f327,f318]) ).
fof(f380,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),complement(X1)))) = complement(join(complement(X0),complement(X1))),
inference(paramodulation,[status(thm)],[f19,f335]) ).
fof(f383,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f335,f19]) ).
fof(f388,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = complement(join(complement(X0),complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f380]) ).
fof(f389,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f19,f388]) ).
fof(f1065,plain,
! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
inference(paramodulation,[status(thm)],[f28,f226]) ).
fof(f1066,plain,
! [X0] : complement(X0) = join(meet(complement(X0),X0),complement(complement(complement(X0)))),
inference(paramodulation,[status(thm)],[f383,f226]) ).
fof(f1089,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f16,f1065]) ).
fof(f1090,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f58,f1089]) ).
fof(f1102,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f291,f1090]) ).
fof(f1103,plain,
! [X0] : complement(X0) = join(complement(complement(complement(X0))),meet(complement(X0),X0)),
inference(forward_demodulation,[status(thm)],[f16,f1066]) ).
fof(f1104,plain,
! [X0] : complement(X0) = join(complement(X0),meet(complement(X0),X0)),
inference(forward_demodulation,[status(thm)],[f1102,f1103]) ).
fof(f1105,plain,
! [X0] : complement(X0) = join(complement(X0),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f58,f1104]) ).
fof(f1106,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(forward_demodulation,[status(thm)],[f28,f1105]) ).
fof(f1112,plain,
! [X0] : meet(X0,top) = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1113,f308]) ).
fof(f1113,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[status(thm)],[f16,f1106]) ).
fof(f1160,plain,
! [X0] : meet(X0,top) = X0,
inference(forward_demodulation,[status(thm)],[f1102,f1112]) ).
fof(f1202,plain,
! [X0] : meet(top,X0) = X0,
inference(paramodulation,[status(thm)],[f58,f1160]) ).
fof(f1816,plain,
! [X0] : join(X0,meet(top,X0)) = meet(top,X0),
inference(paramodulation,[status(thm)],[f1202,f389]) ).
fof(f1833,plain,
! [X0] : join(X0,X0) = meet(top,X0),
inference(forward_demodulation,[status(thm)],[f1202,f1816]) ).
fof(f1837,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f1202,f1833]) ).
fof(f1876,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X1,X0),
inference(paramodulation,[status(thm)],[f1837,f69]) ).
fof(f2253,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),meet(X0,X1)) = join(X0,meet(X0,X1)),
inference(paramodulation,[status(thm)],[f1876,f220]) ).
fof(f2300,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),X1))) = join(X0,meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f16,f2253]) ).
fof(f2301,plain,
composition(sK0_skl,meet(sK1_skl,sK2_skl)) != composition(sK0_skl,meet(sK1_skl,sK2_skl)),
inference(backward_demodulation,[status(thm)],[f2306,f44]) ).
fof(f2306,plain,
! [X0,X1] : X0 = join(X0,meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f45,f2300]) ).
fof(f2372,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL023+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:07:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.45 % Refutation found
% 0.14/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.48 % Elapsed time: 0.093205 seconds
% 0.14/0.48 % CPU time: 0.620138 seconds
% 0.14/0.48 % Total memory used: 22.340 MB
% 0.14/0.48 % Net memory used: 22.008 MB
%------------------------------------------------------------------------------