%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL004-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:03:10 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.98s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 12
% Syntax : Number of formulae : 117 ( 117 unt; 0 def)
% Number of atoms : 117 ( 116 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 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 : 164 ( 164 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : join(A,B) = join(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : join(A,join(B,C)) = join(join(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : meet(A,B) = complement(join(complement(A),complement(B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : composition(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : converse(converse(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : converse(join(A,B)) = join(converse(A),converse(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : converse(composition(A,B)) = composition(converse(B),converse(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] : join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : top = join(A,complement(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : zero = meet(A,complement(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
converse(complement(sk1)) != complement(converse(sk1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f34,plain,
converse(complement(sk1)) != complement(converse(sk1)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f18,f20]) ).
fof(f41,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f21,f40]) ).
fof(f42,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f18,f28]) ).
fof(f43,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f18,f41]) ).
fof(f45,plain,
! [X0,X1,X2] : meet(join(complement(X0),complement(X1)),X2) = complement(join(meet(X0,X1),complement(X2))),
inference(paramodulation,[status(thm)],[f21,f21]) ).
fof(f46,plain,
! [X0,X1,X2] : meet(X0,join(complement(X1),complement(X2))) = complement(join(complement(X0),meet(X1,X2))),
inference(paramodulation,[status(thm)],[f21,f21]) ).
fof(f47,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f25,f26]) ).
fof(f50,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f51,plain,
! [X0,X1,X2] : join(meet(X0,X1),composition(converse(X2),complement(composition(X2,join(complement(X0),complement(X1)))))) = complement(join(complement(X0),complement(X1))),
inference(paramodulation,[status(thm)],[f21,f42]) ).
fof(f52,plain,
! [X0,X1] : join(complement(X0),composition(X1,complement(composition(converse(X1),X0)))) = complement(X0),
inference(paramodulation,[status(thm)],[f25,f42]) ).
fof(f54,plain,
! [X0,X1,X2] : join(meet(X0,X1),composition(converse(X2),complement(composition(X2,join(complement(X0),complement(X1)))))) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f21,f51]) ).
fof(f199,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f43]) ).
fof(f201,plain,
! [X0,X1] : X0 = join(meet(X0,composition(converse(X1),complement(composition(X1,X0)))),complement(complement(X0))),
inference(paramodulation,[status(thm)],[f42,f43]) ).
fof(f205,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f18,f199]) ).
fof(f207,plain,
! [X0,X1] : X0 = join(complement(complement(X0)),meet(X0,composition(converse(X1),complement(composition(X1,X0))))),
inference(forward_demodulation,[status(thm)],[f18,f201]) ).
fof(f252,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f23,f50]) ).
fof(f256,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f25,f252]) ).
fof(f268,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f18,f21]) ).
fof(f287,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f21,f268]) ).
fof(f298,plain,
! [X0] : converse(top) = join(X0,converse(complement(converse(X0)))),
inference(paramodulation,[status(thm)],[f29,f47]) ).
fof(f300,plain,
! [X0,X1] : meet(X0,top) = complement(join(complement(X0),meet(X1,complement(X1)))),
inference(paramodulation,[status(thm)],[f29,f46]) ).
fof(f302,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f29,f21]) ).
fof(f303,plain,
! [X0] : X0 = join(meet(X0,complement(complement(X0))),complement(top)),
inference(paramodulation,[status(thm)],[f29,f43]) ).
fof(f307,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(forward_demodulation,[status(thm)],[f30,f300]) ).
fof(f308,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[status(thm)],[f18,f307]) ).
fof(f311,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f30,f302]) ).
fof(f312,plain,
! [X0] : X0 = join(complement(top),meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f18,f303]) ).
fof(f313,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f311,f312]) ).
fof(f354,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f23,f256]) ).
fof(f359,plain,
! [X0] : join(complement(X0),composition(one,complement(X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f256,f52]) ).
fof(f362,plain,
! [X0,X1] : join(meet(X0,X1),composition(converse(converse(one)),complement(join(complement(X0),complement(X1))))) = meet(X0,X1),
inference(paramodulation,[status(thm)],[f256,f54]) ).
fof(f366,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,composition(converse(converse(one)),complement(X0)))),
inference(paramodulation,[status(thm)],[f256,f207]) ).
fof(f369,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f354,f256]) ).
fof(f371,plain,
! [X0,X1] : join(meet(X0,X1),composition(one,complement(join(complement(X0),complement(X1))))) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f25,f362]) ).
fof(f372,plain,
! [X0,X1] : join(meet(X0,X1),composition(one,meet(X0,X1))) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f21,f371]) ).
fof(f377,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,composition(one,complement(X0)))),
inference(forward_demodulation,[status(thm)],[f25,f366]) ).
fof(f381,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = meet(X0,X1),
inference(backward_demodulation,[status(thm)],[f369,f372]) ).
fof(f383,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
inference(backward_demodulation,[status(thm)],[f369,f377]) ).
fof(f384,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f369,f359]) ).
fof(f388,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f30,f383]) ).
fof(f389,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f18,f388]) ).
fof(f459,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f287,f205]) ).
fof(f489,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f384,f21]) ).
fof(f539,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(join(meet(X0,X1),complement(complement(complement(join(complement(X0),complement(X1)))))))),
inference(paramodulation,[status(thm)],[f45,f313]) ).
fof(f542,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(join(meet(X0,X1),complement(complement(meet(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f21,f539]) ).
fof(f549,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f287,f459]) ).
fof(f551,plain,
! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
inference(paramodulation,[status(thm)],[f30,f459]) ).
fof(f553,plain,
! [X0] : complement(X0) = join(meet(complement(X0),X0),complement(complement(complement(X0)))),
inference(paramodulation,[status(thm)],[f489,f459]) ).
fof(f566,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f18,f551]) ).
fof(f567,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f287,f566]) ).
fof(f570,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f581,f389]) ).
fof(f572,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(join(meet(X0,X1),meet(X0,X1)))),
inference(backward_demodulation,[status(thm)],[f581,f542]) ).
fof(f581,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f313,f567]) ).
fof(f583,plain,
! [X0] : complement(X0) = join(complement(complement(complement(X0))),meet(complement(X0),X0)),
inference(forward_demodulation,[status(thm)],[f18,f553]) ).
fof(f584,plain,
! [X0] : complement(X0) = join(complement(X0),meet(complement(X0),X0)),
inference(forward_demodulation,[status(thm)],[f581,f583]) ).
fof(f585,plain,
! [X0] : complement(X0) = join(complement(X0),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f287,f584]) ).
fof(f586,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(forward_demodulation,[status(thm)],[f30,f585]) ).
fof(f594,plain,
! [X0] : meet(X0,top) = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f595,f308]) ).
fof(f595,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[status(thm)],[f18,f586]) ).
fof(f606,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(join(meet(X0,X1),meet(X0,X1))),
inference(forward_demodulation,[status(thm)],[f595,f572]) ).
fof(f622,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f381,f606]) ).
fof(f633,plain,
! [X0] : meet(X0,top) = X0,
inference(forward_demodulation,[status(thm)],[f581,f594]) ).
fof(f740,plain,
! [X0] : meet(top,X0) = X0,
inference(paramodulation,[status(thm)],[f287,f633]) ).
fof(f966,plain,
! [X0] : X0 = join(meet(X0,converse(complement(converse(complement(X0))))),complement(converse(top))),
inference(paramodulation,[status(thm)],[f298,f43]) ).
fof(f981,plain,
! [X0] : X0 = join(complement(converse(top)),meet(X0,converse(complement(converse(complement(X0)))))),
inference(forward_demodulation,[status(thm)],[f18,f966]) ).
fof(f983,plain,
! [X0] : join(X0,meet(top,X0)) = meet(top,X0),
inference(paramodulation,[status(thm)],[f740,f381]) ).
fof(f996,plain,
! [X0] : join(X0,X0) = meet(top,X0),
inference(forward_demodulation,[status(thm)],[f740,f983]) ).
fof(f999,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f740,f996]) ).
fof(f1028,plain,
! [X0,X1] : join(X0,join(X0,X1)) = join(X0,X1),
inference(paramodulation,[status(thm)],[f999,f19]) ).
fof(f1043,plain,
! [X0,X1] : join(meet(X0,X1),X1) = join(meet(X0,X1),meet(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f549,f1028]) ).
fof(f1056,plain,
! [X0] : join(X0,top) = join(X0,complement(X0)),
inference(paramodulation,[status(thm)],[f29,f1028]) ).
fof(f1071,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = join(meet(X1,X0),meet(complement(X1),X0)),
inference(forward_demodulation,[status(thm)],[f18,f1043]) ).
fof(f1073,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f549,f1071]) ).
fof(f1100,plain,
! [X0] : join(X0,top) = top,
inference(forward_demodulation,[status(thm)],[f29,f1056]) ).
fof(f1112,plain,
! [X0] : join(top,X0) = top,
inference(paramodulation,[status(thm)],[f18,f1100]) ).
fof(f1290,plain,
converse(top) = top,
inference(paramodulation,[status(thm)],[f298,f1112]) ).
fof(f1314,plain,
! [X0] : X0 = join(complement(top),meet(X0,converse(complement(converse(complement(X0)))))),
inference(backward_demodulation,[status(thm)],[f1290,f981]) ).
fof(f1334,plain,
! [X0] : X0 = join(zero,meet(X0,converse(complement(converse(complement(X0)))))),
inference(forward_demodulation,[status(thm)],[f311,f1314]) ).
fof(f1335,plain,
! [X0] : X0 = meet(X0,converse(complement(converse(complement(X0))))),
inference(forward_demodulation,[status(thm)],[f570,f1334]) ).
fof(f1571,plain,
! [X0] : join(converse(complement(converse(complement(X0)))),X0) = converse(complement(converse(complement(X0)))),
inference(paramodulation,[status(thm)],[f1335,f1073]) ).
fof(f1594,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = converse(complement(converse(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f18,f1571]) ).
fof(f1601,plain,
! [X0,X1] : join(X0,complement(X1)) = complement(meet(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f581,f622]) ).
fof(f2197,plain,
! [X0] : join(X0,complement(converse(complement(converse(complement(complement(X0))))))) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f1335,f1601]) ).
fof(f2223,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = complement(complement(X0)),
inference(forward_demodulation,[status(thm)],[f581,f2197]) ).
fof(f2224,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = X0,
inference(forward_demodulation,[status(thm)],[f581,f2223]) ).
fof(f2271,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(complement(converse(complement(converse(converse(X0))))))),
inference(paramodulation,[status(thm)],[f2224,f47]) ).
fof(f2294,plain,
! [X0] : X0 = join(X0,converse(complement(converse(complement(converse(converse(X0))))))),
inference(forward_demodulation,[status(thm)],[f25,f2271]) ).
fof(f2295,plain,
! [X0] : X0 = join(X0,converse(complement(converse(complement(X0))))),
inference(forward_demodulation,[status(thm)],[f25,f2294]) ).
fof(f2299,plain,
! [X0] : X0 = converse(complement(converse(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f1594,f2295]) ).
fof(f2698,plain,
! [X0] : complement(X0) = converse(complement(converse(X0))),
inference(paramodulation,[status(thm)],[f581,f2299]) ).
fof(f2980,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(paramodulation,[status(thm)],[f25,f2698]) ).
fof(f3004,plain,
complement(converse(sk1)) != complement(converse(sk1)),
inference(backward_demodulation,[status(thm)],[f2980,f34]) ).
fof(f3021,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3004]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL004-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.59 % Computer : n014.cluster.edu
% 0.10/0.59 % Model : x86_64 x86_64
% 0.10/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.59 % Memory : 8046.5625MB
% 0.10/0.59 % OS : Linux 6.8.0-71-generic
% 0.10/0.59 % CPULimit : 300
% 0.10/0.59 % WCLimit : 300
% 0.10/0.59 % DateTime : Mon Sep 21 03:57:35 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.60 % Drodi V4.1.1
% 0.14/0.98 % Refutation found
% 0.14/0.98 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/1.02 % Elapsed time: 0.411815 seconds
% 0.14/1.02 % CPU time: 3.143401 seconds
% 0.14/1.02 % Total memory used: 86.890 MB
% 0.14/1.02 % Net memory used: 83.965 MB
%------------------------------------------------------------------------------