%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL004+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 : Theorem 5.62s 1.13s
% Output : CNFRefutation 5.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 12
% Syntax : Number of formulae : 120 ( 120 unt; 0 def)
% Number of atoms : 120 ( 119 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 167 ( 166 !; 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(f6,axiom,
! [X0] : composition(X0,one) = X0,
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(f17,conjecture,
! [X0] : converse(complement(X0)) = complement(converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] : converse(complement(X0)) = complement(converse(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(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
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(f35,plain,
? [X0] : converse(complement(X0)) != complement(converse(X0)),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f36,plain,
converse(complement(sK0_skl)) != complement(converse(sK0_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f35]) ).
fof(f37,plain,
converse(complement(sK0_skl)) != complement(converse(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f43,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f19,f21]) ).
fof(f44,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f22,f43]) ).
fof(f45,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f19,f29]) ).
fof(f46,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f44]) ).
fof(f48,plain,
! [X0,X1,X2] : meet(join(complement(X0),complement(X1)),X2) = complement(join(meet(X0,X1),complement(X2))),
inference(paramodulation,[status(thm)],[f22,f22]) ).
fof(f49,plain,
! [X0,X1,X2] : meet(X0,join(complement(X1),complement(X2))) = complement(join(complement(X0),meet(X1,X2))),
inference(paramodulation,[status(thm)],[f22,f22]) ).
fof(f50,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f53,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f54,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)],[f22,f45]) ).
fof(f55,plain,
! [X0,X1] : join(complement(X0),composition(X1,complement(composition(converse(X1),X0)))) = complement(X0),
inference(paramodulation,[status(thm)],[f26,f45]) ).
fof(f57,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)],[f22,f54]) ).
fof(f202,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f46]) ).
fof(f204,plain,
! [X0,X1] : X0 = join(meet(X0,composition(converse(X1),complement(composition(X1,X0)))),complement(complement(X0))),
inference(paramodulation,[status(thm)],[f45,f46]) ).
fof(f208,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f19,f202]) ).
fof(f210,plain,
! [X0,X1] : X0 = join(complement(complement(X0)),meet(X0,composition(converse(X1),complement(composition(X1,X0))))),
inference(forward_demodulation,[status(thm)],[f19,f204]) ).
fof(f255,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f53]) ).
fof(f259,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f255]) ).
fof(f271,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f290,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f271]) ).
fof(f301,plain,
! [X0] : converse(top) = join(X0,converse(complement(converse(X0)))),
inference(paramodulation,[status(thm)],[f30,f50]) ).
fof(f303,plain,
! [X0,X1] : meet(X0,top) = complement(join(complement(X0),meet(X1,complement(X1)))),
inference(paramodulation,[status(thm)],[f30,f49]) ).
fof(f305,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f30,f22]) ).
fof(f306,plain,
! [X0] : X0 = join(meet(X0,complement(complement(X0))),complement(top)),
inference(paramodulation,[status(thm)],[f30,f46]) ).
fof(f310,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(forward_demodulation,[status(thm)],[f31,f303]) ).
fof(f311,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f310]) ).
fof(f314,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f31,f305]) ).
fof(f315,plain,
! [X0] : X0 = join(complement(top),meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f306]) ).
fof(f316,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f314,f315]) ).
fof(f357,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f259]) ).
fof(f362,plain,
! [X0] : join(complement(X0),composition(one,complement(X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f259,f55]) ).
fof(f365,plain,
! [X0,X1] : join(meet(X0,X1),composition(converse(converse(one)),complement(join(complement(X0),complement(X1))))) = meet(X0,X1),
inference(paramodulation,[status(thm)],[f259,f57]) ).
fof(f369,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,composition(converse(converse(one)),complement(X0)))),
inference(paramodulation,[status(thm)],[f259,f210]) ).
fof(f372,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f357,f259]) ).
fof(f374,plain,
! [X0,X1] : join(meet(X0,X1),composition(one,complement(join(complement(X0),complement(X1))))) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f26,f365]) ).
fof(f375,plain,
! [X0,X1] : join(meet(X0,X1),composition(one,meet(X0,X1))) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f22,f374]) ).
fof(f380,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,composition(one,complement(X0)))),
inference(forward_demodulation,[status(thm)],[f26,f369]) ).
fof(f384,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = meet(X0,X1),
inference(backward_demodulation,[status(thm)],[f372,f375]) ).
fof(f386,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
inference(backward_demodulation,[status(thm)],[f372,f380]) ).
fof(f387,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f372,f362]) ).
fof(f391,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f31,f386]) ).
fof(f392,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f391]) ).
fof(f462,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f290,f208]) ).
fof(f492,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f387,f22]) ).
fof(f542,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)],[f48,f316]) ).
fof(f545,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)],[f22,f542]) ).
fof(f552,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f290,f462]) ).
fof(f554,plain,
! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
inference(paramodulation,[status(thm)],[f31,f462]) ).
fof(f556,plain,
! [X0] : complement(X0) = join(meet(complement(X0),X0),complement(complement(complement(X0)))),
inference(paramodulation,[status(thm)],[f492,f462]) ).
fof(f569,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f19,f554]) ).
fof(f570,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f290,f569]) ).
fof(f573,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f584,f392]) ).
fof(f575,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(join(meet(X0,X1),meet(X0,X1)))),
inference(backward_demodulation,[status(thm)],[f584,f545]) ).
fof(f584,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f316,f570]) ).
fof(f586,plain,
! [X0] : complement(X0) = join(complement(complement(complement(X0))),meet(complement(X0),X0)),
inference(forward_demodulation,[status(thm)],[f19,f556]) ).
fof(f587,plain,
! [X0] : complement(X0) = join(complement(X0),meet(complement(X0),X0)),
inference(forward_demodulation,[status(thm)],[f584,f586]) ).
fof(f588,plain,
! [X0] : complement(X0) = join(complement(X0),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f290,f587]) ).
fof(f589,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(forward_demodulation,[status(thm)],[f31,f588]) ).
fof(f597,plain,
! [X0] : meet(X0,top) = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f598,f311]) ).
fof(f598,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[status(thm)],[f19,f589]) ).
fof(f609,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(join(meet(X0,X1),meet(X0,X1))),
inference(forward_demodulation,[status(thm)],[f598,f575]) ).
fof(f625,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f384,f609]) ).
fof(f636,plain,
! [X0] : meet(X0,top) = X0,
inference(forward_demodulation,[status(thm)],[f584,f597]) ).
fof(f743,plain,
! [X0] : meet(top,X0) = X0,
inference(paramodulation,[status(thm)],[f290,f636]) ).
fof(f969,plain,
! [X0] : X0 = join(meet(X0,converse(complement(converse(complement(X0))))),complement(converse(top))),
inference(paramodulation,[status(thm)],[f301,f46]) ).
fof(f984,plain,
! [X0] : X0 = join(complement(converse(top)),meet(X0,converse(complement(converse(complement(X0)))))),
inference(forward_demodulation,[status(thm)],[f19,f969]) ).
fof(f986,plain,
! [X0] : join(X0,meet(top,X0)) = meet(top,X0),
inference(paramodulation,[status(thm)],[f743,f384]) ).
fof(f999,plain,
! [X0] : join(X0,X0) = meet(top,X0),
inference(forward_demodulation,[status(thm)],[f743,f986]) ).
fof(f1002,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f743,f999]) ).
fof(f1031,plain,
! [X0,X1] : join(X0,join(X0,X1)) = join(X0,X1),
inference(paramodulation,[status(thm)],[f1002,f20]) ).
fof(f1046,plain,
! [X0,X1] : join(meet(X0,X1),X1) = join(meet(X0,X1),meet(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f552,f1031]) ).
fof(f1059,plain,
! [X0] : join(X0,top) = join(X0,complement(X0)),
inference(paramodulation,[status(thm)],[f30,f1031]) ).
fof(f1074,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = join(meet(X1,X0),meet(complement(X1),X0)),
inference(forward_demodulation,[status(thm)],[f19,f1046]) ).
fof(f1076,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f552,f1074]) ).
fof(f1103,plain,
! [X0] : join(X0,top) = top,
inference(forward_demodulation,[status(thm)],[f30,f1059]) ).
fof(f1115,plain,
! [X0] : join(top,X0) = top,
inference(paramodulation,[status(thm)],[f19,f1103]) ).
fof(f1293,plain,
converse(top) = top,
inference(paramodulation,[status(thm)],[f301,f1115]) ).
fof(f1317,plain,
! [X0] : X0 = join(complement(top),meet(X0,converse(complement(converse(complement(X0)))))),
inference(backward_demodulation,[status(thm)],[f1293,f984]) ).
fof(f1337,plain,
! [X0] : X0 = join(zero,meet(X0,converse(complement(converse(complement(X0)))))),
inference(forward_demodulation,[status(thm)],[f314,f1317]) ).
fof(f1338,plain,
! [X0] : X0 = meet(X0,converse(complement(converse(complement(X0))))),
inference(forward_demodulation,[status(thm)],[f573,f1337]) ).
fof(f1574,plain,
! [X0] : join(converse(complement(converse(complement(X0)))),X0) = converse(complement(converse(complement(X0)))),
inference(paramodulation,[status(thm)],[f1338,f1076]) ).
fof(f1597,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = converse(complement(converse(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f1574]) ).
fof(f1604,plain,
! [X0,X1] : join(X0,complement(X1)) = complement(meet(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f584,f625]) ).
fof(f2200,plain,
! [X0] : join(X0,complement(converse(complement(converse(complement(complement(X0))))))) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f1338,f1604]) ).
fof(f2226,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = complement(complement(X0)),
inference(forward_demodulation,[status(thm)],[f584,f2200]) ).
fof(f2227,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = X0,
inference(forward_demodulation,[status(thm)],[f584,f2226]) ).
fof(f2274,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(complement(converse(complement(converse(converse(X0))))))),
inference(paramodulation,[status(thm)],[f2227,f50]) ).
fof(f2297,plain,
! [X0] : X0 = join(X0,converse(complement(converse(complement(converse(converse(X0))))))),
inference(forward_demodulation,[status(thm)],[f26,f2274]) ).
fof(f2298,plain,
! [X0] : X0 = join(X0,converse(complement(converse(complement(X0))))),
inference(forward_demodulation,[status(thm)],[f26,f2297]) ).
fof(f2302,plain,
! [X0] : X0 = converse(complement(converse(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f1597,f2298]) ).
fof(f2701,plain,
! [X0] : complement(X0) = converse(complement(converse(X0))),
inference(paramodulation,[status(thm)],[f584,f2302]) ).
fof(f2983,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(paramodulation,[status(thm)],[f26,f2701]) ).
fof(f3007,plain,
complement(converse(sK0_skl)) != complement(converse(sK0_skl)),
inference(backward_demodulation,[status(thm)],[f2983,f37]) ).
fof(f3024,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3007]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL004+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 03:57:06 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 5.62/1.13 % Refutation found
% 5.62/1.13 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.62/1.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.62/1.20 % Elapsed time: 0.823275 seconds
% 5.62/1.20 % CPU time: 6.280871 seconds
% 5.62/1.20 % Total memory used: 125.066 MB
% 5.62/1.20 % Net memory used: 120.030 MB
%------------------------------------------------------------------------------