%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL010+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 : n012.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 02:03:14 PM UTC 2026
% Result : Theorem 6.04s 1.23s
% Output : CNFRefutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 15
% Syntax : Number of formulae : 109 ( 105 unt; 0 def)
% Number of atoms : 113 ( 112 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 153 ( 150 !; 3 ?)
% 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,X1,X2] :
( meet(composition(X0,X1),X2) = zero
=> meet(X1,composition(converse(X0),X2)) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( meet(composition(X0,X1),X2) = zero
=> meet(X1,composition(converse(X0),X2)) = zero ),
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,X1,X2] :
( meet(X1,composition(converse(X0),X2)) != zero
& meet(composition(X0,X1),X2) = zero ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f36,plain,
( meet(sK1_skl,composition(converse(sK0_skl),sK2_skl)) != zero
& meet(composition(sK0_skl,sK1_skl),sK2_skl) = zero ),
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)],[f35]) ).
fof(f37,plain,
meet(composition(sK0_skl,sK1_skl),sK2_skl) = zero,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
meet(sK1_skl,composition(converse(sK0_skl),sK2_skl)) != zero,
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(f52,plain,
! [X0,X1] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f53,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f54,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f110,plain,
! [X0,X1,X2] : converse(composition(X0,composition(X1,converse(X2)))) = composition(X2,converse(composition(X0,X1))),
inference(paramodulation,[status(thm)],[f23,f53]) ).
fof(f624,plain,
! [X0,X1,X2] : join(meet(composition(converse(X0),X1),X2),composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2)))) = composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(converse(converse(X0)),X2))),
inference(paramodulation,[status(thm)],[f26,f32]) ).
fof(f682,plain,
! [X0,X1,X2] : join(meet(composition(converse(X0),X1),X2),composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2)))) = composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f26,f624]) ).
fof(f759,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f54]) ).
fof(f768,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f759]) ).
fof(f776,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f768]) ).
fof(f796,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f776,f768]) ).
fof(f898,plain,
! [X0] : converse(join(X0,one)) = join(converse(X0),one),
inference(paramodulation,[status(thm)],[f776,f52]) ).
fof(f932,plain,
! [X0] : converse(join(X0,one)) = join(one,converse(X0)),
inference(forward_demodulation,[status(thm)],[f19,f898]) ).
fof(f1088,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f30,f22]) ).
fof(f1089,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f1095,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f31,f1088]) ).
fof(f1096,plain,
meet(sK2_skl,composition(sK0_skl,sK1_skl)) = zero,
inference(backward_demodulation,[status(thm)],[f1120,f37]) ).
fof(f1120,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f1089]) ).
fof(f1146,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(paramodulation,[status(thm)],[f1095,f22]) ).
fof(f1150,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f1146]) ).
fof(f1169,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f30,f20]) ).
fof(f1310,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f30,f1169]) ).
fof(f1334,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f796,f25]) ).
fof(f1339,plain,
! [X0,X1] : composition(join(X0,one),X1) = join(composition(X0,X1),X1),
inference(paramodulation,[status(thm)],[f796,f25]) ).
fof(f1354,plain,
! [X0,X1] : composition(join(X0,one),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f1339]) ).
fof(f1366,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(paramodulation,[status(thm)],[f1095,f45]) ).
fof(f1369,plain,
! [X0] : join(complement(X0),composition(one,complement(composition(one,X0)))) = complement(X0),
inference(paramodulation,[status(thm)],[f776,f45]) ).
fof(f1390,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f1095,f1366]) ).
fof(f1393,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f796,f1369]) ).
fof(f1394,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f796,f1393]) ).
fof(f1496,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f1394,f22]) ).
fof(f1497,plain,
! [X0] : X0 = join(meet(X0,complement(X0)),complement(complement(X0))),
inference(paramodulation,[status(thm)],[f1394,f46]) ).
fof(f1498,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f1394,f1169]) ).
fof(f1518,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f1497]) ).
fof(f1519,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f31,f1518]) ).
fof(f1520,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f1519]) ).
fof(f1523,plain,
! [X0] : join(X0,top) = top,
inference(backward_demodulation,[status(thm)],[f1525,f1310]) ).
fof(f1525,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f30,f1498]) ).
fof(f1538,plain,
! [X0] : join(top,X0) = top,
inference(paramodulation,[status(thm)],[f19,f1523]) ).
fof(f1542,plain,
! [X0] : X0 = join(meet(X0,top),complement(top)),
inference(paramodulation,[status(thm)],[f1523,f46]) ).
fof(f1571,plain,
! [X0] : X0 = join(complement(top),meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f19,f1542]) ).
fof(f1573,plain,
! [X0] : X0 = join(zero,meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f1095,f1571]) ).
fof(f1624,plain,
! [X0] : meet(complement(X0),top) = complement(X0),
inference(paramodulation,[status(thm)],[f1520,f1150]) ).
fof(f1628,plain,
! [X0] : meet(top,complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f1120,f1624]) ).
fof(f1645,plain,
! [X0] : X0 = join(zero,meet(top,X0)),
inference(paramodulation,[status(thm)],[f1120,f1573]) ).
fof(f1697,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(paramodulation,[status(thm)],[f1628,f1645]) ).
fof(f1708,plain,
! [X0] : X0 = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1697,f1520]) ).
fof(f1710,plain,
! [X0] : meet(X0,top) = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1697,f1150]) ).
fof(f1728,plain,
! [X0] : meet(X0,X0) = X0,
inference(backward_demodulation,[status(thm)],[f1708,f1496]) ).
fof(f1742,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f1745,f1573]) ).
fof(f1745,plain,
! [X0] : meet(X0,top) = X0,
inference(forward_demodulation,[status(thm)],[f1708,f1710]) ).
fof(f1793,plain,
! [X0] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(backward_demodulation,[status(thm)],[f1742,f1390]) ).
fof(f1816,plain,
! [X0] : X0 = join(X0,complement(join(complement(X0),X0))),
inference(paramodulation,[status(thm)],[f1728,f46]) ).
fof(f1832,plain,
! [X0] : X0 = join(X0,complement(join(X0,complement(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f1816]) ).
fof(f1833,plain,
! [X0] : X0 = join(X0,complement(top)),
inference(forward_demodulation,[status(thm)],[f30,f1832]) ).
fof(f1834,plain,
! [X0] : X0 = join(X0,zero),
inference(forward_demodulation,[status(thm)],[f1095,f1833]) ).
fof(f4219,plain,
! [X0] : composition(join(one,converse(X0)),complement(composition(join(X0,one),top))) = zero,
inference(paramodulation,[status(thm)],[f932,f1793]) ).
fof(f4266,plain,
! [X0] : composition(join(one,converse(X0)),complement(join(top,composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f1354,f4219]) ).
fof(f4267,plain,
! [X0] : composition(join(one,converse(X0)),complement(top)) = zero,
inference(forward_demodulation,[status(thm)],[f1538,f4266]) ).
fof(f4268,plain,
! [X0] : composition(join(one,converse(X0)),zero) = zero,
inference(forward_demodulation,[status(thm)],[f1095,f4267]) ).
fof(f4269,plain,
! [X0] : join(zero,composition(converse(X0),zero)) = zero,
inference(forward_demodulation,[status(thm)],[f1334,f4268]) ).
fof(f4272,plain,
! [X0] : composition(converse(X0),zero) = zero,
inference(forward_demodulation,[status(thm)],[f1742,f4269]) ).
fof(f4377,plain,
! [X0,X1,X2] : composition(composition(X0,converse(composition(X1,X2))),zero) = zero,
inference(paramodulation,[status(thm)],[f110,f4272]) ).
fof(f4418,plain,
! [X0,X1,X2] : composition(X0,composition(converse(composition(X1,X2)),zero)) = zero,
inference(forward_demodulation,[status(thm)],[f23,f4377]) ).
fof(f4448,plain,
! [X0] : composition(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f4272,f4418]) ).
fof(f5236,plain,
join(meet(composition(converse(sK0_skl),sK2_skl),sK1_skl),composition(meet(converse(sK0_skl),composition(sK1_skl,converse(sK2_skl))),zero)) = composition(meet(converse(sK0_skl),composition(sK1_skl,converse(sK2_skl))),meet(sK2_skl,composition(sK0_skl,sK1_skl))),
inference(paramodulation,[status(thm)],[f1096,f682]) ).
fof(f5439,plain,
join(meet(sK1_skl,composition(converse(sK0_skl),sK2_skl)),composition(meet(converse(sK0_skl),composition(sK1_skl,converse(sK2_skl))),zero)) = composition(meet(converse(sK0_skl),composition(sK1_skl,converse(sK2_skl))),meet(sK2_skl,composition(sK0_skl,sK1_skl))),
inference(forward_demodulation,[status(thm)],[f1120,f5236]) ).
fof(f5440,plain,
join(meet(sK1_skl,composition(converse(sK0_skl),sK2_skl)),zero) = composition(meet(converse(sK0_skl),composition(sK1_skl,converse(sK2_skl))),meet(sK2_skl,composition(sK0_skl,sK1_skl))),
inference(forward_demodulation,[status(thm)],[f4448,f5439]) ).
fof(f5441,plain,
meet(sK1_skl,composition(converse(sK0_skl),sK2_skl)) = composition(meet(converse(sK0_skl),composition(sK1_skl,converse(sK2_skl))),meet(sK2_skl,composition(sK0_skl,sK1_skl))),
inference(forward_demodulation,[status(thm)],[f1834,f5440]) ).
fof(f5442,plain,
meet(sK1_skl,composition(converse(sK0_skl),sK2_skl)) = composition(meet(converse(sK0_skl),composition(sK1_skl,converse(sK2_skl))),zero),
inference(forward_demodulation,[status(thm)],[f1096,f5441]) ).
fof(f5443,plain,
meet(sK1_skl,composition(converse(sK0_skl),sK2_skl)) = zero,
inference(forward_demodulation,[status(thm)],[f4448,f5442]) ).
fof(f5444,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5443,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : REL010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 03:57:51 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Drodi V4.1.1
% 6.04/1.23 % Refutation found
% 6.04/1.23 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.04/1.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.21/1.29 % Elapsed time: 0.980729 seconds
% 4.21/1.29 % CPU time: 7.565026 seconds
% 4.21/1.29 % Total memory used: 181.846 MB
% 4.21/1.29 % Net memory used: 176.695 MB
%------------------------------------------------------------------------------