%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL012-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:03:15 PM UTC 2026
% Result : Unsatisfiable 8.80s 1.57s
% Output : CNFRefutation 8.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% 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 : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 163 ( 163 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : join(A,B) = join(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : join(A,join(B,C)) = join(join(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : meet(A,B) = complement(join(complement(A),complement(B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : composition(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : converse(converse(A)) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : converse(join(A,B)) = join(converse(A),converse(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : converse(composition(A,B)) = composition(converse(B),converse(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] : join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : top = join(A,complement(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : zero = meet(A,complement(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) != complement(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f28,plain,
join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) != complement(sk1),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f36,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f15,f17]) ).
fof(f37,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f18,f36]) ).
fof(f38,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f15,f25]) ).
fof(f39,plain,
join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))) != complement(sk1),
inference(forward_demodulation,[status(thm)],[f15,f28]) ).
fof(f40,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f15,f37]) ).
fof(f46,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f16]) ).
fof(f73,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f74,plain,
! [X0,X1] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f82,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f22,f24]) ).
fof(f83,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f22,f24]) ).
fof(f109,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X1,X0)),
inference(paramodulation,[status(thm)],[f15,f46]) ).
fof(f339,plain,
! [X0,X1,X2] : converse(join(X0,composition(X1,converse(X2)))) = join(converse(X0),composition(X2,converse(X1))),
inference(paramodulation,[status(thm)],[f82,f74]) ).
fof(f499,plain,
! [X0,X1] : join(complement(converse(X0)),composition(converse(converse(X1)),complement(converse(composition(X0,X1))))) = complement(converse(X0)),
inference(paramodulation,[status(thm)],[f24,f38]) ).
fof(f512,plain,
! [X0,X1] : join(complement(converse(X0)),composition(X1,complement(converse(composition(X0,X1))))) = complement(converse(X0)),
inference(forward_demodulation,[status(thm)],[f22,f499]) ).
fof(f543,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f20,f83]) ).
fof(f553,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f22,f543]) ).
fof(f557,plain,
! [X0] : converse(top) = join(X0,converse(complement(converse(X0)))),
inference(paramodulation,[status(thm)],[f26,f73]) ).
fof(f559,plain,
! [X0] : X0 = join(meet(X0,complement(complement(X0))),complement(top)),
inference(paramodulation,[status(thm)],[f26,f40]) ).
fof(f567,plain,
! [X0] : X0 = join(complement(top),meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f15,f559]) ).
fof(f572,plain,
! [X0] : X0 = join(zero,complement(join(complement(X0),complement(X0)))),
inference(paramodulation,[status(thm)],[f27,f40]) ).
fof(f573,plain,
! [X0] : X0 = join(zero,meet(X0,X0)),
inference(forward_demodulation,[status(thm)],[f18,f572]) ).
fof(f575,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f20,f553]) ).
fof(f576,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f553,f38]) ).
fof(f585,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f575,f553]) ).
fof(f594,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f585,f576]) ).
fof(f641,plain,
! [X0] : X0 = join(meet(X0,complement(X0)),complement(complement(X0))),
inference(paramodulation,[status(thm)],[f594,f40]) ).
fof(f649,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f15,f641]) ).
fof(f650,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f27,f649]) ).
fof(f651,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f15,f650]) ).
fof(f664,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f594,f18]) ).
fof(f665,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f26,f18]) ).
fof(f666,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f15,f18]) ).
fof(f670,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f40]) ).
fof(f671,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(meet(X0,X1))),
inference(paramodulation,[status(thm)],[f18,f651]) ).
fof(f678,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(backward_demodulation,[status(thm)],[f679,f567]) ).
fof(f679,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f27,f665]) ).
fof(f680,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f18,f666]) ).
fof(f682,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f15,f670]) ).
fof(f744,plain,
! [X0] : join(meet(X0,X0),complement(complement(X0))) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f664,f594]) ).
fof(f745,plain,
! [X0] : zero = meet(complement(X0),meet(X0,X0)),
inference(paramodulation,[status(thm)],[f664,f27]) ).
fof(f746,plain,
! [X0] : top = join(complement(X0),meet(X0,X0)),
inference(paramodulation,[status(thm)],[f664,f26]) ).
fof(f1004,plain,
! [X0] : X0 = join(meet(X0,meet(X0,X0)),complement(top)),
inference(paramodulation,[status(thm)],[f746,f40]) ).
fof(f1015,plain,
! [X0] : X0 = join(complement(top),meet(X0,meet(X0,X0))),
inference(forward_demodulation,[status(thm)],[f15,f1004]) ).
fof(f1016,plain,
! [X0] : X0 = join(zero,meet(X0,meet(X0,X0))),
inference(forward_demodulation,[status(thm)],[f679,f1015]) ).
fof(f1036,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f680,f682]) ).
fof(f1040,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f680,f682]) ).
fof(f1234,plain,
! [X0] : meet(X0,X0) = join(meet(meet(X0,X0),X0),zero),
inference(paramodulation,[status(thm)],[f745,f1040]) ).
fof(f1235,plain,
! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
inference(paramodulation,[status(thm)],[f27,f1040]) ).
fof(f1255,plain,
! [X0] : meet(X0,X0) = join(zero,meet(meet(X0,X0),X0)),
inference(forward_demodulation,[status(thm)],[f15,f1234]) ).
fof(f1256,plain,
! [X0] : meet(X0,X0) = join(zero,meet(X0,meet(X0,X0))),
inference(forward_demodulation,[status(thm)],[f680,f1255]) ).
fof(f1261,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f1279,f573]) ).
fof(f1275,plain,
! [X0] : join(X0,complement(complement(X0))) = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1279,f744]) ).
fof(f1279,plain,
! [X0] : meet(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f1016,f1256]) ).
fof(f1280,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f15,f1235]) ).
fof(f1281,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f680,f1280]) ).
fof(f1289,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f678,f1281]) ).
fof(f1305,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f1261,f671]) ).
fof(f1319,plain,
! [X0] : join(X0,X0) = complement(complement(X0)),
inference(forward_demodulation,[status(thm)],[f1289,f1275]) ).
fof(f1324,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f1289,f1319]) ).
fof(f1403,plain,
! [X0,X1] : join(X0,join(X0,X1)) = join(X1,X0),
inference(paramodulation,[status(thm)],[f1324,f109]) ).
fof(f1902,plain,
! [X0,X1] : join(meet(X0,X1),X1) = join(meet(X1,complement(X0)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f1036,f1403]) ).
fof(f1914,plain,
! [X0] : join(X0,top) = join(complement(X0),X0),
inference(paramodulation,[status(thm)],[f26,f1403]) ).
fof(f1954,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = join(meet(X0,complement(X1)),meet(X1,X0)),
inference(forward_demodulation,[status(thm)],[f15,f1902]) ).
fof(f1955,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = join(meet(X1,X0),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f15,f1954]) ).
fof(f1957,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f1036,f1955]) ).
fof(f1986,plain,
! [X0] : join(X0,top) = join(X0,complement(X0)),
inference(forward_demodulation,[status(thm)],[f15,f1914]) ).
fof(f1989,plain,
! [X0] : join(X0,top) = top,
inference(forward_demodulation,[status(thm)],[f26,f1986]) ).
fof(f2035,plain,
! [X0] : join(top,X0) = top,
inference(paramodulation,[status(thm)],[f15,f1989]) ).
fof(f2198,plain,
! [X0,X1] : converse(converse(X0)) = join(X0,converse(meet(X1,converse(X0)))),
inference(paramodulation,[status(thm)],[f1957,f73]) ).
fof(f2212,plain,
! [X0,X1] : X0 = join(X0,converse(meet(X1,converse(X0)))),
inference(forward_demodulation,[status(thm)],[f22,f2198]) ).
fof(f2982,plain,
converse(top) = top,
inference(paramodulation,[status(thm)],[f2035,f557]) ).
fof(f3003,plain,
! [X0] : X0 = join(meet(X0,converse(complement(converse(complement(X0))))),complement(converse(top))),
inference(paramodulation,[status(thm)],[f557,f40]) ).
fof(f3070,plain,
! [X0] : X0 = join(complement(converse(top)),meet(X0,converse(complement(converse(complement(X0)))))),
inference(forward_demodulation,[status(thm)],[f15,f3003]) ).
fof(f3071,plain,
! [X0] : X0 = join(complement(top),meet(X0,converse(complement(converse(complement(X0)))))),
inference(forward_demodulation,[status(thm)],[f2982,f3070]) ).
fof(f3072,plain,
! [X0] : X0 = join(zero,meet(X0,converse(complement(converse(complement(X0)))))),
inference(forward_demodulation,[status(thm)],[f679,f3071]) ).
fof(f3073,plain,
! [X0] : X0 = meet(X0,converse(complement(converse(complement(X0))))),
inference(forward_demodulation,[status(thm)],[f1261,f3072]) ).
fof(f3348,plain,
! [X0] : complement(converse(complement(X0))) = join(complement(converse(complement(X0))),converse(X0)),
inference(paramodulation,[status(thm)],[f3073,f2212]) ).
fof(f3373,plain,
! [X0] : complement(converse(complement(X0))) = join(converse(X0),complement(converse(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f15,f3348]) ).
fof(f3383,plain,
! [X0,X1] : join(X0,complement(X1)) = complement(meet(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f1289,f1305]) ).
fof(f3789,plain,
! [X0] : join(X0,complement(converse(complement(converse(complement(complement(X0))))))) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f3073,f3383]) ).
fof(f3822,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = complement(complement(X0)),
inference(forward_demodulation,[status(thm)],[f1289,f3789]) ).
fof(f3823,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = X0,
inference(forward_demodulation,[status(thm)],[f1289,f3822]) ).
fof(f3887,plain,
! [X0] : join(converse(X0),complement(converse(complement(X0)))) = converse(X0),
inference(paramodulation,[status(thm)],[f22,f3823]) ).
fof(f3930,plain,
! [X0] : complement(converse(complement(X0))) = converse(X0),
inference(forward_demodulation,[status(thm)],[f3373,f3887]) ).
fof(f4006,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(paramodulation,[status(thm)],[f1289,f3930]) ).
fof(f4031,plain,
! [X0,X1] : join(complement(converse(X0)),composition(X1,converse(complement(composition(X0,X1))))) = complement(converse(X0)),
inference(backward_demodulation,[status(thm)],[f4006,f512]) ).
fof(f4078,plain,
! [X0,X1] : join(converse(complement(X0)),composition(X1,converse(complement(composition(X0,X1))))) = complement(converse(X0)),
inference(forward_demodulation,[status(thm)],[f4006,f4031]) ).
fof(f4079,plain,
! [X0,X1] : converse(join(complement(X0),composition(complement(composition(X0,X1)),converse(X1)))) = complement(converse(X0)),
inference(forward_demodulation,[status(thm)],[f339,f4078]) ).
fof(f4080,plain,
! [X0,X1] : converse(join(complement(X0),composition(complement(composition(X0,X1)),converse(X1)))) = converse(complement(X0)),
inference(forward_demodulation,[status(thm)],[f4006,f4079]) ).
fof(f7233,plain,
! [X0,X1] : converse(converse(complement(X0))) = join(complement(X0),composition(complement(composition(X0,X1)),converse(X1))),
inference(paramodulation,[status(thm)],[f4080,f22]) ).
fof(f7304,plain,
complement(sk1) != complement(sk1),
inference(backward_demodulation,[status(thm)],[f7315,f39]) ).
fof(f7315,plain,
! [X0,X1] : complement(X0) = join(complement(X0),composition(complement(composition(X0,X1)),converse(X1))),
inference(forward_demodulation,[status(thm)],[f22,f7233]) ).
fof(f7317,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f7304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL012-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.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 03:58:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 8.80/1.57 % Refutation found
% 8.80/1.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.80/1.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.39/1.62 % Elapsed time: 1.250264 seconds
% 0.39/1.62 % CPU time: 9.633879 seconds
% 0.39/1.62 % Total memory used: 116.060 MB
% 0.39/1.62 % Net memory used: 113.489 MB
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