%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL024+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 02:03:19 PM UTC 2026
% Result : Theorem 12.08s 7.11s
% Output : CNFRefutation 12.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 13
% 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 : 5 ( 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 : 141 ( 138 !; 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(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,conjecture,
! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(meet(X0,converse(X1)),X2)) = composition(meet(X0,converse(X1)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(meet(X0,converse(X1)),X2)) = composition(meet(X0,converse(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(f24,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(thm)],[f9]) ).
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(meet(X0,converse(X1)),X2)) != composition(meet(X0,converse(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(meet(sK0_skl,converse(sK1_skl)),sK2_skl)) != composition(meet(sK0_skl,converse(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(meet(sK0_skl,converse(sK1_skl)),sK2_skl)) != composition(meet(sK0_skl,converse(sK1_skl)),sK2_skl),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f42,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f16,f18]) ).
fof(f43,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f19,f42]) ).
fof(f44,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f16,f26]) ).
fof(f45,plain,
join(composition(meet(sK0_skl,converse(sK1_skl)),sK2_skl),composition(meet(sK0_skl,converse(sK1_skl)),meet(sK1_skl,sK2_skl))) != composition(meet(sK0_skl,converse(sK1_skl)),sK2_skl),
inference(forward_demodulation,[status(thm)],[f16,f31]) ).
fof(f46,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f16,f43]) ).
fof(f55,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f16,f19]) ).
fof(f59,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f19,f55]) ).
fof(f68,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f74,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(forward_demodulation,[status(thm)],[f17,f68]) ).
fof(f76,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f77,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f93,plain,
! [X0,X1,X2] : converse(join(composition(converse(X0),X1),X2)) = join(composition(converse(X1),X0),converse(X2)),
inference(paramodulation,[status(thm)],[f77,f24]) ).
fof(f94,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f23,f24]) ).
fof(f217,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f46]) ).
fof(f222,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f16,f217]) ).
fof(f224,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f59,f222]) ).
fof(f234,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f59,f224]) ).
fof(f307,plain,
! [X0,X1,X2] : composition(join(X0,converse(X1)),converse(X2)) = join(composition(X0,converse(X2)),converse(composition(X2,X1))),
inference(paramodulation,[status(thm)],[f25,f22]) ).
fof(f340,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f21,f77]) ).
fof(f346,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f23,f340]) ).
fof(f350,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f21,f346]) ).
fof(f351,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f346,f44]) ).
fof(f360,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f350,f346]) ).
fof(f368,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f360,f351]) ).
fof(f404,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f27,f19]) ).
fof(f405,plain,
! [X0] : X0 = join(meet(X0,complement(complement(X0))),complement(top)),
inference(paramodulation,[status(thm)],[f27,f46]) ).
fof(f408,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f28,f404]) ).
fof(f409,plain,
! [X0] : X0 = join(complement(top),meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f16,f405]) ).
fof(f410,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f408,f409]) ).
fof(f426,plain,
! [X0] : complement(complement(X0)) = join(meet(X0,complement(complement(X0))),zero),
inference(paramodulation,[status(thm)],[f28,f234]) ).
fof(f436,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f16,f426]) ).
fof(f439,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f410,f436]) ).
fof(f449,plain,
! [X0,X1] : complement(meet(X0,X1)) = join(complement(X0),complement(X1)),
inference(paramodulation,[status(thm)],[f19,f439]) ).
fof(f462,plain,
! [X0] : complement(meet(X0,X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f449,f368]) ).
fof(f512,plain,
! [X0] : complement(complement(X0)) = meet(X0,X0),
inference(paramodulation,[status(thm)],[f462,f439]) ).
fof(f523,plain,
! [X0] : X0 = meet(X0,X0),
inference(forward_demodulation,[status(thm)],[f439,f512]) ).
fof(f1452,plain,
! [X0,X1] : complement(meet(complement(X0),X1)) = join(X0,complement(X1)),
inference(paramodulation,[status(thm)],[f439,f449]) ).
fof(f3116,plain,
! [X0] : complement(complement(X0)) = join(X0,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f523,f1452]) ).
fof(f3155,plain,
! [X0] : X0 = join(X0,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f439,f3116]) ).
fof(f3167,plain,
! [X0] : X0 = join(X0,X0),
inference(forward_demodulation,[status(thm)],[f439,f3155]) ).
fof(f3374,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X1,X0),
inference(paramodulation,[status(thm)],[f3167,f74]) ).
fof(f4047,plain,
! [X0,X1] : join(meet(complement(X0),X1),X1) = join(meet(X0,X1),meet(complement(X0),X1)),
inference(paramodulation,[status(thm)],[f234,f3374]) ).
fof(f4107,plain,
! [X0,X1] : join(X0,meet(complement(X1),X0)) = join(meet(X1,X0),meet(complement(X1),X0)),
inference(forward_demodulation,[status(thm)],[f16,f4047]) ).
fof(f4108,plain,
! [X0,X1] : join(X0,meet(complement(X1),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f234,f4107]) ).
fof(f4190,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f439,f4108]) ).
fof(f8928,plain,
! [X0,X1,X2] : converse(composition(join(converse(X0),converse(X1)),converse(X2))) = join(composition(converse(converse(X2)),X0),converse(converse(composition(X2,X1)))),
inference(paramodulation,[status(thm)],[f307,f93]) ).
fof(f9014,plain,
! [X0,X1,X2] : composition(X0,converse(join(converse(X1),converse(X2)))) = join(composition(converse(converse(X0)),X1),converse(converse(composition(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f76,f8928]) ).
fof(f9015,plain,
! [X0,X1,X2] : composition(X0,join(X1,converse(converse(X2)))) = join(composition(converse(converse(X0)),X1),converse(converse(composition(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f94,f9014]) ).
fof(f9016,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(converse(converse(X0)),X1),converse(converse(composition(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f23,f9015]) ).
fof(f9017,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),converse(converse(composition(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f23,f9016]) ).
fof(f9018,plain,
composition(meet(sK0_skl,converse(sK1_skl)),join(sK2_skl,meet(sK1_skl,sK2_skl))) != composition(meet(sK0_skl,converse(sK1_skl)),sK2_skl),
inference(backward_demodulation,[status(thm)],[f9022,f45]) ).
fof(f9022,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f23,f9017]) ).
fof(f9127,plain,
composition(meet(sK0_skl,converse(sK1_skl)),sK2_skl) != composition(meet(sK0_skl,converse(sK1_skl)),sK2_skl),
inference(forward_demodulation,[status(thm)],[f4190,f9018]) ).
fof(f9128,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f9127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL024+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n008.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Mon Sep 21 04:02:15 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.45 % Drodi V4.1.1
% 12.08/7.11 % Refutation found
% 12.08/7.11 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.08/7.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.08/7.15 % Elapsed time: 1.697462 seconds
% 12.08/7.15 % CPU time: 13.135011 seconds
% 12.08/7.15 % Total memory used: 124.952 MB
% 12.08/7.15 % Net memory used: 121.993 MB
%------------------------------------------------------------------------------