%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL023+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 02:03:19 PM UTC 2026
% Result : Theorem 0.06s 0.70s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 46 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 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 : 73 ( 70 !; 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(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(f17,conjecture,
! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
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(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(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(f35,plain,
? [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) != composition(X0,meet(X1,X2)),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f36,plain,
join(composition(meet(sK0_skl,converse(sK1_skl)),meet(sK1_skl,sK2_skl)),composition(sK0_skl,meet(sK1_skl,sK2_skl))) != composition(sK0_skl,meet(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)],[f35]) ).
fof(f37,plain,
join(composition(meet(sK0_skl,converse(sK1_skl)),meet(sK1_skl,sK2_skl)),composition(sK0_skl,meet(sK1_skl,sK2_skl))) != composition(sK0_skl,meet(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f46,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f19,f21]) ).
fof(f47,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f22,f46]) ).
fof(f48,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f19,f29]) ).
fof(f49,plain,
composition(join(meet(sK0_skl,converse(sK1_skl)),sK0_skl),meet(sK1_skl,sK2_skl)) != composition(sK0_skl,meet(sK1_skl,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f25,f37]) ).
fof(f50,plain,
composition(join(sK0_skl,meet(sK0_skl,converse(sK1_skl))),meet(sK1_skl,sK2_skl)) != composition(sK0_skl,meet(sK1_skl,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f19,f49]) ).
fof(f51,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f47]) ).
fof(f72,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f212,plain,
! [X0,X1,X2] : join(meet(X0,X1),join(complement(join(complement(X0),X1)),X2)) = join(X0,X2),
inference(paramodulation,[status(thm)],[f51,f20]) ).
fof(f261,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f72]) ).
fof(f267,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f261]) ).
fof(f275,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f267]) ).
fof(f276,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f267,f48]) ).
fof(f285,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f275,f267]) ).
fof(f294,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f285,f276]) ).
fof(f353,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f371,plain,
composition(join(sK0_skl,meet(sK0_skl,converse(sK1_skl))),meet(sK1_skl,sK2_skl)) != composition(sK0_skl,meet(sK2_skl,sK1_skl)),
inference(backward_demodulation,[status(thm)],[f377,f50]) ).
fof(f377,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f353]) ).
fof(f391,plain,
composition(join(sK0_skl,meet(sK0_skl,converse(sK1_skl))),meet(sK2_skl,sK1_skl)) != composition(sK0_skl,meet(sK2_skl,sK1_skl)),
inference(forward_demodulation,[status(thm)],[f377,f371]) ).
fof(f1434,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X0),X1))),
inference(paramodulation,[status(thm)],[f294,f212]) ).
fof(f1480,plain,
! [X0,X1] : X0 = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f51,f1434]) ).
fof(f1595,plain,
! [X0,X1] : X0 = join(X0,meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f1480]) ).
fof(f1624,plain,
composition(sK0_skl,meet(sK2_skl,sK1_skl)) != composition(sK0_skl,meet(sK2_skl,sK1_skl)),
inference(backward_demodulation,[status(thm)],[f1595,f391]) ).
fof(f1642,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1624]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL023+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.41 % Computer : n014.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.06/0.41 % CPULimit : 300
% 0.06/0.41 % WCLimit : 300
% 0.06/0.41 % DateTime : Mon Sep 21 04:01:34 UTC 2026
% 0.06/0.42 % CPUTime :
% 0.06/0.43 % Drodi V4.1.1
% 0.06/0.70 % Refutation found
% 0.06/0.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.06/0.75 % Elapsed time: 0.312649 seconds
% 0.06/0.75 % CPU time: 2.149672 seconds
% 0.06/0.75 % Total memory used: 46.633 MB
% 0.06/0.75 % Net memory used: 45.684 MB
%------------------------------------------------------------------------------