%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL024+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 11.18s 6.90s
% Output : CNFRefutation 11.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 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 : 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 : 107 ( 104 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,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)],[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(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(f35,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)],[f18]) ).
fof(f36,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)],[f35]) ).
fof(f37,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)],[f36]) ).
fof(f48,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f19,f21]) ).
fof(f49,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f22,f48]) ).
fof(f50,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f19,f29]) ).
fof(f51,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)],[f19,f37]) ).
fof(f52,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f49]) ).
fof(f61,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f62,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f89,plain,
! [X0,X1,X2] : converse(join(composition(converse(X0),X1),X2)) = join(composition(converse(X1),X0),converse(X2)),
inference(paramodulation,[status(thm)],[f62,f27]) ).
fof(f90,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f213,plain,
! [X0,X1,X2] : join(meet(X0,X1),join(complement(join(complement(X0),X1)),X2)) = join(X0,X2),
inference(paramodulation,[status(thm)],[f52,f20]) ).
fof(f343,plain,
! [X0,X1,X2] : composition(join(X0,converse(X1)),converse(X2)) = join(composition(X0,converse(X2)),converse(composition(X2,X1))),
inference(paramodulation,[status(thm)],[f28,f25]) ).
fof(f433,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f62]) ).
fof(f441,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f433]) ).
fof(f462,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f441]) ).
fof(f463,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f441,f50]) ).
fof(f475,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f462,f441]) ).
fof(f498,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f475,f463]) ).
fof(f594,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f618,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f594]) ).
fof(f1080,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X0),X1))),
inference(paramodulation,[status(thm)],[f498,f213]) ).
fof(f1130,plain,
! [X0,X1] : X0 = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f52,f1080]) ).
fof(f1182,plain,
! [X0,X1] : X0 = join(X0,meet(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f1130]) ).
fof(f1991,plain,
! [X0,X1] : X0 = join(X0,meet(X1,X0)),
inference(paramodulation,[status(thm)],[f618,f1182]) ).
fof(f12296,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)],[f343,f89]) ).
fof(f12405,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)],[f61,f12296]) ).
fof(f12406,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)],[f90,f12405]) ).
fof(f12407,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)],[f26,f12406]) ).
fof(f12408,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),converse(converse(composition(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f26,f12407]) ).
fof(f12409,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)],[f12414,f51]) ).
fof(f12414,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f26,f12408]) ).
fof(f12543,plain,
composition(meet(sK0_skl,converse(sK1_skl)),sK2_skl) != composition(meet(sK0_skl,converse(sK1_skl)),sK2_skl),
inference(forward_demodulation,[status(thm)],[f1991,f12409]) ).
fof(f12544,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f12543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL024+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n017.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.38 % CPULimit : 300
% 0.08/5.38 % WCLimit : 300
% 0.08/5.38 % DateTime : Mon Sep 21 03:57:02 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.39 % Drodi V4.1.1
% 11.18/6.90 % Refutation found
% 11.18/6.90 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.18/6.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.62/6.97 % Elapsed time: 1.576159 seconds
% 11.62/6.97 % CPU time: 12.405404 seconds
% 11.62/6.97 % Total memory used: 238.678 MB
% 11.62/6.97 % Net memory used: 234.750 MB
%------------------------------------------------------------------------------