%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL008+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 02:03:13 PM UTC 2026
% Result : Theorem 16.70s 2.72s
% Output : CNFRefutation 15.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 51 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,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(f17,conjecture,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,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(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(f35,plain,
? [X0,X1,X2] : composition(X0,join(X1,X2)) != join(composition(X0,X1),composition(X0,X2)),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f36,plain,
composition(sK0_skl,join(sK1_skl,sK2_skl)) != join(composition(sK0_skl,sK1_skl),composition(sK0_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,
composition(sK0_skl,join(sK1_skl,sK2_skl)) != join(composition(sK0_skl,sK1_skl),composition(sK0_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f44,plain,
composition(sK0_skl,join(sK1_skl,sK2_skl)) != join(composition(sK0_skl,sK2_skl),composition(sK0_skl,sK1_skl)),
inference(backward_demodulation,[status(thm)],[f19,f37]) ).
fof(f45,plain,
composition(sK0_skl,join(sK2_skl,sK1_skl)) != join(composition(sK0_skl,sK2_skl),composition(sK0_skl,sK1_skl)),
inference(forward_demodulation,[status(thm)],[f19,f44]) ).
fof(f204,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f212,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f215,plain,
! [X0,X1,X2] : composition(join(converse(X0),X1),converse(X2)) = join(converse(composition(X2,X0)),composition(X1,converse(X2))),
inference(paramodulation,[status(thm)],[f28,f25]) ).
fof(f1266,plain,
! [X0,X1,X2] : join(composition(X0,X1),converse(composition(X2,converse(X0)))) = converse(composition(join(converse(X1),X2),converse(X0))),
inference(paramodulation,[status(thm)],[f215,f204]) ).
fof(f16650,plain,
! [X0,X1,X2] : join(composition(X0,X1),composition(X0,converse(X2))) = converse(composition(join(converse(X1),X2),converse(X0))),
inference(forward_demodulation,[status(thm)],[f212,f1266]) ).
fof(f16651,plain,
! [X0,X1,X2] : join(composition(X0,X1),composition(X0,converse(X2))) = composition(X0,converse(join(converse(X1),X2))),
inference(forward_demodulation,[status(thm)],[f212,f16650]) ).
fof(f16652,plain,
! [X0,X1,X2] : join(composition(X0,X1),composition(X0,converse(X2))) = composition(X0,join(X1,converse(X2))),
inference(forward_demodulation,[status(thm)],[f204,f16651]) ).
fof(f16681,plain,
! [X0,X1,X2] : composition(X0,join(X1,converse(converse(X2)))) = join(composition(X0,X1),composition(X0,X2)),
inference(paramodulation,[status(thm)],[f26,f16652]) ).
fof(f16758,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f26,f16681]) ).
fof(f16759,plain,
$false,
inference(resolution,[status(thm)],[f16758,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL008+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.46 % Computer : n015.cluster.edu
% 0.16/0.46 % Model : x86_64 x86_64
% 0.16/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.46 % Memory : 8046.5625MB
% 0.16/0.46 % OS : Linux 6.8.0-71-generic
% 0.16/0.46 % CPULimit : 300
% 0.16/0.46 % WCLimit : 300
% 0.16/0.46 % DateTime : Mon Sep 21 04:01:35 UTC 2026
% 0.16/0.47 % CPUTime :
% 0.16/0.49 % Drodi V4.1.1
% 16.70/2.72 % Refutation found
% 16.70/2.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 16.70/2.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.64/2.81 % Elapsed time: 2.314753 seconds
% 15.64/2.81 % CPU time: 17.885953 seconds
% 15.64/2.81 % Total memory used: 183.268 MB
% 15.64/2.81 % Net memory used: 166.492 MB
%------------------------------------------------------------------------------