%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL008+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 : n016.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 02:03:12 PM UTC 2026
% Result : Theorem 6.53s 1.31s
% Output : CNFRefutation 6.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 58 ( 55 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(f14,conjecture,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(negated_conjecture,[status(cth)],[f14]) ).
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(f29,plain,
? [X0,X1,X2] : composition(X0,join(X1,X2)) != join(composition(X0,X1),composition(X0,X2)),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f30,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)],[f29]) ).
fof(f31,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)],[f30]) ).
fof(f106,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f23,f24]) ).
fof(f107,plain,
! [X0,X1] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(paramodulation,[status(thm)],[f23,f24]) ).
fof(f160,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f164,plain,
! [X0,X1,X2] : composition(join(converse(X0),X1),converse(X2)) = join(converse(composition(X2,X0)),composition(X1,converse(X2))),
inference(paramodulation,[status(thm)],[f25,f22]) ).
fof(f199,plain,
! [X0,X1,X2] : converse(composition(join(converse(X0),X1),X2)) = composition(converse(X2),join(X0,converse(X1))),
inference(paramodulation,[status(thm)],[f106,f25]) ).
fof(f573,plain,
! [X0,X1,X2] : converse(join(X0,composition(converse(X1),X2))) = join(converse(X0),composition(converse(X2),X1)),
inference(paramodulation,[status(thm)],[f160,f107]) ).
fof(f5768,plain,
! [X0,X1,X2] : converse(composition(join(converse(X0),converse(X1)),converse(X2))) = join(converse(converse(composition(X2,X0))),composition(converse(converse(X2)),X1)),
inference(paramodulation,[status(thm)],[f164,f573]) ).
fof(f5844,plain,
! [X0,X1,X2] : composition(converse(converse(X0)),join(X1,converse(converse(X2)))) = join(converse(converse(composition(X0,X1))),composition(converse(converse(X0)),X2)),
inference(forward_demodulation,[status(thm)],[f199,f5768]) ).
fof(f5845,plain,
! [X0,X1,X2] : composition(X0,join(X1,converse(converse(X2)))) = join(converse(converse(composition(X0,X1))),composition(converse(converse(X0)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f5844]) ).
fof(f5846,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(converse(converse(composition(X0,X1))),composition(converse(converse(X0)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f5845]) ).
fof(f5847,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(converse(converse(X0)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f5846]) ).
fof(f5848,plain,
composition(sK0_skl,join(sK1_skl,sK2_skl)) != composition(sK0_skl,join(sK1_skl,sK2_skl)),
inference(backward_demodulation,[status(thm)],[f5852,f31]) ).
fof(f5852,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f23,f5847]) ).
fof(f5941,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f5848]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL008+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:02:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 6.53/1.31 % Refutation found
% 6.53/1.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.53/1.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.53/1.34 % Elapsed time: 0.969748 seconds
% 6.53/1.34 % CPU time: 7.474054 seconds
% 6.53/1.34 % Total memory used: 101.209 MB
% 6.53/1.34 % Net memory used: 98.998 MB
%------------------------------------------------------------------------------