%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL009-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 : Unsatisfiable 84.74s 11.23s
% Output : CNFRefutation 84.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 29 unt; 2 def)
% Number of atoms : 55 ( 38 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 11 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : join(A,B) = join(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] : composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : converse(converse(A)) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : converse(join(A,B)) = join(converse(A),converse(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : converse(composition(A,B)) = composition(converse(B),converse(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
join(sk1,sk2) = sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2)
| join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
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] : X0 = converse(converse(X0)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [X0,X1] : join(converse(X0),converse(X1)) = converse(join(X0,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,
join(sk1,sk2) = sk2,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f30,plain,
( join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2)
| join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f31,definition,
( sQ0_spl
<=> join(composition(sk1,sk3),composition(sk2,sk3)) = composition(sk2,sk3) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( sQ0_spl
| join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,definition,
( sQ1_spl
<=> join(composition(sk3,sk1),composition(sk3,sk2)) = composition(sk3,sk2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( sQ1_spl
| join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f31,f34]) ).
fof(f38,plain,
( sQ0_spl
| composition(join(sk1,sk2),sk3) != composition(sk2,sk3) ),
inference(forward_demodulation,[status(thm)],[f22,f33]) ).
fof(f40,plain,
( sQ0_spl
| composition(sk2,sk3) != composition(sk2,sk3) ),
inference(backward_demodulation,[status(thm)],[f29,f38]) ).
fof(f41,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f40]) ).
fof(f42,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f41]) ).
fof(f48,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(f60,plain,
sk2 = join(sk2,sk1),
inference(paramodulation,[status(thm)],[f16,f29]) ).
fof(f69,plain,
! [X0,X1] : join(converse(X0),converse(X1)) = converse(join(X1,X0)),
inference(paramodulation,[status(thm)],[f16,f24]) ).
fof(f72,plain,
! [X0,X1] : converse(join(X0,X1)) = converse(join(X1,X0)),
inference(forward_demodulation,[status(thm)],[f24,f69]) ).
fof(f138,plain,
! [X0,X1] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(paramodulation,[status(thm)],[f23,f24]) ).
fof(f139,plain,
! [X0,X1] : join(X0,converse(X1)) = converse(join(converse(X0),X1)),
inference(paramodulation,[status(thm)],[f23,f24]) ).
fof(f141,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f239,plain,
! [X0,X1,X2] : converse(composition(join(X0,converse(X1)),converse(X2))) = converse(join(converse(composition(X2,X1)),composition(X0,converse(X2)))),
inference(paramodulation,[status(thm)],[f48,f72]) ).
fof(f252,plain,
! [X0,X1,X2] : composition(X0,converse(join(X1,converse(X2)))) = converse(join(converse(composition(X0,X2)),composition(X1,converse(X0)))),
inference(forward_demodulation,[status(thm)],[f141,f239]) ).
fof(f253,plain,
! [X0,X1,X2] : composition(X0,join(converse(X1),X2)) = converse(join(converse(composition(X0,X2)),composition(X1,converse(X0)))),
inference(forward_demodulation,[status(thm)],[f138,f252]) ).
fof(f254,plain,
! [X0,X1,X2] : composition(X0,join(converse(X1),X2)) = join(composition(X0,X2),converse(composition(X1,converse(X0)))),
inference(forward_demodulation,[status(thm)],[f139,f253]) ).
fof(f255,plain,
! [X0,X1,X2] : composition(X0,join(converse(X1),X2)) = join(composition(X0,X2),composition(X0,converse(X1))),
inference(forward_demodulation,[status(thm)],[f141,f254]) ).
fof(f9166,plain,
! [X0,X1,X2] : composition(X0,join(converse(converse(X1)),X2)) = join(composition(X0,X2),composition(X0,X1)),
inference(paramodulation,[status(thm)],[f23,f255]) ).
fof(f9237,plain,
( sQ1_spl
| composition(sk3,join(sk2,sk1)) != composition(sk3,sk2) ),
inference(backward_demodulation,[status(thm)],[f9244,f36]) ).
fof(f9244,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X2),composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f23,f9166]) ).
fof(f9250,plain,
( sQ1_spl
| composition(sk3,sk2) != composition(sk3,sk2) ),
inference(forward_demodulation,[status(thm)],[f60,f9237]) ).
fof(f9251,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f9250]) ).
fof(f9252,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f9251]) ).
fof(f9253,plain,
$false,
inference(sat_refutation,[status(thm)],[f37,f42,f9252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL009-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.44 % Computer : n020.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Mon Sep 21 03:59:02 UTC 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.46 % Drodi V4.1.1
% 84.74/11.23 % Refutation found
% 84.74/11.23 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 84.74/11.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 84.74/11.29 % Elapsed time: 10.825314 seconds
% 84.74/11.29 % CPU time: 85.208591 seconds
% 84.74/11.29 % Total memory used: 317.909 MB
% 84.74/11.29 % Net memory used: 306.787 MB
%------------------------------------------------------------------------------