%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL009+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 : n010.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 96.82s 12.73s
% Output : CNFRefutation 96.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 32 unt; 2 def)
% Number of atoms : 73 ( 55 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 18 ~; 14 |; 5 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 74 !; 7 ?)
% 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] :
( join(X0,X1) = X1
=> ( join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1)
& join(composition(X0,X2),composition(X1,X2)) = composition(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( join(X0,X1) = X1
=> ( join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1)
& join(composition(X0,X2),composition(X1,X2)) = composition(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(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] : join(converse(X0),converse(X1)) = converse(join(X0,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] :
( ( join(composition(X2,X0),composition(X2,X1)) != composition(X2,X1)
| join(composition(X0,X2),composition(X1,X2)) != composition(X1,X2) )
& join(X0,X1) = X1 ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f36,plain,
? [X0,X1] :
( ( ? [X2] : join(composition(X2,X0),composition(X2,X1)) != composition(X2,X1)
| ? [X2] : join(composition(X0,X2),composition(X1,X2)) != composition(X1,X2) )
& join(X0,X1) = X1 ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
( ( join(composition(sK3_skl,sK0_skl),composition(sK3_skl,sK1_skl)) != composition(sK3_skl,sK1_skl)
| join(composition(sK0_skl,sK2_skl),composition(sK1_skl,sK2_skl)) != composition(sK1_skl,sK2_skl) )
& join(sK0_skl,sK1_skl) = sK1_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl),skolemize(X2,sK3_skl)],[f36]) ).
fof(f38,plain,
join(sK0_skl,sK1_skl) = sK1_skl,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
( join(composition(sK3_skl,sK0_skl),composition(sK3_skl,sK1_skl)) != composition(sK3_skl,sK1_skl)
| join(composition(sK0_skl,sK2_skl),composition(sK1_skl,sK2_skl)) != composition(sK1_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,definition,
( sQ0_spl
<=> join(composition(sK0_skl,sK2_skl),composition(sK1_skl,sK2_skl)) = composition(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( sQ0_spl
| join(composition(sK0_skl,sK2_skl),composition(sK1_skl,sK2_skl)) != composition(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f40]) ).
fof(f43,definition,
( sQ1_spl
<=> join(composition(sK3_skl,sK0_skl),composition(sK3_skl,sK1_skl)) = composition(sK3_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f45,plain,
( sQ1_spl
| composition(sK3_skl,sK1_skl) != join(composition(sK3_skl,sK0_skl),composition(sK3_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f40,f43]) ).
fof(f51,plain,
( sQ0_spl
| composition(join(sK0_skl,sK1_skl),sK2_skl) != composition(sK1_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f25,f42]) ).
fof(f52,plain,
( sQ0_spl
| composition(sK1_skl,sK2_skl) != composition(sK1_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f38,f51]) ).
fof(f53,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f52]) ).
fof(f54,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f53]) ).
fof(f115,plain,
! [X0,X1] : composition(X0,converse(X1)) = converse(composition(X1,converse(X0))),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f116,plain,
! [X0,X1] : composition(converse(X0),X1) = converse(composition(converse(X1),X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f122,plain,
! [X0,X1,X2] : join(converse(composition(X0,X1)),composition(X2,converse(X0))) = composition(join(converse(X1),X2),converse(X0)),
inference(paramodulation,[status(thm)],[f28,f25]) ).
fof(f477,plain,
! [X0,X1] : join(converse(X0),converse(X1)) = converse(join(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f478,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f479,plain,
! [X0,X1] : join(converse(X0),X1) = converse(join(X0,converse(X1))),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f491,plain,
! [X0,X1] : converse(join(X0,X1)) = converse(join(X1,X0)),
inference(forward_demodulation,[status(thm)],[f27,f477]) ).
fof(f2277,plain,
! [X0,X1,X2] : converse(join(composition(X0,converse(X1)),converse(composition(X1,X2)))) = converse(composition(join(converse(X2),X0),converse(X1))),
inference(paramodulation,[status(thm)],[f122,f491]) ).
fof(f2288,plain,
! [X0,X1,X2] : join(converse(composition(X0,converse(X1))),composition(X1,X2)) = converse(composition(join(converse(X2),X0),converse(X1))),
inference(forward_demodulation,[status(thm)],[f479,f2277]) ).
fof(f2289,plain,
! [X0,X1,X2] : join(composition(X0,converse(X1)),composition(X0,X2)) = converse(composition(join(converse(X2),X1),converse(X0))),
inference(forward_demodulation,[status(thm)],[f115,f2288]) ).
fof(f2290,plain,
! [X0,X1,X2] : join(composition(X0,converse(X1)),composition(X0,X2)) = composition(X0,converse(join(converse(X2),X1))),
inference(forward_demodulation,[status(thm)],[f115,f2289]) ).
fof(f2291,plain,
! [X0,X1,X2] : composition(X0,join(X1,converse(X2))) = join(composition(X0,converse(X2)),composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f478,f2290]) ).
fof(f2866,plain,
! [X0,X1,X2] : composition(converse(X0),join(X1,X2)) = converse(composition(converse(join(X2,X1)),X0)),
inference(paramodulation,[status(thm)],[f491,f116]) ).
fof(f2917,plain,
! [X0,X1,X2] : composition(converse(X0),join(X1,X2)) = composition(converse(X0),join(X2,X1)),
inference(forward_demodulation,[status(thm)],[f116,f2866]) ).
fof(f2942,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = composition(converse(converse(X0)),join(X2,X1)),
inference(paramodulation,[status(thm)],[f26,f2917]) ).
fof(f3084,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = composition(X0,join(X2,X1)),
inference(forward_demodulation,[status(thm)],[f26,f2942]) ).
fof(f4827,plain,
! [X0,X1,X2] : composition(X0,join(X1,converse(converse(X2)))) = join(composition(X0,X2),composition(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f2291]) ).
fof(f4893,plain,
( sQ1_spl
| composition(sK3_skl,sK1_skl) != composition(sK3_skl,join(sK1_skl,sK0_skl)) ),
inference(backward_demodulation,[status(thm)],[f4900,f45]) ).
fof(f4900,plain,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X2),composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f26,f4827]) ).
fof(f4954,plain,
( sQ1_spl
| composition(sK3_skl,sK1_skl) != composition(sK3_skl,join(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f3084,f4893]) ).
fof(f4955,plain,
( sQ1_spl
| composition(sK3_skl,sK1_skl) != composition(sK3_skl,sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f38,f4954]) ).
fof(f4956,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4955]) ).
fof(f4957,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f4956]) ).
fof(f4958,plain,
$false,
inference(sat_refutation,[status(thm)],[f46,f54,f4957]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 03:58:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 96.82/12.73 % Refutation found
% 96.82/12.73 % SZS status Theorem for theBenchmark: Theorem is valid
% 96.82/12.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 44.47/14.12 % Elapsed time: 13.535051 seconds
% 44.47/14.12 % CPU time: 92.175554 seconds
% 44.47/14.12 % Total memory used: 442.061 MB
% 44.47/14.12 % Net memory used: 417.604 MB
%------------------------------------------------------------------------------