%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL031+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 02:03:23 PM UTC 2026
% Result : Theorem 17.21s 2.76s
% Output : CNFRefutation 18.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 50 unt; 0 def)
% Number of atoms : 62 ( 61 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 5 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 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 : 69 ( 67 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f17,conjecture,
! [X0,X1] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one )
=> join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one )
=> join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ),
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(f23,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
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(f35,plain,
? [X0,X1] :
( join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) != one
& join(composition(converse(X1),X1),one) = one
& join(composition(converse(X0),X0),one) = one ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f36,plain,
( join(composition(converse(composition(sK0_skl,sK1_skl)),composition(sK0_skl,sK1_skl)),one) != one
& join(composition(converse(sK1_skl),sK1_skl),one) = one
& join(composition(converse(sK0_skl),sK0_skl),one) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f35]) ).
fof(f37,plain,
join(composition(converse(sK0_skl),sK0_skl),one) = one,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
join(composition(converse(sK1_skl),sK1_skl),one) = one,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
join(composition(converse(composition(sK0_skl,sK1_skl)),composition(sK0_skl,sK1_skl)),one) != one,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f48,plain,
join(one,composition(converse(sK0_skl),sK0_skl)) = one,
inference(forward_demodulation,[status(thm)],[f19,f37]) ).
fof(f49,plain,
join(one,composition(converse(sK1_skl),sK1_skl)) = one,
inference(forward_demodulation,[status(thm)],[f19,f38]) ).
fof(f50,plain,
join(one,composition(converse(composition(sK0_skl,sK1_skl)),composition(sK0_skl,sK1_skl))) != one,
inference(forward_demodulation,[status(thm)],[f19,f39]) ).
fof(f60,plain,
! [X0] : join(one,join(composition(converse(sK1_skl),sK1_skl),X0)) = join(one,X0),
inference(paramodulation,[status(thm)],[f49,f20]) ).
fof(f72,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f23]) ).
fof(f87,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f96,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f97,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f98,plain,
! [X0,X1,X2] : composition(converse(X0),composition(converse(X1),X2)) = composition(converse(composition(X1,X0)),X2),
inference(paramodulation,[status(thm)],[f28,f23]) ).
fof(f400,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f97]) ).
fof(f419,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f400]) ).
fof(f431,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f72,f419]) ).
fof(f432,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f419]) ).
fof(f441,plain,
! [X0,X1] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f419,f25]) ).
fof(f446,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f419,f431]) ).
fof(f456,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f432,f441]) ).
fof(f1006,plain,
! [X0] : join(one,composition(join(converse(sK1_skl),X0),sK1_skl)) = join(one,composition(X0,sK1_skl)),
inference(paramodulation,[status(thm)],[f25,f60]) ).
fof(f5677,plain,
! [X0] : composition(one,X0) = join(X0,composition(composition(converse(sK0_skl),sK0_skl),X0)),
inference(paramodulation,[status(thm)],[f48,f456]) ).
fof(f5772,plain,
! [X0] : X0 = join(X0,composition(composition(converse(sK0_skl),sK0_skl),X0)),
inference(forward_demodulation,[status(thm)],[f446,f5677]) ).
fof(f5773,plain,
! [X0] : X0 = join(X0,composition(converse(sK0_skl),composition(sK0_skl,X0))),
inference(forward_demodulation,[status(thm)],[f23,f5772]) ).
fof(f6932,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(composition(converse(sK0_skl),composition(sK0_skl,converse(X0))))),
inference(paramodulation,[status(thm)],[f5773,f87]) ).
fof(f6970,plain,
! [X0] : X0 = join(X0,converse(composition(converse(sK0_skl),composition(sK0_skl,converse(X0))))),
inference(forward_demodulation,[status(thm)],[f26,f6932]) ).
fof(f6971,plain,
! [X0] : X0 = join(X0,composition(converse(composition(sK0_skl,converse(X0))),sK0_skl)),
inference(forward_demodulation,[status(thm)],[f97,f6970]) ).
fof(f6972,plain,
! [X0] : X0 = join(X0,composition(composition(X0,converse(sK0_skl)),sK0_skl)),
inference(forward_demodulation,[status(thm)],[f96,f6971]) ).
fof(f6974,plain,
! [X0] : X0 = join(X0,composition(X0,composition(converse(sK0_skl),sK0_skl))),
inference(forward_demodulation,[status(thm)],[f23,f6972]) ).
fof(f7204,plain,
join(one,composition(converse(sK1_skl),sK1_skl)) = join(one,composition(composition(converse(sK1_skl),composition(converse(sK0_skl),sK0_skl)),sK1_skl)),
inference(paramodulation,[status(thm)],[f6974,f1006]) ).
fof(f7261,plain,
one = join(one,composition(composition(converse(sK1_skl),composition(converse(sK0_skl),sK0_skl)),sK1_skl)),
inference(forward_demodulation,[status(thm)],[f49,f7204]) ).
fof(f7262,plain,
one = join(one,composition(converse(sK1_skl),composition(composition(converse(sK0_skl),sK0_skl),sK1_skl))),
inference(forward_demodulation,[status(thm)],[f23,f7261]) ).
fof(f7263,plain,
one = join(one,composition(converse(sK1_skl),composition(converse(sK0_skl),composition(sK0_skl,sK1_skl)))),
inference(forward_demodulation,[status(thm)],[f23,f7262]) ).
fof(f7264,plain,
one = join(one,composition(converse(composition(sK0_skl,sK1_skl)),composition(sK0_skl,sK1_skl))),
inference(forward_demodulation,[status(thm)],[f98,f7263]) ).
fof(f7265,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f7264,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL031+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n019.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 04:04:34 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 17.21/2.76 % Refutation found
% 17.21/2.76 % SZS status Theorem for theBenchmark: Theorem is valid
% 17.21/2.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.07/2.85 % Elapsed time: 2.390002 seconds
% 2.07/2.85 % CPU time: 18.626981 seconds
% 2.07/2.85 % Total memory used: 217.971 MB
% 2.07/2.85 % Net memory used: 212.936 MB
%------------------------------------------------------------------------------