%------------------------------------------------------------------------------
% 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 : n011.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 21.48s 3.15s
% Output : CNFRefutation 21.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 20 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 6 |; 5 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 43 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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(f14,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(f15,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)],[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] : X0 = converse(converse(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] :
( ( 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)],[f15]) ).
fof(f30,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)],[f29]) ).
fof(f31,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)],[f30]) ).
fof(f32,plain,
sK1_skl = join(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,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)],[f31]) ).
fof(f34,plain,
( composition(join(sK0_skl,sK1_skl),sK2_skl) != composition(sK1_skl,sK2_skl)
| composition(sK3_skl,sK1_skl) != join(composition(sK3_skl,sK0_skl),composition(sK3_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f22,f33]) ).
fof(f36,plain,
( composition(sK1_skl,sK2_skl) != composition(sK1_skl,sK2_skl)
| composition(sK3_skl,sK1_skl) != join(composition(sK3_skl,sK0_skl),composition(sK3_skl,sK1_skl)) ),
inference(backward_demodulation,[status(thm)],[f32,f34]) ).
fof(f37,plain,
composition(sK3_skl,sK1_skl) != join(composition(sK3_skl,sK0_skl),composition(sK3_skl,sK1_skl)),
inference(trivial_equality_resolution,[status(thm)],[f36]) ).
fof(f40,plain,
! [X0,X1,X2] : join(composition(X0,converse(X1)),converse(composition(X1,X2))) = composition(join(X0,converse(X2)),converse(X1)),
inference(paramodulation,[status(thm)],[f25,f22]) ).
fof(f177,plain,
! [X0,X1,X2] : join(converse(composition(X0,X1)),converse(composition(X0,X2))) = composition(join(converse(X1),converse(X2)),converse(X0)),
inference(paramodulation,[status(thm)],[f25,f40]) ).
fof(f197,plain,
! [X0,X1,X2] : converse(join(composition(X0,X1),composition(X0,X2))) = composition(join(converse(X1),converse(X2)),converse(X0)),
inference(forward_demodulation,[status(thm)],[f24,f177]) ).
fof(f198,plain,
! [X0,X1,X2] : converse(join(composition(X0,X1),composition(X0,X2))) = composition(converse(join(X1,X2)),converse(X0)),
inference(forward_demodulation,[status(thm)],[f24,f197]) ).
fof(f199,plain,
! [X0,X1,X2] : converse(composition(X0,join(X1,X2))) = converse(join(composition(X0,X1),composition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f25,f198]) ).
fof(f3720,plain,
! [X0,X1,X2] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(paramodulation,[status(thm)],[f199,f23]) ).
fof(f3738,plain,
composition(sK3_skl,sK1_skl) != composition(sK3_skl,join(sK0_skl,sK1_skl)),
inference(backward_demodulation,[status(thm)],[f3750,f37]) ).
fof(f3750,plain,
! [X0,X1,X2] : join(composition(X0,X1),composition(X0,X2)) = composition(X0,join(X1,X2)),
inference(forward_demodulation,[status(thm)],[f23,f3720]) ).
fof(f3774,plain,
composition(sK3_skl,sK1_skl) != composition(sK3_skl,sK1_skl),
inference(forward_demodulation,[status(thm)],[f32,f3738]) ).
fof(f3775,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3774]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL009+1 : 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 : n011.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 03:58:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 21.48/3.15 % Refutation found
% 21.48/3.15 % SZS status Theorem for theBenchmark: Theorem is valid
% 21.48/3.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.56/3.21 % Elapsed time: 2.826673 seconds
% 1.56/3.21 % CPU time: 22.200015 seconds
% 1.56/3.21 % Total memory used: 220.086 MB
% 1.56/3.21 % Net memory used: 213.996 MB
%------------------------------------------------------------------------------