%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL031+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 : 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 02:03:22 PM UTC 2026
% Result : Theorem 5.05s 1.17s
% Output : CNFRefutation 5.05s
% 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = 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(f14,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,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)],[f14]) ).
fof(f16,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
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] :
( 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)],[f15]) ).
fof(f30,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)],[f29]) ).
fof(f31,plain,
join(composition(converse(sK0_skl),sK0_skl),one) = one,
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
join(composition(converse(sK1_skl),sK1_skl),one) = one,
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
join(composition(converse(composition(sK0_skl,sK1_skl)),composition(sK0_skl,sK1_skl)),one) != one,
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f42,plain,
join(one,composition(converse(sK0_skl),sK0_skl)) = one,
inference(forward_demodulation,[status(thm)],[f16,f31]) ).
fof(f43,plain,
join(one,composition(converse(sK1_skl),sK1_skl)) = one,
inference(forward_demodulation,[status(thm)],[f16,f32]) ).
fof(f44,plain,
join(one,composition(converse(composition(sK0_skl,sK1_skl)),composition(sK0_skl,sK1_skl))) != one,
inference(forward_demodulation,[status(thm)],[f16,f33]) ).
fof(f51,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f52,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f55,plain,
! [X0,X1,X2] : composition(converse(X0),composition(converse(X1),X2)) = composition(converse(composition(X1,X0)),X2),
inference(paramodulation,[status(thm)],[f25,f20]) ).
fof(f56,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f20]) ).
fof(f71,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f23,f24]) ).
fof(f98,plain,
! [X0] : join(one,join(composition(converse(sK1_skl),sK1_skl),X0)) = join(one,X0),
inference(paramodulation,[status(thm)],[f43,f17]) ).
fof(f169,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f21,f52]) ).
fof(f186,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f23,f169]) ).
fof(f198,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f56,f186]) ).
fof(f199,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f21,f186]) ).
fof(f208,plain,
! [X0,X1] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f186,f22]) ).
fof(f213,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f186,f198]) ).
fof(f223,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f199,f208]) ).
fof(f429,plain,
! [X0] : join(one,composition(join(converse(sK1_skl),X0),sK1_skl)) = join(one,composition(X0,sK1_skl)),
inference(paramodulation,[status(thm)],[f22,f98]) ).
fof(f4273,plain,
! [X0] : composition(one,X0) = join(X0,composition(composition(converse(sK0_skl),sK0_skl),X0)),
inference(paramodulation,[status(thm)],[f42,f223]) ).
fof(f4346,plain,
! [X0] : X0 = join(X0,composition(composition(converse(sK0_skl),sK0_skl),X0)),
inference(forward_demodulation,[status(thm)],[f213,f4273]) ).
fof(f4347,plain,
! [X0] : X0 = join(X0,composition(converse(sK0_skl),composition(sK0_skl,X0))),
inference(forward_demodulation,[status(thm)],[f20,f4346]) ).
fof(f4996,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(composition(converse(sK0_skl),composition(sK0_skl,converse(X0))))),
inference(paramodulation,[status(thm)],[f4347,f71]) ).
fof(f5026,plain,
! [X0] : X0 = join(X0,converse(composition(converse(sK0_skl),composition(sK0_skl,converse(X0))))),
inference(forward_demodulation,[status(thm)],[f23,f4996]) ).
fof(f5027,plain,
! [X0] : X0 = join(X0,composition(converse(composition(sK0_skl,converse(X0))),sK0_skl)),
inference(forward_demodulation,[status(thm)],[f52,f5026]) ).
fof(f5028,plain,
! [X0] : X0 = join(X0,composition(composition(X0,converse(sK0_skl)),sK0_skl)),
inference(forward_demodulation,[status(thm)],[f51,f5027]) ).
fof(f5029,plain,
! [X0] : X0 = join(X0,composition(X0,composition(converse(sK0_skl),sK0_skl))),
inference(forward_demodulation,[status(thm)],[f20,f5028]) ).
fof(f5427,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)],[f5029,f429]) ).
fof(f5465,plain,
one = join(one,composition(composition(converse(sK1_skl),composition(converse(sK0_skl),sK0_skl)),sK1_skl)),
inference(forward_demodulation,[status(thm)],[f43,f5427]) ).
fof(f5466,plain,
one = join(one,composition(converse(sK1_skl),composition(composition(converse(sK0_skl),sK0_skl),sK1_skl))),
inference(forward_demodulation,[status(thm)],[f20,f5465]) ).
fof(f5467,plain,
one = join(one,composition(converse(sK1_skl),composition(converse(sK0_skl),composition(sK0_skl,sK1_skl)))),
inference(forward_demodulation,[status(thm)],[f20,f5466]) ).
fof(f5468,plain,
one = join(one,composition(converse(composition(sK0_skl,sK1_skl)),composition(sK0_skl,sK1_skl))),
inference(forward_demodulation,[status(thm)],[f55,f5467]) ).
fof(f5469,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5468,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL031+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:09:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 5.05/1.17 % Refutation found
% 5.05/1.17 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.05/1.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.05/1.21 % Elapsed time: 0.812843 seconds
% 5.05/1.21 % CPU time: 6.113590 seconds
% 5.05/1.21 % Total memory used: 73.798 MB
% 5.05/1.21 % Net memory used: 71.670 MB
%------------------------------------------------------------------------------