%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP019+5 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:50:18 PM UTC 2026
% Result : Theorem 31.50s 24.37s
% Output : CNFRefutation 34.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 37 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 13 ~; 7 |; 4 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 7 ( 6 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16818,axiom,
! [V0z] :
( mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( V0z != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
=> ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,V0z)) = V0z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16821,axiom,
ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16826,conjecture,
! [V0z] :
( mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( V0z != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
=> ap(c_2Ecomplex_2Ecomplex__inv,V0z) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16827,negated_conjecture,
~ ! [V0z] :
( mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( V0z != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
=> ap(c_2Ecomplex_2Ecomplex__inv,V0z) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ),
inference(negated_conjecture,[status(cth)],[f16826]) ).
fof(f88218,plain,
! [V0z] :
( ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,V0z)) = V0z
| V0z = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ~ mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(pre_NNF_transformation,[status(thm)],[f16818]) ).
fof(f88219,plain,
! [X0] :
( ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,X0)) = X0
| X0 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(cnf_transformation,[status(thm)],[f88218]) ).
fof(f88224,plain,
ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(cnf_transformation,[status(thm)],[f16821]) ).
fof(f88234,plain,
? [V0z] :
( ap(c_2Ecomplex_2Ecomplex__inv,V0z) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& V0z != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(pre_NNF_transformation,[status(thm)],[f16827]) ).
fof(f88235,plain,
( ap(c_2Ecomplex_2Ecomplex__inv,sK16093_skl) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& sK16093_skl != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(sK16093_skl,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16093_skl]),skolemize(V0z,sK16093_skl)],[f88234]) ).
fof(f88236,plain,
mem(sK16093_skl,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(cnf_transformation,[status(thm)],[f88235]) ).
fof(f88237,plain,
sK16093_skl != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(cnf_transformation,[status(thm)],[f88235]) ).
fof(f88238,plain,
ap(c_2Ecomplex_2Ecomplex__inv,sK16093_skl) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(cnf_transformation,[status(thm)],[f88235]) ).
fof(f97865,plain,
sK16093_skl != ap(c_2Ecomplex_2Ecomplex__inv,sK16093_skl),
inference(backward_demodulation,[status(thm)],[f88238,f88237]) ).
fof(f99600,plain,
! [X0] :
( ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,X0)) = X0
| X0 = ap(c_2Ecomplex_2Ecomplex__inv,sK16093_skl)
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(forward_demodulation,[status(thm)],[f88238,f88219]) ).
fof(f99601,plain,
( ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,sK16093_skl)) = sK16093_skl
| sK16093_skl = ap(c_2Ecomplex_2Ecomplex__inv,sK16093_skl) ),
inference(resolution,[status(thm)],[f99600,f88236]) ).
fof(f99602,plain,
ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,sK16093_skl)) = sK16093_skl,
inference(forward_subsumption_resolution,[status(thm)],[f99601,f97865]) ).
fof(f100369,plain,
ap(c_2Ecomplex_2Ecomplex__inv,ap(c_2Ecomplex_2Ecomplex__inv,sK16093_skl)) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(forward_demodulation,[status(thm)],[f88238,f88224]) ).
fof(f100370,plain,
ap(c_2Ecomplex_2Ecomplex__inv,sK16093_skl) = sK16093_skl,
inference(backward_demodulation,[status(thm)],[f100371,f88238]) ).
fof(f100371,plain,
sK16093_skl = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(forward_demodulation,[status(thm)],[f99602,f100369]) ).
fof(f100372,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f100370,f97865]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP019+5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n002.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 21:54:19 UTC 2026
% 0.18/0.44 % CPUTime :
% 22.89/23.19 % Drodi V4.1.1
% 31.50/24.37 % Refutation found
% 31.50/24.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 31.50/24.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 23.28/24.99 % Elapsed time: 24.451272 seconds
% 23.28/24.99 % CPU time: 32.608112 seconds
% 23.28/24.99 % Total memory used: 4.799 GB
% 23.28/24.99 % Net memory used: 4.762 GB
%------------------------------------------------------------------------------