%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP019+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:50:17 PM UTC 2026
% Result : Theorem 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 40 ( 28 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 43 ( 20 ~; 11 |; 5 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 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 : 9 ( 8 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [V0z] :
( mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( 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) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,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(f34,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)],[f33]) ).
fof(f111,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)],[f32]) ).
fof(f112,plain,
! [V0z] :
( ( ( 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) )
& ( 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) ) )
| ~ mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(NNF_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [X0] :
( X0 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__inv,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)],[f112]) ).
fof(f115,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)],[f34]) ).
fof(f116,plain,
( ap(c_2Ecomplex_2Ecomplex__inv,sK3_skl) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& sK3_skl != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(sK3_skl,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(V0z,sK3_skl)],[f115]) ).
fof(f117,plain,
mem(sK3_skl,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
sK3_skl != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f119,plain,
ap(c_2Ecomplex_2Ecomplex__inv,sK3_skl) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f123,plain,
sK3_skl != ap(c_2Ecomplex_2Ecomplex__inv,sK3_skl),
inference(backward_demodulation,[status(thm)],[f119,f118]) ).
fof(f124,plain,
! [X0] :
( X0 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__inv,sK3_skl)
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(forward_demodulation,[status(thm)],[f119,f113]) ).
fof(f125,plain,
! [X0] :
( X0 = ap(c_2Ecomplex_2Ecomplex__inv,sK3_skl)
| ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__inv,sK3_skl)
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(forward_demodulation,[status(thm)],[f119,f124]) ).
fof(f126,plain,
( sK3_skl = ap(c_2Ecomplex_2Ecomplex__inv,sK3_skl)
| ap(c_2Ecomplex_2Ecomplex__inv,sK3_skl) != ap(c_2Ecomplex_2Ecomplex__inv,sK3_skl) ),
inference(resolution,[status(thm)],[f125,f117]) ).
fof(f127,plain,
sK3_skl = ap(c_2Ecomplex_2Ecomplex__inv,sK3_skl),
inference(trivial_equality_resolution,[status(thm)],[f126]) ).
fof(f128,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f127,f123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 21:51:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.44 % Elapsed time: 0.051657 seconds
% 0.15/0.44 % CPU time: 0.138666 seconds
% 0.15/0.44 % Total memory used: 99.656 MB
% 0.15/0.44 % Net memory used: 99.579 MB
%------------------------------------------------------------------------------