%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM835+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 01:41:46 PM UTC 2026
% Result : Theorem 0.08s 0.35s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 7 unt; 2 def)
% Number of atoms : 69 ( 46 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 71 ( 27 ~; 30 |; 11 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 33 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( vd151 = vd165
| ? [Vd170] : vd151 = vplus(vd165,Vd170)
| ? [Vd180] : vd165 = vplus(vd151,Vd180) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( vd151 = vd165
| ? [Vd170] : vd151 = vplus(vd165,Vd170)
| ? [Vd180] : vd165 = vplus(vd151,Vd180) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f21,axiom,
! [Vd151,Vd152] :
( m(Vd152)
<=> ( ? [Vd157] : Vd152 = vplus(Vd151,Vd157)
| ? [Vd155] : Vd151 = vplus(Vd152,Vd155)
| Vd151 = Vd152 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,plain,
( vd151 != vd165
& ! [Vd170] : vd151 != vplus(vd165,Vd170)
& ! [Vd180] : vd165 != vplus(vd151,Vd180) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
! [X0] : vd165 != vplus(vd151,X0),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] : vd151 != vplus(vd165,X0),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,plain,
vd151 != vd165,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f85,plain,
! [Vd151,Vd152] :
( ( ( ! [Vd157] : Vd152 != vplus(Vd151,Vd157)
& ! [Vd155] : Vd151 != vplus(Vd152,Vd155)
& Vd151 != Vd152 )
| m(Vd152) )
& ( ? [Vd157] : Vd152 = vplus(Vd151,Vd157)
| ? [Vd155] : Vd151 = vplus(Vd152,Vd155)
| Vd151 = Vd152
| ~ m(Vd152) ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f86,plain,
( ! [Vd152] :
( ( ! [Vd151,Vd157] : Vd152 != vplus(Vd151,Vd157)
& ! [Vd151,Vd155] : Vd151 != vplus(Vd152,Vd155)
& ! [Vd151] : Vd151 != Vd152 )
| m(Vd152) )
& ! [Vd152] :
( ! [Vd151] :
( ? [Vd157] : Vd152 = vplus(Vd151,Vd157)
| ? [Vd155] : Vd151 = vplus(Vd152,Vd155)
| Vd151 = Vd152 )
| ~ m(Vd152) ) ),
inference(miniscoping,[status(thm)],[f85]) ).
fof(f87,plain,
( ! [Vd152] :
( ( ! [Vd151,Vd157] : Vd152 != vplus(Vd151,Vd157)
& ! [Vd151,Vd155] : Vd151 != vplus(Vd152,Vd155)
& ! [Vd151] : Vd151 != Vd152 )
| m(Vd152) )
& ! [Vd152] :
( ! [Vd151] :
( Vd152 = vplus(Vd151,sK2_skl(Vd151,Vd152))
| Vd151 = vplus(Vd152,sK1_skl(Vd151,Vd152))
| Vd151 = Vd152 )
| ~ m(Vd152) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(Vd155,sK1_skl(Vd151,Vd152)),skolemize(Vd157,sK2_skl(Vd151,Vd152))],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( X0 = vplus(X1,sK2_skl(X1,X0))
| X1 = vplus(X0,sK1_skl(X1,X0))
| X1 = X0
| ~ m(X0) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( X1 != X0
| m(X0) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f172,definition,
( sQ10_spl
<=> vd151 = vd165 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ10_spl
| vd151 = vd165 ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f194,plain,
! [X0] : m(X0),
inference(destructive_equality_resolution,[status(thm)],[f89]) ).
fof(f288,plain,
! [X0,X1] :
( X1 = vplus(X0,sK2_skl(X0,X1))
| X0 = vplus(X1,sK1_skl(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f194]) ).
fof(f290,plain,
( vd151 = vplus(vd165,sK1_skl(vd151,vd165))
| vd151 = vd165 ),
inference(resolution,[status(thm)],[f288,f42]) ).
fof(f312,definition,
( sQ18_spl
<=> vd151 = vplus(vd165,sK1_skl(vd151,vd165)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( ~ sQ18_spl
| vd151 = vplus(vd165,sK1_skl(vd151,vd165)) ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,plain,
( sQ18_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f290,f172,f312]) ).
fof(f334,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f44]) ).
fof(f335,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f334]) ).
fof(f336,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f43]) ).
fof(f337,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f336]) ).
fof(f338,plain,
$false,
inference(sat_refutation,[status(thm)],[f315,f335,f337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM835+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 21 03:11:52 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.32 % Drodi V4.1.1
% 0.08/0.35 % Refutation found
% 0.08/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.38 % Elapsed time: 0.050758 seconds
% 0.08/0.38 % CPU time: 0.121424 seconds
% 0.08/0.38 % Total memory used: 103.360 MB
% 0.08/0.38 % Net memory used: 103.249 MB
%------------------------------------------------------------------------------