%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM835+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 01:41:46 PM UTC 2026
% Result : Theorem 0.25s 0.51s
% Output : CNFRefutation 0.25s
% 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(f18,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(f26,plain,
( vd151 != vd165
& ! [Vd170] : vd151 != vplus(vd165,Vd170)
& ! [Vd180] : vd165 != vplus(vd151,Vd180) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0] : vd165 != vplus(vd151,X0),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0] : vd151 != vplus(vd165,X0),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
vd151 != vd165,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,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)],[f18]) ).
fof(f62,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)],[f61]) ).
fof(f63,plain,
( ! [Vd152] :
( ( ! [Vd151,Vd157] : Vd152 != vplus(Vd151,Vd157)
& ! [Vd151,Vd155] : Vd151 != vplus(Vd152,Vd155)
& ! [Vd151] : Vd151 != Vd152 )
| m(Vd152) )
& ! [Vd152] :
( ! [Vd151] :
( Vd152 = vplus(Vd151,sK1_skl(Vd151,Vd152))
| Vd151 = vplus(Vd152,sK0_skl(Vd151,Vd152))
| Vd151 = Vd152 )
| ~ m(Vd152) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Vd155,sK0_skl(Vd151,Vd152)),skolemize(Vd157,sK1_skl(Vd151,Vd152))],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( X0 = vplus(X1,sK1_skl(X1,X0))
| X1 = vplus(X0,sK0_skl(X1,X0))
| X1 = X0
| ~ m(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( X1 != X0
| m(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f117,definition,
( sQ10_spl
<=> vd151 = vd165 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ10_spl
| vd151 = vd165 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f126,plain,
! [X0] : m(X0),
inference(destructive_equality_resolution,[status(thm)],[f65]) ).
fof(f435,plain,
! [X0,X1] :
( X1 = vplus(X0,sK1_skl(X0,X1))
| X0 = vplus(X1,sK0_skl(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f64,f126]) ).
fof(f437,plain,
( vd151 = vplus(vd165,sK1_skl(vd165,vd151))
| vd165 = vd151 ),
inference(resolution,[status(thm)],[f435,f27]) ).
fof(f464,definition,
( sQ14_spl
<=> vd151 = vplus(vd165,sK1_skl(vd165,vd151)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( ~ sQ14_spl
| vd151 = vplus(vd165,sK1_skl(vd165,vd151)) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( sQ14_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f437,f117,f464]) ).
fof(f493,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f28]) ).
fof(f494,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f493]) ).
fof(f495,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f29]) ).
fof(f496,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f497,plain,
$false,
inference(sat_refutation,[status(thm)],[f467,f494,f496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM835+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/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 : Mon Sep 21 03:14:32 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.25/0.51 % Refutation found
% 0.25/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.25/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.54 % Elapsed time: 0.082351 seconds
% 0.25/0.54 % CPU time: 0.261685 seconds
% 0.25/0.54 % Total memory used: 103.138 MB
% 0.25/0.54 % Net memory used: 102.919 MB
%------------------------------------------------------------------------------