%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS186+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:59:53 PM UTC 2026
% Result : Theorem 0.17s 5.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 8 unt; 2 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 144 ( 54 ~; 55 |; 25 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 76 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Ax,C] :
( ( ! [I2] :
( model(I2,Ax)
<=> model(I2,C) )
& ? [I1] : model(I1,Ax) )
<=> status(Ax,C,eqv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
isa(eqv,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ isa(eqv,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f62,plain,
! [Ax,C] :
( ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) )
<=> status(Ax,C,thm) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f63,plain,
! [Ax,C] :
( ( ~ status(Ax,C,thm)
| ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) ) )
& ( status(Ax,C,thm)
| ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ) ),
inference(NNF_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
( ! [Ax,C] :
( ~ status(Ax,C,thm)
| ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,thm)
| ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
( ! [Ax,C] :
( ~ status(Ax,C,thm)
| ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,thm)
| ( ~ model(sK9_skl(C,Ax),C)
& model(sK9_skl(C,Ax),Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(I1,sK9_skl(C,Ax))],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( status(X1,X0,thm)
| model(sK9_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( status(X1,X0,thm)
| ~ model(sK9_skl(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
! [Ax,C] :
( ( ~ status(Ax,C,eqv)
| ( ! [I2] :
( ( ~ model(I2,C)
| model(I2,Ax) )
& ( model(I2,C)
| ~ model(I2,Ax) ) )
& ? [I1] : model(I1,Ax) ) )
& ( status(Ax,C,eqv)
| ? [I2] :
( ( model(I2,C)
| model(I2,Ax) )
& ( ~ model(I2,C)
| ~ model(I2,Ax) ) )
| ! [I1] : ~ model(I1,Ax) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f70,plain,
( ! [Ax,C] :
( ~ status(Ax,C,eqv)
| ( ! [I2] :
( ~ model(I2,C)
| model(I2,Ax) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,eqv)
| ? [I2] :
( ( model(I2,C)
| model(I2,Ax) )
& ( ~ model(I2,C)
| ~ model(I2,Ax) ) )
| ! [I1] : ~ model(I1,Ax) ) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f71,plain,
( ! [Ax,C] :
( ~ status(Ax,C,eqv)
| ( ! [I2] :
( ~ model(I2,C)
| model(I2,Ax) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& model(sK11_skl(C,Ax),Ax) ) )
& ! [Ax,C] :
( status(Ax,C,eqv)
| ( ( model(sK10_skl(C,Ax),C)
| model(sK10_skl(C,Ax),Ax) )
& ( ~ model(sK10_skl(C,Ax),C)
| ~ model(sK10_skl(C,Ax),Ax) ) )
| ! [I1] : ~ model(I1,Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl]),skolemize(I2,sK10_skl(C,Ax)),skolemize(I1,sK11_skl(C,Ax))],[f70]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ status(X1,X2,eqv)
| model(X0,X2)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f180,plain,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) )
<=> isa(S1,S2) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f181,plain,
! [S1,S2] :
( ( ~ isa(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ( isa(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) ) ),
inference(NNF_transformation,[status(thm)],[f180]) ).
fof(f182,plain,
( ! [S1,S2] :
( ~ isa(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ! [S1,S2] :
( isa(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) ) ),
inference(miniscoping,[status(thm)],[f181]) ).
fof(f183,plain,
( ! [S1,S2] :
( ~ isa(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ! [S1,S2] :
( isa(S1,S2)
| ( ~ status(sK44_skl(S2,S1),sK45_skl(S2,S1),S2)
& status(sK44_skl(S2,S1),sK45_skl(S2,S1),S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl,sK45_skl]),skolemize(Ax,sK44_skl(S2,S1)),skolemize(C,sK45_skl(S2,S1))],[f182]) ).
fof(f184,plain,
! [X0,X1] :
( isa(X1,X0)
| status(sK44_skl(X0,X1),sK45_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f185,plain,
! [X0,X1] :
( isa(X1,X0)
| ~ status(sK44_skl(X0,X1),sK45_skl(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f240,plain,
~ isa(eqv,thm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f248,plain,
~ status(sK44_skl(thm,eqv),sK45_skl(thm,eqv),thm),
inference(resolution,[status(thm)],[f185,f240]) ).
fof(f250,plain,
~ model(sK9_skl(sK45_skl(thm,eqv),sK44_skl(thm,eqv)),sK45_skl(thm,eqv)),
inference(resolution,[status(thm)],[f248,f67]) ).
fof(f252,plain,
! [X0] :
( ~ status(X0,sK45_skl(thm,eqv),eqv)
| ~ model(sK9_skl(sK45_skl(thm,eqv),sK44_skl(thm,eqv)),X0) ),
inference(resolution,[status(thm)],[f250,f75]) ).
fof(f254,plain,
( isa(eqv,thm)
| ~ model(sK9_skl(sK45_skl(thm,eqv),sK44_skl(thm,eqv)),sK44_skl(thm,eqv)) ),
inference(resolution,[status(thm)],[f252,f184]) ).
fof(f255,definition,
( sQ2_spl
<=> model(sK9_skl(sK45_skl(thm,eqv),sK44_skl(thm,eqv)),sK44_skl(thm,eqv)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ2_spl
| ~ model(sK9_skl(sK45_skl(thm,eqv),sK44_skl(thm,eqv)),sK44_skl(thm,eqv)) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,definition,
( sQ3_spl
<=> isa(eqv,thm) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ3_spl
| isa(eqv,thm) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f254,f255,f258]) ).
fof(f262,plain,
( sQ2_spl
| status(sK44_skl(thm,eqv),sK45_skl(thm,eqv),thm) ),
inference(resolution,[status(thm)],[f257,f66]) ).
fof(f266,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f248]) ).
fof(f267,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f268,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f240]) ).
fof(f269,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f270,plain,
$false,
inference(sat_refutation,[status(thm)],[f261,f267,f269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS186+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n003.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.40 % CPULimit : 300
% 0.11/5.40 % WCLimit : 300
% 0.11/5.40 % DateTime : Sun Sep 20 22:57:36 UTC 2026
% 0.11/5.40 % CPUTime :
% 0.17/5.41 % Drodi V4.1.1
% 0.17/5.45 % Refutation found
% 0.17/5.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/5.48 % Elapsed time: 0.069221 seconds
% 0.17/5.48 % CPU time: 0.248093 seconds
% 0.17/5.48 % Total memory used: 21.646 MB
% 0.17/5.48 % Net memory used: 21.452 MB
%------------------------------------------------------------------------------