%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS256+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 : n014.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 12:59:59 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 11 unt; 1 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 149 ( 64 ~; 56 |; 22 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 127 ( 108 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [Ax,C] :
( ( ? [I1] : model(I1,Ax)
<=> ? [I2] : model(I2,C) )
<=> status(Ax,C,esa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [S1,S2] :
( ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) )
<=> mighta(S1,S2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
? [F] :
! [I] : model(I,F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
mighta(esa,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ mighta(esa,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f49,plain,
! [Ax,C] :
( ( ~ status(Ax,C,esa)
| ( ( ! [I2] : ~ model(I2,C)
| ? [I1] : model(I1,Ax) )
& ( ? [I2] : model(I2,C)
| ! [I1] : ~ model(I1,Ax) ) ) )
& ( status(Ax,C,esa)
| ( ( ? [I2] : model(I2,C)
| ? [I1] : model(I1,Ax) )
& ( ! [I2] : ~ model(I2,C)
| ! [I1] : ~ model(I1,Ax) ) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f50,plain,
( ! [Ax,C] :
( ~ status(Ax,C,esa)
| ( ( ! [I2] : ~ model(I2,C)
| ? [I1] : model(I1,Ax) )
& ( ? [I2] : model(I2,C)
| ! [I1] : ~ model(I1,Ax) ) ) )
& ! [Ax,C] :
( status(Ax,C,esa)
| ( ( ? [I2] : model(I2,C)
| ? [I1] : model(I1,Ax) )
& ( ! [I2] : ~ model(I2,C)
| ! [I1] : ~ model(I1,Ax) ) ) ) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
( ! [Ax,C] :
( ~ status(Ax,C,esa)
| ( ( ! [I2] : ~ model(I2,C)
| model(sK7_skl(C,Ax),Ax) )
& ( model(sK6_skl(C,Ax),C)
| ! [I1] : ~ model(I1,Ax) ) ) )
& ! [Ax,C] :
( status(Ax,C,esa)
| ( ( model(sK5_skl(C,Ax),C)
| model(sK4_skl(C,Ax),Ax) )
& ( ! [I2] : ~ model(I2,C)
| ! [I1] : ~ model(I1,Ax) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(I1,sK4_skl(C,Ax)),skolemize(I2,sK5_skl(C,Ax)),skolemize(I2,sK6_skl(C,Ax)),skolemize(I1,sK7_skl(C,Ax))],[f50]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( status(X1,X3,esa)
| ~ model(X2,X3)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
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(f174,plain,
! [S1,S2] :
( ( ~ mighta(S1,S2)
| ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ( mighta(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f175,plain,
( ! [S1,S2] :
( ~ mighta(S1,S2)
| ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ! [S1,S2] :
( mighta(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(miniscoping,[status(thm)],[f174]) ).
fof(f176,plain,
( ! [S1,S2] :
( ~ mighta(S1,S2)
| ( status(sK42_skl(S2,S1),sK43_skl(S2,S1),S2)
& status(sK42_skl(S2,S1),sK43_skl(S2,S1),S1) ) )
& ! [S1,S2] :
( mighta(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42_skl,sK43_skl]),skolemize(Ax,sK42_skl(S2,S1)),skolemize(C,sK43_skl(S2,S1))],[f175]) ).
fof(f177,plain,
! [X0,X1,X2,X3] :
( mighta(X2,X3)
| ~ status(X0,X1,X3)
| ~ status(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f215,plain,
! [I] : model(I,sK52_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl]),skolemize(F,sK52_skl)],[f27]) ).
fof(f216,plain,
! [X0] : model(X0,sK52_skl),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f240,plain,
~ mighta(esa,thm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f248,plain,
! [X0,X1] :
( ~ status(X0,X1,thm)
| ~ status(X0,X1,esa) ),
inference(resolution,[status(thm)],[f177,f240]) ).
fof(f249,plain,
! [X0,X1] :
( ~ status(X1,X0,esa)
| ~ model(sK9_skl(X0,X1),X0) ),
inference(resolution,[status(thm)],[f67,f248]) ).
fof(f250,plain,
! [X0,X1,X2,X3] :
( ~ model(X3,X0)
| ~ model(X2,X1)
| ~ model(sK9_skl(X0,X1),X0) ),
inference(resolution,[status(thm)],[f249,f52]) ).
fof(f251,plain,
! [X0,X1,X2] :
( status(X1,X1,thm)
| ~ model(X2,X1)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f250,f66]) ).
fof(f253,plain,
! [X0,X1,X2] :
( ~ status(X1,X1,esa)
| ~ model(X2,X1)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f251,f248]) ).
fof(f254,plain,
! [X0,X1,X2] :
( ~ model(X2,X1)
| ~ model(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f52]) ).
fof(f255,plain,
! [X0,X1,X2] :
( status(X1,X2,thm)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f254,f66]) ).
fof(f257,plain,
! [X0,X1] : status(X0,X1,thm),
inference(backward_subsumption_resolution,[status(thm)],[f66,f255]) ).
fof(f260,plain,
! [X0,X1] : ~ status(X0,X1,esa),
inference(backward_subsumption_resolution,[status(thm)],[f248,f257]) ).
fof(f261,plain,
! [X0,X1,X2,X3] :
( ~ model(X2,X3)
| ~ model(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f52,f260]) ).
fof(f262,definition,
! [X0,X1] :
( sQ2_spl
<=> ~ model(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f263,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ model(X0,X1) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f261,f262]) ).
fof(f270,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f263]) ).
fof(f271,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f272,plain,
$false,
inference(sat_refutation,[status(thm)],[f265,f271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS256+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n014.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 22:59:49 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.066432 seconds
% 0.13/0.42 % CPU time: 0.185766 seconds
% 0.13/0.42 % Total memory used: 21.725 MB
% 0.13/0.42 % Net memory used: 21.502 MB
%------------------------------------------------------------------------------