%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS216+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:59:56 PM UTC 2026
% Result : Theorem 0.62s 16.31s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 15 unt; 5 def)
% Number of atoms : 180 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 206 ( 97 ~; 76 |; 22 &)
% ( 9 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 158 ( 144 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [Ax,C] :
( ( ! [I2] : model(I2,not(C))
& ! [I1] : model(I1,Ax) )
<=> status(Ax,C,uns) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [S1,S2] :
( ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) )
<=> nota(S1,S2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [I,F] :
( model(I,F)
<~> model(I,not(F)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
? [F] :
! [I] : model(I,F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
? [F] :
! [I] : ~ model(I,F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
nota(uns,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ nota(uns,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(f67,plain,
! [X0,X1] :
( status(X1,X0,thm)
| ~ model(sK9_skl(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ status(X1,X2,thm)
| model(X0,X2)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f160,plain,
! [Ax,C] :
( ( ~ status(Ax,C,uns)
| ( ! [I2] : model(I2,not(C))
& ! [I1] : model(I1,Ax) ) )
& ( status(Ax,C,uns)
| ? [I2] : ~ model(I2,not(C))
| ? [I1] : ~ model(I1,Ax) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f161,plain,
( ! [Ax,C] :
( ~ status(Ax,C,uns)
| ( ! [I2] : model(I2,not(C))
& ! [I1] : model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,uns)
| ? [I2] : ~ model(I2,not(C))
| ? [I1] : ~ model(I1,Ax) ) ),
inference(miniscoping,[status(thm)],[f160]) ).
fof(f162,plain,
( ! [Ax,C] :
( ~ status(Ax,C,uns)
| ( ! [I2] : model(I2,not(C))
& ! [I1] : model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,uns)
| ~ model(sK39_skl(C,Ax),not(C))
| ~ model(sK38_skl(C,Ax),Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl,sK39_skl]),skolemize(I1,sK38_skl(C,Ax)),skolemize(I2,sK39_skl(C,Ax))],[f161]) ).
fof(f163,plain,
! [X0,X1] :
( status(X1,X0,uns)
| ~ model(sK39_skl(X0,X1),not(X0))
| ~ model(sK38_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f165,plain,
! [X0,X1,X2] :
( ~ status(X2,X1,uns)
| model(X0,not(X1)) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f187,plain,
! [S1,S2] :
( ( ~ nota(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ( nota(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f188,plain,
( ! [S1,S2] :
( ~ nota(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ! [S1,S2] :
( nota(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(miniscoping,[status(thm)],[f187]) ).
fof(f189,plain,
( ! [S1,S2] :
( ~ nota(S1,S2)
| ( ~ status(sK46_skl(S2,S1),sK47_skl(S2,S1),S2)
& status(sK46_skl(S2,S1),sK47_skl(S2,S1),S1) ) )
& ! [S1,S2] :
( nota(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46_skl,sK47_skl]),skolemize(Ax,sK46_skl(S2,S1)),skolemize(C,sK47_skl(S2,S1))],[f188]) ).
fof(f190,plain,
! [X0,X1,X2,X3] :
( nota(X2,X3)
| status(X0,X1,X3)
| ~ status(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f191,plain,
! [X0,X1] :
( ~ nota(X1,X0)
| status(sK46_skl(X0,X1),sK47_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f192,plain,
! [X0,X1] :
( ~ nota(X1,X0)
| ~ status(sK46_skl(X0,X1),sK47_skl(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f207,plain,
! [I,F] :
( ( ~ model(I,not(F))
| ~ model(I,F) )
& ( model(I,not(F))
| model(I,F) ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f208,plain,
( ! [I,F] :
( ~ model(I,not(F))
| ~ model(I,F) )
& ! [I,F] :
( model(I,not(F))
| model(I,F) ) ),
inference(miniscoping,[status(thm)],[f207]) ).
fof(f209,plain,
! [X0,X1] :
( model(X0,not(X1))
| model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f210,plain,
! [X0,X1] :
( ~ model(X0,not(X1))
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
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(f220,plain,
! [I] : ~ model(I,sK56_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56_skl]),skolemize(F,sK56_skl)],[f29]) ).
fof(f221,plain,
! [X0] : ~ model(X0,sK56_skl),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f240,plain,
~ nota(uns,thm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f248,plain,
! [X0,X1] :
( status(X0,X1,thm)
| ~ status(X0,X1,uns) ),
inference(resolution,[status(thm)],[f190,f240]) ).
fof(f250,plain,
! [X0,X1,X2] :
( ~ status(X2,X1,uns)
| status(X0,not(X1),thm) ),
inference(resolution,[status(thm)],[f67,f165]) ).
fof(f261,definition,
! [X2,X3] :
( sQ3_spl
<=> ~ status(X2,X3,uns) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f262,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ status(X0,X1,uns) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f363,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ model(sK39_skl(X0,X1),not(X0))
| ~ model(sK38_skl(X0,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f262]) ).
fof(f530,definition,
! [X2,X3] :
( sQ8_spl
<=> ~ model(X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f531,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ model(X0,X1) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f544,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ model(sK38_skl(X0,X1),X1)
| model(sK39_skl(X0,X1),X0) ),
inference(resolution,[status(thm)],[f209,f363]) ).
fof(f558,plain,
! [X0,X1,X2] :
( ~ status(X2,not(X1),thm)
| ~ model(X0,X2)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f210,f68]) ).
fof(f570,plain,
! [X0,X1] :
( ~ sQ8_spl
| model(X0,not(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f209,f531]) ).
fof(f588,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f570,f531]) ).
fof(f589,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f588]) ).
fof(f631,plain,
! [X0] :
( ~ sQ3_spl
| ~ model(sK38_skl(sK56_skl,X0),X0) ),
inference(resolution,[status(thm)],[f544,f221]) ).
fof(f633,plain,
( ~ sQ3_spl
| $false ),
inference(resolution,[status(thm)],[f631,f216]) ).
fof(f635,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f633]) ).
fof(f643,plain,
! [X0] :
( ~ nota(uns,X0)
| status(sK46_skl(X0,uns),sK47_skl(X0,uns),thm) ),
inference(resolution,[status(thm)],[f248,f191]) ).
fof(f669,plain,
( ~ nota(uns,thm)
| ~ nota(uns,thm) ),
inference(resolution,[status(thm)],[f643,f192]) ).
fof(f686,definition,
( sQ9_spl
<=> nota(uns,thm) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f689,plain,
~ sQ9_spl,
inference(split_clause,[status(thm)],[f669,f686]) ).
fof(f724,plain,
! [X0,X1,X2] :
( ~ status(X2,X0,uns)
| status(X1,X0,uns)
| ~ model(sK38_skl(X0,X1),X1) ),
inference(resolution,[status(thm)],[f163,f165]) ).
fof(f727,plain,
! [X0,X1] :
( ~ status(X1,X0,uns)
| status(sK52_skl,X0,uns) ),
inference(resolution,[status(thm)],[f724,f216]) ).
fof(f775,plain,
! [X0,X1] :
( status(sK52_skl,X1,thm)
| ~ status(X0,X1,uns) ),
inference(resolution,[status(thm)],[f727,f248]) ).
fof(f792,plain,
! [X0,X1,X2] :
( model(X2,X1)
| ~ model(X2,sK52_skl)
| ~ status(X0,X1,uns) ),
inference(resolution,[status(thm)],[f775,f68]) ).
fof(f842,definition,
( sQ21_spl
<=> model(sK60_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f844,plain,
( sQ21_spl
| ~ model(sK60_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f842]) ).
fof(f849,definition,
! [X1] :
( sQ23_spl
<=> ~ model(X1,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f850,plain,
! [X0] :
( ~ sQ23_spl
| ~ model(X0,sK52_skl) ),
inference(component_clause,[status(thm)],[f849]) ).
fof(f861,plain,
! [X0,X1,X2] :
( model(X2,X1)
| ~ status(X0,X1,uns) ),
inference(forward_subsumption_resolution,[status(thm)],[f792,f216]) ).
fof(f884,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f850,f216]) ).
fof(f885,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f884]) ).
fof(f886,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f844,f216]) ).
fof(f887,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f886]) ).
fof(f898,plain,
! [X0,X1,X2,X3] :
( ~ status(X3,X1,uns)
| ~ model(X0,X2)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f558,f250]) ).
fof(f900,plain,
! [X0,X1,X2,X3] :
( ~ status(X2,X3,uns)
| ~ model(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f898,f861]) ).
fof(f947,plain,
! [X0,X1,X2,X3] :
( ~ status(X2,X3,uns)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f900,f727]) ).
fof(f951,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f947,f530,f261]) ).
fof(f964,plain,
$false,
inference(sat_refutation,[status(thm)],[f589,f635,f689,f885,f887,f951]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS216+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.99 % CPULimit : 300
% 0.09/15.99 % WCLimit : 300
% 0.09/15.99 % DateTime : Sun Sep 20 22:57:36 UTC 2026
% 0.09/15.99 % CPUTime :
% 0.09/16.00 % Drodi V4.1.1
% 0.62/16.31 % Refutation found
% 0.62/16.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.62/16.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.62/16.33 % Elapsed time: 0.332206 seconds
% 0.62/16.33 % CPU time: 2.347110 seconds
% 0.62/16.33 % Total memory used: 38.203 MB
% 0.62/16.33 % Net memory used: 34.985 MB
%------------------------------------------------------------------------------