%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS073+1 : TPTP v9.3.1. Released v3.1.0.
% 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 12:59:37 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 4 unt; 3 def)
% Number of atoms : 165 ( 7 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 191 ( 75 ~; 71 |; 34 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 84 ( 72 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ~ cp(X)
& ? [Y] :
( ! [Z] :
( rinvF(Y,Z)
=> ? [W] :
( cp(W)
& rs(Z,W) ) )
& ! [Z] :
( rinvS(Y,Z)
=> cp(Z) )
& rf(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
cUnsatisfiable(i2003_11_14_17_18_54369),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Y] :
( rs(X,Y)
=> rf(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ~ cp(X)
& ? [Y] :
( ! [Z] :
( ? [W] :
( cp(W)
& rs(Z,W) )
| ~ rinvF(Y,Z) )
& ! [Z] :
( cp(Z)
| ~ rinvS(Y,Z) )
& rf(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f93,plain,
! [X] :
( ( cp(X)
| ! [Y] :
( ? [Z] :
( ! [W] :
( ~ cp(W)
| ~ rs(Z,W) )
& rinvF(Y,Z) )
| ? [Z] :
( ~ cp(Z)
& rinvS(Y,Z) )
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ( ( ~ cp(X)
& ? [Y] :
( ! [Z] :
( ? [W] :
( cp(W)
& rs(Z,W) )
| ~ rinvF(Y,Z) )
& ! [Z] :
( cp(Z)
| ~ rinvS(Y,Z) )
& rf(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f92]) ).
fof(f94,plain,
( ! [X] :
( cp(X)
| ! [Y] :
( ? [Z] :
( ! [W] :
( ~ cp(W)
| ~ rs(Z,W) )
& rinvF(Y,Z) )
| ? [Z] :
( ~ cp(Z)
& rinvS(Y,Z) )
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ~ cp(X)
& ? [Y] :
( ! [Z] :
( ? [W] :
( cp(W)
& rs(Z,W) )
| ~ rinvF(Y,Z) )
& ! [Z] :
( cp(Z)
| ~ rinvS(Y,Z) )
& rf(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f93]) ).
fof(f95,plain,
( ! [X] :
( cp(X)
| ! [Y] :
( ( ! [W] :
( ~ cp(W)
| ~ rs(sK3_skl(Y,X),W) )
& rinvF(Y,sK3_skl(Y,X)) )
| ( ~ cp(sK2_skl(Y,X))
& rinvS(Y,sK2_skl(Y,X)) )
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ~ cp(X)
& ! [Z] :
( ( cp(sK1_skl(Z,X))
& rs(Z,sK1_skl(Z,X)) )
| ~ rinvF(sK0_skl(X),Z) )
& ! [Z] :
( cp(Z)
| ~ rinvS(sK0_skl(X),Z) )
& rf(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(Y,sK0_skl(X)),skolemize(W,sK1_skl(Z,X)),skolemize(Z,sK2_skl(Y,X)),skolemize(Z,sK3_skl(Y,X))],[f94]) ).
fof(f96,plain,
! [X0] :
( rf(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( cp(X1)
| ~ rinvS(sK0_skl(X0),X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f98,plain,
! [X0,X1] :
( rs(X1,sK1_skl(X1,X0))
| ~ rinvF(sK0_skl(X0),X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f100,plain,
! [X0] :
( ~ cp(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f105,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f106,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rf(X,Z)
| ~ rf(X,Y) ) ),
inference(miniscoping,[status(thm)],[f105]) ).
fof(f107,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X2)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f111,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f112,plain,
( ! [X,Y] :
( ~ rf(Y,X)
| rinvF(X,Y) )
& ! [X,Y] :
( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f114,plain,
! [X0,X1] :
( ~ rf(X1,X0)
| rinvF(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f119,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f120,plain,
( ! [X,Y] :
( ~ rs(Y,X)
| rinvS(X,Y) )
& ! [X,Y] :
( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f122,plain,
! [X0,X1] :
( ~ rs(X1,X0)
| rinvS(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f126,plain,
cUnsatisfiable(i2003_11_14_17_18_54369),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f129,plain,
! [X,Y] :
( rf(X,Y)
| ~ rs(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f130,plain,
! [X0,X1] :
( rf(X0,X1)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
! [X0] :
( rs(X0,sK1_skl(X0,i2003_11_14_17_18_54369))
| ~ rinvF(sK0_skl(i2003_11_14_17_18_54369),X0) ),
inference(resolution,[status(thm)],[f98,f126]) ).
fof(f133,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| X1 = sK0_skl(X0)
| ~ rf(X0,X1) ),
inference(resolution,[status(thm)],[f107,f96]) ).
fof(f135,plain,
! [X0] :
( X0 = sK0_skl(i2003_11_14_17_18_54369)
| ~ rf(i2003_11_14_17_18_54369,X0) ),
inference(resolution,[status(thm)],[f133,f126]) ).
fof(f140,definition,
( sQ1_spl
<=> cUnsatisfiable(i2003_11_14_17_18_54369) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( sQ1_spl
| ~ cUnsatisfiable(i2003_11_14_17_18_54369) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f145,plain,
! [X0] :
( ~ rf(X0,sK0_skl(i2003_11_14_17_18_54369))
| rs(X0,sK1_skl(X0,i2003_11_14_17_18_54369)) ),
inference(resolution,[status(thm)],[f132,f114]) ).
fof(f146,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| rs(i2003_11_14_17_18_54369,sK1_skl(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369)) ),
inference(resolution,[status(thm)],[f145,f96]) ).
fof(f147,definition,
( sQ2_spl
<=> rs(i2003_11_14_17_18_54369,sK1_skl(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( ~ sQ2_spl
| rs(i2003_11_14_17_18_54369,sK1_skl(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369)) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f146,f147,f140]) ).
fof(f151,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f126]) ).
fof(f152,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f154,plain,
( ~ sQ2_spl
| rf(i2003_11_14_17_18_54369,sK1_skl(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369)) ),
inference(resolution,[status(thm)],[f148,f130]) ).
fof(f156,plain,
( ~ sQ2_spl
| rinvS(sK1_skl(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369),i2003_11_14_17_18_54369) ),
inference(resolution,[status(thm)],[f148,f122]) ).
fof(f157,plain,
( ~ sQ2_spl
| sK1_skl(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369) = sK0_skl(i2003_11_14_17_18_54369) ),
inference(resolution,[status(thm)],[f154,f135]) ).
fof(f163,plain,
( ~ sQ2_spl
| rinvS(sK0_skl(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369) ),
inference(backward_demodulation,[status(thm)],[f157,f156]) ).
fof(f180,plain,
( ~ sQ2_spl
| cp(i2003_11_14_17_18_54369)
| ~ cUnsatisfiable(i2003_11_14_17_18_54369) ),
inference(resolution,[status(thm)],[f163,f97]) ).
fof(f182,definition,
( sQ6_spl
<=> cp(i2003_11_14_17_18_54369) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ6_spl
| cp(i2003_11_14_17_18_54369) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( ~ sQ2_spl
| sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f180,f140,f182,f147]) ).
fof(f186,plain,
( ~ sQ6_spl
| ~ cUnsatisfiable(i2003_11_14_17_18_54369) ),
inference(resolution,[status(thm)],[f183,f100]) ).
fof(f187,plain,
( ~ sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f186,f140,f182]) ).
fof(f188,plain,
$false,
inference(sat_refutation,[status(thm)],[f150,f152,f185,f187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS073+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 22:52:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.033423 seconds
% 0.10/0.41 % CPU time: 0.089043 seconds
% 0.10/0.41 % Total memory used: 2.893 MB
% 0.10/0.41 % Net memory used: 2.801 MB
%------------------------------------------------------------------------------