%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS072+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 : n018.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 0.02s 0.39s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 7 unt; 2 def)
% Number of atoms : 136 ( 15 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 162 ( 63 ~; 57 |; 35 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 61 ( 49 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cp2(X)
& ? [Y] :
( ? [Z] :
( cp1(Z)
& rr(Y,Z) )
& ! [Z0,Z1] :
( ( rr(Y,Z1)
& rr(Y,Z0) )
=> Z0 = Z1 )
& rinvR(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] :
( cp1(X)
=> ~ ( cp5(X)
| cp4(X)
| cp2(X)
| cp3(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
cUnsatisfiable(i2003_11_14_17_18_50190),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( cp2(X)
& ? [Y] :
( ? [Z] :
( cp1(Z)
& rr(Y,Z) )
& ! [Z0,Z1] :
( Z0 = Z1
| ~ rr(Y,Z1)
| ~ rr(Y,Z0) )
& rinvR(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f74,plain,
! [X] :
( ( ~ cp2(X)
| ! [Y] :
( ! [Z] :
( ~ cp1(Z)
| ~ rr(Y,Z) )
| ? [Z0,Z1] :
( Z0 != Z1
& rr(Y,Z1)
& rr(Y,Z0) )
| ~ rinvR(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp2(X)
& ? [Y] :
( ? [Z] :
( cp1(Z)
& rr(Y,Z) )
& ! [Z0,Z1] :
( Z0 = Z1
| ~ rr(Y,Z1)
| ~ rr(Y,Z0) )
& rinvR(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
( ! [X] :
( ~ cp2(X)
| ! [Y] :
( ! [Z] :
( ~ cp1(Z)
| ~ rr(Y,Z) )
| ? [Z0,Z1] :
( Z0 != Z1
& rr(Y,Z1)
& rr(Y,Z0) )
| ~ rinvR(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cp2(X)
& ? [Y] :
( ? [Z] :
( cp1(Z)
& rr(Y,Z) )
& ! [Z0,Z1] :
( Z0 = Z1
| ~ rr(Y,Z1)
| ~ rr(Y,Z0) )
& rinvR(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f76,plain,
( ! [X] :
( ~ cp2(X)
| ! [Y] :
( ! [Z] :
( ~ cp1(Z)
| ~ rr(Y,Z) )
| ( sK2_skl(Y,X) != sK3_skl(Y,X)
& rr(Y,sK3_skl(Y,X))
& rr(Y,sK2_skl(Y,X)) )
| ~ rinvR(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cp2(X)
& cp1(sK1_skl(X))
& rr(sK0_skl(X),sK1_skl(X))
& ! [Z0,Z1] :
( Z0 = Z1
| ~ rr(sK0_skl(X),Z1)
| ~ rr(sK0_skl(X),Z0) )
& rinvR(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(Z,sK1_skl(X)),skolemize(Z0,sK2_skl(Y,X)),skolemize(Z1,sK3_skl(Y,X))],[f75]) ).
fof(f77,plain,
! [X0] :
( rinvR(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rr(sK0_skl(X0),X2)
| ~ rr(sK0_skl(X0),X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
! [X0] :
( rr(sK0_skl(X0),sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
! [X0] :
( cp1(sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f81,plain,
! [X0] :
( cp2(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f85,plain,
! [X] :
( ( ~ cp5(X)
& ~ cp4(X)
& ~ cp2(X)
& ~ cp3(X) )
| ~ cp1(X) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f87,plain,
! [X0] :
( ~ cp2(X0)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f99,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f100,plain,
( ! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) )
& ! [X,Y] :
( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( rr(X1,X0)
| ~ rinvR(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f103,plain,
cUnsatisfiable(i2003_11_14_17_18_50190),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f104,plain,
cp1(sK1_skl(i2003_11_14_17_18_50190)),
inference(resolution,[status(thm)],[f80,f103]) ).
fof(f109,plain,
~ cp2(sK1_skl(i2003_11_14_17_18_50190)),
inference(resolution,[status(thm)],[f104,f87]) ).
fof(f111,plain,
~ cUnsatisfiable(sK1_skl(i2003_11_14_17_18_50190)),
inference(resolution,[status(thm)],[f109,f81]) ).
fof(f121,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rr(sK0_skl(X0),X0) ),
inference(resolution,[status(thm)],[f101,f77]) ).
fof(f124,plain,
! [X0,X1] :
( X1 = X0
| ~ rr(sK0_skl(X0),X1)
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f121,f78]) ).
fof(f125,plain,
! [X0,X1] :
( X1 = X0
| ~ rr(sK0_skl(X0),X1)
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f124]) ).
fof(f126,plain,
! [X0] :
( X0 = i2003_11_14_17_18_50190
| ~ rr(sK0_skl(i2003_11_14_17_18_50190),X0) ),
inference(resolution,[status(thm)],[f125,f103]) ).
fof(f128,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
| sK1_skl(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 ),
inference(resolution,[status(thm)],[f126,f79]) ).
fof(f130,definition,
( sQ2_spl
<=> sK1_skl(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ2_spl
| sK1_skl(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ3_spl
<=> cUnsatisfiable(i2003_11_14_17_18_50190) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( sQ3_spl
| ~ cUnsatisfiable(i2003_11_14_17_18_50190) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f128,f130,f133]) ).
fof(f141,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f103]) ).
fof(f142,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f141]) ).
fof(f143,plain,
( ~ sQ2_spl
| ~ cUnsatisfiable(i2003_11_14_17_18_50190) ),
inference(backward_demodulation,[status(thm)],[f131,f111]) ).
fof(f150,plain,
( ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f143,f133,f130]) ).
fof(f155,plain,
$false,
inference(sat_refutation,[status(thm)],[f136,f142,f150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS072+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 22:54:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 0.02/0.39 % Refutation found
% 0.02/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.02/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.40 % Elapsed time: 0.033486 seconds
% 0.02/0.40 % CPU time: 0.079290 seconds
% 0.02/0.40 % Total memory used: 2.649 MB
% 0.02/0.40 % Net memory used: 2.582 MB
%------------------------------------------------------------------------------