%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS077+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 : n015.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 12:59:38 PM UTC 2026
% Result : Unsatisfiable 0.09s 5.59s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 12 unt; 1 def)
% Number of atoms : 150 ( 13 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 177 ( 64 ~; 59 |; 46 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 87 ( 71 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cp(Y)
& rs(X,Y) )
& ~ cp(X)
& ? [Y] :
( ! [Z] :
( rinvS(Y,Z)
=> cp(Z) )
& rr(X,Y) )
& ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
cUnsatisfiable(i2003_11_14_17_19_09372),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y] :
( rs(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cp(Y)
& rs(X,Y) )
& ~ cp(X)
& ? [Y] :
( ! [Z] :
( cp(Z)
| ~ rinvS(Y,Z) )
& rr(X,Y) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f63,definition,
! [Y,Z] :
( sP0_prd(Z,Y)
<=> ( cp(Z)
| ~ rinvS(Y,Z) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f64,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cp(Y)
& rs(X,Y) )
& ~ cp(X)
& ? [Y] :
( ! [Z] : sP0_prd(Z,Y)
& rr(X,Y) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ),
inference(formula_renaming,[status(thm)],[f62,f63]) ).
fof(f65,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| cp(X)
| ! [Y] :
( ? [Z] : ~ sP0_prd(Z,Y)
| ~ rr(X,Y) )
| ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
| cUnsatisfiable(X) )
& ( ( ? [Y] :
( cp(Y)
& rs(X,Y) )
& ~ cp(X)
& ? [Y] :
( ! [Z] : sP0_prd(Z,Y)
& rr(X,Y) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
( ! [X] :
( ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| cp(X)
| ! [Y] :
( ? [Z] : ~ sP0_prd(Z,Y)
| ~ rr(X,Y) )
| ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ? [Y] :
( cp(Y)
& rs(X,Y) )
& ~ cp(X)
& ? [Y] :
( ! [Z] : sP0_prd(Z,Y)
& rr(X,Y) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f67,plain,
( ! [X] :
( ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| cp(X)
| ! [Y] :
( ~ sP0_prd(sK4_skl(Y,X),Y)
| ~ rr(X,Y) )
| ( sK2_skl(X) != sK3_skl(X)
& rr(X,sK3_skl(X))
& rr(X,sK2_skl(X)) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cp(sK1_skl(X))
& rs(X,sK1_skl(X))
& ~ cp(X)
& ! [Z] : sP0_prd(Z,sK0_skl(X))
& rr(X,sK0_skl(X))
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(Y,sK0_skl(X)),skolemize(Y,sK1_skl(X)),skolemize(Y0,sK2_skl(X)),skolemize(Y1,sK3_skl(X)),skolemize(Z,sK4_skl(Y,X))],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rr(X0,X2)
| ~ rr(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0] :
( rr(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,plain,
! [X0,X1] :
( sP0_prd(X1,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f71,plain,
! [X0] :
( ~ cp(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f72,plain,
! [X0] :
( rs(X0,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f77,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f78,plain,
( ! [X,Y] :
( ~ rs(Y,X)
| rinvS(X,Y) )
& ! [X,Y] :
( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f80,plain,
! [X0,X1] :
( ~ rs(X1,X0)
| rinvS(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f81,plain,
cUnsatisfiable(i2003_11_14_17_19_09372),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f82,plain,
! [X,Y] :
( rr(X,Y)
| ~ rs(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f83,plain,
! [X0,X1] :
( rr(X0,X1)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [Y,Z] :
( ( ( ~ cp(Z)
& rinvS(Y,Z) )
| sP0_prd(Z,Y) )
& ( cp(Z)
| ~ rinvS(Y,Z)
| ~ sP0_prd(Z,Y) ) ),
inference(NNF_transformation,[status(thm)],[f63]) ).
fof(f85,plain,
( ! [Y,Z] :
( ( ~ cp(Z)
& rinvS(Y,Z) )
| sP0_prd(Z,Y) )
& ! [Y,Z] :
( cp(Z)
| ~ rinvS(Y,Z)
| ~ sP0_prd(Z,Y) ) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( cp(X0)
| ~ rinvS(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f90,plain,
~ cp(i2003_11_14_17_19_09372),
inference(resolution,[status(thm)],[f71,f81]) ).
fof(f93,plain,
rr(i2003_11_14_17_19_09372,sK0_skl(i2003_11_14_17_19_09372)),
inference(resolution,[status(thm)],[f69,f81]) ).
fof(f94,plain,
! [X0] :
( sK0_skl(i2003_11_14_17_19_09372) = X0
| ~ rr(i2003_11_14_17_19_09372,X0)
| ~ cUnsatisfiable(i2003_11_14_17_19_09372) ),
inference(resolution,[status(thm)],[f93,f68]) ).
fof(f95,plain,
! [X0] :
( sK0_skl(i2003_11_14_17_19_09372) = X0
| ~ rr(i2003_11_14_17_19_09372,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f81]) ).
fof(f96,plain,
! [X0] : sP0_prd(X0,sK0_skl(i2003_11_14_17_19_09372)),
inference(resolution,[status(thm)],[f70,f81]) ).
fof(f97,plain,
rs(i2003_11_14_17_19_09372,sK1_skl(i2003_11_14_17_19_09372)),
inference(resolution,[status(thm)],[f72,f81]) ).
fof(f98,plain,
rr(i2003_11_14_17_19_09372,sK1_skl(i2003_11_14_17_19_09372)),
inference(resolution,[status(thm)],[f97,f83]) ).
fof(f99,plain,
rinvS(sK1_skl(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
inference(resolution,[status(thm)],[f97,f80]) ).
fof(f103,plain,
sK0_skl(i2003_11_14_17_19_09372) = sK1_skl(i2003_11_14_17_19_09372),
inference(resolution,[status(thm)],[f95,f98]) ).
fof(f106,plain,
! [X0] : sP0_prd(X0,sK1_skl(i2003_11_14_17_19_09372)),
inference(backward_demodulation,[status(thm)],[f103,f96]) ).
fof(f112,plain,
! [X0] :
( cp(X0)
| ~ rinvS(sK1_skl(i2003_11_14_17_19_09372),X0) ),
inference(resolution,[status(thm)],[f86,f106]) ).
fof(f114,plain,
cp(i2003_11_14_17_19_09372),
inference(resolution,[status(thm)],[f112,f99]) ).
fof(f115,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f114,f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS077+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.57 % Computer : n015.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Sun Sep 20 22:55:57 UTC 2026
% 0.09/5.57 % CPUTime :
% 0.09/5.58 % Drodi V4.1.1
% 0.09/5.59 % Refutation found
% 0.09/5.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/5.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.61 % Elapsed time: 0.031839 seconds
% 0.14/5.61 % CPU time: 0.083475 seconds
% 0.14/5.61 % Total memory used: 2.438 MB
% 0.14/5.61 % Net memory used: 2.386 MB
%------------------------------------------------------------------------------