%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS113+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:59:43 PM UTC 2026
% Result : Unsatisfiable 0.10s 10.54s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 12 unt; 0 def)
% Number of atoms : 186 ( 13 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 218 ( 83 ~; 75 |; 49 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 109 ( 89 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cpxcomp(X)
& ? [Y] :
( cp(Y)
& rs(X,Y) )
& ? [Y] :
( ca_Vx2(Y)
& rr(X,Y) )
& ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] :
( cp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] :
( cpxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X] :
( ca_Vx2(X)
<=> ! [Y] :
( rinvS(X,Y)
=> cp(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
cUnsatisfiable(i2003_11_14_17_21_22376),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X,Y] :
( rs(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( cpxcomp(X)
& ? [Y] :
( cp(Y)
& rs(X,Y) )
& ? [Y] :
( ca_Vx2(Y)
& rr(X,Y) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f82,plain,
! [X] :
( ( ~ cpxcomp(X)
| ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
| cUnsatisfiable(X) )
& ( ( cpxcomp(X)
& ? [Y] :
( cp(Y)
& rs(X,Y) )
& ? [Y] :
( ca_Vx2(Y)
& rr(X,Y) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
( ! [X] :
( ~ cpxcomp(X)
| ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cpxcomp(X)
& ? [Y] :
( cp(Y)
& rs(X,Y) )
& ? [Y] :
( ca_Vx2(Y)
& rr(X,Y) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f84,plain,
( ! [X] :
( ~ cpxcomp(X)
| ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ( sK2_skl(X) != sK3_skl(X)
& rr(X,sK3_skl(X))
& rr(X,sK2_skl(X)) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cpxcomp(X)
& cp(sK1_skl(X))
& rs(X,sK1_skl(X))
& ca_Vx2(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]),skolemize(Y,sK0_skl(X)),skolemize(Y,sK1_skl(X)),skolemize(Y0,sK2_skl(X)),skolemize(Y1,sK3_skl(X))],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rr(X0,X2)
| ~ rr(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
! [X0] :
( rr(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f87,plain,
! [X0] :
( ca_Vx2(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f88,plain,
! [X0] :
( rs(X0,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f90,plain,
! [X0] :
( cpxcomp(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f94,plain,
! [X] :
( cp(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f95,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(NNF_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(miniscoping,[status(thm)],[f95]) ).
fof(f97,plain,
( ! [X] :
( ra_Px1(X,sK4_skl(X))
| cp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Y,sK4_skl(X))],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cp(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f100,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f101,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ! [X] :
( ra_Px1(X,sK5_skl(X))
| ~ cpxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(Y0,sK5_skl(X))],[f101]) ).
fof(f103,plain,
! [X0] :
( ra_Px1(X0,sK5_skl(X0))
| ~ cpxcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
! [X] :
( ca_Vx2(X)
<=> ! [Y] :
( cp(Y)
| ~ rinvS(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f106,plain,
! [X] :
( ( ? [Y] :
( ~ cp(Y)
& rinvS(X,Y) )
| ca_Vx2(X) )
& ( ! [Y] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ca_Vx2(X) ) ),
inference(NNF_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
( ! [X] :
( ? [Y] :
( ~ cp(Y)
& rinvS(X,Y) )
| ca_Vx2(X) )
& ! [X] :
( ! [Y] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ca_Vx2(X) ) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f108,plain,
( ! [X] :
( ( ~ cp(sK6_skl(X))
& rinvS(X,sK6_skl(X)) )
| ca_Vx2(X) )
& ! [X] :
( ! [Y] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ca_Vx2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(Y,sK6_skl(X))],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( cp(X1)
| ~ rinvS(X0,X1)
| ~ ca_Vx2(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f112,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f113,plain,
( ! [X,Y] :
( ~ rs(Y,X)
| rinvS(X,Y) )
& ! [X,Y] :
( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(miniscoping,[status(thm)],[f112]) ).
fof(f115,plain,
! [X0,X1] :
( ~ rs(X1,X0)
| rinvS(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f116,plain,
cUnsatisfiable(i2003_11_14_17_21_22376),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f117,plain,
! [X,Y] :
( rr(X,Y)
| ~ rs(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f118,plain,
! [X0,X1] :
( rr(X0,X1)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
cpxcomp(i2003_11_14_17_21_22376),
inference(resolution,[status(thm)],[f116,f90]) ).
fof(f120,plain,
rs(i2003_11_14_17_21_22376,sK1_skl(i2003_11_14_17_21_22376)),
inference(resolution,[status(thm)],[f116,f88]) ).
fof(f121,plain,
rr(i2003_11_14_17_21_22376,sK0_skl(i2003_11_14_17_21_22376)),
inference(resolution,[status(thm)],[f116,f86]) ).
fof(f122,plain,
! [X0,X1] :
( X0 = X1
| ~ rr(i2003_11_14_17_21_22376,X1)
| ~ rr(i2003_11_14_17_21_22376,X0) ),
inference(resolution,[status(thm)],[f116,f85]) ).
fof(f123,plain,
ra_Px1(i2003_11_14_17_21_22376,sK5_skl(i2003_11_14_17_21_22376)),
inference(resolution,[status(thm)],[f119,f103]) ).
fof(f143,plain,
! [X0] :
( X0 = sK0_skl(i2003_11_14_17_21_22376)
| ~ rr(i2003_11_14_17_21_22376,X0) ),
inference(resolution,[status(thm)],[f122,f121]) ).
fof(f146,plain,
~ cp(i2003_11_14_17_21_22376),
inference(resolution,[status(thm)],[f123,f98]) ).
fof(f149,plain,
! [X0] :
( ~ rinvS(X0,i2003_11_14_17_21_22376)
| ~ ca_Vx2(X0) ),
inference(resolution,[status(thm)],[f146,f109]) ).
fof(f152,plain,
! [X0] :
( ~ rs(i2003_11_14_17_21_22376,X0)
| X0 = sK0_skl(i2003_11_14_17_21_22376) ),
inference(resolution,[status(thm)],[f143,f118]) ).
fof(f160,plain,
! [X0] :
( ~ rs(i2003_11_14_17_21_22376,X0)
| ~ ca_Vx2(X0) ),
inference(resolution,[status(thm)],[f149,f115]) ).
fof(f165,plain,
sK1_skl(i2003_11_14_17_21_22376) = sK0_skl(i2003_11_14_17_21_22376),
inference(resolution,[status(thm)],[f152,f120]) ).
fof(f167,plain,
rs(i2003_11_14_17_21_22376,sK0_skl(i2003_11_14_17_21_22376)),
inference(backward_demodulation,[status(thm)],[f165,f120]) ).
fof(f183,plain,
~ ca_Vx2(sK0_skl(i2003_11_14_17_21_22376)),
inference(resolution,[status(thm)],[f160,f167]) ).
fof(f185,plain,
~ cUnsatisfiable(i2003_11_14_17_21_22376),
inference(resolution,[status(thm)],[f183,f87]) ).
fof(f188,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f185,f116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS113+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.52 % Computer : n010.cluster.edu
% 0.10/10.52 % Model : x86_64 x86_64
% 0.10/10.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.52 % Memory : 8046.5625MB
% 0.10/10.52 % OS : Linux 6.8.0-71-generic
% 0.10/10.52 % CPULimit : 300
% 0.10/10.52 % WCLimit : 300
% 0.10/10.52 % DateTime : Sun Sep 20 22:54:08 UTC 2026
% 0.10/10.52 % CPUTime :
% 0.10/10.53 % Drodi V4.1.1
% 0.10/10.54 % Refutation found
% 0.10/10.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/10.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/10.55 % Elapsed time: 0.025508 seconds
% 0.10/10.55 % CPU time: 0.084641 seconds
% 0.10/10.55 % Total memory used: 2.826 MB
% 0.10/10.55 % Net memory used: 2.753 MB
%------------------------------------------------------------------------------