%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS121+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 : n004.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 12:59:44 PM UTC 2026
% Result : Unsatisfiable 0.02s 0.38s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 7 unt; 0 def)
% Number of atoms : 186 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 219 ( 88 ~; 83 |; 38 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 110 ( 96 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cp1(X)
& ? [Y] :
( ca_Vx3(Y)
& rr(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X] :
( cp1(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X] :
( cp1xcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( rinvR(X,Y)
=> cp1xcomp(Y) )
& cp1(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( ca_Ax2(Y)
& rr(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Y,Z] :
( ( rr(Y,Z)
& rr(X,Y) )
=> rr(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
cUnsatisfiable(i2003_11_14_17_21_5199),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,plain,
! [X] :
( ( ~ cp1(X)
| ! [Y] :
( ~ ca_Vx3(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp1(X)
& ? [Y] :
( ca_Vx3(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f97,plain,
( ! [X] :
( ~ cp1(X)
| ! [Y] :
( ~ ca_Vx3(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cp1(X)
& ? [Y] :
( ca_Vx3(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
( ! [X] :
( ~ cp1(X)
| ! [Y] :
( ~ ca_Vx3(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cp1(X)
& ca_Vx3(sK0_skl(X))
& rr(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y,sK0_skl(X))],[f97]) ).
fof(f99,plain,
! [X0] :
( rr(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0] :
( ca_Vx3(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X0] :
( cp1(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f103,plain,
! [X] :
( cp1(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f104,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp1(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(NNF_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cp1(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
( ! [X] :
( ra_Px1(X,sK1_skl(X))
| cp1(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl(X))],[f105]) ).
fof(f107,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cp1xcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f110,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cp1xcomp(X) ) ),
inference(miniscoping,[status(thm)],[f109]) ).
fof(f111,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ! [X] :
( ra_Px1(X,sK2_skl(X))
| ~ cp1xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y0,sK2_skl(X))],[f110]) ).
fof(f112,plain,
! [X0] :
( ra_Px1(X0,sK2_skl(X0))
| ~ cp1xcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f114,plain,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) )
& cp1(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f115,plain,
! [X] :
( ( ? [Y] :
( ~ cp1xcomp(Y)
& rinvR(X,Y) )
| ~ cp1(X)
| ca_Ax2(X) )
& ( ( ! [Y] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) )
& cp1(X) )
| ~ ca_Ax2(X) ) ),
inference(NNF_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
( ! [X] :
( ? [Y] :
( ~ cp1xcomp(Y)
& rinvR(X,Y) )
| ~ cp1(X)
| ca_Ax2(X) )
& ! [X] :
( ( ! [Y] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) )
& cp1(X) )
| ~ ca_Ax2(X) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
( ! [X] :
( ( ~ cp1xcomp(sK3_skl(X))
& rinvR(X,sK3_skl(X)) )
| ~ cp1(X)
| ca_Ax2(X) )
& ! [X] :
( ( ! [Y] :
( cp1xcomp(Y)
| ~ rinvR(X,Y) )
& cp1(X) )
| ~ ca_Ax2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y,sK3_skl(X))],[f116]) ).
fof(f119,plain,
! [X0,X1] :
( cp1xcomp(X1)
| ~ rinvR(X0,X1)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f122,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) )
| ca_Vx3(X) )
& ( ? [Y] :
( ca_Ax2(Y)
& rr(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f123,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ? [Y] :
( ca_Ax2(Y)
& rr(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(miniscoping,[status(thm)],[f122]) ).
fof(f124,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ( ca_Ax2(sK4_skl(X))
& rr(X,sK4_skl(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Y,sK4_skl(X))],[f123]) ).
fof(f125,plain,
! [X0] :
( rr(X0,sK4_skl(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
! [X0] :
( ca_Ax2(sK4_skl(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
! [X0,X1] :
( ~ ca_Ax2(X1)
| ~ rr(X0,X1)
| ca_Vx3(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f135,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f136,plain,
( ! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) )
& ! [X,Y] :
( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(miniscoping,[status(thm)],[f135]) ).
fof(f138,plain,
! [X0,X1] :
( ~ rr(X1,X0)
| rinvR(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f139,plain,
! [X,Y,Z] :
( rr(X,Z)
| ~ rr(Y,Z)
| ~ rr(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f140,plain,
! [X,Z] :
( rr(X,Z)
| ! [Y] :
( ~ rr(Y,Z)
| ~ rr(X,Y) ) ),
inference(miniscoping,[status(thm)],[f139]) ).
fof(f141,plain,
! [X0,X1,X2] :
( rr(X0,X2)
| ~ rr(X1,X2)
| ~ rr(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f142,plain,
cUnsatisfiable(i2003_11_14_17_21_5199),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f144,plain,
cp1(i2003_11_14_17_21_5199),
inference(resolution,[status(thm)],[f101,f142]) ).
fof(f151,plain,
! [X0] :
( ~ cp1(X0)
| ~ cp1xcomp(X0) ),
inference(resolution,[status(thm)],[f112,f107]) ).
fof(f153,plain,
! [X0] :
( rinvR(sK4_skl(X0),X0)
| ~ ca_Vx3(X0) ),
inference(resolution,[status(thm)],[f125,f138]) ).
fof(f157,plain,
! [X0] :
( ~ ca_Vx3(X0)
| cp1xcomp(X0)
| ~ ca_Ax2(sK4_skl(X0)) ),
inference(resolution,[status(thm)],[f119,f153]) ).
fof(f159,plain,
! [X0] :
( ~ ca_Vx3(X0)
| cp1xcomp(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f126]) ).
fof(f167,plain,
! [X0,X1] :
( ~ ca_Vx3(X1)
| rr(X0,sK4_skl(X1))
| ~ rr(X0,X1) ),
inference(resolution,[status(thm)],[f141,f125]) ).
fof(f175,plain,
! [X0,X1] :
( ~ ca_Ax2(sK4_skl(X1))
| ca_Vx3(X0)
| ~ ca_Vx3(X1)
| ~ rr(X0,X1) ),
inference(resolution,[status(thm)],[f167,f127]) ).
fof(f178,plain,
! [X0,X1] :
( ca_Vx3(X0)
| ~ ca_Vx3(X1)
| ~ rr(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f126]) ).
fof(f182,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ca_Vx3(X0)
| ~ ca_Vx3(sK0_skl(X0)) ),
inference(resolution,[status(thm)],[f178,f99]) ).
fof(f183,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ca_Vx3(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f182,f100]) ).
fof(f184,plain,
ca_Vx3(i2003_11_14_17_21_5199),
inference(resolution,[status(thm)],[f183,f142]) ).
fof(f185,plain,
cp1xcomp(i2003_11_14_17_21_5199),
inference(resolution,[status(thm)],[f184,f159]) ).
fof(f186,plain,
~ cp1(i2003_11_14_17_21_5199),
inference(resolution,[status(thm)],[f185,f151]) ).
fof(f187,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f186,f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS121+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sun Sep 20 22:54:08 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Drodi V4.1.1
% 0.02/0.38 % Refutation found
% 0.02/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.02/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.40 % Elapsed time: 0.037063 seconds
% 0.02/0.40 % CPU time: 0.083305 seconds
% 0.02/0.40 % Total memory used: 2.892 MB
% 0.02/0.40 % Net memory used: 2.776 MB
%------------------------------------------------------------------------------