%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS122+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 : 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 12:59:44 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 15 unt; 0 def)
% Number of atoms : 164 ( 6 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 178 ( 69 ~; 65 |; 34 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 97 ( 83 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ? [Y] :
( ca_Ax2(Y)
& rf(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] :
( rinvF(X,Y)
=> ca_Vx3(Y) )
& cp1(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cp1xcomp(Y)
& rf(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
cUnsatisfiable(i2003_11_14_17_21_55116),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ( ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f97,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ca_Ax2(sK0_skl(X))
& rf(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] :
( rf(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0] :
( ca_Ax2(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f102,plain,
! [X] :
( cp1(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f103,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp1(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(NNF_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cp1(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(miniscoping,[status(thm)],[f103]) ).
fof(f105,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))],[f104]) ).
fof(f106,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f108,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cp1xcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f109,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cp1xcomp(X) ) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f110,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))],[f109]) ).
fof(f111,plain,
! [X0] :
( ra_Px1(X0,sK2_skl(X0))
| ~ cp1xcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& cp1(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f114,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Vx3(Y)
& rinvF(X,Y) )
| ~ cp1(X)
| ca_Ax2(X) )
& ( ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& cp1(X) )
| ~ ca_Ax2(X) ) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
( ! [X] :
( ? [Y] :
( ~ ca_Vx3(Y)
& rinvF(X,Y) )
| ~ cp1(X)
| ca_Ax2(X) )
& ! [X] :
( ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& cp1(X) )
| ~ ca_Ax2(X) ) ),
inference(miniscoping,[status(thm)],[f114]) ).
fof(f116,plain,
( ! [X] :
( ( ~ ca_Vx3(sK3_skl(X))
& rinvF(X,sK3_skl(X)) )
| ~ cp1(X)
| ca_Ax2(X) )
& ! [X] :
( ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& cp1(X) )
| ~ ca_Ax2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y,sK3_skl(X))],[f115]) ).
fof(f117,plain,
! [X0] :
( cp1(X0)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( ca_Vx3(X1)
| ~ rinvF(X0,X1)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f121,plain,
! [X] :
( ( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) )
| ca_Vx3(X) )
& ( ? [Y] :
( cp1xcomp(Y)
& rf(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f122,plain,
( ! [X] :
( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ? [Y] :
( cp1xcomp(Y)
& rf(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(miniscoping,[status(thm)],[f121]) ).
fof(f123,plain,
( ! [X] :
( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ( cp1xcomp(sK4_skl(X))
& rf(X,sK4_skl(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Y,sK4_skl(X))],[f122]) ).
fof(f124,plain,
! [X0] :
( rf(X0,sK4_skl(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [X0] :
( cp1xcomp(sK4_skl(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f127,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f128,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rf(X,Z)
| ~ rf(X,Y) ) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X2)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f131,plain,
( ! [X,Y] :
( ~ rf(Y,X)
| rinvF(X,Y) )
& ! [X,Y] :
( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f133,plain,
! [X0,X1] :
( ~ rf(X1,X0)
| rinvF(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f141,plain,
cUnsatisfiable(i2003_11_14_17_21_55116),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f143,plain,
rf(i2003_11_14_17_21_55116,sK0_skl(i2003_11_14_17_21_55116)),
inference(resolution,[status(thm)],[f99,f141]) ).
fof(f144,plain,
ca_Ax2(sK0_skl(i2003_11_14_17_21_55116)),
inference(resolution,[status(thm)],[f100,f141]) ).
fof(f145,plain,
cp1(sK0_skl(i2003_11_14_17_21_55116)),
inference(resolution,[status(thm)],[f144,f117]) ).
fof(f150,plain,
rinvF(sK0_skl(i2003_11_14_17_21_55116),i2003_11_14_17_21_55116),
inference(resolution,[status(thm)],[f143,f133]) ).
fof(f151,plain,
! [X0] :
( X0 = sK0_skl(i2003_11_14_17_21_55116)
| ~ rf(i2003_11_14_17_21_55116,X0) ),
inference(resolution,[status(thm)],[f143,f129]) ).
fof(f157,plain,
( ca_Vx3(i2003_11_14_17_21_55116)
| ~ ca_Ax2(sK0_skl(i2003_11_14_17_21_55116)) ),
inference(resolution,[status(thm)],[f150,f118]) ).
fof(f158,plain,
ca_Vx3(i2003_11_14_17_21_55116),
inference(forward_subsumption_resolution,[status(thm)],[f157,f144]) ).
fof(f161,plain,
rf(i2003_11_14_17_21_55116,sK4_skl(i2003_11_14_17_21_55116)),
inference(resolution,[status(thm)],[f158,f124]) ).
fof(f162,plain,
cp1xcomp(sK4_skl(i2003_11_14_17_21_55116)),
inference(resolution,[status(thm)],[f158,f125]) ).
fof(f163,plain,
sK4_skl(i2003_11_14_17_21_55116) = sK0_skl(i2003_11_14_17_21_55116),
inference(resolution,[status(thm)],[f161,f151]) ).
fof(f168,plain,
ra_Px1(sK4_skl(i2003_11_14_17_21_55116),sK2_skl(sK4_skl(i2003_11_14_17_21_55116))),
inference(resolution,[status(thm)],[f162,f111]) ).
fof(f174,plain,
ra_Px1(sK0_skl(i2003_11_14_17_21_55116),sK2_skl(sK4_skl(i2003_11_14_17_21_55116))),
inference(forward_demodulation,[status(thm)],[f163,f168]) ).
fof(f175,plain,
ra_Px1(sK0_skl(i2003_11_14_17_21_55116),sK2_skl(sK0_skl(i2003_11_14_17_21_55116))),
inference(forward_demodulation,[status(thm)],[f163,f174]) ).
fof(f177,plain,
~ cp1(sK0_skl(i2003_11_14_17_21_55116)),
inference(resolution,[status(thm)],[f175,f106]) ).
fof(f178,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f177,f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS122+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n011.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 22:54:12 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.11/0.36 % Refutation found
% 0.11/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.38 % Elapsed time: 0.031067 seconds
% 0.11/0.38 % CPU time: 0.087162 seconds
% 0.11/0.38 % Total memory used: 2.904 MB
% 0.11/0.38 % Net memory used: 2.790 MB
%------------------------------------------------------------------------------