%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS108+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 : n007.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 12:59:42 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 15 unt; 0 def)
% Number of atoms : 189 ( 12 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 214 ( 79 ~; 75 |; 50 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 97 ( 80 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( cp2(X)
& ? [Y] :
( ca_Ax14(Y)
& rinvR(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [X] :
( cp1(X)
=> ca_Cx1(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [X] :
( cp2(X)
<=> ? [Y0] : ra_Px5(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [X] :
( cp2xcomp(X)
<=> ~ ? [Y] : ra_Px5(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [X] :
( ca_Ax14(X)
<=> ( ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 )
& ? [Y] :
( cp1(Y)
& rr(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [X] :
( ca_Cx1(X)
<=> ( cp4xcomp(X)
& cp3xcomp(X)
& cp5xcomp(X)
& cp2xcomp(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
cUnsatisfiable(i2003_11_14_17_21_04740),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,plain,
! [X] :
( ( ~ cp2(X)
| ! [Y] :
( ~ ca_Ax14(Y)
| ~ rinvR(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp2(X)
& ? [Y] :
( ca_Ax14(Y)
& rinvR(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f42]) ).
fof(f192,plain,
( ! [X] :
( ~ cp2(X)
| ! [Y] :
( ~ ca_Ax14(Y)
| ~ rinvR(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cp2(X)
& ? [Y] :
( ca_Ax14(Y)
& rinvR(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f191]) ).
fof(f193,plain,
( ! [X] :
( ~ cp2(X)
| ! [Y] :
( ~ ca_Ax14(Y)
| ~ rinvR(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cp2(X)
& ca_Ax14(sK0_skl(X))
& rinvR(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y,sK0_skl(X))],[f192]) ).
fof(f194,plain,
! [X0] :
( rinvR(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f195,plain,
! [X0] :
( ca_Ax14(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f196,plain,
! [X0] :
( cp2(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f198,plain,
! [X] :
( ca_Cx1(X)
| ~ cp1(X) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f199,plain,
! [X0] :
( ca_Cx1(X0)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f200,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px5(X,Y0)
| cp2(X) )
& ( ? [Y0] : ra_Px5(X,Y0)
| ~ cp2(X) ) ),
inference(NNF_transformation,[status(thm)],[f44]) ).
fof(f201,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px5(X,Y0)
| cp2(X) )
& ! [X] :
( ? [Y0] : ra_Px5(X,Y0)
| ~ cp2(X) ) ),
inference(miniscoping,[status(thm)],[f200]) ).
fof(f202,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px5(X,Y0)
| cp2(X) )
& ! [X] :
( ra_Px5(X,sK1_skl(X))
| ~ cp2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y0,sK1_skl(X))],[f201]) ).
fof(f203,plain,
! [X0] :
( ra_Px5(X0,sK1_skl(X0))
| ~ cp2(X0) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f207,plain,
! [X] :
( cp2xcomp(X)
<=> ! [Y] : ~ ra_Px5(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f208,plain,
! [X] :
( ( ? [Y] : ra_Px5(X,Y)
| cp2xcomp(X) )
& ( ! [Y] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f207]) ).
fof(f209,plain,
( ! [X] :
( ? [Y] : ra_Px5(X,Y)
| cp2xcomp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ),
inference(miniscoping,[status(thm)],[f208]) ).
fof(f210,plain,
( ! [X] :
( ra_Px5(X,sK2_skl(X))
| cp2xcomp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X))],[f209]) ).
fof(f211,plain,
! [X0,X1] :
( ~ ra_Px5(X0,X1)
| ~ cp2xcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f250,plain,
! [X] :
( ca_Ax14(X)
<=> ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cp1(Y)
& rr(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f251,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ca_Ax14(X) )
& ( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cp1(Y)
& rr(X,Y) ) )
| ~ ca_Ax14(X) ) ),
inference(NNF_transformation,[status(thm)],[f250]) ).
fof(f252,plain,
( ! [X] :
( ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ca_Ax14(X) )
& ! [X] :
( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cp1(Y)
& rr(X,Y) ) )
| ~ ca_Ax14(X) ) ),
inference(miniscoping,[status(thm)],[f251]) ).
fof(f253,plain,
( ! [X] :
( ( sK10_skl(X) != sK11_skl(X)
& rr(X,sK11_skl(X))
& rr(X,sK10_skl(X)) )
| ! [Y] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ca_Ax14(X) )
& ! [X] :
( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& cp1(sK9_skl(X))
& rr(X,sK9_skl(X)) )
| ~ ca_Ax14(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl]),skolemize(Y,sK9_skl(X)),skolemize(Y0,sK10_skl(X)),skolemize(Y1,sK11_skl(X))],[f252]) ).
fof(f254,plain,
! [X0] :
( rr(X0,sK9_skl(X0))
| ~ ca_Ax14(X0) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f255,plain,
! [X0] :
( cp1(sK9_skl(X0))
| ~ ca_Ax14(X0) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f256,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rr(X0,X2)
| ~ rr(X0,X1)
| ~ ca_Ax14(X0) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f260,plain,
! [X] :
( ( ~ cp4xcomp(X)
| ~ cp3xcomp(X)
| ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ca_Cx1(X) )
& ( ( cp4xcomp(X)
& cp3xcomp(X)
& cp5xcomp(X)
& cp2xcomp(X) )
| ~ ca_Cx1(X) ) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f261,plain,
( ! [X] :
( ~ cp4xcomp(X)
| ~ cp3xcomp(X)
| ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ca_Cx1(X) )
& ! [X] :
( ( cp4xcomp(X)
& cp3xcomp(X)
& cp5xcomp(X)
& cp2xcomp(X) )
| ~ ca_Cx1(X) ) ),
inference(miniscoping,[status(thm)],[f260]) ).
fof(f262,plain,
! [X0] :
( cp2xcomp(X0)
| ~ ca_Cx1(X0) ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f311,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f65]) ).
fof(f312,plain,
( ! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) )
& ! [X,Y] :
( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(miniscoping,[status(thm)],[f311]) ).
fof(f313,plain,
! [X0,X1] :
( rr(X1,X0)
| ~ rinvR(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f312]) ).
fof(f315,plain,
cUnsatisfiable(i2003_11_14_17_21_04740),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f317,plain,
rinvR(i2003_11_14_17_21_04740,sK0_skl(i2003_11_14_17_21_04740)),
inference(resolution,[status(thm)],[f194,f315]) ).
fof(f318,plain,
cp2(i2003_11_14_17_21_04740),
inference(resolution,[status(thm)],[f196,f315]) ).
fof(f319,plain,
ca_Ax14(sK0_skl(i2003_11_14_17_21_04740)),
inference(resolution,[status(thm)],[f195,f315]) ).
fof(f320,plain,
ra_Px5(i2003_11_14_17_21_04740,sK1_skl(i2003_11_14_17_21_04740)),
inference(resolution,[status(thm)],[f203,f318]) ).
fof(f341,plain,
cp1(sK9_skl(sK0_skl(i2003_11_14_17_21_04740))),
inference(resolution,[status(thm)],[f319,f255]) ).
fof(f342,plain,
rr(sK0_skl(i2003_11_14_17_21_04740),sK9_skl(sK0_skl(i2003_11_14_17_21_04740))),
inference(resolution,[status(thm)],[f319,f254]) ).
fof(f352,plain,
rr(sK0_skl(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740),
inference(resolution,[status(thm)],[f317,f313]) ).
fof(f357,plain,
~ cp2xcomp(i2003_11_14_17_21_04740),
inference(resolution,[status(thm)],[f320,f211]) ).
fof(f359,plain,
ca_Cx1(sK9_skl(sK0_skl(i2003_11_14_17_21_04740))),
inference(resolution,[status(thm)],[f341,f199]) ).
fof(f364,plain,
! [X0] :
( X0 = sK9_skl(sK0_skl(i2003_11_14_17_21_04740))
| ~ rr(sK0_skl(i2003_11_14_17_21_04740),X0)
| ~ ca_Ax14(sK0_skl(i2003_11_14_17_21_04740)) ),
inference(resolution,[status(thm)],[f342,f256]) ).
fof(f365,plain,
! [X0] :
( X0 = sK9_skl(sK0_skl(i2003_11_14_17_21_04740))
| ~ rr(sK0_skl(i2003_11_14_17_21_04740),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f364,f319]) ).
fof(f391,plain,
cp2xcomp(sK9_skl(sK0_skl(i2003_11_14_17_21_04740))),
inference(resolution,[status(thm)],[f359,f262]) ).
fof(f396,plain,
i2003_11_14_17_21_04740 = sK9_skl(sK0_skl(i2003_11_14_17_21_04740)),
inference(resolution,[status(thm)],[f365,f352]) ).
fof(f417,plain,
cp2xcomp(i2003_11_14_17_21_04740),
inference(backward_demodulation,[status(thm)],[f396,f391]) ).
fof(f428,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f417,f357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS108+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 22:51:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.038565 seconds
% 0.13/0.40 % CPU time: 0.103305 seconds
% 0.13/0.40 % Total memory used: 5.591 MB
% 0.13/0.40 % Net memory used: 5.329 MB
%------------------------------------------------------------------------------