%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS109+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 : n016.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 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 8 unt; 2 def)
% Number of atoms : 223 ( 6 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 252 ( 100 ~; 94 |; 43 &)
% ( 11 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 123 ( 107 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) )
& cpxcomp(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X] :
( cp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X] :
( cpxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( rinvF(X,Y)
=> ca_Vx3(Y) )
& ! [Y] :
( rinvS(X,Y)
=> cp(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cp(Y)
& rs(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
cUnsatisfiable(i2003_11_14_17_21_08508),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [X,Y] :
( rs(X,Y)
=> rf(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| ~ cpxcomp(X)
| cUnsatisfiable(X) )
& ( ( ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) )
& cpxcomp(X) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f117,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| ~ cpxcomp(X)
| cUnsatisfiable(X) )
& ! [X] :
( ( ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) )
& cpxcomp(X) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f118,plain,
( ! [X] :
( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| ~ cpxcomp(X)
| cUnsatisfiable(X) )
& ! [X] :
( ( ca_Ax2(sK0_skl(X))
& rf(X,sK0_skl(X))
& cpxcomp(X) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y,sK0_skl(X))],[f117]) ).
fof(f119,plain,
! [X0] :
( cpxcomp(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
! [X0] :
( rf(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f121,plain,
! [X0] :
( ca_Ax2(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f123,plain,
! [X] :
( cp(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f124,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(NNF_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(miniscoping,[status(thm)],[f124]) ).
fof(f126,plain,
( ! [X] :
( ra_Px1(X,sK1_skl(X))
| cp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl(X))],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cp(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f129,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f130,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(miniscoping,[status(thm)],[f129]) ).
fof(f131,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ! [X] :
( ra_Px1(X,sK2_skl(X))
| ~ cpxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y0,sK2_skl(X))],[f130]) ).
fof(f132,plain,
! [X0] :
( ra_Px1(X0,sK2_skl(X0))
| ~ cpxcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f134,plain,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& ! [Y] :
( cp(Y)
| ~ rinvS(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f135,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Vx3(Y)
& rinvF(X,Y) )
| ? [Y] :
( ~ cp(Y)
& rinvS(X,Y) )
| ca_Ax2(X) )
& ( ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& ! [Y] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ca_Ax2(X) ) ),
inference(NNF_transformation,[status(thm)],[f134]) ).
fof(f136,plain,
( ! [X] :
( ? [Y] :
( ~ ca_Vx3(Y)
& rinvF(X,Y) )
| ? [Y] :
( ~ cp(Y)
& rinvS(X,Y) )
| ca_Ax2(X) )
& ! [X] :
( ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& ! [Y] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ca_Ax2(X) ) ),
inference(miniscoping,[status(thm)],[f135]) ).
fof(f137,plain,
( ! [X] :
( ( ~ ca_Vx3(sK4_skl(X))
& rinvF(X,sK4_skl(X)) )
| ( ~ cp(sK3_skl(X))
& rinvS(X,sK3_skl(X)) )
| ca_Ax2(X) )
& ! [X] :
( ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) )
& ! [Y] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ca_Ax2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(Y,sK3_skl(X)),skolemize(Y,sK4_skl(X))],[f136]) ).
fof(f138,plain,
! [X0,X1] :
( cp(X1)
| ~ rinvS(X0,X1)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [X0,X1] :
( ca_Vx3(X1)
| ~ rinvF(X0,X1)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f144,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ca_Vx3(X) )
& ( ? [Y] :
( cp(Y)
& rs(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f145,plain,
( ! [X] :
( ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ? [Y] :
( cp(Y)
& rs(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f146,plain,
( ! [X] :
( ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ( cp(sK5_skl(X))
& rs(X,sK5_skl(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(Y,sK5_skl(X))],[f145]) ).
fof(f147,plain,
! [X0] :
( rs(X0,sK5_skl(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f150,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f151,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rf(X,Z)
| ~ rf(X,Y) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f152,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X2)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f156,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f157,plain,
( ! [X,Y] :
( ~ rf(Y,X)
| rinvF(X,Y) )
& ! [X,Y] :
( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(miniscoping,[status(thm)],[f156]) ).
fof(f159,plain,
! [X0,X1] :
( ~ rf(X1,X0)
| rinvF(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f164,plain,
! [X,Y] :
( ( ~ rs(Y,X)
| rinvS(X,Y) )
& ( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f165,plain,
( ! [X,Y] :
( ~ rs(Y,X)
| rinvS(X,Y) )
& ! [X,Y] :
( rs(Y,X)
| ~ rinvS(X,Y) ) ),
inference(miniscoping,[status(thm)],[f164]) ).
fof(f167,plain,
! [X0,X1] :
( ~ rs(X1,X0)
| rinvS(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f171,plain,
cUnsatisfiable(i2003_11_14_17_21_08508),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f172,plain,
! [X,Y] :
( rf(X,Y)
| ~ rs(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f173,plain,
! [X0,X1] :
( rf(X0,X1)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f176,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ra_Px1(X0,sK2_skl(X0)) ),
inference(resolution,[status(thm)],[f132,f119]) ).
fof(f177,plain,
rf(i2003_11_14_17_21_08508,sK0_skl(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[f171,f120]) ).
fof(f178,plain,
! [X0] :
( X0 = sK0_skl(i2003_11_14_17_21_08508)
| ~ rf(i2003_11_14_17_21_08508,X0) ),
inference(resolution,[status(thm)],[f177,f152]) ).
fof(f179,plain,
rinvF(sK0_skl(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[f177,f159]) ).
fof(f187,definition,
( sQ2_spl
<=> ca_Ax2(sK0_skl(i2003_11_14_17_21_08508)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( sQ2_spl
| ~ ca_Ax2(sK0_skl(i2003_11_14_17_21_08508)) ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f191,plain,
( sQ2_spl
| ~ cUnsatisfiable(i2003_11_14_17_21_08508) ),
inference(resolution,[status(thm)],[f189,f121]) ).
fof(f194,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f171]) ).
fof(f195,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( ca_Vx3(i2003_11_14_17_21_08508)
| ~ ca_Ax2(sK0_skl(i2003_11_14_17_21_08508)) ),
inference(resolution,[status(thm)],[f179,f139]) ).
fof(f198,definition,
( sQ3_spl
<=> ca_Vx3(i2003_11_14_17_21_08508) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( ~ sQ3_spl
| ca_Vx3(i2003_11_14_17_21_08508) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f197,f187,f198]) ).
fof(f202,plain,
ra_Px1(i2003_11_14_17_21_08508,sK2_skl(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[f176,f171]) ).
fof(f205,plain,
~ cp(i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[f202,f127]) ).
fof(f206,plain,
( ~ sQ3_spl
| rs(i2003_11_14_17_21_08508,sK5_skl(i2003_11_14_17_21_08508)) ),
inference(resolution,[status(thm)],[f199,f147]) ).
fof(f208,plain,
! [X0] :
( ~ rinvS(X0,i2003_11_14_17_21_08508)
| ~ ca_Ax2(X0) ),
inference(resolution,[status(thm)],[f205,f138]) ).
fof(f212,plain,
( ~ sQ3_spl
| rf(i2003_11_14_17_21_08508,sK5_skl(i2003_11_14_17_21_08508)) ),
inference(resolution,[status(thm)],[f206,f173]) ).
fof(f213,plain,
( ~ sQ3_spl
| rinvS(sK5_skl(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ),
inference(resolution,[status(thm)],[f206,f167]) ).
fof(f224,plain,
( ~ sQ3_spl
| sK5_skl(i2003_11_14_17_21_08508) = sK0_skl(i2003_11_14_17_21_08508) ),
inference(resolution,[status(thm)],[f212,f178]) ).
fof(f234,plain,
( ~ sQ3_spl
| rinvS(sK0_skl(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ),
inference(backward_demodulation,[status(thm)],[f224,f213]) ).
fof(f255,plain,
( ~ sQ3_spl
| ~ ca_Ax2(sK0_skl(i2003_11_14_17_21_08508)) ),
inference(resolution,[status(thm)],[f234,f208]) ).
fof(f257,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f255,f187,f198]) ).
fof(f258,plain,
$false,
inference(sat_refutation,[status(thm)],[f195,f201,f257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS109+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 22:58:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.40 % Elapsed time: 0.033801 seconds
% 0.10/0.40 % CPU time: 0.086280 seconds
% 0.10/0.40 % Total memory used: 3.373 MB
% 0.10/0.40 % Net memory used: 3.264 MB
%------------------------------------------------------------------------------