%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS112+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 : n013.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 0.79s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 19 unt; 0 def)
% Number of atoms : 210 ( 13 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 226 ( 87 ~; 83 |; 43 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 129 ( 112 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cp(Y)
& rf(X,Y) )
& ? [Y] :
( ca_Ax2(Y)
& rf1(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X] :
( cp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X] :
( cpxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( rinvF1(X,Y)
=> ca_Vx3(Y) )
& cpxcomp(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cowlThing(Y)
& rs(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X,Y,Z] :
( ( rf1(X,Z)
& rf1(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X,Y] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
cUnsatisfiable(i2003_11_14_17_21_19256),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [X,Y] :
( rs(X,Y)
=> rf(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X,Y] :
( rs(X,Y)
=> rf1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| cUnsatisfiable(X) )
& ( ( ? [Y] :
( cp(Y)
& rf(X,Y) )
& ? [Y] :
( ca_Ax2(Y)
& rf1(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f117,plain,
( ! [X] :
( ! [Y] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ? [Y] :
( cp(Y)
& rf(X,Y) )
& ? [Y] :
( ca_Ax2(Y)
& rf1(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f118,plain,
( ! [X] :
( ! [Y] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf1(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cp(sK1_skl(X))
& rf(X,sK1_skl(X))
& ca_Ax2(sK0_skl(X))
& rf1(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl(X)),skolemize(Y,sK1_skl(X))],[f117]) ).
fof(f119,plain,
! [X0] :
( rf1(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
! [X0] :
( ca_Ax2(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f121,plain,
! [X0] :
( rf(X0,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f122,plain,
! [X0] :
( cp(sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f124,plain,
! [X] :
( cp(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f125,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(NNF_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(miniscoping,[status(thm)],[f125]) ).
fof(f127,plain,
( ! [X] :
( ra_Px1(X,sK2_skl(X))
| cp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X))],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cp(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f131,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f132,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ! [X] :
( ra_Px1(X,sK3_skl(X))
| ~ cpxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y0,sK3_skl(X))],[f131]) ).
fof(f133,plain,
! [X0] :
( ra_Px1(X0,sK3_skl(X0))
| ~ cpxcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f135,plain,
! [X] :
( ca_Ax2(X)
<=> ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) )
& cpxcomp(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f136,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Vx3(Y)
& rinvF1(X,Y) )
| ~ cpxcomp(X)
| ca_Ax2(X) )
& ( ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) )
& cpxcomp(X) )
| ~ ca_Ax2(X) ) ),
inference(NNF_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
( ! [X] :
( ? [Y] :
( ~ ca_Vx3(Y)
& rinvF1(X,Y) )
| ~ cpxcomp(X)
| ca_Ax2(X) )
& ! [X] :
( ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) )
& cpxcomp(X) )
| ~ ca_Ax2(X) ) ),
inference(miniscoping,[status(thm)],[f136]) ).
fof(f138,plain,
( ! [X] :
( ( ~ ca_Vx3(sK4_skl(X))
& rinvF1(X,sK4_skl(X)) )
| ~ cpxcomp(X)
| ca_Ax2(X) )
& ! [X] :
( ( ! [Y] :
( ca_Vx3(Y)
| ~ rinvF1(X,Y) )
& cpxcomp(X) )
| ~ ca_Ax2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Y,sK4_skl(X))],[f137]) ).
fof(f139,plain,
! [X0] :
( cpxcomp(X0)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
! [X0,X1] :
( ca_Vx3(X1)
| ~ rinvF1(X0,X1)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f143,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y) )
| ca_Vx3(X) )
& ( ? [Y] :
( cowlThing(Y)
& rs(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f144,plain,
( ! [X] :
( ! [Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ? [Y] :
( cowlThing(Y)
& rs(X,Y) )
| ~ ca_Vx3(X) ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f145,plain,
( ! [X] :
( ! [Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y) )
| ca_Vx3(X) )
& ! [X] :
( ( cowlThing(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))],[f144]) ).
fof(f146,plain,
! [X0] :
( rs(X0,sK5_skl(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f149,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f150,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rf(X,Z)
| ~ rf(X,Y) ) ),
inference(miniscoping,[status(thm)],[f149]) ).
fof(f151,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X2)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf1(X,Z)
| ~ rf1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f153,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rf1(X,Z)
| ~ rf1(X,Y) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X2)
| ~ rf1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f159,plain,
! [X,Y] :
( ( ~ rf1(Y,X)
| rinvF1(X,Y) )
& ( rf1(Y,X)
| ~ rinvF1(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f34]) ).
fof(f160,plain,
( ! [X,Y] :
( ~ rf1(Y,X)
| rinvF1(X,Y) )
& ! [X,Y] :
( rf1(Y,X)
| ~ rinvF1(X,Y) ) ),
inference(miniscoping,[status(thm)],[f159]) ).
fof(f162,plain,
! [X0,X1] :
( ~ rf1(X1,X0)
| rinvF1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f170,plain,
cUnsatisfiable(i2003_11_14_17_21_19256),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f171,plain,
! [X,Y] :
( rf(X,Y)
| ~ rs(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f172,plain,
! [X0,X1] :
( rf(X0,X1)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f173,plain,
! [X,Y] :
( rf1(X,Y)
| ~ rs(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f174,plain,
! [X0,X1] :
( rf1(X0,X1)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f176,plain,
rf1(i2003_11_14_17_21_19256,sK0_skl(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[f119,f170]) ).
fof(f177,plain,
ca_Ax2(sK0_skl(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[f120,f170]) ).
fof(f178,plain,
rf(i2003_11_14_17_21_19256,sK1_skl(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[f121,f170]) ).
fof(f179,plain,
cpxcomp(sK0_skl(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[f177,f139]) ).
fof(f180,plain,
cp(sK1_skl(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[f122,f170]) ).
fof(f182,plain,
ra_Px1(sK0_skl(i2003_11_14_17_21_19256),sK3_skl(sK0_skl(i2003_11_14_17_21_19256))),
inference(resolution,[status(thm)],[f133,f179]) ).
fof(f186,plain,
rinvF1(sK0_skl(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256),
inference(resolution,[status(thm)],[f176,f162]) ).
fof(f187,plain,
! [X0] :
( X0 = sK0_skl(i2003_11_14_17_21_19256)
| ~ rf1(i2003_11_14_17_21_19256,X0) ),
inference(resolution,[status(thm)],[f176,f154]) ).
fof(f190,plain,
! [X0] :
( X0 = sK1_skl(i2003_11_14_17_21_19256)
| ~ rf(i2003_11_14_17_21_19256,X0) ),
inference(resolution,[status(thm)],[f178,f151]) ).
fof(f192,plain,
( ca_Vx3(i2003_11_14_17_21_19256)
| ~ ca_Ax2(sK0_skl(i2003_11_14_17_21_19256)) ),
inference(resolution,[status(thm)],[f186,f140]) ).
fof(f193,plain,
ca_Vx3(i2003_11_14_17_21_19256),
inference(forward_subsumption_resolution,[status(thm)],[f192,f177]) ).
fof(f194,plain,
rs(i2003_11_14_17_21_19256,sK5_skl(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[f193,f146]) ).
fof(f197,plain,
rf1(i2003_11_14_17_21_19256,sK5_skl(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[f194,f174]) ).
fof(f199,plain,
rf(i2003_11_14_17_21_19256,sK5_skl(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[f194,f172]) ).
fof(f204,plain,
~ cp(sK0_skl(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[f182,f128]) ).
fof(f206,plain,
sK5_skl(i2003_11_14_17_21_19256) = sK0_skl(i2003_11_14_17_21_19256),
inference(resolution,[status(thm)],[f197,f187]) ).
fof(f211,plain,
sK5_skl(i2003_11_14_17_21_19256) = sK1_skl(i2003_11_14_17_21_19256),
inference(resolution,[status(thm)],[f199,f190]) ).
fof(f230,plain,
cp(sK0_skl(i2003_11_14_17_21_19256)),
inference(backward_demodulation,[status(thm)],[f231,f180]) ).
fof(f231,plain,
sK0_skl(i2003_11_14_17_21_19256) = sK1_skl(i2003_11_14_17_21_19256),
inference(forward_demodulation,[status(thm)],[f206,f211]) ).
fof(f232,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f230,f204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS112+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.76 % Computer : n013.cluster.edu
% 0.10/0.76 % Model : x86_64 x86_64
% 0.10/0.76 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.76 % Memory : 8046.5625MB
% 0.10/0.76 % OS : Linux 6.8.0-71-generic
% 0.10/0.76 % CPULimit : 300
% 0.10/0.76 % WCLimit : 300
% 0.10/0.76 % DateTime : Sun Sep 20 22:53:22 UTC 2026
% 0.10/0.76 % CPUTime :
% 0.10/0.77 % Drodi V4.1.1
% 0.10/0.79 % Refutation found
% 0.10/0.79 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.80 % Elapsed time: 0.034915 seconds
% 0.13/0.80 % CPU time: 0.082872 seconds
% 0.13/0.80 % Total memory used: 3.423 MB
% 0.13/0.80 % Net memory used: 3.285 MB
%------------------------------------------------------------------------------