%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS084+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 : n019.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 12:59:39 PM UTC 2026
% Result : Unsatisfiable 0.12s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 15 unt; 0 def)
% Number of atoms : 165 ( 6 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 186 ( 71 ~; 65 |; 42 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 88 ( 75 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ~ cc(X)
& ! [Y] :
( rinvR(X,Y)
=> ? [Z] :
( cd(Z)
& rinvF(Y,Z) ) )
& ? [Y] :
( cd(Y)
& rinvF(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] :
( cd(X)
<=> ( cc(X)
& ? [Y] :
( ~ cc(Y)
& rf(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
cUnsatisfiable(i2003_11_14_17_19_35232),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X,Y] :
( rf(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ~ cc(X)
& ! [Y] :
( ? [Z] :
( cd(Z)
& rinvF(Y,Z) )
| ~ rinvR(X,Y) )
& ? [Y] :
( cd(Y)
& rinvF(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f79,plain,
! [X] :
( ( cc(X)
| ? [Y] :
( ! [Z] :
( ~ cd(Z)
| ~ rinvF(Y,Z) )
& rinvR(X,Y) )
| ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| cUnsatisfiable(X) )
& ( ( ~ cc(X)
& ! [Y] :
( ? [Z] :
( cd(Z)
& rinvF(Y,Z) )
| ~ rinvR(X,Y) )
& ? [Y] :
( cd(Y)
& rinvF(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
( ! [X] :
( cc(X)
| ? [Y] :
( ! [Z] :
( ~ cd(Z)
| ~ rinvF(Y,Z) )
& rinvR(X,Y) )
| ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ~ cc(X)
& ! [Y] :
( ? [Z] :
( cd(Z)
& rinvF(Y,Z) )
| ~ rinvR(X,Y) )
& ? [Y] :
( cd(Y)
& rinvF(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f79]) ).
fof(f81,plain,
( ! [X] :
( cc(X)
| ( ! [Z] :
( ~ cd(Z)
| ~ rinvF(sK2_skl(X),Z) )
& rinvR(X,sK2_skl(X)) )
| ! [Y] :
( ~ cd(Y)
| ~ rinvF(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ~ cc(X)
& ! [Y] :
( ( cd(sK1_skl(Y,X))
& rinvF(Y,sK1_skl(Y,X)) )
| ~ rinvR(X,Y) )
& cd(sK0_skl(X))
& rinvF(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Y,sK0_skl(X)),skolemize(Z,sK1_skl(Y,X)),skolemize(Y,sK2_skl(X))],[f80]) ).
fof(f82,plain,
! [X0] :
( rinvF(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
! [X0] :
( cd(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f84,plain,
! [X0,X1] :
( rinvF(X1,sK1_skl(X1,X0))
| ~ rinvR(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f85,plain,
! [X0,X1] :
( cd(sK1_skl(X1,X0))
| ~ rinvR(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f89,plain,
! [X] :
( ( ~ cc(X)
| ! [Y] :
( cc(Y)
| ~ rf(X,Y) )
| cd(X) )
& ( ( cc(X)
& ? [Y] :
( ~ cc(Y)
& rf(X,Y) ) )
| ~ cd(X) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f90,plain,
( ! [X] :
( ~ cc(X)
| ! [Y] :
( cc(Y)
| ~ rf(X,Y) )
| cd(X) )
& ! [X] :
( ( cc(X)
& ? [Y] :
( ~ cc(Y)
& rf(X,Y) ) )
| ~ cd(X) ) ),
inference(miniscoping,[status(thm)],[f89]) ).
fof(f91,plain,
( ! [X] :
( ~ cc(X)
| ! [Y] :
( cc(Y)
| ~ rf(X,Y) )
| cd(X) )
& ! [X] :
( ( cc(X)
& ~ cc(sK3_skl(X))
& rf(X,sK3_skl(X)) )
| ~ cd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y,sK3_skl(X))],[f90]) ).
fof(f92,plain,
! [X0] :
( rf(X0,sK3_skl(X0))
| ~ cd(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [X0] :
( ~ cc(sK3_skl(X0))
| ~ cd(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
! [X0] :
( cc(X0)
| ~ cd(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f96,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f97,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rf(X,Z)
| ~ rf(X,Y) ) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X2)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f100,plain,
( ! [X,Y] :
( ~ rf(Y,X)
| rinvF(X,Y) )
& ! [X,Y] :
( rf(Y,X)
| ~ rinvF(X,Y) ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( rf(X1,X0)
| ~ rinvF(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f103,plain,
! [X,Y] :
( ( ~ rr(Y,X)
| rinvR(X,Y) )
& ( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f104,plain,
( ! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) )
& ! [X,Y] :
( rr(Y,X)
| ~ rinvR(X,Y) ) ),
inference(miniscoping,[status(thm)],[f103]) ).
fof(f106,plain,
! [X0,X1] :
( ~ rr(X1,X0)
| rinvR(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f110,plain,
cUnsatisfiable(i2003_11_14_17_19_35232),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f111,plain,
! [X,Y] :
( rr(X,Y)
| ~ rf(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f112,plain,
! [X0,X1] :
( rr(X0,X1)
| ~ rf(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f114,plain,
rinvF(i2003_11_14_17_19_35232,sK0_skl(i2003_11_14_17_19_35232)),
inference(resolution,[status(thm)],[f82,f110]) ).
fof(f115,plain,
cd(sK0_skl(i2003_11_14_17_19_35232)),
inference(resolution,[status(thm)],[f83,f110]) ).
fof(f116,plain,
cc(sK0_skl(i2003_11_14_17_19_35232)),
inference(resolution,[status(thm)],[f115,f94]) ).
fof(f119,plain,
rf(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
inference(resolution,[status(thm)],[f114,f101]) ).
fof(f121,plain,
rr(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
inference(resolution,[status(thm)],[f119,f112]) ).
fof(f130,plain,
rinvR(i2003_11_14_17_19_35232,sK0_skl(i2003_11_14_17_19_35232)),
inference(resolution,[status(thm)],[f121,f106]) ).
fof(f132,plain,
( cd(sK1_skl(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))
| ~ cUnsatisfiable(i2003_11_14_17_19_35232) ),
inference(resolution,[status(thm)],[f130,f85]) ).
fof(f133,plain,
( rinvF(sK0_skl(i2003_11_14_17_19_35232),sK1_skl(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))
| ~ cUnsatisfiable(i2003_11_14_17_19_35232) ),
inference(resolution,[status(thm)],[f130,f84]) ).
fof(f134,plain,
cd(sK1_skl(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)),
inference(forward_subsumption_resolution,[status(thm)],[f132,f110]) ).
fof(f135,plain,
rinvF(sK0_skl(i2003_11_14_17_19_35232),sK1_skl(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)),
inference(forward_subsumption_resolution,[status(thm)],[f133,f110]) ).
fof(f147,plain,
rf(sK1_skl(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),sK3_skl(sK1_skl(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))),
inference(resolution,[status(thm)],[f134,f92]) ).
fof(f150,plain,
rf(sK1_skl(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),sK0_skl(i2003_11_14_17_19_35232)),
inference(resolution,[status(thm)],[f135,f101]) ).
fof(f155,plain,
! [X0] :
( X0 = sK3_skl(sK1_skl(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))
| ~ rf(sK1_skl(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),X0) ),
inference(resolution,[status(thm)],[f147,f98]) ).
fof(f169,plain,
sK0_skl(i2003_11_14_17_19_35232) = sK3_skl(sK1_skl(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)),
inference(resolution,[status(thm)],[f155,f150]) ).
fof(f196,plain,
( ~ cc(sK0_skl(i2003_11_14_17_19_35232))
| ~ cd(sK1_skl(sK0_skl(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)) ),
inference(paramodulation,[status(thm)],[f169,f93]) ).
fof(f200,plain,
~ cc(sK0_skl(i2003_11_14_17_19_35232)),
inference(forward_subsumption_resolution,[status(thm)],[f196,f134]) ).
fof(f201,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f200,f116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS084+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.37 % Computer : n019.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Sun Sep 20 22:53:28 UTC 2026
% 0.12/5.37 % CPUTime :
% 0.12/5.38 % Drodi V4.1.1
% 0.12/5.40 % Refutation found
% 0.12/5.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.41 % Elapsed time: 0.030208 seconds
% 0.14/5.41 % CPU time: 0.084996 seconds
% 0.14/5.41 % Total memory used: 2.695 MB
% 0.14/5.41 % Net memory used: 2.598 MB
%------------------------------------------------------------------------------