%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS110+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 : n014.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 0.07s 0.34s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 4 unt; 0 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 157 ( 63 ~; 54 |; 33 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 74 ( 59 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( rs(X,Y)
=> cpxcomp(Y) )
& ? [Y] :
( ca_Ax2(Y)
& rs(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X] :
( cp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X] :
( cpxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X] :
( ca_Ax2(X)
<=> ( ? [Y] :
( cp(Y)
& rinvS(X,Y) )
& cp(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
cUnsatisfiable(i2003_11_14_17_21_12565),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f111,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( cpxcomp(Y)
| ~ rs(X,Y) )
& ? [Y] :
( ca_Ax2(Y)
& rs(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f112,plain,
! [X] :
( ( ? [Y] :
( ~ cpxcomp(Y)
& rs(X,Y) )
| ! [Y] :
( ~ ca_Ax2(Y)
| ~ rs(X,Y) )
| cUnsatisfiable(X) )
& ( ( ! [Y] :
( cpxcomp(Y)
| ~ rs(X,Y) )
& ? [Y] :
( ca_Ax2(Y)
& rs(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
( ! [X] :
( ? [Y] :
( ~ cpxcomp(Y)
& rs(X,Y) )
| ! [Y] :
( ~ ca_Ax2(Y)
| ~ rs(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y] :
( cpxcomp(Y)
| ~ rs(X,Y) )
& ? [Y] :
( ca_Ax2(Y)
& rs(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f112]) ).
fof(f114,plain,
( ! [X] :
( ( ~ cpxcomp(sK1_skl(X))
& rs(X,sK1_skl(X)) )
| ! [Y] :
( ~ ca_Ax2(Y)
| ~ rs(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y] :
( cpxcomp(Y)
| ~ rs(X,Y) )
& ca_Ax2(sK0_skl(X))
& rs(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))],[f113]) ).
fof(f115,plain,
! [X0] :
( rs(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0] :
( ca_Ax2(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f117,plain,
! [X0,X1] :
( cpxcomp(X1)
| ~ rs(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f120,plain,
! [X] :
( cp(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f121,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(NNF_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(miniscoping,[status(thm)],[f121]) ).
fof(f123,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))],[f122]) ).
fof(f124,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cp(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f126,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f127,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cpxcomp(X) ) ),
inference(miniscoping,[status(thm)],[f126]) ).
fof(f128,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))],[f127]) ).
fof(f129,plain,
! [X0] :
( ra_Px1(X0,sK3_skl(X0))
| ~ cpxcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rinvS(X,Y) )
| ~ cp(X)
| ca_Ax2(X) )
& ( ( ? [Y] :
( cp(Y)
& rinvS(X,Y) )
& cp(X) )
| ~ ca_Ax2(X) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f132,plain,
( ! [X] :
( ! [Y] :
( ~ cp(Y)
| ~ rinvS(X,Y) )
| ~ cp(X)
| ca_Ax2(X) )
& ! [X] :
( ( ? [Y] :
( cp(Y)
& rinvS(X,Y) )
& cp(X) )
| ~ ca_Ax2(X) ) ),
inference(miniscoping,[status(thm)],[f131]) ).
fof(f133,plain,
( ! [X] :
( ! [Y] :
( ~ cp(Y)
| ~ rinvS(X,Y) )
| ~ cp(X)
| ca_Ax2(X) )
& ! [X] :
( ( cp(sK4_skl(X))
& rinvS(X,sK4_skl(X))
& cp(X) )
| ~ ca_Ax2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Y,sK4_skl(X))],[f132]) ).
fof(f134,plain,
! [X0] :
( cp(X0)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f159,plain,
cUnsatisfiable(i2003_11_14_17_21_12565),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f169,plain,
! [X0] :
( ~ cp(X0)
| ~ cpxcomp(X0) ),
inference(resolution,[status(thm)],[f129,f124]) ).
fof(f170,plain,
! [X0,X1] :
( ~ rs(X1,X0)
| ~ cUnsatisfiable(X1)
| ~ cp(X0) ),
inference(resolution,[status(thm)],[f169,f117]) ).
fof(f178,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0)
| ~ cp(sK0_skl(X0)) ),
inference(resolution,[status(thm)],[f170,f115]) ).
fof(f180,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ~ cp(sK0_skl(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f178]) ).
fof(f185,plain,
! [X0] :
( ~ ca_Ax2(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f180,f134]) ).
fof(f186,plain,
! [X0] : ~ cUnsatisfiable(X0),
inference(forward_subsumption_resolution,[status(thm)],[f185,f116]) ).
fof(f188,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f159,f186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS110+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n014.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sun Sep 20 22:53:52 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.34 % Drodi V4.1.1
% 0.07/0.34 % Refutation found
% 0.07/0.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.36 % Elapsed time: 0.019512 seconds
% 0.07/0.36 % CPU time: 0.021140 seconds
% 0.07/0.36 % Total memory used: 663.888 KB
% 0.07/0.36 % Net memory used: 646.528 KB
%------------------------------------------------------------------------------