%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS105+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 : n026.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 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 5 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 126 ( 57 ~; 46 |; 12 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 67 ( 59 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( cUnsatisfiable(X)
=> cdxcomp(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( cUnsatisfiable(X)
=> cc(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( cc(X)
=> ! [Y] :
( rr(X,Y)
=> cc(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( cd(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( cdxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( ca_Ax2(X)
<=> ! [Y] :
( rr(X,Y)
=> cc(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( ca_Ax2(X)
=> cd(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
cUnsatisfiable(i2003_11_14_17_20_53634),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X] :
( cdxcomp(X)
| ~ cUnsatisfiable(X) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0] :
( cdxcomp(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X] :
( cc(X)
| ~ cUnsatisfiable(X) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0] :
( cc(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [X] :
( ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
| ~ cc(X) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
! [X0,X1] :
( cc(X1)
| ~ rr(X0,X1)
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X] :
( cd(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cd(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cd(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
( ! [X] :
( ra_Px1(X,sK0_skl(X))
| cd(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y,sK0_skl(X))],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cd(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cdxcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cdxcomp(X) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ! [X] :
( ra_Px1(X,sK1_skl(X))
| ~ cdxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y0,sK1_skl(X))],[f31]) ).
fof(f33,plain,
! [X0] :
( ra_Px1(X0,sK1_skl(X0))
| ~ cdxcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
! [X] :
( ca_Ax2(X)
<=> ! [Y] :
( cc(Y)
| ~ rr(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
! [X] :
( ( ? [Y] :
( ~ cc(Y)
& rr(X,Y) )
| ca_Ax2(X) )
& ( ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
| ~ ca_Ax2(X) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
( ! [X] :
( ? [Y] :
( ~ cc(Y)
& rr(X,Y) )
| ca_Ax2(X) )
& ! [X] :
( ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
| ~ ca_Ax2(X) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
( ! [X] :
( ( ~ cc(sK2_skl(X))
& rr(X,sK2_skl(X)) )
| ca_Ax2(X) )
& ! [X] :
( ! [Y] :
( cc(Y)
| ~ rr(X,Y) )
| ~ ca_Ax2(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X))],[f37]) ).
fof(f40,plain,
! [X0] :
( rr(X0,sK2_skl(X0))
| ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,plain,
! [X0] :
( ~ cc(sK2_skl(X0))
| ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [X] :
( cd(X)
| ~ ca_Ax2(X) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f43,plain,
! [X0] :
( cd(X0)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
cUnsatisfiable(i2003_11_14_17_20_53634),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
! [X0] :
( cd(X0)
| ~ cc(sK2_skl(X0)) ),
inference(resolution,[status(thm)],[f41,f43]) ).
fof(f46,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cc(sK2_skl(X0)) ),
inference(resolution,[status(thm)],[f45,f28]) ).
fof(f47,plain,
! [X0] :
( ~ cdxcomp(X0)
| ~ cc(sK2_skl(X0)) ),
inference(resolution,[status(thm)],[f46,f33]) ).
fof(f50,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ~ cc(sK2_skl(X0)) ),
inference(resolution,[status(thm)],[f47,f19]) ).
fof(f51,plain,
~ cc(sK2_skl(i2003_11_14_17_20_53634)),
inference(resolution,[status(thm)],[f50,f44]) ).
fof(f53,plain,
! [X0] :
( ~ rr(X0,sK2_skl(i2003_11_14_17_20_53634))
| ~ cc(X0) ),
inference(resolution,[status(thm)],[f51,f23]) ).
fof(f56,plain,
( ca_Ax2(i2003_11_14_17_20_53634)
| ~ cc(i2003_11_14_17_20_53634) ),
inference(resolution,[status(thm)],[f53,f40]) ).
fof(f57,plain,
( cd(i2003_11_14_17_20_53634)
| ~ cc(i2003_11_14_17_20_53634) ),
inference(resolution,[status(thm)],[f56,f43]) ).
fof(f58,plain,
! [X0] :
( ~ ra_Px1(i2003_11_14_17_20_53634,X0)
| ~ cc(i2003_11_14_17_20_53634) ),
inference(resolution,[status(thm)],[f57,f28]) ).
fof(f59,plain,
( ~ cdxcomp(i2003_11_14_17_20_53634)
| ~ cc(i2003_11_14_17_20_53634) ),
inference(resolution,[status(thm)],[f58,f33]) ).
fof(f62,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_53634)
| ~ cc(i2003_11_14_17_20_53634) ),
inference(resolution,[status(thm)],[f59,f19]) ).
fof(f63,plain,
~ cUnsatisfiable(i2003_11_14_17_20_53634),
inference(forward_subsumption_resolution,[status(thm)],[f62,f21]) ).
fof(f64,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f63,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS105+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 22:56:08 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.030774 seconds
% 0.12/0.39 % CPU time: 0.079631 seconds
% 0.12/0.39 % Total memory used: 1.358 MB
% 0.12/0.39 % Net memory used: 1.331 MB
%------------------------------------------------------------------------------