%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS067+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 : n002.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 12:59:36 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 8 unt; 3 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 123 ( 48 ~; 47 |; 21 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ( ca(X)
& cc(X) )
| ( ca(X)
& cb(X) )
| ( cb(X)
& cc(X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ca(X)
=> ~ ( cb(X)
| cc(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( cb(X)
=> ~ cc(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
cUnsatisfiable(i2003_11_14_17_18_1956),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,definition,
! [X] :
( sP0_prd(X)
<=> ( ( ca(X)
& cb(X) )
| ( cb(X)
& cc(X) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f15,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ( ca(X)
& cc(X) )
| sP0_prd(X) ) ),
inference(formula_renaming,[status(thm)],[f3,f14]) ).
fof(f16,plain,
! [X] :
( ( ( ( ~ ca(X)
| ~ cc(X) )
& ~ sP0_prd(X) )
| cUnsatisfiable(X) )
& ( ( ca(X)
& cc(X) )
| sP0_prd(X)
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [X] :
( ( ( ~ ca(X)
| ~ cc(X) )
& ~ sP0_prd(X) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ca(X)
& cc(X) )
| sP0_prd(X)
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0] :
( cc(X0)
| sP0_prd(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0] :
( ca(X0)
| sP0_prd(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f22,plain,
! [X] :
( ( ~ cb(X)
& ~ cc(X) )
| ~ ca(X) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0] :
( ~ cc(X0)
| ~ ca(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0] :
( ~ cb(X0)
| ~ ca(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X] :
( ~ cc(X)
| ~ cb(X) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [X0] :
( ~ cc(X0)
| ~ cb(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
cUnsatisfiable(i2003_11_14_17_18_1956),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X] :
( ( ( ( ~ ca(X)
| ~ cb(X) )
& ( ~ cb(X)
| ~ cc(X) ) )
| sP0_prd(X) )
& ( ( ca(X)
& cb(X) )
| ( cb(X)
& cc(X) )
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f29,plain,
( ! [X] :
( ( ( ~ ca(X)
| ~ cb(X) )
& ( ~ cb(X)
| ~ cc(X) ) )
| sP0_prd(X) )
& ! [X] :
( ( ca(X)
& cb(X) )
| ( cb(X)
& cc(X) )
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f31,plain,
! [X0] :
( ca(X0)
| cc(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0] :
( cb(X0)
| cb(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f36,plain,
! [X0] :
( cb(X0)
| ~ sP0_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f32]) ).
fof(f39,plain,
! [X0] :
( ~ cc(X0)
| sP0_prd(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f19,f23]) ).
fof(f40,plain,
! [X0] :
( sP0_prd(X0)
| ~ cUnsatisfiable(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f39,f18]) ).
fof(f41,plain,
sP0_prd(i2003_11_14_17_18_1956),
inference(resolution,[status(thm)],[f40,f27]) ).
fof(f43,plain,
cb(i2003_11_14_17_18_1956),
inference(resolution,[status(thm)],[f41,f36]) ).
fof(f44,plain,
~ cc(i2003_11_14_17_18_1956),
inference(resolution,[status(thm)],[f43,f26]) ).
fof(f45,plain,
( ca(i2003_11_14_17_18_1956)
| cc(i2003_11_14_17_18_1956) ),
inference(resolution,[status(thm)],[f31,f41]) ).
fof(f46,definition,
( sQ0_spl
<=> cc(i2003_11_14_17_18_1956) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( ~ sQ0_spl
| cc(i2003_11_14_17_18_1956) ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,definition,
( sQ1_spl
<=> ca(i2003_11_14_17_18_1956) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ1_spl
| ca(i2003_11_14_17_18_1956) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f46,f49]) ).
fof(f53,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f44]) ).
fof(f54,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f53]) ).
fof(f55,plain,
( ~ sQ1_spl
| ~ cb(i2003_11_14_17_18_1956) ),
inference(resolution,[status(thm)],[f50,f24]) ).
fof(f57,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f43]) ).
fof(f58,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f57]) ).
fof(f59,plain,
$false,
inference(sat_refutation,[status(thm)],[f52,f54,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS067+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 : n002.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 22:55:02 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.39 % Elapsed time: 0.033979 seconds
% 0.14/0.39 % CPU time: 0.066494 seconds
% 0.14/0.39 % Total memory used: 1.237 MB
% 0.14/0.39 % Net memory used: 1.214 MB
%------------------------------------------------------------------------------