%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS168+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 : 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 12:59:51 PM UTC 2026
% Result : Theorem 0.08s 10.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 7 unt; 8 def)
% Number of atoms : 218 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 261 ( 106 ~; 106 |; 32 &)
% ( 13 <=>; 0 =>; 0 <=; 4 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 7 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 46 ( 33 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
( ! [X] :
( ( ~ cA(X)
& ~ cB(X) )
<=> ~ ( cB(X)
| cA(X) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ( ! [X] :
( ( ~ cA(X)
& ~ cB(X) )
<=> ~ ( cB(X)
| cA(X) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
( ! [X] :
( xsd_integer(X)
| xsd_string(X) )
& ! [X] :
( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f12,plain,
( ? [X] :
( ( ~ cA(X)
& ~ cB(X) )
<~> ( ~ cB(X)
& ~ cA(X) ) )
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f13,definition,
! [X] :
( sP0_prd(X)
<=> ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f14,definition,
! [X] :
( sP1_prd(X)
<=> ( ~ cA(X)
& ~ cB(X) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f15,plain,
( ? [X] :
( sP1_prd(X)
<~> ( ~ cB(X)
& ~ cA(X) ) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(formula_renaming,[status(thm)],[f12,f14,f13]) ).
fof(f16,plain,
( ? [X] :
( ( cB(X)
| cA(X)
| ~ sP1_prd(X) )
& ( ( ~ cB(X)
& ~ cA(X) )
| sP1_prd(X) ) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
( ? [X] :
( ( cB(X)
| cA(X)
| ~ sP1_prd(X) )
& ( ( ~ cB(X)
& ~ cA(X) )
| sP1_prd(X) ) )
| ? [X] : sP0_prd(X)
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
( ( ( cB(sK3_skl)
| cA(sK3_skl)
| ~ sP1_prd(sK3_skl) )
& ( ( ~ cB(sK3_skl)
& ~ cA(sK3_skl) )
| sP1_prd(sK3_skl) ) )
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl),skolemize(X,sK2_skl),skolemize(X,sK3_skl)],[f17]) ).
fof(f19,plain,
( ~ cA(sK3_skl)
| sP1_prd(sK3_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
( ~ cB(sK3_skl)
| sP1_prd(sK3_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
( cB(sK3_skl)
| cA(sK3_skl)
| ~ sP1_prd(sK3_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,plain,
! [X] :
( ( ( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) )
| sP0_prd(X) )
& ( ( ( xsd_integer(X)
| ~ xsd_string(X) )
& ( ~ xsd_integer(X)
| xsd_string(X) ) )
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f23,plain,
( ! [X] :
( ( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) )
| sP0_prd(X) )
& ! [X] :
( ( ( xsd_integer(X)
| ~ xsd_string(X) )
& ( ~ xsd_integer(X)
| xsd_string(X) ) )
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0] :
( ~ xsd_integer(X0)
| xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0] :
( xsd_integer(X0)
| ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f28,plain,
! [X] :
( ( cA(X)
| cB(X)
| sP1_prd(X) )
& ( ( ~ cA(X)
& ~ cB(X) )
| ~ sP1_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f29,plain,
( ! [X] :
( cA(X)
| cB(X)
| sP1_prd(X) )
& ! [X] :
( ( ~ cA(X)
& ~ cB(X) )
| ~ sP1_prd(X) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0] :
( ~ cB(X0)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0] :
( ~ cA(X0)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0] :
( cA(X0)
| cB(X0)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f33,definition,
( sQ0_spl
<=> cowlThing(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( sQ0_spl
| ~ cowlThing(sK0_skl) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,definition,
( sQ1_spl
<=> cowlNothing(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ1_spl
| cowlNothing(sK1_skl) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ2_spl
<=> sP0_prd(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( ~ sQ2_spl
| sP0_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,definition,
( sQ3_spl
<=> sP1_prd(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( ~ sQ3_spl
| sP1_prd(sK3_skl) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,definition,
( sQ4_spl
<=> cA(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( ~ sQ4_spl
| cA(sK3_skl) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f47,plain,
( sQ4_spl
| ~ cA(sK3_skl) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( ~ sQ4_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f33,f36,f39,f42,f45]) ).
fof(f49,definition,
( sQ5_spl
<=> cB(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ5_spl
| cB(sK3_skl) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( ~ sQ5_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f33,f36,f39,f42,f49]) ).
fof(f53,plain,
( sQ5_spl
| sQ4_spl
| ~ sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f21,f33,f36,f39,f42,f45,f49]) ).
fof(f54,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f24,f10]) ).
fof(f57,plain,
! [X0] : ~ sP0_prd(X0),
inference(backward_subsumption_resolution,[status(thm)],[f54,f58]) ).
fof(f58,plain,
! [X0] :
( xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f11]) ).
fof(f60,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f40,f57]) ).
fof(f61,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f7]) ).
fof(f63,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f62]) ).
fof(f64,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f35,f6]) ).
fof(f65,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f64]) ).
fof(f66,plain,
( ~ sQ4_spl
| ~ sP1_prd(sK3_skl) ),
inference(resolution,[status(thm)],[f46,f31]) ).
fof(f67,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f66,f43]) ).
fof(f68,plain,
( ~ sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f67]) ).
fof(f69,plain,
( sQ4_spl
| cB(sK3_skl)
| sP1_prd(sK3_skl) ),
inference(resolution,[status(thm)],[f32,f47]) ).
fof(f71,plain,
( sQ4_spl
| sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f69,f42,f49,f45]) ).
fof(f72,plain,
( ~ sQ5_spl
| ~ sP1_prd(sK3_skl) ),
inference(resolution,[status(thm)],[f50,f30]) ).
fof(f73,plain,
( ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f72,f42,f49]) ).
fof(f74,plain,
$false,
inference(sat_refutation,[status(thm)],[f48,f52,f53,f61,f63,f65,f68,f71,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS168+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n014.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Sun Sep 20 22:55:00 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.38 % Drodi V4.1.1
% 0.08/10.39 % Refutation found
% 0.08/10.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/10.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/10.41 % Elapsed time: 0.033437 seconds
% 0.13/10.41 % CPU time: 0.082619 seconds
% 0.13/10.41 % Total memory used: 10.515 MB
% 0.13/10.41 % Net memory used: 10.221 MB
%------------------------------------------------------------------------------