%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS134+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 : n006.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 12:59:46 PM UTC 2026
% Result : Theorem 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 7 unt; 6 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 170 ( 66 ~; 64 |; 24 &)
% ( 9 <=>; 5 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 51 ( 38 !; 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,axiom,
! [X,Y] :
( rprop(X,Y)
=> cA(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
( ! [X] :
( cowlThing(X)
=> ! [Y] :
( rprop(X,Y)
=> cA(Y) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ( ! [X] :
( cowlThing(X)
=> ! [Y] :
( rprop(X,Y)
=> cA(Y) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
( ! [X] :
( xsd_integer(X)
| xsd_string(X) )
& ! [X] :
( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [X,Y] :
( cA(Y)
| ~ rprop(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [Y] :
( cA(Y)
| ! [X] : ~ rprop(X,Y) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( cA(X1)
| ~ rprop(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( ? [X] :
( ? [Y] :
( ~ cA(Y)
& rprop(X,Y) )
& cowlThing(X) )
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f17,definition,
! [X] :
( sP0_prd(X)
<=> ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f18,plain,
( ? [X] :
( ? [Y] :
( ~ cA(Y)
& rprop(X,Y) )
& cowlThing(X) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(formula_renaming,[status(thm)],[f16,f17]) ).
fof(f19,plain,
( ? [X] :
( ? [Y] :
( ~ cA(Y)
& rprop(X,Y) )
& cowlThing(X) )
| ? [X] : sP0_prd(X)
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f20,plain,
( ( ~ cA(sK4_skl)
& rprop(sK3_skl,sK4_skl)
& cowlThing(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,sK4_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl),skolemize(X,sK2_skl),skolemize(X,sK3_skl),skolemize(Y,sK4_skl)],[f19]) ).
fof(f22,plain,
( rprop(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
( ~ cA(sK4_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f24,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)],[f17]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
! [X0] :
( ~ xsd_integer(X0)
| xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0] :
( xsd_integer(X0)
| ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f30,definition,
( sQ0_spl
<=> cowlThing(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f32,plain,
( sQ0_spl
| ~ cowlThing(sK0_skl) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,definition,
( sQ1_spl
<=> cowlNothing(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( ~ sQ1_spl
| cowlNothing(sK1_skl) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,definition,
( sQ2_spl
<=> sP0_prd(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ2_spl
| sP0_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f43,definition,
( sQ4_spl
<=> rprop(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ4_spl
| rprop(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,plain,
( sQ4_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f22,f30,f33,f36,f43]) ).
fof(f47,definition,
( sQ5_spl
<=> cA(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ5_spl
| ~ cA(sK4_skl) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( ~ sQ5_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f23,f30,f33,f36,f47]) ).
fof(f51,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f26,f11]) ).
fof(f52,plain,
! [X0] :
( ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f27,f11]) ).
fof(f53,plain,
! [X0] :
( ~ sP0_prd(X0)
| xsd_integer(X0) ),
inference(resolution,[status(thm)],[f12,f52]) ).
fof(f54,plain,
! [X0] : ~ sP0_prd(X0),
inference(forward_subsumption_resolution,[status(thm)],[f53,f51]) ).
fof(f55,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f37,f54]) ).
fof(f56,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f55]) ).
fof(f57,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f8]) ).
fof(f58,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f57]) ).
fof(f59,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f32,f7]) ).
fof(f60,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] :
( sQ5_spl
| ~ rprop(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f49,f15]) ).
fof(f62,plain,
( ~ sQ4_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f61]) ).
fof(f63,plain,
( ~ sQ4_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f62]) ).
fof(f64,plain,
$false,
inference(sat_refutation,[status(thm)],[f46,f50,f56,f58,f60,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS134+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 22:54:12 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.41 % Elapsed time: 0.043600 seconds
% 0.15/0.41 % CPU time: 0.107696 seconds
% 0.15/0.41 % Total memory used: 16.783 MB
% 0.15/0.41 % Net memory used: 16.286 MB
%------------------------------------------------------------------------------