%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS142+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 : n017.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 12:59:47 PM UTC 2026
% Result : Theorem 0.10s 0.61s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 9 unt; 11 def)
% Number of atoms : 263 ( 17 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 294 ( 106 ~; 120 |; 44 &)
% ( 14 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 89 ( 64 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] :
( cc(X)
=> ( ! [Y0,Y1] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 )
& ? [Y0] : rp(X,Y0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
( ! [X] :
( cc(X)
=> ! [Y0,Y1] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 ) )
& ! [X] :
( cc(X)
=> ? [Y0] : rp(X,Y0) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ( ! [X] :
( cc(X)
=> ! [Y0,Y1] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 ) )
& ! [X] :
( cc(X)
=> ? [Y0] : rp(X,Y0) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f34,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f35,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
( ! [X] :
( xsd_integer(X)
| xsd_string(X) )
& ! [X] :
( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,plain,
! [X] :
( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rp(X,Y1)
| ~ rp(X,Y0) )
& ? [Y0] : rp(X,Y0) )
| ~ cc(X) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f42,plain,
! [X] :
( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rp(X,Y1)
| ~ rp(X,Y0) )
& rp(X,sK0_skl(X)) )
| ~ cc(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y0,sK0_skl(X))],[f41]) ).
fof(f43,plain,
! [X0] :
( rp(X0,sK0_skl(X0))
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rp(X0,X2)
| ~ rp(X0,X1)
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
( ? [X] :
( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y1)
& rp(X,Y0) )
& cc(X) )
| ? [X] :
( ! [Y0] : ~ rp(X,Y0)
& cc(X) )
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f46,definition,
! [X] :
( sP0_prd(X)
<=> ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f47,definition,
! [X] :
( sP1_prd(X)
<=> ( ! [Y0] : ~ rp(X,Y0)
& cc(X) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f48,plain,
( ? [X] :
( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y1)
& rp(X,Y0) )
& cc(X) )
| ? [X] : sP1_prd(X)
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(formula_renaming,[status(thm)],[f45,f47,f46]) ).
fof(f49,plain,
( ? [X] :
( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y1)
& rp(X,Y0) )
& cc(X) )
| ? [X] : sP1_prd(X)
| ? [X] : sP0_prd(X)
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
( ( sK6_skl != sK7_skl
& rp(sK5_skl,sK7_skl)
& rp(sK5_skl,sK6_skl)
& cc(sK5_skl) )
| sP1_prd(sK4_skl)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl)
| ~ cowlThing(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(X,sK1_skl),skolemize(X,sK2_skl),skolemize(X,sK3_skl),skolemize(X,sK4_skl),skolemize(X,sK5_skl),skolemize(Y0,sK6_skl),skolemize(Y1,sK7_skl)],[f49]) ).
fof(f51,plain,
( cc(sK5_skl)
| sP1_prd(sK4_skl)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl)
| ~ cowlThing(sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
( rp(sK5_skl,sK6_skl)
| sP1_prd(sK4_skl)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl)
| ~ cowlThing(sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
( rp(sK5_skl,sK7_skl)
| sP1_prd(sK4_skl)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl)
| ~ cowlThing(sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
( sK6_skl != sK7_skl
| sP1_prd(sK4_skl)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl)
| ~ cowlThing(sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,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)],[f46]) ).
fof(f56,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)],[f55]) ).
fof(f57,plain,
! [X0] :
( ~ xsd_integer(X0)
| xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0] :
( xsd_integer(X0)
| ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f61,plain,
! [X] :
( ( ? [Y0] : rp(X,Y0)
| ~ cc(X)
| sP1_prd(X) )
& ( ( ! [Y0] : ~ rp(X,Y0)
& cc(X) )
| ~ sP1_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f62,plain,
( ! [X] :
( ? [Y0] : rp(X,Y0)
| ~ cc(X)
| sP1_prd(X) )
& ! [X] :
( ( ! [Y0] : ~ rp(X,Y0)
& cc(X) )
| ~ sP1_prd(X) ) ),
inference(miniscoping,[status(thm)],[f61]) ).
fof(f63,plain,
( ! [X] :
( rp(X,sK8_skl(X))
| ~ cc(X)
| sP1_prd(X) )
& ! [X] :
( ( ! [Y0] : ~ rp(X,Y0)
& cc(X) )
| ~ sP1_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(Y0,sK8_skl(X))],[f62]) ).
fof(f64,plain,
! [X0] :
( cc(X0)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ~ rp(X0,X1)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f67,definition,
( sQ0_spl
<=> cowlThing(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( sQ0_spl
| ~ cowlThing(sK1_skl) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,definition,
( sQ1_spl
<=> cowlNothing(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ1_spl
| cowlNothing(sK2_skl) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ2_spl
<=> sP0_prd(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ2_spl
| sP0_prd(sK3_skl) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,definition,
( sQ3_spl
<=> sP1_prd(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ3_spl
| sP1_prd(sK4_skl) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,definition,
( sQ4_spl
<=> cc(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( sQ4_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f67,f70,f73,f76,f79]) ).
fof(f83,definition,
( sQ5_spl
<=> rp(sK5_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ5_spl
| rp(sK5_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ5_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f67,f70,f73,f76,f83]) ).
fof(f87,definition,
( sQ6_spl
<=> rp(sK5_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ6_spl
| rp(sK5_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( sQ6_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f67,f70,f73,f76,f87]) ).
fof(f91,definition,
( sQ7_spl
<=> sK6_skl = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( sQ7_spl
| sK6_skl != sK7_skl ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( ~ sQ7_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f54,f67,f70,f73,f76,f91]) ).
fof(f95,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f57,f39]) ).
fof(f96,plain,
! [X0] : ~ sP0_prd(X0),
inference(backward_subsumption_resolution,[status(thm)],[f95,f97]) ).
fof(f97,plain,
! [X0] :
( xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f40]) ).
fof(f98,plain,
! [X0] :
( ~ sP1_prd(X0)
| rp(X0,sK0_skl(X0)) ),
inference(resolution,[status(thm)],[f43,f64]) ).
fof(f99,plain,
! [X0] : ~ sP1_prd(X0),
inference(forward_subsumption_resolution,[status(thm)],[f98,f65]) ).
fof(f100,plain,
( ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f77,f99]) ).
fof(f101,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f100]) ).
fof(f102,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f96]) ).
fof(f103,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f102]) ).
fof(f104,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f36]) ).
fof(f105,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f104]) ).
fof(f106,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f35]) ).
fof(f107,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f106]) ).
fof(f109,plain,
! [X0] :
( ~ sQ5_spl
| X0 = sK6_skl
| ~ rp(sK5_skl,X0)
| ~ cc(sK5_skl) ),
inference(resolution,[status(thm)],[f84,f44]) ).
fof(f110,definition,
! [X0] :
( sQ8_spl
<=> ( X0 = sK6_skl
| ~ rp(sK5_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f111,plain,
! [X0] :
( ~ sQ8_spl
| X0 = sK6_skl
| ~ rp(sK5_skl,X0) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( ~ sQ5_spl
| sQ8_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f109,f79,f110,f83]) ).
fof(f125,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| sK7_skl = sK6_skl ),
inference(resolution,[status(thm)],[f111,f88]) ).
fof(f127,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f93]) ).
fof(f128,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f127]) ).
fof(f129,plain,
$false,
inference(sat_refutation,[status(thm)],[f82,f86,f90,f94,f101,f103,f105,f107,f113,f128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS142+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n017.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sun Sep 20 22:49:58 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.59 % Drodi V4.1.1
% 0.10/0.61 % Refutation found
% 0.10/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.65 % Elapsed time: 0.059299 seconds
% 0.15/0.65 % CPU time: 0.163031 seconds
% 0.15/0.65 % Total memory used: 80.327 MB
% 0.15/0.65 % Net memory used: 80.025 MB
%------------------------------------------------------------------------------