%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS143+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 10 unt; 1 def)
% Number of atoms : 206 ( 22 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 224 ( 81 ~; 97 |; 33 &)
% ( 4 <=>; 7 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 76 ( 56 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] :
( cc(X)
=> ? [Y0] : rp(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( cc(X)
=> ! [Y0,Y1] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
( ! [X] :
( cc(X)
=> ( ! [Y0,Y1] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 )
& ? [Y0] : rp(X,Y0) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ( ! [X] :
( cc(X)
=> ( ! [Y0,Y1] :
( ( rp(X,Y1)
& rp(X,Y0) )
=> Y0 = Y1 )
& ? [Y0] : rp(X,Y0) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f35,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f36,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
( ! [X] :
( xsd_integer(X)
| xsd_string(X) )
& ! [X] :
( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
! [X] :
( ? [Y0] : rp(X,Y0)
| ~ cc(X) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f43,plain,
! [X] :
( rp(X,sK0_skl(X))
| ~ cc(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y0,sK0_skl(X))],[f42]) ).
fof(f44,plain,
! [X0] :
( rp(X0,sK0_skl(X0))
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [X] :
( ! [Y0,Y1] :
( Y0 = Y1
| ~ rp(X,Y1)
| ~ rp(X,Y0) )
| ~ cc(X) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rp(X0,X2)
| ~ rp(X0,X1)
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
( ? [X] :
( ( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y1)
& rp(X,Y0) )
| ! [Y0] : ~ rp(X,Y0) )
& cc(X) )
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f48,definition,
! [X] :
( sP0_prd(X)
<=> ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f49,plain,
( ? [X] :
( ( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y1)
& rp(X,Y0) )
| ! [Y0] : ~ rp(X,Y0) )
& cc(X) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(formula_renaming,[status(thm)],[f47,f48]) ).
fof(f50,plain,
( ? [X] :
( ( ? [Y0,Y1] :
( Y0 != Y1
& rp(X,Y1)
& rp(X,Y0) )
| ! [Y0] : ~ rp(X,Y0) )
& cc(X) )
| ? [X] : sP0_prd(X)
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
( ( ( ( sK5_skl != sK6_skl
& rp(sK4_skl,sK6_skl)
& rp(sK4_skl,sK5_skl) )
| ! [Y0] : ~ rp(sK4_skl,Y0) )
& cc(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]),skolemize(X,sK1_skl),skolemize(X,sK2_skl),skolemize(X,sK3_skl),skolemize(X,sK4_skl),skolemize(Y0,sK5_skl),skolemize(Y1,sK6_skl)],[f50]) ).
fof(f52,plain,
( cc(sK4_skl)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl)
| ~ cowlThing(sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0] :
( rp(sK4_skl,sK5_skl)
| ~ rp(sK4_skl,X0)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl)
| ~ cowlThing(sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
! [X0] :
( rp(sK4_skl,sK6_skl)
| ~ rp(sK4_skl,X0)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl)
| ~ cowlThing(sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
! [X0] :
( sK5_skl != sK6_skl
| ~ rp(sK4_skl,X0)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl)
| ~ cowlThing(sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f56,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)],[f48]) ).
fof(f57,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)],[f56]) ).
fof(f58,plain,
! [X0] :
( ~ xsd_integer(X0)
| xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0] :
( xsd_integer(X0)
| ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f64,plain,
! [X0] :
( rp(sK4_skl,sK5_skl)
| ~ rp(sK4_skl,X0)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f53,f36]) ).
fof(f65,plain,
! [X0] :
( sK5_skl != sK6_skl
| ~ rp(sK4_skl,X0)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f55,f36]) ).
fof(f66,plain,
( cc(sK4_skl)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f52,f36]) ).
fof(f67,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f58,f40]) ).
fof(f68,plain,
! [X0] :
( ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f59,f40]) ).
fof(f70,plain,
( cc(sK4_skl)
| sP0_prd(sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f66,f37]) ).
fof(f71,plain,
( ~ xsd_string(sK3_skl)
| cc(sK4_skl) ),
inference(resolution,[status(thm)],[f70,f68]) ).
fof(f72,plain,
( ~ xsd_integer(sK3_skl)
| cc(sK4_skl) ),
inference(resolution,[status(thm)],[f70,f67]) ).
fof(f73,plain,
( xsd_string(sK3_skl)
| cc(sK4_skl) ),
inference(resolution,[status(thm)],[f72,f41]) ).
fof(f74,plain,
cc(sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f73,f71]) ).
fof(f75,plain,
! [X0] :
( sK5_skl != sK6_skl
| ~ rp(sK4_skl,X0)
| sP0_prd(sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f37]) ).
fof(f76,plain,
! [X0] :
( rp(sK4_skl,sK6_skl)
| ~ rp(sK4_skl,X0)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f36]) ).
fof(f77,plain,
! [X0] :
( rp(sK4_skl,sK5_skl)
| ~ rp(sK4_skl,X0)
| sP0_prd(sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f64,f37]) ).
fof(f78,plain,
rp(sK4_skl,sK0_skl(sK4_skl)),
inference(resolution,[status(thm)],[f44,f74]) ).
fof(f79,plain,
( rp(sK4_skl,sK5_skl)
| sP0_prd(sK3_skl) ),
inference(resolution,[status(thm)],[f78,f77]) ).
fof(f80,plain,
( rp(sK4_skl,sK6_skl)
| sP0_prd(sK3_skl)
| cowlNothing(sK2_skl) ),
inference(resolution,[status(thm)],[f78,f76]) ).
fof(f81,plain,
( sK5_skl != sK6_skl
| sP0_prd(sK3_skl) ),
inference(resolution,[status(thm)],[f78,f75]) ).
fof(f82,plain,
! [X0] :
( sK0_skl(sK4_skl) = X0
| ~ rp(sK4_skl,X0)
| ~ cc(sK4_skl) ),
inference(resolution,[status(thm)],[f78,f46]) ).
fof(f83,plain,
( rp(sK4_skl,sK6_skl)
| sP0_prd(sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f37]) ).
fof(f84,plain,
! [X0] :
( sK0_skl(sK4_skl) = X0
| ~ rp(sK4_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f74]) ).
fof(f92,plain,
( sP0_prd(sK3_skl)
| sK0_skl(sK4_skl) = sK6_skl ),
inference(resolution,[status(thm)],[f84,f83]) ).
fof(f93,plain,
( sP0_prd(sK3_skl)
| sK0_skl(sK4_skl) = sK5_skl ),
inference(resolution,[status(thm)],[f84,f79]) ).
fof(f95,plain,
( ~ xsd_string(sK3_skl)
| sK0_skl(sK4_skl) = sK6_skl ),
inference(resolution,[status(thm)],[f92,f68]) ).
fof(f96,plain,
( ~ xsd_integer(sK3_skl)
| sK0_skl(sK4_skl) = sK6_skl ),
inference(resolution,[status(thm)],[f92,f67]) ).
fof(f99,plain,
( xsd_string(sK3_skl)
| sK0_skl(sK4_skl) = sK6_skl ),
inference(resolution,[status(thm)],[f96,f41]) ).
fof(f100,plain,
sK0_skl(sK4_skl) = sK6_skl,
inference(forward_subsumption_resolution,[status(thm)],[f99,f95]) ).
fof(f103,plain,
( sP0_prd(sK3_skl)
| sK6_skl = sK5_skl ),
inference(backward_demodulation,[status(thm)],[f100,f93]) ).
fof(f107,plain,
sP0_prd(sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f103,f81]) ).
fof(f108,plain,
~ xsd_string(sK3_skl),
inference(resolution,[status(thm)],[f107,f68]) ).
fof(f109,plain,
~ xsd_integer(sK3_skl),
inference(resolution,[status(thm)],[f107,f67]) ).
fof(f110,plain,
xsd_string(sK3_skl),
inference(resolution,[status(thm)],[f109,f41]) ).
fof(f111,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f110,f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS143+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 22:55:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.040417 seconds
% 0.12/0.40 % CPU time: 0.117522 seconds
% 0.12/0.40 % Total memory used: 55.222 MB
% 0.12/0.40 % Net memory used: 55.027 MB
%------------------------------------------------------------------------------