%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS172+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 : n012.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 0.02s 0.32s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 11 unt; 1 def)
% Number of atoms : 212 ( 13 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 230 ( 87 ~; 102 |; 25 &)
% ( 8 <=>; 4 =>; 0 <=; 4 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 98 ( 81 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( cd(X)
<=> rq(X,iv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] :
( cd(X)
<=> rp(X,iv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( ( rp(X,Z)
& rp(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] :
( rp(X,Y)
=> cd(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,Z] :
( ( rq(X,Z)
& rq(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] :
( rq(X,Y)
=> cd(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
( ! [X,Y] :
( rq(X,Y)
<=> rp(X,Y) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ( ! [X,Y] :
( rq(X,Y)
<=> rp(X,Y) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f48,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f49,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f52,plain,
( ! [X] :
( xsd_integer(X)
| xsd_string(X) )
& ! [X] :
( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f55,plain,
! [X] :
( ( ~ rq(X,iv)
| cd(X) )
& ( rq(X,iv)
| ~ cd(X) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f56,plain,
( ! [X] :
( ~ rq(X,iv)
| cd(X) )
& ! [X] :
( rq(X,iv)
| ~ cd(X) ) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0] :
( rq(X0,iv)
| ~ cd(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f59,plain,
! [X] :
( ( ~ rp(X,iv)
| cd(X) )
& ( rp(X,iv)
| ~ cd(X) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f60,plain,
( ! [X] :
( ~ rp(X,iv)
| cd(X) )
& ! [X] :
( rp(X,iv)
| ~ cd(X) ) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] :
( rp(X0,iv)
| ~ cd(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
! [X,Y,Z] :
( Y = Z
| ~ rp(X,Z)
| ~ rp(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f64,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rp(X,Z)
| ~ rp(X,Y) ) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rp(X0,X2)
| ~ rp(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X,Y] :
( cd(X)
| ~ rp(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f67,plain,
! [X] :
( cd(X)
| ! [Y] : ~ rp(X,Y) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( cd(X0)
| ~ rp(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X,Y,Z] :
( Y = Z
| ~ rq(X,Z)
| ~ rq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f70,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rq(X,Z)
| ~ rq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rq(X0,X2)
| ~ rq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [X,Y] :
( cd(X)
| ~ rq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f73,plain,
! [X] :
( cd(X)
| ! [Y] : ~ rq(X,Y) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( cd(X0)
| ~ rq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f76,plain,
( ? [X,Y] :
( rq(X,Y)
<~> rp(X,Y) )
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f77,definition,
! [X] :
( sP0_prd(X)
<=> ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f78,plain,
( ? [X,Y] :
( rq(X,Y)
<~> rp(X,Y) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(formula_renaming,[status(thm)],[f76,f77]) ).
fof(f79,plain,
( ? [X,Y] :
( ( ~ rp(X,Y)
| ~ rq(X,Y) )
& ( rp(X,Y)
| rq(X,Y) ) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(NNF_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
( ? [X,Y] :
( ( ~ rp(X,Y)
| ~ rq(X,Y) )
& ( rp(X,Y)
| rq(X,Y) ) )
| ? [X] : sP0_prd(X)
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f79]) ).
fof(f81,plain,
( ( ( ~ rp(sK3_skl,sK4_skl)
| ~ rq(sK3_skl,sK4_skl) )
& ( rp(sK3_skl,sK4_skl)
| rq(sK3_skl,sK4_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)],[f80]) ).
fof(f82,plain,
( rp(sK3_skl,sK4_skl)
| rq(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
( ~ rp(sK3_skl,sK4_skl)
| ~ rq(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f84,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)],[f77]) ).
fof(f85,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)],[f84]) ).
fof(f86,plain,
! [X0] :
( ~ xsd_integer(X0)
| xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
! [X0] :
( xsd_integer(X0)
| ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f90,plain,
( ~ rp(sK3_skl,sK4_skl)
| ~ rq(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f83,f49]) ).
fof(f91,plain,
( rp(sK3_skl,sK4_skl)
| rq(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f82,f49]) ).
fof(f92,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f86,f53]) ).
fof(f94,plain,
! [X0] : ~ sP0_prd(X0),
inference(backward_subsumption_resolution,[status(thm)],[f92,f95]) ).
fof(f95,plain,
! [X0] :
( xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f54]) ).
fof(f96,plain,
( ~ rp(sK3_skl,sK4_skl)
| ~ rq(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f50]) ).
fof(f97,plain,
( rp(sK3_skl,sK4_skl)
| rq(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f50]) ).
fof(f99,plain,
( cd(sK3_skl)
| rp(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl) ),
inference(resolution,[status(thm)],[f97,f74]) ).
fof(f100,plain,
! [X0] :
( X0 = sK4_skl
| ~ rq(sK3_skl,X0)
| rp(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl) ),
inference(resolution,[status(thm)],[f97,f71]) ).
fof(f101,plain,
( cd(sK3_skl)
| rp(sK3_skl,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f94]) ).
fof(f102,plain,
! [X0] :
( X0 = sK4_skl
| ~ rq(sK3_skl,X0)
| rp(sK3_skl,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f94]) ).
fof(f103,plain,
cd(sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f101,f68]) ).
fof(f104,plain,
rp(sK3_skl,iv),
inference(resolution,[status(thm)],[f103,f61]) ).
fof(f105,plain,
rq(sK3_skl,iv),
inference(resolution,[status(thm)],[f103,f57]) ).
fof(f108,plain,
! [X0] :
( X0 = iv
| ~ rp(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f104,f65]) ).
fof(f109,plain,
( iv = sK4_skl
| rp(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f105,f102]) ).
fof(f118,plain,
rq(sK3_skl,sK4_skl),
inference(backward_demodulation,[status(thm)],[f122,f105]) ).
fof(f119,plain,
rp(sK3_skl,sK4_skl),
inference(backward_demodulation,[status(thm)],[f122,f104]) ).
fof(f122,plain,
iv = sK4_skl,
inference(forward_subsumption_resolution,[status(thm)],[f109,f108]) ).
fof(f125,plain,
( ~ rp(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f96,f118]) ).
fof(f129,plain,
~ rp(sK3_skl,sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f125,f94]) ).
fof(f132,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f119,f129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KRS172+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sun Sep 20 22:55:22 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 0.02/0.32 % Refutation found
% 0.02/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.34 % Elapsed time: 0.038266 seconds
% 0.07/0.34 % CPU time: 0.090697 seconds
% 0.07/0.34 % Total memory used: 80.545 MB
% 0.07/0.34 % Net memory used: 80.287 MB
%------------------------------------------------------------------------------