%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS131+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 : 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 12:59:45 PM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 8 unt; 6 def)
% Number of atoms : 241 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 278 ( 114 ~; 111 |; 32 &)
% ( 14 <=>; 3 =>; 0 <=; 4 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 91 ( 70 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( cA(X)
<=> ? [Y] :
( cowlThing(Y)
& rq(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( cNothing(X)
=> ~ ? [Y] : rp(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( cNothing(X)
=> ? [Y0] : rp(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( cnotA(X)
<=> ! [Y] :
( rq(X,Y)
=> cNothing(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
( ! [X] :
( cnotA(X)
<=> ~ cA(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ( ! [X] :
( cnotA(X)
<=> ~ cA(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f12,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
( ! [X] :
( xsd_integer(X)
| xsd_string(X) )
& ! [X] :
( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) )
| cA(X) )
& ( ? [Y] :
( cowlThing(Y)
& rq(X,Y) )
| ~ cA(X) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
( ! [X] :
( ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) )
| cA(X) )
& ! [X] :
( ? [Y] :
( cowlThing(Y)
& rq(X,Y) )
| ~ cA(X) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
( ! [X] :
( ! [Y] :
( ~ cowlThing(Y)
| ~ rq(X,Y) )
| cA(X) )
& ! [X] :
( ( cowlThing(sK0_skl(X))
& rq(X,sK0_skl(X)) )
| ~ cA(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y,sK0_skl(X))],[f17]) ).
fof(f19,plain,
! [X0] :
( rq(X0,sK0_skl(X0))
| ~ cA(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( ~ cowlThing(X1)
| ~ rq(X0,X1)
| cA(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,plain,
! [X] :
( ! [Y] : ~ rp(X,Y)
| ~ cNothing(X) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0,X1] :
( ~ rp(X0,X1)
| ~ cNothing(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X] :
( ? [Y0] : rp(X,Y0)
| ~ cNothing(X) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f25,plain,
! [X] :
( rp(X,sK1_skl(X))
| ~ cNothing(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y0,sK1_skl(X))],[f24]) ).
fof(f26,plain,
! [X0] :
( rp(X0,sK1_skl(X0))
| ~ cNothing(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X] :
( cnotA(X)
<=> ! [Y] :
( cNothing(Y)
| ~ rq(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X] :
( ( ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) )
| cnotA(X) )
& ( ! [Y] :
( cNothing(Y)
| ~ rq(X,Y) )
| ~ cnotA(X) ) ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
( ! [X] :
( ? [Y] :
( ~ cNothing(Y)
& rq(X,Y) )
| cnotA(X) )
& ! [X] :
( ! [Y] :
( cNothing(Y)
| ~ rq(X,Y) )
| ~ cnotA(X) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
( ! [X] :
( ( ~ cNothing(sK2_skl(X))
& rq(X,sK2_skl(X)) )
| cnotA(X) )
& ! [X] :
( ! [Y] :
( cNothing(Y)
| ~ rq(X,Y) )
| ~ cnotA(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X))],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( cNothing(X1)
| ~ rq(X0,X1)
| ~ cnotA(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0] :
( rq(X0,sK2_skl(X0))
| cnotA(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
( ? [X] :
( cnotA(X)
<~> ~ cA(X) )
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f35,definition,
! [X] :
( sP0_prd(X)
<=> ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f36,plain,
( ? [X] :
( cnotA(X)
<~> ~ cA(X) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(formula_renaming,[status(thm)],[f34,f35]) ).
fof(f37,plain,
( ? [X] :
( ( cA(X)
| ~ cnotA(X) )
& ( ~ cA(X)
| cnotA(X) ) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(NNF_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
( ? [X] :
( ( cA(X)
| ~ cnotA(X) )
& ( ~ cA(X)
| cnotA(X) ) )
| ? [X] : sP0_prd(X)
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f39,plain,
( ( ( cA(sK6_skl)
| ~ cnotA(sK6_skl) )
& ( ~ cA(sK6_skl)
| cnotA(sK6_skl) ) )
| sP0_prd(sK5_skl)
| cowlNothing(sK4_skl)
| ~ cowlThing(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(X,sK3_skl),skolemize(X,sK4_skl),skolemize(X,sK5_skl),skolemize(X,sK6_skl)],[f38]) ).
fof(f40,plain,
( ~ cA(sK6_skl)
| cnotA(sK6_skl)
| sP0_prd(sK5_skl)
| cowlNothing(sK4_skl)
| ~ cowlThing(sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
( cA(sK6_skl)
| ~ cnotA(sK6_skl)
| sP0_prd(sK5_skl)
| cowlNothing(sK4_skl)
| ~ cowlThing(sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,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)],[f35]) ).
fof(f43,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)],[f42]) ).
fof(f44,plain,
! [X0] :
( ~ xsd_integer(X0)
| xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0] :
( xsd_integer(X0)
| ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f48,definition,
( sQ0_spl
<=> cowlThing(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( sQ0_spl
| ~ cowlThing(sK3_skl) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,definition,
( sQ1_spl
<=> cowlNothing(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( ~ sQ1_spl
| cowlNothing(sK4_skl) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ2_spl
<=> sP0_prd(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( ~ sQ2_spl
| sP0_prd(sK5_skl) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,definition,
( sQ3_spl
<=> cnotA(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( ~ sQ3_spl
| cnotA(sK6_skl) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f59,plain,
( sQ3_spl
| ~ cnotA(sK6_skl) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,definition,
( sQ4_spl
<=> cA(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ4_spl
| cA(sK6_skl) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( ~ sQ4_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f48,f51,f54,f57,f60]) ).
fof(f64,plain,
( sQ4_spl
| ~ sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f48,f51,f54,f57,f60]) ).
fof(f65,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f44,f14]) ).
fof(f66,plain,
! [X0] :
( ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f45,f14]) ).
fof(f68,plain,
! [X0] :
( xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f65,f15]) ).
fof(f69,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f55,f70]) ).
fof(f70,plain,
! [X0] : ~ sP0_prd(X0),
inference(forward_subsumption_resolution,[status(thm)],[f68,f66]) ).
fof(f71,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f52,f11]) ).
fof(f73,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f72]) ).
fof(f74,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f50,f10]) ).
fof(f75,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f74]) ).
fof(f76,plain,
! [X0] : ~ cNothing(X0),
inference(forward_subsumption_resolution,[status(thm)],[f26,f23]) ).
fof(f77,plain,
! [X0,X1] :
( ~ rq(X0,X1)
| cA(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f21,f10]) ).
fof(f78,plain,
! [X0] :
( cnotA(X0)
| cA(X0) ),
inference(resolution,[status(thm)],[f77,f32]) ).
fof(f80,plain,
! [X0,X1] :
( ~ rq(X0,X1)
| ~ cnotA(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f31,f76]) ).
fof(f81,plain,
! [X0] :
( ~ sQ3_spl
| ~ rq(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f80,f58]) ).
fof(f84,plain,
( ~ sQ3_spl
| ~ cA(sK6_skl) ),
inference(resolution,[status(thm)],[f81,f19]) ).
fof(f85,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f61]) ).
fof(f86,plain,
( ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( sQ3_spl
| cA(sK6_skl) ),
inference(resolution,[status(thm)],[f59,f78]) ).
fof(f88,plain,
( sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f87,f60,f57]) ).
fof(f89,plain,
$false,
inference(sat_refutation,[status(thm)],[f63,f64,f71,f73,f75,f86,f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS131+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n017.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 20 22:49:41 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.042286 seconds
% 0.13/0.39 % CPU time: 0.112228 seconds
% 0.13/0.39 % Total memory used: 16.976 MB
% 0.13/0.39 % Net memory used: 16.551 MB
%------------------------------------------------------------------------------