%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS169+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 : n011.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 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 10 unt; 7 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 192 ( 80 ~; 81 |; 19 &)
% ( 11 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 32 ( 25 !; 7 ?)
% 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(f4,axiom,
rhasLeader(iX,iY),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
( cowlThing(iY)
& rhasHead(iX,iY)
& cowlThing(iX)
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ( cowlThing(iY)
& rhasHead(iX,iY)
& cowlThing(iX)
& ! [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(f17,plain,
rhasLeader(iX,iY),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X,Y] :
( ( ~ rhasHead(X,Y)
| rhasLeader(X,Y) )
& ( rhasHead(X,Y)
| ~ rhasLeader(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
( ! [X,Y] :
( ~ rhasHead(X,Y)
| rhasLeader(X,Y) )
& ! [X,Y] :
( rhasHead(X,Y)
| ~ rhasLeader(X,Y) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( rhasHead(X0,X1)
| ~ rhasLeader(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ? [X] :
( ( xsd_integer(X)
| ~ xsd_string(X) )
& ( ~ xsd_integer(X)
| xsd_string(X) ) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ? [X] :
( ( xsd_integer(X)
| ~ xsd_string(X) )
& ( ~ xsd_integer(X)
| xsd_string(X) ) )
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ( ( xsd_integer(sK2_skl)
| ~ xsd_string(sK2_skl) )
& ( ~ xsd_integer(sK2_skl)
| xsd_string(sK2_skl) ) )
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl),skolemize(X,sK2_skl)],[f25]) ).
fof(f27,plain,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| ~ xsd_integer(sK2_skl)
| xsd_string(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
( ~ cowlThing(iY)
| ~ rhasHead(iX,iY)
| ~ cowlThing(iX)
| xsd_integer(sK2_skl)
| ~ xsd_string(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,definition,
( sQ0_spl
<=> cowlThing(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f31,plain,
( sQ0_spl
| ~ cowlThing(sK0_skl) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,definition,
( sQ1_spl
<=> cowlNothing(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( ~ sQ1_spl
| cowlNothing(sK1_skl) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,definition,
( sQ2_spl
<=> xsd_string(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( ~ sQ2_spl
| xsd_string(sK2_skl) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
( sQ3_spl
<=> xsd_integer(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ3_spl
| xsd_integer(sK2_skl) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f40,plain,
( sQ3_spl
| ~ xsd_integer(sK2_skl) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,definition,
( sQ4_spl
<=> cowlThing(iX) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( sQ4_spl
| ~ cowlThing(iX) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,definition,
( sQ5_spl
<=> rhasHead(iX,iY) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ5_spl
| ~ rhasHead(iX,iY) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,definition,
( sQ6_spl
<=> cowlThing(iY) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ6_spl
| ~ cowlThing(iY) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f27,f29,f32,f35,f38,f41,f44,f47]) ).
fof(f51,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ3_spl
| ~ sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f28,f29,f32,f35,f38,f41,f44,f47]) ).
fof(f52,plain,
( sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f49,f10]) ).
fof(f53,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( sQ5_spl
| ~ rhasLeader(iX,iY) ),
inference(resolution,[status(thm)],[f21,f46]) ).
fof(f56,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f17]) ).
fof(f57,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f56]) ).
fof(f58,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f10]) ).
fof(f59,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f58]) ).
fof(f60,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f11]) ).
fof(f61,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f31,f10]) ).
fof(f63,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f62]) ).
fof(f64,plain,
( ~ sQ3_spl
| ~ xsd_string(sK2_skl) ),
inference(resolution,[status(thm)],[f39,f14]) ).
fof(f65,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f64,f36]) ).
fof(f66,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f65]) ).
fof(f67,plain,
( sQ3_spl
| xsd_string(sK2_skl) ),
inference(resolution,[status(thm)],[f40,f15]) ).
fof(f68,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f67,f35,f38]) ).
fof(f69,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f51,f53,f57,f59,f61,f63,f66,f68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS169+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 : n011.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 22:54:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.041785 seconds
% 0.14/0.40 % CPU time: 0.108687 seconds
% 0.14/0.40 % Total memory used: 14.699 MB
% 0.14/0.40 % Net memory used: 14.238 MB
%------------------------------------------------------------------------------