%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS171+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 : n005.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 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 7 unt; 6 def)
% Number of atoms : 175 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 192 ( 75 ~; 81 |; 19 &)
% ( 11 <=>; 2 =>; 0 <=; 4 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 58 ( 41 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( rhasHead(X,Y)
=> rhasLeader(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( rhasLeader(X,Y)
=> rhasHead(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
( ! [X,Y] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ ( ! [X,Y] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
( ! [X] :
( xsd_integer(X)
| xsd_string(X) )
& ! [X] :
( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f14,plain,
! [X,Y] :
( rhasLeader(X,Y)
| ~ rhasHead(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( rhasLeader(X0,X1)
| ~ rhasHead(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X,Y] :
( rhasHead(X,Y)
| ~ rhasLeader(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( rhasHead(X0,X1)
| ~ rhasLeader(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
( ? [X,Y] :
( rhasLeader(X,Y)
<~> rhasHead(X,Y) )
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f19,definition,
! [X] :
( sP0_prd(X)
<=> ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f20,plain,
( ? [X,Y] :
( rhasLeader(X,Y)
<~> rhasHead(X,Y) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(formula_renaming,[status(thm)],[f18,f19]) ).
fof(f21,plain,
( ? [X,Y] :
( ( ~ rhasHead(X,Y)
| ~ rhasLeader(X,Y) )
& ( rhasHead(X,Y)
| rhasLeader(X,Y) ) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
( ? [X,Y] :
( ( ~ rhasHead(X,Y)
| ~ rhasLeader(X,Y) )
& ( rhasHead(X,Y)
| rhasLeader(X,Y) ) )
| ? [X] : sP0_prd(X)
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
( ( ( ~ rhasHead(sK3_skl,sK4_skl)
| ~ rhasLeader(sK3_skl,sK4_skl) )
& ( rhasHead(sK3_skl,sK4_skl)
| rhasLeader(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)],[f22]) ).
fof(f24,plain,
( rhasHead(sK3_skl,sK4_skl)
| rhasLeader(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
( ~ rhasHead(sK3_skl,sK4_skl)
| ~ rhasLeader(sK3_skl,sK4_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,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)],[f19]) ).
fof(f27,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)],[f26]) ).
fof(f28,plain,
! [X0] :
( ~ xsd_integer(X0)
| xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0] :
( xsd_integer(X0)
| ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f32,definition,
( sQ0_spl
<=> cowlThing(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( sQ0_spl
| ~ cowlThing(sK0_skl) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,definition,
( sQ1_spl
<=> cowlNothing(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( ~ sQ1_spl
| cowlNothing(sK1_skl) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
( sQ2_spl
<=> sP0_prd(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ2_spl
| sP0_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,definition,
( sQ3_spl
<=> rhasLeader(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( ~ sQ3_spl
| rhasLeader(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f43,plain,
( sQ3_spl
| ~ rhasLeader(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,definition,
( sQ4_spl
<=> rhasHead(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ4_spl
| ~ rhasHead(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( sQ4_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f24,f32,f35,f38,f41,f44]) ).
fof(f48,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f25,f32,f35,f38,f41,f44]) ).
fof(f49,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f28,f12]) ).
fof(f50,plain,
! [X0] :
( ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f29,f12]) ).
fof(f52,plain,
! [X0] :
( xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f49,f13]) ).
fof(f54,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f39,f55]) ).
fof(f55,plain,
! [X0] : ~ sP0_prd(X0),
inference(forward_subsumption_resolution,[status(thm)],[f52,f50]) ).
fof(f56,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f36,f9]) ).
fof(f58,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f57]) ).
fof(f59,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f8]) ).
fof(f60,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f59]) ).
fof(f61,plain,
( ~ sQ3_spl
| rhasHead(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f42,f17]) ).
fof(f62,plain,
( ~ sQ3_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f46]) ).
fof(f63,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f62]) ).
fof(f64,plain,
( sQ3_spl
| ~ rhasHead(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f43,f15]) ).
fof(f65,plain,
( sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f64,f44,f41]) ).
fof(f66,plain,
$false,
inference(sat_refutation,[status(thm)],[f47,f48,f56,f58,f60,f63,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS171+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:55:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.41 % Elapsed time: 0.035658 seconds
% 0.09/0.41 % CPU time: 0.082206 seconds
% 0.09/0.41 % Total memory used: 9.970 MB
% 0.09/0.41 % Net memory used: 9.661 MB
%------------------------------------------------------------------------------