%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS170+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 : n019.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 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 9 unt; 8 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 217 ( 84 ~; 85 |; 30 &)
% ( 12 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 79 ( 60 !; 19 ?)
% 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,Y] :
( rhasLeader(X,Y)
<=> rhasHead(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
( ! [X,Y] :
( rhasHead(X,Y)
=> rhasLeader(X,Y) )
& ! [X,Y] :
( rhasLeader(X,Y)
=> rhasHead(X,Y) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ( ! [X,Y] :
( rhasHead(X,Y)
=> rhasLeader(X,Y) )
& ! [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)],[f4]) ).
fof(f6,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
( ! [X] :
( xsd_integer(X)
| xsd_string(X) )
& ! [X] :
( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [X,Y] :
( ( ~ rhasHead(X,Y)
| rhasLeader(X,Y) )
& ( rhasHead(X,Y)
| ~ rhasLeader(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
( ! [X,Y] :
( ~ rhasHead(X,Y)
| rhasLeader(X,Y) )
& ! [X,Y] :
( rhasHead(X,Y)
| ~ rhasLeader(X,Y) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( rhasHead(X0,X1)
| ~ rhasLeader(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ~ rhasHead(X0,X1)
| rhasLeader(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
( ? [X,Y] :
( ~ rhasLeader(X,Y)
& rhasHead(X,Y) )
| ? [X,Y] :
( ~ rhasHead(X,Y)
& rhasLeader(X,Y) )
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f18,definition,
! [X] :
( sP0_prd(X)
<=> ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f19,definition,
! [X,Y] :
( sP1_prd(Y,X)
<=> ( ~ rhasHead(X,Y)
& rhasLeader(X,Y) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f20,plain,
( ? [X,Y] :
( ~ rhasLeader(X,Y)
& rhasHead(X,Y) )
| ? [X,Y] : sP1_prd(Y,X)
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(formula_renaming,[status(thm)],[f17,f19,f18]) ).
fof(f21,plain,
( ? [X,Y] :
( ~ rhasLeader(X,Y)
& rhasHead(X,Y) )
| ? [X,Y] : sP1_prd(Y,X)
| ? [X] : sP0_prd(X)
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
( ( ~ rhasLeader(sK5_skl,sK6_skl)
& rhasHead(sK5_skl,sK6_skl) )
| sP1_prd(sK4_skl,sK3_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,sK5_skl,sK6_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl),skolemize(X,sK2_skl),skolemize(X,sK3_skl),skolemize(Y,sK4_skl),skolemize(X,sK5_skl),skolemize(Y,sK6_skl)],[f21]) ).
fof(f23,plain,
( rhasHead(sK5_skl,sK6_skl)
| sP1_prd(sK4_skl,sK3_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
( ~ rhasLeader(sK5_skl,sK6_skl)
| sP1_prd(sK4_skl,sK3_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,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)],[f18]) ).
fof(f26,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)],[f25]) ).
fof(f27,plain,
! [X0] :
( ~ xsd_integer(X0)
| xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0] :
( xsd_integer(X0)
| ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f31,plain,
! [X,Y] :
( ( rhasHead(X,Y)
| ~ rhasLeader(X,Y)
| sP1_prd(Y,X) )
& ( ( ~ rhasHead(X,Y)
& rhasLeader(X,Y) )
| ~ sP1_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f32,plain,
( ! [X,Y] :
( rhasHead(X,Y)
| ~ rhasLeader(X,Y)
| sP1_prd(Y,X) )
& ! [X,Y] :
( ( ~ rhasHead(X,Y)
& rhasLeader(X,Y) )
| ~ sP1_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( rhasLeader(X1,X0)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ~ rhasHead(X1,X0)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,definition,
( sQ0_spl
<=> cowlThing(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( sQ0_spl
| ~ cowlThing(sK0_skl) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ1_spl
<=> cowlNothing(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( ~ sQ1_spl
| cowlNothing(sK1_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,definition,
( sQ2_spl
<=> sP0_prd(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( ~ sQ2_spl
| sP0_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,definition,
( sQ3_spl
<=> sP1_prd(sK4_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( ~ sQ3_spl
| sP1_prd(sK4_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,definition,
( sQ4_spl
<=> rhasHead(sK5_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( ~ sQ4_spl
| rhasHead(sK5_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( sQ4_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f23,f36,f39,f42,f45,f48]) ).
fof(f52,definition,
( sQ5_spl
<=> rhasLeader(sK5_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( sQ5_spl
| ~ rhasLeader(sK5_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( ~ sQ5_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f24,f36,f39,f42,f45,f52]) ).
fof(f56,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f27,f11]) ).
fof(f58,plain,
! [X0,X1] :
( ~ sP1_prd(X1,X0)
| ~ rhasLeader(X0,X1) ),
inference(resolution,[status(thm)],[f15,f34]) ).
fof(f59,plain,
! [X0,X1] : ~ sP1_prd(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f58,f33]) ).
fof(f61,plain,
! [X0] : ~ sP0_prd(X0),
inference(backward_subsumption_resolution,[status(thm)],[f56,f62]) ).
fof(f62,plain,
! [X0] :
( xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f28,f12]) ).
fof(f63,plain,
( ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f46,f59]) ).
fof(f64,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f61]) ).
fof(f66,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f65]) ).
fof(f67,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f40,f8]) ).
fof(f68,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f67]) ).
fof(f69,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f7]) ).
fof(f70,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f69]) ).
fof(f71,plain,
( ~ sQ4_spl
| rhasLeader(sK5_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f49,f16]) ).
fof(f72,plain,
( ~ sQ4_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f54]) ).
fof(f73,plain,
( ~ sQ4_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f72]) ).
fof(f74,plain,
$false,
inference(sat_refutation,[status(thm)],[f51,f55,f64,f66,f68,f70,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS170+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 22:55:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.036139 seconds
% 0.10/0.41 % CPU time: 0.092064 seconds
% 0.10/0.41 % Total memory used: 11.616 MB
% 0.10/0.41 % Net memory used: 11.287 MB
%------------------------------------------------------------------------------