%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS174+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 : n009.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 12:59:52 PM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 88 ( 11 unt; 9 def)
% Number of atoms : 269 ( 36 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 293 ( 112 ~; 130 |; 30 &)
% ( 17 <=>; 0 =>; 0 <=; 4 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 59 ( 46 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] :
( cA(X)
<=> X = ia ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( cA_and_B(X)
<=> ( X = ia
| X = ib ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( cB(X)
<=> X = ib ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
( ! [X] :
( cA_and_B(X)
<=> ( cA(X)
| cB(X) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ( ! [X] :
( cA_and_B(X)
<=> ( cA(X)
| cB(X) ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f38,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f39,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
( ! [X] :
( xsd_integer(X)
| xsd_string(X) )
& ! [X] :
( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X] :
( ( X != ia
| cA(X) )
& ( X = ia
| ~ cA(X) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f46,plain,
( ! [X] :
( X != ia
| cA(X) )
& ! [X] :
( X = ia
| ~ cA(X) ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0] :
( X0 = ia
| ~ cA(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0] :
( X0 != ia
| cA(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
! [X] :
( ( ( X != ia
& X != ib )
| cA_and_B(X) )
& ( X = ia
| X = ib
| ~ cA_and_B(X) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f50,plain,
( ! [X] :
( ( X != ia
& X != ib )
| cA_and_B(X) )
& ! [X] :
( X = ia
| X = ib
| ~ cA_and_B(X) ) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0] :
( X0 = ia
| X0 = ib
| ~ cA_and_B(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0] :
( X0 != ib
| cA_and_B(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
! [X0] :
( X0 != ia
| cA_and_B(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
! [X] :
( ( X != ib
| cB(X) )
& ( X = ib
| ~ cB(X) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f55,plain,
( ! [X] :
( X != ib
| cB(X) )
& ! [X] :
( X = ib
| ~ cB(X) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0] :
( X0 = ib
| ~ cB(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0] :
( X0 != ib
| cB(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f60,plain,
( ? [X] :
( cA_and_B(X)
<~> ( cA(X)
| cB(X) ) )
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f61,definition,
! [X] :
( sP0_prd(X)
<=> ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f62,plain,
( ? [X] :
( cA_and_B(X)
<~> ( cA(X)
| cB(X) ) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(formula_renaming,[status(thm)],[f60,f61]) ).
fof(f63,plain,
( ? [X] :
( ( ( ~ cA(X)
& ~ cB(X) )
| ~ cA_and_B(X) )
& ( cA(X)
| cB(X)
| cA_and_B(X) ) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(NNF_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
( ? [X] :
( ( ( ~ cA(X)
& ~ cB(X) )
| ~ cA_and_B(X) )
& ( cA(X)
| cB(X)
| cA_and_B(X) ) )
| ? [X] : sP0_prd(X)
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
( ( ( ( ~ cA(sK3_skl)
& ~ cB(sK3_skl) )
| ~ cA_and_B(sK3_skl) )
& ( cA(sK3_skl)
| cB(sK3_skl)
| cA_and_B(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]),skolemize(X,sK0_skl),skolemize(X,sK1_skl),skolemize(X,sK2_skl),skolemize(X,sK3_skl)],[f64]) ).
fof(f66,plain,
( cA(sK3_skl)
| cB(sK3_skl)
| cA_and_B(sK3_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
( ~ cB(sK3_skl)
| ~ cA_and_B(sK3_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
( ~ cA(sK3_skl)
| ~ cA_and_B(sK3_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,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)],[f61]) ).
fof(f70,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)],[f69]) ).
fof(f71,plain,
! [X0] :
( ~ xsd_integer(X0)
| xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0] :
( xsd_integer(X0)
| ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f75,definition,
( sQ0_spl
<=> cowlThing(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( sQ0_spl
| ~ cowlThing(sK0_skl) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,definition,
( sQ1_spl
<=> cowlNothing(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ1_spl
| cowlNothing(sK1_skl) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,definition,
( sQ2_spl
<=> sP0_prd(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ2_spl
| sP0_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,definition,
( sQ3_spl
<=> cA_and_B(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( ~ sQ3_spl
| cA_and_B(sK3_skl) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ4_spl
<=> cB(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ4_spl
| cB(sK3_skl) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,definition,
( sQ5_spl
<=> cA(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ5_spl
| cA(sK3_skl) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f92,plain,
( sQ5_spl
| ~ cA(sK3_skl) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f75,f78,f81,f84,f87,f90]) ).
fof(f94,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f75,f78,f81,f84,f87]) ).
fof(f95,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f75,f78,f81,f84,f90]) ).
fof(f96,plain,
cA(ia),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f97,plain,
cA_and_B(ib),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f98,plain,
cA_and_B(ia),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f99,plain,
cB(ib),
inference(destructive_equality_resolution,[status(thm)],[f57]) ).
fof(f103,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f71,f43]) ).
fof(f104,plain,
! [X0] :
( ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f72,f43]) ).
fof(f107,plain,
! [X0] :
( xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f104,f44]) ).
fof(f108,plain,
! [X0] : ~ sP0_prd(X0),
inference(forward_subsumption_resolution,[status(thm)],[f107,f103]) ).
fof(f109,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f82,f108]) ).
fof(f110,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f109]) ).
fof(f111,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f40]) ).
fof(f112,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f111]) ).
fof(f113,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f39]) ).
fof(f114,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f113]) ).
fof(f154,plain,
( ~ sQ4_spl
| sK3_skl = ib ),
inference(resolution,[status(thm)],[f56,f88]) ).
fof(f161,definition,
( sQ9_spl
<=> ia = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ9_spl
| ia = sK3_skl ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f167,plain,
( ~ sQ3_spl
| sK3_skl = ia
| sK3_skl = ib ),
inference(resolution,[status(thm)],[f51,f85]) ).
fof(f170,definition,
( sQ10_spl
<=> sK3_skl = ib ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( ~ sQ10_spl
| sK3_skl = ib ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( ~ sQ3_spl
| sQ9_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f167,f170,f161,f84]) ).
fof(f179,plain,
( ~ sQ4_spl
| cA_and_B(sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f154,f97]) ).
fof(f181,plain,
( ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f179,f84,f87]) ).
fof(f184,plain,
( ~ sQ9_spl
| cA(sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f162,f96]) ).
fof(f185,plain,
( ~ sQ9_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f92]) ).
fof(f186,plain,
( ~ sQ9_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f189,plain,
( ~ sQ5_spl
| sK3_skl = ia ),
inference(resolution,[status(thm)],[f47,f91]) ).
fof(f192,plain,
( ~ sQ5_spl
| cA_and_B(sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f189,f98]) ).
fof(f193,plain,
( ~ sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f192,f84,f90]) ).
fof(f195,plain,
( ~ sQ10_spl
| cB(sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f171,f99]) ).
fof(f197,plain,
( ~ sQ10_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f195,f87,f170]) ).
fof(f198,plain,
$false,
inference(sat_refutation,[status(thm)],[f93,f94,f95,f110,f112,f114,f173,f181,f186,f193,f197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS174+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n009.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 22:55:27 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % 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
% 0.13/0.40 % Elapsed time: 0.042835 seconds
% 0.13/0.40 % CPU time: 0.124034 seconds
% 0.13/0.40 % Total memory used: 50.333 MB
% 0.13/0.40 % Net memory used: 50.170 MB
%------------------------------------------------------------------------------