%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS175+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 : n026.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 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 97 ( 10 unt; 11 def)
% Number of atoms : 324 ( 47 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 369 ( 142 ~; 170 |; 34 &)
% ( 19 <=>; 0 =>; 0 <=; 4 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 11 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 58 ( 45 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] :
( cA(X)
<=> X = ia ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( cA_and_B(X)
<=> ( cB(X)
| cA(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( cB(X)
<=> X = ib ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
( cowlThing(ib)
& cowlThing(ia)
& ! [X] :
( cA_and_B(X)
<=> ( X = ia
| X = ib ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ( cowlThing(ib)
& cowlThing(ia)
& ! [X] :
( cA_and_B(X)
<=> ( X = ia
| X = ib ) )
& ! [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] :
( ( ( ~ cB(X)
& ~ cA(X) )
| cA_and_B(X) )
& ( cB(X)
| cA(X)
| ~ cA_and_B(X) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f50,plain,
( ! [X] :
( ( ~ cB(X)
& ~ cA(X) )
| cA_and_B(X) )
& ! [X] :
( cB(X)
| cA(X)
| ~ cA_and_B(X) ) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0] :
( cB(X0)
| cA(X0)
| ~ cA_and_B(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ cA(X0)
| cA_and_B(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
! [X0] :
( ~ cB(X0)
| 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,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ? [X] :
( cA_and_B(X)
<~> ( X = ia
| X = ib ) )
| ? [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,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ? [X] :
( cA_and_B(X)
<~> ( X = ia
| X = ib ) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(formula_renaming,[status(thm)],[f60,f61]) ).
fof(f63,plain,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ? [X] :
( ( ( X != ia
& X != ib )
| ~ cA_and_B(X) )
& ( X = ia
| X = ib
| cA_and_B(X) ) )
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(NNF_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ? [X] :
( ( ( X != ia
& X != ib )
| ~ cA_and_B(X) )
& ( X = ia
| X = ib
| cA_and_B(X) ) )
| ? [X] : sP0_prd(X)
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| ( ( ( sK3_skl != ia
& sK3_skl != ib )
| ~ cA_and_B(sK3_skl) )
& ( sK3_skl = ia
| sK3_skl = ib
| 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,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK3_skl = ia
| sK3_skl = ib
| cA_and_B(sK3_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK3_skl != ib
| ~ cA_and_B(sK3_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
( ~ cowlThing(ib)
| ~ cowlThing(ia)
| sK3_skl != ia
| ~ 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(f86,plain,
( sQ3_spl
| ~ cA_and_B(sK3_skl) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ4_spl
<=> sK3_skl = ib ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ4_spl
| sK3_skl = ib ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,definition,
( sQ5_spl
<=> sK3_skl = ia ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ5_spl
| sK3_skl = ia ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,definition,
( sQ6_spl
<=> cowlThing(ia) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( sQ6_spl
| ~ cowlThing(ia) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,definition,
( sQ7_spl
<=> cowlThing(ib) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( sQ7_spl
| ~ cowlThing(ib) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f75,f78,f81,f84,f87,f90,f93,f96]) ).
fof(f100,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f75,f78,f81,f84,f87,f93,f96]) ).
fof(f101,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f75,f78,f81,f84,f90,f93,f96]) ).
fof(f102,plain,
cA(ia),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f103,plain,
cB(ib),
inference(destructive_equality_resolution,[status(thm)],[f57]) ).
fof(f104,plain,
( sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f98,f39]) ).
fof(f105,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f104]) ).
fof(f106,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f39]) ).
fof(f107,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f106]) ).
fof(f108,plain,
( ~ sQ2_spl
| xsd_integer(sK2_skl)
| ~ xsd_string(sK2_skl) ),
inference(resolution,[status(thm)],[f82,f72]) ).
fof(f110,definition,
( sQ8_spl
<=> xsd_string(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( sQ8_spl
| ~ xsd_string(sK2_skl) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,definition,
( sQ9_spl
<=> xsd_integer(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ9_spl
| xsd_integer(sK2_skl) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f115,plain,
( sQ9_spl
| ~ xsd_integer(sK2_skl) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( ~ sQ2_spl
| sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f108,f110,f113,f81]) ).
fof(f118,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f40]) ).
fof(f119,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f118]) ).
fof(f120,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f39]) ).
fof(f121,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f120]) ).
fof(f124,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f71,f43]) ).
fof(f126,plain,
( sQ8_spl
| xsd_integer(sK2_skl) ),
inference(resolution,[status(thm)],[f44,f112]) ).
fof(f127,plain,
( sQ8_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f115]) ).
fof(f128,plain,
( sQ8_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f127]) ).
fof(f129,plain,
( ~ sQ9_spl
| ~ sP0_prd(sK2_skl) ),
inference(resolution,[status(thm)],[f114,f124]) ).
fof(f131,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f82]) ).
fof(f132,plain,
( ~ sQ9_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f133,plain,
( sQ3_spl
| ~ sQ4_spl
| ~ cA_and_B(ib) ),
inference(backward_demodulation,[status(thm)],[f88,f86]) ).
fof(f135,plain,
cA_and_B(ia),
inference(resolution,[status(thm)],[f52,f102]) ).
fof(f136,plain,
( sQ3_spl
| ~ sQ4_spl
| ~ cB(ib) ),
inference(resolution,[status(thm)],[f53,f133]) ).
fof(f137,plain,
( sQ3_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f103]) ).
fof(f138,plain,
( sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f140,plain,
! [X0] :
( cA(X0)
| ~ cA_and_B(X0)
| X0 = ib ),
inference(resolution,[status(thm)],[f56,f51]) ).
fof(f142,plain,
! [X0] :
( X0 = ia
| ~ cA_and_B(X0)
| X0 = ib ),
inference(resolution,[status(thm)],[f140,f47]) ).
fof(f143,plain,
( ~ sQ3_spl
| sK3_skl = ia
| sK3_skl = ib ),
inference(resolution,[status(thm)],[f142,f85]) ).
fof(f146,plain,
( ~ sQ3_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f143,f87,f90,f84]) ).
fof(f155,plain,
( sQ3_spl
| ~ sQ5_spl
| ~ cA_and_B(ia) ),
inference(backward_demodulation,[status(thm)],[f91,f86]) ).
fof(f157,plain,
( sQ3_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f135]) ).
fof(f158,plain,
( sQ3_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f159,plain,
$false,
inference(sat_refutation,[status(thm)],[f99,f100,f101,f105,f107,f116,f119,f121,f128,f132,f138,f146,f158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS175+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.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
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:58:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.057429 seconds
% 0.12/0.42 % CPU time: 0.143412 seconds
% 0.12/0.42 % Total memory used: 80.521 MB
% 0.12/0.42 % Net memory used: 80.290 MB
%------------------------------------------------------------------------------