%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS138+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 : n013.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 12:59:46 PM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 31
% Syntax : Number of formulae : 150 ( 21 unt; 23 def)
% Number of atoms : 463 ( 71 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 535 ( 222 ~; 229 |; 49 &)
% ( 27 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 22 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 101 ( 82 !; 19 ?)
% 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
| X = ib ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] :
( ( requalityOnA(Z,X)
& requalityOnA(Y,X) )
=> Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] :
( requalityOnA(X,Y)
=> cA(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
requalityOnA(ia,ia),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
requalityOnA(ib,ib),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
( cowlThing(ic)
& cowlThing(ib)
& requalityOnA(ia,ia)
& cowlThing(ia)
& ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ic
| X = ib
| X = ia ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ( cowlThing(ic)
& cowlThing(ib)
& requalityOnA(ia,ia)
& cowlThing(ia)
& ! [X,Y] :
( requalityOnA(X,Y)
=> requalityOnA(Y,X) )
& ! [X,Y] :
( requalityOnA(X,Y)
=> ( X = ic
| X = ib
| X = ia ) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( ~ cowlNothing(X)
& cowlThing(X) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f41,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f42,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,plain,
! [X] :
( ( xsd_integer(X)
| xsd_string(X) )
& ( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f45,plain,
( ! [X] :
( xsd_integer(X)
| xsd_string(X) )
& ! [X] :
( ~ xsd_integer(X)
| ~ xsd_string(X) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
! [X] :
( ( ( X != ia
& X != ib )
| cA(X) )
& ( X = ia
| X = ib
| ~ cA(X) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f49,plain,
( ! [X] :
( ( X != ia
& X != ib )
| cA(X) )
& ! [X] :
( X = ia
| X = ib
| ~ cA(X) ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0] :
( X0 = ia
| X0 = ib
| ~ cA(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X,Y,Z] :
( Y = Z
| ~ requalityOnA(Z,X)
| ~ requalityOnA(Y,X) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f54,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ requalityOnA(Z,X)
| ~ requalityOnA(Y,X) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ requalityOnA(X2,X1)
| ~ requalityOnA(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X,Y] :
( cA(Y)
| ~ requalityOnA(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f57,plain,
! [Y] :
( cA(Y)
| ! [X] : ~ requalityOnA(X,Y) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( cA(X1)
| ~ requalityOnA(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f60,plain,
requalityOnA(ia,ia),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f62,plain,
requalityOnA(ib,ib),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f64,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ? [X,Y] :
( ~ requalityOnA(Y,X)
& requalityOnA(X,Y) )
| ? [X,Y] :
( X != ic
& X != ib
& X != ia
& requalityOnA(X,Y) )
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f65,definition,
! [X] :
( sP0_prd(X)
<=> ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f66,definition,
! [X,Y] :
( sP1_prd(Y,X)
<=> ( X != ic
& X != ib
& X != ia
& requalityOnA(X,Y) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f67,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ? [X,Y] :
( ~ requalityOnA(Y,X)
& requalityOnA(X,Y) )
| ? [X,Y] : sP1_prd(Y,X)
| ? [X] : sP0_prd(X)
| ? [X] :
( cowlNothing(X)
| ~ cowlThing(X) ) ),
inference(formula_renaming,[status(thm)],[f64,f66,f65]) ).
fof(f68,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ? [X,Y] :
( ~ requalityOnA(Y,X)
& requalityOnA(X,Y) )
| ? [X,Y] : sP1_prd(Y,X)
| ? [X] : sP0_prd(X)
| ? [X] : cowlNothing(X)
| ? [X] : ~ cowlThing(X) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f69,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ( ~ requalityOnA(sK6_skl,sK5_skl)
& requalityOnA(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)],[f68]) ).
fof(f70,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| requalityOnA(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)],[f69]) ).
fof(f71,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ~ requalityOnA(sK6_skl,sK5_skl)
| sP1_prd(sK4_skl,sK3_skl)
| sP0_prd(sK2_skl)
| cowlNothing(sK1_skl)
| ~ cowlThing(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f72,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)],[f65]) ).
fof(f73,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)],[f72]) ).
fof(f74,plain,
! [X0] :
( ~ xsd_integer(X0)
| xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
! [X0] :
( xsd_integer(X0)
| ~ xsd_string(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f78,plain,
! [X,Y] :
( ( X = ic
| X = ib
| X = ia
| ~ requalityOnA(X,Y)
| sP1_prd(Y,X) )
& ( ( X != ic
& X != ib
& X != ia
& requalityOnA(X,Y) )
| ~ sP1_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f66]) ).
fof(f79,plain,
( ! [X,Y] :
( X = ic
| X = ib
| X = ia
| ~ requalityOnA(X,Y)
| sP1_prd(Y,X) )
& ! [X,Y] :
( ( X != ic
& X != ib
& X != ia
& requalityOnA(X,Y) )
| ~ sP1_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( requalityOnA(X1,X0)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( X1 != ia
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f82,plain,
! [X0,X1] :
( X1 != ib
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f85,definition,
( sQ0_spl
<=> cowlThing(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( sQ0_spl
| ~ cowlThing(sK0_skl) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ1_spl
<=> cowlNothing(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ1_spl
| cowlNothing(sK1_skl) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,definition,
( sQ2_spl
<=> sP0_prd(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ2_spl
| sP0_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,definition,
( sQ3_spl
<=> sP1_prd(sK4_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ3_spl
| sP1_prd(sK4_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ4_spl
<=> requalityOnA(sK5_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ4_spl
| requalityOnA(sK5_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
( sQ5_spl
<=> cowlThing(ia) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( sQ5_spl
| ~ cowlThing(ia) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,definition,
( sQ6_spl
<=> requalityOnA(ia,ia) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( sQ6_spl
| ~ requalityOnA(ia,ia) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,definition,
( sQ7_spl
<=> cowlThing(ib) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( sQ7_spl
| ~ cowlThing(ib) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,definition,
( sQ8_spl
<=> cowlThing(ic) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( sQ8_spl
| ~ cowlThing(ic) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f70,f85,f88,f91,f94,f97,f100,f103,f106,f109]) ).
fof(f113,definition,
( sQ9_spl
<=> requalityOnA(sK6_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( sQ9_spl
| ~ requalityOnA(sK6_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ9_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f85,f88,f91,f94,f113,f100,f103,f106,f109]) ).
fof(f119,plain,
! [X0] :
( ~ xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f46]) ).
fof(f120,plain,
! [X0] : ~ sP0_prd(X0),
inference(backward_subsumption_resolution,[status(thm)],[f119,f121]) ).
fof(f121,plain,
! [X0] :
( xsd_integer(X0)
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f47]) ).
fof(f122,plain,
! [X0] : ~ sP1_prd(X0,ia),
inference(destructive_equality_resolution,[status(thm)],[f81]) ).
fof(f123,plain,
! [X0] : ~ sP1_prd(X0,ib),
inference(destructive_equality_resolution,[status(thm)],[f82]) ).
fof(f125,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f42]) ).
fof(f126,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f125]) ).
fof(f127,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f42]) ).
fof(f128,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f127]) ).
fof(f129,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f60]) ).
fof(f130,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f129]) ).
fof(f131,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f42]) ).
fof(f132,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f134,plain,
! [X0] :
( X0 = ib
| ~ requalityOnA(X0,ib) ),
inference(resolution,[status(thm)],[f62,f55]) ).
fof(f135,plain,
( ~ sQ3_spl
| requalityOnA(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f95,f80]) ).
fof(f138,plain,
! [X0] :
( ~ sQ3_spl
| X0 = sK3_skl
| ~ requalityOnA(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f135,f55]) ).
fof(f142,definition,
( sQ10_spl
<=> sK3_skl = ia ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( ~ sQ10_spl
| sK3_skl = ia ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f152,definition,
( sQ13_spl
<=> sP1_prd(ib,ib) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ13_spl
| sP1_prd(ib,ib) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f165,definition,
( sQ17_spl
<=> sP1_prd(ia,ia) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ17_spl
| sP1_prd(ia,ia) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f190,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f123]) ).
fof(f191,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f192,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f120]) ).
fof(f193,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f43]) ).
fof(f195,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f196,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f42]) ).
fof(f197,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f196]) ).
fof(f212,definition,
! [X0] :
( sQ20_spl
<=> ~ requalityOnA(ib,X0) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f213,plain,
! [X0] :
( ~ sQ20_spl
| ~ requalityOnA(ib,X0) ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f216,plain,
( ~ sQ20_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f62,f213]) ).
fof(f217,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f221,plain,
! [X0,X1] :
( ~ requalityOnA(X1,X0)
| X0 = ia
| X0 = ib ),
inference(resolution,[status(thm)],[f50,f58]) ).
fof(f223,plain,
( ~ sQ3_spl
| sK4_skl = ia
| sK4_skl = ib ),
inference(resolution,[status(thm)],[f221,f135]) ).
fof(f224,definition,
( sQ21_spl
<=> sK4_skl = ib ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( ~ sQ21_spl
| sK4_skl = ib ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,definition,
( sQ22_spl
<=> sK4_skl = ia ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( ~ sQ22_spl
| sK4_skl = ia ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,plain,
( ~ sQ3_spl
| sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f223,f224,f227,f94]) ).
fof(f231,plain,
( ~ sQ3_spl
| ~ sQ21_spl
| requalityOnA(sK3_skl,ib) ),
inference(backward_demodulation,[status(thm)],[f225,f135]) ).
fof(f232,plain,
( ~ sQ3_spl
| ~ sQ21_spl
| sP1_prd(ib,sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f225,f95]) ).
fof(f250,plain,
( ~ sQ3_spl
| ~ sQ21_spl
| sK3_skl = ib ),
inference(resolution,[status(thm)],[f231,f134]) ).
fof(f254,plain,
( ~ sQ3_spl
| ~ sQ21_spl
| sP1_prd(ib,ib) ),
inference(backward_demodulation,[status(thm)],[f250,f232]) ).
fof(f261,plain,
( ~ sQ3_spl
| ~ sQ21_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f254,f152,f224,f94]) ).
fof(f269,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ22_spl
| X0 = sK3_skl
| ~ requalityOnA(X0,ia) ),
inference(backward_demodulation,[status(thm)],[f228,f138]) ).
fof(f270,plain,
( ~ sQ3_spl
| ~ sQ22_spl
| sP1_prd(ia,sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f228,f95]) ).
fof(f273,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f122]) ).
fof(f274,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f273]) ).
fof(f283,plain,
( ~ sQ4_spl
| sK6_skl = ia
| sK6_skl = ib ),
inference(resolution,[status(thm)],[f98,f221]) ).
fof(f285,plain,
! [X0] :
( ~ sQ4_spl
| X0 = sK5_skl
| ~ requalityOnA(X0,sK6_skl) ),
inference(resolution,[status(thm)],[f98,f55]) ).
fof(f286,definition,
( sQ24_spl
<=> sK6_skl = ib ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( ~ sQ24_spl
| sK6_skl = ib ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,definition,
( sQ25_spl
<=> sK6_skl = ia ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( ~ sQ25_spl
| sK6_skl = ia ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,plain,
( ~ sQ4_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f283,f286,f289,f97]) ).
fof(f296,definition,
( sQ27_spl
<=> sK5_skl = ia ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ27_spl
| sK5_skl = ia ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,definition,
( sQ28_spl
<=> sK5_skl = ib ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( ~ sQ28_spl
| sK5_skl = ib ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f303,plain,
( sQ9_spl
| ~ sQ28_spl
| ~ requalityOnA(sK6_skl,ib) ),
inference(backward_demodulation,[status(thm)],[f300,f115]) ).
fof(f311,plain,
( sQ9_spl
| ~ sQ27_spl
| ~ requalityOnA(sK6_skl,ia) ),
inference(backward_demodulation,[status(thm)],[f297,f115]) ).
fof(f321,plain,
( sQ9_spl
| ~ sQ28_spl
| ~ sQ24_spl
| ~ requalityOnA(ib,ib) ),
inference(forward_demodulation,[status(thm)],[f287,f303]) ).
fof(f322,plain,
( sQ9_spl
| ~ sQ28_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f321,f62]) ).
fof(f323,plain,
( sQ9_spl
| ~ sQ28_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f322]) ).
fof(f333,definition,
( sQ29_spl
<=> sP1_prd(sK5_skl,ia) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( ~ sQ29_spl
| sP1_prd(sK5_skl,ia) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f337,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f122]) ).
fof(f338,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f352,plain,
( ~ sQ3_spl
| ~ sQ22_spl
| ~ sQ10_spl
| sP1_prd(ia,ia) ),
inference(backward_demodulation,[status(thm)],[f143,f270]) ).
fof(f380,plain,
( ~ sQ3_spl
| ~ sQ22_spl
| ia = sK3_skl ),
inference(resolution,[status(thm)],[f60,f269]) ).
fof(f384,plain,
( ~ sQ3_spl
| ~ sQ22_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f380,f142,f227,f94]) ).
fof(f387,plain,
( ~ sQ3_spl
| ~ sQ22_spl
| ~ sQ10_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f352,f165,f142,f227,f94]) ).
fof(f433,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ25_spl
| X0 = sK5_skl
| ~ requalityOnA(X0,ia) ),
inference(forward_demodulation,[status(thm)],[f290,f285]) ).
fof(f470,plain,
( sQ9_spl
| ~ sQ27_spl
| ~ sQ25_spl
| ~ requalityOnA(ia,ia) ),
inference(forward_demodulation,[status(thm)],[f290,f311]) ).
fof(f471,plain,
( sQ9_spl
| ~ sQ27_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f470,f60]) ).
fof(f472,plain,
( sQ9_spl
| ~ sQ27_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f471]) ).
fof(f476,plain,
( ~ sQ4_spl
| ~ sQ24_spl
| requalityOnA(sK5_skl,ib) ),
inference(backward_demodulation,[status(thm)],[f287,f98]) ).
fof(f478,plain,
( ~ sQ4_spl
| ~ sQ24_spl
| sK5_skl = ib ),
inference(resolution,[status(thm)],[f476,f134]) ).
fof(f482,plain,
( ~ sQ4_spl
| ~ sQ24_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f478,f299,f286,f97]) ).
fof(f500,plain,
( ~ sQ4_spl
| ~ sQ25_spl
| ia = sK5_skl ),
inference(resolution,[status(thm)],[f60,f433]) ).
fof(f504,plain,
( ~ sQ4_spl
| ~ sQ25_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f500,f296,f289,f97]) ).
fof(f507,plain,
$false,
inference(sat_refutation,[status(thm)],[f112,f116,f126,f128,f130,f132,f191,f193,f195,f197,f217,f230,f261,f274,f292,f323,f338,f384,f387,f472,f482,f504]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS138+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 22:53:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.049589 seconds
% 0.11/0.42 % CPU time: 0.128539 seconds
% 0.11/0.42 % Total memory used: 18.177 MB
% 0.11/0.42 % Net memory used: 18.141 MB
%------------------------------------------------------------------------------