%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS138+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 : Fri Sep 25 01:54:15 PM UTC 2026
% Result : Theorem 2.05s 1.28s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 121 ( 14 unt; 1 def)
% Number of atoms : 544 ( 127 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 666 ( 284 ~; 308 |; 58 &)
% ( 5 <=>; 8 =>; 0 <=; 3 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 137 ( 0 sgn 107 !; 30 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( ~ cowlNothing(X0)
& cowlThing(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
fof(f9,axiom,
! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f10,axiom,
! [X0] :
( cA(X0)
<=> ( X0 = ia
| X0 = ib ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f11,axiom,
! [X0,X1,X2] :
( ( requalityOnA(X2,X0)
& requalityOnA(X1,X0) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f12,axiom,
! [X0,X1] :
( requalityOnA(X0,X1)
=> cA(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f14,axiom,
requalityOnA(ia,ia),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(f16,axiom,
requalityOnA(ib,ib),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
fof(f18,conjecture,
( cowlThing(ic)
& cowlThing(ib)
& requalityOnA(ia,ia)
& cowlThing(ia)
& ! [X0,X1] :
( requalityOnA(X0,X1)
=> requalityOnA(X1,X0) )
& ! [X0,X1] :
( requalityOnA(X0,X1)
=> ( X0 = ic
| X0 = ib
| X0 = ia ) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( ~ cowlNothing(X0)
& cowlThing(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
fof(f19,negated_conjecture,
~ ( cowlThing(ic)
& cowlThing(ib)
& requalityOnA(ia,ia)
& cowlThing(ia)
& ! [X0,X1] :
( requalityOnA(X0,X1)
=> requalityOnA(X1,X0) )
& ! [X0,X1] :
( requalityOnA(X0,X1)
=> ( X0 = ic
| X0 = ib
| X0 = ia ) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( ~ cowlNothing(X0)
& cowlThing(X0) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
~ ( cowlThing(ic)
& cowlThing(ib)
& requalityOnA(ia,ia)
& cowlThing(ia)
& ! [X4,X5] :
( requalityOnA(X4,X5)
=> requalityOnA(X5,X4) )
& ! [X2,X3] :
( requalityOnA(X2,X3)
=> ( ic = X2
| ib = X2
| ia = X2 ) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& ! [X0] :
( ~ cowlNothing(X0)
& cowlThing(X0) ) ),
inference(rectify,[],[f19]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ requalityOnA(X2,X0)
| ~ requalityOnA(X1,X0)
| X1 = X2 ),
inference(ennf_transformation,[],[f11]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ requalityOnA(X2,X0)
| ~ requalityOnA(X1,X0)
| X1 = X2 ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ~ requalityOnA(X0,X1)
| cA(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f38,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ? [X4,X5] :
( requalityOnA(X4,X5)
& ~ requalityOnA(X5,X4) )
| ? [X2,X3] :
( requalityOnA(X2,X3)
& ic != X2
& ib != X2
& ia != X2 )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f39,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ? [X4,X5] :
( requalityOnA(X4,X5)
& ~ requalityOnA(X5,X4) )
| ? [X2,X3] :
( requalityOnA(X2,X3)
& ic != X2
& ib != X2
& ia != X2 )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(flattening,[],[f38]) ).
fof(f42,plain,
! [X0] :
( ( ~ xsd_string(X0)
| ~ xsd_integer(X0) )
& ( xsd_integer(X0)
| xsd_string(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f43,plain,
! [X0] :
( ( ~ cA(X0)
| X0 = ia
| X0 = ib )
& ( ( ia != X0
& ib != X0 )
| cA(X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f44,plain,
! [X0] :
( ( ~ cA(X0)
| X0 = ia
| X0 = ib )
& ( ( ia != X0
& ib != X0 )
| cA(X0) ) ),
inference(flattening,[],[f43]) ).
fof(f48,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ? [X4,X5] :
( requalityOnA(X4,X5)
& ~ requalityOnA(X5,X4) )
| sP0
| ? [X1] :
( ( xsd_string(X1)
| ~ xsd_integer(X1) )
& ( ~ xsd_string(X1)
| xsd_integer(X1) ) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f49,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ? [X2,X3] :
( requalityOnA(X2,X3)
& ~ requalityOnA(X3,X2) )
| sP0
| ? [X1] :
( ( xsd_string(X1)
| ~ xsd_integer(X1) )
& ( ~ xsd_string(X1)
| xsd_integer(X1) ) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(rectify,[],[f48]) ).
fof(f50,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ( requalityOnA(sK5,sK6)
& ~ requalityOnA(sK6,sK5) )
| sP0
| ( ( xsd_string(sK4)
| ~ xsd_integer(sK4) )
& ( ~ xsd_string(sK4)
| xsd_integer(sK4) ) )
| cowlNothing(sK3)
| ~ cowlThing(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f49]) ).
fof(f58,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f60,plain,
! [X0] :
( ~ xsd_string(X0)
| ~ xsd_integer(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f61,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f62,plain,
! [X0] :
( ~ cA(X0)
| ia = X0
| ib = X0 ),
inference(cnf_transformation,[],[f44]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ requalityOnA(X2,X0)
| ~ requalityOnA(X1,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f66,plain,
! [X0,X1] :
( ~ requalityOnA(X0,X1)
| cA(X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f68,plain,
requalityOnA(ia,ia),
inference(cnf_transformation,[],[f14]) ).
fof(f70,plain,
requalityOnA(ib,ib),
inference(cnf_transformation,[],[f16]) ).
fof(f76,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| requalityOnA(sK5,sK6)
| sP0
| xsd_string(sK4)
| ~ xsd_integer(sK4)
| cowlNothing(sK3)
| ~ cowlThing(sK3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f77,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ~ requalityOnA(sK6,sK5)
| sP0
| xsd_string(sK4)
| ~ xsd_integer(sK4)
| cowlNothing(sK3)
| ~ cowlThing(sK3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f78,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| requalityOnA(sK5,sK6)
| sP0
| ~ xsd_string(sK4)
| xsd_integer(sK4)
| cowlNothing(sK3)
| ~ cowlThing(sK3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f79,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ~ requalityOnA(sK6,sK5)
| sP0
| ~ xsd_string(sK4)
| xsd_integer(sK4)
| cowlNothing(sK3)
| ~ cowlThing(sK3) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_49,plain,
! [X0: $i] : cowlThing(X0),
inference(cnf_transformation,[],[f59]) ).
tcf(c_50,plain,
! [X0: $i] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f58]) ).
tcf(c_51,plain,
! [X0: $i] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_52,plain,
! [X0: $i] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_55,plain,
! [X0: $i] :
( ( X0 = ia )
| ( X0 = ib )
| ~ cA(X0) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ requalityOnA(X2,X1)
| ~ requalityOnA(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( cA(X1)
| ~ requalityOnA(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_59,plain,
requalityOnA(ia,ia),
inference(cnf_transformation,[],[f68]) ).
tcf(c_61,plain,
requalityOnA(ib,ib),
inference(cnf_transformation,[],[f70]) ).
tcf(c_67,negated_conjecture,
( sP0
| xsd_integer(sK4)
| cowlNothing(sK3)
| ~ xsd_string(sK4)
| ~ cowlThing(sK3)
| ~ cowlThing(ic)
| ~ cowlThing(ia)
| ~ cowlThing(ib)
| ~ requalityOnA(sK6,sK5)
| ~ requalityOnA(ia,ia) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_68,negated_conjecture,
( sP0
| xsd_integer(sK4)
| cowlNothing(sK3)
| requalityOnA(sK5,sK6)
| ~ xsd_string(sK4)
| ~ cowlThing(sK3)
| ~ cowlThing(ic)
| ~ cowlThing(ia)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_69,negated_conjecture,
( sP0
| xsd_string(sK4)
| cowlNothing(sK3)
| ~ xsd_integer(sK4)
| ~ cowlThing(sK3)
| ~ cowlThing(ic)
| ~ cowlThing(ia)
| ~ cowlThing(ib)
| ~ requalityOnA(sK6,sK5)
| ~ requalityOnA(ia,ia) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_70,negated_conjecture,
( sP0
| xsd_string(sK4)
| cowlNothing(sK3)
| requalityOnA(sK5,sK6)
| ~ xsd_integer(sK4)
| ~ cowlThing(sK3)
| ~ cowlThing(ic)
| ~ cowlThing(ia)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_75,plain,
( ( ia = ia )
| ~ requalityOnA(ia,ia) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_114,plain,
( sP0
| xsd_integer(sK4)
| requalityOnA(sK5,sK6)
| ~ xsd_string(sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_68,c_50,c_49,c_49,c_49,c_49,c_59]) ).
tcf(c_119,plain,
( sP0
| xsd_integer(sK4)
| requalityOnA(sK5,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_114,c_51]) ).
tcf(c_129,plain,
( sP0
| xsd_string(sK4)
| requalityOnA(sK5,sK6)
| ~ xsd_integer(sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_70,c_50,c_49,c_49,c_49,c_49,c_59]) ).
tcf(c_134,plain,
( sP0
| xsd_string(sK4)
| requalityOnA(sK5,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_129,c_51]) ).
tcf(c_144,plain,
( sP0
| xsd_integer(sK4)
| ~ xsd_string(sK4)
| ~ requalityOnA(sK6,sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67,c_50,c_49,c_49,c_49,c_49,c_59]) ).
tcf(c_149,plain,
( sP0
| xsd_integer(sK4)
| ~ requalityOnA(sK6,sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_144,c_51]) ).
tcf(c_159,plain,
( sP0
| xsd_string(sK4)
| ~ xsd_integer(sK4)
| ~ requalityOnA(sK6,sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69,c_50,c_49,c_49,c_49,c_49,c_59]) ).
tcf(c_164,plain,
( sP0
| xsd_string(sK4)
| ~ requalityOnA(sK6,sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_159,c_51]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = ia )
| ( X0 = ib )
| ~ requalityOnA(X2,X1)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_57]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] :
( ( X1 = ia )
| ( X1 = ib )
| ~ requalityOnA(X0,X1) ),
inference(unflattening,[status(thm)],[c_185]) ).
tcf(c_202,plain,
! [X0: $i] :
( sP0
| ~ xsd_integer(X0)
| ~ requalityOnA(sK6,sK5)
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_164]) ).
tcf(c_203,plain,
( sP0
| ~ xsd_integer(sK4)
| ~ requalityOnA(sK6,sK5) ),
inference(unflattening,[status(thm)],[c_202]) ).
tcf(c_204,plain,
( sP0
| ~ requalityOnA(sK6,sK5) ),
inference(global_subsumption_just,[status(thm)],[c_203,c_149,c_203]) ).
tcf(c_212,plain,
! [X0: $i] :
( sP0
| requalityOnA(sK5,sK6)
| ~ xsd_integer(X0)
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_134]) ).
tcf(c_213,plain,
( sP0
| requalityOnA(sK5,sK6)
| ~ xsd_integer(sK4) ),
inference(unflattening,[status(thm)],[c_212]) ).
tcf(c_214,plain,
( sP0
| requalityOnA(sK5,sK6) ),
inference(global_subsumption_just,[status(thm)],[c_213,c_119,c_213]) ).
tcf(c_410,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( requalityOnA(X0,X2)
| ~ requalityOnA(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_416,plain,
! [X0: $i] :
( ( ia = sK1 )
| ~ requalityOnA(sK1,X0)
| ~ requalityOnA(ia,X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_418,plain,
! [X0: $i] :
( ( ib = sK1 )
| ~ requalityOnA(sK1,X0)
| ~ requalityOnA(ib,X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_428,plain,
( ( ia = sK1 )
| ~ requalityOnA(sK1,sK2)
| ~ requalityOnA(ia,sK2) ),
inference(instantiation,[status(thm)],[c_416]) ).
tcf(c_431,plain,
( ( ib = sK1 )
| ~ requalityOnA(sK1,sK2)
| ~ requalityOnA(ib,sK2) ),
inference(instantiation,[status(thm)],[c_418]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i] :
( requalityOnA(ia,sK2)
| ~ requalityOnA(X0,X1)
| ( sK2 != X1 )
| ( ia != X0 ) ),
inference(instantiation,[status(thm)],[c_413]) ).
tcf(c_453,plain,
( requalityOnA(ia,sK2)
| ~ requalityOnA(ia,ia)
| ( sK2 != ia )
| ( ia != ia ) ),
inference(instantiation,[status(thm)],[c_452]) ).
tcf(c_496,plain,
! [X0: $i] :
( ( sK2 = ia )
| ( sK2 = ib )
| ~ requalityOnA(X0,sK2) ),
inference(instantiation,[status(thm)],[c_186]) ).
tcf(c_540,plain,
( ( sK2 = ia )
| ( sK2 = ib )
| ~ requalityOnA(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_496]) ).
tcf(c_561,plain,
! [X0: $i,X1: $i] :
( requalityOnA(sK6,sK5)
| ~ requalityOnA(X0,X1)
| ( sK5 != X1 )
| ( sK6 != X0 ) ),
inference(instantiation,[status(thm)],[c_413]) ).
tcf(c_562,plain,
( requalityOnA(sK6,sK5)
| ~ requalityOnA(ia,ia)
| ( sK5 != ia )
| ( sK6 != ia ) ),
inference(instantiation,[status(thm)],[c_561]) ).
tcf(c_582,plain,
! [X0: $i,X1: $i] :
( ( sK5 = X0 )
| ~ requalityOnA(sK5,X1)
| ~ requalityOnA(X0,X1) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_599,plain,
! [X0: $i] :
( ( sK5 = X0 )
| ~ requalityOnA(sK5,sK6)
| ~ requalityOnA(X0,sK6) ),
inference(instantiation,[status(thm)],[c_582]) ).
tcf(c_600,plain,
( ( sK5 = ia )
| ~ requalityOnA(sK5,sK6)
| ~ requalityOnA(ia,sK6) ),
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_618,plain,
! [X0: $i,X1: $i,X2: $i] :
( requalityOnA(X0,sK6)
| ~ requalityOnA(X1,X2)
| ( sK6 != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_413]) ).
tcf(c_619,plain,
( requalityOnA(ia,sK6)
| ~ requalityOnA(ia,ia)
| ( sK6 != ia )
| ( ia != ia ) ),
inference(instantiation,[status(thm)],[c_618]) ).
tcf(c_652,plain,
sK6 = sK6,
inference(instantiation,[status(thm)],[c_410]) ).
tcf(c_655,plain,
! [X0: $i] :
( ( sK6 = ia )
| ( sK6 = ib )
| ~ requalityOnA(X0,sK6) ),
inference(instantiation,[status(thm)],[c_186]) ).
tcf(c_674,plain,
( ( sK6 = ia )
| ( sK6 = ib )
| ~ requalityOnA(sK5,sK6) ),
inference(instantiation,[status(thm)],[c_655]) ).
tcf(c_734,plain,
! [X0: $i,X1: $i] :
( requalityOnA(ib,sK2)
| ~ requalityOnA(X0,X1)
| ( sK2 != X1 )
| ( ib != X0 ) ),
inference(instantiation,[status(thm)],[c_413]) ).
tcf(c_830,plain,
! [X0: $i] :
( requalityOnA(ib,sK2)
| ~ requalityOnA(X0,ib)
| ( sK2 != ib )
| ( ib != X0 ) ),
inference(instantiation,[status(thm)],[c_734]) ).
tcf(c_878,plain,
! [X0: $i,X1: $i,X2: $i] :
( requalityOnA(X0,ib)
| ~ requalityOnA(X1,X2)
| ( ib != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_413]) ).
tcf(c_880,plain,
( requalityOnA(ib,sK2)
| ~ requalityOnA(ib,ib)
| ( sK2 != ib )
| ( ib != ib ) ),
inference(instantiation,[status(thm)],[c_830]) ).
tcf(c_889,plain,
! [X0: $i,X1: $i,X2: $i] :
( requalityOnA(ib,X0)
| ~ requalityOnA(X2,X1)
| ( ib != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_413]) ).
tcf(c_911,plain,
ib = ib,
inference(instantiation,[status(thm)],[c_410]) ).
tcf(c_941,plain,
! [X0: $i,X1: $i] :
( requalityOnA(ib,X0)
| ~ requalityOnA(ib,X1)
| ( ib != ib )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_889]) ).
tcf(c_942,plain,
! [X0: $i,X1: $i] :
( requalityOnA(X0,ib)
| ~ requalityOnA(X1,ib)
| ( ib != ib )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_878]) ).
tcf(c_963,plain,
! [X0: $i,X1: $i] :
( ( sK5 = X0 )
| ~ requalityOnA(sK5,X1)
| ~ requalityOnA(X0,X1) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_976,plain,
! [X0: $i] :
( ( sK5 = X0 )
| ~ requalityOnA(sK5,sK6)
| ~ requalityOnA(X0,sK6) ),
inference(instantiation,[status(thm)],[c_963]) ).
tcf(c_986,plain,
! [X0: $i] :
( requalityOnA(ib,X0)
| ~ requalityOnA(ib,ib)
| ( ib != ib )
| ( X0 != ib ) ),
inference(instantiation,[status(thm)],[c_941]) ).
tcf(c_989,plain,
! [X0: $i] :
( requalityOnA(X0,ib)
| ~ requalityOnA(ib,ib)
| ( ib != ib )
| ( X0 != ib ) ),
inference(instantiation,[status(thm)],[c_942]) ).
tcf(c_1044,plain,
! [X0: $i,X1: $i,X2: $i] :
( requalityOnA(sK6,X0)
| ~ requalityOnA(X2,X1)
| ( sK6 != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_413]) ).
tcf(c_1067,plain,
( requalityOnA(sK6,ib)
| ~ requalityOnA(ib,ib)
| ( sK6 != ib )
| ( ib != ib ) ),
inference(instantiation,[status(thm)],[c_989]) ).
tcf(c_1068,plain,
( requalityOnA(ib,sK6)
| ~ requalityOnA(ib,ib)
| ( sK6 != ib )
| ( ib != ib ) ),
inference(instantiation,[status(thm)],[c_986]) ).
tcf(c_1091,plain,
! [X0: $i,X1: $i] :
( requalityOnA(sK6,X0)
| ~ requalityOnA(sK6,X1)
| ( sK6 != sK6 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1044]) ).
tcf(c_1137,plain,
( ( sK5 = ib )
| ~ requalityOnA(sK5,sK6)
| ~ requalityOnA(ib,sK6) ),
inference(instantiation,[status(thm)],[c_976]) ).
tcf(c_1154,plain,
! [X0: $i] :
( requalityOnA(sK6,X0)
| ~ requalityOnA(sK6,ib)
| ( sK6 != sK6 )
| ( X0 != ib ) ),
inference(instantiation,[status(thm)],[c_1091]) ).
tcf(c_1320,plain,
( requalityOnA(sK6,sK5)
| ~ requalityOnA(sK6,ib)
| ( sK5 != ib )
| ( sK6 != sK6 ) ),
inference(instantiation,[status(thm)],[c_1154]) ).
fof(f40,definition,
( ~ sP0
| ? [X2,X3] :
( requalityOnA(X2,X3)
& ic != X2
& ib != X2
& ia != X2 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f41,plain,
( ~ cowlThing(ic)
| ~ cowlThing(ib)
| ~ requalityOnA(ia,ia)
| ~ cowlThing(ia)
| ? [X4,X5] :
( requalityOnA(X4,X5)
& ~ requalityOnA(X5,X4) )
| sP0
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(definition_folding,[],[f39,f40]) ).
fof(f45,plain,
( ~ sP0
| ? [X2,X3] :
( requalityOnA(X2,X3)
& ic != X2
& ib != X2
& ia != X2 ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f46,plain,
( ~ sP0
| ? [X0,X1] :
( requalityOnA(X0,X1)
& ic != X0
& ib != X0
& ia != X0 ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
( ~ sP0
| ( requalityOnA(sK1,sK2)
& ic != sK1
& ib != sK1
& ia != sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f46]) ).
fof(f72,plain,
( ~ sP0
| requalityOnA(sK1,sK2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f74,plain,
( ~ sP0
| ib != sK1 ),
inference(cnf_transformation,[],[f47]) ).
fof(f75,plain,
( ~ sP0
| ia != sK1 ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_63,plain,
( ~ sP0
| ( ia != sK1 ) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_64,plain,
( ~ sP0
| ( ib != sK1 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_66,plain,
( requalityOnA(sK1,sK2)
| ~ sP0 ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_226,plain,
( requalityOnA(sK5,sK6)
| requalityOnA(sK1,sK2) ),
inference(resolution,[status(thm)],[c_214,c_66]) ).
tcf(c_240,plain,
( requalityOnA(sK5,sK6)
| ( ib != sK1 ) ),
inference(resolution,[status(thm)],[c_214,c_64]) ).
tcf(c_247,plain,
( requalityOnA(sK5,sK6)
| ( ia != sK1 ) ),
inference(resolution,[status(thm)],[c_214,c_63]) ).
tcf(c_254,plain,
( requalityOnA(sK1,sK2)
| ~ requalityOnA(sK6,sK5) ),
inference(resolution,[status(thm)],[c_204,c_66]) ).
tcf(c_268,plain,
( ~ requalityOnA(sK6,sK5)
| ( ib != sK1 ) ),
inference(resolution,[status(thm)],[c_204,c_64]) ).
tcf(c_275,plain,
( ~ requalityOnA(sK6,sK5)
| ( ia != sK1 ) ),
inference(resolution,[status(thm)],[c_204,c_63]) ).
tcf(c_1572,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1320,c_1137,c_1067,c_1068,c_911,c_880,c_674,c_652,c_619,c_600,c_562,c_540,c_453,c_431,c_428,c_275,c_268,c_254,c_247,c_240,c_226,c_75,c_59,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS138+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n002.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 : Wed Sep 23 19:32:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.05/1.28 % SZS status Started for theBenchmark.p
% 2.05/1.28 % SZS status Theorem for theBenchmark.p
% 2.05/1.28
% 2.05/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.05/1.28
% 2.05/1.28 % ------ iProver source info
% 2.05/1.28
% 2.05/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.05/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.05/1.28 % git: non_committed_changes: false
% 2.05/1.28
% 2.05/1.28 % ------ Parsing...
% 2.05/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_eq
% 2.05/1.28 %
% 2.05/1.28
% 2.05/1.28 % ------ Preprocessing... sup_sim: 7 sf_s rm: 3 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 2.05/1.28
% 2.05/1.28 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_eq
% 2.05/1.28 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Option_epr_non_horn_eq
% 2.05/1.28 %
% 2.05/1.28
% 2.05/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.05/1.28 % ------ Proving...
% 2.05/1.28 % ------ Problem Properties
% 2.05/1.28
% 2.05/1.28 %
% 2.05/1.28 % clauses 10
% 2.05/1.28 % conjectures 0
% 2.05/1.28 % EPR 10
% 2.05/1.28 % Horn 8
% 2.05/1.28 % unary 2
% 2.05/1.28 % binary 6
% 2.05/1.28 % lits 20
% 2.05/1.28 % lits eq 6
% 2.05/1.28 % fd_pure 0
% 2.05/1.28 % fd_pseudo 0
% 2.05/1.28 % fd_cond 1
% 2.05/1.28 % fd_pseudo_cond 1
% 2.05/1.28 % AC symbols 0
% 2.05/1.28
% 2.05/1.28 % ------ Schedule EPR non Horn eq is on
% 2.05/1.28
% 2.05/1.28 % ------ no conjectures: strip conj schedule
% 2.05/1.28
% 2.05/1.28 % ------ Option_epr_non_horn_eq stripped conjectures Time Limit: Unbounded
% 2.05/1.28
% 2.05/1.28
% 2.05/1.28 % ------
% 2.05/1.28 % Current options:
% 2.05/1.28 % ------
% 2.05/1.28
% 2.05/1.28
% 2.05/1.28 %
% 2.05/1.28
% 2.05/1.28 % ------ Proving...
% 2.05/1.28 %
% 2.05/1.28
% 2.05/1.28 % SZS status Theorem for theBenchmark.p
% 2.05/1.28
% 2.05/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.05/1.28
% 2.05/1.28
%------------------------------------------------------------------------------