%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS145+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 : n011.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 01:54:16 PM UTC 2026
% Result : Theorem 2.11s 1.25s
% Output : CNFRefutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 7
% Syntax : Number of formulae : 137 ( 20 unt; 3 def)
% Number of atoms : 735 ( 191 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 676 ( 260 ~; 316 |; 83 &)
% ( 4 <=>; 10 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 219 ( 0 sgn 177 !; 42 ?; 101 :)
% 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] :
( cc(X0)
=> ( ? [X1,X2] :
( X1 != X2
& rp(X0,X2)
& rp(X0,X1) )
& ! [X1,X2,X3] :
( ( rp(X0,X3)
& rp(X0,X2)
& rp(X0,X1) )
=> ( X2 = X3
| X1 = X3
| X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f11,conjecture,
( ! [X0] :
( cc(X0)
=> ( ! [X1,X2,X3] :
( ( rp(X0,X3)
& rp(X0,X2)
& rp(X0,X1) )
=> ( X2 = X3
| X1 = X3
| X1 = X2 ) )
& ? [X1,X2] :
( X1 != X2
& rp(X0,X2)
& rp(X0,X1) ) ) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( ~ cowlNothing(X0)
& cowlThing(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
fof(f12,negated_conjecture,
~ ( ! [X0] :
( cc(X0)
=> ( ! [X1,X2,X3] :
( ( rp(X0,X3)
& rp(X0,X2)
& rp(X0,X1) )
=> ( X2 = X3
| X1 = X3
| X1 = X2 ) )
& ? [X1,X2] :
( X1 != X2
& rp(X0,X2)
& rp(X0,X1) ) ) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( ~ cowlNothing(X0)
& cowlThing(X0) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0] :
( cc(X0)
=> ( ? [X4,X5] :
( X4 != X5
& rp(X0,X5)
& rp(X0,X4) )
& ! [X1,X2,X3] :
( ( rp(X0,X3)
& rp(X0,X2)
& rp(X0,X1) )
=> ( X2 = X3
| X1 = X3
| X1 = X2 ) ) ) ),
inference(rectify,[],[f10]) ).
fof(f14,plain,
~ ( ! [X2] :
( cc(X2)
=> ( ! [X5,X6,X7] :
( ( rp(X2,X7)
& rp(X2,X6)
& rp(X2,X5) )
=> ( X6 = X7
| X5 = X7
| X5 = X6 ) )
& ? [X3,X4] :
( X3 != X4
& rp(X2,X4)
& rp(X2,X3) ) ) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& ! [X0] :
( ~ cowlNothing(X0)
& cowlThing(X0) ) ),
inference(rectify,[],[f12]) ).
fof(f29,plain,
! [X0] :
( ~ cc(X0)
| ( ? [X4,X5] :
( X4 != X5
& rp(X0,X5)
& rp(X0,X4) )
& ! [X1,X2,X3] :
( ~ rp(X0,X3)
| ~ rp(X0,X2)
| ~ rp(X0,X1)
| X2 = X3
| X1 = X3
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f30,plain,
! [X0] :
( ~ cc(X0)
| ( ? [X4,X5] :
( X4 != X5
& rp(X0,X5)
& rp(X0,X4) )
& ! [X1,X2,X3] :
( ~ rp(X0,X3)
| ~ rp(X0,X2)
| ~ rp(X0,X1)
| X2 = X3
| X1 = X3
| X1 = X2 ) ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
( ? [X2] :
( cc(X2)
& ( ? [X5,X6,X7] :
( rp(X2,X7)
& rp(X2,X6)
& rp(X2,X5)
& X6 != X7
& X5 != X7
& X5 != X6 )
| ! [X3,X4] :
( X3 = X4
| ~ rp(X2,X4)
| ~ rp(X2,X3) ) ) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f32,plain,
( ? [X2] :
( cc(X2)
& ( ? [X5,X6,X7] :
( rp(X2,X7)
& rp(X2,X6)
& rp(X2,X5)
& X6 != X7
& X5 != X7
& X5 != X6 )
| ! [X3,X4] :
( X3 = X4
| ~ rp(X2,X4)
| ~ rp(X2,X3) ) ) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(flattening,[],[f31]) ).
fof(f35,plain,
! [X0] :
( ( ~ xsd_string(X0)
| ~ xsd_integer(X0) )
& ( xsd_integer(X0)
| xsd_string(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0] :
( ~ cc(X0)
| ( sK1(X0) != sK2(X0)
& rp(X0,sK2(X0))
& rp(X0,sK1(X0))
& ! [X1,X2,X3] :
( ~ rp(X0,X3)
| ~ rp(X0,X2)
| ~ rp(X0,X1)
| X2 = X3
| X1 = X3
| X1 = X2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X4,sK1(X0)),skolemize(X5,sK2(X0))],[f30]) ).
fof(f40,plain,
( sP0
| ? [X1] :
( ( xsd_string(X1)
| ~ xsd_integer(X1) )
& ( ~ xsd_string(X1)
| xsd_integer(X1) ) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f41,plain,
( sP0
| ( ( xsd_string(sK8)
| ~ xsd_integer(sK8) )
& ( ~ xsd_string(sK8)
| xsd_integer(sK8) ) )
| cowlNothing(sK7)
| ~ cowlThing(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f40]) ).
fof(f49,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f50,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f51,plain,
! [X0] :
( ~ xsd_string(X0)
| ~ xsd_integer(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f52,plain,
! [X0] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f53,plain,
! [X0] :
( ~ cc(X0)
| sK1(X0) != sK2(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
! [X0] :
( ~ cc(X0)
| rp(X0,sK2(X0)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X0] :
( ~ cc(X0)
| rp(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ cc(X0)
| ~ rp(X0,X3)
| ~ rp(X0,X2)
| ~ rp(X0,X1)
| X2 = X3
| X1 = X3
| X1 = X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f64,plain,
( sP0
| xsd_string(sK8)
| ~ xsd_integer(sK8)
| cowlNothing(sK7)
| ~ cowlThing(sK7) ),
inference(cnf_transformation,[],[f41]) ).
fof(f65,plain,
( sP0
| ~ xsd_string(sK8)
| xsd_integer(sK8)
| cowlNothing(sK7)
| ~ cowlThing(sK7) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_49,plain,
! [X0: $i] : cowlThing(X0),
inference(cnf_transformation,[],[f50]) ).
tcf(c_50,plain,
! [X0: $i] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f49]) ).
tcf(c_51,plain,
! [X0: $i] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_52,plain,
! [X0: $i] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ cc(X0)
| ~ rp(X0,X3)
| ~ rp(X0,X2)
| ~ rp(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_54,plain,
! [X0: $i] :
( rp(X0,sK1(X0))
| ~ cc(X0) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_55,plain,
! [X0: $i] :
( rp(X0,sK2(X0))
| ~ cc(X0) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_56,plain,
! [X0: $i] :
( ~ cc(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_64,negated_conjecture,
( sP0
| xsd_integer(sK8)
| cowlNothing(sK7)
| ~ xsd_string(sK8)
| ~ cowlThing(sK7) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_65,negated_conjecture,
( sP0
| xsd_string(sK8)
| cowlNothing(sK7)
| ~ xsd_integer(sK8)
| ~ cowlThing(sK7) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_80,plain,
! [X0: $i] :
( ~ xsd_string(X0)
| ~ xsd_integer(X0) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
tcf(c_81,plain,
! [X0: $i] :
( ~ xsd_integer(X0)
| ~ xsd_string(X0) ),
inference(renaming,[status(thm)],[c_80]) ).
tcf(c_82,plain,
! [X0: $i] :
( xsd_string(X0)
| xsd_integer(X0) ),
inference(prop_impl_just,[status(thm)],[c_51]) ).
tcf(c_83,plain,
! [X0: $i] :
( xsd_integer(X0)
| xsd_string(X0) ),
inference(renaming,[status(thm)],[c_82]) ).
tcf(c_84,plain,
! [X0: $i] :
( rp(X0,sK1(X0))
| ~ cc(X0) ),
inference(prop_impl_just,[status(thm)],[c_54]) ).
tcf(c_86,plain,
! [X0: $i] :
( rp(X0,sK2(X0))
| ~ cc(X0) ),
inference(prop_impl_just,[status(thm)],[c_55]) ).
tcf(c_88,plain,
! [X0: $i] :
( ( sK1(X0) != sK2(X0) )
| ~ cc(X0) ),
inference(prop_impl_just,[status(thm)],[c_56]) ).
tcf(c_89,plain,
! [X0: $i] :
( ~ cc(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(renaming,[status(thm)],[c_88]) ).
tcf(c_138,plain,
( sP0
| xsd_string(sK8)
| cowlNothing(sK7)
| ~ xsd_integer(sK8) ),
inference(backward_subsumption_resolution,[status(thm)],[c_65,c_49]) ).
tcf(c_139,plain,
( sP0
| xsd_integer(sK8)
| cowlNothing(sK7)
| ~ xsd_string(sK8) ),
inference(backward_subsumption_resolution,[status(thm)],[c_64,c_49]) ).
tcf(c_142,plain,
( sP0
| xsd_integer(sK8)
| ~ xsd_string(sK8) ),
inference(backward_subsumption_resolution,[status(thm)],[c_139,c_50]) ).
tcf(c_143,plain,
( sP0
| xsd_string(sK8)
| ~ xsd_integer(sK8) ),
inference(backward_subsumption_resolution,[status(thm)],[c_138,c_50]) ).
tcf(c_147,plain,
( sP0
| xsd_integer(sK8) ),
inference(backward_subsumption_resolution,[status(thm)],[c_142,c_83]) ).
tcf(c_149,plain,
( sP0
| xsd_string(sK8) ),
inference(backward_subsumption_resolution,[status(thm)],[c_143,c_83]) ).
tcf(c_365,plain,
! [X0: $i] :
( sP0
| ~ xsd_integer(X0)
| ( X0 != sK8 ) ),
inference(resolution_lifted,[status(thm)],[c_81,c_149]) ).
tcf(c_366,plain,
( sP0
| ~ xsd_integer(sK8) ),
inference(unflattening,[status(thm)],[c_365]) ).
tcf(c_367,plain,
sP0,
inference(global_subsumption_just,[status(thm)],[c_366,c_147,c_366]) ).
tcf(c_559,definition,
iPr_def_10 = sK1(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_560,definition,
iPr_def_11 = sK2(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
fof(f33,definition,
( ~ sP0
| ? [X2] :
( cc(X2)
& ( ? [X5,X6,X7] :
( rp(X2,X7)
& rp(X2,X6)
& rp(X2,X5)
& X6 != X7
& X5 != X7
& X5 != X6 )
| ! [X3,X4] :
( X3 = X4
| ~ rp(X2,X4)
| ~ rp(X2,X3) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f34,plain,
( sP0
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X0] :
( cowlNothing(X0)
| ~ cowlThing(X0) ) ),
inference(definition_folding,[],[f32,f33]) ).
fof(f37,plain,
( ~ sP0
| ? [X2] :
( cc(X2)
& ( ? [X5,X6,X7] :
( rp(X2,X7)
& rp(X2,X6)
& rp(X2,X5)
& X6 != X7
& X5 != X7
& X5 != X6 )
| ! [X3,X4] :
( X3 = X4
| ~ rp(X2,X4)
| ~ rp(X2,X3) ) ) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f38,plain,
( ~ sP0
| ? [X0] :
( cc(X0)
& ( ? [X3,X4,X5] :
( rp(X0,X5)
& rp(X0,X4)
& rp(X0,X3)
& X4 != X5
& X3 != X5
& X3 != X4 )
| ! [X1,X2] :
( X1 = X2
| ~ rp(X0,X2)
| ~ rp(X0,X1) ) ) ) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
( ~ sP0
| ( cc(sK3)
& ( ( rp(sK3,sK6)
& rp(sK3,sK5)
& rp(sK3,sK4)
& sK5 != sK6
& sK4 != sK6
& sK4 != sK5 )
| ! [X1,X2] :
( X1 = X2
| ~ rp(sK3,X2)
| ~ rp(sK3,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6)],[f38]) ).
fof(f57,plain,
( ~ sP0
| cc(sK3) ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X2,X1] :
( ~ sP0
| rp(sK3,sK6)
| X1 = X2
| ~ rp(sK3,X2)
| ~ rp(sK3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
! [X2,X1] :
( ~ sP0
| rp(sK3,sK5)
| X1 = X2
| ~ rp(sK3,X2)
| ~ rp(sK3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
! [X2,X1] :
( ~ sP0
| rp(sK3,sK4)
| X1 = X2
| ~ rp(sK3,X2)
| ~ rp(sK3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f61,plain,
! [X2,X1] :
( ~ sP0
| sK5 != sK6
| X1 = X2
| ~ rp(sK3,X2)
| ~ rp(sK3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f62,plain,
! [X2,X1] :
( ~ sP0
| sK4 != sK6
| X1 = X2
| ~ rp(sK3,X2)
| ~ rp(sK3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f63,plain,
! [X2,X1] :
( ~ sP0
| sK4 != sK5
| X1 = X2
| ~ rp(sK3,X2)
| ~ rp(sK3,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ sP0
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK4 != sK5 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ sP0
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK4 != sK6 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ sP0
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK5 != sK6 ) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( rp(sK3,sK4)
| ( X0 = X1 )
| ~ sP0
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( rp(sK3,sK5)
| ( X0 = X1 )
| ~ sP0
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( rp(sK3,sK6)
| ( X0 = X1 )
| ~ sP0
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_63,plain,
( cc(sK3)
| ~ sP0 ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_92,plain,
( cc(sK3)
| ~ sP0 ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_373,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK4 != sK5 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_367]) ).
tcf(c_374,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK4 != sK6 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_367]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i] :
( rp(sK3,sK4)
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_60,c_367]) ).
tcf(c_376,plain,
cc(sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_92,c_367]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK5 != sK6 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_59,c_367]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( rp(sK3,sK5)
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_61,c_367]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i] :
( rp(sK3,sK6)
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_62,c_367]) ).
tcf(c_386,plain,
! [X0: $i] :
( ( X0 != sK3 )
| ( sK1(X0) != sK2(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_89,c_376]) ).
tcf(c_387,plain,
sK1(sK3) != sK2(sK3),
inference(unflattening,[status(thm)],[c_386]) ).
tcf(c_391,plain,
! [X0: $i] :
( rp(X0,sK2(X0))
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_86,c_376]) ).
tcf(c_392,plain,
rp(sK3,sK2(sK3)),
inference(unflattening,[status(thm)],[c_391]) ).
tcf(c_396,plain,
! [X0: $i] :
( rp(X0,sK1(X0))
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_84,c_376]) ).
tcf(c_397,plain,
rp(sK3,sK1(sK3)),
inference(unflattening,[status(thm)],[c_396]) ).
tcf(c_401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 )
| ~ rp(X0,X3)
| ~ rp(X0,X2)
| ~ rp(X0,X1)
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_376]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ rp(sK3,X2)
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(unflattening,[status(thm)],[c_401]) ).
tcf(c_561,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( X0 = X1 )
| ~ rp(sK3,X2)
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(demodulation,[status(thm)],[c_402]) ).
tcf(c_562,plain,
rp(sK3,iPr_def_10),
inference(demodulation,[status(thm)],[c_397,c_559]) ).
tcf(c_563,plain,
rp(sK3,iPr_def_11),
inference(demodulation,[status(thm)],[c_392,c_560]) ).
tcf(c_564,plain,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_387]) ).
tcf(c_565,plain,
! [X0: $i,X1: $i] :
( rp(sK3,sK6)
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(demodulation,[status(thm)],[c_379]) ).
tcf(c_566,plain,
! [X0: $i,X1: $i] :
( rp(sK3,sK5)
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(demodulation,[status(thm)],[c_378]) ).
tcf(c_567,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK5 != sK6 ) ),
inference(demodulation,[status(thm)],[c_377]) ).
tcf(c_568,plain,
! [X0: $i,X1: $i] :
( rp(sK3,sK4)
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(demodulation,[status(thm)],[c_375]) ).
tcf(c_569,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK4 != sK6 ) ),
inference(demodulation,[status(thm)],[c_374]) ).
tcf(c_570,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK4 != sK5 ) ),
inference(demodulation,[status(thm)],[c_373]) ).
tcf(c_815,plain,
! [X0: $i] :
( rp(sK3,sK4)
| ( X0 = iPr_def_10 )
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_562,c_568]) ).
tcf(c_816,plain,
! [X0: $i] :
( rp(sK3,sK5)
| ( X0 = iPr_def_10 )
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_562,c_566]) ).
tcf(c_817,plain,
! [X0: $i] :
( rp(sK3,sK6)
| ( X0 = iPr_def_10 )
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_562,c_565]) ).
tcf(c_857,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_10 )
| ( X0 = iPr_def_10 )
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_562,c_561]) ).
tcf(c_876,plain,
( rp(sK3,sK4)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_563,c_815]) ).
tcf(c_877,plain,
rp(sK3,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_876,c_564]) ).
tcf(c_902,plain,
( rp(sK3,sK5)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_563,c_816]) ).
tcf(c_903,plain,
rp(sK3,sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_902,c_564]) ).
tcf(c_924,plain,
( rp(sK3,sK6)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_563,c_817]) ).
tcf(c_925,plain,
rp(sK3,sK6),
inference(forward_subsumption_resolution,[status(thm)],[c_924,c_564]) ).
tcf(c_954,plain,
! [X0: $i] :
( ( sK4 = iPr_def_10 )
| ( X0 = iPr_def_10 )
| ( X0 = sK4 )
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_877,c_857]) ).
tcf(c_958,plain,
! [X0: $i] :
( ( iPr_def_10 = iPr_def_11 )
| ( X0 = iPr_def_11 )
| ( X0 = iPr_def_10 )
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_563,c_857]) ).
tcf(c_959,plain,
! [X0: $i] :
( ( X0 = iPr_def_11 )
| ( X0 = iPr_def_10 )
| ~ rp(sK3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_958,c_564]) ).
tcf(c_1016,plain,
( ( sK4 = iPr_def_11 )
| ( sK4 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_877,c_959]) ).
tcf(c_1017,plain,
( ( sK5 = iPr_def_11 )
| ( sK5 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_903,c_959]) ).
tcf(c_1018,plain,
( ( sK6 = iPr_def_11 )
| ( sK6 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_925,c_959]) ).
tcf(c_1027,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ rp(sK3,iPr_def_11)
| ~ rp(sK3,iPr_def_10)
| ( sK4 != sK6 ) ),
inference(instantiation,[status(thm)],[c_569]) ).
tcf(c_1028,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ rp(sK3,iPr_def_11)
| ~ rp(sK3,iPr_def_10)
| ( sK4 != sK5 ) ),
inference(instantiation,[status(thm)],[c_570]) ).
tcf(c_1111,plain,
! [X0: $i,X1: $i] :
( ( sK5 = iPr_def_10 )
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK4 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_1017,c_570]) ).
tcf(c_1122,plain,
! [X0: $i,X1: $i] :
( ( sK6 = iPr_def_10 )
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK4 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_1018,c_569]) ).
tcf(c_1123,plain,
! [X0: $i,X1: $i] :
( ( sK6 = iPr_def_10 )
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK5 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_1018,c_567]) ).
tcf(c_1143,plain,
( ( sK5 = iPr_def_10 )
| ( sK4 = iPr_def_10 )
| ( sK4 = sK5 ) ),
inference(superposition,[status(thm)],[c_903,c_954]) ).
tcf(c_1144,plain,
( ( sK6 = iPr_def_10 )
| ( sK4 = iPr_def_10 )
| ( sK4 = sK6 ) ),
inference(superposition,[status(thm)],[c_925,c_954]) ).
tcf(c_1163,plain,
! [X0: $i,X1: $i] :
( ( sK5 = iPr_def_10 )
| ( sK4 = iPr_def_10 )
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_1016,c_1111]) ).
tcf(c_1179,plain,
! [X0: $i,X1: $i] :
( ( sK6 = iPr_def_10 )
| ( sK4 = iPr_def_10 )
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_1016,c_1122]) ).
tcf(c_1197,plain,
! [X0: $i,X1: $i] :
( ( sK6 = iPr_def_10 )
| ( sK5 = iPr_def_10 )
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_1017,c_1123]) ).
tcf(c_1203,plain,
( ( sK5 = iPr_def_10 )
| ( sK4 = iPr_def_10 ) ),
inference(global_subsumption_just,[status(thm)],[c_1163,c_562,c_563,c_564,c_1028,c_1143]) ).
tcf(c_1221,plain,
( ( sK6 = iPr_def_10 )
| ( sK4 = iPr_def_10 ) ),
inference(global_subsumption_just,[status(thm)],[c_1179,c_562,c_563,c_564,c_1027,c_1144]) ).
tcf(c_1231,plain,
! [X0: $i,X1: $i] :
( ( sK4 = iPr_def_10 )
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK5 != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1221,c_567]) ).
tcf(c_1237,plain,
! [X0: $i,X1: $i] :
( ( sK4 = iPr_def_10 )
| ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1231,c_1203,c_1231]) ).
tcf(c_1247,plain,
! [X0: $i] :
( ( sK4 = iPr_def_10 )
| ( X0 = sK4 )
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_877,c_1237]) ).
tcf(c_1290,plain,
sK4 = iPr_def_10,
inference(superposition,[status(thm)],[c_562,c_1247]) ).
tcf(c_1296,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK5 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_570,c_1290]) ).
tcf(c_1297,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0)
| ( sK6 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_569,c_1290]) ).
tcf(c_1306,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ rp(sK3,X1)
| ~ rp(sK3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1296,c_1197,c_1297,c_1296]) ).
tcf(c_1316,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ rp(sK3,X0) ),
inference(superposition,[status(thm)],[c_562,c_1306]) ).
tcf(c_1339,plain,
iPr_def_10 = iPr_def_11,
inference(superposition,[status(thm)],[c_563,c_1316]) ).
tcf(c_1340,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1339,c_564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS145+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 19:30:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 2.11/1.25 % SZS status Started for theBenchmark.p
% 2.11/1.25 % SZS status Theorem for theBenchmark.p
% 2.11/1.25
% 2.11/1.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.11/1.25
% 2.11/1.25 % ------ iProver source info
% 2.11/1.25
% 2.11/1.25 % git: date: 2026-07-19 20:42:38 +0200
% 2.11/1.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.11/1.25 % git: non_committed_changes: false
% 2.11/1.25
% 2.11/1.25 % ------ Parsing...
% 2.11/1.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.11/1.25
% 2.11/1.25 % ------ Preprocessing... sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 2.11/1.25
% 2.11/1.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.11/1.25
% 2.11/1.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.11/1.25 % ------ Proving...
% 2.11/1.25 % ------ Problem Properties
% 2.11/1.25
% 2.11/1.25 %
% 2.11/1.25 % clauses 12
% 2.11/1.25 % conjectures 0
% 2.11/1.25 % EPR 10
% 2.11/1.25 % Horn 8
% 2.11/1.25 % unary 5
% 2.11/1.25 % binary 0
% 2.11/1.25 % lits 35
% 2.11/1.25 % lits eq 15
% 2.11/1.25 % fd_pure 0
% 2.11/1.25 % fd_pseudo 0
% 2.11/1.25 % fd_cond 0
% 2.11/1.25 % fd_pseudo_cond 7
% 2.11/1.25 % AC symbols 0
% 2.11/1.25
% 2.11/1.25 % ------ Schedule dynamic 5 is on
% 2.11/1.25
% 2.11/1.25 % ------ no conjectures: strip conj schedule
% 2.11/1.25
% 2.11/1.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.11/1.25
% 2.11/1.25
% 2.11/1.25 % ------
% 2.11/1.25 % Current options:
% 2.11/1.25 % ------
% 2.11/1.25
% 2.11/1.25
% 2.11/1.25 %
% 2.11/1.25
% 2.11/1.25 % ------ Proving...
% 2.11/1.25 %
% 2.11/1.25
% 2.11/1.25 % SZS status Theorem for theBenchmark.p
% 2.11/1.25
% 2.11/1.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.11/1.25
% 2.11/1.25
%------------------------------------------------------------------------------